Exergy Analysis and Thermoeconomics of Buildings: Design and Analysis for Sustainable Energy Systems 0128176113, 9780128176115

Table of contents :
Cover
Exergy Analysis and Thermoeconomics of Buildings: Design and Analysis for Sustainable
Energy Systems
Copyright
Dedication
Biography
Preface
Acknowledgement
Section A: Foundations of exergy theory
1 -
Efficient buildings and the arguments for incorporating exergy
1.1 Summary
1.2 Concept and laws of energy
1.3 Energy sources. Fossil and renewable energies
1.4 Energy chains
1.5 Energy and sustainability
1.5.1 Life cycle
1.5.2 Externalities
1.5.3 Limited nature of natural resources
1.6 Energy and the building sector
1.6.1 The building as an energy system
1.6.1.1 Demand
1.6.1.2 System components
1.6.1.3 Energy sources
1.6.2 Energy consumption data in buildings
1.7 Current regulatory environment regarding energy in buildings
1.7.1 Directives of the European Union
1.7.2 Transposition to Spanish legislation
1.8 New materials in buildings
1.8.1 Thermal insulation
1.8.2 Glass
1.8.3 Other materials
1.9 New types of building skins
1.9.1 Advanced integrated façades
1.9.2 Green roofs and green façades
1.9.3 Different types of inertial systems
1.9.4 Thermo-active slabs
1.9.5 Thermo-active foundations
1.9.6 Active glazing
1.9.7 Envelopes with phase change materials
1.9.8 Dynamic insulation
1.10 New thermal installations
1.10.1 Condensing boilers
1.10.2 Biomass boilers
1.10.3 Heat pumps
1.10.4 Solar collectors
1.10.5 Ventilation systems
1.10.6 Cogeneration
1.10.7 Trigeneration
1.10.8 Energy storage
1.10.9 Hybrid installations
1.10.10 District heating and cooling systems
1.10.11 Intelligent control
1.11 The integrated design process
1.11.1 Phase 1 - where and what to build
1.11.2 Phase 2 - preliminary design
1.11.3 Phase 3 - design of the building and preliminary evaluation
1.11.4 Phase 4 - control for optimized operation
1.12 Arguments for incorporating exergy in buildings
1.12.1 Some basic notions about exergy
1.12.2 Characteristics of exergy
1.12.3 The need for an exergy methodology
1.12.4 Exergy and economic aspects
1.12.5 Exergy and the environment
1.12.6 Exergy and the Administrations
1.12.7 Limitations of exergy analysis
1.13 Brief history of exergy use in buildings
1.14 The road towards sustainable buildings
References
2 -
Quality of energy and exergy
2.1 Summary
2.2 Brief introduction to Thermodynamics and its different formulations
2.2.1 Different formulations of Thermodynamics
2.2.2 The Thermodynamics of Irreversible Processes
2.2.3 Some considerations on Statistical Thermodynamics
2.2.4 Thermodynamics and energy
2.3 The First Law of Thermodynamics
2.3.1 Energy balance in closed systems
2.3.2 Examples
2.3.3 Meaning of control volume
2.3.4 Energy balance in a control volume
2.3.5 Examples
2.4 Brief history of the Second Law of Thermodynamics
2.5 Review of the concept of entropy
2.5.1 Entropy generation
2.5.2 Entropy change of the universe
2.5.2.1 Examples
2.6 Different quality of energy
2.7 The environment and natural resources
2.8 Reference environment
2.9 Exergy by heat transfer
2.9.1 Examples
2.10 Available work and physical exergy of a closed system
2.10.1 Available work
2.10.2 Physical exergy
2.11 Exergy destruction in irreversible processes
2.12 Exergy balance in a closed system
2.12.1 Examples
2.13 Physical flow exergy
2.13.1 Thermal and mechanical components
2.14 Exergy balance in a control volume
2.14.1 Examples
2.15 Exergy of thermal radiation
2.15.1 Review of some preliminary concepts
2.15.1.1 Blackbody radiation
2.15.1.2 Grey and diffuse surfaces
2.15.1.3 Absorptivity, reflectivity and transmissivity
2.15.1.4 Kirchhoff’s law
2.15.1.5 Greenhouse effect
2.15.2 Thermodynamics of blackbody radiation
2.15.3 Exergy of blackbody radiation
2.15.4 Rate of exergy destruction in radiation exchange
2.15.5 Exergy of solar radiation
2.15.6 Examples
2.16 Benefits of the exergy analysis method
2.16.1 Different definitions of exergy efficiency
2.17 Mechanisms of irreversibilities
2.17.1 Exergy destruction due to mechanical irreversibilities
2.17.2 Exergy destruction due to thermal irreversibilities
2.17.3 Exergy destruction due to chemical irreversibilities
2.17.3.1 Same substance at different temperatures
2.17.3.2 Mixture of different substances
2.17.3.3 Chemical reactions
Superscripts
Subscripts
Symbols
Constants
References
3 -
Calculation of physical and chemical exergy
3.1 Summary
3.2 Calculation of physical exergy
3.2.1 Physical exergy of an ideal gas
3.2.2 Physical exergy of a mixture of ideal gases
3.2.3 Physical exergy of humid air
3.2.4 Physical exergy of incompressible solids and fluids
3.2.5 Physical exergy of liquid-vapour mixtures
3.2.6 Calculation of physical exergy through departure properties
3.2.7 Examples
3.3 Modelling the reference environment
3.3.1 Reference environment associated with process
3.3.2 Reference environment in internal equilibrium
3.3.3 Reference environment based on stability
3.3.4 Reference environment in buildings
3.4 Some thermodynamic notions of multicomponent systems
3.4.1 Definition of chemical potential
3.4.2 Standard states
3.4.3 Enthalpy of formation
3.4.4 Enthalpy of reaction and entropy of reaction
3.4.5 Gibbs function of formation and Gibbs function of reaction
3.4.6 Maximum work and change of Gibbs function
3.5 Calculation of standard chemical exergy
3.5.1 Substances present in the RE
3.5.2 Substances not present in the RE
3.5.2.1 Calculation of the standard chemical exergy by the general method
3.5.2.2 Alternative method
3.5.3 Examples
3.6 Chemical exergy of substances of interest in buildings
3.6.1 Exergy of construction materials
3.6.2 Exergy of water
3.6.3 Exergy of the combustion gases in a boiler
3.6.4 Exergy of humid air
3.6.5 Exergy of a mixture of real gases
3.6.6 Chemical exergy of fuels
3.6.7 Examples
Superscripts
Subscripts
Symbols
References
Section B: Exergy analysis of the envelope and thermal installations
4 -
Exergy analysis of heat transfer in buildings
4.1 Summary
4.2 Heat exchanges in a building
4.3 Heat conduction in a wall
4.3.1 Energy balance
4.3.2 Exergy balance
4.3.3 Examples
4.4 Exergy and inertia of walls
4.4.1 The concept of thermal inertia
4.4.2 Inertia and exergy
4.5 Transport of exergy by convection
4.5.1 Energy balance
4.5.2 Exergy balance
4.5.3 Examples
4.6 Exchange of radiation exergy between surfaces
4.6.1 Radiation exergy exchange between two grey surfaces
4.6.2 Radiation exchange between the interior surfaces of a room
4.6.2.1 Radiative energy exchange
4.6.2.2 Radiation exergy exchange
4.7 Energy and exergy balances on the interior surface of a façade
4.7.1 Energy balance
4.7.2 Exergy balance
4.7.3 Examples
4.8 Energy and exergy balances in the exterior surface of a façade
4.8.1 Energy exchanges
4.8.1.1 Convection coefficient on the exterior surface
4.8.1.2 Radiation exchange with the sky and surroundings
4.8.1.3 Equivalent temperature and sun-air temperature
4.8.2 Exergy balance
4.8.3 Examples
4.9 Exergy exchanged by a building through an opaque envelope
4.9.1 Steady-state method
4.9.2 Quasi-steady method
4.9.3 Simplified dynamic method
4.9.4 Detailed dynamic method
4.10 Indicator of exergy behaviour of a wall
4.10.1 Examples
4.11 Exergy and thermal comfort
4.11.1 Thermal comfort standards
4.11.2 Thermal model of the human body and energy balance
4.11.3 Exergy balance in the human body
4.12 Energy and exergy demand of a building
4.12.1 Calculation of energy demand
4.12.1.1 Gains (losses) of heat
4.12.1.2 Thermal load and energy demand
4.12.1.3 Indirect method for calculating energy demand
4.12.2 Calculation of exergy demand
4.12.2.1 Preliminary comments
4.12.2.2 Simplified method
4.12.2.3 Detailed method
4.12.3 Examples
Subscripts
Symbols
References
5 -
Exergy analysis of thermal facilities equipment in buildings (I)
5.1 Summary
5.2 Introduction
5.3 Indoor air
5.4 End elements
5.4.1 Exergy analysis of a radiator
5.4.2 Examples
5.5 Distribution system
5.5.1 Examples
5.6 Three-way valves
5.7 Heat exchangers
5.7.1 Types and characteristics
5.7.2 Conventional energy analysis
5.7.3 Exergy analysis
5.7.4 Analysis of the mechanisms of irreversibilities
5.7.5 Examples
5.8 Heating and DHW boilers
5.8.1 Types and characteristics
5.8.2 Classical energy analysis
5.8.3 Instantaneous and seasonal efficiency
5.8.4 Exergy analysis
5.8.5 Examples
5.9 Heat pumps
5.9.1 Types and characteristics
5.9.2 Global energy balance
5.9.3 Seasonal average efficiency
5.9.4 Global exergy balance
5.9.5 Exergy analysis of a vapor-compression cycle
5.9.6 Examples
5.10 Cogeneration in buildings
5.10.1 General comments on cogeneration
5.10.2 Cogeneration and the energy demand in buildings
5.10.3 Micro-cogeneration technologies
5.10.3.1 Internal combustion micromotors
5.10.3.2 Gas microturbines
5.10.3.3 Stirling engines
5.10.3.4 Fuel cells
5.10.4 Cogeneration with Organic Rankine Cycles (ORC)
5.10.5 District heating and cooling
5.10.6 Cogeneration energy parameters
5.10.7 Cogeneration exergy parameters
5.10.8 Feasibility of cogeneration in buildings
5.10.9 Examples
5.10.10 Some final comments on cogeneration
5.11 Thermal energy storage systems (TES)
5.11.1 Preliminary considerations
5.11.2 Conventional energy analysis
5.11.3 Exergy analysis
5.11.4 Examples
Subscripts
Symbols
References
6. Exergy analysis of thermal facilities equipment in buildings (II)
6.1 Summary
6.2 Absorption refrigerators
6.2.1 Types and characteristics
6.2.2 Simple absorption cycle
6.2.3 Energy analysis of components
6.2.3.1 Generator
6.2.3.2 Absorber
6.2.3.3 Heat recuperator
6.2.3.4 Regulation valve
6.2.3.5 Solution pump
6.2.3.6 Condenser
6.2.3.7 Expansion valve
6.2.3.8 Evaporator
6.2.3.9 Total cycle
6.2.4 Exergy analysis of components
6.2.4.1 Generator
6.2.4.2 Absorber
6.2.4.3 Heat recuperator
6.2.4.4 Regulation valve
6.2.4.5 Solution pump
6.2.4.6 Condenser
6.2.4.7 Expansion valve
6.2.4.8 Evaporator
6.2.4.9 Total cycle
6.2.5 Examples
6.3 Adsorption cooling systems
6.3.1 Basic principle of adsorption/desorption
6.3.2 Operation of a single-effect adsorption system
6.3.3 Energy and exergy analysis of an adsorption system
6.3.4 Rotary desiccant dryers
6.3.5 Energy analysis of an AHU with a rotary desiccant dryer
6.3.6 Exergy analysis of an AHU with rotary desiccant dryer
6.3.6.1 Rotary desiccant dryer
6.3.6.2 Regenerative heat exchanger
6.3.6.3 Process evaporative cooler
6.3.6.4 Regeneration evaporative cooler
6.3.6.5 Regeneration heat battery
6.3.6.6 Complete AHU system
6.3.7 Examples
6.4 Exergy analysis of basic air conditioning processes
6.4.1 Sensitive heating or cooling
6.4.2 Dehumidification by cooling
6.4.3 Humidifying or dehumidifying by mixing with water
6.4.4 Adiabatic mixture of two flows
6.4.5 Combination of the basic processes for air conditioning
6.4.6 Examples
6.5 Ventilation systems
6.5.1 Air quality and regulatory development of ventilation in Spain
6.5.2 Types of ventilation installations
6.5.3 Heat recuperators
6.5.4 Energy and exergy analysis of a ventilation system with heat recovery
6.5.5 Examples
6.6 Use of solar energy. Photovoltaic and thermal modules
6.6.1 Types and characteristics of solar photovoltaic cells
6.6.2 Energy analysis of a solar photovoltaic array
6.6.3 Exergy analysis of a solar photovoltaic array
6.6.4 Types and characteristics of solar thermal collectors
6.6.5 Energy analysis of a solar thermal collector
6.6.6 Exergy analysis of a solar thermal collector
6.6.7 Hybrid thermal/photovoltaic modules (PVT)
6.6.8 Comments on the frame of reference for exergy analysis of solar systems
6.6.9 Examples
Subscripts
Symbols
References
Section C: Thermoeconomics and symbolic thermoeconomics. Costs and diagnosis of installations
7. Thermoeconomics and its application to buildings
7.1 Summary
7.2 Introduction
7.3 Thermoeconomics
7.3.1 Brief history of Thermoeconomics
7.4 The physical structure of the installations
7.5 Mass, energy and exergy balances
7.5.1 Examples
7.6 Productive structure of the installations
7.6.1 Definition of fuel, product and losses
7.6.2 New form of exergy balance
7.6.3 Exergy efficiency and unit exergy consumption
7.6.4 Dissipative equipment
7.6.5 Examples
7.7 Exergy analysis of systems
7.7.1 Definition of various indexes
7.7.2 Exergy analysis methodology
7.8 Cost accounting and exergy
7.8.1 Exergy cost and exergoeconomic cost
7.8.2 Review of some basic concepts of engineering economy
7.8.3 Example of a sequential system
7.9 Exergy cost theory
7.9.1 Propositions of Exergy Cost Theory
7.9.2 Closure of the system of equations
7.9.3 Exergy cost of fuel and products of the components
7.9.4 Accumulated exergy cost
7.9.5 Exergoeconomic costs
7.9.6 Exergoeconomic costs of fuel and products of components
7.9.7 Examples
7.10 Other methods of allocating costs
7.10.1 Thermoeconomic Functional Analysis
7.10.2 SPECO method
Subscripts
Superscripts
Scalars
Matrices and vectors.
References
8. Symbolic Thermoeconomics applied to thermal facilities
8.1 Summary
8.2 Introduction
8.3 FP representation or supply-driven model
8.3.1 Expressions for the exergy of the flows
8.3.2 Expressions for the exergy costs and exergoeconomic costs of flows
8.3.3 Expressions for the fuel and product of components
8.3.4 Expression of the installation global efficiency
8.3.5 Expressions for the exergy costs and exergoeconomic costs of fuel and product
8.3.6 Examples
8.4 Representation PF or demand-driven model
8.4.1 Expressions for the exergies of flows
8.4.2 Expressions for the fuel and product of components
8.4.3 Expression of the installation global efficiency
8.4.4 Expressions for the exergy costs and exergoeconomic costs of fuel and product
8.4.5 Relationship between FP and PF representations
8.4.6 Examples
8.5 FP and PF representations with residues
8.5.1 The process of residues cost formation
8.5.2 The negentropy method
8.5.3 FP(R) formulation
8.5.3.1 Exergy costs and exergoeconomic costs
8.5.4 PF(R) formulation
8.5.4.1 Exergy costs and exergoeconomic costs
8.5.5 Examples
8.6 Symbolic Thermoeconomics in thermal installations analysis
Nomenclature
References
9. Operational diagnosis of thermal installations in buildings
9.1 Summary
9.2 Introduction to energy diagnosis
9.3 Thermoeconomic diagnosis
9.3.1 Intrinsic anomalies and induced anomalies
9.4 Exergy indicators. Impact on fuel
9.5 Diagnosis through malfunctions and dysfunctions
9.5.1 Malfunctions and dysfunctions
9.5.2 Cost of malfunctions
9.5.3 Inclusion of residues in the diagnosis
9.5.4 Intrinsic and induced malfunctions
9.5.5 Filtering malfunctions due to the control system
9.5.6 Impact on fuel expressed in exergoeconomic costs
9.5.7 The problem of intrinsic malfunctions detection
9.5.8 Examples
9.6 Method of characteristic curves
9.6.1 Discrimination between the intrinsic and the induced malfunctions
9.6.2 Examples
9.7 Advanced exergy theory
9.7.1 Avoidable and unavoidable exergy destruction and costs
9.7.2 Endogenous and exogenous exergy destruction
9.7.3 Applications of Advanced Exergy Theory
9.7.4 Examples
Subscripts
Superscripts
Scalars
Matrices and vectors
References
Section D: Sustainability and exergy in buildings
10. Sustainability and exergy in buildings
10.1 Summary
10.2 Considerations concerning sustainability
10.2.1 Life cycle
10.2.2 Environmental externalities
10.2.3 Social externalities
10.2.4 Limitation of resources
10.3 Sustainability in buildings
10.3.1 What is sustainable construction?
10.4 Conventional methodologies for the analysis of sustainability
10.4.1 Analysis of environmental risks
10.4.2 Environmental impact assessment
10.4.3 Carbon footprint
10.4.4 Environmental product declaration
10.4.5 Environmental audit
10.4.6 Cumulative energy content
10.4.7 Life cycle assessment (LCA)
10.4.7.1 LCA stages
10.4.7.1.1 Definition of objectives and scope
10.4.7.1.2 Life Cycle Inventory
10.4.7.1.3 Impact assessment
10.4.7.1.4 Evaluation and interpretation of results
10.4.8 Examples
10.5 Exergy and sustainability
10.5.1 Exergy as a method of resources characterization
10.5.2 Exergy as a method of emissions characterization
10.6 Exergy methodologies for the analysis of sustainability
10.6.1 Cumulative exergy content
10.6.2 Emergy analysis
10.6.3 Exergy life cycle assessment
10.6.4 Extended exergy accounting
10.6.5 Exergoenvironmental analysis
10.6.6 Examples
Superscripts
Symbols
References
11. Application of exergecoeconomic and exergoenvironmental analysis to several cases of building thermal installations
11.1 Overview
11.2 Introduction
11.3 Case 1: heating and DHW facility with natural gas boilers
11.3.1 Description of the building and its thermal facility
11.3.2 Heating and DHW demands
11.3.3 Functional analysis
11.3.4 Energy analysis
11.3.5 Exergy analysis
11.3.6 Exergy costs
11.3.7 Exergoeconomic costs
11.3.8 Impact on CO2 emissions
11.4 Case 2: heating and DHW facility with geothermal heat pump
11.4.1 Description of the building and its thermal facility
11.4.2 Heating and DHW demands
11.4.3 Functional analysis
11.4.4 Energy analysis
11.4.5 Exergy analysis
11.4.6 Exergy costs
11.4.7 Exergoeconomic costs
11.4.8 Impact on CO2 emissions
11.5 Case 3: heating and DHW facility with boiler and CHP
11.5.1 Description of the building and its thermal facility
11.5.2 Heating and DHW demands
11.5.3 Functional analysis
11.5.4 Energy analysis
11.5.5 Exergy analysis
11.5.6 Exergy costs
11.5.7 Exergoeconomic costs
11.5.8 Impact on CO2 emissions
11.6 Case 4: trigeneration facility of a hospital
11.6.1 Description of the building and its facility
11.6.2 Functional analysis
11.6.3 Energy analysis
11.6.4 Exergy analysis
11.6.5 Exergy costs
11.6.6 Exergoeconomic costs
11.6.7 Impact on CO2 emissions
Subscript
Superscript
Scalars
Matrices and vectors
References
Section E: Design and thermoeconomics in buildings
12. Design and optimization of the envelope and thermal installations of buildings
12.1 Summary
12.2 Introduction
12.3 Modelling and simulation
12.4 Stages in the thermal systems design process
12.4.1 The problem of synthesis
12.5 Mathematical formulation of optimization
12.5.1 Mathematical background
12.6 Different mathematical optimization methods
12.6.1 Decomposition methods in complex problems
12.7 Optimization in the design of thermal installations in buildings
12.7.1 Simple optimization problems
12.7.2 Equipment selection with optimal efficiency
12.7.3 Choosing the best alternative
12.7.4 Equipment cost functions
12.7.5 Optimization of thermal installations operation mode
12.7.6 Solution of the optimization problem
12.7.7 Examples
12.8 Application of Thermoeconomics to the design of thermal systems in buildings
12.8.1 Thermoeconomic optimization through calculus
12.8.2 Local optimization based on the Thermoeconomic Isolation Principle
12.8.3 Heuristic method by successive approximations
12.8.4 Examples
12.9 Energy renovation of buildings
12.9.1 Envelope renovation
12.9.2 Legislation relating to the buildings energy renovation
12.9.2.1 European Union Directives
12.9.2.2 Spanish legislation
12.9.3 Simulation and optimization tools for renovation
12.9.4 Renovation optimization searching for the nZEB building
12.9.5 Renovation optimization based on Thermoeconomics
12.9.6 Examples
Subscripts
Superscripts
Nomenclature
References
Section F: Exergy in the thermodynamics of continuous media
13. Exergy in continuous media. Application to equipment design
13.1 Summary
13.2 Introduction
13.3 Brief review of some notions of fluid mechanics
13.3.1 Material and spatial description of the motion
13.3.2 Meaning of the material derivative
13.3.3 Transport theorem
13.3.4 Stress tensor
13.3.5 The notion of continuum in multicomponent systems
13.3.6 Considerations concerning turbulence
13.4 Conservation of mass
13.4.1 Continuity equation
13.4.2 Continuity equation in multicomponent systems
13.4.3 Control volume mass balance
13.5 Energy balance
13.5.1 Energy local balance
13.5.2 Energy local balance in multicomponent systems
13.5.3 Some particular cases of interest
13.5.4 Control volume energy balance
13.6 Entropy balance
13.6.1 Some consequences of the entropy local balance
13.6.2 Entropy local balance in multicomponent systems
13.6.3 Control volume entropy balance
13.7 Introduction to Onsager theory
13.8 Exergy in continuous media
13.8.1 Control mass exergy balance
13.8.2 Physical exergy local balance
13.8.3 Chemical exergy local balance
13.8.4 Control volume exergy balance
13.8.5 Exergy balance in multicomponent systems
13.8.6 Examples
13.9 Exergy cost in continuous media
13.9.1 Local exergy cost balance
Superscripts
Subscripts
Nomenclature
References
Index
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
Back Cover

Citation preview

Exergy Analysis and Thermoeconomics of Buildings Design and Analysis for Sustainable Energy Systems

José M_a P Sala Lizarraga Ana Picallo-Perez

Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2020 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-817611-5 For information on all Butterworth-Heinemann publications visit our website at https://www.elsevier.com/books-and-journals

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This book is dedicated to my beloved sons, grandson Aimar Sala and to my grandson who is now in gestation.

Biography

José M_a P Sala Lizarraga

José M_a P Sala Lizarraga has a PhD in Thermal Engineering from the School of Engineering of Bilbao, a degree in Physical Sciences from the Complutense University of Madrid, Spain and an M.Phil in Theoretical Physics from the School of Mathematical and Physical Sciences of the University of Sussex (U.K.) His professional life has been devoted mainly to lecturing and research. Since 1983, he is the Professor of Thermodynamics and Physical Chemistry at the School of Engineering of Bilbao, University of the Basque Country, Spain. He has also worked for several years as Technical Director of an engineering company dedicated mainly to the development of power plant projects. His lines of research are energy analysis and the simulation of industrial equipment and processes, as well as energy efficiency in buildings. He has published more than 100 articles in international journals, has presented lectures in more than 80 international congresses, is the author of three patents, and has written numerous technical reports and also 12 books on thermodynamics and cogeneration.

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Biography

Ana Picallo-Perez

Ana Picallo-Perez, currently an interim university professor (at ETSI Bilbao) and a researcher at the consolidated ENEDI group, got her PhD in Energy Efficiency and Sustainability in Engineering and Architecture in January, 2019 thanks to the Basque Government’s predoctoral fellowship. In addition, she has previously participated as a Personal Researcher on Contract with the School of Engineering of Bilbao. Her research areas are related to testing, analysis, and optimization of building energy supply systems, thermoeconomics, and diagnosis application in buildings. Corresponding to those areas, she made six publications in JCR journals, written a book chapter and has also made her contribution to more than 15 international and national congresses since 2015. She had done three quarterly terms: first one at Technische Universit€at Berlin (2017), second at L’Universita degli Studi di Palermo (2018) and the third at L’Universita degli Studi di Padova (2018) for deepening her PhD. Additionally, she attended her fifth academic year in Mechanical Engineering at Politecnico di Torino (Italy, 2014).

Preface

In the seventies and eighties, efforts in the field of energy were aimed at improving the efficiency of its use, and towards the use of renewable energy. In the mid-nineties concern began to be directed towards the protection of the environment, seeking to satisfy energy needs with the least environmental impact. Analysis methods were developed that took into account not only energy consumption and economic profitability, but which also began to place importance on aspects such as the life cycle, the limited nature of natural resources, externalities, etc. Today’s society and its standard of living and well-being are closely linked to the consumption of a large number of natural resources. An important part of these resources is consumed in the tertiary sector (residential and services) which, together with transport, form the so-called diffuse sectors. The measures that need to be carried out to limit energy consumption in these sectors are more complex to implement than in the case of industry. In recent years, significant progress has been made in this search for increasingly efficient buildings, with the aim of achieving buildings with almost zero energy consumption or even going one step beyond, and constructing energy-positive buildings i.e., with surplus energy. In order to contribute towards this objective, we present this book in which the Method of Exergy Analysis and Thermoeconomics is applied to the analysis of buildings, both in terms of their envelope and installations. The methodology called Exergy Analysis is very useful for the analysis and design of the different systems and installations that we find in buildings, as well as for the building considered in its entirety. We will see throughout the book that, by use of exergy analysis, not only the amount of energy but also its different quality is taken into account, so that the true energy losses can be detected and quantified, which as we will observe, are nothing other than exergy destruction. In a world with a growing demand for energy and finite natural resources, it is fundamental to understand the mechanisms that degrade energy and resources in general and develop systematic procedures to improve systems, and therefore, reduce their environmental impact. Exergy Analysis combined with Economics, in other words, Thermoeconomics, is a powerful tool for the systematic study and optimization of systems. Despite the interesting possibilities offered by the method of exergy analysis, which for some years has been incorporated into the curricula of schools of engineering, the reality is that this analysis methodology is virtually unknown in the building sector, even if it is often used in the industrial world, mainly in generation plants. It is in the last few years that terms such as low-exergy buildings have begun to appear in some architectural magazines, works have been published in technical journals on

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exergy related to buildings and lectures have been presented in some congresses and conferences. However, in the professional world, this type of analysis is not used and remains mostly unknown. Some of the possible reasons that might explain this situation may be that it seems complex, and that the concepts and definitions of the industrial world need to be adapted to the building sector, etc. This book precisely aims to overcome these obstacles, so that professionals in the building sector, both engineers and architects and other technicians, see the need to make a leap forward in the methodology of analysis, from the conventional method based on energy balances using the First Law of Thermodynamics, to the method presented in this book, which proposes a more comprehensive analysis, since it simultaneously takes into account the First and Second Laws of Thermodynamics, two natural laws that are unfailingly fulfilled in all processes. The book was born as the result of a collaboration between the Laboratory for the Quality Control in Buildings (LCCE) of the Basque Government and ENEDI research group at the University of the Basque Country (UPV/EHU), dedicated to studying in-depth the different aspects of energy efficiency in buildings. The aim of the book is to make known the possibilities of this methodology to professionals in the sector: engineers and architects. That is ultimately its reason for being. The book aims to serve both professions, although certainly not all chapters are written for both; some chapters may be of interest to installation engineers and others to architects, although the study of all the chapters will provide a complete view of the methodology. It is divided into 13 chapters, which can be considered to be structured in six Sections. The first Section A comprises Chapters 1 to 3, in which the foundations of the Theory of Exergy and the way of calculating exergy associated with the different types of energy are shown. It has been considered appropriate to begin in Chapter 1 with a brief presentation of the concept of energy and its types, for later reference when considering energy in the building sector. Once the current regulatory environment in relation to energy in buildings has been presented, a description is made of the latest developments in buildings, both in terms of new types of materials and new construction solutions as well as with regards to modern installations. Once this general overview has been given, the need for incorporating the exergy method in buildings is explained, and a general bibliographical review of the application of the method is undertaken. Chapter 2 has as its fundamental objective the presentation of the basis for understanding the significance of exergy. A review is made of the central ideas of the First and Second Law of Thermodynamics, and the meaning of the different qualities of the different forms of energy is developed, such that the exergy concept appears in a natural way. The expression for the calculation of exergy of heat flux is then given, and a detailed study is made of the exergy of thermal radiation. The expression for the calculation of the exergy associated with internal energy is then obtained, both in closed and open systems, and it is shown that in any real process, although energy is conserved, there is exergy destruction. The chapter ends with a presentation of the different ways of defining efficiency, serving as the basis for exergy analysis of processes. Various examples of its application are developed throughout the chapter.

Preface

xvii

In Chapter 3, we obtain a series of expressions for the calculation of the physical exergy of substances, related to physical desequilibrium (thermal and mechanical) with the environment and the chemical exergy, related to chemical desequilibrium with the environment. Various examples are given, both for the calculation of physical exergy and chemical exergy, and expressions are obtained for the physical and chemical exergy of the substances of interest in the building sector, such as construction materials, water, humid air, combustion gases, fuels, etc. The second Section B of the book contains Chapters 4 to 6. Chapter 4 looks at the application of this theory to the envelope of buildings. After a review of the mechanisms of heat exchange that take place on the interior and exterior surfaces of the envelope, these exchanges are analysed from the exergy point of view. The exergy destruction in heat conduction through a building envelope is evaluated, as well as that which occurs in the boundary layer due to heat transfer by convection and that associated with the absorption and emission of radiation. Several examples of specific cases are developed in the chapter. In Chapters 5 and 6, exergy analysis is applied to the different components of the heating, domestic hot water (DHW) and air conditioning installations. Chapter 5 looks at the components of the heating and DHW installations, from the terminal elements to the generation equipment, such as boilers or heat pumps. The chapter ends by analysing those components that must be considered as being in a dynamic regime due to their condition, such as energy storage systems. Chapter 6 looks first at basic equipment in refrigeration and air conditioning installations and ends the chapter considering components in renewable energy facilities. The chapter begins by performing exergy analysis on absorption and adsorption refrigerators, as they are less well known than compression refrigerators, and continues with an analysis of the basic air conditioning processes, clearly showing the differences between conventional energy analysis and exergy analysis. The chapter ends with the analysis of solar thermal panels and photovoltaic panels. Throughout Chapters 5 and 6, different examples of the exergy analysis application on the components of installations are given. In the third section of the book, Section C, the different versions of Thermoeconomics are developed, covering Chapters 7 to 9. Chapter 7 presents the basic concepts of Thermoeconomics, a discipline that combines Thermodynamics with Economics and which is based on exergy analysis. The Exergy Cost Theory (ECT) is developed, presenting a detailed analysis of the thermodynamic process of cost formation, which has its physical roots deep in the Second Law of Thermodynamics, as well as the foundations of other methods of cost allocation. Chapter 8 develops Symbolic Thermoeconomics (ST), which works with functions, allowing the function that relates a thermoeconomic property with selected independent properties to be obtained. We present the two ST formulations, called supply model and demand model, ending the chapter with an analysis of residues. Chapter 9 develops Thermoeconomic Diagnosis, which is a variant of the installations energy diagnosis and which aims to discover and interpret the anomalous functioning of equipment in an installation and to evaluate the effect that the anomalous behaviour has on additional fuel consumption.

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Section four of the book, Section D, looks at sustainability in buildings and consists of Chapters 10 and 11. Chapter 10 makes clear the usefulness of exergy in evaluating the sustainability of buildings and their installations. After a brief review of different tools for the sustainability analysis, we present the exergy tools that have been developed for this purpose. Chapter 11 applies the concepts discussed so far in the book, considering different examples of typical heating, DHW and air conditioning installations. Section five of the book, Section E, includes Chapter 12, which concerns the design of installations and their mode of operation. In this chapter, after a presentation of the mathematical problem of optimization, the importance of Thermoeconomics in the design of thermal systems is highlighted and a distinction is made between the two basic methods, one based on multipliers and the other on approximations, developing these ideas through several examples. Finally, in Section F, which consists of Chapter 13, we present exergy analysis in the context of the Thermodynamics of Continuous Media. After considering the local balance of mass, energy and entropy in a continuous medium, the local exergy balance is presented, analysing in detail the exergy destruction due to irreversibilities in heat transfer and flow of fluids. As has been said, this book is aimed at professionals in the world of buildings, both engineers and architects, and other technicians. Sections A, C, D, E and F are of considerable significance for the world of engineering, while for architects Sections A, B, C and D will be more interesting. The book may also be of great interest to students of undergraduate and postgraduate degrees in Engineering, Architecture and Science, who aim to be trained in the field of energy efficiency and sustainability of buildings and want to undertake their doctoral thesis. THE AUTHORS.

Acknowledgement

My thanks go to the Department of Housing of the Basque Government and especially to the different Directors of Housing over the recent years. My special thanks to Agustín de Lorenzo, Head of Regulation and Quality Control in the Department of Housing of the Basque Government and Director of the Laboratory for the Quality Control in Buildings (LCCE). In 2005, a collaborative agreement was signed between the Housing Council of the Basque Government and the University of the Basque Country (UPV/EHU), to develop the Thermal Area of the LCCE. During these years, a new phase was started, with a growing concern for the consumption of energy in buildings. In order to rigorously perform tests on materials and construction elements and be able to address the diverse problems anticipated in future years with regard to the thermal characteristics of buildings, he had the vision to combine the efforts of the LCCE with the ENEDI research group at the University of the Basque Country. We would also like to thank Dr Alberto Aapolaza, as without any doubt he can be considered the father of the Thermal Area of the LCCE, since it was he, with talent and scientific rigor, who began to carry out the first thermal transmittance tests in the guarded hot box equipment. My thanks also goes to Elvira Salazar, Head of the Laboratory, for her enormous practical sense, always knowing how to approach and find solutions to problems with the appropriate perspective. I also cannot forget the staff of the Thermal Area, Ivan Flores, César Escudero, Imanol Ruiz de Vergara, Eider Iribar, Carlos García, Daniel Pérez and Laura Angulo as well as all the other staff of the LCCE, whom it has been a pleasure to work with over the last 15 years. Lastly, we would also like to thank the doctoral students of the last few years of the Doctoral Programme in Energy Efficiency and Sustainability in Engineering and Architecture at the University of the Basque Country, having used some of the results of their doctoral theses in the book, particularly, those of Ivan Flores, Estibaliz Pérez and Eneko Iturriaga.

Section A Foundations of exergy theory

Efficient buildings and the arguments for incorporating exergy

1.1

1

Summary

This first chapter aims to serve as an introduction to the book and is dedicated to the application of the Method of Exergy Analysis and Thermoeconomics in buildings, with regard to both the envelop and the facilities. It was considered convenient to start with a brief presentation of the concept of energy and its types, in order to refer later to energy in the building sector, talk about energy systems and provide some data on energy consumption in buildings around the world, in the EU, Spain and the Basque Country. Once the current regulatory environment regarding energy in buildings has been presented, a description is made of new types of materials, of new constructive solutions and of modern facilities that allow buildings to better meet the requirements of comfort and to have greater energy efficiency. After the presentation of this general overview of the sector, a brief introduction to the concept of exergy is made, and the arguments for incorporating the exergy method in buildings are given, both from a purely energetic point of view, as well as from an economic and environmental point of view. Finally, a general bibliographic review of Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00001-1 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

the application of the method is presented, since in the chapters following, the specific bibliography of each of the topics dealt with will be added in the corresponding sections.

1.2

Concept and laws of energy

Matter and energy are the fundamental concepts in natural sciences, but they are not easily defined. In addition, one of the consequences of Einstein’s theory of relativity is that, we know that mass can be converted into energy and vice versa, through his famous equation. The term energy was used for the first time by the English scientist Thomas Young in 1807 when he referred to what we call kinetic energy [1]. By energy, we mean something that appears in many forms that are all related to each other because one form of energy can be converted into another. Although it is very difficult for us to define the concept of energy in a simple way, we can speak with precision about the different ways in which it is manifested. In effect, we find different types of mechanical energy, such as gravitational potential energy, associated with the position of bodies, and the kinetic energy of translation and rotation, associated with the movement. Considering the configuration of its molecules and its vibrations, the energy stored in a body, such as the energy of a mass of steam, hot gasses, etc., is called internal energy, These forms of energy can be stored in bodies, which means that they can be considered as static forms of energy. There are other forms of energy that are not stored but are transferred from one body to another. They can be considered as dynamic forms of energy, and in this category, we can find work (in its various forms of mechanical and electrical work) and heat, which constitute a form of energy exchange, associated with the temperature difference between two bodies. It was already observed in the mid-19th century that, just as with mass, energy can change its form or nature, but cannot be created or destroyed. This experimental evidence is gathered in a universal law well known by all, which we call the First Law of Thermodynamics, or also Law of Energy Conservation. Therefore, when a body (closed system) interacts with others, the following principle is always fulfilled: its energy variation is equal to the energy exchanged, which can only be in the form of work or heat, as mentioned earlier. In addition to quantity, another fundamental aspect of energy is its quality, which means its capacity to produce a change. In this way, the capacity to cause a change (move a machine, heat a room, etc.) of 1 kWh of propane (72.28 g of propane stored in a bottle) is greater than that of 1 kWh of thermal energy in the mass of air at 20
C contained in a 150 m3 room (Fig. 1.1) and the capacity to cause a change in a mass of air with the same amount of energy is lower when stored at 15
C. The quality of the energy depends on whether it is ordered energy, such as potential energy, the elastic energy of a spring, the kinetic energy of a spinning wheel, etc., or is disordered energy, such as the internal energy of matter.

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5

Figure 1.1 Different quality of energy.

This aspect of the quality of energy is what is taken into account in the Second Law of Thermodynamics. Precisely, this book aims to delve into the meaning of the quality of energy and its connotations in the building industry. While the transformations of some types of energy into other forms are carried out with ease and with an efficiency that can reach 100%, for some, the efficiency of these transformations is relatively low, even assuming that they are made through perfect processes, i.e., reversible processes, Blair et al., 1976 [2], which shows that there is something that distinguishes the different forms of energy, in short, that their quality is different. The more disordered an energy (heat, internal energy) is, the lower its quality is, which means, its capacity to produce useful effects is low, while ordered energies (electrical, all forms of mechanical energy) have the highest quality and are convertible into other forms of energy. Then, in any transformation of energy that is considered, in any process that takes place in a unit or an installation, although the energy is conserved, the quality of that energy decreases. Only in a theoretical transformation, where everything is perfect (reversible is the term used in Thermodynamics), would the quality be maintained. In any real transformation of energy, there is a decrease in its quality, precisely due to imperfections (irreversibilities). We must bear in mind that what really matters about energy is its ability to do something useful; so we transform it into a form that can meet a series of requirements. It is interesting to note how, throughout history, human beings have always focused their attention on the use of energy. It has happened since the discovery of fire, coal mines, etc., until the present modern times when energy has become the central protagonist of modern technology. The technology that has been developed around the conversion of energy, its transport and storage would not have been possible without the guidelines marked out by Thermodynamics. By clearly establishing the different qualities of types of energy, Thermodynamics sets the optimal limits for that conversion, allowing the quantification of inferior results achieved as a consequence of the imperfections of technological processes; besides, it also indicates the points on which one must act to achieve an improvement. To accomplish the use of energy, it is necessary to use devices and equipment built thanks to human ingenuity and knowledge. Thermodynamics serves

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Exergy Analysis and Thermoeconomics of Buildings

as a guide to assess the processes and machines used, and thus, obtain increasingly perfect energy transformations, LeGoff 1979 [3].

1.3

Energy sources. Fossil and renewable energies

As we know, solar radiation is the most important source of energy at our disposal. It is a very high-temperature source, which unfortunately is exploited inefficiently due to the great degradation (loss of quality) suffered by the radiated energy that reaches us; it is a result of its interaction with the atmosphere and the surface of the land and the limitations of the equipment available to us. The solar resource is much more abundant and durable than any of the fossil fuels that we use. In addition, it is freely available and distributed over the surface of the earth; the problem is that we do not know how to take proper advantage of it. In fact, the solar energy that reaches the surface of the earth each year is tens of thousands of times more than the global energy consumption of human beings in a given year. On the other hand, reserves of fossil fuels will exist only for several tens or hundreds of years more. Regardless of the uncertainties associated with these estimates, the existing reserves are just a trifle compared to solar energy, which highlights the nonsense of the continuity of the fossil fuel model. The interaction of solar radiation with the atmosphere, the seas, and the earth is very complicated. Additionally, a small fraction is absorbed via photosynthesis, forming biological molecules, both terrestrial and maritime; it is what we call biomass. The fossilization of various types of biomass stored geologically over tens of millions of years and subject to different kinds of physicalechemicalegeological processes is the origin of fossil fuels. In view of what has been said, we can distinguish two types of energies: we will call renewable energies those that have an inexhaustible potential, because they come from solar radiation that continuously reaches our planet, from gravitational attraction, or because they are linked to permanent processes, such as the water cycle in nature, the winds, etc. Thus, the renewable energies are solar, hydro, wind, biomass, etc. On the other hand, the non-renewable ones comprise the energy potential, stored in the earth from millions of years ago and which, therefore, are depleted as they are consumed. Fossil fuels (coal, oil, natural gas) and to some extent nuclear energy are non-renewable resources, whose reserves are limited. Therefore, at some point, they will run out, and millions of years will be needed to provide them again, Fig. 1.2. Hydraulics is the first renewable energy to experience a notable development. It takes advantage of the potential energy of water evaporated by solar action and precipitated in the form of rain. Its historical contribution to the development of electricity and economic and social progress has been truly extraordinary. Wind energy, through windmills, has also been one of the oldest energies of solar origin, although its industrial development came to a standstill until a few years ago, due to low power density and the problem of storage, Fig. 1.3. Technologies are currently being developed for wave energy and its use.

Efficient buildings and the arguments for incorporating exergy

Figure 1.2 Oil extraction.

Figure 1.3 Wind-power generator.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 1.4 Parabolic trough collectors of a solar power plant.

Solar radiation can be exploited energetically by creating a hot focus at a sufficiently high temperature, for which concentration of the radiation is needed: this is what is called heliothermic energy, which is used in solar power plants for the generation of electricity, Fig. 1.4. Another way of using solar radiation is the generation of electric current through the mechanism of solid-state electronics, which is known as photovoltaic energy. In both cases, given the random nature of solar radiation, some mode of energy storage is required. There are also other energies that do not depend on limited reserves but are not activated by solar radiation. We are referring to tidal energy, which has its origin fundamentally in the gravitational action of the moon, and geothermal energy, which can only be efficiently exploited in some suitable sites. In addition to the aforementioned energies, there are the nuclear energies, which are linked to Einstein’s famous equation, stating that mass can be converted into energy and vice versa. Nuclear fission, which has been commercially exploited for the production of electricity, consists of the decomposition reaction of the heavier nuclides, particularly of uranium. With existing reserves, current reactors could be functioning for thousands of years. However, due to the environmental risk of the waste and the possibilities of accidents, it is a type of energy that some countries have rejected as an alternative. The other type of nuclear energy is fusion, consisting of two nuclei of light atoms (deuterium, tritium, etc.) joined to form a heavier core, simultaneously releasing a huge amount of energy. As there are about 1025 deuterium atoms in 1 m3 of seawater, it can be said that 1 m3 of water energetically equals 200 tons of oil, so the reserves are huge, practically inexhaustible. The problem with fusion is not of reserves, but of the technology necessary to exploit them. According to the BP Statistical Review 2016 [4], the global consumption of primary energy in 2015 was 13; 100 Mtpe, having grown in that year 1%, with 1% being the lowest level of growth since 1998. Of this total consumption, 32.8% corresponded to oil, 29.8% to coal, and 24.4% to natural gas. In short, 87% of primary energy came from fossil fuels. Nuclear energy represented 3.8%, while renewable

Efficient buildings and the arguments for incorporating exergy

9

energy accounted for 9.2%, with hydroelectricity accounting for 6.9% and other renewables for 2.3%. We then see that currently the world’s demand for energy is basically satisfied with non-renewable sources. The available reserves of these energy sources, all exhaustible, are relatively abundant, although their geographical distribution is quite unequal around the planet. This relative abundance cannot justify either wastefulness or deny the need for a change in the energy model, in which renewable energies prevail.

1.4

Energy chains

Although in the previous Section, we have referred to the different forms of energy from a physical point of view, we are now going to make a differentiation based on their utility, and so from an economic perspective. We will distinguish the resources obtained directly from nature in the first place, before any transformation by technical means, from what we call primary energy. We can define primary energy as the direct or indirect available natural resources that do not undergo any chemical or physical modification for energy use, CEPAL 2003 [5]. Thus, petroleum, coal, natural gas, hydro, solar, geothermal, etc., are in this group. Since these primary energies are not immediately useful, it is necessary to subject them to a series of transformation operations, which we call energy chains, until they are converted into secondary energies. Within these secondary energies there are the intermediate energies, also called energy vectors, among which, electricity and combustible fuels (gasoline, fuel oil, gas oil, kerosene, etc.) are the most important, and the final energies are those that satisfy the final needs in buildings, industry or transport, such as heat, cold, light, hot water, movement, etc. Some factors are used that take into account the energy consumption in the extraction, transport and processing, for calculating the primary energy from the final consumed energy, that is, in the whole energy chain. These conversion factors apply only to fossil fuels and so for renewable energies just the auxiliary energy required for the operation of their systems is taken into account. In order to recognize the environmental benefits in terms of CO2 emissions from renewable energies, there is the DIN V 18,559-1 standard [6]. In Spain, we have the Document CO2 Emission Factors and Coefficients of Conversion to Primary Energy of IDAE 2016 [7] that reviews and updates the conversion coefficients of final energy to primary energy and CO2 emissions of the different energies used in the building sector. The technical complexity and economic cost of energy chains vary greatly, depending on the primary and final energy involved. Thus, in the case of coals, the complexity is small since it can be a simple washing and sorting by size and agglomerating to form briquettes. In the case of oil, the chain is long and complex, including prospecting, drilling, extracting, crude transporting, refining, and distributing of derivative products. However, the most complex and costly chain is that of nuclear fuel, especially the stages of enrichment and manufacture of fuel elements, Gonz
alez 2004 [8]. Fig. 1.5 shows the energy chain of biomass for the generation of electricity with a schematic presentation of photovoltaics.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 1.5 Examples of energy chains.

Energy is absolutely indispensable in our current way of life. But the use of energy is not exclusive in today’s society, as already in ancient times human beings, in addition to their own effort, were able to use some domestic animals, as well as wind, fire and water currents. However, with the Industrial Revolution, the hitherto prevailing energy consumption and production model disappeared, and energy sources used during the millennia were replaced with new ones, exponentially increasing their use. Thanks to the use of the scientific method and the identification of the laws that govern the phenomena that take place in the physical world, human beings have been able, over the centuries, to make successive energy revolutions. Leaving aside the most ancient, that of the domain of fire, if we move to more recent times, we find ourselves with the coal revolution, associated with steam engines, both for transport and for industrial operation. Then there was the oil revolution, which allowed the deployment of the automotive and aeronautical industry, as well as petrochemistry and plastics. Then came the nuclear revolution, whose possibilities we have barely begun to realize, through fission power stations, and the great challenge of fusion power stations still pending. The last revolution, in which we find ourselves immersed, is that of large-scale renewable energies.

1.5

Energy and sustainability

In the 70s and 80s, efforts in the field of energy were aimed at improving efficiency in energy chains and their final use, as well as towards the use of new energy sources. However, already in the mid-1980s and early1990s, concern began to be directed towards the protection of the environment, seeking energy systems that had a lower environmental impact. Analytical methods were developed considering not only energy consumption and economic profitability but also the scarcity of energy sources,

Efficient buildings and the arguments for incorporating exergy

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as well as the degradation of the environment as a result of those energy conversion processes. In fact, to make energy activities sustainable, it is not enough to merely consider the classical aspects in relation to production, consumption, conversion yields and costs. It is necessary to include considerations of a political, social and ecological nature, in the short- and long-term, which in general are difficult to quantify. Sustainability is an emerging science, which must be developed and applied as quickly as possible. Its development will provide tools for analysis and evaluation of great importance in the conversion and use of energy; after all, these activities have great environmental, economic and social impacts and so all energy projects must be designed and implemented under the criteria that arise from the application of sustainability. In this respect, exergy can make interesting contributions.

1.5.1

Life cycle

These effects related to the scarcity of resources and environmental impact began to be taken into account not only during the phase of use of the equipment or energy system considered but throughout its life cycle, so from its design, construction, use, and end of useful life, with the corresponding recycling of materials. Thus, at the end of the 90s, sustainability considerations began to be introduced in the design and operation of energy systems, Groenewegen et al. 1996 [9]. Fig. 1.6 presents the life cycle stages of a product. The degradation of the environment has given rise to the development of environmental conscience in society, so that today we keep in mind that, depending on the consumption, the environmental implications can vary greatly. Indeed, products that apparently provide the same service can, however, be radically different if environmental costs are accounted for in their life cycle; that is, from the natural resources used, the production process and transportation to final consumption.

Figure 1.6 Life cycle stages of a product.

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Exergy Analysis and Thermoeconomics of Buildings

At present, the idea that the resolution of environmental problems involves considering the global nature of the environment is being imposed. The actions taken, aimed at improving the environment, based on a local and short-term vision are doomed to fail in the long term, since they do not optimize the resources, and may even be counterproductive. Without a global analysis, what happens is the transfer of the environmental load (quantity of pollutants that reaches the environment or amount of resources extracted from it) or its effects, and not its reduction. This transfer can occur between facilities, geographical areas, temporary spaces, between environmental goods (air, water, soil), or between impact categories (acidification, toxicity, destruction of the ozone layer, etc.). So, for example, if we consider the purification of waste water, it seems obvious that it is a benefit for the environment, but to what extent? This purification implies the consumption of energy (generated elsewhere through polluting processes), the use of chemical products (whose production processes also contaminate) and the emission of certain gases into the atmosphere and deposits of certain sludges. The current evidence seems to indicate that the activities of human beings, and in particular, those related to energy are affecting the chemical composition of the earth and the energy balances; besides, the consequences may be catastrophic as is being manifested in what we call climate change. Therefore, the analysis and design of energy systems must be extended in space and time, considering the ecosystem as a whole system to be analysed and the life cycle as the relevant time scale, Energy Working Group 2001 [10]. A global analysis of the whole life cycle is the only way to be able to compare different technologies, in spite of subjective aspects that may be incorporated in the methodology. In fact, the only way to evaluate renewable energies is through these life-cycle methodologies. Thus, a photovoltaic system does not generate emissions in its operation phase, so that the life cycle is the only way to account for emissions; after all, these can only occur in the preparation phases of the semiconductor material and the manufacturing of the modules. Likewise, the impacts associated with the rest of the elements that make up a photovoltaic installation, that is, supports, electronics, integration in the building, etc., can be evaluated.

1.5.2

Externalities

Another aspect that should be emphasized is the one that refers to environmental externalities. As we have said, since the mid-1980s, there has been a growing general concern about the degradation of the environment, as a consequence of emissions caused by fuels. Since then, the effects of acidifiers, ozone-depleting agents, and greenhouse gases have been of great interest. It is reflected in recent trends, particularly in the emphasis on sustainable development and the use of market mechanisms for environmental regulation. It is clear that the energy sector is already on a path of no return, towards a new energy model that will leave behind the predominance of fossil fuels. The current energy model is based on technologies that do not include the health, social and environmental costs, associated with its pollutant character. These non-internalized costs are

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real and do not affect the price of energy, but they do affect other budgetary items and our health. Thus, the global warming associated with climate change is added to the pollution of large cities, as well as the gradual depletion of oil. The damage that pollution produces to the environment is then translated into costs that fall on society and are not reflected in the market economy (external costs). The existence of these costs means inefficiency in the economy and poor distribution of resources. There are several reasons for the growing interest in the quantification and monetization of environmental cost impacts, such as: • • • • •

The need to integrate environmental aspects when selecting between different materials and energy technologies. The need to evaluate the costs and benefits of stricter environmental standards. The use of economic instruments in environmental policy. The need to develop general indicators of environmental behaviour of different technologies to allow comparison between them. Different political initiatives to achieve a greater impact of market mechanisms in the energy sector (privatizations, limitation of subsidies, liberalization of the energy market, etc.).

The monetization allows the internal costs and environmental costs to be put on the same basis, which makes it possible to compare both and also make a comparison between different energy alternatives, something that cannot be achieved with the use of other tools. Fig. 1.7 presents two examples of the environmental impact caused by energy-related activities. All these issues are reflected in recent legislations at the European level. The Maastricht Treaty of 1993 introduced the principle of sustainable economic development, the main objective of the European Union, and the Fifth Environmental Action Program articulated the need for analysis and economic valuation of externalities. It was this European framework wherein an important project was developed with the

Figure 1.7 Examples of externalities.

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Exergy Analysis and Thermoeconomics of Buildings

aim of establishing a methodology in the analysis of external costs and applying it to the energy sector within the EU. The so-called ExternE Project, which was developed between the beginning of the 90s and the year 2005 [11], represented a considerable advance with respect to previous works on the calculation of externalities, developing a much more reliable methodology. In the United States, there is a greater tradition in the monetary valuation of impacts on the environment and health and in the use of political instruments to internalize external costs in decision-making, especially in the energy sector. In this regard, the best example of the potential use of the results of the analysis of externalities is the requirement made by several state energy commissions to include externalities in their planning and decision-making. The trade in sulphur dioxide emissions is another example of possible use of the results. Despite the progress made, there are enormous difficulties in the analysis of external costs and large uncertainties accompany their estimation. For most pollutants, the damage caused on a global scale is not known precisely and, in addition, the interactions between different pollutants are very complex at this scale. However, this does not mean that these costs are less real, which is why their existence should be acknowledged by governments when considering possible energy options. There are some facts that we must take into account: there are limits in the capacity of the planet to regenerate, and it seems that we are about to, or have already overcome those limits. Also, we must think that economic development is not a panacea that justifies the reduction of environmental quality. Possibly, the problem is that prices reflect the marginal costs of production, when in fact, externalities would have to be internalized so that prices reflect the marginal social opportunity costs.

1.5.3

Limited nature of natural resources

Finally, another essential aspect related to sustainability refers to the impact associated with the reduction in the availability of natural resources, which are limited; so we must preserve them. The term natural resources include soil (all minerals and fossil fuels), water, air and biological diversity and considering this, there are other related aspects that should be kept in mind: • • •

The exhaustion of reserves. The loss of options for future generations. The increase in environmental impacts in the future, because easily accessible resources are the first to run out.

However, some argue that the depletion of energy resources is not problematic, due to the still increasing discovery of new fossil fuel deposits and the greater potential for substitution with clean energies. However, this substitution will be a long-term process and may never be completely successful; so, it is better to have a conservative stance as relying on this substitution means passing on an unfair obligation to the future generations.

Efficient buildings and the arguments for incorporating exergy

1.6

15

Energy and the building sector

As we have just mentioned, current society, its level of quality of life and well-being are closely linked to the consumption of a large number of material resources and energy. An important part of these resources is consumed in the tertiary sector (residential and services), which together with the transport sector, form the so-called diffuse sectors. The measures to be carried out to limit energy consumption in them are more complex to implement than in the case of the industry. Buildings use energy throughout their life cycle, from construction to demolition, although we must distinguish between direct and indirect energy consumption. Direct energy is used in the construction, operation, reconstruction and demolition of the building, while indirect energy is consumed to obtain the materials needed in the construction and technical facilities, Sharma et al. 2011 [12]. However, most of the energy consumption in buildings is the direct energy associated with the provision of heating, domestic hot water (DHW), ventilation and air conditioning (HVAC) during the use phase.

1.6.1

The building as an energy system

A building can be described as an energy system consisting of the demand of energy on the one hand, and energy sources on the other, and between these two, the components that transform those sources into the desired form of final energy, in place and time. Fig. 1.8 presents a scheme of the system, with its three elements that we describe below.

1.6.1.1

Demand

The energy demand represents the amount of energy that is required by the users of the building to enjoy comfortable conditions. It, therefore, comprises the demand for thermal energy and the demand for electricity. The demand for thermal energy is due to the

Figure 1.8 Scheme of the energy system of a building.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 1.9 Annual energy demand for a typical house in a housing block in Bizkaia.

need to maintain certain indoor air conditions (temperature, humidity, pressure and indoor air quality) as well as other uses such as DHW, cleaning, cooking, etc. The demand for the maintenance of comfortable indoor air conditions is the result of the balance between losses, due to ventilation and infiltration, and heat transfer through the façade and gains, solar and internal gains, due to occupants and interior equipment. The electrical demand is due to the different appliances using electrical power, as well as the requirements of lighting. The demand for energy varies significantly from one building to another, depending on the use to which it is destined (residential, commercial, educational, industrial, sanitary, etc.) on its location and climatology, on the design of the building itself, on the quality of its construction and, also, in an important way, on the behaviour of the users. By way of example, Fig. 1.9 shows the average energy demand of a Basque house located in Bizkaia, according to data obtained from the Basque Energy Agency (EVE).

1.6.1.2

System components

Various components are needed for the conversion, distribution and storage of energy since energy sources are not generally available in the correct form, in the correct place or at the right time. Components, such as boilers, heat pumps, distribution pipes, etc., are found to be inside the building itself, but in some cases, they can be found outside it, as in the case of district heating systems. There are losses in the different components when energy transformations take place, so the energy consumption is always higher than the demand.

1.6.1.3

Energy sources

The beginning of the energy chain has its origin in primary energy sources, outside the building, which includes both renewable and non-renewable energies. Fig. 1.10 also shows the annual primary energy required to meet the requirements of a typical

Efficient buildings and the arguments for incorporating exergy

Figure 1.10 Annual demand, consumption, and primary energy of a typical house in Bizkaia.

17

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Exergy Analysis and Thermoeconomics of Buildings

house in Bizkaia. The heating and DHW are considered to have been produced in a natural gas condensing boiler and that the appliances are rated Aþ . Electricity is imported from the grid, according to the Primary Energy Conversion Coefficients mentioned earlier, IDAE 2016 [7].

1.6.2

Energy consumption data in buildings

The consumption of energy in buildings has been augmenting in recent years due to the increase in population, the increasing demand for healthy and comfortable environments, etc. At the global level, the building sector is responsible for approximately one-third of greenhouse gas emissions, one-third of energy consumption and onethird of the consumption of material resources and the generation of waste. The trend is moving towards a very alarming increase in these percentages in such a way that in the last 10 years, the extraction of materials alone has multiplied eight times. In Europe, buildings are responsible for 40% of final energy consumption (of which 26.7% corresponds to households [13]) and for 50% of CO2 emissions to the atmosphere. In Spain, these percentages are somewhat lower, so that in 2015, buildings represented 29.8% of the final energy consumed, with the residential sector responsible for 18.6% and the services sector (schools, hospitals, shops, offices and restaurants) the remaining 11.2%, IDAE 2013 [14]. According to the data collected in the Sech-Spahousec project [15], the average annual consumption per Spanish household is 0.852 tpe, with an average electrical consumption of 3847 kWh. Of the total consumption, 47.0% corresponds to heating, 18.9% to DHW, 19.4% to household appliances and the rest to lighting, refrigeration, etc. Referring to the case of the Basque Country, between 1990 and 2010, there was a twofold increase in consumption in buildings. However, in the 4 years between 2010 and 2014, it decreased by 10%, EVE 2015 [16], due to the economic crisis, the increase in energy prices, and undoubtedly, the actions taken by the administration to improve energy efficiency, see Fig. 1.11. Unfortunately, at the global level, the current trend is moving towards an increase in consumption in a very alarming way. According to the International Energy Outlook 2016, for the building sector, between 2012 and 2040, an average annual increase of 1.5% is foreseen, with a growth of 2.1% for countries that are not part of the OECD, which is almost three times the expected growth for the OECD countries. However, energy saving and efficiency policies at the EU level consider buildings as the sector with the greatest potential for energy savings [17]. In particular, the Commission quantifies this potential for residential buildings as 27% and commercial buildings as 30% [18]. At a national level, the Energy Savings and Efficiency Action Plan 2010e20 [19] indicates that measures should be prioritized over those sectors that have the greatest difficulty in tackling energy efficiency measures, such as diffuse sectors. The importance of energy consumption in buildings and the enormous possibilities for improvement have meant that nobody today denies the need to reduce this consumption, seeking greater energy efficiency and greater incorporation of renewable energies and, ultimately, making our buildings sustainable. There has been an important evolution of European standards in recent years precisely to achieve these objectives. We present below a summary of the EU regulatory environment in the buildings sector.

Efficient buildings and the arguments for incorporating exergy

19

Figure 1.11 Evolution of the buildings’ energy consumption in the Basque Country, 1990e2014. EVE, Euskadi’s Energy Strategy 2025, Basque government (2015) (in Spanish).

1.7

Current regulatory environment regarding energy in buildings

In the last decade in the EU, several directives have been approved that impose energy efficiency requirements for new construction as well as for renovation. The European vision for the recovery of economic growth in the construction sector, in the current context of economic and social crisis, considers activities aimed at fulfilling the potential of buildings with low energy consumption as the main action line, investing mainly in the renovation and maintenance of existing buildings, as well as in new buildings. In March 2007, the European Council established the 20/20/20 Targets. One of the keys to the implementation of these ambitious objectives is the significant number of buildings in Europe that can energetically be considered as old. If these buildings were modernized, gaining efficiency and taking advantage of renewable energies (envelope and facilities), Europe could save 20% on its imports of fossil fuels.

1.7.1

Directives of the European Union

Three lines in the EU Directives have particular relevance: Directives on the total energy performance of buildings, EPBD (Directive 2010/31/ EU (recast) [20], which updates 2002/91 and Directive 2012/27/EU [21]). The first establishes an European framework for the determination of minimum energy standards in the member states (MS) and the second  complements the previous one, imposing limits on maximum consumption (kWh m2 year). Directives on ecodesign and labelling of energy-using products, EuP (Directive 2009/125/EC [22] and Directive 2010/30/EU [23]). These directives determine the minimum requirements in relation to the ecological properties of products that consume energy.

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Exergy Analysis and Thermoeconomics of Buildings

Directive on the promotion of the use of renewable energy sources, RES (Directive 2009/28/EC [24]). According to this Directive, the MS commit themselves to take measures through which the percentage of renewable energies will be increased, by at least 20% by 2020. Before the adoption of Directive 2010/31/EU, most definitions of low-energy buildings in European countries were expressed by a percentage of reduction of their minimum requirements. This directive defines the nearly zero energy buildings (nZEB) in terms of consumption as a building that has a very high energy performance, as determined in accordance with Annex I. The nearly zero, or little of energy required, should be covered to a very significant extent by energy from renewable sources, including energy from renewable sources produced on-site or nearby. The 2010 Directive establishes that by 31 December 2020 at the latest, all new buildings must be nZEB, while this obligation is advanced by 2 years for public buildings. Therefore, the targets of the 20/20/20 strategy have no relevance in the definition of the limiting values of the nZEB, since the nZEB being mandatory, these objectives would have been reached or not reached. Actually, the 2050 objectives will condition the greater or lesser ambition of the limiting values that are established. These objectives for 2050 are defined in the Energy Roadmap 2050 [25] in which the EU intends to reduce greenhouse gas emissions by 80% by 2050 compared to emissions from 1990. The objective is to make important investments in low-carbon technologies, renewable energies, energy savings and efficiency and network infrastructure. One of the pillars of the Roadmap is, therefore, saving and energy efficiency. The 2010 Directive introduces the principles of energy performance at the costoptimal level, which will be decisive in moving the minimum national requirements to higher levels. It establishes that national requirements must be settled with the aim of reaching that optimal level, so that the energy performance level leads to the lowest cost during the economic lifecycle, applying a harmonized calculation methodology. The Commission asks MS to apply this methodology to calculate these performance levels and compare them with the minimum requirements that are already established. Despite the emphasis on objectives, the definition of nZEB is itself qualitative. There may be discrepancies, for example, allowing inefficient buildings to reach the status of nZEB thanks to oversized photovoltaic systems; in addition, it will be necessary to specify the surroundings of a building, or how “on-site” it is, or what the scope is of the concept of energy demand, whether it is gross or net, etc. Thus, in the definition of an nZEB several issues must be considered and several criteria must be set, as well as aspects on which we have to agree, Torcellini and al. 2006 [26]. Thus, it will be necessary to define: •

•

The boundaries of the building, both the physical ones (it can be a building or a set of buildings), as well as those on the balance sheet; in such way, we may or may not consider the consumption associated with household appliances (the HE0 standard determines the heating, refrigeration and DHW for housing as consumption). In addition, the condition of the boundaries, such as functionality, conditions of use, climate, comfort, etc., must be established. It is also necessary to agree on the weighting system used since we can refer to nonrenewable primary energy, but also define the nZEB referring to the energy consumed in the building, the exergy, the emissions, or referring to cost.

Efficient buildings and the arguments for incorporating exergy

•

•

21

On the other hand, the way of establishing the balance sheet can also vary, so the balance between the energy that is supplied to the building and the energy that the building exports to the networks (electrical, heating), can be established in a way that the balance (exporte import) is positive; however, we can establish the balance between what it generates and what it consumes, so that the balance (generationeconsumption) is positive. There are also other ways of establishing the balance. Another aspect to consider is the temporary interaction of the building with the networks, since it may occur that when the building actually exports the network needs it or, on the contrary, a problem arises. If there is a poor correlation between generation and consumption, for example, generation in summer and consumption in winter, the building will rely heavily on the network.

We can ask several practical questions: • • • •

How do we keep the definition of nZEB flexible enough to lean on existing low-energy standards and accommodate positive energy buildings in the future? How do we establish the proportion of renewable energies? How do we determine the optimal balance between energy efficiency and renewable energy? How do we link the definition of the nZEB with the principles of optimization in cost (Article five Directive 2010/31/EU) so that there will be convergence and continuity?

The 2010 Directive does not establish a single path to reach the nZEB nor does it describe a calculation methodology to establish energy balances. It asks MS to develop their own paths, taking into account national, regional and local conditions. Interestingly, in Annex I of the aforementioned Directive, the consumption of heating and cooling, excluding the consumption of electricity and that of the DHW, is included for the calculation of the building’s energy efficiency. In 2016, the EU Commission approved the Recommendation EU 2016/1318 (OJ of 2 August 2016) on the guidelines to promote nZEB and the best practices to ensure that before the end of 2020 all new buildings are nZEB. Fig. 1.12 shows an image of an nZEB building in the Basque Country.

Figure 1.12 nZEB example. Enertic Business Centre.

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Exergy Analysis and Thermoeconomics of Buildings

Directive 2012/27/EU arises in a framework in which it was found that the EU was not going to achieve the objective of increasing energy efficiency by 20% by 2020. In this context it was necessary to update the legal framework of the Union on energy efficiency, creating a common framework through this new Directive, which not only reinforces this objective but also encourages further energy efficiency improvements to go beyond 2020. In the aspects that affect buildings, we highlight the obligation imposed by this Directive on the MS to establish a long-term strategy to mobilize investments in the renovation of the national park of residential and commercial buildings, both public and private. Likewise, it establishes that the MS will ensure that, as of January 1/2014, 3% of the total area of the buildings with heating and/or cooling system, which their central administration owns and occupies, should be renewed every year. In addition, another important aspect is that MS should promote the market for energy services and facilitate access to small and medium businesses (SMBs). The Building Performance Institute Europe (BPIE) [27] summarizes the current status of the different approaches and indicators of MS for the definition of nZEB, for both new and existing buildings. By the middle of 2017 there are 15 countries in which an nZEB has already been defined, in another three the requirements have been defined and in the remaining 11 MS it is under study, although already five of them have provided indicators of what an nZEB may be, compared to the other six (including Spain) that have not done that. Based on the indicators published to date, it can be seen that the range of primary energy consumption for newly constructed 2 residential buildings in the EU is between 20 and 217 kWh=m  2 year. This range narrows in most countries to values between 40 and 50 kWh m year.

1.7.2

Transposition to Spanish legislation

We present below a brief summary of how the Directives on Energy Efficiency have been transposed into Spanish legislation. Directive 93/76/EEC (SAVE) to limit carbon dioxide emissions by improving energy efficiency (SAVE) was transposed into Spanish legislation by R.D. 1751/1998 which approved the Regulation of Thermal Installations in Buildings (RITE in Spanish) [28], particularly regarding the billing of heating, air conditioning, and DHW expenses according to actual consumption. However, this Royal Decree does not mention the rest of the objectives of the European Directive (energy certification, financing by third parties of investments in energy efficiency in the public sector, thermal insulation of new buildings, periodic inspection of boilers or energy audits in companies with high energy consumption). Directive 2002/91/EC on the energy performance of buildings has been transposed by three Royal Decrees: • • •

R.D. 1027/2007 approving the Regulation of Thermal Installations in Buildings (new RITE), [29]. R.D. 314/2006 approving the Technical Building Code (CTE in Spanish), [30]. R.D. 47/2007 approving the Basic Procedure for the certification of energy efficiency of newly constructed buildings, [31].

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23

The new RITE transposes the aforementioned European Directive as regards to: • • •

The minimum efficiency requirements for new buildings (together with the HE of the TBC). The obligatory nature of periodic inspections of boilers and air-conditioning systems. The obligation to evaluate the state of heating installations with boilers of over 15 years.

The Technical Building Code (CTE) is the basic document that collects the quality requirements of buildings and their facilities. It is divided into different basic documents that reflect the requirements of each area: structural safety, safety in case of fire, the safety of use and accessibility, energy saving, protection against noise and health. The document relating to the energy consumption of the building and its facilities is known as Basic Document DB-HE, of Energy Saving, approved by Order FOM/1635/2013, of September 10. With this standard, the legal framework was renewed, until then in force in the Spanish state, seeking to integrate it within the European context. This document was presented with a focus based on objectives or benefits, these being the requirements that the building or its parts and the characteristics of its materials, products or systems must meet. This new approach corresponds to that employed by the main international official bodies related to building codes. The Basic Document DB-HE consists of six minimum requirements that must be met by all new buildings, expansion or renovation of existing buildings and renovation of thermal installations. Thus, the requirements that these buildings must meet include the limitation on primary energy consumption not coming from renewable energies, on the energy demand, on the performance of thermal installations, on the efficiency of lighting installations and on the establishment of a minimum contribution of thermal and electrical renewable energies. Lastly, Royal Decree 47/2007 determines the calculation methodology for the energy qualification of buildings and approves the energy efficiency label for newly constructed buildings. The Directive 2006/32/EC on energy end-use efficiency and energy services sets a minimum objective for energy saving of 9% in 2016. This objective is still valid since Directive 2012/27/EU does not repeal it. Both Directives insist on the obligation of the MS to present National Action Plans for energy efficiency, in which the actions and mechanisms to achieve the set objectives are established. In compliance with this, Spain has sent to the Commission the last of these Plans: Energy Savings and Efficiency Action Plan 2011e20 [19]. With regard to the building sector, this Plan points out the following relevant aspects: • • • •

The expected savings are more localized in the tertiary sector than in the housing sector. With regard to housing, savings are expected from better envelopes and an improvement in the efficiency of the systems used. However, this effect will be partially mitigated by increased demand for domestic air conditioning equipment. Improvement in the performance of facilities is expected, due to a greater presence of cold and heat networks at the urban level managed by energy services companies, where renewable energy sources and/or cogeneration are present.

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Exergy Analysis and Thermoeconomics of Buildings

There will be a development of intelligent networks with optimization of management systems and the development of measurement and control elements. The expected savings in the period 2011e20 in the group of housing and tertiary buildings are 73%, attributable to improvements in the envelopes and thermal installations, and 29%, in improvements to energy efficiency in lighting (mainly in tertiary buildings).

Subsequently, Directive 2010/31/EU on the energy performance of buildings was promulgated as a recast of the previous Directive 2002/91/EC, so for its transposition to Spanish legislation, it was necessary to modify the RITE and the CTE, modifications that are included in RD 238/2013 [32]. The entry into force of this European Directive represented a very significant change in the design of buildings in Spain. Until now, the regulations in the building sector had a clearly prescriptive nature, forcing the designers to justify that the buildings met minimum requirements. However, from the transposition of this Directive, the regulation becomes more optional; meaning the whole building must have an impact less than or equal to a certain value, generally measured in terms of primary energy. In addition, it has also been necessary to modify the energy certification of the buildings. Royal Decree 235/2013 approved the basic procedure for the certification of the energy efficiency of buildings [33] and repealed the previous Royal Decree 47/2007, taking into account the provisions of Directive 2010/31/EU and including the energy certification of existing buildings. The Directive 2012/27/EU was partially transposed into Spanish legislation through the Royal Decree 56/2016. This Royal Decree transposed mainly that related to energy audits, accreditation systems for energy service providers and energy auditors, and the promotion of energy efficiency in the production and use of heat and cold. However, this Royal Decree does not mention the following aspects and, therefore, they are still to be transposed. These aspects of the Directive are related to: • •

The renovation of public buildings (in an exemplary way and with the objective of the administration having high-performance buildings, services and products in terms of energy efficiency). The evaluation of the application potential of high-efficiency cogeneration and urban heating and cooling systems.

The update of the Basic Energy Saving Document, DB-HE [34] and the requirements that were established in it, constituted the first phase of approximation in Spain towards the objective of achieving nZEB before the cited dates. Therefore, a new normative update is expected before September 2018. In this regard, the Ministry of Public Works and Transport has published a new document which presents the basis on which this update will be supported. It should be continued in the short term with new stricter requirements, which must be approved in a regulatory manner before the aforementioned date of 2020 is reached. Therefore, the definition of what an nZEB is currently remains pending in Spain, as well as the definition of the numerical indicator that limits the use of primary energy. However, the publication of the aforementioned RD 47/2007 and later of

Efficient buildings and the arguments for incorporating exergy

25

Figure 1.13 Classification of buildings according to their energy efficiency.

the RD235/2013 provoked a study that was carried out in Spain for the design of the energy label of the buildings, IDAE 2001 [35] and IDAE 2009 [36]. These documents provide an idea of what the requirements may be for the limitations of the energy consumption of buildings, since they establish the limiting values of primary energy consumed that make up each of the different energy rating steps of a building (from A, the most efficient, up to G, the least efficient, Fig. 1.13). While it will be necessary to wait, this standard is aimed at some autonomous communities. For example, in the Basque Country, Decree 178/2015 on the energy sustainability of the public sector of the Autonomous Community of Euskadi [37] indicates that until the concrete regulation or methodology to quantify is established, the energy consumption in a building, which is almost zero, is considered equivalent to: • •

Having type A energy rating (minimum). Having 70% of its primary energy consumption from renewable sources.

As we can see in this brief review of European and Spanish legislation, the term exergy is not explicitly mentioned. Undoubtedly the European Directives have in some way taken into account the conclusions that are derived from the application of the Second Principle, but the concept of exergy has not been used explicitly. However, more than 10 years ago, the canton of Geneva introduced an exergetic index, Favrat et al., 2006 [38], that must be calculated in order to obtain the corresponding permit both in the construction of a new building and in the renovation. On the other hand, in increasingly broad layers of professionals, exergy analyses are being carried using the term low-ex buildings for those buildings with high efficiency. Through increasingly demanding regulations, such as the European Directives to which we have referred, this reduction has been sought through several different but complementary ways: the reduction of demand by improving the elements of the envelope (facades, windows, roofs), the improvement of the performance of the installations (heating, ventilation, cooling and lighting) and the use of renewable energies. Next, we present schematically, the new materials used, the improvements in the envelope with new construction solutions and new thermal installations.

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1.8

Exergy Analysis and Thermoeconomics of Buildings

New materials in buildings

Buildings use a lot of materials in their construction. The search for sustainability and the increase in costs demand to be increasingly efficient in its use, as well as the selection of new materials, which have better performance or whose manufacturing process is less polluting. For example, limestone from cement can be replaced by waste from thermal power plants or from the steel industry; likewise, through new treatment processes, waste from demolished buildings has more and more applications. Materials that have not been used much so far, such as wood, are used more and more, since wooden structures are beginning to be used instead of concrete ones, due to their high impact and the fact that they are not very recyclable. Similarly, biodegradable plastics, recycled materials such as certified aluminium, as well as natural fibre boards and insulations of natural origin are of great interest. There are natural materials, such as cotton, with a very low energy content, while polyurethane or expanded polystyrene, conversely, have very high values. However, there are also some natural materials, such as wood fibre, with high energy content. The new materials that have been incorporated or will be incorporated in the future come from progress in the field of building itself, as well as from other technological areas, such as transport and telecommunications. Among these we can find polymeric concretes and mortars, concretes and mortars reinforced with fibres, high-performance steels for construction, etc. The current trend is therefore towards the use of materials with minimal environmental impact, in addition to adequate management of waste.

1.8.1

Thermal insulation

Although not a proper thermal insulator, we refer first to radiant barriers since they reduce one of the basic mechanisms of heat transfer. They are formed by one or several layers of aluminium foils that sometimes include one or several layers of felts or sheets with air bubbles, Fig. 1.14. Given their low emissivity, they create barriers to heat transfer by radiation, but of course, they are only effective if they are associated with a well-sealed air chamber, which requires careful installation what is difficult to achieve in the usual construction process.

Figure 1.14 (a) Reflective foil (b) Placement in an air chamber.

Efficient buildings and the arguments for incorporating exergy

27

One of the most relevant developments in the field of thermal insulation is vacuum insulation panels (VIP). The VIPs were developed some years ago by the refrigeration industry, for use in refrigerators and freezers. Its insulation capacity is 6 to 10 times higher than that of conventional insulation, which is achieved by creating a vacuum in a microporous material. Nowadays, VIPs are beginning to be considered as an alternative to conventional insulation in the envelopes of buildings, thanks to a significant reduction in thermal transmittance that can be achieved with weak thicknesses, Caps and Fricke 2000 [39]. If materials with micro or nano-pores are used, a very low vacuum is required to achieve very low conductivities. In addition, it needs to be a material resistant to compression, and that does not allow infrared radiation to pass. Various insulating, organic and inorganic materials can be used. One of the most frequent is silicon dioxide, with a conductivity of 0:003 W=mK at 50 mbar, taking into account that its conductivity is 0:020 W=mK at ambient pressure, Gazhi et al., 2004 [40]. A very detailed characterization of this material has been carried out, as regards the distribution of the pore size, its permeability, the variation of its conductivity with temperature and with water vapour content, as well as its behaviour towards fire. The external casing of the panel is one of the most critical components since it keeps the vacuum inside. Various alternatives have been used, including a central layer of aluminium, with an exterior PET sheet and another interior one for sealing, with the problem of high conductivity at the ends and corners. Multilayer polymer foils laminated to one another are also employed. The air and vapour permeability of this envelope is one of the fundamental aspects for evaluating the useful life of the insulation, Fig. 1.15. As they are mainly aluminium layers, the casing has a very low permeability to water vapour; besides, the vacuum in the core of the panels produces a high-pressure gradient on both sides of the foil, so if the casing is not totally watertight, the flow of water vapour is not negligible. The same can be said about air permeability, which is a critical value since it damages the existing vacuum in the core, Shawb et al., 2005 [41].

Figure 1.15 Vacuum insulation panels.

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Exergy Analysis and Thermoeconomics of Buildings

Aerogels, which may be silica, alumina, chromium oxide, etc., Soleimani et al., 2007 [42] are also considered as super-insulating materials. These are colloidal substances similar to gel, in which the liquid component is changed for air, thereby maintaining its structure. It is achieved only with treatments at pressures and temperatures higher than the critical point of the liquid trapped inside the framework. The result is a very low density solid (between 0.4 and 0.004 g=cm3 ), highly porosity (80%e99%) and with very low conductivity (14 mW=m K), [43]. There are two types of silica-based aerogels that are used in building: some are opaque and in the form of panels, which are beginning to be used as insulation in facades, attics, floors, etc. Other types of aerogels are characterized by being translucent, so they combine their extraordinary low thermal conductivity with a high transmittance of solar radiation and specifically to the visible spectrum. Very insulating windows have been constructed using granular or monolithic aerogels, Reim et al., 2007 [44].

1.8.2

Glass

With regard to glass, in recent years there have been very significant advances, which have made glass one of the materials that has evolved the most. In addition to tinted glass and reflective coatings to reduce the gain of solar radiation and low-emissivity glass, there is glass with variable optical properties. The latter can be classified as a passive glass, when it responds to changes in environmental conditions (temperature, irradiation, lighting) or active if controlled by the occupants themselves [45]. Among passive glass, there is a photochromic one, which varies its transparency depending on the intensity of the light and thermochromic glass, which acts depending on the external temperature. There are different types of active glass, such as liquid crystals, dispersed particles, and electrochromic ones. Liquid crystals are placed between two transparent electrical conductors on thin plastic foils, and the assembly is laminated between two glass panels. When the glass is deactivated, the crystals are disordered and light is diffused; conversely, when the activated crystals are aligned, the glass is in a clear state. Active glass can be activated manually or by means of a control system.

1.8.3

Other materials

A light-emitting diode (LED) is a semiconductor material with two terminals that emits light when activated. Due to their low consumption LEDs are used today in all areas of the market, from commercial to domestic use. In all cases, electric lighting must be controlled to meet the requirements of the occupants, maximizing energy efficiency, and minimizing electrical demand. In this regard, the possibilities of LEDs must be pointed out since they provide high optical quality illumination with minimum energy consumption. For the lighting of the interior of buildings, LEDs have to be able to reproduce the natural light sources to which humans are accustomed.

Efficient buildings and the arguments for incorporating exergy

29

Finally, nanotechnology, which is already applied in vehicle manufacturing and electronics, seems to be arriving in construction, [46]. It is used in coatings, especially in treatments to obtain super-hydrophobic surfaces that repel water, thus avoiding the appearance of frost or causing corrosion, as well as in paint with self-cleaning properties. Its application is also interesting as self-repairing materials, or in magnesiumcarbon oxide bricks, in which nano-additives improve their resistance to corrosion and thermal shock.

1.9

New types of building skins

In the current design of envelopes, ecological and economic considerations have gained a special prominence. That is why traditional envelope design has been changed to the reactive envelope, able to adapt to changing climatic conditions in such a way that they can detect, diagnose and control its response to changing requirements according to weather conditions, Hausladen 2008 [47]. This dynamic and adaptive behaviour implies that the characteristics and the thermophysical behaviour of these reactive envelops change over time and adapt to the different needs of the building (greater or lower demand for heating or cooling, greater or lesser ventilation, etc.) and different boundary conditions. These are elements/components of the building that are actively used for the transport and storage of heat, light, water and air. This means that the elements of the envelope, such as floors, walls, roofs, foundations, etc., are combined in a rational way and integrated with the functions of the building such as heating, air conditioning, lighting and ventilation. From the classical point of view, the efficient building is achieved by separating the interior environment from the exterior by employing construction with good insulation and without infiltrations. The interior comfort conditions are achieved through automatic control of efficient mechanical systems. However, the current point of view is to build buildings that collaborate with nature and use available environmental conditions. From this point of view, the shape and envelope of the building are used as an intermediary between the interior and exterior environment. The internal comfort conditions are established through the control of the envelope and the mechanical systems. The building is reactive to fluctuations in the external environmental conditions and the changing needs of the occupants. Thus, the separation between the interior and the exterior is a hybrid zone, where energy gains can be stored, redirected, attenuated, etc., depending on the desired interior conditions. In short, the skin of the buildings is a living skin that keeps the occupants in contact with nature and at the same time protects them when necessary, Xin 2014 [48]. The main difference between the concept of reactive building and other concepts of the efficient building is, therefore, in the use of reactive elements and their integration with energy systems and building services through advanced control.

30

1.9.1

Exergy Analysis and Thermoeconomics of Buildings

Advanced integrated façades

In the architecture of a building, the façade is the main component. After all, architecture is the natural consequence of human being’s abilities to manipulate materials and to modify the factors that affect comfort, such as temperature, humidity, natural illumination, intimacy, security, noise, etc. That is why the façade is one of the components of the building that has evolved the most in recent years. The new façades improve the energy efficiency of buildings by controlling energy flows through them, reducing energy consumption and avoiding seasonal fluctuations in temperature. Of special relevance are ventilated façades, façades that incorporate insulation together with a ventilated air chamber, with an outer sheet joined to the interior through a substructure, Fig. 1.16. The air chamber is the primary component of the system, performing various functions; it prevents the dynamic efforts of the wind from reaching internal components; it acts as a drainage system in case of possible water infiltration; allows the escape of water vapour coming from the perspiration of the building casing; likewise, the circulation of air allows the cooling of excess solar radiation incident on the skin of the coating or supports the heating system taking advantage of the hot air energy of the chamber. There are numerous variants of ventilated façades. They can be classified according to the characteristics of the outer and inner sheets as opaqueeopaque, semitransparenteopaque, semitransparentesemitransparent; according to the origin of the airflow as exterioreexterior, interioreinterior or interioreexterior or exterioreinterior air curtains; according to whether the air chamber is ventilated naturally or by forced ventilation; and, finally, according to the type of partition, where basically three types can be distinguished, depending on whether the façade is divided plant by plant or by several plants or in a mixed way. On the other hand, the materials used are very diverse, such as glasses, metals, ceramics, etc.

Figure 1.16 Ventilated façade.

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31

There is an extensive bibliography of ventilated façades: Renckens 1999 [49] presents a description of the different types of ventilated façades, although fundamentally it focuses on solutions for tall buildings. Detailed studies on the behaviour of naturally ventilated façades can also be found in Faist 1998 [50] and Oesterle et al. 2001 [51]. Numerous models of ventilated façades have been developed, both natural and mechanical ventilation. There are several architecture journals, such as DBZ, Architectural Review, Architects’ Journal, etc., with examples of projects where ventilated façades are incorporated. Generally, they include an exhibition of the typology, accompanied by quite a detailed analysis. In addition to the authors Faist and Oesterle already named, the projects described by Baker et al. M€ uller, as well as the thesis by Saelens 2002 [52], etc., are rather interesting. A variant of the ventilated façade is the photovoltaic façade, in which a photovoltaic module (BiPV) is integrated onto the external surface. Consequently, it not only performs the functions of the ventilated facade but also at the same time, generates electrical energy from solar radiation, Bonomo 2012 [53]. The cells can be covered with transparent photovoltaic glass that in addition to producing electricity, allows the entry of sunlight into the interior, while preventing the entry of UVA and infrared radiation. They can have different colours, adapting to each project, Fig. 1.17. Unlike a traditional PV installation, which is added to the building at a later stage, a BiPV system is incorporated in the initial phase of its design, as an essential part of it. Photovoltaic technology is also being used in refurbishment, and it is even possible to integrate it aesthetically in buildings of historical value. Finally, in order to prevent solar radiation from reaching the building’s envelope, translucent metallic screens are frequently used nowadays, which are perforated metal sheets. Those are designed in such a way that they do not limit views of the exterior to the users, homogenizing the external image of the building, by blurring the differences between form and space and also functioning as rain screens. These elements overshadow the building and are sufficiently ventilated so that they do not overheat and radiate in turn towards the building, Fig. 1.18.

Figure 1.17 Ventilated photovoltaic façade.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 1.18 Building façade with metal screen.

1.9.2

Green roofs and green façades

The limitations of space diminish the possibilities of green areas in the surroundings of buildings, and it is in this context that green roofs are of great interest. The roof is the part of the building that is subject to the greatest thermal fluctuations since the absorption of solar radiation with the consequent heat transfer to its constituent elements can cause an excessive rise in temperatures. A possible solution to this problem is vegetable roofs or green roofs. This is a type of inverted roof with the addition of an organic substrate and plants on top. Due to biological functions such as photosynthesis, respiration, evaporation and transpiration, the green roof absorbs a substantial fraction of the incident solar radiation. Green roofs can not only contribute to reducing the thermal loads of the building but also to reducing the effect of the urban island in areas with high population density and few green areas, Kumar and Kaushik 2005 [54]. It is important to have a thermally active material with respect to the climatic conditions as the roof’s main characteristic since its thermal behaviour depends to a large extent on the rainfall and, a lesser extent, on the humidity of the atmospheric air, Fig. 1.19. In addition to green roofs, green façades are also currently very important, with a great diversity of vertical vegetal systems. It is possible to differentiate two main groups: on the one hand, living walls or façades that use modular panels or geotextile, which are anchored to the façade wall as support for all types of plants and bushes of small size. On the other hand, there are plant façades that use a mesh, wiring or lattice

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33

Figure 1.19 Example of a vegetable cover.

Figure 1.20 Example of a vegetable façade.

system as support, mainly for climbing plants, Fig. 1.20. Furthermore, there are also retaining walls and anti-noise screens. We can say that in addition to its aesthetic aspect and CO2 consumption, green façades and green roofs also present a series of advantages from the energy point of view. In Mediterranean climates, they reduce the demand for refrigeration, without having a considerable effect on heating demand, Erkoreka 2012 [55].

1.9.3

Different types of inertial systems

The mass of the building itself has the capacity to store thermal energy, which can be used for heating or cooling purposes. This energy storage allows for the reduction of variations in the load of the building and a decrease in the fluctuations of the interior temperature, maintaining it in a comfortable range. Thus, inertia plays a fundamental role in the thermal behaviour of the building and, when used appropriately, it can achieve significant energy savings.

34

Exergy Analysis and Thermoeconomics of Buildings

Solar gains stored in the thermal mass can be released into the building at night, compensating a great deal for heat losses. During summer the thermal mass can store a large part of the internal gains, as well as delay the transfer of heat from outside to the inside, thus reducing the building’s peak cooling load. During the night, by means of natural or mechanical ventilation, the stored heat can be extracted by cooling this thermal mass. Thermal inertia allows decoupling between production and demand. In a building with little inertia, it is necessary to produce the maximum amount of cooling just when the temperature is at its maximum outside, which is when the coolers have the lowest performance. Inertia allows the cold produced during the night to absorb the heat generated during the day. In Chapter 4, we will see that exergy analysis can provide an interesting point of view in the treatment of inertia. There are numerous concepts and techniques to use that energy storage capacity passively. These applications include night cooling (free cooling), passive solar heating systems, etc., IDAE 2010 [56]. But components of the building (relatively new) are also available in which this process of storage/release of energy is intensified and carried out in a controlled manner. This type of systems is described below.

1.9.4

Thermo-active slabs

These systems, which are usually referred to by the acronym TABS (Thermo-Active Building Systems), are an intrinsic part of the architecture of buildings, and therefore, move away from standardized designs. They consist of the introduction of water circuits (in some cases air) through the interior of the building structure, normally concrete slabs, thus controlling their temperature, Fig. 1.21. They are of especial interest in office buildings. The mechanisms of heat transfer that determine their performance are complex since they combine conduction, convection and radiation, as well as a transitory behaviour. Additionally, the regulation is complicated due to the crucial thermal inertia of the active element. On the other hand, there is a delicate relationship between the heating and cooling mode and the feeling of comfort; this occurs because the systems directly affect the average radiant temperature of the rooms and, therefore, the operating temperature. In short, this type of system presents complexities in its design.

Figure 1.21 Thermo-active slab.

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35

From an energy performance point of view, they offer evident advantages due to the use of moderate thermal levels, forming part of the so-called low-ex or low exergy technologies. Furthermore, these systems allow decoupling the supply from the energy demand, due to their cumulative characteristic; in addition, they control the average radiant temperature in a natural way. However, inappropriate use can lead to counterproductive results. There is diverse literature on embedded heating and cooling systems, Fenercom 2014 [57], which are used with some assiduity in northern European countries, but design criteria that are not based on complex simulation tools are lacking. Some of the advantages of TABS are: • • •

Activating the mass of the building reduces and moves the peak load to the period of non-occupation; thus the size of the production equipment is reduced and significant energy savings are achieved. Because refrigeration systems operate at temperatures close to ambient temperatures, the performance of heat pumps, geothermal heat exchangers and other systems using renewable energy sources are improved. They achieve more stable and consistent indoor temperatures, thus improving comfort conditions.

With regard to their control, criteria for predictive control has begun to be considered, including the effects of the thermal inertia of the TABS and of the building itself, in solutions that use the weather forecast and scheduling as input variables.

1.9.5

Thermo-active foundations

Among the various means of storing thermal energy, the soil is a very good option because of its enormous thermal capacity and availability. The high inertia of the soil allows it to dampen the oscillations of the ambient temperature and at a certain depth to maintain a relatively constant temperature, so that this makes it an interesting heat source, sink or storage medium. The ways of storing thermal energy in the soil for heating and cooling can be classified into three types, Sanner et al. 2003 [58]: direct method, which is based on increasing the direct contact of the building with the ground; indirect method, which consists of preheating or precooling the ventilation air before sending it to the indoor environment (the air passes through a series of buried pipes); and finally, the isolated method, which uses an intermediate fluid to exchange energy between the ground and the interior environment. Referring to the latter, tubes of synthetic material, usually watertight and sealed circuits of polyethylene tube, are inserted into piles or slurry walls, Fig. 1.22. Liquid circulates through these tubes, generally, water with an antifreeze fluid, and transports energy to the building, Florides and Kalogirou 2007 [59]. In many cases, prefabricated energy exchanger piles are used for their economic advantages and speed of execution, Jegadheeswaran and Pohekar 2003 [60]. By means of a heat pump, the heat extracted from the foundation rises to a higher temperature (about 35
C), suitable for heating. If the heat pump is reversible, the

36

Exergy Analysis and Thermoeconomics of Buildings

Figure 1.22 Thermo-active foundations.

building can be cooled, so that the heat extracted from the building during the summer is transferred and accumulated in the ground. In this way, in the summertime, the soil is loaded, and, in winter, it is discharged by increasing its energy potential.

1.9.6

Active glazing

To solve the problems that arise with the use of glass in architecture, given that it is a bad thermal insulator and also allows the passage of much of solar radiation, new technologies have emerged such as double or triple glazing, low emission glass, solar control glass, etc. The main drawback of these solutions is their lack of thermal inertia, a problem that is solved by means of active glazing. Active glazing, mainly used in façades, curtain walls, roofs, skylights, etc., combines the lightness and transparency of glass with the thermal capacity of opaque and heavy solutions. They can also be used in the interior of buildings, with the double function of spatial division and radiant surface for heating or cooling. The main idea is to replace the air chamber with a circulating water chamber, Fig. 1.23. Due to its spectral properties, water absorbs most of the infrared radiation, while it is transparent to the visible spectrum. Therefore, these glazings have a luminosity equivalent to that of conventional glazing, decreasing the heat flux into the interior. Triple glazing combines high light transmission, with high insulation and high absorption capacity of infrared radiation. The energy of the water can be stored and used later when appropriate so that different strategies can be developed.

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37

Figure 1.23 Active glazing.

The air conditioning system using active glass basically consists of two circuits: a primary one of water with the appropriate temperature for heating (for example, by solar collectors) or cooling (for example, by means of a geothermal heat pump, or a water tank, etc.) and the secondary one that distributes the water to the glass. In the summertime, the infrared radiation is absorbed by the water chamber. If the temperature of the water is lower than that of the interior, internal loads due to equipment and people can be eliminated. In winter, the water chamber minimizes heat losses to the outside and, if the water temperature is higher than the interior temperature, it functions as a transparent heat emitter. The active glass is being introduced into the building industry. It attenuates an excess of solar radiation and provides greater thermal inertia to glazed surfaces which results in energy savings in heating and cooling and improvement in environmental comfort. However, the design and construction of this type of system must be done very carefully and requires significant maintenance.

1.9.7

Envelopes with phase change materials

Phase change materials (PCM) allow an improvement in the thermal response of the building, modifying the effective thermal mass. Basically, two types of materials are used: paraffin and salt, Dutil et al. 2011 [61]. Due to their latent enthalpy, these materials act as accumulators of energy, absorbing and discharging heat, and maintaining a constant temperature. It makes it possible to reduce daily fluctuations in temperature, displace peak loads and store renewable energies such as solar energy, or use free cooling, Raj and Velraj 2010 [62]. In addition to their use in storage tanks, in which the charging and discharging are done actively, we will also refer to their application on façades or other components of the building envelope, where loading and unloading are done passively. The incorporation of PCMs into the envelope can be done in various ways. One is by way of direct incorporation, in which the PCM, as a powder or liquid, is mixed with gypsum, concrete, etc. Another is by immersion, so that porous construction materials are submerged in molten PCM, which is absorbed into the pores by capillary action. Macro-encapsulation means the PCM is packaged in bags, tubes, spheres, etc.,

38

Exergy Analysis and Thermoeconomics of Buildings

while another technique is microencapsulation, where PCM particles are enclosed in thin sheets of polymer and mixed with the materials. There are different ways to apply PCMs to façades, which differ in technological and thermal behaviour, but in all cases, the objective is to increase thermal inertia. One possibility is to place the PCM in contact, or almost in contact with the internal environment. The PCM stores and transfers the solar and internal gains, maintaining its constant temperature around its melting temperature. When the interior temperature decreases, the PCM gives thermal energy up to maintain the comfort conditions in the indoor environment, Fig. 1.24. The second mode of application is on the external side of the façade, Fig. 1.25. The PCM layer has the function of capturing and storing the thermal energy that comes

Figure 1.24 PCM layer placed on the inner side (inertia).

Figure 1.25 PCM layer placed on the external side (storage).

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39

from the outside, mainly the solar radiation incident on the exterior surface. During the day, the PCM stores the energy due to solar irradiation, changing its phase from solid to liquid and preventing heat from entering the building. During the night, when the temperature decreases below the melting point, the stored energy is given up, solidifying the material and yielding most of the energy to the outside and the rest to the inside. Another type of application is in solar walls, which are made out of a transparent layer facing the exterior, an air chamber and an opaque wall. The opaque wall absorbs the incident solar radiation on its external surface and transmits this heat. The external surface of the opaque layer is generally painted with a dark colour to increase the absorptivity. Once the heat is transferred by conduction through the opaque layer, it is then distributed to the interior space by radiation and by convection from the interior surface. The use of PCM in the ground or under radiant or cooling floors reduces the overheating of areas exposed to solar radiation. The PCM can stabilize the surface temperature at a value close to the phase changing temperature. The energy stored during the day, which prevents overheating, can be extracted or used to heat the building at night. In addition, in winter, the PCM can avoid or at least reduce temperature fluctuations due to the cyclic behaviour of the heating system. If the PCM is placed on the ceiling, its function is the same, although the configuration is different. In this case, the PCM is not usually embedded in the roof layers, but between the ceiling and a false ceiling. Air is circulated through the cavity by means of independent ventilators or by using the air-conditioning system. The goal is to store cold at night and release it during the day, using the mechanical ventilation system. It allows the removal of part of the internal heat load and to smooth peaks of temperature. The use of PCMs presents some disadvantages: on the one hand, they require an extra cost in construction, with respect to the usual materials; in addition, they age with cycles and have a low thermal conductivity, which can be a problem especially in active systems. Finally, another mode of energy storage is thermochemical storage. It is based on the reversibility of some chemical reactions so that during daytime the captured energy is used to carry out an endothermic reaction (charge); and during the night, the products of that reaction are recombined producing an exothermic reaction (discharge). Its main advantages are high storage densities and small losses, whereas the main disadvantages are the low speeds of the charging and discharging processes and the difficulty of finding materials and chemical reactions appropriate to the application. At the present time, this technique is in an incipient state of development and cannot be considered as an energy storage alternative in buildings, Gil et al. 2010 [63].

1.9.8

Dynamic insulation

Dynamic insulation (DI) represents a new and efficient way to supply filtered and preconditioned air to the interior of the building through an air-permeable casing. If the interior of the building is maintained with a pressure slightly lower than that of

40

Exergy Analysis and Thermoeconomics of Buildings

Figure 1.26 Dynamic insulation in operation.

the exterior, an airflow is generated from the exterior to the interior through the part of the permeable envelope, Samuel 2002 [64]. As the air passes through the insulation, it picks up the heat that is conducted indoor (in winter). In this way, the dynamic insulation performs the double function of reducing heat losses through the façade and/or roof, and at the same time, supplying preheated air to the interior space. In order to regulate the airflow that is extracted from the building, the dynamic insulation requires a mechanical ventilation system, Fig. 1.26. Due to its microstructure, polyurethane panels are not permeable to air and, therefore, cannot be used in DI systems. Insulators such as rock wool, glass wool or cellulose are permeable to air and, therefore, appropriate. Basically, a DI envelope consists of an outer layer, which can be made out of concrete plates or perforated sheet metal, an insulation layer and an air chamber separates both layers. The DI stationary model is suitable for the design and evaluation of the behaviour of a dynamic insulation system. From the temperature gradient on the cold side of the insulation, it is possible to calculate the thermal transmittance equivalent to what is called dynamic transmittance. Its value decreases exponentially with the air speed. In a building with dynamic insulation, there is no airflow to the outside, which could cause interstitial condensation. As the air moves towards the hot part (where its capacity to contain vapour is higher) and as typical air velocities exceed vapour diffusion outwards, condensation cannot occur. However, it is important to ensure that the resistance to the passage of air is consistent.

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41

The current DI systems are basically of two types: systems in which the movement of air is parallel to the wall (parieto-dynamic wall), or the simplest and currently used type, when the air movement is vertical so that the system functions as a counter-flow exchanger, Salah-Eldin 2012 [65]. They have very interesting advantages, such as a reduction in the energy consumption of heating and cooling, a reduction in construction costs, as thick walls are not needed to meet the requirements of the regulations, cost reduction in the ventilation pipeline system and a reduction in the risk of condensation, and therefore, the growth of mould and spores is prevented.

1.10

New thermal installations

The saving and the improvement of energy efficiency in buildings are both clear objectives for our society, in two aspects, in terms of the buildings themself and their contents (installations), with the aim of arriving at nZEBs or even to positive energy buildings. Even if these conditions of maximum efficiency are met, there will be a minimum consumption of energy that must be compensated by the integration of renewable energies that provide this energy. Renewables should be trusted, but especially the renewables located in the building itself or as close as possible to the consumption point. In any case, the facilities must be designed in such a way that they adapt optimally to the characteristics of the building. In its day, due to the need to transpose the Directive 2002/91/EC and after the CTE, a new Regulation of Thermal Installations for Buildings (RITE) was approved in Spain [29] which regulates the requirements for energy efficiency and safety, as well as the environmental aspects that thermal installations in buildings must comply with. Subsequently, having to transpose the Directive 2010/31/EU, as well as the RITE’s own need to update the energy efficiency requirement, RD 238/2013 was approved [32] which has modified certain articles and technical instructions of the RITE, highlighting the new minimum performance values and the incorporation of the residual energy concept for thermal production. Directive 2010/31/EU establishes that the MS will ensure that, before the construction of a building begins, the technical, environmental and economic viability of alternative high-efficiency facilities are considered and taken into account, among which are cogeneration, urban heating or cooling, heat pumps, etc. The same needs to be done in existing buildings when major reforms are made. Likewise, MS should encourage the introduction of intelligent measurement systems and, where appropriate, the use of active control, automation and management of systems aimed at saving energy. It must be taken into account that in residential buildings of normal use and with certain thermal inertia, the most comfortable and efficient situation is achieved with a continuous operation of heating and cooling at low temperature and with systems of heat emission or absorption by radiation. In addition, it is important to reduce distribution losses and hydraulic imbalances, which is why all modern installations incorporate variable speed control in pumps and fans. Basically, the present and the future moves towards the improvement in energy efficiency of facilities and the progressive incorporation of renewable energies.

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Exergy Analysis and Thermoeconomics of Buildings

Consequently, many modern installations are made in hybridization with renewable energies. We are going to review the technologies currently available and those of the immediate future, for which we present the most outstanding characteristics of the new equipment that is being incorporated into the thermal installations of buildings. In Chapters 5 and 6, we will refer to this equipment and analyse its behaviour, both from an energy and exergy point of view.

1.10.1

Condensing boilers

Currently, and in the coming years, the boilers installed in the EU will be the condensing type. The Energy-Related Products Directive (ErP), transposed into Spanish legislation through Royal Decree 187/2011 [66] and Regulation No. 813/2013, by which the Directive is developed with regard to ecodesign requirements for fuel boiler space heaters and combination heaters [67] (mainly with regard to the minimum required seasonal energy efficiency ratio), require fossil fuel boilers commercialized in the coming years to be condensing, Fig. 1.27. Heating diesel oil, with low sulphur content, conforms to the requirements of the condensation technique, achieving high performance and maximum operational safety in the boiler. In any case, natural gas is the main fuel in condensing boilers, being the most commonly used equipment in new heating installations, as well as when modernizing existing facilities, Fenercom 2009 [68]. The dew point for diesel is about 47
C, and about 53
C for natural gas, so reaching these temperatures in the fumes requires that the water enters the boiler at a significantly lower temperature. Therefore, the low-temperature systems 40/30
C offer the maximum energy use since the working temperatures are always below the dew point. It is worth noting that condensing boilers can work at maximum performance even in traditional radiator installations. To do so, the delivery temperature to the emitters

Figure 1.27 Condensing waterproof boiler.

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43

should not always be the maximum, but must be modulated throughout the winter and adapted according to the external conditions, to the demand of each day.

1.10.2 Biomass boilers Biomass boilers have an important presence in our facilities, with pellets and firewood being the most used fuels for thermal uses in buildings. Wood boilers gasify the firewood in the first phase, reaching high efficiencies and relatively low emissions, and being suitable for housing blocks, schools, etc. The pellet boilers achieve better performance and in all cases are provided with anti-return protection that prevents the storage location from catching fire. Fig. 1.28 shows the different components of a biomass boiler.

1.10.3 Heat pumps Heat pumps are a very efficient alternative, especially when they are combined with low-temperature emitting elements, such as underfloor heating, radiant walls and ceilings, fan coils, low-temperature radiators, etc., which work continuously, Chua et al. 2010 [69]. Ground-to-water heat pumps extract heat from the ground and pass it to heating water. If the heat pump is reversible, it can also be used to cool overheated rooms in the summer, Fig. 1.29. Water-to-water heat pumps take advantage of the practically constant groundwater temperature, reaching maximum annual operating rates. On the other hand, air-to-water heat pumps are the preferred ones in the renovation and improvement of the heating of buildings, also using reversible ones for cooling by reversing the cycle. In addition to being driven by electricity, the most common type, it is worth mentioning the existence on the market of heat pumps powered by natural gas, through an internal combustion engine.

Figure 1.28 Components of a biomass boiler.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 1.29 Scheme of a geothermal heat pump. Cooling mode.

Figure 1.30 Solar thermal collectors.

1.10.4

Solar collectors

According to the CTE, a percentage of the DHW demand, which depends on the climate zone and the type of a building, must be produced by means of solar collectors. Flat collectors are the most used, Fig. 1.30, there being different possibilities for architectural integration, while those using vacuum tubes reach higher temperatures and have higher efficiencies. In DHW installations, storage tanks with a high stratification are used to improve efficiency; moreover, if support is given to heating, a second storage tank is used, or other different solutions. In recent years, hybrid solar panels have appeared on the market, producing electricity and hot water simultaneously. Their electrical performance is usually around 15%, reaching thermal efficiencies of between 30% and 60%, depending on the average working temperature. They need approximately half of the surface area to generate the same energy as thermal collectors and conventional photovoltaic panels.

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1.10.5 Ventilation systems Ventilation is always associated with a loss of energy since outside air is introduced into the building. Systems of simple continuous flow must be discarded due to their high energy consumption, with simple flow by presence control, concentration of CO2 or by moisture content control being the alternatives. Other alternatives are the double-flow systems that recover the energy of the extracted air, by using plate exchangers, rotary exchangers, liquid circuits, or heat pumps, Odriozola 2014 [70], In decentralized units, in which each room can be regulated separately, a grid is placed near the window for the entry and exit of air, heating the new air by radiators and fans under the windows.

1.10.6 Cogeneration For low-power cogeneration installations, alternative internal combustion micro engines and gas microturbines have appeared in recent years, Gonz
alez-Longatt 2008 [71], Fig. 1.31. For their part, Stirling engines which are external combustion engines, have the feature that they can use solid fuels, such as biomass. There are different manufacturers, but the reality is that in the current Spanish market they are not competitive, Alanne et al. 2010 [72]. Fuel cells offer the possibility of converting fuel, usually hydrogen, into electricity by means of a catalytic electrochemical reaction, additionally using residual heat. There are two types of cells suitable for cogeneration purposes. Proton exchange membrane cells use hydrogen and oxygen from the air to generate electricity with an electrical efficiency of up to 35% and residual heat of 85
C. For converting natural gas to hydrogen, the cell needs a reformer and a purification process at the top of the fuel cell. Solid oxide cells use a ceramic material as an electrolyte and operate at temperatures above 650
C, with an electrical efficiency of around 50%.

Figure 1.31 Gas microturbine.

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Exergy Analysis and Thermoeconomics of Buildings

Fuel cells have great advantages, such as low emissions, excellent performance at partial load, low noise levels, and can achieve an overall performance of 80%e90% in small installations. Their main drawbacks are their high cost and their short useful life, which means that they are not yet commercially competitive in the Spanish market. Current developments are focused on the use of less expensive materials and on maintaining high performance, Technical Secretariat of the PTE HPC 2011 [73]. A more detailed study of cogeneration in buildings and technologies is presented in Chapter 5.

1.10.7

Trigeneration

Trigeneration is used in buildings such as hotels, hospitals, universities, etc., with demands for heating, cooling and electricity. Absorption refrigerators are the type of equipment most commonly used for the production of cold from waste heat. The most common refrigerant-absorbent pair is water-lithium bromide with operating temperatures of 75e90
C and producing cold water for air conditioners between 12 and 7
C. Adsorption cooling is not a widely used technology. It also produces cold through residual heat, although it has the disadvantage of low COP (0.3e0.5) and low cooling power per unit volume and weight. Trigeneration configurations can be classified into basic and advanced. In the former, the refrigeration equipment is activated indirectly using heat recovery equipment, which usually uses hot water or oil as thermal fluids, Fig. 1.32. The advanced configurations are those in which the refrigeration equipment activates directly, without an intermediate fluid, either through the exhaust gases of the cogeneration equipment, or simultaneously with the exhaust gases and the hot water of the cogeneration engine jackets, Marim
on 2011 [74]. An important aspect is the debate on the scale of thermal installations, whether a district heating system or decentralized generation is preferable or not. In any case, we must not fall into a mono-technological discourse; all technologies may be interesting according to different circumstances, either alone or combined.

Figure 1.32 Trigeneration installation scheme.

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1.10.8 Energy storage Thermal storage is an essential component of heating and air conditioning installations. Its main objective is to solve the problem of the mismatch between demand and production, a typical problem that occurs with renewable energies. In heating, water is the most frequently used substance, whereas, in cooling, it is ice. PCMs are starting to be used, in order to decrease space requirements and yield the stored energy at a constant temperature. Inter-seasonal storage is also interesting, via large deposits, where the energy needed to cover part of the thermal demand of the building in winter is stored during the summer months, Tecnalia 2014 [75]. In the immediate future, electric storage in batteries is expected to be relevant in the domestic sector, with the incorporation of renewable energies or with cogeneration systems that follow the thermal demand. A battery for a single-family home can store between 4 and 8 kWh with a power of up to 5 kW. A DC-AC inverter with a management system is required to connect it to the electrical system and ensure its correct operation. In addition to the classic lead-acid batteries, there are currently several other types, such as nickel-cadmium, nickel metal hydrides, sodium sulphide, lithium polymers, etc.

1.10.9 Hybrid installations A current solution to improving the efficiency of facilities lies in hybridization. A hybrid is a combination of two or more technologies, which together form a new system. There are two types of hybridization: one that combines several sources of energy (for example, solar thermal þ natural gas), or one that combines different technologies with the same source (for example, condensing boilers þ gas heat pumps). Hybrid systems are gas boiler þ solar thermal, gas boiler þ air-to-ater heat pump, gas boiler þ micro-cogeneration, air-to-water heat pump þ solar thermal, geothermal heat pump þ solar thermal, etc., Gonz
alez 2012 [76]. The solar þ gas binomial is one of the most commonly used. The production of DHW is the most widespread application for solar thermal energy, which in many cases also gives support to heating. There are many different types of installations, either individual solutions such as solar preheating with an individual accumulator, or centralized solar preheating with an individual boiler, etc., or centralized solutions. The combinations of conventional technologies with renewable sources means they work in the best conditions suitable for each of them, allowing an improvement in the installation efficiency and a reduction in the cost of energy for the user.

1.10.10 District heating and cooling systems These are centralized systems of heating and/or cooling, based on a network of thermally insulated pipes, which connect generation with various users who are provided with heating and DHW service (district heating networks, DH) and refrigeration (district heating and cooling networks, DHC) or in some cases only cooling, Fig. 1.33.

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Figure 1.33 District heating installation.

They have significant advantages over conventional heating and air conditioning systems. They are characterized by great flexibility in the sources and heat technologies, being able to use the waste heat from industrial processes, the energy recovery of urban solid waste and other renewable sources such as biomass, solar energy or geothermal energy, which in general make them easier to integrate into centralized systems. The main elements of a district network are the generation centre, the network of distribution pipes and the substations connecting with the consumers. As the generation is carried out centrally, it is possible to have technologies with better energy efficiency, such as cogeneration and, in addition, the units will have higher efficiencies, since they will have greater powers with more uniform demand profiles. The network of distribution pipes is made out of thermally insulated pipes, which may be in a branched, ring or mesh layout. Depending on the number of pipes, there may be systems of two pipes (one outgoing and one return pipe), of three pipes (less frequent) or four pipes (one outgoing and one return line, both for hot water and cold water). Finally, the thermal transfer between the distribution network and the consumers is carried out through the substations, consisting of an exchanger and the appropriate regulation and control elements for correct operation, as well as the measurement elements, Catalan Energy Institute 2011 [77]. The district systems are efficient technologies, as stated in Directive 2012/27/EU. In this Directive, Article 14 promotes high-efficiency cogeneration systems and urban heating and cooling systems. Therefore, the Directive requires that this type of system should be studied before certain new works and/or renovations are carried out; and, moreover, it also requires each MS to conduct a potential study of these technologies. The Directive establishes the obligation to apply these technologies in those studies in which the economic result is favourable, through the methodology based on life-cycle cost evaluation.

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Figure 1.34 Heating and cooling networks registered in Spain in 2016.

Centralized heating networks are widespread in central and northern Europe. In Spain, according to the ADHAC census [78] in 2016, the number of networks was 306, of which a high percentage are fed with biomass, Fig. 1.34. This type of facility is better described in Section 5.10.5 of Chapter 5.

1.10.11 Intelligent control Current and future energy systems are not conceived without intelligent control. They are based on innovative microelectronics that provides interaction between all the components. As many systems operate with different sources of energy, the regulation allows the requirements to be met by minimizing the operating costs. With specific reference to the regulation of heating systems with a boiler, the current control solution is intelligent self-adaptive regulation, so that the boiler reduces the temperature of the water flow as the ambient temperature increases to the one that the user has chosen. The boiler calculates the useful power for the building demands and in the next start, it adjusts to this power, thus avoiding numerous starts and improving the seasonal performance, del Castillo 2015 [79]. Since the individual measurement of consumption is mandatory as of 2017, modern horizontal distribution facilities are provided with individual meters to measure the heating consumed in each household. For old distributions, the solution is to place a heat-allocation meter on each radiator so the proportion of heating provided by each radiator to total heat used can be worked out. In order to maintain different temperatures in the different rooms of the house, a thermostatic valve is also needed on each radiator. If they are electronic, the options significantly increase since each radiator can be programmed independently. The regulation system combined with a modern communication technology has enormous potential, since, for example, one can operate the heating system located in the basement with a remote control located in the living room, or even through the mobile. Likewise, to make a diagnosis of the heating installation, the technician only needs to have a laptop, getting all the information through it for management. Currently, the extensive use of ICT for the monitoring, control and optimization of all building functions and systems is being promoted.

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1.11

Exergy Analysis and Thermoeconomics of Buildings

The integrated design process

The efforts that have been made in recent years to improve the energy efficiency of buildings have focused on improving the elements of the envelope and its facilities, and have achieved significant progress. As the efficiency of the individual equipment depends, to a large extent, on the systems of which they are part, innovation has been transferred from the component level to the system level. However, a building is a set of integrated systems, in which these different systems work together. The buildings act as a whole and, for this reason, it is necessary to consider them integrally, simultaneously contemplating architectural aspects, structural aspects, the use of energy, the environmental quality of indoor air, noise, etc. Thus, the design process changes completely, from the design of individual systems to the integrated design of the building as a whole. The concept of integral design contemplates all aspects of construction (architecture, façades, structure, materials, behaviour to fire, noise, energy use, environmental quality, etc.) in a coordinated manner. The integral design aims to achieve the optimal building, in terms of material consumption, ecological loads, energy efficiency and indoor air quality. The design teams, architects and engineers, must work using an iterative process, from conceptual ideas to the final detailed design. The aspects associated with architecture and structure and those related to energy and the environment will be developed in parallel by the corresponding professionals, with their own methods and tools, but in an integral process, Van der Aa et al. 2011 [80]. This way of working is what we call BIM (Building Information Modelling) methodology today. BIM is the process of generation and management of building data during its lifecycle. This model of building information encompasses geometry, spatial relationships, geographic information and the quantities and properties of building components. This work methodology requires some computer programs, already existing in the market, as well as file exchange mechanisms. Fig. 1.35 shows how the different agents act from the first day in a BIM project. Thus, in this integral design process, the contribution of the engineers takes place from the beginning, so that the optimization of the architectural aspects and of the installations begins at the same time as the conceptual designs of the building. Consequently, the building’s equipment and aspects related to energy no longer appear as complementary to the architectural design, but from the beginning, as an integral part. Given the different trainings of the members of these mixed teams, they must make a conscious effort to communicate between themselves. The strategy to follow can be considered to be broken down into the following phases:

1.11.1

Phase 1 - where and what to build

The climatological characteristics of the location are fundamental, not only to estimate heating and cooling loads but to incorporate the concepts of passive design. A preliminary analysis is carried out to define the best location for the building, the optimal orientation, the effect of the wind, solar irradiation (both for its use

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Figure 1.35 Agents participating in a BIM project.

and to protect the building), the possibilities of coupling with the ground, urban development plans, etc.

1.11.2 Phase 2 - preliminary design In this phase, architectural ideas, functional demands and construction principles are linked to the concepts of energy and environment, as well as to the interior environmental conditions. Different solutions are developed, and their merits and demerits are evaluated continuously. The objective focuses on the reduction of heating and cooling, lighting and ventilation demands, reducing internal and external loads. This stage is about optimizing the use of natural light, thus reducing the energy consumption for lighting. In short, we proceed to optimize the natural and free gains of the sun, using storage in the mass of the building, as well as natural ventilation and free cooling.

1.11.3 Phase 3 - design of the building and preliminary evaluation In this phase, the developed concepts are specified in architectural solutions and specific techniques. In order to meet the conditions of the loads that are not yet covered and the comfort conditions can be fulfilled, the mechanical heating, cooling, lighting and ventilation systems are defined. For that, priority is given to the most efficient systems, in order to support the use of renewable energies, such as solar collectors, PV cells, biomass, geothermal energy, etc. The generation, distribution and terminal elements of the mechanical systems must be taken into account. It is important to make sure that the different services of the building work in harmony, without conflict between them. In this phase, the technical solutions are defined and the corresponding documents are created, with plans and specifications.

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1.11.4

Exergy Analysis and Thermoeconomics of Buildings

Phase 4 - control for optimized operation

Intelligent control must be applied, in order for the building and its different systems to function efficiently. The control must achieve the adaptation of the different systems to changing external and internal conditions and to comply with the comfort requirements of the occupants. Advanced sensor technology, as well as sophisticated control algorithms, including predictive control, are still under development and improvements are needed.

1.12

Arguments for incorporating exergy in buildings

In the previous Sections, we have made a brief review of the current situation of buildings. Besides, we have highlighted the advances achieved in recent years in this search for increasingly efficient buildings, with the aim of achieving the nZEB and even a step further, positive energy buildings. In order to achieve this objective, we will present a series of reasons that justify the need for incorporating the exergy method in the analysis of buildings, both in regard to its envelope and its facilities. Ultimately, it is this reason that justifies this book. As it is possible that some readers do not have previous knowledge of this methodology and do not even know the concept, some basic ideas about exergy with a detailed explanation of its meaning and how to calculate it are presented in Chapters 2 and 3.

1.12.1

Some basic notions about exergy

We have seen in Section 1.1 that energy is presented in various forms, such as electricity, heat, work, etc., and we also know that these forms of energy can be converted into one another and in that conversion, there is no loss of energy. This is what the First Law of Thermodynamics tells us, which we also call the Law of Energy Conservation. However, we have also seen, and it is common knowledge, that one form of energy cannot always be converted 100% into another, that is, with an efficiency equal to one. This is what happens, for example, to heat, which can be only partially converted into work, while the rest of it will be transferred to a cold sink (Carnot). This affirmation is precisely what the Second Law of Thermodynamics tells us, while the First Law does not address this fact about the different convertibility of some forms of energy into others. Thus, the different forms of energy have different capacities to convert themselves into other forms. This different convertibility is reflected by the idea of the quality of energy and that the same amount of energy will have a different quality according to its capacity to become other forms. Among all forms of energy, work will be used as a reference, so we will express the quality of energy by its ability to become work.

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Figure 1.36 Profile of annual energy and exergy flow in a building.

This idea is reflected by the concept of exergy that exactly expresses the capacity of energy to become work. There are various forms of energy that can be converted entirely into work, as is the case of electricity so that in this case the energy is identified with the exergy. Conversely, there are other forms of energy, such as heat, which can be only partially converted into work so that only a fraction of a heat flux is an exergy flow flux. These ideas about different qualities are included in the Second Law of Thermodynamics, the application of which will allow us to quantitatively evaluate the different levels of the energy quality. Thus, the First Law serves as the basis for energy analysis, while exergy analysis is based on the use of both Laws. As an example, Fig. 1.36 shows the annual energy flow and the corresponding exergy flow in a building with heating and DHW demand, from primary energy, generation, collectors, distribution, storage, terminal elements and finally to the indoor air and the environment. We shall appreciate the important difference in the values of both flows. On the other hand, the ability to transform the internal energy of a body into work depends on the level of imbalance with the environment. Thus, the internal energy of the water in lakes may be enormous. However, its potential to produce work is nil. The further a system is from equilibrium (thermal, mechanical, and chemical) with the environment, the greater its capacity to transform into work. Likewise, we will see (and this is a fundamental idea) that although energy is always conserved, this does not happen with exergy. There is destruction of exergy in all the processes or equipment that we consider, in all transformations of energy. So, although energy is neither created nor destroyed, the quality of that energy is getting smaller every time it is transformed. As we will see, that loss of quality is associated with the imperfections of our equipment and processes, which is what thermodynamics calls irreversibilities. Although we do not have an exhaustive knowledge of these processes, we will be able to quantify the destruction of exergy.

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1.12.2

Characteristics of exergy

With these basic ideas about exergy, following Wall 1993 [81], we will present a series of interesting aspects of exergy, which at this moment deserve to be highlighted: A system in full equilibrium with the environment has no exergy since there is no gradient in temperature, pressure, or concentration that allows any process. The further away a system is from the environment, the more exergy it will have. A mass of hot water at 60
C has more exergy than if it is at 40
C. A mass of hot water has more exergy when the ambient temperature is lower. When energy loses quality, exergy destruction takes place, and it is unrecoverable. Exergy is useful energy for society and, therefore, has an economic value, so we must take care of it. Considering that virtually all energy (and therefore all exergy) reaches the surface of the earth from the sun, an important part is reflected, but another is absorbed on the surface of the earth and is finally emitted as radiation that does not have exergy. The net exergy absorbed by the earth is gradually destroyed, but during that destruction, it gives rise to the cycle of water, wind and life on earth. The plants absorb exergy from the sun and convert it via photosynthesis into chemical exergy and, due to the food chain, this chemical exergy passes through different organisms in the ecosystems of the planet. A deposit of minerals contrasts with the environment and this contrast is as great as the concentration of the mineral. The mineral is thus an exergy vector. One obvious difficulty that will be presented in the definition of exergy is that it depends on the environment and, as with other sciences, this difficulty will be overcome through agreements, for example, with the definition of a reference environment.

1.12.3

The need for an exergy methodology

By taking into account its very interesting meaning, it is not surprising that the development of a methodology based on the use of exergy has been fostered for the analysis of processes and facilities. This methodology, called exergy analysis, is very useful in the design and analysis of different systems and, in particular, those that we find in buildings, as well as a building considered in its entirety. The main advantages of this type of analysis can be summarized in the following points: It considers the qualitative aspect of energy, which means that it takes into account the different qualities of energy. Thus, it provides information on the adequacy between the energy used and the energy demand. A reduction in the need for exergy implies that lesser high-quality energy is needed and that low-quality energy sources (such as residual heat) can be used to meet the demands. Thus, it allows the quantification of the minimum level of exergy necessary to satisfy demand. Therefore, the use of exergy supports both energy efficiency (reduction of energy required) and the promotion and efficient use of renewable energies. Quantifying exergy losses in the energy chain reveals the potential for energy improvement, which cannot be discovered using energy analysis. Efficiencies (yields) based on exergy, unlike energy-based ones, measure the greater or lesser approximation to the ideal situation (reversibility), and therefore, provide more precise information when it comes to evaluating the behaviour of energy systems, Bejan 1997 [82].

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Figure 1.37 Passive single-family house in Vitoria-Gasteiz (Basque Country) (left) in winter, (right) in summer. It provides a common basis for comparing the energy efficiency of the different systems of buildings and their facilities so that the heat supplied by fuel that is burned in a boiler can be compared on the same basis with that resulting from the solar gain through a window. It is, therefore, an efficient technique to reveal if it is possible or not and by how much it is possible to design more efficient energy systems, by reducing inefficiencies in existing systems. Losses and destruction of exergy identify the locations and causes of inefficiencies in a system, as well as their impact on total fuel consumption, favouring decision-making when applying improvement measures.

The demand for energy in buildings has different levels of quality. We consume electricity for lighting and in electrical appliances and, likewise, to satisfy the heating demand, we also use high-quality energies, such as natural gas. Nevertheless, as the demand for heating or cooling is a demand for low-quality energy (we need to keep the indoor air temperature a few degrees above or below the ambient temperature), there is no matching between the quality of the energy used and that of its final destination. As a result, we can expect that significant exergy destruction will occur, so if we quantify exergy destruction (the true losses) we will find that they will be much greater than energy losses. Fig. 1.37 shows a photograph of a passive single-family house in Vitoria-Gasteiz (Basque Country), where exergy methodology was applied in the design and analysis of facilities. For this reason, the potential optimization in the heating system can be better assessed with the exergy method rather than using conventional energy balances. Using energy of inappropriate quality implies greater losses of exergy and, consequently, the need to use more adequate systems to satisfy those demands. It can be said that the building sector has great potential to improve the adequacy of energy supply and demand since high-quality energy sources are used to satisfy demands that require lowquality energy.

1.12.4 Exergy and economic aspects Exergy is also a very interesting concept for economic evaluation. The design of efficient systems, both from the energy and economic point of view, as well as to

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minimize environmental impact, is one of the biggest problems that the engineer and the architect can address. In a world with a growing demand for energy and with finite natural resources it is fundamental to understand the mechanisms that degrade energy and resources. The idea is to develop systematic procedures to improve systems and, thus, reduce their environmental impact. Exergy Analysis combined with Economy is a powerful tool for the systematic study and the optimization of such systems. Furthermore, in complex systems with several products, this combination of the exergy method and the economy helps to evaluate the cost of these different products, expressed in physical or monetary units, although they have very different characteristics. This discipline that is supported by Exergy Analysis and the Economy is known as Exergoeconomics, Tsatsaronis, 1987 [83] and Thermoeconomics in a more general way. This is because costs must reflect true value, so if we attribute costs to energy it will lead to worthless results, because the value does not lie in the energy but the exergy. Exergy is a rational basis for evaluating the resources, processes, equipment and efficiency of systems, and therefore, the costs of what is produced by those systems. For this reason, using exergy content as the basis for cost accounting is a great help in the management of costs, so that once prices are fixed to products, the benefits obtained can be evaluated. All these features discussed above have led exergy analysis to become the ideal tool to guide efforts in relation to the improvement of energy efficiency in the field of engineering and architecture. Both in industrial processes and power plants, it is a tool that has been widely used for years; there are numerous references applied to the analysis, design and optimization of processes and facilities, Costa et al. 2001 [84], Nikulshin et al. 2002 [85] and Sala 1984 [86]. In recent years, studies related to exergy have received great attention from different disciplines, such as Chemical Engineering, Mechanics, Environmental Engineering and Ecology, so the international community that uses exergy has expanded enormously.

1.12.5

Exergy and the environment

The problems of energy and the environment have become very topical in recent years. Environmental issues that are linked to energy include, for example, global warming, the depletion of the stratospheric ozone layer, air pollution and the degradation of visibility, the contamination of both surface and groundwater, solid waste (some of it toxic), the degradation of soils, etc. However, rather than linking this degradation with energy we should link it with exergy. Exergy analysis is a powerful tool for improving the efficiency of processes and facilities and any measure that improves efficiency means a decrease in resources (exergy) used; consequently, a decrease in waste generated. Therefore, problems such as air pollution, liquid or solid spills, etc., are correctly evaluated when exergy methods are used. But the potential of the exergy method in assisting in the reduction of environmental impact goes beyond the simple improvement of the efficiency of processes. There are other relations between exergy and the environment that began to be understood a

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Figure 1.38 The three pillars of Exergoeconomics.

few years ago: the destruction of exergy associated with irreversibilities is linked to the destruction of order in organized systems. The creation of chaos (decrease in order) is linked to the disorderly emission of pollutants into the atmosphere and, therefore, to the loss of the organization of ecosystems. The destruction of exergy that occurs in a clean environment, when it is degraded due to contamination, is a measure of the minimum work (exergy) necessary to clean it and recover its initial state. This idea has given rise in recent years to a new discipline called Exergoenvironmics, Tsatsaronis and Morosuk 2008 [87]. Thus, exergy is a tool to assess the impact on the environment due to the use of energy sources and, ultimately, a tool to achieve sustainable development, Fig. 1.38. In 1970, Reistad [88] proposed a pollution rate for fuels, which would be equivalent to the cost necessary to clean up the environment, or the cost that fuel inflicts on society if the pollutants are not eliminated. Thus, exergy offers a way to assess the depletion of natural resources and the destruction of the environment. Therefore, exergy can be a valuable aid to establish an ecological economy in order to save on the use of natural resources. We will analyse these aspects in detail in Chapter 11.

1.12.6 Exergy and the Administrations As we have said, the exergy method allows us to identify the maximum theoretical efficiency that a process can achieve, as well as to evaluate how close a real process is to its ideal efficiency limit. In addition, it allows for the identification of the causes and the location of the losses that mean this real efficiency does not reach its maximum value. On the contrary, the methods of energy analysis, based on the use of the First Law, do not allow these objectives to be achieved despite the fact that they are widely used. Therefore, Administrations that seek to improve security in the supply of energy and other resources by improving how efficiently society uses them, find exergy to be a solid prospect: it establishes the limits of what can be done and identifies the areas on which to act, which are the areas with the highest losses and destruction of exergy. To this end, several authors have studied exergy flows in various countries and different sectors, such as the studies carried out on the United Kingdom, Gasparatos et al. 2009 [89], on China, Chen et al. 2009 [90], on Turkey, Ozdogan and Marikol 1995 [91], etc.

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Despite the advantages of using the exergy method, its implications are not taken into account on many occasions. Sometimes it happens that funds are allocated for R&D in areas of the economy in which energy losses are large, but losses and destruction of exergy (irreversibilities) are small, and despite the fact that large margins of improvement are found precisely in those areas where irreversibilities are large, Dincer 2002 [92]. An example can be found in the heating systems of buildings; although their energy losses are small and their energy efficiencies are high, the real (second-law) efficiencies are low, generally lower than 10%e12%.

1.12.7

Limitations of exergy analysis

Despite the interesting possibilities offered by the method of exergy analysis, the reality is that until a few years ago no publications referring to buildings existed. In addition, in the professional world, this type of analysis is not used; moreover, it has only been in these last years when this type of analysis has been increasingly mentioned in congresses and conferences. Some of the possible reasons that may explain this situation are summarized below: The topic may seem complex for some professionals (especially when it comes to selecting the reference environment), and in addition, calculations of the exergy method seem tedious, and the results can sometimes be difficult to interpret or understand. It uses concepts and definitions that come from the industrial world, mainly from the chemical industry and power plants, so an adaptation is required to be able to apply exergy analysis in the building world since it has its own and very different characteristics. Exergy analysis reveals the extremely low exergy efficiencies of commonly used systems, Sakulpipatsin 2008 [93]. For example, a conventional gas boiler with a typical energy efficiency of 85%e90% has an exergy efficiency of around 13%e15%. Precisely, exergy analysis shows us that certain processes and commonly used systems are basically incorrect, and this may go against the interests of some companies. Although most industrial systems are not very sensitive to variations in the conditions of the reference environment, Rosen and Dincer, 2004 [94], the energy systems of buildings can vary widely, as we will see in Chapter 3. This is because the reference state is very close to the interior conditions of the building, so any small variation has a great influence.

As a consequence of the above, specific examples of exergy analysis and calculation methodologies specifically designed for buildings are necessary in order to make the concept more familiar and useable by professionals in the sector. This is precisely one of the objectives of this book.

1.13

Brief history of exergy use in buildings

As we have said, the method of exergy analysis is a well-established thermodynamic method that has been applied since the beginning of the 1970s, in power plants and industry, mainly chemical and petrochemical, in order to improve the efficiency of processes. However, in recent years the exergy method has begun to be recognized in a new scenario such as buildings, both at the individual building level and in

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urban planning. Obviously, the objective of using exergy analysis in buildings is similar to that of the industry, that is, having a methodology that facilitates finding a more efficient use of energy, which at the same time, implies reducing the consumption of fossil fuels, increasing the use of renewable energies and using them more efficiently and, in short, adapting the quality of the energy supplied to that of the demand. There are different bibliographic reviews of the development of exergy as a concept and its use, but perhaps one of the most complete is the one carried out by Sciubba and Wall 2007 [95]. In this Section, we will present a brief history exergy use in buildings. Later, in the development of the different chapters, we will present the specific bibliography referring to the specific theme that is developed in the chapter. A pioneer in the use of exergy in buildings is Professor Shukuya, 2012 [96], a Japanese architect who has applied exergy analysis to different components of buildings, highlighting his exergy analysis to the balance of the human body. There has been exergy analysis of different air conditioning systems in buildings, and a detailed review can be found in the publication of Torio, 2012 [97]. Exergy analysis of air or geothermal heat pumps can be found in Tolga-Bata, 2008 [98] and Hepbasli, 2007 [99], while a study of a district heating system is found in Schmidt, 2009 [100]. The work of Dovjak, 2010 [101] is also very interesting, as it presents an exergy analysis of different heating systems in buildings with different levels of insulation. Also noteworthy is the work of Sakupipaltsin, 2008 [102], which performs dynamic analysis using the TRNSYS software and studies the influence of different possible definitions of the reference environment on the exergy of air. There are also numerous publications on micro-generation systems: some refer to exergy analysis of facilities, such as that of Barelli, 2011 [103], while in Doseva et al., 2015 [104] analysis of cogeneration plants with biogas internal combustion engines is made. In recent years, international research groups of the International Energy Agency have been created within the Energy Conservation in Buildings and Community Systems Program. This is how Annex 37 was created [105], with the aim of promoting the rational use of energy through the use of low-quality energy sources. This Annex resulted in the formation of the LowExNet group, and so subsequently, Annex 49 was created [106]. These groups have contributed considerably, through their publications and the design of developed tools, to begin to understand and apply exergy in the field of buildings. Recently, Annex 64 [107] has been created on the application of the exergy method in planning and urban planning. Thermoeconomics, or more specifically Exergoeconomics, has barely been used in buildings, neither in the calculation of costs, nor in the diagnosis of facilities, or in their optimization. However, there are some interesting works related to cogeneration facilities, as in Deng et al., 2008 [108]. There are also some applications of Thermoeconomics in the design of facilities, such as Calise et al., 2015 [109], where a polygeneration plant powered by renewable energies is optimized. Even less known is what is called Environmental Exergoeconomics, to which we have referred before, Açikkalp et al., 2015 [110], and which we will call, in a broad sense, Environmental Thermoeconomy. It is an extension of Thermoeconomics and its objective is to evaluate the environmental impact at the component level in

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any installation. Although there are numerous publications of this branch of Thermoeconomics in the industrial world, there are hardly any published works in the field of buildings. Despite its remarkable interest, the application of Thermoeconomics in buildings is still in the preliminary phase and is practically unknown to professionals related to the design, maintenance and management of buildings and their facilities. As we say, the published works on buildings, and in particular their thermal installations, are relatively recent, scarce, and there are still many methodological aspects that must be solved and that are going to be addressed in this book. However, as we have said before, the concepts associated with exergy begin to be recognized in the field of buildings, so that it is quite common to refer to low-consumption buildings as low-ex buildings.

1.14

The road towards sustainable buildings

With the exhaustion of resources and environmental problems, and in recent times with the emergency of what we know as climate change, action strategies have been developed to limit the energy demand in all sectors of human activity. At the same time, research on new forms of energy, renewable and clean, has significantly grown. In the 70s and 80s, the efforts in the field of energy were oriented towards improving the efficiency of its use and of the transformations up to its final use, as well as in the use of new sources of energy. However, already in the mid-90s, this concern began to be directed towards the protection of the environment, seeking energy systems that have a lower environmental impact. Analysis methods were developed that took into account not only the energy consumption (exergy) and economic profitability but also began to look at other relevant factors such as the scarcity of energy sources, as well as the degradation of the environment. These aspects began to be considered not only during the use phase of the considered system but also throughout its life cycle, from its design, construction, use and end of life, with the corresponding recycling of materials. Thus, at the end of the 90s, sustainability considerations began to be introduced into the design and operation of energy systems. Unlike what happens with the products of industries obtained in series processes, construction is a part of an industry which carries out its processes in situ. Once the work is finished, the industry moves to a new space, with a limited temporary stay. Likewise, while industrial products have a short and intense life cycle, construction products have a long period of existence. On the other hand, once demolition has started, it is difficult to separate components, which makes reuse or recycling difficult. They are mostly inert materials, but they occupy large spaces in dumping areas. The building sector plays a very important role in the consumption of natural resources and emissions into the atmosphere. A significant number of environmental problems are caused or directly related to the intensive use of materials, water, and conventional energy sources, necessary in the construction and use of buildings. In Section 1.5.2 we have presented data on what energy consumption represents in buildings.

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If buildings are analysed throughout their life cycle (construction, use and demolition), they are found to be the source of a large number of environmental impacts, due to the energy used to provide them with the necessary services, as well as the energy contained in the materials used in its construction. They influence the thinning of the ozone layer, as a result of the use of various chemical products, such as CFCs, HCFCs and halons, and climate change due to significant CO2 emissions, both in the phase of construction as well as during its useful life. Sustainable Construction should be understood as traditional construction, but with considerable responsibility for the environment. This implies an analysis of the different alternatives in the construction process, looking for the one that favours the minimization of resource depletion, which prevents environmental degradation and provides a healthy environment, both inside buildings and in their surroundings. Therefore, the term sustainable construction encompasses, not only the buildings themselves, but also takes into account their environment and the way they behave to form cities. Focusing on energy, the reduction of its consumption in buildings is a key element in that objective of the improvement of energy efficiency, and ultimately, of sustainability. For this, the way forward will be to reduce demand, to introduce new forms of energy use, to maximize the use of renewable energy sources and to encourage the extensive use of ICT for the monitoring and control of all functions and systems. A sustainable building must maximize energy efficiency and comfort, with the least environmental impact. Thermodynamics provides light in the analysis of these systems, provided that their limits are well defined, and that the analysis focuses on the transformations of matter and energy. It can be used to analyse the systems that involve interactions between ecological, economic, industrial and social processes, which are therefore, multidisciplinary in nature. In this book, we will apply the First and Second Laws of Thermodynamics to highlight the fundamental role they play in quantifying the impact of human activities on natural resources and the environment. The systematic use of exergy will show that it provides information that is not obtained by conventional energy analysis such that if we do not resort to exergy, many energy and environmental problems and their solutions would remain hidden.

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[6] DIN V 18599-1:2007-02, Energy Efficiency of BuildingsdCalculation of the Energy Needs, Delivered Energy and Primary Energy for Heating, Cooling, Ventilation, Domestic Hot Water and LightingdPart 1: General Balancing Procedures, Terms and Definitions, Zoning and Evaluation of Energy Carriers. [7] IDAE, Factors of CO2 Emission and Coefficients of Passage to Primary Energy of Different Final Energy Sources Consumed in the Building Sector in Spain, Ministry of Industry, Energy and Tourism, 2016 (in Spanish). [8] E. Gonz
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[28] Royal Decree 1751/1998, of July 31, Which Approves the Regulation of Thermal Installations in Buildings (RITE) and its Complementary Technical Instructions (ITE) and Creates the Advisory Committee for Thermal Installations of Buildings, (in Spanish). [29] Royal Decree 1027/2007, of July 20, Approving the Regulation of Thermal Installations in Buildings, (in Spanish). [30] Royal Decree 314/2006 of March 17, Approving the Technical Building Code, (in Spanish). [31] Royal Decree 47/2007, of 19 January, Approving the Basic Procedure for the Certification of Energy Efficiency of New Construction Buildings, (in Spanish). [32] Royal Decree 238/2013, of April 5, by Which Certain Articles and Technical Instructions of the Regulation of Thermal Installations in Buildings Are Modified, Approved by Royal Decree 1027/2007, of July 20, (in Spanish). [33] Royal Decree 235/2013, of April 5, Approving the Basic Procedure for the Certification of the Energy Efficiency of Buildings, (in Spanish). [34] No. 219, Order FOM/1635/2013, of September 10, Which Updates the Basic Document DB-HE Energy Saving of the BTC, B.O.E, September 12, 2013 (in Spanish). [35] Energy Rating Scale. Existing Buildings, Ministry of Industry, Commerce and Tourism, and Institute for Energy Diversification and Saving, Madrid, May 2001 (in Spanish). [36] Energy rating scale, New Buildings, Ministry of Industry, Commerce and Tourism, and Institute for Energy Diversification and Saving (IDAE), Madrid, May 2009 (in Spanish). [37] Decree 178/2015, of September 22, on the Energy Sustainability of the Public Sector of the Autonomous Community of Euskadi, (in Spanih). [38] D. Favrat, F. Maréchal, O. Epelly, The challenge of introducing an exergy indicator in a local law of energy, Energy 33 (2006) 130e136. [39] R. Caps, J. Fricke, Thermal conductivity of opacified powder filler materials for vacuum insulation, International Journal of Thermophysics 21 (2) (2000) 445e452. [40] K. Ghazi, R. Bundi, B. Binder, Effective thermal conductivity of thermal insulation panels, Building Research and Information 32 (4) (2014) 185e215. [41] H. Schawb, U. Heinemann, J. Wachtel, H.P. Ebert, J. Frucke, Prediction for the increase in pressure and water content of vacuum insulation panels integrated into building constructions using model calculations, Journal of Thermal Envelope and Building Science 28 (2005) 327e345. [42] D. Soleimani, M.H. Abbasi, Silica aerogel: synthesis, properties and characterisation, Journal of Materials Processing Technology 199 (1e3) (2007) 10e26. [43] www.aerogel.com/markets, 6.10.2010. [44] M. Reim, et al., Silica aerogel granulate material for thermal insulation and daylight, Solar Energy 79 (2005) 131e139. [45] www.windows.lbl.gov, 6.11.2016. [46] 5.04.2017, https://www.nanowerk.com/products/products.php. [47] G. Hausladen, Climate Skin: Concepts for Building Skins that Can Do More with Less Energy, Biorkhauser Verlag AG, Berlin, 2008. [48] S.Xin, Application of climate adaptive building skin in building renovation, in: Conference Proceedings of the 9th Energy Forum, 2014, 1163e1172. [49] J. Renckens, Façades in glass, Aluminium, Gevels en architectuur, VMRG, Nieuwegein, 1999. [50] A.P. Faist, (coord),The double-skin façade:Measures in situ and in laboratory, Ecole Polytechnique Federale de Lausanne, 1998, Institut de Technique du Batiment Lausanne (in French). ˇ

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[51] E. Oesterle, R.D. Lieb, M. Lutz, W. Heustler, Double Skin Façades e Integrated Planning, Prestel, Munich, 2001. [52] D. Saelens, Energy Performance Assessment of Single Storey Multi-Skin Facades, Catholic University of Leuven, 2002. PhD Thesis. [53] P. Bonomo, PV Integration in Building Envelopes. Development of a Method for Evaluating BiPV Applications, University of Pavía, 2012. PhD Thesis. [54] R. Kumar, S.C. Kaushik, Performance evaluation of green roof and shading for thermal protection of buildings, Building and Environment 40 (2005) 1505e1511. [55] A. Erkoreka, Modelling and Testing of a Green Roof Using the Paslink Methodology for the Characterisation of its Energy Behaviour, Doctoral Thesis, University of the Basque Country, 2013. [56] IDAE, Technical Guide on Saving and Recovery of Energy in Air Conditioning Installations, IDAE’s Editorial Fund, Madrid, 2010 (in Spanish). [57] Fenercom, Guide on Thermoactive Structures and Inertial Systems in the Air Conditioning of Buildings, Energy Foundation of the Community of Madrid, 2014 (in Spanish). [58] B. Sanner, C. Karytsas, D. Mendrinos, L. Rybach, Current status of ground source heat pumps and underground thermal energy storage in Europe, Geothermics 32 (2003) 579e588. [59] G. Florides, S. Kalogirou, Ground heat exchangers e a review of systems, models and applications, Renewable Energy 32 (2007) 2461e2478. [60] S. Jegadheeswaran, S.D. Pohekar, Performance enhancement of latent heat thermal storage system: a review, Renewable and Sustainable Energy Reviews 13 (2009) 2225e2244. [61] Y. Dutil, D.R. Rousse, N. Ben Salah, S. Lasue, L. Zalewski, A review on phase change materials: mathematical modelling and simulations, Renewable and Sustainable Energy Reviews 15 (2011) 112e130. [62] V.A. Raj, R. Velraj, Review on free cooling of buildings using phase change materials, Renewable and Sustainable Energy Reviews 14 (2010) 2819e2829. [63] A. Gil, M. Medrano, I. Martorell, A. L
azaro, P. Dolado, B. Zalba, State of the art on hightemperature thermal energy storage for power generation. Part 1dconcepts, materials and modernisation, Renewable and Sustainable Energy Reviews 14 (2010) 31e55. [64] A.A. Samuel, Simulation Modelling of Dynamic Insulation as a Means for Energy Saving and Human Comfort, University of Strathclyde, 2002. MSc thesis. [65] M. Salah-Eldin Inbabi, A passive-active dynamic insulation for all climates, International Journal of Sustainable Built Environment 1 (2012) 247e258. [66] Royal Decree 187/2011, of February 18, Relating to the Establishment of Ecological Design Requirements Applicable to Energy-Related Products, B.O.E, March 3, 2011 no. 53 (in Spanish). [67] Regulation No. 813/2013 of the Commission of August 2, 2013, by Which the Directive 2009/125/CE Is Developed Regarding Heating Appliances and Combed Heaters, D.O.E.U, 6-9-2013. [68] Fenercom, Basic Guide on Condensation Boilers, Department of Economy and Finance, Community of Madrid, 2009. [69] K.J. Chua, S.K. Chou, W.M. Yang, Advances in heat pump systems, Applied Energy 87 (2010) 3611e3624. [70] M. Odriozola, Ventilation of Homes According to the CTE. Measurement and Simulation of Different Types of Ventilation Systems and Their Impact on Indoor Air Quality and Energy Consumption, University of the Basque Country, 2014 (in Spanish), Doctoral Thesis.

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[71] F.M. Gonz
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on, Modeling and Energy Analysis of Trigeneration Configurations in Buildings, Rovira i Virgili University, 2011 (in Spanish), Doctoral Thesis. [75] Tecnalia, Seasonal Energy Storage, EVE Conference, 2014 (in Spanish). [76] D. Gonz
alez, Hybridationn with Natural Gas, Saunier Duval, 2012 (in Spanish). [77] Instituto Catala d’Energia, Basic Guide for District Networks of Heat and Cold, 2011 (in Spanish), http://creativecommons.org/licenses/by-nc. [78] ADHAC, Association of Companies of District Heating and Cooling, Census of District Heating and Cooling in Spain, 2016 (in Spanish). [79] E. del Castillo, Regulation and efficiency in radiators, in: Conference on Efficient Thermal Installations in Housing, Madrid, 2016. [80] A. Van der Aa, P. Heiselberg, M. Perinio, Designing with Responsive Building Elements, IEA-ECBCS Annex 44, Aalborg University, 2011. [81] G. Wall, Exergy and morals, in: E. Sciubba, M.J. Moran (Eds.), Second-Law Analysis of Energy Systems: Towards the 21st Century, Rome, 1993, pp. 21e29. [82] A. Bejan, Advanced Engineering Thermodynamics, third ed., John Wiley & Sons, New York, 2006. [83] G. Tsatsaronis, A review of exergoeconomic methodologies, in: Second Law Analysis of Thermal Systems, American Society of Mechanical Engineers, New York, 1987, pp. 81e87. [84] M.M. Costa, R. Shaeffer, E. Worrell, Exergy accounting of energy and materials flows in steel production systems, Energy 26 (2001) 363e384. [85] V. Nikulshin, C. Wu, V. Nikulshina, Exergy efficiency calculation of energy-intensive systems, Exergy: An International Journal 2 (2002) 78e86. [86] J.M. Sala, Thermodynamics of Fluids and the Method of Exergetic Analysis, Editorial Service of the University of the Basque Country, 1984 (in Spanish). [87] G. Tsatsaronis, T. Morosuk, A general exergy-based method for combining accost analysis with environmental impact analysis. Part I e theoretical development, in: 2008 ASME International Mechanical Engineering Congress and Exposition, Boston, Massachusetts, 2008. [88] G.M. Reistad, Availability: Concepts and Applications, University of Winsconsin, Madison, 1970. PhD dissertation. [89] A. Gasparatos, M. El-Haram, M. Horner, Assessing the sustainability of the UK society using thermodynamic concepts: part 2, Renewable and Sustainable Energy Reviews 13 (2009) 956e970. [90] G.Q. Chen, B. Chen, Extended-exergy analysis of the Chinese society, Energy 34 (2009) 1127e1144. [91] S. Ozdogan, M. Marikol, Energy and exergy analyses of selected Turkish industries, Energy 20 (1) (1995) 73e80. [92] I. Dincer, The role of exergy in energy policy making, Energy Policy 30 (2002) 137e149. [93] P. Sakulpipatsin, Exergy Efficient Building Design, Technical University of Delft, 2008. Master’s Thesis.

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[94] M.A. Rosen, I. Dincer, Effect of varying dead-state properties on energy and exergy analysis of thermal systems, International Journal of Thermal Sciences 43 (2) (2004) 121e133. [95] E. Sciubba, G. Wall, A brief commented History of Exergy from the beginning to 2004, International Journal of Thermodynamics 10 (1) (2007) 1e26. [96] M. Shukuya, Exergy. Theory and Applications in the Built Environment, SpringerVerlag, London, 2013. [97] H. Torio, Comparison and Optimisation of Building Energy Supply Systems through Exergy Analysis and its Perspectives, Technical University of M€ unchen TUM, 2012. PhD Thesis. [98] M. Tolga-Bata, J. Kalinci, A. Hepbasli, Evaluating a low exergy and heating system from the power plant through the heat pump to the building envelope, Energy and Buildings 40 (10) (2008) 1799e1804. [99] A. Hepbasli, M. Tolga-Bata, A study on modelling and performance assessment of a heat pump system for utilising low-temperature geothermal resources in buildings, Building and Environment 42 (10) (2007) 3747e3756. [100] D. Schmidt, Low exergy systems for high-performance buildings and communities, Energy and Buildings 41 (3) (2009) 331e339. [101] M. Dovjak, M. Shukuya, B.W. Olesen, A. Krainer, Analysis of exergy consumption patterns for space heating in slovenian buildings, Energy Policy 38 (6) (2010) 2998e3007. [102] P. Sakulpipatsin, Exergy Efficient Building Design, Delft University of Technology, Delft, 2008. PhD Thesis. [103] L. Barelli, G. Bidini, F. Gallorini, A. Ottaviano, An energetic-exergetic analysis of a residential CHP system based on PEM fuel cell, Applied Energy 88 (22) (2011) 4334e4342. [104] N. Doseva, D. Chakyrova, Energy and exergy analysis of cogeneration systems with biogas, Journal of Thermal Engineering 1 (3) (2015) 391e401. [105] Annexe 37, Low Exergy Systems for Heating and Cooling, International Energy Agency (IEA), 2003. [106] Annexe 49, Low Exergy Systems for High-Performance Buildings and Communities, IEA, 2009. www.ecbs.org. [107] Annexe 64, LowEx Communities: Optimised Performance of Energy Supply Systems with Exergy Principle, 2014. www.annex64.org. [108] J. Deng, R. Wang, J. Wu, G. Han, D. Wu, S. Li, Exergy cost analysis of a microtrigeneration system based on the structural theory of thermoeconomics, Energy 33 (2008) 1417e1426. [109] F. Calise, M. Dentice d’Accadia, M. Piacentino, M. Vicidomini, Thermoeconomic optimisation of a renewable polygeneration system serving a small isolated community, Energies 8 (2015) 995e1024. [110] E. Açikkalp, A. Hepbasli, C.T. Yucer, T.H. Karakoc, Advanced exergo environmental assessment of a building from the primary energy transformation to the environment, Energy and Buildings 89 (2015) 1e8.

Quality of energy and exergy

2.1

2

Summary

The fundamental aim in this chapter is to present the bases for understanding what is meant by exergy and for obtaining expressions for its calculation, which will be developed further in Chapter 3. For doing this, the most notable characteristics of Classical Thermodynamics will be shown, and it will be extended to continuous media, which will form the basis of the last chapter of this book. Its relationship with Statistical Thermodynamics will be established, thus enabling a greater understanding of the meaning of entropy. Returning again to Classical Thermodynamics, the meaning of the First Law will be looked at as well as the Energy Conservation equation to which it gives rise, developing several examples, both for closed and open systems. Next, the meaning of the Second Law will be presented, reviewing its classical formulation and the concept of entropy. From this point, the essential part of the chapter begins, which refers to the meaning of the different qualities of the distinct forms of energy and their enormous repercussion in energy applications in today’s world, and where the concept of exergy appears.

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Since it is defined in relation to the environment, a precise definition is necessary, and this chapter shows the difficulties that have emerged in this regard. The expression for calculating the exergy of a heat flux will be given, and different examples will be developed. The expression for calculating the exergy associated with the internal energy of matter will then be derived, and it will be shown that in any real process, although energy is conserved, exergy destruction takes place and that destruction is associated with the irreversibilities of the process. A detailed study will then be made of the exergy of thermal radiation, highlighting the irreversible nature of radiation emission and absorption processes and showing various examples of radiation exergy exchanges. In order to apply exergy balance in open systems, the expression to calculate the maximum work associated with a flow of any fluid will be derived. The general exergy balance in an open system (Control Volume [CV]) is then considered, which allows the calculation of the exergy destruction associated with the irreversibilities of that process. Several examples are presented so that the reader can interpret and consider these balances rigorously. Next, a presentation of the different ways of defining efficiency is given, serving as the basis for exergy analysis of processes. The chapter ends with an analysis of the mechanisms of irreversibilities, deriving expressions for calculating exergy destruction associated with mechanical, thermal and chemical irreversibilities.

2.2

Brief introduction to Thermodynamics and its different formulations

In a general sense, Thermodynamics is a part of Physics that studies the transformations of matter associated with its temperature variations, as well as the energy exchanged in those transformations. By using conventional terminology, it can be said that Thermodynamics is related to phenomena involving heat and temperature, Roller 1950 [1]. Its object of study is the thermodynamic system, that is, any region of space that contains in its interior a large number of atoms, molecules, photons, ions, etc. In this broad sense, the field of Thermodynamics is one of the most extensive in Physics, since it comprises most of the chemical, physical or biological systems, in such a way that the object of Thermodynamics embraces nature practically in its entirety. When studying a macroscopic system one can be interested, not in the detailed knowledge of the behaviour of each of the individualities that constitute it, but simply in certain macroscopic parameters that characterize it, that is, quantities such as pressure, volume, temperature, etc. In the eyes of Thermodynamics, systems are black boxes, and it does not matter what their intimate make-up is. If those macroscopic parameters for an isolated system do not vary in time, it is said that the system is in equilibrium. Conversely, if an isolated system is not in equilibrium, in general, those system parameters are being modified. There is no doubt that equilibrium situations require a much simpler theoretical treatment than the more general situations of non-equilibrium, which are dependent on time.

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Within this general context, there is a more limited sense of the field of Thermodynamics, which is called Classical Thermodynamics, which aims to study systems that are in equilibrium and, of course, under a totally macroscopic perspective. Therefore, and as some authors propose to call it, it is in short Thermostatics. Unlike Mechanics, which when studying bodies only considers their external aspects, describing them by means of mechanical coordinates (position, velocity, acceleration, etc.), Thermodynamics not only covers external aspects, but is also directed towards the interior of the system, so that for its description quantities are involved that are related to the internal state. These macroscopic quantities are the thermodynamic properties, and the object of Thermodynamics is precisely to find general relationships between these properties, relationships that are in accordance with the fundamental laws of this science. Thermodynamics is based on three Laws, which in reality must be expanded with another known as the Zeroth Law. These three Laws can be formulated as three negations, so in a humorous tone, it is said that Thermodynamics is the science of the three NOs. The First Law states that it is not possible to build a machine that produces energy without providing at least the same amount of energy. Such a machine would be what is called a perpetual-motion machine of the first kind and Thermodynamics tells us that this machine cannot exist. In short, what this Law says is that energy cannot be created or destroyed, that is, that energy is conserved. The Second Law states that it is not possible to build a machine that spontaneously converts heat (all heat) into work. Such a machine is known as a perpetual-motion machine of the second kind, and according to Thermodynamics, it cannot exist. If these machines existed, we would be able to take advantage of the enormous amount of energy stored in the oceans to propel ships, or we would be able to use the energy of the air to move our automobiles. Unfortunately, the reality is that this is not possible and Thermodynamics assures us of this. The Second Law is very subtle and covers many different aspects. One particularly essential aspect, which is the basis of this book, is that which refers to the quality of energy. This Law tells us that, although there may be sufficient energy available to perform work on a system, it is not always possible to do it. Moreover, the Second Law is intimately linked to entropy, an elusive concept in Physics, which can be difficult to understand, although it controls aspects of systems that are truly fascinating. The Second Law also establishes the thermodynamic temperature scale. A scale is called absolute when the magnitude that this scale measures has an absolute minimum that is taken as its zero. We know that
273.15 C is the lowest possible temperature that can be reached and, therefore, this is the zero value of the absolute scale. This scale was defined by Lord Kelvin, and the unit is called Kelvin degree (K) in his honor, so that 0 K ¼
273.15 C, see Fig. 2.1. Although the First Law is well known from primary school, there are important aspects of the Second Law that are not and which, consequently, are not applied. Precisely the fundamental aim of this book is to extend to professionals in the world of buildings, both to engineers and to architects and other technicians, the possibilities that open up from the use of the two Laws of Thermodynamics to analyse and understand the behaviour of our buildings and, therefore, improve their design and

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Exergy Analysis and Thermoeconomics of Buildings

Figure 2.1 Relationship between the Celsius scale ( C) and the Kelvin (K).

operation, both in terms of what is known as the envelope and in terms of their installations, in order to arrive at buildings which no longer merely have energy consumption of almost zero, but buildings which are actually energy positive. The Third Law, of much less importance for this book, states that it is not possible to reduce the absolute temperature of a body to zero in a finite number of steps. The expression of this Law uses the concept of absolute temperature and establishes that at the absolute zero limit of this scale, the entropy of every substance with a crystalline structure is zero. The Laws of Thermodynamics have been obtained as a result of the experimentation and the generalization of experience, but they are not based on any hypothesis concerning molecular structure, that is, concerning the microscopic behaviour of the systems. Precisely, the strength of its method lies in its generality, which allows for the establishment of a series of relationships and conclusions from a minimum number of Laws or Postulates. But at the same time, the strength of the method shows its weaknesses, since from such general Laws an excessive number of conclusions cannot be obtained, so that many interesting properties of the systems are beyond its reach. A constant application of the results of Thermodynamics to different real situations has shown that these Laws are valid since they have enabled the prediction of correct answers in all cases. This is an empirical justification, which is, of course, sufficient to accept its validity and universal nature. Either way, Thermodynamics does not try to explain why those Laws are such, nor how they are a consequence of other laws of Physics that may be considered as being more fundamental.

2.2.1

Different formulations of Thermodynamics

Classical Thermodynamics or Equilibrium Thermodynamics has been shown according to different formulations. The development that was described in the previous

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section leads to the Clausius-Kelvin-Planck formulation (CKP). It contains the explicit formulation of the First and Second Law, based on the experiences of Joule concerning the mechanical equivalence of heat and Carnot’s ideas on heat engines, used later by Clausius to state the Second Law. The thermodynamic temperature scale is introduced from Carnot’s theorem on the maximum performance of the Carnot machine. This allows for the establishment of the Clausius theorem and the defining of the entropy function. This development of Thermodynamics has the advantage that it is intuitive. However, the CKP treatment, even with Planck’s version of Kelvin’s statement, presents some conceptual inaccuracies and gaps in certain parts of its development. Thus, the temperature gradients that make heat transfer possible in the isothermal stages of the Carnot cycle and that generate irreversibility are omitted, Tiszla 1966 [2]. Gibbs’ Thermodynamics can be considered as an extension of the CKP formulation [3]. Gibbs extends Thermodynamics to the study of heterogeneous systems and chemical reactions, introducing the fundamental equation of a generalized system and thermodynamic potentials. The achievements of the geometrization of his theory are remarkable, having developed a theory of stability based on the analysis of the surface of states. In addition, Gibbs was the first to establish an analytical basis for determining the available energy of a system in terms of maximum useful work. Later, this concept of energy availability of a system was updated by Keenan, Rant, Baehr, etc., after having developed the theory of exergy, which is the basis of this book. A more rigorous treatment than CKP is Carathéodory’s Axiomatic Formulation of Thermodynamics [4]. From a few axioms, Carathéodory developed a thermodynamic theory, Fig. 2.2. Thus, based on these axioms, the internal energy is introduced through mechanical concepts, defined as work developed in a system limited by an adiabatic wall, while heat is a term that appears as a result of a non-adiabatic process. The Second Law is formulated considering that, in the vicinity of an equilibrium state of a system, there are states that cannot be reached by reversible adiabatic processes. By using a purely mathematical formulation and language, it is possible to demonstrate the existence of a property called entropy, such that its value cannot decrease in an adiabatic process. The axiomatic approach of Carathéodory is, of course, more rigorous than the CKP formulation, but instead has the drawback that the mathematical background required is greater and the formulation is more abstract. In later years some revisions to this treatment of Thermodynamics were made, mainly by Landsberg 1961 [5] and Buchdal 1966 [6]. The phenomenological theory of Gibbs was axiomatized in the formulation of the so-called Macroscopic Thermodynamics of Equilibrium or MTE, developed by Tisza and Callen 1966 [7]. This theory is based on four postulates. In the first one, entropy is introduced a priori, without recourse at all to the classic Carnot engine. It is also postulated that the entropy of a composite system is additive, that it takes a maximum value in equilibrium and that it is annulled at absolute zero, which constitutes the Third Law.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 2.2 Image of C. Carathéodory (1873e1950).

Finally, another axiomatic development of Classical Thermodynamics is due to Hatsopoulos and Keenan [8], which was presented in a simplified form by Haywood [8]. This formulation is based on a single axiom, called the Law of Stable Equilibrium, according to which every isolated system evolves over the course of time to reach one and only one state of final equilibrium. The so-called First and Second Laws are deduced from this axiom as simple corollaries. The evolution that Thermodynamics has experienced as a science is very similar to that of other branches of Physics; initially, a theoretical basis was built, developed by directly deducing from experimental observation and, from that, it passed to new formulations based on more concise and abstract postulates. Thus, Newton’s formulation of Mechanics led to the approaches of Lagrange and Hamilton; likewise, from the laws of Coulomb and Amp
ere, we arrived at Maxwell’s equations of electromagnetism. Similarly, the CKP formulation of Thermodynamics was obtained from experimental observation, by means of deduction and, subsequently, new formulations based on axioms and definitions were developed, such as that of Carathéodory, Tisza and Callen, or Hatsopoulos and Keenan. The Thermodynamics of Equilibrium has been precisely the last of the classical theories in experiencing that postulational reformulation. As Callen points out, the reason for this delay is due to the fact that, at the end of the last century, when Classical Thermodynamics underwent its greatest evolution, the molecular theory of matter still had many gaps and, consequently, it was necessary to base the foundations of Classical Thermodynamics on macroscopic experimental observations. Nowadays,

Quality of energy and exergy

73

when Quantum Mechanics and Quantum Statistics are considered even more reliable than macroscopic sciences, it has been possible to reformulate thermodynamics so that, although it continues to be a macroscopic science, its basic postulates are directly related to its ultimately mechanical-statistical foundation.

2.2.2

The Thermodynamics of Irreversible Processes

One obvious limitation of Thermodynamics is that its conclusions are applicable only for systems in equilibrium. However, in most cases, the true equilibrium states are only achieved under exceptional conditions, so that most of the phenomena studied in engineering, biology, meteorology, etc. are irreversible processes, which take place far from equilibrium. This highlights the need for an extension of the methods of Thermodynamics in order to include irreversible processes in its field of study. Thermostatics uses two indirect methods, which in some ways, allows for the acquisition of certain information concerning the processes. One of them is to consider that the initial and final states are equilibrium states, which makes it possible to determine the overall effect of the process. The other method is to compare real processes with idealized, non-physical processes, such as quasi-static processes. Obviously, none of these methods allows us to find an answer to the central problem, which is the determination of the rates at which real physical processes are carried out. Although in 1854, Lord Kelvin had already made a study on the thermoelectric phenomena, the Thermodynamics of Irreversible Processes (TIP) did not experience a great evolution until the formulation of the relationships of reciprocity by Onsager, Hemmer et al. 1996 [9]. In recent years, TIP has advanced extraordinarily, thanks to the contributions of scientists from very different disciplines, such as physicists, engineers, biologists, mathematicians, etc. Onsager’s theory is based on the hypothesis of local equilibrium, according to which thermodynamic systems can, under certain conditions, be assumed to be in local equilibrium locally even if they are not in global equilibrium. This hypothesis allows for the establishment of the local formulation of the Second Law, and as such it constitutes the central postulate on which TIP is based. In Onsager’s theory, the production of entropy is expressed as the sum of the products of the forces and the corresponding fluxes. In the vicinity of equilibrium, the fluxes are expressed as a function of these forces or affinities through linear relationships, in which the phenomenological coefficients appear. This Linear Thermodynamics is valid, as we have said, for systems not too far from equilibrium and, although it may seem surprising, many physical processes of interest can be considered to be linear. However, many of the applications of TIP are in non-linear areas. This is the case for the vast majority of chemical reactions, memory phenomena in solids and viscoelastic materials, etc. Several theories have been developed that extend TIP to non-linear areas. One of these follows Onsager, and was developed by Prigogine, Glansdorff and Nicolis [10]. Another is the proposal in the field of Thermodynamics of Continuous Media, put forward by Coleman, Noll and Truesdell [11]. There are also other theories such as that of M€ uller or the so-called Extended Thermodynamics of Lebon et al. In Chapter 13 the concept of exergy is applied to continuous media,

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Exergy Analysis and Thermoeconomics of Buildings

which will allow us not only to detect and quantify irreversibilities but also to analyse their causes in detail.

2.2.3

Some considerations on Statistical Thermodynamics

Although this book uses Classical Thermodynamics, we have, however, found it convenient in this chapter to make a reference to what is commonly called Statistical Thermodynamics. In short, Statistical Thermodynamics tries to find the link between the mechanical properties of the particles (velocities, positions, kinetic and potential energies, etc.) and the thermodynamic properties of the system (temperature, pressure, etc.), see Fig. 2.3. The antecedents of Statistical Thermodynamics are found in the development of the mechanical theory of heat, based on the theory of Maxwell, who established the law of equipartition of energy, and that of Boltzman, who in 1872, made a detailed microscopic analysis on irreversibility and the approximation of equilibrium. These works led to the integral-differential equation of transport, also known as the MaxwelleBoltzman equation. In 1877, Boltzman established the relationship between the thermodynamic property entropy and the statistical concept of probability of a state, by means of the well-known equation S ¼ kln W

(2.1)

This classical physics formula gives a new view of the Second Law since it can be used to interpret entropy in statistical terms. In addition to the contributions of Maxwell and Boltzman, it is necessary to highlight the important contribution of Gibbs. The Gibbs method introduces the idea of a collective, based on postulates that relate the temporal average of a mechanical property with the spatial average of said property. With Planck’s introduction of quantum theory, Classical Mechanics was replaced by Quantum Mechanics, which simplifies the treatment of Statistical

Figure 2.3 Object of Statistical Thermodynamics.

Quality of energy and exergy

75

Mechanics. The mechanical description of the particles as a function of position coordinates and moments is replaced by the quantum description, by means of wave functions and energy levels. In this context, the relationship between macroscopic (thermodynamic) and microscopic (mechanical) variables is established by Boltzman’s postulate, which relates entropy to the number of microstates or constitutions of the system. In short, the problem consists of calculating that total number of microstates compatible with the thermodynamic state of the system, that is, it is about calculating the total number of wave functions that correspond to the state of the system. In the course of a macroscopic observation, there are continually transitions from one microstate to another. In addition, each of these microstates has a priori equal probability. By specifying the properties of the particles, we obtain the number of microstates, which will be determined by the most probable distribution. With the introduction of the partition function or sum of states, the state functions, the thermal properties, etc. of the system considered can be calculated, Sears and Salinger 1980 [12]. It is striking that many particle systems can be known with sufficient precision, with a relatively simple method of analysis. Precisely the key to success lies in the enormous number of molecules that comprise a real system. In effect, arguments of a statistical nature are all the more satisfactory when the collective on which they are applied is larger. This is the reason why Statistical Thermodynamics has achieved so many successes in its two fundamental objectives: to deduce the general laws of thermodynamic systems, or in other words, the Laws of Thermodynamics and to obtain the peculiar characteristics of each system, as its fundamental equation, its equations of state, or in general, its properties in equilibrium. The contribution of the microscopic approach to Thermodynamics is remarkable for its explanation of the properties of matter and, therefore, for the study of Physical Chemistry. There is no doubt that Statistical Thermodynamics has contributed decisively to the advance of Physical Chemistry. For systems that are not in equilibrium, the application of the statistical method gives rise to the Statistical Mechanics of Processes. It is based on the same postulates as the theory of equilibrium as well as an additional one, which refers to the symmetry in time of physical laws. From these general postulates, a theory is developed that culminates in some theorems that in turn constitute the postulates of TIP.

2.2.4

Thermodynamics and energy

One of the objectives of Thermodynamics is the study of the energy exchanges associated with the processes that matter undergoes. Therefore, in a book which deals with energy in buildings, we thought it appropriate to give some first considerations about the role played by Thermodynamics within the general context of energy. The modern content of the concept of energy was already established by Mayer, although the Law of Mechanical Energy Conservation was stated a century earlier by Lagrange. On the other hand, matter and energy have been the two basic underlying layers of science until Einstein was able to relate them.

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Exergy Analysis and Thermoeconomics of Buildings

But the aspect that we are interested in highlighting here is the transformation and utilization of that energy until it is arranged in such a way that it can satisfy a series of needs. It is interesting to note how, throughout history, human beings have always focused their attention on the use of energy: this has happened since the discovery of fire, coal mines, etc. to the present day, in which energy has become the central protagonist of modern technology. It can be said that energy is at the very base of industrial development. Precisely, the origin of the First Industrial Revolution was in Watt’s steam engine, which allowed muscular work to be replaced with steam and electric power, see Fig. 2.4. At present and also in the future, at least in the short and medium term, energy occupies such a prominent place in industrial development and the well-being of nations, that without it our civilization would not be conceivable. The energy crisis that began in 1973 changed the perspective of the development of society model, which until then had been based on the abundant use and waste of very low price energy. Nowadays, the great challenge for technology is to create equipment with good efficiency, which implies a rational use of energy with the least environmental impact. For overcoming this challenge, without allowing well-being to suffer, technology’s great ally is precisely Thermodynamics. The technology developed around the conversion of energy, its transport and storage would not have been possible without the guidelines marked out by Thermodynamics. By clearly establishing the different quality of the types of energy according to their exergy content, Thermodynamics sets the optimal limits in that conversion, it allows for the quantification of poor results achieved as a consequence of imperfections in technological processes and also indicates those points on which improvements must be carried out. For taking advantage of energy, it is necessary to use apparatus and equipment built thanks to human ingenuity and knowledge. Thermodynamics serves as a guide to assess the processes and machines used, and thus, obtain more and more perfect energy transformations.

Figure 2.4 Watts steam engine.

Quality of energy and exergy

2.3

77

The First Law of Thermodynamics

The study of this book requires having a previously taken basic course knowledge of Classical Thermodynamics. In this regard, there are numerous works that impart the knowledge required to understand without difficulty the concepts that will be presented throughout the various chapters. Relevant authors whom we would refer include Moran and Shapiro 2012 [13], C¸engel 2011 [14], and Kestin 1971 [15]. However, given the importance of knowing how to adequately consider energy balance in the different systems and equipment that we are going to look at, we think it a good idea to dedicate a space to the application of the First Law, examining closed systems first and then referring to open systems.

2.3.1

Energy balance in closed systems

It can be said that it is a mantra of Physics and the rest of the sciences that energy is neither created nor destroyed, only transformed. Therefore, if a phenomenon occurs in which different systems interact, no matter what happens in that interaction, in the final situation we will have the same amount of energy as in the initial situation. In short, a system can gain or lose energy only if that gain or loss is compensated for by losses or gains in other systems that interact with it. Usually transformations of energy in processes occur from one type of energy to another, but the initial amount of energy is equal to the final amount. The energy contained in a system, as defined in Thermodynamics, is a generalization of the concept of energy in Mechanics. In general, for a complex system, energy is the result of various terms. When the different processes that a system experiences can be considered independent, that is, they are not coupled so that the superposition principle can be applied, then the energy change can be represented as a sum of changes, each of them associated with a simple process. If this superoposition principle is admissible, or on the contrary, there are interactions, it can only be known experimentally. When it is not necessary to consider these interactions, the change of energy will be made up of the change of kinetic energy of translation, of rotation of a rigid body around an axis, of elastic, electric, magnetic energy, surface tension, etc. In addition to these forms of energy, there is the energy associated with processes that occur in simple systems at rest, that is, in the absence of electric and magnetic fields and in the absence of surface tension and capillary effects. This form of energy receives the name of internal energy, and we will represent it with the symbol U. Thus, the energy change of a system between two states is DE ¼ DU þ DEc þ DEp þ DEel þ DEmag þ .

(2.2)

and for an infinitesimal process dE ¼ dU þ dEc þ dEp þ dEel þ dEmag þ .

(2.3)

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Exergy Analysis and Thermoeconomics of Buildings

For a closed system, there are only two mechanisms of energy exchange, which are heat and work. The first is associated with temperature gradients, while the second is due to forces whose point of application is displaced. Heat and work are, therefore, forms of energy exchange between the system and the environment; it is energy in transit. Therefore, it is not rigorous to talk about the heat content or heat energy of a system, since heat is not stored; it is, in fact, internal energy that is stored. Given a system that undergoes a process between two states 1 and 2, we call Q12 and W12 the heat and work exchanged, with both symbols representing positive values. Therefore, in a process where Q12 is the heat contributed to the system, and W12 is the work yielded by the system, the First Law allows us to write the following equation: DE ¼ Q12
W12

(2.4)

If the heat had been transferred by the system and the work yielded to the system, the previous equation would be DE ¼
Q12þW12. Eq. (2.4) shows that both the heat and the work exchanged by a system depend on the particular process considered. Now, the sum of both corresponds to the energy change of the system, that is, to the variation of a thermodynamic property and, therefore, does not depend on the details of the process, but on the initial and final states. Thus, specifying states 1 and 2 will define DU although to know Q12 and W12 it is also necessary to have information on the characteristics of the process. In the particular case of a simple system at rest (this means that there are no changes of kinetic energy, or potential energy or effects due to electromagnetic fields, effects of ad the work yielded surface tension, etc.) that undergoes an adiabatic process, being W12 by the system, we can write ad U2
U1 ¼
W12

(2.5)

This Eq. (2.5) constitutes the definition of internal energy according to Classical Thermodynamics. It is, therefore, a macroscopic and operational definition and is not supported at all in any microscopic theory concerning the molecular structure. In Statistical Thermodynamics it is observed that this internal energy is the result of the kinetic energy of the molecules, of their energies of rotation and vibration, in addition to the intermolecular potential energy due to gravitational, electromagnetic, and nuclear forces. That is why when a change in internal energy occurs as a consequence, for example, of the variation of volume, or temperature, etc. that is, without changing the chemical composition of the system, we talk about the change of sensible internal energy. If the change occurs due to modifications in the atomic-molecular structure, then we talk about the chemical internal energy. This is what happens when chemical reactions occur, such as in combustion processes, or when chemical energy is converted into electrical energy in a battery. Energy changes are produced at the nuclear level as a

Quality of energy and exergy

79

consequence of fission or fusion reactions, and here we talk about nuclear internal energy, characterized by the enormous values that these changes of energy can reach. According to the previous definition, the concept of internal energy is associated with two different states of a closed system, so that we can only assign a numerical value to the difference U2eU1, because that difference coincides with the work measured in an adiabatic process between those states. To assign a value to the energy of an equilibrium state it is necessary to select an arbitrary state, known as the reference state and attribute an absolute value to the energy of the system in that state. It is customary, but not necessary, to choose U0 ¼ 0 for that reference state. In this way, any state can be assigned an absolute, albeit arbitrary, value of energy so that U ¼ U0 þ DU

(2.6)

In short, we can say that no physical meaning can be assigned to the difference between the energies of two different systems, even if they are two different portions of the same substance.

2.3.2

Examples

A cylinder with its corresponding piston of straight section 1 dm2, which moves without friction, contains in its interior 10 mol of a gas that we can consider perfect at pressure p1 ¼ 5 bar and temperature T1 ¼ 300 K. The piston is connected by its external side to a spring, so that when the piston is in contact with the bottom of the cylinder, the spring is without tension, the force in the spring being proportional to the displacement of the piston. Heat is supplied to the gas so that it undergoes a quasi-static process until the final volume is 3/2 that of the initial volume. With atmospheric pressure p0 ¼ 1 bar, determine:

Example E 2.1.

(a) The final pressure and temperature of the gas (b) The energy stored in the spring during the process (c) The heat transmitted to the gas in the process

Solution (a) N ¼ 10 mol P1 ¼ 5 bar T1 ¼ 300 K

V1 ¼

NRT1 10$ 8:314$300 ¼ ¼ 0:05 m3 p1 5:105

As the process is quasi-static, the piston does not accelerate. We express the equilibrium of the resulting forces that act on the piston in positions 1 and 2, due to the actions of the gas inside, the atmosphere and the spring, see Fig. E.2.1.

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.2.1 Forces that act on the piston.

In 1: (p1
p0)A ¼ kx1 In 2: (p2
p0)A ¼ kx2 Dividing both expressions, we have p2
p0 x2 V2 3 ¼ ¼ ¼ p1
p0 x1 V1 2 then p2 ¼ p0 þ 32 ðp1
p0 Þ ¼ 7 bar Knowing the final pressure, we can determine the final temperature as T2 ¼ T1

p2 V2 ¼ 630 K p1 V1

(b) The energy stored in the spring is

Z DEs ¼

x2

x1

# # "  "   kx21 kx21 k 2 x2 2 V2 2 2 kxdx ¼ x2
x1 ¼
1 ¼
1 2 2 x1 2 V1 # "  ðp1
p0 ÞA V1 V2 2 ¼
1 ¼ 12:5 kJ 2 A V1

(c) The heat transferred is calculated by applying the First Law to the gas

Q12
W12 ¼ DU The work exchanged is Z W12 ¼

V2

V1

 Z x2 Z V2 kx pdV ¼ p0 dV þ k x dx dV ¼ p0 þ A V1 V1 x1   V2 ¼ p0 ðV2
V1 Þ þ DE ¼ p0 V1
1 þ DEs ¼ 15 kJ V1 Z

V2 

Quality of energy and exergy

81

and the change in internal energy (because it is a perfect gas cv ¼ 20 kJ/kmol$K) DU ¼ Ncv ðT2
T1 Þ ¼ 66 kJ Therefore, Q12 ¼ 15 þ 66 ¼ 81 kJ Example E 2.2.

In a piston-cylinder device placed in an upright position, 3 kg of water are initially at 20 C. The mass of the piston is 5 kg, and its diameter is 20 cm, with the air pressure on the external face of the piston being 1.18 atm. Heat is supplied to the water until the height of the piston from the bottom of the cylinder is ten times the initial position (Fig. E.2.2). Determine (a) The heat and work exchanged by the water, considering that there is no friction in the displacement of the piston in the cylinder. (b) The work and heat that would be exchanged in that 3 kg of water if they were expanded according to an iso-thermo and reversible process, from the same initial state to the same final volume as in the previous case.

Figure E.2.2 (A) Diagram of the cylinder-piston (B) Representation of the process in a p-v diagram.

Solution (a) First, we calculate the work exchanged by the water

v1 ¼ v0 ð20 CÞ ¼ 1:0018 dm3 =kg

v2 ¼ 10:018 dm3 =kg

V ¼ mðv2
v1 Þ ¼ 27:048 dm3 p0 ¼ 1:18 þ

5:9$8
5 10 ¼ 1:19 bar p$0:12

Ww ¼ p0 $DV ¼ 3219 J

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Exergy Analysis and Thermoeconomics of Buildings

We can see that at the pressure of 1.19 bar and with the specific volume of 10.018 dm3/kg, the water is a saturated liquid-vapor mixture. v0 ð1:19 barÞ ¼ 1:047$10
3 m3 =kg

v00 ð1:19 barÞ

¼ 1:419 m3 =kg /v0 < v2 < v00 v2 ¼ v0 þ x2 ðv00
v0 Þ /x2 ¼ 6:33$10
3 It is, therefore, a liquid-vapor mixture of quality x2 ¼ 6.33$10
3. We shall now calculate the heat exchanged Qw
Ww ¼ DUw DUw ¼ mw Du u1 ¼ u0 ð20  CÞ ¼ 83:9

kJ kg

u2 ¼ u0 þ x2 ðu00
u0 Þ ¼ 99:2 Therefore DUw ¼ 45.9 kJ Qw ¼ 3.2 þ 45.9 ¼ 49.1 kJ

u00 ð1:19 barÞ ¼ 2:511$3

kJ kg

kJ /Du ¼ 15:3 kJ=kg kg and

the

heat

exchanged

will

be

(b) We now consider the isothermal process to the same final volume. We call the final state 4 and an intermediate state of saturated liquid 3, see Fig. E.2.3.

Figure E.2.3 Representation of the isothermal process.

Since v1zv3 the work W13 z 0. Since p3 ¼ ps(20 C) ¼ 0.023 bar the work between state 3 and 4 is W34 ¼ ps(20 C) (v4
v3) ¼ 21 J and the total work is Ww ¼ W13þW34 ¼ 21 J.

Quality of energy and exergy

83

We now calculate the internal energy in 4. To do this, we first determine the quality x4   /x4 10:018 $ 10
3 ¼ 1:0018$10
3 þ x4 57:84
1:0018$10
3 ¼ 1:55$10
4 Since we assume the liquid as incompressible, states 3 and 1 have the same internal energy when on the isotherm of 20 C, then u3 ¼ u1 ¼ u’(20 C). The internal energy of state 4 is u4 ¼ 84:2

kJ kg

Therefore, DUw ¼ mw ðu4
u3 Þ ¼ 900 J so that Qw ¼ DUw þ Ww ¼ 921 J A mass of 0.5 kg of H2O at a temperature of 130 C and a pressure of 10 bar, is heated reversibly and isobarically to a final temperature of 200 C. It is then cooled according to a reversible isochoric process until it reaches a final pressure of 2 bar. Determine the heat and work exchanged in each of the processes. Solution From tables of saturated water (Table E.2.1).

Example E 2.3.

Table E.2.1 Tables of saturated water. t (8C)

p(bar)

180

10

120

2

v0 (dm3/kg)

v00 (m3/kg)

u0 (kJ/kg)

u00 (kJ/kg)

1.06

0.866

505

2530

From tables of superheated steam (Table E.2.2). Table E.2.2 Tables of superheated steam. p [ 10 bar t (8C)

v (m3/kg)

h(kJ/kg)

200

0.206

2829

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Exergy Analysis and Thermoeconomics of Buildings

From tables of liquid water (Table E.2.3). Table E.2.3 Tables of liquid water. p [ 10 bar t (8C)

v (dm3/kg)

h(kJ/kg)

130

1.07

546

At 10 bar the saturation temperature is 180 C so the water is initially a compressed liquid, state 1. At the end of the isobaric heating, the water is superheated steam, state 2, since at that pressure the saturation temperature is 180 C. In the following Fig. E.2.4 we represent the two elementary processes in p-v and p-T diagrams.

Figure E.2.4 Representation of processes in p-v and p-T diagrams.

Energy balance in process 1e2. U2
U1 ¼ Q12
W12 Z2 w12 ¼

p$dv ¼ pðv2
v1 Þ ¼ 204:9 kJ=kg 1

u1 ¼ 546:9 kJ=kg

u2 ¼ h2
pv2 ¼ 2623:0 kJ=kg

q12 ¼ Du þ w12 ¼ 2281:0 kJ=kg Q12 ¼ m q12 ¼ 1140:5 kJ

W12 ¼ m w12 ¼ 102:4 kJ

Process 2e3. Because it is an isochoric cooling v2 ¼ v3 ¼ 0.206 m3/kg. We can see that state 3 is a saturated liquid-vapor mixture, since in fact v0 < v3 < v00 and calculate the quality x3.   0:206 ¼ 1:06$10
3 þ x3 0:886
1:06$10
3 /x3 ¼ 0:23

Quality of energy and exergy

85

Energy balance in process 2e3. u3
u2 ¼
q23 þ w23   u3 ¼ u0120o C þ x3 u00120o C
u0120o C ¼ 970:7 kJ=kg w23 ¼ 0


q23 ¼ u3
u2 ¼ 1752:1 kJ=kg

W23 ¼ 0


Q23 ¼
m q23 ¼
876 kJ

Therefore, in this isochoric cooling 2e3, the water does not exchange work and yields 876.0 kJ of heat to the exterior.

2.3.3

Meaning of control volume

In the previous section, we considered the energy balance with reference to a closed system, that is, a system that does not exchange mass with the external environment, since it is limited by an impermeable surface. However, when applying Thermodynamics in the world of engineering or architecture, the most frequent is to deal with systems that exchange mass with the exterior through their surface area. Suppose, for example, that we intend to study equipment such as a hot water boiler, a heat pump, a heat exchanger or the building itself, which in addition to heat, is continuously exchanging air and water with the environment. In principle, to study such systems, we could adopt two completely different points of view. One of them would be to consider a certain portion of the fluid that passes through the system, which is called a control mass and to follow its evolution from entering to leaving the system under consideration. As expected, in most cases, it is virtually impossible to follow the thermodynamic process experienced by this control mass, calculating work exchanges and heat from its entrance to the exit. Apart from the fact that this study would be extraordinarily complicated, it happens that, in general, we are not interested in the individual behaviour of each of the parts in which we can divide that mass, but in the average behaviour of all of them. Therefore, the point of view we are going to adopt is to consider a certain region of physical space, perfectly delimited, so that at every moment, the system under consideration is the portion of the fluid that is occupying that region of space. The system thus defined is called CV. The surface that limits a CV can be real or imaginary and, in general, it can change position, size and shape. In Fig. 2.5 the surface that limits the CV consisting of a water heater, with an inlet section and an outlet section, is shown by a dashed line. While in a closed system the surface that limits it is impermeable, the surface that defines the limits of a CV is permeable, or at least, there are some portions of that surface that are permeable, since, by definition, a CV is an open system, so that it exchanges mass with the external medium (it receives mass through the input sections and yields mass through the output ones). On the other hand, in the vast majority of the

86

Exergy Analysis and Thermoeconomics of Buildings

Figure 2.5 Example of a CV.

CVs that we are going to consider, i.e. building envelope components such as ventilated facades, roofs, etc. or installation equipment such as pumps, heat exchangers, pipes, etc. that surface area remains fixed and does not change shape or size. There are, however, exceptions where the simplifications introduced by these characteristics cannot be taken into account, as is the case with the cylinders of reciprocating internal combustion engines. The CV methodology is one of the most used in engineering since the balance of the different magnitudes is expressed by means of algebraic equations or differential equations that are relatively simple. This simplicity is a consequence of approximations based on intuition or an experimental knowledge of similar situations. In fact, this methodology is used when what is needed is a global knowledge of the behaviour of the system, without a detailed description of the fluid within the CV being considered necessary. When considering the energy balance in a CV, it will be necessary to take into account, in addition to the heat and work exchanged through the limits of the system, the energy associated with the mass entering and leaving the permeable surface. To be able to carry out this energy balance, it will be necessary to know the state of the flows in the input and output sections. To be precise, when describing the state in those sections, we will admit the hypothesis that, in the regions near the input and output sections, the thermodynamic and flow properties change in a continuous manner. Thus, in the vicinity of these sections, we will assume that the fluid behaves as a continuous medium, in which the Local Thermodynamic Equilibrium Principle, to which we will refer in Chapter 13, is valid. This means that, where Y is a certain intensive variable, the change of that variable between two adjacent sections is much smaller than the value of the variable, that is dY/Y > > > >
> > > > =

> > > contained in the CV > > > > > > > ; : at time t

¼

9 8 Net rate at which > > > > > > > > > > > > energy is being > > > > = < transferred > > > > > > > > > > by heat > > > > > > ; : at time t

9 8 8 9 Net rate at which > > Net rate at which > > > > > > > > > > > > > > > > > > > > > > energy is being energy is exhanged > > > > > > > > = < = < transferred þ þ by the CV accompanying > > > > > > > > > > > > > > > > > > > > by work mass flow > > > > > > > > > > > > : ; ; : at time t at time t

Figure 2.6 (A) Control Volume (B) Diagram of the generic output section i.

(2.7)

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Exergy Analysis and Thermoeconomics of Buildings

This equation would obviously become Eq. (2.4) if there was no mass exchange, that is to say, if it were a closed system. We call Q_ the heat exchanged per unit of time through the surface that limits the CV, due to the different mechanisms of heat exchange. The rate of work exchanged will be due in part to the forces of contact between the fluid and the surfaces that limit the CV and due to external fields. In the cases that interest us, the only external field is the gravitational one, which is a conservative field, so that this work will coincide with the change of the gravitational potential energy. As for the work due to contact forces, we can break it down into two parts. One part is always present, since it is the one that manifests itself in the entry and exit sections; it is the so-called flow work, and it is the work required to push the fluid into the CV and the work that the fluid in the CV does when it leaves, on the fluid that is already outside. In effect, the portion of the fluid that is occupying the CV under consideration at a given moment must push the fluid that lies ahead when leaving the CV. It is as if it had to move a piston and perform work against it. Likewise, the fluid that enters the CV at a given moment is pushed by the fluid coming from behind. By neglecting tangential components, the rate of work exchanged, for example, in the output section i, see Fig. 2.6B is W_ i ¼ ðpAÞi Vi ¼ ðpvÞi ðrVAÞi ¼ ðpvÞi m_ i

(2.8)

and therefore, for the set of input and output sections, we have W_ f ¼

out X i

ðpvÞi m_ i


in X

ðpvÞj m_ j

(2.9)

j

In addition to this flow work in the entry and exit sections, it may be that part of the CV surface is in motion. This is the case of a circulation pump, a compressor, etc. The fluid that is in contact with this part of the surface exchanges work. This term is called technical work or shaft work, and per unit time is the shaft power W_ t . Naturally, if the totality of that surface were fixed, as is the case of a heat exchanger, or a piece of pipe, the value of that shaft work would be zero. In the vast majority of applications, it can be assumed that the flow in the input and output sections is one-dimensional, so the balance equation becomes  in  X d 1 ðU þ Ec þ Ep ÞVC ¼ Q_
W_ t þ h þ V 2 þ gz m_ i dt 2 i i   out X 1
h þ V 2 þ gz m_ j 2 j j

(2.10)

This equation is the energy conservation equation per unit of time. If we want to write the balance equation for a time interval Dt we need to integrate each one of the terms of the equation over time. In the particular case of a steady state, the term

Quality of energy and exergy

89

on the left of the equality is cancelled, and everything is independent of time, so that _ W_ t ; hi ; . are not a function of time. In this case, the above equation takes the Q; following form Q_
W_ t ¼

  out  in  X X 1 1 h þ V 2 þ gz m_ j
h þ V 2 þ gz m_ i 2 2 j i j i

(2.11)

In the particular and very frequent case that there is only one input Section 1 and one output Section 2, since in steady-state m_ 1 ¼ m_ 2 , we have _ 2
h1 Þ þ ðeK2
eK1 Þ þ ðeP2
eP1 Þ Q_
W_ t ¼ m½ðh

(2.12)

Integrating this equation over unit time tu, that is, the time in which a unit of mass enters and, therefore, another one leaves the CV and doing Ztþtu

_ ¼ Qt _ u¼q Qdt

t

Ztþtu

W_ t dt ¼ W_ t tu ¼ wt

(2.13)

t

finally gives q
wt ¼ Dh þ DeK þ DeP

(2.14)

which is the form of the energy balance that is most often used in applications. Regarding this equation, it is interesting to note that the terms on the right of the equality depend only on the conditions of the fluid in the inlet and outlet sections, while those on the left are a function of the thermodynamic path that it undergoes from when it enters until it leaves the CV, so its direct determination is especially difficult. Obviously, the energy balance gives us an equation, and an equation can find an unknown. Thus, knowing all the other terms we can calculate, for example, the heat exchanged. However, in those problems in which q has to be calculated based on the local transfer coefficients and the local temperature differences, it is more convenient to write the equation of energy balance for a differential volume, thus generating a differential equation and then integrate that equation between the input and output sections.

2.3.5

Examples

A mass flow rate of steam of 1.2 kg/s at 10 bar and 300 C flows through a pipe of 15 cm in diameter, with an average speed of 50 m/s. In order to reduce the degree of overheating, a length of 10 m pipe is left without insulation. Knowing that the rate of heat lost per meter of that length is 3.97 kW, determine

Example E 2.4.

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Exergy Analysis and Thermoeconomics of Buildings

(a) Steam temperature at the end of the uninsulated length. (b) The exergy of the heat lost in that length, assuming that the temperature decrease is linear.

Assume that the pressure of the stream remains constant and that the ambient temperature is T0 ¼ 290 K (Fig. E.2.5).

Figure E.2.5 Uninsulated section of the pipe.

Solution (a) From the tables of superheated vapor we have

v1 ð10 bar; 300 CÞ ¼ 258:10
3 m3 =kg h1 ¼ 3048 kJ=kg The mass flow rate of steam will be m_ ¼

V1 p v1

d2 4 ¼ 3:42 kg=s

The heat lost in the uninsulated length is 39.7 kW; so per kg of steam, it is 39.7/ 3.42 ¼ 11.6 kJ/kg. Therefore, the specific enthalpy of the steam, after the uninsulated length is h2 ¼ h1
11.6 ¼ 3036.4 kJ/kg, which corresponds to superheated steam at the same pressure of 10 bar and a temperature of 295 C. (b) We assume that the temperature variation of the steam is linear so that when T1 ¼ 573 K, T2 ¼ 568 K we have T ¼
0.5L þ 573, an expression that is represented in Fig. E.2.6.

Figure E.2.6 Change of temperature in the uninsulated section.

Quality of energy and exergy

91

Therefore, the exergy transfer by the heat lost is B_ Q ¼

  Z10 Z10 T0 dQ 290 dL ¼ 3:97dL ¼ 19:5 kW 1
1
dL 573
0:5L T 0

0

A tank initially contains 5 m3 of liquid water at 18 C. From a certain instant, a water flow rate of 75 L/min at 60 C is supplied to the tank through pipe A and an equal volume flow rate is extracted along pipe B, of the same section as A, see Fig. E.2.7.

Example E 2.5.

Figure E.2.7 Diagram of the tank.

A vapor mass flow rate of 20.3 kg/min circulates through the heater at 4.8 kg/cm2, entering into the reservoir as saturated vapor in state 1, and exiting in state 2 as liquidvapor mixture of quality 0.2. The agitator power is 8 hp. Assume that the walls of the tank are adiabatic, that the amount of water evaporated and the heat exchanged in the free surface is negligible, that the specific heat capacity of the liquid water is constant and that its isobaric expansion coefficient is zero. Write the equation which allows the determining of the temperature variation of the water in the tank (assuming it to be uniform) as a function of time, until it reaches the temperature of the vapor that circulates through the heater. Solution Taking CV as the volume defined by the water in the tank with an input section A and output B, as m_ A ¼ m_ B , the energy balance for the said system is dUVC ¼ Q_ þ W_ þ m_ A ðhA
hB Þ dt The rate of heat given by the coil is _ 1
h2 Þ Q_ ¼ mðh

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Exergy Analysis and Thermoeconomics of Buildings

From the tables of saturated water, we have h1 ¼ 2740 kJ=kg

h2 ¼ h0 þ 0:2ðh00
h0 Þ ¼ 1036:5 kJ=kg

and, therefore, Q_ ¼ 57:6 kW The mechanical power exchanged by the CV is W_ ¼ 8 HP ¼ 5:95 kW On the other hand, T being the temperature in the tank, we have m_ A ðhA
hB Þ ¼ 313:5
5:225T dUVC dT dT ¼ 20; 900 ¼ 9Vc dt dt dt Returning to the energy balance equation, we have 20; 900

dT ¼ 377:05
5:225 T dt

dT ¼ 0:018
0:25$10
3 T / dt

ZT 18

dT ¼t 0:018
0:25$10
3 T

where T is expressed in o C and time t in s. Example E 2.6.

In a counter-current and adiabatic air-water heat exchanger, a water mass flow rate of 5 kg/s enters at 1 atm and 20 C, leaving as superheated steam at 240 C and at the same pressure. The air, which can be assumed to be an ideal gas mixture of O2 (21%) and N2, enters the heat exchanger at 800 C and exits at 150 C. Determine (a) (b) (c) (d)

Air mass flow rate Specific entropy changes of air and water between the inlet and outlet of the heat exchanger The representation of the specific enthalpy change of water in h-s and T-s diagrams The rate of entropy increase of the universe. What is the reason for this increase in entropy?

Solution In Fig. E.2.8 there is an outline of the heat exchanger, with the states of entry and exit of the water flow being designated 1 and 2 and of the air I and II, respectively.

Quality of energy and exergy

93

Figure E.2.8 Diagram of the heat exchanger.

(a) The energy balance is m_ ai ðhI
hII Þ ¼ m_ w ðh2
h1 Þ

Water enters the exchanger as a compressed liquid and exits as superheated steam. From the water thermodynamic tables we have that h2 ¼ 2954.0 kJ/kg h1 ¼ 83.9 kJ/ kg and then h2
h1 ¼ 2870.1 kJ/kg. The specific enthalpy change of the air is Z TI   hI
hII ¼ xO2 cp;O2 þ xN2 cp;N2 dT ¼ 20:69 kJ=mol ¼ 596:70 kJ=kg. TII

Returning to the equation of energy balance, we have m_ ai ¼ 24:05 kg=s (b) Change of specific entropy of air

Dsai ¼

X

xi Dsi ¼ xO2 cp;O2 ln

i

TII TII þ xN2 cp;N2 ln ¼
29; 648 kJ=kmol$K TI TI

¼
1:028 kJ=kg$K Since r is the enthalpy of vaporization at temperature Tv ¼ 373 K, the specific entropy change of water is Dsw ¼ cw ln

Tv r T2 kJ þ þ cp;v ln ¼ 7:652 kg$K T1 Tv Tv

(c) In the h-s and T-s diagrams, we show the change of the specific enthalpy of the water (Fig. E.2.9).

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.2.9 Representation of the process in T-s and h-s diagrams.

(d) Change of the entropy of the universe

S_un ¼ m_ ai Dsai þ m_ w Dsw ¼ 13:537 kW=K This increase in entropy is a consequence of the irreversibilities in the heat transfer between air and water, due to the temperature jump that exists. Although it has not been taken into account in this Example, there will also be mechanical irreversibilities due to pressure losses, in both the flow of air and flow of water. Example E 2.7.

The combustion gases from a boiler, in which the combustion of pro-

pane is carried out, have the following composition in molar fractions: 7.9% CO2, 10.6% H2O, 6.6% O2 and the rest N2. These gases leave the boiler at a pressure of 985 mbar and temperature 160 C, with a mass flow rate of 1.2 kg/s. In order to make integral use of energy, and given the heating needs, these combustion gases are passed through a heat exchanger, where they are cooled to a temperature of 46 C, with the pressure at the outlet being 890 mbar. The inlet and outlet sections are both 0.15 m2. The heating water enters the heat exchanger at a room temperature of 15 C and a pressure of 5 kp/cm2 and exits at a temperature of 52 C. What are: (a) The velocity of the gases at the inlet and outlet of the heat exchanger. (b) The rate of heat given up by the flow of gases. Verify that the change in kinetic energy is negligible. (c) The rate of water mass flow.

Solution (a) From the specific heats of the perfect gases expressed in a polynomial form and with the molar fractions of the statement, Table E.2.4 can be constructed.

Quality of energy and exergy

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Table E.2.4 Specific heat and molar fractions of perfect gases. Const.

a

b$102

c$103

Mi

xi(%)

Mixi

CO2

5.316

1.428

0.836

44

7.9

3.476

H20

7.7

0.046

0.252

18

10.6

1.908

O2

6.085

0.363


0.171

32

6.6

2.112

N2

6.903


0.037

0.193

28

74.6

20.972

100

28.47

S

The molar fraction of N2 is 74.9%, with the apparent molar mass of the gases being Mm ¼ xCO2 MCO2 þ xH2 OMH2 O þ xO2 MO2 þ xN2 MN2 ¼ 28:47 with the constant of the gases being Rm ¼ R/Mm. The density of the combustion gases at the inlet and outlet of the heat exchanger is 91 ¼

p1 g ¼¼ 779:29 3 m Rm T1

92 ¼

p2 g ¼ 955:77 3 m Rm T2

Therefore, the velocities at the inlet and the outlet sections are V1 ¼

m m_ ¼ 10:26 s A1 91

V2 ¼

m m_ ¼ 8:37 s A2 92

(b) Applying the energy balance in the heat exchanger, and taking into account the change of kinetic energy, we have

   1 2 2 _
Q ¼ m_ h2
h1 þ V2
V1 2 Z

T2

where h2
h1 ¼

cpm dT, T1

with

cpm ¼

P i

xi cp;i ¼ 6808 þ 0:1135$10
2 Tþ

0.094$10
1T 2. So that h2
h1 ¼
123,34 kJ/kg. The heat given up by the gases is Q_ ¼ 148:0 kW

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Exergy Analysis and Thermoeconomics of Buildings

We can verify that the change is practically negligible compared to  in kinetic energy    the enthalpy change, since m_ 12 V22
V12 ¼
0:02 kW, so it is not usually taken into account. (c) The specific enthalpy change of water is

hII
hI ¼ vw ðpII
pI Þ þ cw ðTII
TI Þ w cw ðTII
TI Þ ¼ 154:7 m_ w ðhII
hI Þ ¼ 148:0 / m_ w ¼ 0:96

kJ kg

kg s

A solution of density 1.3 g/cm3 is pumped from a high capacity storage tank to another elevated tank, according to the diagram of Fig. E.2.10. The diameter of the suction pipe is 9 cm, and the velocity of the stream in it is 1.1 m/s, with the diameter of the discharge pipe being 7 cm. The total head loss is 30 J/kg. Determine the power consumed by the pump.

Example E 2.8.

Figure E.2.10 Diagram of the installation.

Solution Considering the pump assembly, suction pipe and discharge pipe as the CV, the equation of energy balance per unit mass is q þ wB ¼ Du þ Dðp=9Þ þ Dec þ Dep and using the incompressible fluid model for the solution, we have p1 1 2 p2 1 þ v þ gz1 ¼ þ v22 þ gz2
wB þ D12 9 2 1 9 2

Quality of energy and exergy

97

where D12 ¼ q
Du is the head loss term and, therefore, D12 ¼ 30 kJ/kg. As we do not know the state of the flow in Section 1 (at the entrance of the suction pipe), we can consider another CV that covers from the free surface of the tank to Section 1. By applying the energy balance we have pfs 1 2 p1 1 þ v þ gzfs ¼ þ v21 þ gz1 9 2 fs 9 2 Putting together these two equations of energy balance, we get pfs 1 2 p2 1 þ vfs þ gzfs ¼ þ v22 þ gz2
wB þ D12 9 2 9 2 Obviously, this equation could have been obtained directly considering the CV between the free surface of the tank and the outlet section of the discharge pipe. We see that pfs ¼ p2 ¼ p0, vfs ¼ 0 and z2
zfs ¼ 20 m w$c. The speed in the discharge pipe is A1 V2 ¼ V1 ¼ A2

 2 D1 V1 ¼ 1:8 m=s D2

Substituting values in the energy balance equation, we have wB ¼ 227:5 J=kg As the mass flow rate circulating through the pipe is m_ ¼ 9A1 V1 ¼ 9:09 kg=s the power of the pump results _ B ¼ 2:07 kW W_ B ¼ mw Example E 2.9. A pump drives a water flow rate of 360 L/min through a pipe. The pressures in the mouths of the inlet and outlet of the pump are 1.2 and 12.5 atm and the diameters of the pipes are 6 and 10 cm, respectively. The water temperatures at the inlet and outlet of the pump are measured with great precision, showing an increase of 0.4 C. The compression process is adiabatic, with the mechanical efficiency of the pump being 0.92. Calculate

(a) the power of the pump (b) the fraction of energy that dissipates due to friction

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Exergy Analysis and Thermoeconomics of Buildings

Solution (a) Sections of the inlet and outlet pipe

A1 ¼

pD21 ¼ 28:27 cm2 4

A2 ¼

pD22 ¼ 78:54 cm2 4

The flow velocities are V_ V_ ¼ A1 V1 /V1 ¼ ¼ 2:12 m=s A1

V2 ¼

V_ ¼ 0:76 m=s A2

Applying the energy balance in the pump, per unit mass, we have wP ¼ Dh þ DeK where Dh ¼ Du þ DðpvÞ ¼ cDT þ vDp ¼ 2:82 kJ=kg DeK ¼
1:96

m2 kJ ¼
1:96$10
3 kg s2

We thus show that the change in kinetic energy is negligible compared to the enthalpy change. As the mechanical efficiency of the pump is 0.92, the specific mechanical work is 2.82/0.92 ¼ 3.06 kJ/kg, so the mechanical power of the pump is W_ m;P ¼ m_ wm;P ¼ 18:36 kW (b) The objective of the pump is to increase the mechanical energy of the flow so that the internal energy increase of the water flow is due to the fact that the internal performance of the pump is not one. In addition, it is necessary to take into account the losses due to its mechanical performance, so that the fraction of energy dissipated is

Du þ wm;P ð1
hm Þ 1:67 þ 0:24 ¼ 62:4% ¼ wm;P 3:06

2.4

Brief history of the Second Law of Thermodynamics

In the formulation of the Second Law, apparently, three independent, but essential, questions converge. One of them refers to the direction of evolution of the real processes. As an example, suppose two bodies, A at 80 C and another B at 30 C

Quality of energy and exergy

99

are isolated from all others. Initially suppose that body A has an energy of 100 kJ and B has 40 kJ so that the total energy is 140 kJ. Now suppose that there is a process in which body B gives heat to A so that in the end, body B has an energy of 20 kJ and the energy of A is 120 kJ. The energy is conserved, so that, if only the First Law was fulfilled in nature, the imagined process could be carried out without problems, since it agrees with the Law of Energy Conservation. This conclusion, however, raises an alarm: our everyday experience tells us that heat is transferred spontaneously from a higher temperature to a lower temperature body, but not vice versa. In terms of energy conservation, the described process is possible; however, it is clear that it seems impossible. There are many examples that we can consider: a wheel with blades fixed on it and submerged in a tank filled with oil, powered by a mechanical system of weights and pulleys, will heat the oil in the tank when turning. We could think of the inverse process in which the oil, when cooled, moves the blades and transforms its internal energy into energy that is stored in the system of weights and pulleys so that the decrease of internal energy of the oil coincides with the increase in mechanical energy. The Law of Conservation of Energy allows this process, but our experience tells us that it is impossible. Why does all the air in a room not go into a corner if it is energetically possible? Why is the immense amount of energy stored in the oceans not used to power our ships? The phenomena described and the questions raised show us the fact that nature is not reversible since there is always a direction in which the spontaneous evolution of a system is impossible. There must, therefore, be some physical quantity that controls the viability of phenomena, at the same level as energy and other magnitudes such as electric charge or moment. A second issue that the Second Law addresses is that which refers to the criteria of equilibrium and stability: not all possible sets of values of state properties are capable of representing states of equilibrium between the system and its environment, and not all equilibrium states are stable equilibriums. A third aspect is the degradation of energy, that is, the fact that in processes energy is transformed and although the quantity is the same, this energy has less utility once the process is finished, so that the ways in which energy is manifested are not qualitatively equivalent. This is a matter of great importance, given the limited nature of the energy resources available to us. It is precisely the concept of exergy, the foundation of this book, which clarifies and gives meaning to these ideas about the quality of energy. Historically, the Second Law arises as a consequence of the problem of heat transformation in work that was observed in heat engines. The central question that arose at that time (the first half of the nineteenth century) was to accept the idea of the transformation between the different forms of energy and, at the same time, to recognize the Law of Conservation in this series of transformations. To this, we had to add an additional difficulty, which was the asymmetry in those conversion processes, an idea that also had to be incorporated into the theory. The first to unify these ideas in one theory was the engineer Carnot, 1824 [16], who when studying an eminently technical problem such as the thermal efficiency of heat

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Exergy Analysis and Thermoeconomics of Buildings

engines, developed a series of concepts that were going to be of fundamental importance, both in Physics and in Chemistry. As we know, the key concept of his reflections is the idea of the reversible heat engine. Carnot remained attached to the caloric theory which was dominant in his time and, thus, considered that the work performed is a consequence of the decrease of the hot source to a cold one of some quantity that is preserved, which was known as the caloric, see Fig. 2.7. If the heat engine works in the opposite direction, that is, as a heat pump, the work previously done is now used to restore the initial distribution of the caloric. Consequently, in Carnot’s theory, the conservation of caloric is only satisfied in the reversible limit. This presented a series of difficulties, such as the production of heat through friction, of which Carnot was aware. Hence, his doubts and the need that he raised to reconsider his theory. Although in Carnot’s theory caloric appears as a different magnitude to work, Mayer and Joule developed the idea that heat is a magnitude of the same kind as work and obeys a conservation law, Joule 1843 [17]. Mayer was the first to publish, from the existing experimental data, the value of the conversion factor between heat and work, the so-called mechanical equivalent of heat. Joule has the great merit of having made the most complete experimental research on the subject, Holton and Roller 1958 [18]. The formulation of the Second Law is a consequence of the reconciliation effort of those, apparently, two irreconcilable points of view. On the one hand, the unitary nature of the different forms of energy reflected in the principle of Mayer-Joule. On the other, that duality that Carnot’s theory establishes between reversible and irreversible processes, a duality that is characteristic of Thermodynamics since it does not appear in Mechanics or in Electrodynamics. It was Clausius who, in a work published in 1850, managed to harmonize both ideas [19]. Clausius accepts Carnot’s idea that it is necessary to pass the heat from a hot source to a cold source in order to achieve the transformation of heat into work,

Figure 2.7 Carnot direct cycle of a gas in a p-v diagram.

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101

but at the same time, it rejects that the amount of heat is preserved. This idea really marks a point in the history of Physics and represents the birth of Thermodynamics as a science. A little later, W Thomson (Lord Kelvin), who in 1848, had defined the absolute temperature scale based on the work of Carnot, explicitly stated the First and Second Laws. Later, in 1854, Clausius defined entropy, which comes from a Greek word that means transformation and which allows an accurate formulation of the Second Law.

2.5

Review of the concept of entropy

Any quantity whose value is fixed by initial and final states and which does not depend on the peculiarities of a process must measure the change in the value of some thermodynamic property. Precisely, this is what happens with exchanged heat divided by temperature along any reversible process. We call this property entropy, and we represent it by the letter S so that Z2 S2
S 1 ¼

dQ T

(2.15)

1

This equality establishes that the entropy change of a closed system between two states of equilibrium is obtained by taking the system along any reversible path between said states and integrating, along the way, the heat exchanged divided by the thermodynamic temperature of the system at all times. Let us again consider a closed system and suppose that it experiences an infinitesimal process, internally reversible, in the course of which it exchanges heat dQ, where T is its temperature. According to its definition, the entropy change of the system is dS ¼

dQ T

(2.16)

This change in entropy is undoubtedly due to the heat flux exchanged by the system through its boundary surface, which is at temperature T. It can, therefore, be interpreted that the entropy varies in dS as a consequence of the heat exchanged dQ, for which reason it is called entropy transfer, of magnitude dQ/T. Depending on the direction of dQ, that is, on whether the heat is absorbed or transferred, the entropy of the system will increase or decrease. We know that the previous expression is valid only when the process is internally reversible. However, we could try to extend this concept to those processes that are not internally reversible, for which we shall generalize their definition in the way we describe below. The concept of entropy can even be applied to those systems that exchange heat through different areas of their boundary surface, each of these areas being at a different temperature. Indeed, whenever we can identify the temperature of each

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Exergy Analysis and Thermoeconomics of Buildings

area, we can associate with each heat flow, its corresponding entropy transfer. Strictly, this would require that in each area, the (macroscopic) part of the corresponding system is in a stable state during heat transfer since the temperature is a property applicable only in equilibrium. In short, the entropy change due to these different heat exchanges would be obtained in the following way DS ¼ fS ¼

XZ i

1

2

dQi Ti

(2.17)

where the sum refers to each of the surface areas where there is heat exchange. If the temperatures of these areas were constant during the exchanges, then fS ¼

X Qi i

(2.18)

Ti

We have seen that when a process is internally reversible, the entropy change of the system is equal to the entropy transfer exchanged. We can say that in these circumstances there is conservation of entropy. However, when a process is internally irreversible, the entropy change is always greater than the entropy transfer exchanged by the system so we can write the following inequality Z2 S2
S 1 >

dQ T

(2.19)

1

2.5.1

Entropy generation

However, we can transform this inequality into an equality, including a term that we will call entropy generation, Sg, and which by definition is intrinsically positive. Thus, the previous inequality becomes this equality Z2 S2
S1 ¼

dQ þ Sg T

(2.20)

1

In short, we conclude that the internal irreversibilities of a system originate a positive generation of entropy, see Sala and L opez 2010 [20]. This entropy generation is, therefore, due to dissipative effects, such as viscosity, friction, etc. to the internal heat exchanges in the system, to the diffusion, etc. that is, to everything that contributes to the mechanical, thermal and chemical irreversibilities. Generally, we define the entropy generation term in the following way: The entropy generation, due to the irreversibilities within a system, is that fraction of the entropy change that cannot be assigned to the entropy transfer, associated with the heat exchanges that take place through the boundaries of the system.

Quality of energy and exergy

103

Thus, in an internally irreversible process, the entropy change of the system is the sum of two terms: the entropy transfer and the generation. Considering the general case in which the heat exchange occurs through different areas of the boundary surface with different temperatures, we have X Z dQi DS ¼ þ Sg ¼ f S þ Sg Ti i 2

(2.21)

1

In the case of an adiabatic and closed system, there is no heat exchange through its boundaries, meaning that the entropy transfer is also zero, so that according to Eq. (2.20) we have S2
S 1 ¼ S g > 0

(2.22)

An isolated system is certainly adiabatic, so we can affirm that when an isolated system experiences an irreversible process between a stable initial state and a stable final state, its entropy increases. This is the case that occurs when some constraint of the initial state of the isolated system is eliminated, and it experiences a relaxation process. In the limit, when the process is reversible, the entropy generation is zero and, consequently, the entropy of the system remains constant. The previous statements are known as the principle of increasing entropy, but it is obvious that it is simply another way of stating the Second Law. Coming back to Eq. (2.20), we see that in all real processes that are carried out adiabatically, the entropy of the system must increase and never decrease. Note that if the process is not adiabatic, the entropy can decrease, no matter how irreversible the process, since the term due to the entropy transfer can be negative and of absolute value greater than that of generation. From the mathematical definition of entropy, it is obvious that its units are those of heat divided by absolute temperature, so that in S.I. units, it will be expressed in J/K. It is an extensive property, which means that when considering two parts of the same system, the part that has more matter will have greater entropy.

2.5.2

Entropy change of the universe

Until now, we have been referring exclusively to the thermodynamic system that undergoes the process. Now, in general, when a system evolves, it interacts with the external environment (ee); the whole that is formed by the system and the external environment we will call the universe, understood naturally in a restricted sense. It is clear that the universe is an isolated system and, therefore, according to Eq. (2.22) we can write DSun ¼ DS þ DSee  0

(2.23)

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Exergy Analysis and Thermoeconomics of Buildings

That is, in every irreversible process, the entropy of the universe increases, remaining constant at the limit of the reversible process. Obviously, the entropy of the system can increase or decrease, provided that this decrease is more than compensated for with the increase in entropy of the external environment, so as to satisfy the previous inequality. In the particular case that the system is isolated, then DSun ¼ DS, that is, we come back to inequality (2.22). All natural processes, which occur spontaneously, are irreversible so that for them the inequality (2.23) is satisfied, and the entropy increase of the universe will be greater when more irreversible the process. Entropy is a measure of the irreversibility, or if you like, of the spontaneity of a process. In this sense, entropy is precisely the quantity that satisfies the need to have an indicator that shows the permitted direction and the prohibited direction in the realization of a process. In effect, this verifies that the allowed direction is that for which DSun>0 is satisfied, and for reversible processes, it is DSun ¼ 0. A process whose realization would suppose that DSunT2. The bar is covered with a thermal insulator, except at its ends, so that there is only heat transfer longitudinally along the axis of the bar. _ determine Assuming that once a steady state is reached, the rate of heat transfer is Q, (1) The rate of entropy production and entropy transfer in the bar per unit of time. (2) The rate of entropy change of the heat reservoirs and the universe.

Solution (1) We have the diagram in Fig. E.2.11. Once the steady state has been reached, the entropy of the bar does not change, and there will only be changes of entropy in the heat reservoirs.

Figure E.2.11 Heat reservoirs and conductive bar.

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Exergy Analysis and Thermoeconomics of Buildings

We must remember that Thermodynamics normally uses the heat reservoir model to refer to systems that meet these three conditions: (1) they only exchange heat (they cannot exchange work nor mass), (2) whatever the heat exchanged their temperature is constant and (3) all the processes that occur inside are reversible. Making an entropy balance in the bar, we see that the entropy transfer due to the heat exchanged is compensated for with the entropy generated in it due to the irreversibilities in heat transfer. In effect, the rate of entropy transfer in the bar is fS ¼

Q_ Q_
T 1 T2

and since the bar is in a steady state, we have Q_ Q_ T1
T2 _ S_b ¼ 0 ¼
þ S_g;b / S_g;b ¼ Q T 1 T2 T1 T2 We see that the rate of entropy generation is greater when greater the heat flux and the difference between the temperatures of the heat reservoirs; what is more, for the same temperature jump, the lower the temperatures of the heat reservoirs, greater is the entropy generation. (2) In the heat reservoirs, there is no entropy generation, but their entropies vary due to the heat flux exchanged, and this is

Q_ S_T1 ¼
T1

Q_ S_T2 ¼ T2

The total change of entropy (entropy change of the ‘universe’) is the sum of entropy changes in the heat reservoirs and the bar, and therefore, S_un ¼ S_T1 þ S_T2 þ S_b ¼ S_g;b We see that it effectively coincides with the entropy generation. About 3 kg of water at 18 C are combined with 9 kg at 72 C at atmospheric pressure. Once thermal equilibrium has been reached, the initial states are restored, placing 3 kg of water in thermal contact with a heat reservoir at 18 C and the remaining 9 kg of water in contact with another heat reservoir at 72 C. What are

Example E. 2.11.

(a) The change of entropy of the water in the first process. (b) The change of entropy of the water in the second process. (c) The change of entropy of the universe in the whole of the two processes.

Quality of energy and exergy

107

Figure E.2.12 Bodies of water.

Solution (a) First, we determine the final state of equilibrium. The heat given up by one body of water is the same as that which the other receives, which is the same as saying the set of the two bodies of water is an isolated system (we do not take into account the exchanged work associated with density variations). We call the 3 kg of water system A and the 9 kg system B, and so it must be true that

    DUA þ DUB ¼ 0 / mA c Tf
Ti;A þ mB c Tf
Ti;B ¼ 0 / 3ðTf
18Þ þ 9ðTf
72Þ ¼ 0 Tf ¼ 331:6 Kð58:5 CÞ The entropy change of A and B is DSA ¼ mA c ln

Tf kJ ¼ 1:633 K Ti;A

DSB ¼ mB c ln

Tf kJ ¼
1:501 K Ti;B

Therefore, the entropy change of the water in the first process is DSA þ DSB ¼ 0:132

kJ K

(b) The entropy change of the water in the second process is the same as in the first process, but of opposite sign, that is


ðDSA þ DSB Þ ¼
0:132

kJ K

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Exergy Analysis and Thermoeconomics of Buildings

(c) The universe is made up of the two bodies of water and the two heat reservoirs. The entropy change of the water is zero, since the two bodies of water return to the initial state at the end of the two processes. We need to calculate the entropy change of the two heat reservoirs, for which we will first have to calculate the heat exchanged (Fig. E.2.13).

Figure E.2.13 Heat exchange between the bodies of water and heat reservoirs.

The heat exchanged between the heat reservoir, and the body of water A is   Q ¼ mA c Ti;A
Tf ¼
507:8 kJ This is the same heat exchanged by the mass of water B to reach 72 C, only now it receives the heat from the heat reservoir. Consequently, the change of entropy of both heat reservoirs is DSRA ¼


Q kJ ¼ 1:745 TRA K

DSRB ¼
1:471

kJ K

In short, the entropy change of the universe, once both processes have been carried out, is DSun ¼ Sg ¼ 0:274

kJ K

This increase in entropy of the universe is effectively the entropy generation due to the irreversibilities of the process (mixing the two water masses at different temperatures and exchanges of heat with the heat reservoirs).

2.6

Different quality of energy

We know the concept of energy, and we know that it manifests itself in diverse forms, such as mechanical energy (in its variants of kinetic, potential, elastic energy, etc.),

Quality of energy and exergy

109

electrical, heat, thermal energy, etc. We also know that energy is conserved in any process or equipment that we consider; thus, the energy that enters a system like fuel, electricity, in the flow of matter, etc. will be the same as that which appears in the products and byproducts of that equipment plus the possible change of the accumulated energy in the equipment. However, as we have commented in Section 2.3, the concept of energy and its conservation alone cannot explain many interesting aspects of the use of energy and natural resources in general. These distinct types of energy, although equivalent from the point of view of the First Law, are all different when the Second Law is taken into account. Ratifying this idea, under the perspective of Molecular Biology, life is considered as an ordered set of physical-chemical processes, in which exchanges of matter and energy take place. Now, there is an essential difference between the exchanges of matter and those of energy, since matter is recycled, but energy is not. In this way, we talk about material cycles in the biosphere, such as the carbon cycle, the nitrogen cycle, etc. but we cannot talk about an energy cycle. Rather we speak of the flow of energy in the biosphere. This is because, in addition to quantity, a fundamental aspect of energy is its quality, understood as its capacity to produce a change, as we have seen in Chapter 1. Thus, the capacity to cause a change (moving a machine, heating a room, etc.) of 100 kJ of electricity is greater than that of 100 kJ of thermal energy in a body at 900 K and this, in turn, is higher than that of the same energy stored at 500 K. The quality of the energy depends on whether it is an ordered energy, such as potential energy, the elastic energy of a spring, the kinetic energy of a spinning wheel, etc. or it is a disordered energy, as is the internal energy of matter, or that of thermal radiation, Kotas 1985 [22]. We have previously commented that entropy is a measure of uncertainty about the microscopic states of a system, but it can also be interpreted as a measure of the inability of a disordered form of energy to become an ordered form. We have already said that Carnot realized that work is a form of energy of more quality than heat. In effect, work can be transformed entirely into heat, but only a part of the heat given up by a source can be transformed into work; the rest must be transferred to a lower temperature sink so that the maximum fraction of heat that can be converted into work is defined by Carnotefficiency. Thus, although, according to the First Law the same amount of energy, either in the form of heat, or work, or internal energy, etc. should be equivalent to any other, what is mentioned above breaks that symmetry and allows another value to be given to those forms of energy; work is a nobler form of energy, of higher value than heat. This distinction or hierarchy in terms of the quality between work and heat can be generalized to the different ways in which energy is manifested. While the transformations of some types of energy into others are carried out with ease and with efficiencies that can be 100%, on the other hand, for other types of energy the efficiency of these transformations is relatively low, even assuming that they are carried out through perfect processes, that is, they are reversible. The foregoing shows us that there is

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something that distinguishes different forms of energy; in short, that their quality is different. While the quality of disordered energies is variable, depending on the form of the energy and the properties of the environment, ordered energies are totally convertible to other forms of energy. Due precisely to its interest, the maximum useful work that can be obtained from one form of energy has been adopted as the standard comparison energy, using the environment as a reference state. The measure of the quality of energy is, therefore, the ability to produce useful work, and we call this exergy. This last term was coined by Rant 1954 [23], and its use has been extended to different countries. It turns out that according to its aptitude for work, energy can be classified into two broad categories: energies that can be transformed into work in their totality, which are ordered energies, such as the different forms of mechanical energy, electric energy, etc. which we will call higher quality energies and disordered energies that are only partially transformable into work, such as internal energy, heat, etc. which we will call lower quality energies, see Fig. 2.9. Now, the convertibility to work is no more than a particular aspect of a general property of energy, that of its aptitude for transformation. All energy that can be completely transformed into work is equally transformable into any other form of energy, while energy of lower quality and, therefore, only partially transformable into work, will also only be partially transformable into another form of energy. In short, in each type of energy of lower quality, only a fraction is directly transformable into any other type, while higher quality energies are fully transformable into any other type. The discrepancies between energy and exergy can be radical. Thus, when a body is heated, its energy always increases. As we will study later, the same happens with exergy when the temperature of the body is above the ambient temperature since it increases its capacity to produce useful work. However, if the temperature is lower than that of the environment and the body is warmed, exergy decreases, because when the

Figure 2.9 Higher quality of electrical energy.

Quality of energy and exergy

111

body is brought closer to equilibrium with the environment, we are diminishing its ability to produce useful work. Moreover, unlike energy, exergy is not preserved but is destroyed by the irreversibilities of real processes. Generally, the inefficiency of a device or a process is precisely a consequence of that destruction. In lower quality energy, a fraction of it or its entirety cannot be transformed into work. This is the case of heat at room temperature or the internal energy of a fluid in thermodynamic equilibrium with the environment. This energy, which has no capacity to be transformed into work, should not be considered, however, as if it had no interest whatsoever. Consider, for example, the possibility of pumping heat from the ambient air by means of a heat pump to be used for heating purposes.

2.7

The environment and natural resources

As we will see later, the introduction of the concept of exergy allows for the development of a method of analysis of great interest in the thermodynamic study of processes and systems. The concepts that are part of what is generally understood as exergy analysis methods (based on the First and Second Laws) collect a series of characteristics in a formal and systematic way, which are common to processes and which we will now review. A first characteristic common to all processes is that all of them are carried out on planet Earth, within what we call the environment. In a later section, we will delve into the model that we will adapt to describe that environment. A second aspect to take into account is that the economic activity of human beings, and therefore, all the processes we perform, are possible, thanks to the existence of natural substances that are not in equilibrium with that environment. These substances are precisely the natural resources of raw materials and energy, see Fig. 2.10. Unlike what happens with the

Figure 2.10 Photo of an abandoned open mine.

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Exergy Analysis and Thermoeconomics of Buildings

environment, we attribute an economic value to these resources, and we are aware that they are not inexhaustible. By causing the modification of the thermodynamic state of these resources in processes, we obtain heating, cooling, work, etc., that is, useful energy and finished products, which are valuable from the economic point of view. A third interesting aspect is based on the fact that the most we can obtain from a resource is achieved when we transform its state to one of thermodynamic equilibrium with the environment. When this happens, no further useful process is possible, and for this reason, we will say, along with some other authors, that the resource has reached a dead state, Moran 1982 [24]. By imposing a series of conditions on that transformation, that is, it is specifically, as close as possible to the reversible limit condition, we will obtain maximum benefit from this natural resource. Finally, another aspect to consider is that a natural resource can be used to transform the state of a system that is passively present in the atmosphere, that is, in equilibrium with it, in order to confer an economic value on it. We have said in the previous section that exergy is the reference for assessing the thermodynamic quality of different types of energy. Now, as a conclusion to the above, we can already predict that the useful work that can be obtained, or that which is required in a given process, will depend on the following factors: (1) the thermodynamic characteristics of the environment, (2) the type of system considered, (3) the types of interaction allowed between the system and the environment, (4) the initial and final state of the system and (5) the degree of irreversibility in the process. All this means that the maximum useful work that can be done by a system cannot be described in principle by a simple formula since it depends on various circumstances. However, we can introduce idealized models of environment, system and permitted types of interaction, and thus, consider all possible cases within a small number of categories. The purpose of Thermodynamics is to establish general principles in order to set the optimum in certain circumstances, and thus, evaluate the maximum that can be obtained from our natural resources. Since these resources are limited, our interest is to conserve them, in the sense that we want to use them so that we can achieve economic objectives with the least waste.

2.8

Reference environment

It is clear that the environment is a tremendously complex system, so to include all its details in an analysis would not be practical or possible. Therefore, in order to describe it, it will be necessary to introduce certain simplifications, that is, it is necessary to work with some kind of model. Of course, the validity and usefulness of an analysis that makes use of such a model are limited by the idealizations introduced when formulating the said model. Any system other than the environment, whose temperature, pressure or chemical potentials of its components differ from those of the environment, has a capacity to perform work so that the environment is the means of reference for evaluating the work potential of different systems. The environment can interact with the systems

Quality of energy and exergy

113

in three different ways: thermally, that is, by exchanging heat, mechanically, when the system experiences a volume change, or chemically when the open system exchanges mass. When a system reaches environmental pressure and temperature, it is said to be in thermal and mechanical equilibrium with the environment. This type of equilibrium is called restricted equilibrium, and it is said that the system reaches the ambient state. If the equilibrium were complete, that is, mechanical, thermal and chemical, then the equilibrium is unrestricted, and a system that is in total equilibrium with the environment is said to be in a dead state. In this chapter, we are going to refer to systems that only exchange heat and/or work with the environment, so that the final equilibrium will be restricted. We will take chemical interactions into account in Chapter 3, where we will study the chemical exergy of substances. Although the environment, by itself, is not capable of producing work, it determines through the value of its intensive properties p0 and T0, the working potential of the whole (system þ environment). In effect, the work that can be done by a certain closed system is cancelled if no interaction between it and the environment is possible, that is, when it is in the ambient state. Therefore, the maximum work that can be done by a system will undoubtedly depend on its state and the ambient state. The tables of thermodynamic data of substances generally refer to the temperature of T0 ¼ 298.15 K (25 C) and P0 ¼ 1 bar (previously the pressure chosen was P0 ¼ 1 atm ¼ 1.013 bar). The states of the substances under these conditions are called standard states and are usually represented with a superscript  . Therefore, a reference environment is usually chosen with these conditions. The environment model is a specific concept of exergy analysis, which will be discussed in depth in Chapter 3. At this moment, we will say that the environment model, which we will refer to as the reference environment (RE), is conceived as a great medium, in which there are no pressure gradients, nor temperature or chemical potential gradients, so that there is no possibility of producing work due to interactions between different parts of it. Therefore, the RE is in thermodynamic equilibrium and its intensive properties should not be modified as a consequence of the mass and energy exchanges with the system under consideration. In addition, the RE can be considered, in the manner of Kestin 1980 [25], as the union of three large reservoirs: a thermal reservoir (of constant temperature T0), a volume reservoir (of constant pressure p0) and a mass reservoir that contains m chemicals (with constant chemical potentials mi,0). The extensive properties are so large that the RE remains in a situation of internal equilibrium during its interaction with the systems under consideration, which means that it is capable of carrying out only reversible processes. For exergy analysis, the RE cannot be chosen arbitrarily, unlike the reference states of the thermodynamic tables. The reason for this is that the energy analysis is based on the difference between two states and the effect of the chosen reference state disappears in the energy balance for systems of constant composition. On the other hand, in exergy analysis, the reference state is not eliminated in the exergy balance, so that, for example, the values chosen for T0 greatly influence the results of the analysis.

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Exergy Analysis and Thermoeconomics of Buildings

For a system to be chosen as RE, it must meet three conditions: (1) it must be unlimited (either acting as a source or sink), (2) its status is not modified by the effect of the processes to be analysed and (3) it must always be available. For use in the exergy analysis of buildings, the ECBCS Annex 49 [26] performed an analysis of exergy flows in a building considering four different REs: •

• • •

The celestial vault, with a temperature of around 3 K. It can be considered as the ultimate energy reservoir of the processes that take place in buildings; it is also infinite and its state is not modified as a result of the exchanges of mass and heat that occur in buildings. However, the cold radiation of the universe is not available, since otherwise it would not be necessary to refrigerate. The air inside the building. This has the limitation that it is not an infinite reservoir and not in thermodynamic equilibrium, so it does not meet the requirements for being an RE. The Earth’s crust. This can be considered as an infinite reservoir, whose properties are not modified by the processes in the building. However, the same as for the celestial vault, it is not available to be used directly by the building. Ambient air around the building. Most of the energy processes that take place in buildings are due to differences in temperature and/or pressure with the ambient air. Therefore, the surrounding environmental air can be considered the source or sink for the energy processes that take place in them. In addition, the volume of air around the building can be considered large enough so that changes in temperature, pressure or composition due to interactions with the building do not occur and, furthermore, it is available and can be used. For these reasons, Annex 49 recommends using the air around the building as RE for the exergy analysis of buildings and their energy facilities.

However, the reality is that the outside air around the buildings is not in equilibrium since its temperature and pressure vary in time and space. Consequently, the RE model must find a compromise between the theoretical requirements and its real behaviour. For modelling the air as an RE, it is assumed that its temperature and pressure are uniform, as well as the concentration of the different chemicals that make it up, even though these values are modified over time. A detailed study of the different reference environments can be found in Sakulpipatsin, 2008 [27]. As an example, in Table 2.1, the monthly and annual values calculated for the energy demand and exergy of heating in a house located in Bilbao are shown. Two different cases were selected for the ambient temperature: in the first, the average temperature relative to the heating period was used; and in the second, the hourly values. As we see, the values obtained do not differ appreciably (except in November, which was especially hot), with a difference between the annual values obtained of 6%. Thermodynamics does not indicate which exactly is the system that should play the role of RE, although we have already said that for the exergy analysis of a building and its facilities we will use the ambient air around it as RE. For the thermal and mechanical aspects of the exergy analysis, which are what we shall contemplate in this chapter, there is no difficulty. However, there may be difficulties when using exergy in the analysis of chemical processes, for example, in combustion in a hot water boiler, when it must be considered that, in addition to heat and work, the system exchanges mass with the RE, or also in the process of air conditioning with humidification or dehumidification. We shall consider these types of situations in Chapter 3, in which we will delve into the definition of RE.

Quality of energy and exergy

115

Table 2.1 Demand for energy and exergy in housing based on (A) average temperature of the heating period (B) hourly temperature.

Energy

Exergy

Exergy

Avge heating T

Hourly T

(kWh)

(kWh/m2)

(kWh)

(kWh/m2)

(kWh)

(kWh/m2)

January

411.90

5.67

12.22

0.17

14.43

0.20

February

289.78

3.99

8.65

0.12

13.08

0.18

March

220.34

3.03

6.59

0.09

6.87

0.09

April

148.21

2.04

4.59

0.06

4.32

0.06

May

e

e

e

e

e

e

June

e

e

e

e

e

e

July

e

e

e

e

e

e

August

e

e

e

e

e

e

September

e

e

e

e

e

e

October

e

e

e

e

e

e

November

257.29

3.54

8.03

0.11

4.67

0.06

December

373.06

5.14

11.04

0.15

11.08

0.15

Total

1700.57

23.42

51.11

0.70

54.45

0.75

2.9

Exergy by heat transfer

As already established by Carnot, the maximum work that can be done by a heat flux at temperature T (assuming that T > T0, where T0 is the ambient temperature) is what would result in a perfect heat engine working between two thermal energy reservoirs at temperatures T and T0. As all the heat cannot be transformed into work, part of that heat is given to a cold sink, and that cold sink is the environment, which is freely available. As we know, that maximum power is the product of the Carnot factor by the heat transferred, that is   T0 _ Q 1
T

(2.24)

According to the concept of exergy, the previous expression reflects the exergy _ and we will designate it with the symbol transfer accompanying heat transfer Q, _ BQ . The factor (1
T0/T) is called by some authors, for example, Torio and Schmidt

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Exergy Analysis and Thermoeconomics of Buildings

2011 [26], the heat quality factor. Naturally, if the temperature associated with the heat transferred were variable, the expression for the exergy transfer would be B_ Q ¼

 ZT2  T0 1
dQ_ T

(2.25)

T1

We are going to analyse the exergy transfer of heat as a function of the temperature T. For this, in Fig. 2.11. we represent the Carnot factor as a function of the temperature T for a value of T0 ¼ 298 K. Obviously, for T ¼ T0 the exergy transfer of heat is zero, that is, the heat transferred at ambient temperature has no capacity to produce work. For values of T > T0 we see that the Carnot factor is positive and less than unity and tends asymptotically to unity when T/N. This means that the exergy transfer always has the same sign as the heat, and its value is lower, approaching it as the temperature increases. This exergy transfer of heat is precisely the power that would be obtained in a reversible heat engine (one of Carnot’s) operating between a hot temperature source T and the cold temperature sink T0. However, when T < T0 the situation changes completely. We see that the Carnot factor becomes negative, and when T/0 K, the Carnot factor tends to minus infinity. This means that a heat transfer at a temperature very close to absolute zero is associated with an exergy transfer with a direction opposite to that of the heat and with a very high absolute value; thus, for T0 ¼ 290 K a heat transfer of 1 kW at the temperature of T ¼ 50 K is associated with an exergy transfer of 4.8 kW and for T ¼ 10 K the exergy transfer is 20 kW. This somewhat strange result requires an explanation that we will see below.

Figure 2.11 Carnot factor as a function of temperature values.

Quality of energy and exergy

117

Figure 2.12 Sense of heat fluxes and associated exergy flows.

Let us consider a closed system that exchanges heat. When the temperature of the system is T > T0, if the system receives heat from outside (Q > 0) its energy evidently increases and so does its exergy, since the exergy transfer is positive, whereas if the system is the one that yields the heat (- Q < 0), its energy decreases and equally its exergy decreases, since the exergy transfer is negative, see Fig. 2.12. Now, when the temperature of the system is lower than the ambient temperature T < T0, if the system receives heat its energy of course increases, the Carnot factor takes a negative value, and therefore, the exergy transfer is negative, and this means that exergy leaves the system. What is happening is that when receiving heat, the cold body (its temperature is below the ambient temperature) is approaching thermal equilibrium with the environment. On the other hand, if the system yields heat and consequently its energy decreases, the heat transfer is negative, but as the Carnot factor is also negative, the exergy transfer by heat is positive, that is to say, exergy enters the system. What is happening is that, if a cold body gives up heat, it is moving away from equilibrium with the environment (it is getting colder) and this means that its exergy increases. This implies that in order to extract heat from a cold body and give it to the environment, it is necessary to carry out work. In short, when T > T0 the direction of the exergy transfer is the same as that of the heat, whereas when T < T0 exactly the opposite occurs, the direction of the heat and the associated exergy transfer are opposite. In addition, the exergy transfer associated with a heat transfer at very low temperature has a very high value. The somewhat enigmatic phrase that appeared in some older texts of Thermodynamics, in which it was said that ‘cold is worth more than heat’, thus, acquires meaning.

2.9.1

Examples

Example E 2.12.

Calculate the heat and exergy transfer and draw the corresponding Sankey and Grassmann diagrams of an irreversible heat engine with a net power output of 10 kW, which works between a high-termperature medium at 1000 K and a lowtemperature medium at 400 K and has a thermal efficiency of 45%. Assume that the ambient temperature is T0 ¼ 290 K (Fig. E.2.14).

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.2.14 Diagram of the heat engine.

Solution The heat exchanged with the high-temperature medium is W_ 10 Q_ ¼ ¼ ¼ 22:22 kW h 0:45 and the heat exchanged with the low-temperature medium is Q_ 0 ¼ Q_
W_ ¼ 12:22 kW The exergy transfer associated with these heat transfers are       T0 _ 290 T0 _ Q¼ 1
Q0 1
22:22 ¼ 15:77 kW 1
1000 Th Tc   290 ¼ 1
12:22 ¼ 3:36 kW 400 The working fluid describing the cyclic process of the heat engine receives an exergy by heat of 15.77 kW. Part of that exergy is transformed into 10 kW of mechanical power, and another part is the exergy transfer given by heat to the low-temperature medium, 3.36 kW. As we see, there is no conservation of exergy, since 15.77 s 10 þ 3.36. The difference of 2.41 kW is, as we will see in Section 2.11, the rate of exergy destruction in the heat engine, that is to say D_ ¼ 15:77d10
3:36 ¼ 2:41 kW In Fig. E.2.15 (A) the energy diagram is shown (Sankey diagram) and in (B) the exergy diagram (Grassmann diagram) of the heat engine.

Quality of energy and exergy

119

Figure E.2.15 (A) Sankey diagram (B) Grassmann diagram.

2.10

Available work and physical exergy of a closed system

Let us consider a closed system, which, like all systems, is submerged in the RE. We will call this whole system formed by the system and the RE, the combined system. We will limit our attention, first, to systems that interact with the environment through impermeable walls, that is to say, closed systems, see Fig. 2.13.

2.10.1 Available work Suppose that the system undergoes a process, in general irreversible, and that the initial and final states of the system are 1 and 2 respectively. Referring to the combined system, the First Law allows us to write that DEc ¼
Wc

Figure 2.13 Closed system and environment.

(2.26)

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Exergy Analysis and Thermoeconomics of Buildings

where Wc is the work yielded by the combined system, i.e., the useful work and DEc is the energy change of the combined system, so that we have DEc ¼ DE þ DU0 ¼ U2
U1 þ EK2
EK1 þ EP2
EP1 þ DU0

(2.27)

where DU0 is the internal energy change of the RE. Since in general, the volume of the system varies by DV, the volume of the RE varies by DV0, with DVþDV0 ¼ 0. Applying the energy balance in the RE, we have that DU0 ¼ Q0
W0. Now, the work exchanged by the RE is W0 ¼ p0DV0 ¼
p0DV and the heat exchanged by the RE with the system is Q0 ¼ T0DS0, since the ambient temperature is constant and in the RE model, all processes are reversible. By making the entropy balance in the combined system, we have that DS þ DS0 ¼ Sg

(2.28)

where Sg is the entropy generated in the system by the irreversibilities of the process that has taken place. Taking into account these relationships, we have that the internal energy change of the RE is DU0 ¼ T0 Sg
T0 DS þ p0 DV

(2.29)

Substituting this result in Eq. (2.26), we have Wc ¼
DE þ T0 DS
p0 DV
T0 Sg

(2.30)

that is Wc ¼ E1
E2
T0 ðS1
S2 Þ þ p0 ðV1
V2 Þ
T0 Sg

(2.31)

If in the total energy change of the system we do not consider the change of kinetic or potential energy, which are forms of mechanical energy, that is, ordered energy and, therefore, exergy, and we only take into account the properties associated with the thermodynamic state, we get Wc ¼ U1
U2
T0 ðS1
S2 Þ þ p0 ðV1
V2 Þ
T0 Sg

(2.32)

Since Sg is intrinsically positive, the work of the combined system is a maximum when Sg ¼ 0, that is, when there are no irreversibilities in the process under consideration. This work is called available work. Therefore, for any closed system that evolves between two states 1 and 2, the maximum work exchanged by the combined system, that is the available work, is expressed by the following equation Wcavail ¼ U1
U2
T0 ðS1
S2 Þ þ p0 ðV1
V2 Þ

(2.33)

Quality of energy and exergy

121

At this point, it is worthwhile being precise about the work of the combined system, which we call useful work. When a system expands and, therefore, increases its volume by DV, a part of the work of expansion is done against the environment and since the pressure of this is constant and equal to p0 that work is poDV. This part of the work performed by the system is not available in a technical application, so the difference Wc ¼ W12
p0DV we will call useful work Wc ¼ Wu. Now, in compression, of the work received by the system, a part p0DV is contributed by the RE, so the useful work that must be provided is less than the total work received by the system. After a course of Classical Thermodynamics we know that, given two states of a system, in all the reversible processes that we consider between those two states, the work performed is the same and, in addition, that in any irreversible process between these states, less work is performed than in a reversible one. By means of the analysis that we have now carried out, we have been able to quantify this maximum work, as well as the difference between the maximum work and that performed in an irreversible process, an aspect that we will refer to later on. Obviously, if the work is contributed to the system, given two states the lower value corresponds to any reversible process between these states so that for any irreversible process the work that must be contributed is greater. We see that the available work is independent of the particular details of the reversible process, since it is expressed in terms of DU, DS and DV, in addition to the ambient temperature and pressure (T0,p0). On the other hand, the entropy generation Sg is not a thermodynamic property; it varies from one irreversible process to another according to the characteristics of that process. According to Eqs. (2.32) and (2.33), the difference between the work in a real process and the available work is given by the product of the ambient temperature and the entropy generation. Obviously, the more imperfect a process is, the further away it moves from the ideal model that is the reversible process, the greater the entropy generation and, therefore, the greater the difference between real work and available work.

2.10.2 Physical exergy At this point, we are able to obtain an expression to calculate the exergy of any material system, be it a pure substance or a multicomponent, single-phase or multiphase system. The question that we now ask ourselves is: if given a closed system (that is, one that cannot exchange mass with the environment) which is in a certain state 1, what is the maximum useful work that can be done by the said system? To answer this question, we must assess what conditions have to be met in order to get the maximum work out of the combined system. Of course, as long as the final state is not a state of equilibrium with the RE, it will be possible to consider another additional process and obtain work from the system under consideration. This possibility ends when the system reaches the ambient pressure p0 and the ambient temperature T0; that is, the state we call the ambient state. As we have seen before, this is a state of restricted equilibrium, in that the system reaches thermal and mechanical equilibrium with the environment, but not chemical equilibrium. To complete the answer to the question, it is clear that another condition is that the process that the

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system experiences between the initial state and this ambient state must be a reversible process. Coming back to Eq. (2.33), and replacing now the final state 2 by the ambient state 0, we have an expression that allows us to calculate the maximum useful work that can be done by the system in any initial state. We will designate this expression with the symbol A, and we will call it the physical (thermomechanical) exergy of the system, this is A ¼ U
U0
T0 ðS
S0 Þ þ P0 ðV
V0 Þ

(2.34)

In conclusion, the physical exergy of a system can be considered as the measure of its ability to perform useful work, with that capacity depending on the way it is coupled with the environment. Thus, if the surface that limits it was fixed instead of mobile, we would have obtained that the maximum work that can be achieved from the combined system, that is, the physical exergy of the system would be A ¼ UeU0
T0(SeS0), which is evidently a particular case of the previous expression. In any case, the physical exergy thus defined can never reach a value below zero; it is always positive. In effect, when a closed system is in a certain state of equilibrium, it can always modify that state by interaction with the RE, until reaching the restricted dead state. This process is carried out as a consequence of the thermal and mechanical imbalance with the RE and combined system work will always be performed. Therefore, A>0, in all possible states where T s T0 and p s p0. The minimum value of A, A ¼ 0, corresponds to the ambient state, that is, when T ¼ T0 and p ¼ p0. Thus, for certain states, exergy A may be greater than the internal energy. Think of a container with an initially closed tap, inside which is a gas at very low pressure. Undoubtedly, this system allows us to perform work since by opening the tap that puts the gas in connection with the atmospheric air, a current of air is created as a consequence of the pressure difference, which could be used to perform work. The lower the pressure, that is, the smaller the mass of gas contained in the tank, the lower its internal energy and yet, the greater the pressure difference and, therefore, the greater the work per unit of mass that can be done. Strictly speaking, the physical exergy A is not a thermodynamic property, since it depends not only on the state of the system but also on the ambient conditions p0 and T0. Now, with fixed environmental pressure and temperature, the value of A depends solely on the state, and therefore, in this sense, it can be considered as a thermodynamic property. It is an extensive property so that the corresponding specific property will be a¼

A ¼ u
u0
T0 ðs
s0 Þ þ P0 ðv
v0 Þ m

(2.35)

In Chapter 3, we will see the form that this expression has for the case of substances that are of interest in buildings, mainly water, air, building materials, and fuels and combustion gases. In short, in the absence of nuclear, magnetic, electrical and surface tension effects, the total exergy of a system will be the sum of the physical exergy

Quality of energy and exergy

123

A whose expression we have just obtained, the kinetic energy, the potential energy and the chemical exergy, which will be obtained in Chapter 3.

2.11

Exergy destruction in irreversible processes

We refer again to the situation described in Section 2.10. We have seen that, if we consider an irreversible process, the work that could be done by the combined system, once the initial and final states 1 and 2 are set, is lower than that which would be done in any reversible process between said states. The difference Wuavail
Wu ¼ T0 Sg

(2.36)

is proportional to the entropy generated in the system as a consequence of irreversibilities and also depends on the ambient temperature. The more irreversible a process is, the greater the entropy generation and, therefore, the term on the right of the previous equality will also be greater. Substituting Eq. (2.33) in this equality, we have A1
A2 ¼ Wu þ T0 Sg

(2.37)

This expression shows that the work done by the combined system in an irreversible process is less than the decrease in exergy of the system, since Sg > 0. Therefore, the term T0Sg, which we represent with the symbol D and which some authors call internal irreversibility, represents the exergy destruction in the system, and this is D ¼ T0 S g

(2.38)

Eq. (2.38) is usually known as the Gouy Stodola equation, Wepfer 1979 [28]. In conclusion, the useful work done in an irreversible process between any two states 1 and 2 is less than the decrease in the physical exergy of the system, precisely less by the term D, which then represents the exergy destroyed in the process. Since 1 and 2 are any two states, Eq. (2.37) can also be interpreted as saying that the work that must be supplied to the system to pass from state 1 to 2 is greater than the increase of exergy that it experiences (which is precisely the minimum necessary work) and greater by the term that represents the exergy destruction D. A limiting situation occurs when the exergy of a system is completely destroyed. This would occur when the ambient state has been reached, and no combined system work would have been done, for example, when a spontaneous state change occurs. A simple example can clarify this idea. Let us consider a system made up of two subsystems. One of them is an ideal gas, consisting of N moles at a temperature T0þDT and occupying a certain volume at a pressure p0(T0þDT)/T0. The other subsystem is also an ideal gas, similarly consisting of N moles at a temperature T0
DT and occupying a certain volume at a pressure p0(T0-DT)/T0. Initially, this system has the capacity to produce work that is the sum of the exergy of the two

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subsystems. Suppose that a heat exchange takes place between them so that if there is no heat or work exchanged with the external environment, final equilibrium is reached when the temperature of the two subsystems is T0, with the final pressure of the two subsystems p0. Thus, when this spontaneous process ends, with all the potential work that it initially had having been completely destroyed, the system is in the ambient state, and that was reflected by the value of its exergy. In conclusion, both in a reversible process and in an irreversible one there is conservation of energy since the First Law is satisfied. In addition, in a reversible process, the quality of that energy is conserved, that is, the exergy before the process coincides with the exergy later. On the other hand, in an irreversible process, there is exergy destruction, so that there is a degradation in the quality of energy. Therefore, the exergy before carrying out the process is greater than what can be counted afterwards. Irreversibilities, whether mechanical, thermal or chemical, cause exergy destruction, that is, degradation of the quality of energy. This is, in short, the meaning of the irreversibility of greatest interest to an engineer or an architect, concerned about the efficiency of processes.

2.12

Exergy balance in a closed system

In a general situation, a closed system can exchange both heat and work with other systems, which may or may not include the RE. In these interactions, in addition to the irreversibilities in the system, there will also be irreversibilities in the external environment with which the system interacts. However, the exergy balance that we are going to develop refers to the system under consideration so that the irreversibility term reflects the exergy destruction due to internal irreversibilities, not those that take place in the other systems with which it interacts. Let there be a process between states 1 and 2. Considering the changes of kinetic and potential energy that the system may experience, according to the First Law, we have DU þ DEK þ DEP ¼ Q12
W12 while the Second Law allows us to write Z 2 dQ DS ¼ þ Sg 1 Ts

(2.39)

(2.40)

where Ts is the surface temperature that limits the system, which varies throughout the process. By linearly combining the first equation with the second one multiplied by T0 and subtracting the term p0DV from both members of the equality, we get Z2  DA þ DEK þ DEP ¼ 1

 T0 1
dQ
ðW12
p0 DVÞ
D Ts

(2.41)

Quality of energy and exergy

125

Eq. (2.41) is the general exergy balance referring to the closed system in the 1 / 2 process. In effect, the term on the left represents the change of physical exergy, plus that of kinetic energy and gravitational potential, which are forms of mechanical energy and, therefore, of higher quality. The first term on the right is the exergy transfer by the heat exchanged, the second the exergy transfer by work, the third being the exergy destroyed in the system. In short, Eq. (2.41) reflects the following relationship 9 9 8 8 Exergy Change of > > > > ) ( > > > > = = < < Exergy exergy of ¼ exchanged by
> > > > > > > destruction ; : ; > : heat and work the system We have shown that to perform an exergy balance in a system for any process we need to linearly combine the energy balance and the entropy balance, that is, the exergy balance simultaneously comprises the First and the Second Laws. An equation allows us to find the value of an unknown quantity; in the equation of the energy balance, the unknown quantity is often the heat exchanged. Similarly, if all the terms minus D are known in the equation of exergy balance, we can calculate exergy destruction, even if we do not have detailed information on the mechanisms that cause irreversibilities. If, instead of Eq. (2.41) we express the exergy balance with reference to unit of time, we would have d ðA þ EK þ EP Þ ¼ dt

 Z2    T0 1
dQ_
W_
p0 V_
D_ Ts

(2.42)

1

A particular case of interest arises when the above equation can be written ! X   d T0 _ ðA þ EK þ EP Þ ¼ Qj
W_
P0 V_
D_ 1
dt T j j

(2.43)

where Tj is the temperature of that portion of the system surface in which the rate of heat exchanged is Q_ j . In these equations, W_ is the rate of work exchanged, V_ the rate of change of the volume and D_ is the rate of exergy destruction.

2.12.1 Examples Let a mass of gas be in state 1(p1,T1), where p1p0 and T1>T0, see Fig. 2.15. Consider a pair of reversible processes that can be used to determine b: an isobaric process from state 1 to state i, at temperature T0 and an isothermal process to the ambient state 0. The exergy difference between states 1 and i is the physical exergy component due to the temperature difference between the given state 1 and the environment and therefore, is the thermal component of physical flow exergy. Since the process between 1 and i is isobaric, we have bDT 1 ¼

Z i  1
1

  T0 dh T P1

(2.49)

The exergy change between state i and ambient state 0 is the other component of the physical exergy. It is associated with the pressure difference between state i and the RE, so it is the mechanical component of physical exergy, being bDP 1 ¼ ðhi
h0 Þ
T0 ðsi
s0 Þ

(2.50)

Thus, the physical flow exergy of any substance can be expressed as the sum of these two components. b ¼ bDT þ bDp

(2.51)

This difference between the thermal and mechanical component can be of interest when allocating costs, allowing a detailed follow-up of the formation process. We will have an opportunity to look at these aspects in Chapter 7.

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Exergy Analysis and Thermoeconomics of Buildings

2.14

Exergy balance in a control volume

Now that the flow exergy has been defined and the way to calculate it explained, we are in a position to carry out the exergy balance in a CV. Let there be a CV, such as the one shown in Fig. 2.6, with various input and output sections. The exergy balance can be expressed as follows: 9 8 Net rate at which > > > > > > > > > > > > exergy is being > > > > = < transferred ¼ > > > > > > > contained in the CV > > > > > > by heat transfer > > > > > > > > > ; : > > > > at time t ; : at time t 8 9 > Net rate of > 9 > 8 9 8 > > Net rate at which > > Rate of > > > > > > > > > > > > > > > > > > > > > > > > exergy transfer > > > > > > > > > > > > > exergy is being exergy destruction > > > > > > > > > = > < = < = > < into the CV > þ transferred þ due to
> > > > > > > > > > > accompanying > > > > > > > > > > > > > > > > > > > by work irreversibilities > > > > > > > > > > > > > > > > > > mass flow ; > : ; > : > > > > at time t at time t > > ; : at time t (2.52) 9 8 Time rate of change of > > > > > > > > > > = < exergy

Using the one-dimensional flow model in the input and output sections and assuming that the heat is transferred to the CV and the technical work is done by it, we have the following equation in out X X d ðA þ Ec þ Ep Þ ¼ B_ Q
W_ t þ m_ i ðb þ eK þ eP Þi
m_ j ðb þ eK þ eP Þj
D_ dt i j

(2.53) This equation reflects the rate of exergy balance. If we want to obtain the balance with reference to a certain interval between t and t þ Dt, we integrate the equation for that interval. In the particular case of steady-state, the term on the left of the equality is cancelled, and all others are independent of time so that the balance can be written according to the equation B_ Q
W_ t ¼

out X j

m_ j ðb þ eK þ eP Þj


in X i

m_ i ðb þ eK þ eP Þi þ D_

(2.54)

Quality of energy and exergy

139

and when there is only one input and one output Sections, then  B_ Q
W_ t ¼ m_ ðb þ eK þ eP Þ2
ðb þ eK þ eP Þ1 þ D_

(2.55)

Looking at this equation with reference to unit of mass, that is, integrating it into unit time, gives bq
wt ¼ Db þ DeK þ DeP þ d

(2.56)

Sometimes, we can consider the surface A that limits the CV divided into a series of surfaces Aj, such that the temperature in each of them is uniform Tj. Calling Q_ j the rate of heat exchanged through Aj, Eq. (2.54) becomes X j

! out in X X T0 _ Qj
W_ t ¼ m_ j ðb þ eK þ eP Þj
m_ i ðb þ eK þ eP Þi þ D_ 1
Tj j i (2.57)

and for only one input and one output Sections X j

! T0 _ _ Qj
W_ t ¼ mðDb þ DeK þ DeP Þ þ D_ 1
Tj

(2.58)

Integrating this equation over unit time, that is, the time in which a mass unit enters and leaves the CV, we have X j

! T0 1
qj
wt ¼ Db þ DeK þ DeP þ d Tj

(2.59)

Sometimes, to interpret Eq. (2.57) it is easier to write it in a way that reflects that the rate of exergy that enters the CV is equal to the rate of exergy that comes out plus the destroyed exergy within the CV, which is X j

! in out X X T0 _ Qj þ m_ i ðb þ eK þ eP Þi ¼ W_ t þ m_ j ðb þ eK þ eP Þj þ D_ 1
Tj i j (2.60)

Unlike Eq. (2.11) that reflects the energy balance in steady state, and that clearly shows that the energy entering the CV is equal to that coming out, the equation of

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Exergy Analysis and Thermoeconomics of Buildings

the exergy balance tells us that the rate at which exergy is transferred to the CV is greater than the rate at which it is extracted. There is, therefore, exergy destruction due to internal irreversibilities, rate of destruction that is represented by the term D_ (Fig. E.2.22).

2.14.1

Examples

Example E 2.18.

An adiabatic compressor that consumes a power of 100 kW compresses a mass flow rate of atmospheric air m_ ¼ 0:5 kg=s from p1 ¼ p0 ¼ 1 bar and T1 ¼ T0 ¼ 15 C to p2 ¼ 4 bar. Then, the air at the compressor outlet is cooled in a heat exchanger to T3 ¼ 35 C, through a flow of cooling water that enters the exchanger at Te ¼ 17 C, and leaves it at Ts ¼ 22 C. What are (a) (b) (c) (d) (e)

The air temperature at the compressor outlet. The rate of exergy destruction in the compressor. The rate of mass flow of cooling water. The rate of exergy destruction in the exchanger. Draw the Sankey diagram and the Grassmann diagram of the process.

Figure E.2.22 Schema of the compressor and heat exchanger.

Solution (a) Calling W_ c the power of the compressor (with positive sign) of the energy balance in the compressor and assuming for the air a constant specific heat in the temperature range of the compression, cp,a ¼ 1.004 kJ/kg$K, gives

_ 2
h1 Þ ¼ mc _ p;a ðT2
T1 Þ W_ c ¼ mðh

/

T2 ¼ 214 C

Quality of energy and exergy

141

(b) The exergy balance in the compressor gives

_ 2
b1 Þ þ D_ c W_ c ¼ mðb b2
b1 ¼ b2 ¼ cp;a ðT2
T1 Þ
T0 cp;a ln

T2 p2 þ Ra T0 ln ¼ 163:0 kJ=kg T1 p0

From the exergy balance equation, we get that the rate of exergy destruction in the compressor is D_ c ¼ 18:50 kW (c) Through the balance of energy in the cooler we determine the rate of mass flow of cooling water

m_ a ðh2
h3 Þ ¼ m_ w ðho
hi Þ

/

_ w ¼ 4:30 kg=s m

(d) The rate of exergy destruction in the exchanger is

D_ exch ¼ m_ a ðb2
b3 Þ
m_ w ðbo
bi Þ   T2 b2
b3 ¼ cp;a T2
T3
T0 ln ¼ 47:23 kJ=kg T3 bo
bi ¼ 0:32 kJ=kg D_ exch ¼ 23:43 kW (e) Exergies of each state

B_ 1 ¼ 0 B_ 2 ¼ m_ a b2 ¼ 81:50 kW    T3 p3 _ B3 ¼ m_ a cp;a ðT3
T0 Þ
T0 cp;a ln
Ra ln ¼ 56:69 kW T0 p0   Ti B_ i ¼ m_ w cw ðTi
T0 Þ
T0 ln ¼ 0:12 kW T0   To _ ¼ 1:50 kW Bo ¼ m_ w cw ðTo
T0 Þ
T0 ln T0

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.2.23 (A) Sankey diagram (B) Grassmann diagram. Example E 2.19. Let us consider a geothermal heat pump whose thermodynamic fluid is R-12 (CCl2F2) that supplies sanitary hot water and heating to a small detached house. The heat pump produces 1 t/h of water at 80 C, the water being supplied by the municipal supply network at 10 C and 1 bar (conditions that coincide with atmospheric conditions). The evaporator consists of an underground coil that is installed under the garden, whose constant temperature is
5 C. The isentropic performance of the compressor is 0.75. What are:(Fig. E.2.24)

(a) (b) (c) (d)

The COP of the heat pump and the power of the compressor. The exergy exchanged with the water and the soil. The rate of total exergy destruction and exergy efficiency. The global schematic diagram of the exergy in the heat pump (Fig. E.2.24).

Using the thermodynamic data of R-12 and according to the nomenclature used in the p-h diagram, we have the following values h1 ¼ 186

kJ kg

h2s ¼ 253

kJ kg

h3 ¼ h4 ¼ 46

kJ kg

Solution (a) From the isentropic performance of the compressor, the value of h2, the specific enthalpy of the state at the compressor outlet, is obtained. Effectively,

hs ¼

h2s
h1 h2
h1

0:75 ¼

253
186 h2
186

/ h2 ¼ 276

kJ kg

Quality of energy and exergy

Figure E.2.24 (A) Schema of the installation (B) Representation of the cycle in a p-h diagram.

143

144

Exergy Analysis and Thermoeconomics of Buildings

Therefore, COP ¼

h 2
h3 ¼ 2:56 h 2
h1

Applying the energy balance in the condenser, we have m_ R
12 ðh2
h3 Þ ¼ m_ w ðhII
hI Þ ¼ m_ w cw ðTII
TI Þ / m_ R
12 ¼ 0:35

kg s

so that the power of the compressor is W_ c ¼ m_ R
12 ðh2
h1 Þ ¼ 31:80 kW (b) Exergy delivered to the water

   TII B_ II
B_ I ¼ B_ II ¼ m_ ag cag TII
TI
T0 ln ¼ 8:66 kW TI Exergy exchanged by heat with the ground     T0 _ T0 _ Q0 ¼ 1
BQ0 ¼ 1
m_ R
12 ðh1
h4 Þ ¼
2:74 kW Ts Ts Since the refrigerant is in the evaporator at a temperature of
30 C, the ground gives heat to the refrigerant, and since the temperature is lower than the ambient temperature, this means that the refrigerant supplies the ground through the evaporator with an exergy transfer by heat of 2.74 kW. (c) By the global exergy balance in the heat pump, we have

  W_ c ¼ B_ Q0 þ B_ II
B_ I þ D_T / D_ T ¼ 20:40 kW and the exergy efficiency is 4¼

B_ II
B_ I ¼ 27:23% W_ c

(b) Diagram of exergy flow (Grassmann diagram) (Fig. E.2.25).

Quality of energy and exergy

145

Figure E.2.25 Grassmann diagram.

A large tank D containing air at ambient temperature T0 ¼ 20 C and a pressure of 25 bar is connected, via a valve, to a bottle B of compressed air of 120 L volume, see Fig. E.2.26. Initially, the valve is closed and inside the bottle the air is under ambient conditions (T0, P0 ¼ 1 atm).

Example E 2.20.

Figure E.2.26 Big tank, valve and bottle.

The valve is opened, the filling process is carried out very quickly, and then the valve is closed. Knowing that for the air the relation of specific heats is ga ¼ 1.4, what are (a) The exergy destruction in the filling process. Justify the cause of the destruction. (b) The decrease of exergy in the tank and the exergy efficiency of said filling process. (c) The exergy destruction taking place from the end of the filling until the air inside the bottle reaches the final state of thermal equilibrium with the atmosphere, as well as the final exergy of the air in that state.

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Exergy Analysis and Thermoeconomics of Buildings

Solution (a) If we apply the energy balance in the CV consisting of the bottle, which has an input section, for all the time that the filling process lasts, we have

N2 u2
N1 u1
ðN2
N1 ÞhD ¼ 0 where 2 and 1 correspond to the thermodynamic states of the air at the end and at the start of the filling, respectively, and hD is the specific enthalpy of the air found in the tank D. Using the perfect gas model, the initial number of moles in the bottle is N1 ¼

p1 V B ¼ 4:99 moles RT1

Returning to the equation of energy balance and using absolute zero as the reference state, we have   p2 VB p1 V B p2 VB p1 VB cv;a T2
cv;a T1

cp;a TD ¼ 0 RT2 RT1 RT2 RT1 from which we get   p2 p 1
p2
p1
g TD ¼ 0 / T2 ¼ 403:6 K T2 T1 a Therefore, the final number of moles in the bottle is N2 ¼

p2 V B ¼ 90:56 moles RT2

Once we know the final state, we calculate the exergy destruction in the filling process. With DSB being the entropy change in the bottle and DSD that of the tank, we have D ¼ T0 DSu ¼ T0 ðDSB þ DSD Þ Initially, we have an entropy N1s1þ(N2eN1)sD and the final entropy is N2s2. Therefore, the entropy change of the universe is DSu ¼ N2(s2
sD)
N1(s1
sD). And so     T2 p2 T1 p1
R ln
R ln DSu ¼ N2 cp;a ln
N1 cp;a ln TD pD TD pD As cp,a ¼ 29.1 kJ/kmol$K, p2 ¼ pD and T1 ¼ TD we have DSu ¼ 710:417

J K

Quality of energy and exergy

147

so that the exergy destruction due to the irreversibilities in the filling process, fundamentally associated with the pressure gradients, is D ¼ T0 $DSu ¼ T0 Sg ¼ 208:15 kJ (b) The decrease of exergy in the tank D is

DAD ¼ ðN2
N1 Þ½uD
u0
T0 ðsD
s0 Þ þ p0 ðvD
v0 Þ that is    p D p0
1 / DAD ¼ 662:81 kJ DAD ¼ ðN2
N1 Þ RT0 ln þ p0 pD The exergy efficiency can be defined as the increase in the exergy of the bottle divided by the decrease in the exergy of the tank D. The exergy increase of the air in the bottle is its final exergy, that is to say DAB ¼ AB;2 ¼ N2 ½uB
u0
T0 ðsB
s0 Þ þ p0 ðvB
v0 Þ      T2 p2 p1 ¼ N2 cv;a ðT2
T0 Þ
T0 cp;a ln
Rln þ R T2
T 0 T0 p1 p2 giving DAB ¼ 462:70 kJ Therefore, the exergy efficiency of the filling process is 4¼

DAB ¼ 69:8% DAD

(c) In the final thermal equilibrium with the environment, the temperature is 293 K, the number of moles is 90.56 and the volume is 120 L. Therefore, the final pressure is

pf ¼

N2 RT0 ¼ 18:38 bar VB

The final exergy of the air in the bottle is  AB;f ¼ N2 RT0

pf p0 ln þ
1 p0 pf

 ¼ 430:94 kJ

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Exergy Analysis and Thermoeconomics of Buildings

Therefore, the exergy destruction in the process of cooling the air in the bottle until it reaches the ambient temperature is Dcooling ¼ AB;2
AB;f ¼ 31:76 kW

2.15

Exergy of thermal radiation

Radiation is the energy emitted by matter in the form of electromagnetic waves, as a result of changes in the electronic configurations of atoms or molecules. Although the transport of heat by conduction or convection requires a material medium, heat transfer by radiation does not require the presence of matter; it is the way in which the Sun’s energy reaches the Earth. Radiation plays a very important role in the heat exchanges of buildings. Its energy behaviour can only be understood if the heat exchanges associated with radiation, both the absorption of solar radiation and the emission and absorption of long-wave radiation, are known and can be accurately evaluated. Since we want to analyse thermal radiation from the perspective of the First and Second Laws, the fundamental objective of this Section is to obtain an expression for the calculation of exergy associated with thermal radiation.

2.15.1

Review of some preliminary concepts

Electromagnetic waves carry energy, propagating in a vacuum at the speed of light, that is, c0 ¼ 2,99979$108 m/s. They are characterized by their wavelength l or their frequency n, which are related by l ¼ c/n, where c is the speed of propagation in the medium under consideration. They cover a wide range of wavelengths, ranging from 10
10 mm for cosmic rays to more than 1010 mm for electrical power waves. The different types of electromagnetic radiation, such as cosmic rays, gamma rays, X-rays, microwaves, etc. have their origin in different mechanisms. The electromagnetic waves emitted as a result of the energy transitions of the atoms, molecules and electrons of a substance constitute what is called thermal radiation. Thermal radiation is emitted by all matter so that all the objects that surround us and our bodies are emitting and absorbing thermal radiation continuously. The part of the spectrum between 0.1 and 100 mm constitutes thermal radiation since the radiation emitted by bodies falls in that wavelength range. Within that range, the visible part of the spectrum, which we call light, is between 0.40 and 0.76 mm. Therefore, light is no more than the part of the radiation spectrum that triggers the sensation of vision in the human eye. A body that emits radiation in the visible spectrum is called a light source. The Sun is our main source of light, while other bodies begin to emit visible radiation above 800 C, Modest 1993 [29]. At room temperature bodies emit radiation in the so-called infrared region of the spectrum, which is

Quality of energy and exergy

149

between 0.76 and 100 mm, while ultraviolet radiation includes the low-wavelength end and is between 0.01 and 0.40 mm. In addition to electromagnetic waves, in quantum physics, radiation is interpreted as consisting of energy quanta or photons. Radiation energy is emitted by bodies (solids, liquids and gases) in a discontinuous way through those energy units, which are the photons. If a body that emits radiation is not supplied with energy from another source, its temperature will decrease. Thus, due to this double nature, radiation can be considered as the energy of photons or the energy of electromagnetic waves. Therefore, the radiation process can be interpreted as a macroscopic phenomenon of heat transfer, as studied in engineering books, or as a process of energy exchange associated with photons. It is common practice in radiation studies applied to buildings to divide the radiation spectrum into two groups: short-wave radiation (l  2.5 mm), which practically covers the totality of solar radiation and long-wave radiation (l > 2.5 mm), which comprises practically all the radiation emitted by bodies at temperatures close to ambient temperature. Since the components of a building do not emit short-wave radiation, it can only be absorbed, reflected and transmitted; thus, solar radiation is absorbed and reflected on the outside of the opaque enclosures. On the other hand, semitransparent enclosures absorb part of the solar radiation that reaches them and transmit the other part to the interior of the building. This radiation, together with the short-wave radiant fraction of building illumination, is absorbed and reflected by the opaque enclosures and, in turn, a part can be transmitted to the exterior, through the semitransparent enclosures. Long-wave radiation heat fluxes appear in both the exterior and interior surfaces of the building. On the outer surfaces, there are exchanges of long-wave radiation with the celestial vault and the surroundings. In the interior, there are radiant exchanges between each surface and also interior objects, as well as the occupants and various pieces of equipment. It is clear that although we often talk about the radiation emitted by a surface, only the material particles occupying a volume, and not the surfaces, can emit radiation. Radiation is a volumetric phenomenon, although, for solids that are opaque to thermal radiation, it is usually considered as a superficial phenomenon. This is because the radiation emitted by the interior areas of a material can never reach the surface and on the other hand, the radiation incident on those bodies does not penetrate more than a few microns into the interior of the solid.

2.15.1.1 Blackbody radiation That said, it is interesting to know the maximum radiation that can be emitted by a surface at a given temperature. This requires the definition of a model, of an idealized body, which we call a blackbody. A blackbody is defined as one that absorbs all incident radiation so that all the radiation that comes from its surface is its own emission. In 1900, Planck [30] developed a detailed model of the atomic processes that take place in the walls of a cavity with a small hole that represents the behaviour of the

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black surface, which gave rise to modern Quantum Physics. He obtained the following expression for the radiation energy density ul(J/m4) at the wavelength l 8phc0  ul ¼ hc l elkT
1

(2.61)

where k ¼ 1.3805$10
23 J/K is the Boltzmann constant and h ¼ 6.626$10
34 J$s is the Planck constant. For obtaining the radiation flux e_b;l , the spectral energy density ul must be multiplied by c0/4, as deduced by Guggenheim 1957 [31] from geometric considerations. This means that the monochromatic emission power of the blackbody is e_b;l ¼



c1 c2 kT

l5 e
1



(2.62)

where c1 ¼ 2phc20 ¼ 3:74$10
16 Wm2 , c2 ¼ hc0/k ¼ 1.4388$10
2 mK and T is the blackbody radiation temperature. Fig. 2.16 represents the monochromatic emission curves e_b;l for different wavelengths l and different temperature values T. The dashed line represents the points of maximum value of e_b;l and as we can see, the higher the temperature, the lower the value of l that corresponds to the maximum, fulfilling the so-called Wien’s displacement law, Siegle and Howell 1992 [32].

Figure 2.16 Monochromatic radiation emission of the blackbody.

The energy emitted per unit area and time, that is, the area included between each line and the abscissa axis in Figure 2.16 was determined experimentally by J. Stefan, who expressed it as e_b ¼ sT 4

(2.63)

Quality of energy and exergy

151

where s is the StefaneBoltzman constant, with s ¼ 5.670$10
8 W/m2$K4 and e_b is the so-called blackbody emission power, which is the sum (the integral) of the radiation emitted over all wavelengths, that is ZN e_b ðTÞ ¼

e_bl ðl; TÞdl ¼ sT 4

(2.64)

0

2.15.1.2 Grey and diffuse surfaces Radiation is a complex phenomenon since it depends on the wavelength, but also on the spatial direction under consideration. Even assuming that there were sufficient data, the calculations would be very complex, so for radiation calculations in buildings, the grey and diffuse surface model is often used. A surface is said to be diffuse if the radiation emitted is independent of the direction and grey if it is independent of the wavelength.

Figure 2.17 Monochromatic radiation emission for three types of surfaces.

The emissivity of a grey surface is then defined as the ratio between the radiation emitted by the surface at a given temperature and the radiation emitted by the blackbody at the same temperature. The emissivity of a surface is denoted by ε and varies between 0 and 1: 0 ε  1, so that the emission power of a grey surface at temperature T is εsT4. The emissivity depends on the substance in question, but to a larger extent on the state of the surface, such as its degree of oxidation, roughness, type of finish and cleanliness. Therefore, in many cases, there is a certain amount of doubt about the values used. Fig. 2.17 shows the spectral emission power for three types of surfaces; blackbody, grey and real, confirming that the maximum values always correspond to the blackbody surface. Table 2.2 shows the typical emissivity ranges for various construction materials.

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Table 2.2 Emissivity of some materials. Material

ε

Paints

0.80e0.95

Glasses

0.75e0.90

Ceramics

0.40e0.80

Rusted metals

0.25e0.70

Polished metals

0.05e0.20

2.15.1.3 Absorptivity, reflectivity and transmissivity Every body receives radiation from the emission of other bodies, so we are now going to analyse how bodies behave when receiving this incident radiation. When the radiation reaches a surface, a part of it is absorbed, a part is reflected and the rest, if any left, is transmitted, as shown in Fig. 2.18. The flux of radiation that hits a surface is called irradiation, and we will designate it G. The fraction of the radiation absorbed by the surface is called the absorptivity a, which is a¼

Gabs G

(2.65)

Likewise, the fraction reflected by the surface is named the reflectivity r, being r¼

Gref G

(2.66)

Figure 2.18 Behaviour of a semi-transparent material when receiving incident radiation.

Quality of energy and exergy

153

The fraction transmitted is the transmissivity s, which is s¼

Gtr G

(2.67)

The First Law requires that the incident radiation be equal to the sum of the reflected plus the absorbed plus the transmitted radiation and, therefore, it must be that aþr þ s ¼ 1

(2.68)

In the case of opaque surfaces, the transmissivity is zero and, therefore, a þr ¼ 1. This relationship is very important since (for an opaque surface) it allows us to determine the reflectivity or the absorptivity when we know the value of the other property. These properties, as defined, are in fact average values, for all directions and all wavelengths, since, similar to emissivity, the properties for incident radiation can be defined for each direction and each wavelength. If a body can absorb all the incident radiation, that is, a ¼ 1 and, therefore, r ¼ s ¼ 0 it is said to be a blackbody. If a body reflects all the incident radiation, then r ¼ 1 and, therefore, a ¼ s ¼ 0 and it is said that the body is white. When the reflection is mirror-like, the incident and reflected angles are identical, and the surface is said to be smooth. Smooth surfaces that fully reflect the incident radiation are said to be perfectly reflective. When, on the other hand, the reflected radiation has different intensities according to the direction, then we say that the surface is rough. Real surfaces, covered with rust, paint, with impurities, etc. are rough surfaces, in which the analytical predictions of the electromagnetic theory are inadequate in most cases, Incropera and DeWitt 2002 [33]. Reflectivity, actually has a bidirectional nature, since it depends not only on the incident radiation but also on the direction of the reflected one. In practice, surfaces are usually considered to reflect like a mirror, that is, when the angle of reflection is equal to that of incidence, or in a diffuse way, when the radiation is reflected equally in all directions. According to what has been said up to now, the radiation coming from a surface is in general composed of the emission from said surface and by the radiation coming from other surfaces that is reflected by the surface and which is dependent on its temperatures. However, in radiation energy balances, it is not usually possible to distinguish between different possible temperatures and so the emitted and reflected radiation is taken together and called radiosity. For a blackbody, the radiosity is equal to the emission, since the reflectivity is zero.

2.15.1.4 Kirchhoff’s law Kirchhoff’s law greatly simplifies the analysis of radiation. This law establishes that the emissivity of a surface at temperature Tis equal to its absorptivity for radiation from a blackbody at the same temperature, that is to say εðTÞ ¼ aðTÞ

(2.69)

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Exergy Analysis and Thermoeconomics of Buildings

This relation, together with the previous one, r ¼ 1
a, allows us to determine the three properties of an opaque surface when we know only one of them. However, Kirchhoff’s law cannot be used when there is a significant difference between the temperature of the surface and that of the incident radiation source, Petela 2010 [34]. Therefore, it is usual to distinguish between absorptivity for short-wave radiation and absorptivity for long-wave radiation, with long-wave equating to emissivity. Table 2.3 shows values for short-wave absorptivity asw and emissivity ε (equal to long-wave absorptivity) of some materials of interest. As can be seen, black nickel oxide has a high absorptivity for solar irradiation, while its emissivity is low. This means that it is beneficial to use these materials in those applications in which it is important to capture solar radiation and when this captured energy is not to be re-emitted, which is the case of the surfaces used for solar collectors. On the other hand, white paint absorbs little solar radiation while its emissivity is high, so it is beneficial to coat the envelope of buildings in warm climates with paint of this colour.

2.15.1.5 Greenhouse effect Consider a material like white glass. In typical thicknesses in a window, glass transmits more than 90% of the radiation of wavelengths between 0.3 mm< l < 3 mm, where most of the solar radiation is emitted, including the visible spectrum. In the regions of the spectrum corresponding to infrared radiation, for l > 3 mm glass is opaque, that is, it does not let this radiation pass through. In short, glass allows solar radiation to enter but does not allow infrared radiation from other surfaces to escape. Therefore, the interior air of an enclosure limited by glass, such as the interior of a car, heats up much more than the air outside. This behaviour of glass gives rise to what is known as a heat trap or the greenhouse effect. This greenhouse effect occurs on a much larger scale on the Earth. The Earth’s surface absorbs solar radiation and heats up, but during the night it emits infrared radiation by radiating energy into space. The clouds absorb part of that radiation and send part of it back to the surface of the Earth. This means there is less cooling Table 2.3 Absorptivity and emissivity of some materials of interest. Surface

asw

ε

Black nickel oxide

0.92

0.08

Concrete

0.6

0.88

Black paint

0.97

70.97

White paint

0.14

0.93

Anodized aluminium

0.14

0.84

Snow

0.28

0.97

Human skin

0.62

0.97

Quality of energy and exergy

155

on a cloudy night than when the sky is clear. On the other hand, gases like CO2 absorb the infrared radiation emitted by the Earth’s surface, while transmitting solar radiation. Thus, the energy trapped on the Earth can cause global warming and climate change, which is one of the biggest concerns of the present day.

2.15.2 Thermodynamics of blackbody radiation As we have seen previously, in the study of thermal radiation, the first model is that of radiation in thermodynamic equilibrium with matter, which is called blackbody radiation. Consider a cavity with a small hole to which we referred earlier, and inside which we have blackbody radiation. The energy per unit volume and unit of the spectral interval is given by Planck’s law, Eq. (2.61). Integrating the previous equation for the whole spectrum, we obtain the energy per unit volume, which is ZN u¼

ul dl ¼ aT 4

(2.70)

0

where a ¼ 8p5k4/15h3c3 ¼ 7.565$10
6 Jm
3K
4. As can be seen, the energy of the blackbody radiation depends exclusively on the temperature of that radiation. For an in-depth look at the meaning of the temperature of radiation, consult the work of Petela 2010 [34]. The total energy of the radiation in volume V is U ¼ uV ¼ aT 4 V

(2.71)

The blackbody radiation contained inside the cavity exerts a pressure on its walls. Both from Classic Electromagnetism and from the quantum point of view (photons of momentum hn/c that create an impulse when they hit a wall), it can be shown, Petela 2010 [34] that the pressure exerted by the blackbody radiation is ZN p¼

pl dl ¼

aT 4 u ¼ 3 3

(2.72)

0

Let us now derive an expression for the entropy of blackbody radiation. Far too many texts of Thermodynamics mistakenly state that the entropy of radiation can be determined in a similar way to the entropy of heat transferred by conduction or convection, that is, as the quotient between the heat of radiation exchanged divided by the temperature of the surface under consideration. However, this interpretation does not take into account the entropy generated in the emission and absorption processes, which take place in the mechanism of heat exchange by radiation.

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Exergy Analysis and Thermoeconomics of Buildings

The entropy of radiation can be obtained in various ways. Thus, taking into account that any simple system must fulfil the differential equation 1 1 dS ¼ dU þ pdV T T

(2.73)

for blackbody radiation, we have 1 4 dS ¼ aT 3 dV þ aT 3 dV ¼ aT 3 dV 3 3

(2.74)

so that the blackbody radiation of temperature T and occupying volume V has an entropy of 4 S ¼ aT 3 V 3

(2.75)

The entropy per unit volume is then 4 4u s ¼ aT 3 ¼ 3 3T

(2.76)

Therefore, just as for other thermodynamic properties, the entropy of the blackbody radiation depends only on the temperature. For a detailed study of the spectral entropy of blackbody radiation, see Sala 1978 [35]. Interestingly, the Gibbs function for blackbody radiation is zero, since a 4 g ¼ u þ p
Ts ¼ aT 4 þ T 4
aT 4 ¼ 0 3 3

(2.77)

Likewise, calling N the number of photons per unit of volume, we have that the chemical potential of the blackbody radiation is also zero, since  m¼

2.15.3

vg vN

 ¼0

(2.78)

T

Exergy of blackbody radiation

Now that we have undertaken a brief introduction of the thermodynamics of radiation, we are going to follow the steps of Petela 1964 [36] and deduce the expression for calculating the exergy. Consider a cylinder-piston that can move without friction, located in a vacuum and that has blackbody radiation in its interior at an initial temperature T1. All the surfaces of the cylinder and piston are white, so they do not exchange heat by radiation, and the process that takes place in the cylinder is adiabatic. There is no heat exchange by conduction or convection because there is no material

Quality of energy and exergy

157

Figure 2.19 Isentropic expansion of blackbody radiation.

medium, since, on the outside of the cylinder, there is only blackbody radiation at the ambient temperature T0, see Fig. 2.19. The external face of the piston is subjected to the pressure of the ambient radiation, that is, blackbody radiation at the temperature T0, while its internal face is subjected to the pressure of the radiation at temperature T1. Whenever T1 s T0 the piston will move to the right if T1>T0 and to the left if T1 0, so that the enthalpy of the products is greater than that of the reactants, the reaction is said to be endothermic; on the contrary, when DH 0 < 0, the reaction is exothermic. In this way, in the chemical equation, which is a formulation of the principle of conservation of mass of each one of the elements taking part in it, the value of the enthalpy of reaction is added to its right-hand side, thus completing the thermochemical equation, that is nA A þ nB B þ //nM M þ nN N þ / þ DH 0

(3.73)

Similarly, given a chemical reaction in which the reactants and products are in their standard states, the standard entropy of reaction is defined as DS0 ¼

X ni s0i

(3.74)

i

Although DH 0 is calculated from the enthalpies of formation h0fi ð298Þ (which come in tables and are obtained, as we have seen, from calorimetric data), on the other hand, DS0 cannot be obtained in the same way. This is because the entropy of formation cannot be deduced from heats of formation, since the chemical reactions are not reversible, and they would have to be to apply the Clausius equality. At this point, we must remember that there is the Third Law of Thermodynamics that establishes the origin of entropy, Krest ovnikov and Vigdor ovich [24]. The formulation of the Third Law of greatest implication is that given by Planck based on an analysis made using Statistical Mechanics applied to systems at the zero temperature limit and states that when the absolute temperature tends to zero, the entropy of any perfect crystalline solid tends to zero limST/0 ðT; VÞ ¼ 0

(3.75)

There are also other formulations of the Third Law, such as the so-called Heat Theorem orNernst Statement, which was obtained empirically and states that absolute zero cannot be reached by any procedure; it is possible to approach it indefinitely but never reach it.

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Exergy Analysis and Thermoeconomics of Buildings

Unlike enthalpy, there is, therefore, an origin for entropy, so that the entropy of substances referring to this natural origin we call absolute entropy. Consequently, the entropy of a chemical element in the standard state is not zero and so the entropy of hydrogen is s0H2 ¼ 130:57 kJ=kmol K, that of oxygen s0O2 ¼ 205:03 kJ=kmol K, etc. Once the enthalpy of reaction and the entropy of reaction in the standard conditions (1 bar, 298 K) are known, we can refer them to other temperatures, using the specific heats of the substances. Obviously, the enthalpy of reaction at a temperature T and the standard pressure is linked to the enthalpy of reaction at 25 C by the equation Z 0 þ DHT0 ¼ DH298

T

Dc0p dT

298

(3.76)

and similarly for entropy Z DS0 ¼ DS0298 þ

3.4.5

T

Dc0p

298

T

dT

(3.77)

Gibbs function of formation and Gibbs function of reaction

In the same way that we have defined the enthalpy of formation, we can define the Gibbs function of formation of a compound. Thermodynamic tables are available that provide the values of Gibbs function of formation g0fi for different compounds at 298 K and 1 bar. Considering again the formation reaction Eq. (3.65), the Gibbs function of formation for a compound C is 0 g0f ;C ¼ h0f ;C  T 0 @s0C 

X j¼El

1 nj s0j A

(3.78)

where s0C and s0j are respectively the absolute entropy of compound C and the chemical element j that is involved in its formation. Similarly, returning to Eq. (3.69) the standard Gibbs function of reaction DG0 will be DG0 ¼

X ni g0i

(3.79)

i

where g0i ¼ h0i  T$s0i is the standard Gibbs function of substance i. Evidently DG0 ¼ DH 0  T 0 DS0

(3.80)

and as a function of the Gibbs function of formation DG0 ¼

R þP X i

ni g0f ;i

(3.81)

Calculation of physical and chemical exergy

217

Knowledge of the change of the Gibbs function of a chemical reaction is a fundamental thermodynamic tool for establishing reactivity criteria in chemical processes. Those interested in these questions can consult the numerous existing bibliographies, such as the aforementioned Krest ovnikov and Vigdorovich [24], or the works of Denbigh [25], or Levine [26].

3.4.6

Maximum work and change of Gibbs function

As is studied in a course of Classical Thermodynamics, for a system in which the pressure and temperature are kept constant, the maximum work that can be obtained from the system coincides with the decrease of the Helmholtz potential (or free energy). If the pressure and temperature are those of the RE, that is, p0 and T0 , that work can be divided into work against the environment and useful work, meaning that dWu  dGT0 ;p0

(3.82)

Thus, the maximum useful work that can be obtained from a system in thermal and mechanical equilibrium with the environment is equal to the decrease in the free enthalpy or Gibbs function. This result is the basis for calculating the chemical exergy of substances, as we will see in Section 3.5. In order to clarify these ideas, consider an ideal enclosure in which flows of substances, A; B; .; enter with each of them in their corresponding standard state. Inside the system, a reversible chemical reaction occurs nA A þ nB B þ ::/nM M þ nN N þ . and as a result of it, substances, M; N; . are generated which leave the enclosure also in their corresponding standard states, see Fig. 3.4(a). To visualize this system, consider the scheme of Fig. 3.4(b). We assume that inside the system the pressure p is greater than the standard pressures of the substances. Therefore, for the process to be reversible, each of the substances is compressed in an isothermal compressor, according to a reversible isothermal compression up to the pressure p of the interior. Once at that pressure they are passed through semipermeable membranes that are only permeable to the substance under consideration. Next, the chemical reaction takes place reversibly, so that the reactants disappear and others, the products of the reaction, are formed. Again, to extract the formed products, they are passed through semi-permeable membranes and isothermal expanders, where the products reach the standard pressure in a reversible manner. This ideal device is what is known as the van’t Hoff box. If we undertake an energy balance in the system, we will have the equation Q  Wumax ¼ HP0  HR0

(3.83)

Applying the Second Law, we have

 Q ¼ T 0 S0P  S0R

(3.84)

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Exergy Analysis and Thermoeconomics of Buildings

Figure 3.4 (a) van’t Hoff box (b) Details of van’t Hoff box.

Combining both equations gives





 Wumax ¼  HP0  HR0 þ T 0 S0P  S0R ¼  G0P  G0R

(3.85)

that is Wumax ¼ DG0

3.5

(3.86)

Calculation of standard chemical exergy

We have already seen that the chemical exergy of a system represents the maximum useful work that can be obtained when the system is brought from the environmental state or restricted dead state (thermal and mechanical equilibrium with the RE) to a state of total equilibrium (dead state) with the RE, and without the intervention of any other system, except the RE. Similarly, the chemical exergy can be defined as the minimum work necessary to obtain that system, with its structure and concentration, from the substances existing in the RE. Thus, chemical exergy reflects the existing chemical imbalance between the system under consideration and the RE and is of course always positive. The values that appear in tables in the bibliography, Kotas [16], refer to a standard RE, therefore, with the composition, pressure and temperature corresponding to standard conditions. As we have said in Section 3.3.3, the substances in the RE belong to three groups: gaseous components of the atmosphere, solid substances in the lithosphere and ionic and non-ionic substances in the oceans. In the calculation of the chemical exergy of any system, two different situations can be presented: • •

The system is made up of substances that are present in the defined RE, that is, they are reference substances. The system is made up of substances that are not present in the RE.

Calculation of physical and chemical exergy

219

We will refer first to the case of substances present in the RE and then generalize the study to the other case.

3.5.1

Substances present in the RE

We will refer in the first place to the case of systems that are made up of substances that are present in the standard RE. Although no chemical reaction is necessary, the maximum work that can be obtained from that substance is its chemical exergy, which some authors call chemical exergy of concentration. According to Eq. (3.86), the standard chemical exergy of a substance that is part of the standard RE is the difference between the standard Gibbs function of the substance and the partial Gibbs function (chemical potential) of that substance in the standard RE, that is  0 o 0 0 0 bch;0 ¼ g ðT ; p Þ  m ; p ; x ; ::x T 0 0 i;0 i 1:0 c;0 i

(3.87)

The calculation of this exergy associated with changes in concentration generally involves complex calculations, particularly in the case of liquid or solid phase reference substances, Szargut, Morris and Steward [15]. In the case of substances in the gas phase, which are part of the atmosphere, the calculation is simple, since the ideal gas model can be applied. For example, if the system is CO2 , the reference substance is CO2 , which is part of the standard RE at the partial pressure at which  we find it. Since the molar fraction of CO2 in air is very small

xCO2 ;0 ¼ 3:5$104 , the pressure drop from p0 ¼ 1 bar to that partial pressure, p0CO2 ;0 ¼ 3:5$104 p0 allows work to be done. Using the ideal gas mixture model, as we have seen in Section 3.4.1, for the generic component i we can write that 

m0i;0 T 0 ; p0 ; x01:0 ; ::x0c;0 ¼ m0i T 0 ; p0i;0 where p0i;0 ¼ xi;0 p0 is the partial pressure, in this case that of the CO2 and therefore 

 ¼ g0i T 0 ; p0  m0i T 0 ; p0i;0 bch;o i

(3.88)

Applying this expression for the case of CO2 , and taking into account Eq. (3.64), gives its standard chemical exergy as 0 bch;0 CO2 ¼ RT ln

x0CO2 ;0 p0 p0

¼ R298:15ln0:00328 ¼ 14; 179

kJ k mol

(3.89)

We are now going to obtain the chemical exergy of a mixture of ideal gases, such that all its components are also found in the standard RE, in turn forming a mixture of ideal gases in the RE. The chemical potentials of component i in the mixture m0i and in the standard RE m0i;0 are, respectively,

 p0 m0i ¼ g0 T 0 ; p0 þ RT 0 ln i0 p

(3.90)

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Exergy Analysis and Thermoeconomics of Buildings

p0i;0

 m0i;0 ¼ g0 T 0 ; p0 þ RT 0 ln 0 p

(3.91)

where p0i ¼ xi po is the partial pressure of component i in the mixture under consideration, and p0i;0 ¼ xi;0 p0 is its partial pressure in the standard RE. Substituting into the expression for chemical exergy, we have bch;0 ¼ RT 0

X i

xi ln

xi x0i;0

(3.92)

By developing the logarithm, the previous expression can be written bch;0 ¼

X X ch;0 xi bi þ RT 0 xi lnxi i

(3.93)

i

that is, the chemical exergy of the mixture is the sum of the chemical exergy of the components minus the exergy destruction in the mixing process, Eq. (2.120). With N being the total number of moles of the mixture, the total chemical exergy will be Bch;0 ¼ Nbch;0

(3.94)

The scheme of Fig. 3.5 provides a clear interpretation of this result. The objective is to determine the minimum work required to extract the ideal gas mixture under consideration from the RE and obtain it in the standard state. The extraction unit in the figure comprises N sub-units, one for each gas. Each one of them consists of its corresponding semi-permeable membrane, through which passes the component of the mixture that leaves the standard RE, a compression unit and a second semi-permeable membrane. Since we are determining the minimum work, the compression units must operate according to reversible isothermal processes.

3.5.2

Substances not present in the RE

In this section, the calculation of the chemical exergy expands on the situation considered above, since now the substance whose chemical exergy is to be determined is not one of the reference substances that is part of the standard RE. As we saw in Section 3.3, the standard RE consists of a certain number of reference substances, one for each chemical element, with concentrations x0i;0 and a pressure and temperature of standard values ð1 bar; 25 CÞ. In this general case, the standard chemical exergy of a substance can be obtained by two different methods: • •

General method: The chemical exergy of the substance is calculated from the chemical exergy of the elements that make it up and the Gibbs function of formation. Alternative method: The chemical exergy of the substance under consideration is obtained from the chemical exergy of substances that are part of the RE and with which it is stoichiometrically bound.

Calculation of physical and chemical exergy

221

Figure 3.5 Outline for interpreting the calculation of chemical exergy.

3.5.2.1

Calculation of the standard chemical exergy by the general method

The general method bases the calculation of the chemical exergy of a substance on the values of the standard chemical exergy of the different elements that make it up. Once the standard RE has been defined, numerous authors have calculated the chemical exergy of the different chemical elements, by means of exergy balances in the formation reactions of the reference substances and by using the thermo-chemical data of the Gibbs function of formation. These values are obviously fixed, so they can be displayed in tables. Table 3.1, culled from Rivero and Garfias [27] and from Szargut [14] shows the values of the chemical exergy of some elements. In order to clarify what this calculation process consisted of, let us refer to an example. Let us look at the chemical element Ca whose reference substance is CaCO3. We can consider the following chemical reaction 1 CaðsÞ þ O2ðgÞ þ CO2ðgÞ 2

/ CaCO3ðsÞ

(3.95)

Ca, O2 and CO2 are reference substances and therefore their chemical exergy has already been calculated; they are the exergies of concentration. From these values and

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Exergy Analysis and Thermoeconomics of Buildings

Table 3.1 Standard chemical exergy of some chemical elements’. Standard chemical exergy of elements Element

bch;0 el

Element

bch;0 el

Ag (s)

70,2

Kr (g)

34,36

Al (s)

888,4

Li (s)

393

Ar (g)

11,69

Mg (s)

633,8

As (s)

494,6

Mn (sa)

482,3

Au (s)

15,4

Mo (s)

730,3

B (s)

628,5

N2 (g)

0,72

Ba (s)

747,7

Na (s)

336,6

Bi (s)

274,5

Ne (g)

27,19

Cs (s)

404,4

Se (s, black)

346,5

Cu (S)

134,2

Si (s)

854,6

D2 (g)

263,8

Sn (s, white)

544,8

F2 (g)

466,3

Sn (s)

730,2

Fe (sa)

376,4

Ti (s)

906,9

H2 (g)

236,1

U (s)

1190,7

He (g)

30,37

V (s)

721,1

Hg (L)

115,9

W (s)

827,5

I2 (s)

174,7

Xe (g)

40,33

K (s)

366,6

Zn (s)

339,2

the Gibbs function of reaction of the previous chemical reaction, the chemical exergy of Ca is deduced. This approach is undertaken for each chemical element and in this way the chemical exergy of the elements is calculated and Table 3.1 is developed, which collects together the values of some elements. With the chemical exergy of the elements and the value of the Gibbs function for the formation of the chemical compound X under consideration, its standard chemical exergy is calculated, since bch;0 ¼ g0f ;X þ X

X nEl bch;0 El

(3.96)

El

where bch;0 El is the standard chemical exergy of the elements involved in the formation reaction and nEl the corresponding stoichiometric coefficients, where g0f ;X is the Gibbs potential of formation. Once the chemical exergy is calculated, adding to this value the

Calculation of physical and chemical exergy

223

physical exergy corresponding to the state under consideration, the total exergy in that state is obtained. As an example, we are going to calculate the chemical exergy of methane. Taking into account that the formation reaction of methane is C þ 2H2 /CH4

(3.97)

ch;0 and knowing that bch;0 C ¼ 410:27 kJ=mol; bH2 ¼ 236:12 kJ=mol and that the Gibbs 0 function of formation for methane is gf ;CH4 ¼ 50:5 KJ=mol, we find that the standard chemical exergy of methane is ch;0 ch;0 0 bch;0 CH4 ¼ gf ;CH4 þ bC þ 2bH2 ¼ 832:01 kJ=mol

3.5.2.2

(3.98)

Alternative method

This method is based on evaluating the maximum work that would be obtained if the substance under consideration in the environmental state reacted with substances obtained from the standard RE, to produce other substances, also present in the RE. This is the method that is usually used in the calculation of the exergy of fuels, through reactions of complete combustion. In order to interpret this way of calculating the chemical exergy of a substance in this general situation, we will go back to the van’t Hoff box and consider a series of devices that work in a reversible way and that allow us to take the substance under consideration from the initial state of restricted equilibrium with the environment to the final state of complete equilibrium. For the moment, we will assume that it is a pure substance and, later, we will generalize it for the case of any mixture. Basically, the process that we are considering is made up of two stages, see Fig. 3.6. In the first stage, which corresponds to the Reference Chemical Reaction module,

Figure 3.6 Calculation of the chemical exergy when the substance is not part of the RE.

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Exergy Analysis and Thermoeconomics of Buildings

the substance undergoes a reversible chemical reaction with constituents of the RE to form reaction products, which are also common constituents of the RE. As an example, suppose that the substance is methane. The chemical reaction that we can consider is CH4 þ 2O2 #CO2 þ 2H2 O

(3.99)

In this reaction, oxygen is the co-reactant, while carbon dioxide and water are the products. The three substances are common constituents of the RE. Both the substance whose chemical exergy is to be determined, as well as the co-reactants, are delivered to the Reference Chemical Reaction module at the pressure p0 and the temperature T 0 , while the products of the reaction leave the module as pure substances at that same pressure and temperature. In general, for a substance X, the chemical reaction is described by the equation Xþ

R X i

ni C i /

P X j

nj C j

(3.100)

Taking into account what was said in Section 3.4, the maximum work that can be obtained in the chemical reaction is wu ¼

R X i

ni g0i 

P X j

nj g0j ¼ DG0

(3.101)

where DGo is the Gibbs function of reaction per mole of X. The second stage corresponds to the Isothermal Change of Concentration module of Fig. 3.6. Here there is a change in the isothermal concentration of the RE substances which are used as co-reactants and the products obtained and which are finally sent to the standard RE. It consists, therefore, of a series of sub-systems, each of them equipped with two semi-permeable membranes and a compressor (expander) that compresses (expands) in an isothermal and reversible manner, as we saw in Fig. 3.5. The calculation of the reversible work necessary to isothermally compress (or expand) each of the co-reactants and products requires knowledge of the concentrations (in fact, the activities) of these substances in the RE. In any case, this isothermal work coincides with the change of the chemical potential, so that, referring to the co-reactants, the total work that is necessary to supply the sub-systems is WtR ¼ 

R  X ni g0i  m0i;0

(3.102)

i

where m0i;0 is the chemical potential (partial Gibbs function) of the chemical species i in the standard RE, while g0i is its Gibbs function in the standard state. On the other hand, the work exchanged in the compressors (expanders) in the units corresponding to the products of the reaction is P  X WtP ¼ nj g0j  m0j;0 (3.103) j

Calculation of physical and chemical exergy

225

In short, the total work that is obtained from both modules, that is, the chemical exergy of substance X is bch;0 ¼ DG0  X

R P  X  X ni g0i  m0i;0 þ nj g0j  m0j;0 i

(3.104)

j

Taking into account that, according to Eq. (3.88), the difference g0i  m0i;0 is the chemical exergy of the co-reactant or product i, Eq. (3.104) can also be written as bch;0 ¼ DG0 þ X

P X i

ni bch;0  i

R X j

nj bch;0 j

(3.105)

It is the expression for the calculation of the standard molar chemical exergy bch;0 X of the substance under consideration. For a number of moles N the chemical exergy is Bch;0 ¼ Nbch;0 X X

(3.106)

Instead of using the Gibbs function of reaction, we can express the chemical exergy as a function of Gibbs function of formation of the co-reactants and products. Taking into account the expression DG0 , we can retrace our steps and since DG0 ¼

R þP X i

ni g0f ;i ¼

R þP X i

ni bch;0 i

(3.107)

we have þP   RX q;0 0 nX bX  g0f ;X þ ni bch;0  g f ;i ¼ 0 i

(3.108)

i

finally resulting in another equivalent expression for the calculation of the standard chemical exergy bch;0 ¼ g0f ;X þ X

þP  1 RX 0 ni bch;0  g f ;i i nX i

(3.109)

In the more general case, in that the substance under consideration is not a unique chemical species, but is part of a mixture, all the above points are equally valid. In the final result, the Gibbs function must be replaced by the partial Gibbs function in the mixture, that is, its chemical potential. Finally, to indicate if the ambient temperature T0 differed appreciably from the standard temperature T 0 it may be necessary to make a correction to the value of the standard chemical exergy obtained, Kotas [16].

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Exergy Analysis and Thermoeconomics of Buildings

3.5.3

Examples

Example E 3.8.

Determine the chemical exergy (in kJ/kg) of an enriched air with a composition of 35% molar O2 while the rest is nitrogen. Assume that the air of the standard reference environment is made up of 21% of O2 while the rest is N2 and that the ambient temperature is T0 ¼ 288 K. Solution Using Eq. (3.92) deduced in the text, we have b

ch;0

¼ RT

0

xO xN xO2 ln 0 2 þ xN2 ln 0 2 xO2; 0 xN2; 0

! ¼ 128:83

J mol

As the apparent molar mass of the mixture is Mm ¼ xO2 MO2 þ xN2 MN2 ¼ 29:4

g mol

the exergy per unit of mass is bch;0 ¼ 4:38

kJ kg

The value obtained refers to the standard chemical exergy and in the calculation of bch we must use the ambient temperature and not the standard temperature. The relationship between the calculated standard chemical exergy and the chemical exergy, see Kotas [16], is bch ¼

T0 ch;0 kJ b ¼ 4:23 0 kg T

which we can see practically coinciding with a discrepancy of 3.5%. Example E 3.9.

There are two tanks that are thermally insulated and connected by a valve that is initially closed. One of the tanks is 100 L and contains pure O2 at 3 bar and 350 K. The other tank is 400 L and contains 670 g of pure N2 at 2 bar. Assuming that for both gases cp ¼ 7=2R, that the composition of the atmospheric air is 21% O2 and the rest N2, as a molar percentage and that T0 ¼ 293 K and p0 ¼ 1 bar, what is (a) The physical exergy of the O2 and N2. (b) The chemical exergy of the O2 and N2. The valve opens and both tanks are connected. What are: (c) The final physical exergy of the mixture formed. (d) The final chemical exergy of the mixture. (e) The exergy destruction.

Calculation of physical and chemical exergy

227

Solution (a) Applying the thermal equation of ideal gases we can calculate the number of moles of O2 contained in the tank pV ¼ NO2 RT

/

NO2 ¼ 10:3 moles

Likewise, we can calculate the temperature at which we find the N2 pVMN2 ¼ 402 K m N2 R

T¼

With the states defined and the number of moles known, we calculate the physical exergy of the O2 and N2 
 T p þ p0 V  NO2 RT0 ¼ 9:1 kJ AO2 ¼ NO2 cv ðT  T0 Þ  T0 cp ln  Rln T0 p0 AN2 ¼


 0:670 5 7 402 0:670 Rð402  293Þ  293 Rln  Rln2 þ 102 $0:4  293R 28 2 2 293 28

¼ 11:8 kJ (b) The chemical exergy of the O2 is ch Bch O2 ¼ NO2 bO2 ¼ NO2 RT0 lnxO2 ;0 ¼ 39:2 kJ

while the chemical exergy of the N2 is ch Bch N 2 ¼ NN 2 bN 2 ¼ NN 2 RT0 lnxN 2 ;0 ¼ 13:7 kJ

(c) Calculating the final state of the mixture Uf  Ui ¼ 0 /

Tf ¼

NO2 Ti;O2 þ NN 2 Ti;N 2 ¼ 386:3 K NO2 þ NN 2

and the final pressure is pf ¼

ðNO2 þ NN 2 ÞRTf ¼ 2:2 bar V

Since the total number of moles is 34.2, the final physical exergy of the mixture is Af ¼ 0:0342


  5 7 386:3 Rð386:3  293Þ  293 Rln  Rln2:2 2 2 293

þ 102 : 0:5  0:0342R293 ¼ 41:12 kJ

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Exergy Analysis and Thermoeconomics of Buildings

(d) Since the molar fractions in the mixture formed are xO2 ¼ 10:3=34:2 ¼ 0:30 and xN2 ¼ 0:70, the final chemical exergy is
 xO2 xN 2 N ¼ 1:9 kJ Bch ¼ RT ln þ N ln O2 N2 0 f xO2 ;0 xN 2 ;0 (e) Undertaking an exergy balance, we have

  ch ch AO2 þ AN2 þ Bch ¼D O2 þ BN2  Af þ Bf

and so D ¼ 30:8 kJ The process is highly irreversible, with mechanical, thermal and chemical irreversibilities. This is why the exergy destruction represents almost 42% of the exergy initially available. Example E 3.10.

Calculate the heat exchanged, as well as the change of physical and chemical exergy, of a system contained in a tank with rigid walls consisting initially of 3 mol of CH4, 10 mol of O2 and 40 mol of N2 at an ambient temperature of 25 C and ambient pressure of 1 bar, producing the complete combustion of methane, and with a final temperature of 225 C. Use the approximation of the ideal gas mixture. Solution The complete combustion reaction that takes place is CH4 þ 2O2 /CO2 þ 2H2 O

so the final composition of the system is shown in Table E.3.1. Table E3.1 Composition of the products. Products

Ni

CO2

3

H2 O

6

O2

4

N2

40

Total

53

In order to determine if part of the water formed is in the liquid phase or if all of it is vapour, the partial pressure of the water vapour must be calculated; if this partial pressure pH2 O ¼ xH2 OP2 is less than psð225 CÞ ¼ 25:50 bar all the water formed will be in the vapour phase. Initially, assuming that all the water formed is in the vapour phase, as the volume of the vessel is constant, there is no work exchanged.

Calculation of physical and chemical exergy

229

To calculate the heat exchanged, we refer to the thermo-chemical tables, in which we find the following values: h0f ;CH4ðgÞ ðkJ=kmolÞ ¼ 74:8, h0f ;H2 OðgÞ ðkJ=kmolÞ ¼ 241:8, h0f ;CO2ðgÞ ðkJ=kmolÞ ¼ 393:5, with the heat being transferred to the outside Q ¼ DU ¼ DH þ DðpVÞ The change of enthalpy is 





DH ¼ HP  HR ¼ HP  HP0 þ HP0  HR0  HR  HR0 Since the enthalpy is a function only of the temperature, we have that HR ¼ HR0 . On the other hand HP0  HR0 ¼ 6h0f ;H2 OðgÞ þ 3h0f ;CO2  3h0f ;CH4 ¼ 2; 406:9 kJ 2 HP  HP0 ¼ 34

Z

3 498

298

2 þ 44

2

cp dT 5

þ 64 3

498 298

498 298

CO2

Z

3

Z

cp dT 5

2 þ 440

O2

Z

cp dT þ 5 3

498

298

H2 O

cp dT 5

¼ 296:9 kJ

N2

where the values of cp;i have been taken from the tables of specific heats of ideal gases. Since DðpVÞ ¼ RNDT, and since the initial number of moles is 53, equal to the final number of moles, this means that DðpVÞ ¼ 88:1 kJ. Therefore, the heat transferred to the outside is Q ¼ 2; 198:1 kJ The volume of the tank, which at all times remains constant, is p1 V ¼ N1 RT1

/ V ¼ 1:31 m3

Since the final number of moles equals the initial number, the final pressure is p2 ¼ p1

T2 ¼ 1:67 bar T1

Indeed, the initial hypothesis was correct, so that all the water is in the vapour phase and the heat exchanged is calculated.

230

Exergy Analysis and Thermoeconomics of Buildings

We will now determine the change of exergy of the system, beginning with the physical exergy. Initially, the conditions are those of the environment, so the physical exergy is zero, A1 ¼ 0. The final physical exergy is A2 ¼ ðU2  U0 ÞP  T0 ðS2  S0 ÞP þ p0 ðV2  V0 ÞP with

Z ðU2  U0 ÞP ¼

498

298

 3cv;CO2 þ 6cv;H2 O þ 4cv;O2 þ 40cv;N2 dT ¼ 231:0 kJ

 3cp;CO2 þ 6cp;H2 O þ 4cp;O2 þ 40cp;N2 dT  53  Rln 1:67 ðS2  S0 ÞP ¼ T 298 J ¼ 555:4 K Z

498



p0 1 p0 ðV2  V0 ÞP ¼ NP R T2  T0 ¼ 53R 498  298 ¼ 89:7 J 1:67 p2 Therefore, the final physical exergy is A2 ¼ DA ¼ 65:6 kJ We now calculate the change of chemical exergy. All substances are part of the RE, except methane, so we calculate first the chemical exergy of methane. From the table of the chemical exergy of the elements and the methane formation reaction, we see that ch;0 ch;0 0 bch;0 CH4 ¼ gf ;CH4 þ bC þ 2bH2 ¼ 832:0 kJ=mol

As the ambient conditions coincide with the standard ones, the chemical exergy is the standard chemical exergy. Using Szargut’s tables we obtain the chemical exergy of each component of the mixture and afterwards calculate the exergy of the gas mixture applying Eq. (3.93), first in the initial state Bch 1 ¼ 3$832:0 þ 10$3:97 þ 40$0:72
 3 10 40 þ 8:314$103 $298 3ln þ 10ln þ 40ln ¼ 2; 473:9 kJ 53 53 53 and then in the final state Bch 2 ¼ 3$19:87 þ 6$9:5 þ 4$3:97 þ 40$0:72
 3 6 4 40 þ 8:314$103 $298 3ln þ 6ln þ 4ln þ 40ln ¼ 54:1 kJ 53 53 53 53 so the change of chemical exergy is DBch ¼ 2; 419:8 kJ

Calculation of physical and chemical exergy

231

Consequently, the change of the total exergy of the system within the container is DA þ DBch ¼ 2; 354:2 kJ This reduction in exergy will be due to the exergy destruction in the irreversibilities of the combustion reaction and also to the exergy of the heat transferred through the walls of the tank. In a combustion chamber, the complete combustion of 1 m3/s volumetric flow rate of CO is produced with an air flow rate such that the excess coefficient is 1.20. At the entrance to the chamber, both the air and the CO are at a temperature of 400 K and at a pressure of 1.2 bar, with the temperature of the combustion gases at the output being 1000 K and the pressure being 1 bar. The average temperature of the surface of the chamber is 750 K. With the composition of the air in molar fractions being 0.21 of O2 and 0.79 of N2, the ambient conditions being p0 ¼ 1 bar, and T0 ¼ 290 K and considering changes of kinetic and potential energy to be negligible, determine:

Example E 3.11.

(1) (2) (3) (4)

The heat exchanged through the walls of the combustion chamber per unit of time. The physical and chemical exergy of the flow of CO. The chemical exergy of the combustion gases. The exergy destruction in the chamber.

Solution

Figure E3.2 (a) Outline of the chamber and (b) H-T diagram. (1) Fig. E 3.2. contains a diagram of the chamber and an enthalpy-temperature diagram, in which the enthalpy change with respect to temperature for the reactants and products of combustion is shown. The combustion reaction is 1 CO þ O2 0CO2 2

232

Exergy Analysis and Thermoeconomics of Buildings

At least 0.5 mol of O2 are required for each mole of CO. Since the coefficient of excess air is 1.2, the number of moles used is 0.5  1.2 ¼ 0.6 and therefore the number of moles of N2 is 0.6  0.79/0.21 ¼ 2.26. As for the resulting gases 1 mol of CO2 is formed and 0.1 mol of O2 and 2.26 of N2 remain. The number of moles of CO that enters the chamber per second is p _ mol V ¼ 36:1 N_ CO ¼ RT s The change of enthalpy per mole of CO is 





HP  HR ¼ HP  HP0 þ HP0  HR0  HR  HR0 where HP0  HR0 ¼ h0f ;CO2  h0f ;CO ¼ 393:52 þ 110:53 ¼ 283:0 Z HP  HP0 ¼

1000

 cp;CO2 þ 0:1cp;O2 þ 2:26cp;N2 dT ¼ 83:0

298

Z HR  HR0 ¼

kJ mol CO

400

298

 cp;CO þ 0:6cp;O2 þ 2:26cp;N2 dT ¼ 12:4

kJ mol CO

kJ mol CO

so that the heat given to the exterior is Q_ ¼ N_ CO ðHP  HR Þ ¼ 7; 667:6 kW which is the heat transferred to the outside through the surface of the chamber. (2) According to Eq. (3.12) the physical exergy of the CO that enters the chamber is 2 B_ CO ¼ N_ CO 4

Z

3  T0 p5 ¼ 33:5 kW cp;CO dT þ RT0 ln 1 p0 T

400
290

The chemical exergy of the CO can be calculated by the general method, from the chemical exergy of the elements C and O2 and the Gibbs function of formation for CO, or, through the indirect method, through the combustion reaction of CO and knowing the chemical exergy of O2 and CO2 and the Gibbs function of the complete combustion reaction. We are going to use this second method 1 CO þ O2 /CO2 2 1 ch;0 1 ch;0 kJ ch;0 ch;0 0 0 0 bch;0 CO ¼ DG þ bCO2  bO2 ¼ gf ;CO  gf ;CO2 þ bCO2  bO2 ¼ 275:12 2 2 mol

Calculation of physical and chemical exergy

233

and therefore, considering the correction for the temperature to be negligible, the chemical exergy is ch B_ CO ¼ N_ CO bch CO ¼ 9; 931:8 kW

(3) We have seen that in the combustion gases, for each mole of CO, 1 mol of CO2 is formed and 0.1 mol of O2 and 2.26 mol of N2 remain. Therefore, the chemical exergy of the gases per mole of CO is 
1 0:1 2:26 ch ch ch þ 0:1ln þ 2:26ln bch g ¼ bCO2 þ 0:1bO2 þ 2:26bN 2 þ RT0 ln 3:36 3:36 3:36 kJ ¼ 15:96 mole of CO and therefore ch B_ g ¼ N_ CO bch g ¼ 576:1 kW

(4) To obtain the exergy destruction in the combustion chamber, we undertake an exergy balance, giving  


 T0 _ ch _ _ Q þ D_ N_ CO bch CO þ bCO þ nai N CO bai ¼ N CO bg þ bg þ 1  Ts where nai is the number of moles of air entering the chamber per mole of CO, nai ¼ 1:2=0:21 ¼ 5:71, bai is the molar exergy of the air, Ts is the surface temperature of the combustion chamber and D_ is the exergy destruction that we want to calculate. Assuming that the air in the temperature range from 290 to 400 K has an average value of specific heat of cp;ai ¼ 0:030 kJ=mol, according to Eq. (3.12) we have
 400 kJ bai ¼ 0:03 110  290ln þ 8:314  103  290ln1:2 ¼ 0:94 290 mol with the physical exergy of the combustion gases, per mole of CO being Z bg ¼

1000
290

¼ 12:7

1

  Z 1000
 T0 T0

cp;g dT ¼ xCO2 cp;CO2 þ xO2 cp;O2 þ xN 2 cp;N 2 dT 1 T T 290

kJ mole of CO

where xCO2 ¼ 0:30, xO2 ¼ 0:03 and xN2 ¼ 0:67: So, since the exergy of the lost heat is 
T0 _ Q ¼ 4; 702:8 kW 1 Ts

234

Exergy Analysis and Thermoeconomics of Buildings

substituting values in the exergy balance equation, we have D_ ¼ 4; 421:6 kW which as we can see represents 43.5% of the exergy supplied to the chamber.

3.6

Chemical exergy of substances of interest in buildings

In the energy analysis of buildings we find ourselves in the first place with the various materials that constitute its envelope. Likewise, very often we see flows of hot and cold water, for which we will apply the incompressible fluid model, as well as air flows, combustion gases, etc., for which the ideal gas mixture model is valid. Therefore, we will refer in the first place to these cases and, finally, we will address the calculation of the chemical exergy of fuels.

3.6.1

Exergy of construction materials

In the construction of a building various types of materials are used. Among stone materials, the most used are limestone, marble, granite and aggregates. There are also ceramic materials from clays that are subjected to firing processes in ovens at elevated temperatures, such as flooring tiles, glazed tiles, refractory bricks, etc. Glass is a mixture of sand with potash or soda, with the addition of other bases, and can be given different colors by the addition of metal oxides. Binding materials are also used in buildings to join together other materials, such as plaster and cement. Another type is compounds, which are formed of mixtures of different materials with different properties: this is the case of mortars, which are a mixture of sand, cement and water or concrete which are mixtures of cement, aggregates and water. There are also metals, the most commonly used being ferrous and forged steel, and among non-ferrous metals, copper and aluminum. Additionally, there are plastic materials, which are organic materials made from polymers, among which we find PVC, polystyrene, polyurethane, etc. see Fig. 3.7. For the calculation of the physical exergy of building materials, we apply Eq. (3.43), for which we need to know the specific heat of the material and the temperature at which we find it. As the temperature of these materials is usually the ambient temperature, their physical exergy is zero. For the calculation of chemical exergy we need to know the composition of the material and use Eq. (3.96), or the alternative method applying Eq. (3.105).

3.6.2

Exergy of water

The specific chemical exergy of water is bch w ¼ gw ðp0 ; T0 Þ  mw;0

(3.110)

Calculation of physical and chemical exergy

235

Figure 3.7 Various construction materials.

where gw ðT0 ; p0 Þ is the specific Gibbs potential of water at ambient pressure and temperature and mw;0 is the chemical potential of water in the RE. If the chosen RE were the saturated air, then mw;0 ¼ mv ðps ðT0 ÞÞ, where ps is the saturation pressure at the temperature T0 , since the liquid water is in thermodynamic equilibrium with the water vapour in the air when it is saturated. We can then verify that gw ðT0 ; p0 Þ ¼ mv ðps ðT0 ÞÞ, so that the chemical exergy of water is zero. If the chosen RE is not saturated air but ambient air, where xv;o is the molar fraction of the water vapour in the air, in this case, as we have the relationship

 xv;0 p mv T0 ; xv;0 p ¼ mv ðT0 ; ps ðT0 ÞÞ þ RT0 ln (3.111) ps ðT0 Þ it means that the chemical exergy of water is bch w ¼ RT0 ln

xv;0 p0 ps ðT0 Þ

(3.112)

According to the previous expression, the total specific exergy of water, in a state ðT; pÞ gives   xv;0 p0 bT ðT; pÞ ¼ hðT; pÞ  hw;0 ðT0 ; p0 Þ  T0 sðT; pÞ  sw;0 ðT0 ; p0 Þ  RT0 ln ps ðT0 Þ (3.113) an expression that represents the total specific exergy of water, both in the vapour phase and as liquid water. In both cases, the values of enthalpy and entropy can be evaluated by using thermodynamic tables. In the case of liquid water, the incompressible fluid model can be used, in which case hðT; pÞ ¼ h0 ðTÞ þ v0 ½p  ps ðTÞÞ

sðT; pÞ ¼ s0 ðTÞ

(3.114)

236

Exergy Analysis and Thermoeconomics of Buildings

where ðh0 ; v0 ; s0 Þ refer to the state of saturated liquid at temperature T. Therefore   bTw ¼ h0 ðTÞ  hw;0 ðT0 ; p0 Þ þ v0 ½p  ps ðTÞ  T0 s0 ðTÞ  sw;0 ðT0 ; p0 Þ  RT0 ln

3.6.3

xv;0 p0 ps ðT0 Þ

(3.115)

Exergy of the combustion gases in a boiler

The gases produced in the combustion in a boiler are at a pressure very close to the ambient pressure, so they can be considered as a mixture of ideal gases. By knowing the chemical exergy of each of the components, its chemical exergy is calculated as the exergy of a mixture of ideal gases, so that the standard chemical exergy is bch;0 ¼ g

g X i

xi bch;0 þ RT 0 i

g X i

xi lnxi

(3.116)

where bch;0 is the standard molar chemical exergy of component i. In this calculation, it i is necessary to make the distinction, as we have seen in the previous section, between the components that are present as stable species in the RE, such as O2 ; N2 ; CO2 , and those that are not, such as CO or unburnt hydrocarbons. In the first case, the chemical exergy is obtained by applying Eq. (3.92). In the event that the gas component is not part of the RE, either of the two methods described in Section 3.5 will be used. Using the general method, we have the following expression bch;0 g

X

X X xi 0 ¼ RT xi ln þ nEl;i bch;0 g0f ;i þ El;i þ RT xi lnxi x i;0 i3RE i;RE El 0

! (3.117)

To calculate the total exergy of the gases we add to this expression of the chemical exergy the one corresponding to the physical flow exergy obtained by applying Eq. (3.22), giving bTg ¼ bg ðT; pÞ þ bch;0 g

3.6.4

(3.118)

Exergy of humid air

The expressions obtained, which are valid for a mixture of ideal gases, will be adapted in this section to the study of psychometric processes. As we already know, in the vast majority of processes related to heating, ventilation and air conditioning (HVAC), humid air can be considered as a binary mixture of ideal gases made up of dry air and water vapour. Although dry air is itself a mixture, we will treat it as if it were a pure substance with an apparent molar mass Ma ¼ 28:9 g=mol.

Calculation of physical and chemical exergy

237

Using the subscript a for dry air and v for water vapour, according to Eq. (3.88), the specific chemical exergy of humid air is ch ch bch ha ¼ xa ba þ xv bv



 ¼ xa ga ðT0 ; xa p0 Þ  ma;0 T0 ; xa;0 p0 þ xv gv ðT0 ; xv p0 Þ  mv;0 T0 ; xv;0 p0

(3.119) and therefore bch ha


¼ RT0

xa xv þ xv ln xa ln xa;0 xv;0

 (3.120)

Let us now derive an expression for the total exergy of humid air. The total exergy, sum of the chemical and physical exergy is bTha

¼ xa ha ðTÞ  ha ðT0 Þ 

T0 s0a ðTÞ  s0a ðT0 Þ þ

xa RT0 ln xa;0



  xv p þ xv hv ðTÞ  hv ðT0 Þ  T0 s0v ðTÞ  s0v ðT0 Þ þ RT0 ln þ RT0 ln p0 xv;0 (3.121) Assuming that both cpa and cpv are constant, means that the total exergy per mole of humid air is bTha

¼ T0







 T T p xa xv xa cpa þ xv cpv  1  ln þ xv ln þ Rln þ RT0 xa ln T0 T0 p0 xa;0 xv;0 (3.122)

As we already know, it is more usual to use humidity instead of molar fractions and refer to the exergy per unit mass of dry air. Taking into account the relationships between humidity and the molar fractions of dry air and water vapour that we have seen in Section 3.2.3, we have bch ha


 0:622 u0 þ 0:622 u u u0 þ 0:622 ln þ ln ¼ RT0 u þ 0:622 u þ 0:622 u þ 0:622 u0 u þ 0:622 

(3.123) where u0 is the absolute humidity of the air in the RE. But more interesting than this formula, which allows us to calculate the exergy per mole of air, is to obtain the expression for exergy per unit mass of dry air. Dividing the previous expression by the

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Exergy Analysis and Thermoeconomics of Buildings

molar mass of humid air, Eq. (3.33), finally gives the chemical exergy of humid air per unit mass of dry air bch ha



0:622 u0 þ 0:622 ln ¼ 0:461ðu þ 0:622ÞT0 u þ 0:622 u þ 0:622
 u u u0 þ 0:622 þ ln u þ 0:622 u0 u þ 0:622

(3.124)

Therefore, the total exergy of humid air per unit mass of dry air is the result of summing the expressions in Eqs. (3.37) and (3.124), which is bTha ¼ bha þ bch ha

(3.125)

In the most general case, when in addition to saturated air, the presence of liquid or solid water must be considered, it is necessary to incorporate the values of the exergy corresponding to the condensed phases into the previous expression. Thus, with bw ; bic being the specific exergies of liquid water and ice respectively, we can consider the following cases: (a) Supersaturation case, u > us , where T > 273:15 K. The total exergy per unit mass of dry air is bTha þ ðu  us Þbw

(3.126)

(b) Supersaturation case, u > us , where T ¼ 273:15 K. In this case, a part of the excess humidity, uw can appear in the liquid phase, and the rest, uic , in the solid phase, with u ¼ us þ uw þ uic . The specific exergy is now bTha þ uw bw þ uic bic

(3.127)

(c) Supersaturation case, u > us , where T < 273:15 K. The total specific exergy per unit mass of dry air is the exergy of the air plus that of the ice, that is to say bTha þ ðu  us Þbic

(3.128)

When studying air conditioning processes from the point of view of exergy, most of the time the pressure changes are small, so that the exergy variations are due to changes in temperature and/or humidity. However, when these changes of pressure are of some importance, they affect the values of the exergy and must be taken into account. To get an idea of the order of magnitude, if we derive the total exergy with respect to pressure, Sala [28], we get dbTha 1 ¼ T0 ðRa þ uv Þ dp p

(3.129)

Calculation of physical and chemical exergy

239

Fm this expression we get that a pressure change Dp ¼ 10 mm w.c. results in a change of exergy of 0:08 kJ=kgd.a: An approximately equal change of exergy occurs for a change in absolute humidity of u ¼ 3 g=kg. Therefore, when studying air conditioning installations, the changes of exergy that take place in fans and pipes should be taken into account. The mechanical contribution to the exergy of indoor air depends on the difference in pressures Dp between the indoor and outdoor air and since that Dp is usually in the range between 100Pa, which is much smaller than p0 , that mechanical contribution can be expressed in a linear form as a function of Dp. Finally, it is worth mentioning the results of the analysis on the exergy of the air in buildings carried out by Sakulpipatsin [29]. According to his conclusions, in cold climates the contribution of the chemical exergy is insignificant compared to the physical component. Therefore, in these climates temperature can be used as the only characteristic that defines the reference state of the air, and the indoor air and that of the environment can be assumed to be completely dry air. On the other hand, chemical exergy is important in hot and humid climates, so these approximations would lead to very appreciable errors. In addition, in cold climates, an annual average value of the outdoor air temperature can be adopted in exergy balances, while this is not acceptable for temperate and humid climates.

3.6.5

Exergy of a mixture of real gases

Eq. (3.19) is only valid for the mixture of ideal gases model. Although the occasions in which this model cannot be applied will be very rare, we will make some brief comments on how to calculate exergy in real gas mixtures. In these cases, the methods used to correct the thermodynamic properties from their values in a mixture of ideal gases can be used. The RE remains the same so that only the values of the enthalpy and entropy of the mixture must be corrected. In the real mixture, we have h¼

X i

xi h i

$ s¼

P xi s i

(3.130)

i

where hi ; si are the partial molar enthalpy and partial molar entropy respectively of component i, so that bch ¼

X

 X ch xi hi  T0 si  mi;0 ¼ x i bi i

(3.131)

i

An approximate way to make these corrections is by using the generalized departure charts. In order to be able to use these thermodynamic diagrams, a rule is required to define a pseudo-critical temperature and pressure of the mixture. Kay’s rule is one of the most used due to its remarkable simplicity. According to this rule Tc0 ¼

X xi Tci i

p0c ¼

X ı

xi pci

(3.132)

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Exergy Analysis and Thermoeconomics of Buildings

  Using the reduced properties Tr ¼ T TC0 , pr ¼ p p0C , these departures can be read from the enthalpy departure and the entropy departure charts. When these corrections are incorporated into the general equation of the exergy, we get the final expression for the calculation of the exergy of a mixture of real gases. It is also possible to program this correction using virial equations generalized with Tr and pr as variables although, in most cases, the direct use of thermodynamic departure diagrams is faster and sufficiently accurate.

3.6.6

Chemical exergy of fuels

When the substance under study does not exist as a stable species in the RE, we have seen that one way to calculate its chemical exergy is by considering a reaction that allows for the reduction of that substance to some constituents (co-reactants and products) so that each of them are substances that form part of the RE. Using this method that we have called alternative, we will find an expression that facilitates the calculation of the standard chemical exergy of fuels. Let us consider the hydrocarbon Ca Hb as an example. The chemical reaction with reference substances that are part of the RE which form reaction products that are also constituents of the RE is the complete combustion reaction, that is
 b b Ca Hb þ a þ O2 /aCO2 þ H2 O 4 2

(3.133)

Using Eq. (3.105) we have bch;0 Ca H b


  b ch;0 b ch;0 ch;0 ¼ DG þ abCO2 þ bH2 O  a þ bO2 2 4 0

(3.134)

where DG0 is the Gibbs function of the complete combustion reaction and therefore b DG0 ¼ ag0f ;CO2 þ g0f ;H2 O  g0f ;Ca Hb 2

(3.135)

Depending on the calorific value of the fuel, developing the above expression, the chemical exergy of the fuel can be expressed as follows bch;0 Ca H b


  b 0 b0 0 ¼ HHVCa Hb  T þ a þ sO2  asCO2  sH2 O 4 2
   b ch;0 b ch;0 þ abch;0 CO2 þ 2bH2 O  a þ 4 bO2 

0

s0Ca Hb

(3.136)

Calculation of physical and chemical exergy

241

By generalizing for any fuel, the Gibbs function of reaction can also be written ! P X ni s0i;P  s0fuel  nO2 s0O2 ;0 DG0 ðT0 ; p0 Þ ¼ HHVfuel þ T 0 (3.137) i

where ni is the number of moles of substance i per mole of fuel and s0i;P refers to the entropy of component i in mixture P, that is, it includes the entropy term of the mixture. Since the reference substances of the RE that participate in the combustion reactions form a mixture of ideal gases in the atmosphere, we can write the following expression bch;0 fuel

¼ HHVfuel  T  RT 0

P X i

0

s0fuel

þ

nO2 s0O2



P X i

!

! ni s0i (3.138)

ni lnxi;0  nO2 lnxO2 ;0

The calculation of the standard chemical exergy of a fuel requires, therefore, the use of thermo-chemical data, such as the tables of enthalpies of formation and absolute entropies, or the enthalpies of formation and the Gibbs function of formation, which are available for standard conditions. In Eq. (3.136) the greatest difficulty is found in the absolute entropy value of the fuel s0fuel , since it is only known for those fuels that are chemically uniform. Therefore, the exact calculation of the exergy of the solid and liquid fuels normally used, such as gas oils, fuel oils, wood, etc. can only be carried out if its chemical composition is known. Table 3.2 tabulates the values of the chemical exergy of some fossil fuels and different types of biomass. For the calculation of fuel exergy, Baehr and Schmidt [30] proposed using saturated air at temperature T0 and pressure p0 as RE, so that the molar fraction of water vapour in the atmosphere will bexv0 ¼ ps ðT0 Þ=P0 . In general, water forms part of the combustion products and at room temperature can be in the liquid or vapour phase. In this way, by adopting the atmosphere model according to Baehr, the calculation of the exergy of fuels is greatly simplified, since as the exergy of liquid water and that of water vapour in the atmosphere equal zero, it will not be necessary to worry about them, even when they appear among the combustion products. On the other hand, taking into account the average state of atmospheric air, other authors have proposed a state of air with 30% relative humidity as the RE. Apart from the simplification in the calculations, from a strictly thermodynamic point of view, the Baehr proposal is presented as more reasonable. We have already said that in the application of exergy to buildings, the ambient air state is chosen as RE, which varies over time. The air, in general, is not saturated, so that the exergy of water vapour and liquid water under ambient conditions is not zero. Thus, Szargut and Styrlyska [31] consider that the relative air humidity in the standard RE is 70%, meaning a value of 0:9 kJ=mol for the exergy of liquid water.

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Exergy Analysis and Thermoeconomics of Buildings

Table 3.2 Chemical exergy of some fuels. Coal

bch;0 c (kJ/kg)

48%,6%(C) 3%,5%(H2 ) 12%(O2 ) 0%,7%(N2 ) 0%,5%(S) 28%,9%(H2O) 5%,8%(Ash)

21,699

75%(C) 5%,2%(H2 ) 7%(O2 ) 2%(N2 ) 1%(S) 1%(H2O) 3%,2%(Ash)

32,982

Oil

bch;0 oil (kJ/kg)

Crude oil / 90%(C) 3%,3%(H2 ) 3%(O2 ) 0%,8%(N2 ) 0%,9%(S) 2%(Ash)

35,224

Heavy fuel oil / 83%,7%(C) 12%,7%(H2 ) 1%,2%(O2 ) 1%,7%(N2 ) 0%,7%(S) 0%(Ash)

45,666

Natural Gas

bch;0 ng (kJ/kmol)

77%,4% (CH4 ) 11%,7%(C2 H6 ) 8%,5%(C3 H8 ) 1%,3%(C4 H10 ) 1%,1% (N2 )

1,0436$106

60%,1% (CH4 ) 14%,8%(C2 H6 ) 13%,4%(C3 H8 ) 4%,2%(C4 H10 ) 7%,5% (N2 )

1,1331$107

Biomass

HHV (kJ/kg)

bch;0 bio (kJ/kg)

Eucalyptus bark

18,352

19,386

Wood

19,841

20,803

Sawdust

19,629

20,601

Bamboo whole

19,685

20,750

Rice straw

15,511

16,453

Walnut shells

19,430

20,409

14,049

15,327

Biomass mixture

19,274

20,205

Woodestraw residue

18,795

19,713

Classic biomass

Herbaceous and agricultural biomass

Animal biomass Chicken litter

Mixture of biomass

From Eq. (3.138) Szargut and Styrylska calculated the exergy of numerous fuels, whose calorific powers and entropy were known. With the results obtained, they established correlation formulas based on their mass relationships (or their corresponding atomic relationships). They studied three types of fuels: solids without sulphur, solids with sulphur and liquids. In this way, from an elementary analysis and through the

Calculation of physical and chemical exergy

243

application of correlation formulas, the exergy of a fuel can be calculated  with a good approximation. They obtained correlations expressing the relation bch;0 LHV according to the ratios H=C; O=C; N=C. The equations that express this relationship between the exergy and the calorific power for different groups of organic substances and different types of fuels can be found in Szargut, Morris and Steward [15]. In short, the chemical exergy of fuels can be obtained from the standard chemical exergy tables whenever the composition of the fuel is known. However, many solid and liquid fuels are multicomponent solutions of components often unknown, so the exact calculation of the exergy of these fuels is not possible. In that case, the correlations are used, so that the exergy of the fuel is related to the LHV according to the expression bch;0 fuel ¼ w LHVfuel

(3.139)

where w is the correlation coefficient. Thus, for natural gas, we have an average value of 1.04, Kotas [16]. More recently values of different fuels have been obtained from the HHV. Thus, it is worth noting the values obtained for the chemical exergy of carbons, Bilgen and Kaygusuz [32]. Given the interest of biomass as a renewable fuel, recently, values of the chemical exergy of different types of biomass have been obtained for agricultural, forest and industrial residuals, Saidur et al. [33], Eboh et al. [34]. Finally, the work of Valero and Valero [35] is also worth highlighting with interesting reflections on the use of minerals and natural resources, through an analysis based on exergy. An alternative to this thermo-chemical data is the use of the base enthalpy, base entropy and base Gibbs potential. The base enthalpy of a compound is the enthalpy with respect to the stable components that make up the RE, that is to say, with respect to the dead state. Therefore, if a compound exists as a stable component in the reference atmosphere, its base enthalpy is zero by definition. In all other cases, its value will be positive. To understand the meaning of these properties, consult the work of Kotas [16].

3.6.7

Examples

Example E 3.12. Calculate the chemical exergy of 80 kg of lime, which has the following composition as a percentage by mass: 91% CaO, 4% MgO, 3% CO2 and the rest SO3. Solution According to the composition and using the standard chemical exergy tables collected in Annex C of the book by Kotas [16], which presents molar values of chemical exergy, we have ch;0 ch;0 ch;0 ch;0 bch;0 lime ¼ yCaO bCaO þ yMgO bMgO þ yCO2 bCO2 þ ySO3 bSO3

119; 620 59; 170 20; 140 225; 070 þ 0:04 þ 0:03 þ 0:02 56:08 40:31 44:01 80:06 kJ ¼ 2; 069:72 kg

¼ 0:91

244

Exergy Analysis and Thermoeconomics of Buildings ch;0 Bch;0 lime ¼ mlime blime ¼ 165; 577:7 kJ

Example E 3.13. Calculate the chemical exergy of 60 kg of cement, which has the following composition as a percentage by mass: 65% CaO, 21% SiO2, 5% Al2O3, 6% Fe2O3, 1.8% SO3 and the rest is MgO. Solution In the same way, as in Example E 3.12, we have ch;0 ch;0 ch;0 ch;0 ch;0 bch;0 cem ¼ yCaO bCaO þ ySiO2 bSiO2 þ yAl2 O3 bAl2 O3 þ yFe2 O3 bFe2 O3 þ ySO3 bSO3

þ yMgO bch;0 MgO 119; 620 3; 280 204; 270 20; 370 þ 0:21 þ 0:05 þ 0:06 56:08 60:06 102 159:70 225; 070 59; 170 þ 0:012 þ 0:018 80:06 40:31 kJ ¼ 1; 566:3 kg ¼ 0:65

and so ch;0 Bch;0 cem ¼ mcem bcem ¼ 93; 980:0 kJ

A compressed air bottle of 0.2 m3 contains air at 8.1 kgf/cm2, with a relative humidity of 17% and temperature 160 C. By exchanging heat with the atmosphere which is at a pressure of 1 bar, the bottle progressively cools until it reaches the ambient temperature of 15 C. Knowing that the ambient air has a relative humidity of 50%, what is:

Example E 3.14.

(a) The absolute humidity, mass of dry air and mass of vapour of the air in the bottle in the initial conditions. (b) The temperature at which the condensation starts, mass of condensed water and final pressure in the bottle. (c) The heat exchanged by the air in the bottle with the atmosphere. (d) The change of exergy of the air in the bottle. (e) The change of exergy and heat exchanged by the material of the bottle, considering that its heat capacity is constant and equal to 4.5 kJ/K (f) The total exergy destruction.

Solution (a) Since the vapour pressure at 120 C is ps ð160 CÞ ¼ 6:178 bar, the absolute humidity of the air inside the bottle is ps ð160 CÞ gv ¼ 95$103 ¼ 95 u1 ¼ 0:622 p kg d.a.   ps ð160 CÞ 41

Calculation of physical and chemical exergy

245

To find the mass of vapour we determine the partial pressure of the vapour and apply the equation of state of a mixture of ideal gases pv;1 ¼ f1 p ¼ 1:35 bar

/ mv;1 ¼

pv;1 V ¼ 135:0 g Rv T 1

so that the mass of dry air is ma ¼

mv;1 ¼ 1:42 kg u1

(b) Until the condensation starts, the water vapour is cooled at constant volume, so that at temperature T the partial pressure of the vapour is pv ¼ 1:35T=433. With the tables of the vapour pressure we are decreasing that temperature T until it matches the saturation pressure T ¼ 383Kð110 CÞ T ¼ 273 Kð100 CÞ

pv ¼ 1:19 bar pv ¼ 1:16 bar

ps ð110 CÞ ¼ 1:43 bar

/ pv < ps ð110 CÞ

ps ð100 CÞ ¼ 1:013 bar

/ pv > ps ð110 CÞ

We see that the condensation takes place between 100 and 110 C T ¼ 378 Kð105 CÞ pv ¼ 1:18 bar

ps ð105 CÞ ¼ 1:208 bar

/ pv < ps ð105 CÞ

The condensation takes place between 100 and 105 C. Let us look at 104 C T ¼ 377Kð104 CÞ

pv ¼ 1:17 bar

ps ð104 CÞ ¼ 1:17 bar

/ pv ¼ ps ð104 CÞ

Accordingly, the condensation starts at 104 C. Calculating the final vapour mass, for which we determine the final pressure at 15 C. T ¼ 288Kð15 CÞ pv;2 ¼ ps ð15 CÞ ¼ 17:04 mbar verifying the equation pv;2 V 0 ¼ mv;2 Rv T2 where V 0 is the volume occupied by the humid air in state 2, that is, the volume of the bottle V

 minus the volume occupied by the condensate, that is, V 0 ¼ V  139:5  mv;2 106 , assuming that the specific volume of water is 103 m3 =kg. Taking this relation to the previous equation we can calculate the final vapour mass 

  8:314$103 17:04  102 0; 2  139:5  mv;2 106 ¼ mv;2 288 18:06 with the final absolute humidity being u2 ¼

mv;2 gv ¼ 1:70 kg d.a. ma

/ mv;2 ¼ 2:5 g

246

Exergy Analysis and Thermoeconomics of Buildings

It is clear that the effect of having considered the volume of the condensate is totally negligible. Therefore, the condensed water is mw ¼ mv;1  mv;2 ¼ 133:3 g The final pressure in the bottle is the sum of the partial pressure of the dry air plus the partial pressure of the vapour. Since the initial partial pressure of the dry air is pa1 ¼ 6:59 bar, we have T2 p2 ¼ pa;2 þ pv;2 ¼ pa;1 þ pv;2 ¼ 4:40 bar T1 (c) The heat exchanged by the air in the bottle with the atmosphere is the change of internal energy, since the process is isochoric. We will express the change of internal energy as a function of the change of enthalpy, which is the thermodynamic property that appears in the psychometric diagrams. We have DU ¼ ma ðu2  u1 Þ ¼ ma fh2  h1  ½Ra ðT2  T1 Þ þ Rv ðu2 T2  u1 T1 Þg þ mw uw Assuming that for dry air cp;a ¼ 1:004 kJ=kg K, for water vapour cp;v ¼ 1:86 kJ=kg K and the enthalpy of vapourization at the triple point is 2; 500 kJ=kg, the change of enthalpy of the air is   ma ðh2  h1 Þ ¼ ma cp;a ðT2  T1 Þ þ 2; 500ðu2  u1 Þ þ cp;v ðu2 T2  u1 T1 Þ ¼ 645:3 kJ giving DU ¼ 97:7 kJ Therefore, the heat transferred to the atmosphere is Q ¼ 97:7 kJ (d) We now calculate the change of exergy. According to Eq. (3.37), the physical flow exergy in state 1 is 


 T1 p1 ðT1  T0 Þ  T0 ln þ 0:461ðu1 þ 0:622ÞT0 ln b1 ¼ cp;a þ u1 cp;v T0 p0 kJ ¼ 229:7 kg d.a. and therefore a1 ¼ b1  p1 v1 ¼ b1  ðRa þ u1 Rv ÞT1 ¼ 82:1

kJ kg d.a.

while in state 2, since the temperature T2 ¼ T0 is b2 ¼ 0:461ðu2 þ 0:622ÞT0 ln

p2 kJ ¼ 122:7 p0 kg d.a.

Calculation of physical and chemical exergy

247

so that a2 ¼ b2  ðRa þ u2 Rv ÞT2 ¼ 36:9

kJ kg d.a.

For the calculation of the chemical exergy, we previously need to know the absolute humidity of the atmospheric air. According to Eq. (3.39) u0 ¼ 0:622 p0 40

ps ð15 CÞ  ps

ð15 CÞ

¼ 51:6

gv kg d.a.

Applying Eq. (3.124), the chemical exergy in state 1 is  0:622 u0 þ 0:622 bch ln ¼ 0:461T ðu þ 0:622Þ 0 1 1 u1 þ 0:622 u1 þ 0:622
 u1 u1 u0 þ 0:622 þ ln u1 þ 0:622 u0 u1 þ 0:622 kJ ¼ 1:7 kg d.a. and that of state 2 bch 2 ¼ ð0:461  288  0:624Þ


  0:622 0:674 0:002 0:002 0:674 kJ ln þ ln ¼ 5:5 0:624 0:624 0:624 0:052 0:624 kg d.a.

Therefore, the change of exergy of the air is  ch ¼ 58:7 kJ  a  b DA ¼ ma a2 þ bch 1 ;2 1 (e) The change of the internal energy of the material of the bottle is DUb ¼ Cb ðT2  T1 Þ ¼ 652:5 kJ so the heat given by the bottle is Q ¼ 652:5 kJ The change of exergy of this material is DAb ¼ DUb  T0 DSb ¼ Cb ðT2  T1 Þ  T0 Cb ln

T2 ¼ 124:0 kJ T1

(f) Since the final condensate is at ambient temperature its exergy is zero. Consequently, from an exergy balance, we have D ¼ DA  DAb ¼ 182:7 kJ

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Exergy Analysis and Thermoeconomics of Buildings

Example E 3.15. Determine the minimum work that would be necessary to cool the dry air of a hermetically closed room with V ¼ 35 m3 from the environmental conditions P0 ¼ 1 bar and T0 ¼ 20 C to 10 C. Compare this result with the minimum work that would be required to heat said air to 50 C. Assume that the air is a perfect gas of cp ¼ 7 R/2. Solution The minimum work to be done is to increase the exergy of the air from the initial state to a state in which the volume is the same ðVf ¼ V0 Þ and the temperature is 10 C. Since the initial state is the environmental state, the increase in exergy coincides with its final physical exergy. Therefore, we have

W min ¼ Uf  U0  T0 ðSf  S0 Þ ¼ Af Calculating the number of moles of dry air and the final pressure, when the temperature is 10 C N¼

p0 V ¼ 1; 436:8 mol RT0

The final pressure is pf ¼

NRTf ¼ 0:9 bar V

Since cv ¼ 52 R, the minimum work is 
 Tf pf W min ¼ N cv ðTf  T0 Þ  T0 cp ln  Rln ¼ 58:6 kJ T0 p0 If we heat the air to 50 C the final pressure is pf ¼ 1:1 bar and the minimum work is
 5 7 323  ln1; 1 103 ¼ 1; 436:8  8:314 ð323  293Þ  293 ln 2 2 293 

W

min

¼ 35:4 kJ As we can see, this minimum work is smaller, that is, the exergy of the dry air at 50 C is lower than at 10 C. The difference in air temperatures with respect to that of the environment is in both cases 30 C; however, cold air has more exergy. Indeed, it is necessary to provide more exergy to extract a heat flow of 895.9 kJ (the change of internal energy of the air) and to cool the air to 10 C than that needed to heat the air up to 50 C. We see how, from a thermodynamic point of view, cold is worth more than heat.

Calculation of physical and chemical exergy

249

Consider humid air that is at 1 atm and 21 C, its dew point temperature The atmospheric air is at 10 C and 970 mbar of total pressure, with a being relative humidity of 50%. What are:

Example E 3.16.

10 C.

(a) The absolute humidity and humid air density. (b) Relative humidity. (c) The adiabatic saturation temperature of the air, that is to say, temperature of the air when reaching thermodynamic equilibrium with water in an adiabatic way. (d) The exergy of the air.

Solution (a) If the temperature of the dew point is 10 C, it means that at that temperature the air is saturated with moisture. Therefore pv ¼ ps ð10 CÞ ¼ 12:27 mbar. Consequently, the absolute humidity of the air is u¼

mv pv gv ¼ 0:622 ¼ 7:6 kg d.a. ma p  pv

The density of the humid air is 9¼

ma þ mv ma þ mv p 1þu p kg ¼ ¼ 1:173 3 ¼ m V ma Ra þ mv Rv T Ra þ uRv T

(b) The relative humidity of the air is f¼

pv ¼ 50:3% ps ð21 CÞ

(c) The adiabatic saturation temperature is obtained from the energy balance in an adiabatic saturation chamber like the one in Fig. E.3.3 with 1 being the state of the air at the entrance to the chamber and s the state of saturation at the exit. Expressing T in  C the energy balance reads

Figure E3.3 Adiabatic saturation chamber.

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Exergy Analysis and Thermoeconomics of Buildings

 ha;1 þ u1 hv;1 þ ðus  u1 Þcw Tsa ¼ ha;s þ us r0 þ cp;v Tsa and therefore

 

cp;a þ u1 cp;v ðT1  Tsa Þ ¼ ðus  u1 Þ cp;v Tsa þ r0  cw Tsa

where r0 ¼ 2; 500 kJ=kg is the enthalpy of vapourization at 0 C. By removing the adiabatic saturation temperature Tsa, we have Tsa ¼ T1 



ðus  u1 Þ cp;v Tsa þ r0  cw Tsa ðus  u1 ÞrðTsa Þ ¼ T1  cp;a þ u1 cp;v cp;a þ u1 cp;v

This equation can be solved by successive approximations, having the values of the enthalpy of vapourization of water. For example, for Tsa ¼ 20 C, looking in the tables for the saturation pressure at that temperature and the enthalpy of vapourization (r), Tsa ¼ 3.98 C is obtained; obviously, very far from the supposed Tsa. For Tsa ¼ 15 C, operating in the same way, the value Tsa ¼ 13.69 C is obtained, still a value far from the assumed value. For Tsa ¼ 14 C we get a value Tsa ¼ 14.7 C, now close to the assumed initial value. Finally, we adopted as a sufficiently approximate solution Tsa ¼ 14:5 C. (d) Finally to calculate the total exergy of air we use Eq. (3.37) which we developed in Section 3.2.3 for the calculation of physical flow exergy and Eq. (3.124) for the chemical exergy. The physical exergy per unit mass of dry air is


 294 b1 ¼ 1:004 þ 7:6:103 :1:86 21  10  283ln 283 

1013 3 þ 0:461 7:6:10 þ 0:622 283ln 970 kJ ¼ 3:77 kg d.a. As the absolute humidity of atmospheric air is 40 ¼

pv ps ð10 CÞ

/ pv ¼ 61 mbar

/

u0 ¼ 42

gv kg d.a.

the chemical exergy of the humid air under consideration is
  0:622 0:666 0:0076 7:6 0:666 kJ ln þ ln ¼ 2:85 bch 1 ¼ 0:461:283:0:63 0:630 0:630 0:623 42 0:630 kg d.a. Therefore, the total exergy of the humid air is bT1 ¼ b1 þ bch 1 ¼ 6:62

kJ kg d.a.

Calculation of physical and chemical exergy

251

An air flow of 1200 kg/h at 2 C with a relative humidity of 70% is taken from the outside, passing it through a radiator where it is heated up to 12 C. This air is then mixed with another air flow saturated at 20 C and in such a proportion the mass flow of saturated air is double. What are

Example E 3.17.

(a) The absolute and relative humidity of the air at the radiator outlet, as well as the heat given by it. (b) The change of the exergy of the air between the radiator inlet and outlet. (c) The temperature and relative humidity of the air resulting from the mixture. (d) The exergy of the air resulting from the mixture.

Assume that the total pressure is at all times constant and equal to 1 atm. Solution Fig. E3.4 shows schematically the passage of the air flow through the radiator, where it is heated from the 0 state to the temperature of 12 C, state 1, and the subsequent mixing with air at 20 C, state 2, to form a resultant flow in state 3.

Figure E3.4 Diagram of the passage of the air flow through the radiator. (a) From the saturated water tables we see that ps ð2 CÞ ¼ 6:5 mbar and with this value and since f0 ¼ 0:70 we can calculate the absolute humidity of the outside air, state 0 ps ð2 CÞ gv u0 ¼ 0:622 p ¼3 kg d.a.   ps ð2 CÞ 40 The absolute humidity in state 0 is the same as in 1 and since ps ð12 CÞ ¼ 14:03 mbar, we get ps ð12 CÞ u0 ¼ u1 ¼ 0:622 p  ps ð12 CÞ f1

/ f1 ¼ 0:35

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Exergy Analysis and Thermoeconomics of Buildings

In the Carrier diagram we can read the following enthalpy values: T0 ¼ 2 C; T1 ¼ 12 C;

HR0 ¼ 0:7

/ h0 ¼ 10

kJ kg d.a.

HR1 ¼ 0:35 / h1 ¼ 21

kJ kg d.a.

Calculating the mass flow of dry air m_ 0 ¼ m_ a0 ð1 þ u0 Þ / m_ a0 ¼ m_ a1 ¼

m_ 0 kg kg ¼ 1; 196:4 ¼ 0:332 h s 1 þ u0

The heat given by the radiator is the increase in enthalpy of the air and therefore Q_ ¼ m_ a ðh1  h0 Þ ¼ 3:65 kW (b) As the composition of the air is constant, there is no change of humidity, so only the physical exergy changes. Assuming a specific heat cp;a ¼ 1:004 kJ=kg K for dry air and cp;v ¼ 1:89 kJ=kg K for vapour and that the pressure is constant, this change of exergy per kg of dry air, is 
285 kJ ¼ 0:18 Db ¼ b1 ¼ ð1:004 þ 0:003:1:89Þ 12  2  275ln 275 kg d.a. and therefore DB_ ¼ m_ a b1 ¼ 0:06 kW (c) As ps ð20 CÞ ¼ 23:67 mbar, the humidity of the air saturated, air in state 2, is u2 ¼ 0:622

ps ð20 CÞ gv ¼ 15 p  ps ð20 CÞ kg d.a.

According to the proportion of flow of the statement, we have m_ 2 ¼ m_ a2 ð1 þ u2 Þ ¼ 2m_ 0

/

m_ a2 ¼

2m_ 0 kg d.a. ¼ 0:657 s 1 þ u2

In the Carrier diagram we read the enthalpy of state 2, where h2 ¼ 57 kJ=kg d.a. To calculate the resulting state 3 we undertake a balance of mass and energy in the mixture, obtaining the following equations m_ a2 u2 þ m_ a1 u1 ¼ ðm_ a2 þ m_ a1 Þu3

/

u3 ¼ 11

gv kg d.a.

Calculation of physical and chemical exergy

253

The balance of energy in the mixture of the two flows gives m_ a2 h2 þ m_ a1 h1 ¼ ðm_ a2 þ m_ a1 Þh3

/

h3 ¼ 44:9

kJ kg d.a.

Looking at the Carrier diagram the intersection point of the isoline u3 ¼ 0:0015 and h3 ¼ 44:9 kJ=kg d.a. are read for this state T3 ¼ 17 C and f3 ¼ 0:85. (d) The exergy of the air in state 3 is the sum of its physical and chemical exergy. The physical exergy, per unit mass of dry air, is 
290 kJ ¼ 0:40 b3 ¼ ð1:004 þ 0:011:1:89Þ 17  2  275ln 275 kg d.a. while the chemical exergy is 0:622 u0 þ 0:622 ln bch 3 ¼ 0:461T0 ðu3 þ 0:622Þ u3 þ 0:622 u3 þ 0:622
 u3 u3 u0 þ 0:622 ln þ u3 þ 0:622 u0 u3 þ 0:622 kJ ¼ 0:78 kg d.a. Thus the total exergy of the air flow in state 3 is

 B_ 3 ¼ m_ a3 b3 þ bch 3 ¼ 1:17 kW

Example E 3.18.

In an adiabatic combustion chamber and in a stationary regime, the combustion of a butane flow of 0.2 kg/s takes place with the amount of air which is strictly necessary. Both air and butane enter the chamber at an ambient temperature of 25 C and an ambient pressure of 1 bar. Assuming that there is no heat loss in the combustion chamber, determine: (a) The adiabatic combustion temperature. (b) The total exergy of the butane and that of the combustion gases. (c) The exergy destruction in the chamber.

Solution. (a) Fig. E3.5 shows a diagram of the chamber in which the complete combustion of the butane takes place. C4 H 10ðgÞ þ

13 O 2 2ðgÞ

/ 4CO2ðgÞ þ 5H 2 OðgÞ

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Exergy Analysis and Thermoeconomics of Buildings

Figure E3.5 Diagram of the chamber.

For each mole of butane, 6.5 mol of O2 are needed, which will be accompanied by 24.45 mol of N2 . In the complete combustion, per mole of butane, 4 mol of CO2 , 5 mol of vapour H2 O and 24.45 mol of N2 appear in the combustion products. The minimum number of moles of air necessary to carry out the complete combustion of the butane is thus 6:5=0:21 ¼ 30:95. To calculate the adiabatic combustion temperature, we undertake an energy balance in the adiabatic combustion chamber, giving DH ¼ HP  HR ¼ 0 0

 



HP  HP0 þ DH 0  HR  HR0 ¼ 0

 where HP  HP0 is the change  of the products from the standard state to the state

of enthalpy at the outlet of the chamber, HR  HR0 is the change of enthalpy of the reactants from the standard state to the state at the entrance to the chamber and DH 0 is the reaction enthalpy of the complete combustion reaction. These changes of enthalpy are represented in the H-T diagram of Fig. E.3.6 below.

Figure E3.6 Representation of the changes of enthalpy.

Calculation of physical and chemical exergy

255

Since the reactants enter the chamber at precisely 25 C, we have that HR  HR0 ¼ 0. The enthalpy of reaction is DH 0 ¼ 4h0f ;CO2 ðgÞ þ 5h0f ;H 2 OðgÞ  h0f ;CH 4 ðgÞ ¼ 3:078; 1 kJ On the other hand HP  HP0 ¼ 4½hCO2 ðTc Þ  hCO2 ð298 KÞ þ 5½hH 2 OðTc Þ  hH 2 Oð298 KÞ þ 24:45½hN 2 ðTc Þ  hN 2 ð298 KÞ From the balance of energy equation we have left 4½hCO2 ðTc Þ  hCO2 ð298 KÞ þ 5½hH 2 OðTc Þ  hH 2 Oð298 KÞ þ 24:45½hN 2 ðTc Þ  hN 2 ð298 KÞ ¼ 3; 078:07 kJ In this equation the unknown is the combustion temperature Tc . By using the ideal gas thermodynamic data, the above equation can be prepared, so that it takes the following form 4hCO2 ðTc Þ þ 5hH 2 OðTc Þ þ 24:45hN 2 ðTc Þ ¼ 3; 377 By successive approximations, we can calculate the temperature Tc . Thus, naming the member on the left of the equality as A(T), from the values for ideal gases we have that for T ¼ 2450 K, A(T) ¼ 3345.7 kJ. Increasing the value to T ¼ 2500 K gives A(T) ¼ 3427.2 KJ, so the temperature Tc is between these two values. The result that is finally obtained is Tc ¼ 2; 480 K (b) The physical exergy of butane is zero and its standard chemical exergy, according to the Petela tables, is 2818.9 kJ/mol. Therefore, the exergy of butane at the entrance to the chamber is ch B_ C4 H 10 ¼ N_ C4 H 10 bch C 4 H 10 ¼ 9; 720:3 kW

Using the Szargut tables, for every mole of butane that enters the chamber, the standard chemical exergy of the combustion gases is ch;0 ch;0 ¼ 4bch;0 bch;0 g CO2 þ 5bH 2 OðgÞ þ 24:25bN 2 ¼ 155:8

kJ mole of butane

and therefore the chemical exergy of the combustion gases, per unit of time, is ch B_ g ¼ N_ C4 H 10 bch g ¼ 537:4 kW

256

Exergy Analysis and Thermoeconomics of Buildings

To calculate the physical exergy of these gases, taking into account the high temperature, we use polynomial functions up to the first power for the specific heats of the exhaust components. Applying Eq. (3.23) gives Z bg ¼

2480 



 4 28:16 þ 0:167$102 T þ 5 32:24 þ 0:192$102 T

290



þ 24:45 28:90  0:157$102 T dT  298 Z

2480 298







 4 28:16þ0:167$102 T þ5 32:24 þ 0:192$102 T þ24:45 28:900:157$102 T dT T ¼ 1; 467:6

kJ mole of butane

Consequently, the physical exergy associated with the flow of combustion gases is B_ g ¼ N_ C4 H 10 bg ¼ 5; 060:7 kW (c) Carrying out an exergy balance in the combustion chamber we have ch ch B_ C4 H 10 ¼ B_ g þ B_ g þ D_

so that the exergy destruction is D_ ¼ 4; 122:2 kW which represents 42.4% of the exergy supplied.

Superscripts 8 ’,” yi

Standard state Saturated liquid and saturated vapor Partial molar property

Subscripts m a, ha v w 0 s R, P

Mixture Dry air, humid air Water vapor Liquid water Ambient state Saturation parameters Reactants and products of reaction

Calculation of physical and chemical exergy

id C

257

Ideal state Compound

Symbols r V T t h s m_ c cp cp;i cv U Q W Wu Sg b bch bT b bD f R F u f mi Mi Ni xi yi G gi , mi gfi

Density Volume Temperature Time Specific enthalpy Specific entropy Mass flow rate Specific heat of a liquid Specific heat at constant pressure Molar specific heat at constant pressure of component i Specific heat at constant volume Internal energy Heat Work Useful work Entropy generated Specific physical flow exergy Specific chemical exergy Total specific exergy Exergy of the ideal gas state at the same p and T Departure exergy Correlation coefficient Universal gas constant Quality factor Absolute humidity Relative humidity Mass of component i Molar mass of component i Number of moles of component i Molar fraction of component i in a mixture Mass fraction of component i in a mixture Gibbs function Partial Gibbs function of component i, chemical potential Gibbs function of formation of substance i

References [1] Y.A. C¸engel, M.R. Boles, Thermodynamics: An Engineering Approach, McGraw-Hill, New York, 2011.

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Exergy Analysis and Thermoeconomics of Buildings

[2] J.M. Sala, L.M. L opez, Termodynamics For Engineers, Impress Group, University of La Rioja, 1997 (in Spanish). [3] T.D. Eastop, A. Mcconey, Applied Thermodynamics for Engineering Technologists, Longman, London, 1986. [4] G. Reistad, Availability: Concept and Applications, PhD Thesis, University of Wisconsin, United States, 1970. [5] F. Bonsjakovoc, K.F. Knoche, Technical Thermodynamics, seventh ed., 1989. Darmstadt, Germany. [6] R.A. Gaggioli, P.J. Petit, Use the second Law first, Chemtech 7 (1977) 496e506. [7] M.V. Sussman, Choosing A Reference Environment State for Available Energy Computations, 72nd Annual Meeting of the Institute of Chemical Engineers, 1979. [8] J. Ahrendts, Reference states, Energy 5 (1980) 666e677. [9] A.B. Ronov, A.A. Yaroshevsky, A new model for the chemical structure of the earth’s crust, Geochemistry International 13 (1976) 89e121. [10] M.A. Rosen, I. Dincer, On exergy and environmental impact, International Journal of Energy Research 21 (7) (1997) 643e654. [11] A. Valero, A. Valero, Thermodynamic rarity and the loss of mineral wealth, Energies 8 (2015) 821e836. [12] C. Diederichsen, Reference Environments for Calculating Chemical Exergies, Tech. Rep. 50, Fortschr.-Ber. VDI Reihe 19, VDI Verlag, Dusseldorf, 1999 (in German). [13] W. Van Gool, Thermodynamics of Chemical References for Exergy Analysis, Florence World Energy Research Symposium, Editorial SGE, vols. 949e957, 1997. Florence, Italy. [14] J. Szargut, Chemical exergies of the elements, Applied Energy 32 (1989) 269e286. [15] J. Szargut, D.R. Morris, F.R. Steward, Exergy Analysis of Thermal, Chemical and Metallurgical Processes, Springer-Verlag, Berlin, 1988. [16] T.J. Kotas, The Exergy Method of Thermal Plant Analysis, third ed., Exergon Publishing Co., London, 2012. [17] H. Kameyama, K. Yoshida, S. Yamauchi, K. Fueki, Evaluation of reference exergies for the elements, Applied Energy 11 (1982) 69e83. [18] L. Ranz, Analysis of Exergy Costs of the Earth’s Mineral Wealth. Its Application to the Sustainability Management, Ph.D. thesis., University of Zaragoza, 1999 (in Spanish) [19] ECBS Annex 49 final Report, in: H. Torio, D. Schmidt (Eds.), Low Exergy Systems for High-Performance Buildings and Communities, Fraunhofer IBP, 2011. [20] P. Sakulpipatsin, Exergy Efficient Building Design, Ph.D. thesis., Delft University of Technology, The Netherlands, 2008. [21] J.M. Sala, Termodynamics of Multicomponent Systems, Editorial Service of the University of the Basque Countryo, Bilbao, 2016 (in Spanish). [22] D.W. Green, R.H. Perry, Perry’s Chemical Engineers’ Handbook, eighth ed., McGrawHill, New York, 2008. [23] H.B. Callen, Thermodynamics and Introduction to Thermostatics, second ed., J. Wiley, 1985. [24] A.N. Krestovnikov, V.N. Vigdorovich, Chemical Thermodynamics, editorial Mir, Moscow, 1980 (in Spanish). [25] K. Denbigh, Chemical Equilibrium, fourth ed., Editorial AC, Madrid, 1985 (in Spanish). [26] I.N. Levine, Physicalchemistry, McGrawHill Latinoamericana, Bogota, 1981 (in Spanish). [27] R. Ribero, M. Garfias, Standard chemical exergy of elements updated, Energy 31 (2006) 3310e3326. [28] J.M. Sala, Termodynamics of Fluids and the Exergy Method of Analysis, University of the Basque Country, Bilbao, 1987 (in Spanish).

Calculation of physical and chemical exergy

259

[29] P. Sakulpipatsin, Exergy Efficient Building Design, PhD Thesis, University of Delft, The Netherlands, 2008. [30] H. Baehr, E. Schmidt, Definition and calculation of the fuels exergy, 19, BrennstoffW€arme-Kraft, 1967 (in German). [31] J. Szargut, T. Styrylska, Approximate calculation of the fuels exergy, Brennstoff W€arme Kraft 16 (1964) 589e596 (in German). [32] S. Bilgen, S.K. Kaygusuz, The calculation of chemical exergies of coal-based fuels by using the higher heating values, Applied Energy 85 (2008) 776e785. [33] R. Saidur, G. Boroumandjazia, S. Mekhilef, H.A. Mohammed, A review on exergy analysis of biomass based fuels, Renewable and Sustainable Energy Reviews 16 (2012) 1217e1222. [34] F.C. Eboh, P. Alhstr€om, T. Richards, Estimating the specific chemical exergy of municipal solid waste, Energy Science and Engineering 4 (3) (2016) 217e231. [35] A. Valero, A. Valero, Thanatia, the Destiny Of the Earth’s Mineral Resources. A Thermodynamic Cradle to Cradle Assessment, World Scientific Publishing Company, 2014.

Section B Exergy analysis of the envelope and thermal installations

Exergy analysis of heat transfer in buildings

4.1

4

Summary

Traditionally, the analysis of heat transfer through the envelope of buildings has been carried out by applying the First Law of Thermodynamics. However, this type of analysis has its limitations, and it has been shown that, by itself, it does not provide a total understanding of the processes of heat transfer and their consequences for the energy consumption of buildings. In this chapter, we will apply exergy analysis to the processes of heat transfer through the envelope of buildings. After a review of the heat exchange mechanisms that take place on the interior and exterior surfaces of a wall, these exchanges are analysed from an exergy point of view. For this, first, the energy balance and then the exergy balance is performed inside a wall, in which the heat transport mechanism is conduction, taking into account the steady state, but above all looking at the dynamic case. The main objective of the application of the exergy method is to provide a new point of view to thermal inertia and to determine what inertia a façade must have, in order to acquire its best thermal behaviour. For this purpose, a calculation method has been developed, based on the results obtained with a building energy simulation

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00004-7 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

program, which allows for selecting from among the different constructive solutions the one that presents the best energy performance for each of the defined climatic zones in the Spanish Technical Building Code (TBC). Next, the destruction of exergy that occurs in the boundary layer due to convective heat transfer is evaluated. Afterwards, the exchanges of heat by long-wave radiation between the interior surfaces are analysed and, once these exchanges are known, the corresponding exergy balances are considered, which allows the destruction of exergy associated with the absorption and emission of radiation to be evaluated. The case of the exterior surfaces is also considered, in which there is absorption of short-wave solar radiation and the exergy balance in said surfaces is described, which in turn allows the exergy destruction that takes place in them to be quantified. We present a review of the different ways of analysing the behaviour of opaque envelopes and we propose a method, which we have called the detailed dynamic method, which allows us to calculate, in a more precise way, the exergy destruction in the building envelope. A new index is suggested to characterize exergy behaviour, which allows us to classify the walls according to the destroyed exergy. The chapter ends with a summary of the methods for calculating the energy demand of a building and, based on this demand, the two existing methods to calculate the corresponding exergy demand are shown. In short, in order to promote the improvement of energy efficiency of buildings, a methodology based on exergy analysis is given, which allows us to take advantage of everything it offers in terms of identification and quantification of irreversibilities, in order to be able to compare the constructive solutions for façades and roofs and select the most suitable one from the point of view of its energy behaviour.

4.2

Heat exchanges in a building

Both the characteristics of the envelope and those of the interior elements of a building influence the differences between the characteristics of the environment that is generated inside and the outside conditions. Phenomena of exchange of mass flows (air and humidity) and energy occur between these two interior and exterior environments that define the thermal and environmental behaviour of the building. It is appropriate to use the concept of a thermodynamic system when assessing buildings. Thus, we consider the building as a system consisting of a volume of air, which is limited by the exterior and interior envelopes, so that each of the architectural elements (facades, roofs, floors, etc.) cause a filtering of the external climate inward, which results in a global thermal response of the entire building. In addition to the exchanged airflows, the thermal state of the air in the building is the result of the different heat fluxes that take place within it. These heat fluxes are caused by exterior and interior solicitations, ASHRAE [1]. Among the most notable exterior solicitations are: • • • •

Solar radiation. Outside air temperature. Temperature of the surroundings. Sky temperature.

Exergy analysis of heat transfer in buildings

265

Interior solicitations come from within the occupied space and include: • • • •

Occupants. Illumination. Heating and air conditioning equipment. Miscellaneous equipment.

The various architectural factors, such as the shape, orientation, and inclination of walls, the size and location of openings, as well as the characteristics of the surfaces, of the materials making up the envelope and those of the structure condition the behaviour of the building, all of which, in short, act as an intermediary with the external climate. The solicitations listed above give rise to the different heat fluxes that we describe below, for which we consider the surfaces of the envelope in contact with the outside air, the surfaces in contact with the interior air and the interior air of the building itself. Surfaces in contact with the outside air: • • • •

Absorption of short-wave radiation (from the sun). In semi-transparent enclosures (windows), part of that radiation is transmitted to the interior. Emission and absorption (exchange) of long-wave radiation between the surface, the sky and the surroundings. Convection with the outside ambient air. Conduction through the enclosure. This conduction is usually considered 1D, except in the case of thermal bridges.

Fig. 4.1A, shows a diagram of the different mechanisms of heat exchange that take place on the exterior surface of a building. Surfaces in contact with the indoor air: • • • •

Absorption of short-wave radiation from the sun (after redistribution) and that from internal sources (lighting). Emission and absorption of long-wave radiation between the surface and the internal elements and the other internal surfaces of the premises. Convection with the indoor air. Conduction through the wall.

Figure 4.1 Mechanisms of heat exchanges (A) on an exterior surface (B) on an interior surface.

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Exergy Analysis and Thermoeconomics of Buildings

Fig. 4.1B shows a scheme of the mechanisms of heat exchange that take place on a surface in contact with the indoor air of a building. Indoor air of the building: • •

Convection with the interior surfaces and the various objects with which it is in contact. Convection with the surfaces of heating or air conditioning equipment.

Keep in mind that air is practically impervious to exchanges of radiation for distances that we may consider inside a building (tens of meters) so that it only exchanges heat by convection. Once we have presented the different mechanisms of heat exchange that appear in the envelope of buildings, we will show how to perform the exergy balances associated with those exchanges. To do this, we will start by performing energy balances and then compare them with those of exergy, both through the corresponding expressions and in numerical form, through several examples.

4.3

Heat conduction in a wall

4.3.1

Energy balance

We will start by analysing conduction through a wall like the one in Fig. 4.2, whose interior and exterior surface temperatures at a given moment are respectively Tis and Tes, with the situation in winter being Tis > Tes. As we have said, we will first look at the balance of energy in the wall and then we will consider the balance of exergy. The Law of the Conservation of Energy in a dynamic state for the wall in Fig. 4.2a, for any time interval, allows us to say that fEnergy that is storedg ¼ fEnergy that entersg  fEnergy that leavesg

Figure 4.2 (A) Balance of energy in the wall; (B) Balance of exergy in the wall.

(4.1)

Exergy analysis of heat transfer in buildings

267

Referring to the previous balance per unit area of the wall and per unit of time, we have the equation duw ðtÞ ¼ q_is ðtÞ  q_es ðtÞ dt

(4.2)

with uw(t) being the internal energy of the wall in the instant t, q_is ðtÞ being the heat flux that is transmitted by conduction from the inner surface and q_es ðtÞ the heat flux that arrives by conduction to the outer surface, at that time t under consideration. For a homogeneous wall, where r is the density, c the specific heat and L the thickness, the equation can be written as dTðtÞ ¼ q_is ðtÞ  q_es ðtÞ dt

crL

(4.3)

and in the case of a wall composed of N homogeneous layers as N X

ci ri Li

i¼1

dTi ðtÞ ¼ q_is ðtÞ  q_es ðtÞ dt

(4.4)

The above equations refer to the general case of the dynamic state. If we look at the steady-state the term corresponding to the variation of stored energy is zero and the heat fluxes would not be a function of time. In reality, this situation can only be considered in the case of very thin walls or low-density materials, such as a sheet of glass or an insulation sheet, C¸engel [2]. For this steady-state, we have q_is ¼ q_es ¼

Tis  Tes Rw

(4.5)

where Rw is the thermal resistance of the wall, which in the case of a multi-layered wall, is Rwall ¼

N X Li l i¼1 i

(4.6)

with li being the thermal conductivity of layer i and Li its thickness.

4.3.2

Exergy balance

Performing an exergy balance per unit of time and per unit of area of the wall, we have the equation dbw ¼ b_q;is ðtÞ  b_q;es ðtÞ  d_ w dt

(4.7)

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Exergy Analysis and Thermoeconomics of Buildings

where dbw/dt is the rate of change of the exergy stored in the wall, d_ w is the exergy destruction per unit of time that occurs in the wall due to the temperature gradient in the heat transfer by conduction and b_q;is ðtÞ and b_q;es ðtÞ are the rates of exergy associated with the heat fluxes q_is and q_es , respectively. Eq. (4.7) is telling us that of the exergy flow rate that enters the wall b_q;is ðtÞ, a part is destroyed as a consequence of the irreversibility due to the temperature gradient d_ w , another part is stored in the wall dbw/ dt and the rest leaves it, b_q;es ðtÞ. We can also write the above equation as dbw ¼ dt



   T0 ðtÞ T0 ðtÞ 1 q_ ðtÞ  1  q_ ðtÞ  d_ w ðtÞ Tis ðtÞ is Tes ðtÞ es

(4.8)

For an N-layers wall, the above equation becomes       N X dTi ðtÞ T0 ðtÞ T0 ðtÞ T0 ðtÞ ri ci Li 1 ¼ 1 q_ ðtÞ  1  q_ ðtÞ dt Ti ðtÞ Tis ðtÞ is Tes ðtÞ es i¼1 

N X

d_ i ðtÞ

i¼1

(4.9) where, according to the Gouy-Stodola equation N X

d_ i ðtÞ ¼ T0

i¼1

N X

s_g;i ðtÞ

(4.10)

i¼1

The change in the exergy stored in the wall over a period (for example, a day or a year) is obtained by adding the exergy change for each of the I intervals calculated, that is Dbw ¼

I X i¼1

I X   Tf ;i ri ci Li Tf ;i  Ti;i  T0 ri ci Li ln Ti;i i¼1

(4.11)

where Tf,i and Ti,i are the final and initial temperatures, respectively, of the layer i. As can be seen in the previous equations, the resolution of the balances requires knowing the internal temperatures of the different layers that form the wall. The calculation of these temperatures is in no way trivial and to be able to carry it out, either some simplification needs to be made, or a numerical resolution technique needs to be used. Finally, if we consider the steady-state, the term on the left of Eq. (4.9) is zero and everything is independent of time, so that the equation of the exergy balance in an N-layers wall becomes     N X T0 ðtÞ T0 ðtÞ 1 (4.12) d_ i q_is ðtÞ ¼ 1  q_es ðtÞ þ Tis ðtÞ Tes ðtÞ i¼1

Exergy analysis of heat transfer in buildings

4.3.3

269

Examples

Example E.4.1.

An exterior wall of a house is considered to be made up of a 10.2 cm layer of brick (lbrk ¼ 0.7W/m C) followed by a 3.8 cm layer of plaster (lplstr ¼ 0.48W/m C). If the interior surface temperature is 20 C, that of the exterior surface is 12 C and the ambient temperature is 10 C, determine (a) The rate of heat transfer per unit of wall area. (b) The flow exergy rate that is transferred by the interior and exterior surface of the wall. (c) The exergy destroyed in the wall per unit of time.

Solution (a) This is a steady-state so that the heat flux that is transferred by conduction in one layer of the wall is the same as in the other. Therefore Q_ Tis  Tes Tis  Tes 20  12 W ¼ ¼ ¼ 35:57 2 ¼ q_ ¼ Lbrk Lplstr 0:102 0:038 Rwall A m þ þ lbrk lplstr 0:7 0:48 (b) The exergy flows at the boundary surfaces associated with that heat flux are   T0 W 1 q_ ¼ 1:21 2 m Tis   T0 W 1 q_ ¼ 0:25 2 Tes m (c) Undertaking an exergy balance on the wall, we have     T0 T0 1 q_  1  q_ ¼ d_ w Tis Tes W d_w ¼ 0:96 2 m

Consider a 12 m2 façade consisting of a 11 cm thick layer of solid moulded brick with mortar joints, with a thermal resistance of 0.25 m2K/W and with an internal lime mortar render of 2 cm and thermal resistance of 0.03 m2K/W. On a winter day, the outside temperature is 0 C, with the indoor air temperature being 20 C. Using the values of the convection-radiation coefficient of the Spanish Building Code (BTC) for exterior and interior surfaces, determine:

Example E.4.2.

(a) The thermal conductivity of the brick and mortar. (b) The heat transfer rate and the external, internal and intermediate (between the two layers) surface temperatures. (c) The rate of exergy transfer on both outer and inner surfaces and through the interlayer.

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Exergy Analysis and Thermoeconomics of Buildings

(d) The exergy destroyed in the façade per unit of time.

Solution (a) The thermal conductivity of the solid brick layer is Rbrk ¼

Lbrk lbrk

/

lbrk ¼

0:11 W ¼ 0:44 0:25 mK

Likewise, the thermal conductivity of the mortar is Rmor ¼

Lmor lmor

/ lmor ¼

0:02 W ¼ 0:67 0:03 mK

(b) According to the BTC for vertical walls and horizontal flows, the external thermal resistance is Res ¼ 0.04 m2K/W, while the interior thermal resistance is Ris ¼ 0.13 m2K/W. Therefore, the heat flux that is transferred through the facade is q_ ¼

Ti  T0 20 W ¼ 44:44 2 ¼ m Ris þ Rmor þ Rbrk þ Res 0:13 þ 0:03 þ 0:25 þ 0:04

_ ¼ 533 W Q_ ¼ qA To calculate the temperatures, we will use the following equations q_ ¼

Ti  Tis Ris

/

Tis ¼ 14:2 C

q_ ¼

Tes  T0 Res

/

Tes ¼ 1:8 C

q_ ¼

Ti  Tin Ris þ Rmor

/ Tin ¼ 20  44:44ð0:13 þ 0:03Þ ¼ 12:9 C

(c) The corresponding exergy flows are     T0 _ 273:1 1 Q¼ 1 533 ¼ 26:3 W Tis 287:3   T0 _ Q ¼ 3:5 W 1 Tes   T0 _ Q ¼ 24:0 W 1 Tin (d) The exergy destroyed in the façade per unit of time is Tis  Tes _ Q ¼ 22 W D_ ¼ T0 Tis Tes

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Example E.4.3. A renovation is carried out in the wall of Example E.4.2 by means of a direct cladding, consisting of 4 cm rock wool and 3 mm plasterboard, with a total thermal resistance of 1.08 m2 K/W. Answer the questions in Example E.4.2, now with the wall renovated and compare the results obtained with the previous figures.

Solution A new thermal resistance has been added so that the rate of heat transfer is now Ti  T0 20 ¼ Ris þ Rins þ Rmor þ Rbrk þ Res 0:13 þ 1:08 þ 0:03 þ 0:25 þ 0:04 W ¼ 13:07 2 m

q_ ¼

_ ¼ 157 W Q_ ¼ qA As we can see, the rate of heat transfer has been reduced by 71%. The interior surface temperature is q_ ¼

Ti  Tis Ris

/

Tis ¼ 18:3 C

while that of the exterior surface is q_ ¼

Tes  T0 Res

/ Tes ¼ 0:5 C

and the temperature of the intermediate surface is q_ ¼

Ti  Tin Ris þ Rins þ Rmor

/

Tin ¼ 3:8 C

The exergy destruction in the wall per unit time is Tis  Tes _ D_ ¼ T0 Q ¼ 27 ¼ 9 W Tis Tes The fact of having added the insulation layer reduces the exergy destruction by almost 60%.

4.4

Exergy and inertia of walls

For many years, improvements to the envelope of buildings have fundamentally meant lowering the transmittance values of the opaque parts and the transparent elements as much as possible. So-called low-energy buildings are generally based on reducing heat transfer through facades, roofs and windows, basically by increasing the thickness of insulation, Feng [3].

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This approach has even been used in some national regulations on energy efficiency in buildings, for example, in the first version of the BTC in Spain, Spanish Ministry of Housing [4] or its Italian equivalent DL n311/2006 [5], where, according to the climatic zone, limiting values are set for the transmittance of the walls, roof, walls in contact with the ground and windows. Currently, the trend in regulations is aimed at including dynamic effects, either through various dynamic characterization parameters, such as the Réglamentation Thermique [6] or The Building Regulation [7], or as in the latest version of the BTC, Spanish Ministry of Housing [8], by establishing limits on the demand of the building. Therefore, during the last few years, the idea that it is impossible to design energyefficient buildings using only an approach based on the thermal transmittance values of their envelopes has become generally accepted. As such it is essential to look at other aspects, such as their dynamic behaviour, or as it is colloquially called, thermal inertia.

4.4.1

The concept of thermal inertia

Thermal inertia can be defined as the ‘property of a material that expresses the degree of slowness with which its temperature reaches that of the environment’ Ng et al. 2011 [9]. However, the definition that probably best expresses the effects it causes in an enclosure is the ‘capacity of a material to store heat and to delay its transmission’, Ferrari [10]. The term inertia, often used by scientists and engineers, is an analogy with that used in mechanics to relate mass and velocity, where inertia, in that case, is that which limits the acceleration of the object. Similarly, thermal inertia can be interpreted as a measure of the ‘thermal mass’ and the speed with which the heat wave is transmitted through the material. For this reason, it is common to find references to inertia in which it is directly called thermal mass. From a scientific point of view, the diffusion of heat through a solid is a well-known phenomenon. This diffusion plays a double role: on the one hand, the thermal resistance (function of the insulation level) between the interior and the exterior reduces the transferred heat flux; on the other hand, the thermal inertia causes a shift between the maximum external temperature and the maximum instantaneous heat flux transmitted to the interior space. Both effects combined in an appropriate way can serve to reduce the energy consumption of the HVAC equipment. This effect that the inertia causes in the interior conditions (temperature) of a room and associated consumption of energy is something known and used for a long time, and of course before air conditioning equipment existed. Throughout history and the world, there are numerous examples such as castles, churches, wineries and even cave houses dug in the mountains, where the differences between indoor and outdoor environmental conditions can be perceived as soon as one enters, with these being obtained in a ‘natural’ way. These differences can be summarized, on the one hand, by a greater attenuation of the temperature oscillations in the interior in relation to the external oscillations and, on the other hand, in a delay of the instant in which

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the temperature peaks on the inside, compared to when that peak was produced on the outside. Unlike thermal insulation that can be characterized by thermal resistance, thermal inertia is not quantified by a single parameter. Over the years, groups of researchers have used different indicators to characterize it. Thus, coefficients such as thermal diffusivity, and thermal admittance are used, AENOR [11], as well as the offset, Stephan [12], the amortization factor, UNE EN-ISO 1786 [13], the effective heat capacity per unit area, Tsilingiris [14], the time constant, C¸engel and Ghajar [15], etc.

4.4.2

Inertia and exergy

All the references, parameters and aspects related to inertia and commented on so far show that this is a well-known topic, at least from the energy point of view. Unfortunately, there is hardly any work that addresses the inertia of walls through exergy analysis, except for the doctoral thesis of I. Flores [16]. In this respect, Choi et al. [17] is also of great interest, in which a methodology for exergy analysis of heat transmission problems by conduction in dynamic states is shown. In this section, we will interpret the inertia from this exergy perspective, which will provide additional information that may be of interest when selecting the type of envelope. In order to simplify the analysis, the simple case of a homogeneous wall subjected to a 24-hour sinusoidal variation in external surface temperature will be considered, Tes, with the interior surface temperature Tis constant. As a consequence of this sinusoidal excitation, heat fluxes are established, periodic in time, both on the exterior surface q_es and the interior surface q_is , of different amplitudes and out of phase. As an example, we shall consider a homogeneous wall of 20 cm thickness, with a thermal conductivity l ¼ 1 W/mK and a heat capacity c ¼ 1.5 MJ/m3$K. The temperature Tes is characterized by the sun-air temperature, which includes the effects of solar radiation (to which we will refer in Section 4.9.1.3) together with the outside air temperature. The values used are Tis ¼ 20 C and constant while Tes is varying sinusoidally around an average temperature of 10 C and with an amplitude of 15 C during a period of P ¼ 24 h, according to the following expression   2pt p  Tes ðtÞ ¼ 10 þ 15 sin (4.13) P 2 This type of function is a reasonable approximation of what would be obtained with real climatological data, Asan [18]. The following Fig. 4.3 shows the profiles of the external and internal surface temperature for the case under consideration. The numerical values of the heat fluxes obtained corresponding to a full day are shown in Fig. 4.4. These heat fluxes are obtained from the application of the corresponding energy balance in the dynamic state, Eq. (4.2). If the graphs of the temperature profiles and heat fluxes are superimposed, we get Fig. 4.5. Taking into

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Figure 4.3 External surface temperature (left) and interior surface temperature (right) for the example analyzed.

Figure 4.4 Heat fluxes for the example analyzed.

account the respective signs of the temperature difference Tis  Tes, and the heat flux q_is , we can see that there are four different cases: •

•

Case I: q_is < 0 and Tis > Tes. This is the usual situation in winter. The heat flux is from inside to outside, as the interior temperature is higher than the exterior. The exergy flow is also from inside to outside, so that the exergy inside the room will decrease and, to maintain the indoor air temperature constant (constant exergy of indoor air), a contribution of exergy through a heating equipment will be necessary. A heat engine with its thermal energy sources in the indoor and outdoor air in such a case would work as a heat pump and would consume work. Case II: q_is < 0 and Tis < Tes. The heat flux is from inside to outside, although the temperature of the exterior surface is higher than that of the interior. The exergy flow is the opposite, so that exergy is being provided to the room, which allows it to maintain its constant

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Figure 4.5 Possible situations depending on the sign of heat flux qis and the temperature difference between the inner and outer surface.

•

•

temperature. This is, therefore, a favourable case, since air conditioning equipment is not necessary for maintaining comfortable conditions. On the other hand, the supposed heat engine to which we referred earlier would produce work. Case III: q_is > 0 and Tis < Tes. This is the usual situation in summer. The wall gives heat to the interior when the temperature outside is higher than inside. As a consequence of this heat flux there is an exergy flow towards the outside, so to keep the interior temperature constant an air conditionning equipment will be necessary. The heat engine would work like a refrigerating machine and would consume work. Case IV: q_is > 0 and Tis > Tes. The wall gives heat to the interior, although the temperature of the interior surface is greater than that of the exterior. Due to this heat transfer, there is an exergy flow towards the interior, so that in these conditions no air conditioning equipment is necessary to keep the indoor air temperature constant. In this case, the heat engine would extract heat from the heat source (the indoor environment) and give it to the cold source (external environment), generating work.

The exergy flows associated with the heat fluxes for each of the four cases, which keep these indoor temperature conditions constant with the given variation of the outside temperature, are shown schematically in Fig. 4.6. In cases I and IV, the temperature of the exterior surface is lower than the interior. However, due to the effect on the exergy value of the ambient air temperature, although in case I there is an exergy flow that leaves the interior surface, which will have to be compensated for, in case IV the wall provides exergy to the room to be

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air conditioned. Likewise, cases II and III correspond to summer, when the temperature of the exterior surface is higher than that of the interior. Although case III corresponds to the usual case in which there is an exergy flow that leaves the interior environment through the wall and will have to be compensated for to maintain the interior temperature, in case II there is a contribution of exergy from the wall to the room to be air-conditioned. Thus, in cases I and III, the exergy is transmitted from the indoor air to the wall. These situations force the energy system, whether heat pump or refrigeration machine, to replace the lost exergy and, therefore, are not desirable from the point of view of the building’s energy efficiency. On the other hand, in the other two situations, cases II and IV, it is the wall that returns part of the exergy that the indoor air had previously given to it. These situations are desirable from the point of view of energy efficiency, as they allow the constant comfortable interior temperature to be maintained which means, in short, the desired level of exergy of the indoor air without the need for an external contribution, which would be the work consumed by the corresponding equipment.

Figure 4.6 Energy and exergy flow in the four cases.

As time passes, the wall goes through the four previous situations, depending on its inertia and the climatic conditions. If a parametric study of b_q;is is carried out as a function of the thermal transmittance and the heat capacity of the wall, it can be determined, for certain climatic conditions, which wall implies the lowest contribution of exergy to the room to be air-conditioned in order to maintain certain comfort conditions. This study has been carried out by Flores [16] in his doctoral thesis. Taking the above into account, exergy can be a very useful parameter when designing the envelope of energy-efficient buildings. For this, walls will need to be chosen with a thermal transmittance and dynamic characteristics that minimize the

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277

net extracted exergy through the envelope, or in other words, minimize the exergy that needs to be added to the indoor air with the energy supply installation.

4.5

Transport of exergy by convection

Convection is present both on the internal and external surfaces of the envelope and is due to the difference in temperature between the surface of the envelope and the environment in which it is located. It is a phenomenon that occurs within the boundary layer and as we know from the texts on heat transfer, C¸engel [19], despite the complexity of convection, the heat flux is expressed by Newton’s Law of Cooling by introducing a convection coefficient. For the interior surface of a wall we have Q_ cv;i ¼ q_cv;i Ais ¼ Ais hcv;i ðTi  Tis Þ

(4.14)

and analogously for external surfaces. In general, this coefficient of convection depends on the configuration, airspeed, temperature difference between surface and air, and the thermophysical properties of the fluid, in this case, the air. However, given that the usual configurations in buildings are flat surfaces, and the temperature ranges are close enough that we not need to take into account any variation in properties, we can conclude that the main factors that govern the convection coefficient are: the direction and sense of the heat flux (horizontal, vertical, and if vertical, ascending or descending) and, above all, the airspeed. Therefore, there are important differences in their values for interior and exterior surfaces. Indeed, on the outside of buildings, the movement of air is mainly due to the wind. On the other hand, in the interior of buildings, the movement of the air is generally due to natural convection, which is generated by a difference in densities associated with a difference in temperatures close to the wall. This means that the internal convection coefficients hcv,i and external convection coefficients hcv,e will be very different, Ito and Kimura [20]. The differences in values, although not as pronounced, are maintained even in situations with forced ventilation systems, since for reasons of comfort, the interior airspeed is considerably lower than that of the wind outside. As a consequence of the non-slipping condition, the air in contact with the surface of a wall has a zero velocity. Therefore, the heat transfer between the surface of the wall and the air in contact is done by pure conduction, since that air layer is motionless. Then, that heat moves away by convection, as a result of air movement. For a study of convection, consult the aforementioned work of C¸engel or that of Kays and Crawford [21].

4.5.1

Energy balance

Despite these differences between interior and exterior surfaces, the way to mathematically analyse heat transfer is the same. As an example, we shall consider the following case of the boundary layer on the interior surface of a wall, see Fig. 4.7, with Ti and Tsi being the temperatures of the indoor air and the interior surface, respectively. If it is assumed that Ti > Tis, the indoor air in the vicinity of the interior surface will cool,

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Figure 4.7 Heat transfer by convection on the interior boundary layer of the wall.

then increasing its density and, consequently, will tend to descend activating the mechanism of convection. By taking into account the low inertia of the air, the analysis can be carried out as a steady-state without appreciable loss of precision, when the boundary layer is already configured. The energy balance in these conditions, per unit of wall area and per unit of time, is reduced to q_cv;i ¼ q_cd;is ¼ lai

vT j vx x¼0

(4.15)

where lai is the thermal conductivity of the air, T represents the temperature distribution in the air and vT/vxjx¼0 is the temperature gradient in the surface. As we said before, the rate of heat transfer by convection [W/m2] for an interior surface, per unit area, is q_cv;i ¼ hcv;i ðTi  Tis Þ

(4.16)

Referring now to the outer surface, where Tes is the surface temperature and hcv,e the convection coefficient, the rate of heat transferred by convection on the outer surface is q_cv;e ¼ hcv;e ðTes  T0 Þ

(4.17)

Table 4.1 shows the regular values that should be adopted for these convection coefficients. The experimental determination of the external convection coefficient is limited to establishing correlations with air velocity v, generally given by hcv,e ¼ aþbv, with a and b being both constant. The problem with these correlations is that, in the vicinity of the surface, the air velocity can be very different from the natural speed of the wind.

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279

Table 4.1 Internal and external convection coefficients according to the standard UNE-EN ISO 6946 (AENOR 2007).

4.5.2

Direction of heat flux

hcv,i [W/m2$K]

hcv,e [W/m2$K]

Horizontal

2.5

20

Vertical ascending

5

20

Vertical descending

0.7

20

Exergy balance

By performing the corresponding exergy balance in the boundary layer of the inner surface, see Fig. 4.7, we obtain the equation b_cv;i  b_cd;is ¼ d_ cv;i

(4.18)

Clearing the exergy destruction d_ cv;i in the previous expression, we finally have d_ cv;i ¼ T0 q_cv;i



1 1  Tis Ti

 ¼ T0 hcv;i

ðTi  Tis Þ2 Ti Tis

(4.19)

This expression allows us to quantify the rate of exergy destruction that occurs in the heat transfer by convection between the air and the internal surface of a wall. Obviously, for the case of convection in the boundary layer of an external surface, the expression is analogous, simply by substituting the variables hcv,i, Ti and Tis for the corresponding exterior surface variables hcv,e, T0 and Tes, respectively. In effect, if the exergy balance is performed on the outer surface, the resulting equation is b_cd;es ¼ b_cv;e þ d_ cv;e

(4.20)

obtaining the following expression for the rate of exergy destruction 2

ðTes  T0 Þ d_ cv;e ¼ T0 hcv;e Tes T0

4.5.3

(4.21)

Examples

Hot water flows through a pipe with an outer diameter of 50 mm and a length of 9 m, the temperature of the outer surface of the pipe being 42 C. If the

Example E.4.4.

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outside air is at the temperature of 15 C and the coefficient of convection between the pipe and the air is 24 W/m2K, determine: (1) The rate of heat exchanged and the associated rate of exergy. (2) The rate of exergy destruction.

Solution (1) The rate of heat given to the air by the pipe is Q_ ¼ pDe LhðTs  T0 Þ ¼ 916 W The rate of exergy associated with that heat is   T0 _ Q ¼ 78:5 W 1 Ts (2) The flow of exergy calculated above is completely destroyed in the environment (external irreversibilities) so that the rate of exergy destruction is D_ ¼ 78:5 W

The façade of a house of dimensions 7  4 m has a thermal resistance of 4.5 m2K/W. The house is maintained at a temperature of 20 C on a day when the outdoor air temperature drops to 2 C, and the wind speed is 60 km/h. Without taking into account the heat transfer by radiation, determine:

Example E.4.5.

(1) The rate of heat lost through the wall. (2) The rate of exergy coming out of the wall. (3) The rate of exergy destroyed in the inner boundary layer, in the facade and in the outer boundary layer of the wall.

Solution (1) According to the ASHRAE Fundamentals the internal convection coefficient for horizontal convection is hcv,i ¼ 3.06 W/m2K. Therefore, the thermal resistance of the inner boundary layer is Rcv,i ¼ 1/hcv,i ¼ 0.327 m2K/W. On the other hand, for a wind speed of 60 km/h, the ASHRAE Fundamentals proposes a value of hcv,e ¼ 65.5 W/m2K, so the thermal resistance in the outer boundary layer is Rcv,e ¼ 1/hcv,e ¼ 0.015 m2K/W. In short, the rate of heat lost per unit area is q_ ¼

Ti  T0 W ¼ 3:72 2 Rcv;i þ Rfac þ Rcv;e m

and the total heat flux is Q_ ¼ qA _ ¼ 104 W

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281

(2) The flow of exergy associated with that heat flux coming from the indoor air is   T0 _ 1 Q ¼ 6:4 W Ti (3) This flow of exergy is destroyed in the inner boundary layer, in the facade and in the outer boundary layer. Calculating the temperature on the inner surface Tis ¼ Ti  Rcv;i q_ ¼ 291:8 K the exergy destroyed in the inner boundary layer is Ti  Tis ¼ 0:43 W D_ i ¼ T0 Q_ Ti Tis The temperature on the outer surface is Tes ¼ T0 þ Rcv;e q_ ¼ 275:2 K so the rate of exergy destroyed in the outer boundary layer is Tes  T0 ¼ 0:04 W D_ e ¼ T0 Q_ T0 Tes Obviously, the rate of exergy destroyed in the facade is D_ fac ¼ D_  D_ i  D_ e ¼ 5:9 W Practically, all the exergy destruction takes place inside the facade, due to the irreversibility of conduction. In fact Tis  Tes ¼ 5:9 W D_ fac ¼ T0 Q_ Tis Tes

4.6

Exchange of radiation exergy between surfaces

The transfer of heat by radiation represents a very important part of the energy exchanges that occur in buildings. In the case of radiant floor systems, approximately 50% of the heat is directly transmitted to the air by convection, and the other 50% arrives by convection after the mechanisms of conversion of radiant energy to heat of convection, Olesen [22]. The calculation of the exergy associated with this thermal radiation has traditionally been a very controversial topic and has led to much scientific discussion, Torio [23]. Proofs for this are the different approaches and definitions proposed by various authors as shown in Chapter 2.

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One of the main difficulties of radiation problems is the calculation of energy exchanged and, of course, the radiant exergy exchanged between different surfaces. In the ideal case in which the system is formed by black surfaces, the problem is relatively simple, because there is only emission and absorption, and no reflected component. On the other hand, when the system is formed by real surfaces, even when using the model of grey surfaces the problem is considerably complicated, as we need to calculate the reflections of the radiation emitted. In those situations with surfaces of high emissivity, close to unity, an approximate value can be obtained with an acceptable error if it is assumed that there is no reflection. In general, in spite of this greater complexity, the calculations of the energy flows are perfectly described in heat transfer books, such as C¸engel and Ghajar [15], Incropera and DeWitt [24], and Lienhard [25]. However, the calculation of the radiation exergy exchanged is not usually described in the heat transfer books and, moreover, is somewhat more complex. For each flow of radiation exergy that reaches an opaque surface, in addition to the absorbed and reflected components, the remaining part that is destroyed due to irreversibilities will need to be considered, and all of this in the multiple processes of emission, reflection, absorption and destruction that occur in the radiant exchange between surfaces.

4.6.1

Radiation exergy exchange between two grey surfaces

Petela [26] developed a formulation to calculate the exergy exchange between two surfaces 1 and 2, grey, flat, parallel, infinitely long and facing each other. He considered there is a vacuum between the surfaces, so there are no exchanges for conduction and convection. The surfaces are isotherms, and their temperatures T1 and T2 are constant thanks to the action of thermal energy reservoirs that provide or withdraw the necessary heat. The emissivity, absorptivity and reflectivity of the surfaces are ε1 and ε2 , a1 and a2, and r1 and r2 respectively, with the surfaces A1 ¼ A2 ¼ A. The heat exchanged between both surfaces per unit of time and area q_12 is the fraction of the energy absorbed by 2 of the energy emitted by 1 minus the fraction absorbed by 1 of that emitted by 2 and therefore   (4.22) q_12 ¼ ε12 s T14  T24 where ε12 ¼

1 1 1 þ 1 ε1 ε2

(4.23)

Petela similarly deduced that the exergy of radiation exchanged between both surfaces is    4  b_r;12 ¼ ε12 s T14  T24  T0 T13  T23 (4.24) 3

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Once the exergy exchange is calculated, it is important to evaluate the exergy destruction on each surface due to irreversibilities in the emission and absorption. That destruction of exergy can be broken down into the sum of two parts. So for surface 1, we let d_ 1;1 be the term that represents the exergy destruction caused by the emission of the surface itself and the absorption of the fractions of that emission that, having been reflected by surface 2, are absorbed by 1. The second addition d_ 2;1 corresponds to the exergy destruction on surface 1 caused by the absorption of the radiation emitted by surface 2, either directly or through various reflections, so that d_ 1 ¼ d_ 1;1 þ d_ 2;1

(4.25)

and analogously for surface 2. The following expressions are derived in the referenced work of Petela [26].    ε1 ε2 b_r;b1 T0 ε 1 r2 d1;1 ¼ ε1 e_b;1 1  (4.26) 1  T1 1  r1 r2 1  r1 r 2 d_ 2;1 ¼

   ε1 T0 _ _ ε2 br;b2  ε2 eb;2 1  1  r1 r2 T1

(4.27)

where, as we saw in Chapter 2, e_b;1 , e_b;2 are the emission power, that is, the black radiation emitted per unit of time and area of surfaces 1 and 2 respectively and b_r;b1 , b_r;b2 are the exergy of that radiation. Analogous expressions are obtained for the exergy destruction in surface 2. However, when what we want to obtain is the total exergy destruction, which is the sum of the one that takes place on surfaces 1 and 2, there is a simpler alternative method than the previous one. This method consists of looking at the exergy balance of the whole process, so that, given that the temperatures remain constant, the global balance is     T0 T0 q_12 1  ¼ q_12 1  þ d_ 1 þ d_ 2 T1 T2

(4.28)

which gives the rate of total exergy destruction as d_ ¼ d_ 1 þ d_ 2 ¼ q_12 T0



1 1  T2 T1

 (4.29)

an expression which corresponds to the rate of exergy destruction related to the heat exchanged between two systems of temperatures T1 and T2, as we saw in Chapter 2.

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4.6.2

Radiation exchange between the interior surfaces of a room

For those more frequent situations, where there are more than two grey surfaces exchanging radiation, the calculation becomes more complex. This is what happens in the exchange of long-wave radiation between the interior surfaces of a building: the radiation emitted by one surface propagates until it impinges on another, being then partially reflected and again re-reflected and so on, while also being partially absorbed in each contact with a surface. It is therefore impossible to try to follow the radiation as it passes through these complicated processes, unlike the case of two flat and parallel surfaces. Fortunately, this is not necessary, since many methods have been developed over the years to resolve the exchange of radiation between surfaces; among them are, for example, those proposed by Hottel and Sarofin [27], Sparrow and Cess [28], Gebhart [29] or Clark and Korybalski [30]. Although basically all of them are equivalent, the Gebhart method has been chosen due to its simplicity and adaptation to the tools used. The method is based on the so-called radiant exchange factor or Gebhart factor, Gij, which represents the fraction of energy being emitted by the surface i and absorbed by surface j. In this fraction, all possible ways of reaching the surface j are included, that is, the direct path, as well as those originating from the various reflections

Gij ¼

4.6.2.1

Q_ ij εi Si sTis4

(4.30)

Radiative energy exchange

Before addressing the radiative exergy exchanges, let us first consider the energy exchanges. A surface loses energy by emission and gains energy by absorbing the radiation emitted by other surfaces and its own emission, which has been reflected by the other surfaces. Depending on which of the two quantities is the highest, there will be a net gain or loss of energy. The rate of net energy transfer on a surface i of an enclosure composed of N surfaces can be calculated from the Gebhart factors as the net balance between the energy emitted and the energy absorbed, which is Q_ i ¼ Ai εi sTis4 

N X

Aj εj sGji Tjs4

(4.31)

j¼1

Taking into account the following geometric relationship εi Ai Gij ¼ εj Aj Gji

(4.32)

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285

the net heat exchanged between two surfaces i and j can be expressed as  Q_ ij ¼ εi Ai Gij s Ti4  Tj4

(4.33)

For its part, considering the energy balance and using the vision factors, the Gebhart factors are calculated by solving the following system of equations Gij ¼ Fij εj þ

N X

Fik ð1  εk ÞGkj

i ¼ 1; :2.N

(4.34)

k¼1

In order to calculate the configuration factors Fij the rule of addition, the rule of superposition, the reciprocal relationship, the crossed string method, as well as the graphs and analytical expressions that can be found in the books of heat transfer are used. In the previous equation, the first summand of the member on the right represents the fraction of energy emitted by i, which is spread directly on j and is absorbed. The summation, on the other hand, represents the fraction of energy that reaches j after suffering at least one reflection. Thus, the emission of the surface i that reaches the surface k and is reflected will be Fikrk ¼ Fik(1  εk). Of that part, only the fraction Gkj is absorbed by N P the surface j. As with the vision factors, we can verify that Gij ¼ 1. Once the Gebj¼1

hart factors have been obtained, all the components of the radiation energy exchange between the surfaces of the room can be determined by applying Eq. (4.33).

4.6.2.2

Radiation exergy exchange

For its part, the exchange of exergy in an enclosure composed of diffuse-grey surfaces, is at least as complex as the case of energy exchange, since in addition to the components seen above, we must add the inevitable exergy destruction. Fortunately, if diffuse-gray surfaces are considered, the same coefficients of the Gebhart matrix can also be used to study exergy balances. Thus, the term Gij also represents the fraction of radiation exergy that is emitted by the surface i and is absorbed by the surface j, including all possible trajectories. In this way, from Eq. (4.33) and considering two surfaces i and j, the fraction of radiation exergy emitted by the surface i, which is absorbed by the surface j will be  s B_ r;i/j ¼ Gij B_ r;i ¼ Ai Gij εi 3Ti4 þ T04  4T0 Ti3 3 Analogously, the emission by j which is absorbed in i is s B_ r;j/i ¼ Gji B_ r;j ¼ Aj Gji εj 3Tj4 þ T04  4T0 Tj3 3

(4.35)

(4.36)

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Therefore, the radiation exergy exchange per unit of time between both surfaces is  i sh  B_ r;ij ¼ Ai Gij εi 3 Ti4  Tj4  4T0 Ti3  Tj3 (4.37) 3 Finally, the net rate of exergy exchanged by the surface i is obtained from the previous expression by adding up over the total of the interior surfaces of the room, and therefore

B_ r;i ¼

N X

B_ r;ij ¼

j¼1

N X j¼1

Ai Gij εi

 i sh  4 3 Ti  Tj4  4T0 Ti3  Tj3 3

(4.38)

On the other hand, the exergy destruction that takes place on the surface i will be the sum of two contributions, as expressed in the following equation

D_ i ¼ D_ i;i þ

N X

D_ j;i

(4.39)

jsi

The first of the addends of the member on the right represents the exergy destruction caused by the emission of the surface i and the absorption on that surface of its own emission, which, after having been reflected by the other surfaces, is finally absorbed by the surface i. For its part, the second addend represents the exergy destruction caused by the absorption on surface i of the exergy emitted by the other surfaces, which either directly or after a series of reflections, ends up being absorbed by the surface i. For the case of three or more surfaces, a detailed approach, for the calculation of each of the addends of Eq. (4.25), such as the one developed by Petela, is unfeasible. For those situations, however, one can calculate the exergy destruction on each surface i from the corresponding exergy balance on the surface.

4.7

Energy and exergy balances on the interior surface of a façade

So far, we have separately considered the exergy associated with conduction, convection and long-wave radiation. Let us now refer to the interior surface of a façade, in which, as we saw in Section 4.2, the three mechanisms of heat exchange exist. Consider Fig. 4.8 which represents a wall and in which, as a dashed line, we have indicated the system, of infinitesimal thickness, on which we are going to consider the energy balance and later the exergy balance. We shall consider the case of summer so that the heat flux moves from outside to inside.

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287

Figure 4.8 Interior surface of a building envelope.

4.7.1

Energy balance

Carrying out an energy balance per unit of time in the surface under consideration, we have (

Heat transfer by conduction

)

( ¼

Exchange of

)

long wave radiation ) ( Heat exchange þ by convection

( þ

Absorption of

)

short wave radiation

(4.40) which, we show by means of the following mathematical equation Q_ cd ¼ Q_ lwr þ Q_ swr þ Q_ cv

(4.41)

where: • •

• •

Q_ cd : rate of heat transfer by conduction. Q_ lwr : rate of long-wave radiation exchanged (absorption e emission). This radiant exchange is, in turn, often broken down into two terms: one which takes place with the other interior surfaces of the enclosure that are at different temperatures while the second is the radiant exchange with internal components such as furniture, etc. Q_ swr : rate of absorption of redistributed short-wave radiation from the sun and internal sources, such as lighting. Q_ cv : rate of heat exchanged by convection with the indoor air.

The radiant exchange in interior surfaces of a building is of great complexity, due to the different nature of this radiation and the irregular behaviour of those surfaces. In order to simplify the calculations and since both convection and radiation flows are in parallel, a convection-radiation coefficient is used with which the heat exchange

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with the air in the room is calculated, directly by convection and through exchanges by radiation with the other interior surfaces and which is exchanged, finally, with the air by convection, so that hcvr ¼ hcv þ hr

(4.42)

Regulations like the BTC give the limit values of the thermal transmittance that the interior surfaces must have. These values of the thermal transmittance are obtained using values of the normalized convection-radiation coefficients, which depend on whether the flow is horizontal or vertical, and in the latter case of whether it is ascending or descending, BTC [31].

4.7.2

Exergy balance

We refer now to the exergy balance. This balance establishes that 9 9 8 9 8 8 Exergy associated > > Short wave > > Long wave radiation > > > > > > = < = > < = > <  radiation exergy exergy exchanged with heat transfer ¼ > > > > > > > > > > ; : ; > : ; > : absorbed by the surface by conduction 9 9 8 8 Exergy associated > > Exergy destroyed > > > > > = < = > < in the þ with heat transfer þ > > > > > > > ; : ; > : surface by convection (4.43) Mathematically, the exergy balance is expressed according to the following equation     T0 T0 _ _ _ _ Qcd;i 1  (4.44) ¼ Br;i  Bswr;i þ Qcv;i 1  þ D_ i Ti Ti From this equation, the rate of exergy destruction on the surface is obtained. This destruction is due to the absorption of the long-wave radiation that comes from the interior surfaces, to the emission of the surface itself, to the redistributed short-wave absorption from the sun and lights and also includes the exergy destruction associated with convection in the boundary layer between the air and the surface. Naturally, as a prerequisite, it is necessary to have calculated the configuration factors, Gebhart factors and resolve the exchanges of both energy and exergy. Besides, in the interior of the wall, the exergy destruction associated with conduction takes place, which is calculated according to Eq. (4.9).

Exergy analysis of heat transfer in buildings

4.7.3

289

Examples

Example E.4.6.

The main façade of a rectangular industrial warehouse consists of a double-layer base wall. The outer layer is made of solid brick facing the outside with a polyurethane coating of 2 cm, and the inner layer is a double-hollow brick partition of 7.5 cm with internal mortar and plastering, see Table E.4.1. The interior surface of the facade is 16 m2 and the rest of the interior surfaces 90 m2. We will assume that the emissivity of the interior surface of the facade and the rest of the interior surfaces is 0.9.

Table E.4.1 Data for the main facade. Description of layer

Thickness

R(m2/WK)

1

/2 solid facing brick

10.5

0.25

Polyurethane insulation

2

0.72

Double hollow brick partition

7.5

0.15

Layer of mortar

1

0.008

Plastering

0.5

0.017

With a wind speed of 3.3 m/s, the temperature of the indoor air at 20 C, the ambient air at 2 C and assuming that the temperatures of the other internal partitions are at 16 C, determine: (a) The interior surface temperature of the façade. (b) The long-wave radiation exchanged by the inner surface of the facade with the other surfaces, and the corresponding radiation exergy exchanged. (c) The rate of exergy destruction due to convection in the inner boundary layer. (d) The rate of exergy destruction inside the facade due to conduction.

Solution (a) The thermal resistance of the facade, that is, the sum of the thermal resistances of the layers is 1.145 m2K/W. According to ASHRAE Fundamentals, the interior convection-radiation coefficient is 8.9 W/m2K, for a surface of emissivity ε ¼ 0.9. Therefore, the interior resistance is Ri ¼ 0.112 m2K/W. For a wind speed of 3.3 m/s the convection-radiation coefficient is 22.7 W/m2K, so the exterior resistance is Re ¼ 0.044 m2K/W. The rate of heat transfer through the façade is q_ ¼

Ti  T0 W P ¼ 13:8 2 Ri þ j Rj þ Re m

Q_ ¼ 221 W

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Exergy Analysis and Thermoeconomics of Buildings

so the temperature of the interior surface is Tis ¼ Ti  Ri q_ ¼ 18:4 C (b) Since all the other surfaces are at the same temperature of 16 C and have the same emissivity, the heat exchange by radiation is calculated as that which takes place between two surfaces, with is the interior surface of the facade and s2 the other interior surfaces. Therefore, the heat exchanged by radiation is Q_ r;iss2 ¼

    4 s Tis4  Ts2 5:67x108 291:54  2894 ¼ 197:9 W ¼ 1  εis 1 1  εs2 1  0:9 1 1  0:9 þ þ þ þ Ais Fis;s2 As2 εs2 16$0:9 16 90$0:9 Ais εis

The exergy of the exchanged radiation is " sTis4 B_ r;iss2 ¼

# " #     1 T0 4 4 T0 1 T0 4 4 T0 4 1þ  sTs2 1 þ   3 Tis 3 Tis 3 Ts2 3 Ts2 1  εis 1 1  εs2 þ þ Ais Fiss2 As2 εs2 Ais εis

¼ 10:3 W

(c) The coefficient of convection (without radiation) corresponding to the vertical inner surface and horizontal heat flux, according to ASHRAE Fundamentals, is hcv,i ¼ 3.06 W/m2K. The rate of heat transfer due to convection through that boundary layer is Q_ cv;i ¼ Ais hcv;i ðTi  Tis Þ ¼ 78:3 W and the exergy associated with that heat flux by convection B_ cv;i ¼

  T0 _ Qcv;i ¼ 4:4 W 1 Tis

The rate of exergy destruction in the convective boundary layer is Ti  Tis ¼ 0:4 W D_ cv;i ¼ T0 Q_ cv;i Ti Tis (d) To calculate the exergy destruction inside the facade due to conduction, we first determine the temperature of the outer surface Tes ¼ T0 þ Re q_ ¼ 2:6 C with the rate of exergy destruction being Tis  Tes ¼ 11:9 W D_ fac ¼ T0 Q_ Tis Tes

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291

Example E.4.7.

The end elements of a dwelling heating installation are cast iron radiators whose average surface temperature is 60 C, with the interior surface temperature of the walls being 20 C. The total heat given by the radiators is 12 kW, of which 65% is convection. Evaluate the error in the calculation of the transferred exergy, when using the expression corresponding to the exergy of convection, when the ambient temperature is 290 K. Solution Considering that all the heat given is by convection, the exergy of that heat is   T0 _ Q ¼ 1:55 kW 1 Ts

If we consider that the emissivity of the radiators and the surfaces of the walls is the same, we have that the exergy of the radiation exchanged is ! 4 Ts3  Tis3 _ Qr 1  T0 4 3 Ts  Tis4 By breaking down the heat flux into a convective part and a radiative part, the associated exergy is   T0 _ þ 1 0:65Q Ts

! 4 Ts3  Tis3 1  T0 4 0:35Q_ ¼ 1:05 kW 3 Ts  Tis4

Therefore, the error made in this approach is 47%.

4.8

Energy and exergy balances in the exterior surface of a façade

After analysing the mechanisms of heat exchange on the interior surface of a façade and performing an exergy balance on an interior surface, it remains to analyse the exchanges of energy and exergy on the exterior surface of the building envelope.

4.8.1

Energy exchanges

For greater clarity Fig. 4.9 shows the heat exchange mechanisms that act on the exterior surface. Taking as a reference the direction of the flows in the figure, that is to say, under conditions of winter in which there is a net heat flux from the interior to the exterior, the rate of energy balance in the exterior surface per unit area is

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Exergy Analysis and Thermoeconomics of Buildings

Figure 4.9 Energy exchanges on the exterior surface’.

q_cd;es ¼ q_cv;e  q_r;sun þ q_r;sky þ q_r;sur

(4.45)

where: • • • • •

q_cd;es is the rate of heat that is transmitted by conduction from the exterior surface of opaque envelopes and by a combination of mechanisms for semi-transparent envelopes. q_cv;e is the rate of heat exchanged by convection with the outside air. q_r;sun is the rate of short-wave radiation absorbed from the sun. q_r;sky is the rate of long-wave radiation exchanged with the sky, and finally q_r;sur is the rate of long-wave radiation exchanged with the surroundings, such as the terrain, other buildings, etc.

Developing the previous balance equation gives  4  q_cd;es ¼ hcv;e ðTes  T0 Þ  q_r;sun þ εes Fes;sky sTes  εsky sT04  4   sT04 þ εes Fes;sur sTes

(4.46)

where εes is the emissivity of the surface, εsky is the emissivity of the sky and Fes,sky and Fes,sur are the configuration factors of the surface/sky and the surface/surroundings respectively. Next, we will make a series of comments on each of the terms in this equation.

Exergy analysis of heat transfer in buildings

4.8.1.1

293

Convection coefficient on the exterior surface

Unlike what happens inside the building, the exchange of energy by convection on the outside is affected by the presence of wind. As we stated in Section 4.5, the wind can significantly vary the value of the convection coefficient hcv,e, especially in those buildings that are very exposed, Brau [32]. There are various expressions in the literature for the calculation of the coefficient as a function of wind speed. Unfortunately, these types of expressions are generally not very useful. The fundamental reason is that, as we said in Section 4.5.1, weather stations are usually found at airports or areas that are quite exposed, so the wind speed data is not applicable to most buildings. For this reason, it is usual to work with normalized convection coefficient values, such as those seen previously in Table 4.1. Regardless of whether standardized or particularized values are used for specific wind conditions, the heat exchanged between the surface and the environment is given by Newton’s law of cooling, in an identical way to what happens on the inner surface.

4.8.1.2

Radiation exchange with the sky and surroundings

We are now looking at the exchange of long-wave radiation, which takes place between the exterior surface and the sky q_r;sky and between said surface and the surroundings q_r;sur . Covered by this term ‘surroundings’ are the floor and all those objects that the building ‘sees’, such as trees, other buildings, etc. The emission of radiation by the atmosphere is a consequence of the presence of participatory gases, H2O and CO2 fundamentally, and it is concentrated in the regions of the spectrum between 5 and 8 mm and around 13 mm. Although this emission is far from resembling that emitted by a black body, it is convenient and very usual in calculations to consider the atmosphere as an ideal black surface at a fictitious temperature, which emits the same amount of radiant energy as the atmosphere. This fictitious temperature is what is called the effective sky temperature Tsky. Its value depends on atmospheric conditions, fundamentally on the ambient temperature, the relative humidity, the degree of cloud cover and the ambient pressure. This dependence is usually brought together as the so-called emissivity of the sky εsky, so that the effective temperature of the sky can be calculated from the ambient temperature T0 through the 4 ¼ ε T 4 , so that the emission power of the sky is relationship Tsky sky 0 4 e_sky ¼ εsky sT04 ¼ sTsky

(4.47)

This effective sky temperature varies from 230 K for clear and cold sky conditions up to around 285 K for warm sky and with clouds. There are numerous proposed equations for determining the emissivity of the sky, some as simple as supposing a constant value equal to 0.74, while more complex ones are given depending on atmospheric

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Exergy Analysis and Thermoeconomics of Buildings

conditions. Several of the latter are collected in Gliah et al. [33]. The TRNSYS simulation software uses the proposal in Martin and Berdahl [34]. εsky ¼ ε0 þ 0:8ð1  ε0 ÞCcld

(4.48)

where Ccld is the cloud cover factor and ε0 is the emissivity corresponding to a clear sky. The latter can be obtained by the following mathematical expression [34] ε0 ¼ 0:711 þ 0:005Tsat þ

2 7:3x105 Tsat

þ 12x105 ðp0  psea Þ

  time þ 0:013 cos 2p 24 (4.49)

with Tsat being the saturation temperature for that temperature and humidity of the air, time the moment of the day expressed in hours, and p0 and psea are the pressures of the place in question and at sea level, respectively. Thus, the exchange of radiation [W/m2] between the exterior surface of emissivity εes and the sky is given by  4 4  Tsky q_r;hv ¼ εes $s$Fes;sky $ Tes

(4.50)

where Fes,sky represents the configuration factor between the surface and the sky. For its part, the radiation exchange between the surface and the surroundings is obtained through the equation  4  4  Tsur q_r;sur ¼ Aes εes $s$Fes;sur $ Tes

(4.51)

with, in this case, Fes,sur being the configuration factor between the surface and the surroundings. As the exterior surface is usually flat Fes,es ¼ 0, we can see that Fes,sur ¼ 1  Fes,sky. In simulation programs, the exchange of long-wave radiation with the sky and with the surroundings usually appears grouped in a single term, calculated using a fictitious temperature Tf,sky. This temperature is obtained from the temperatures of the sky and the surroundings, weighted according to the respective configuration factors, which is   Tf ;sky ¼ 1  Fes;sky Tsur þ Fes;sky Tsky (4.52) In this way, the heat exchanged by long-wave radiation with the sky and the surroundings, is  4  Tf4;sky q_r;skyþsur ¼ εes s Tes (4.53)

Exergy analysis of heat transfer in buildings

4.8.1.3

295

Equivalent temperature and sun-air temperature

Given these comments on the different mechanisms of energy exchange, we will present in summary the way in which we work with the balance equation. Expression (4.46) can be transformed, in a first step, into an equation of the type q_cd ¼ q_r;sun þ hcvr ðTeq  Tes Þ

(4.54)

with Teq being the equivalent temperature and hcvr a mixed transfer coefficient of convection and radiation. Since both convection and long-wave radiation heat flows are in parallel, a mixed transfer coefficient can be defined, hcvr ¼ hcv þ hr, with hr being a coefficient that satisfies  4  hr ðTes  T0 Þ ¼ εes s Tes  T04

(4.55)

In order to linearize the above expression we use the approximation 4  T 4 y4T 3 ðT  T Þ where T is the arithmetical mean of T and T . The relative Tes 0 m es 0 m es 0 error of this approach, in the usual ranges of temperatures is less than 0.1%, Alvarez [35]. Therefore, the convection-radiation coefficient is hcvr ¼ hcv þ 4sεes Tm3

(4.56)

By carrying out appropriate development, we find that this equivalent temperature is Teq

  εes sT04 Fes;sky εsky þ Fes;sur  1 ¼ T0 þ hcvr

(4.57)

The exchange by short-wave radiation q_r;sun on the exterior surface is produced as a result of the absorption by that surface of a fraction of the incident solar radiation that reaches it. It will be, therefore, a gain of energy for the wall and also, of great consequence in the balance. It can be calculated by the following expression q_r;sun ¼ aes GT

(4.58)

where aes represents the absorptivity for short-wave radiation of the exterior surface of the wall and GT is the solar irradiation [W/m2] that is incident on this surface. Its value will depend on the location (latitude), orientation of the wall and the day and time. As can be seen, direct and diffuse radiation has been considered jointly. According to what was said in Chapter 2, in exergy balances, both types of radiation must be

296

Exergy Analysis and Thermoeconomics of Buildings

considered separately, since the associated exergy is different. According to what we have been saying, the equation of energy balance in a given instant is q_cd;es ¼ aes GT þ hcvr ðTeq  Tes Þ

(4.59)

which can be expressed in the following way q_cd;es ¼ hcvr ðTsa  Tes Þ

(4.60)

where what is known as the sun-air temperature has been introduced Tsa ¼ Teq þ

aes GT hcvr

(4.61)

The heat exchange of a wall on its exterior surface is usually analysed by encompassing the mechanisms of convection and heat exchange by short-wave and long-wave radiation through this concept of sun-air temperature. In this way, all these exchanges can be expressed in a similar way to Newton’s equation, using the convection-radiation coefficient, the temperature of the exterior surface and this sun-air temperature. Given the different thermodynamic quality of the energy exchanged by these different mechanisms, it is evident that it is not possible to apply the concept of sun-air temperature for exergy analysis, as demonstrated by Flores [16] in his doctoral thesis.

4.8.2

Exergy balance

Taking into account the heat fluxes described above, looking at the exergy balance for the exterior surface we have 9 9 8 9 8 8 Exergy associated > > Solar radiation > > Exergy associated > > > > > > = < = > < = > < with the heat flux ¼ with the heat flux  exergyðshort waveÞ > > > > > > > > > > ; : ; > : ; > : absorbed of convection by conduction 9 9 8 8 Radiation exergy > Radiation exergy > > > > > > > = = < < exchanged with þ exchanged with þ > > > > > > > ; : ; > : the surroundings the sky ) ( Exergy destruction þ in the surface (4.62)

Exergy analysis of heat transfer in buildings

297

The exergy destruction associated with radiation has two origins: on the one hand, due to the absorption of the short wave coming from the sun and, on the other hand, due to the absorption of the long wave coming from the sky and the surroundings and to emission from its own surface. The previous balance can be written b_cd;es ¼ b_cv;e  aes b_r;sun þ b_r;hv þ b_r;sur þ d_ es

(4.63)

where the exergy flows due to the heat transferred by conduction and by convection are obtained from the expressions seen in Sections 4.3.2 and 4.5.2, respectively, similar to what has been shown for the interior surface. For its part, the exergy of the absorbed solar radiation can be calculated from the equation ( )   1 T0 4 4 T0 _ aes br;sun ¼ aes GT 1 þ  3 Tsun 3 Tsun

(4.64)

where aes is the absorptivity of the surface for short-wave radiation. According to what was stated in Chapter 2, to make the analysis more accurate, we take into account the components of direct and diffuse irradiation, so that the exergy of the solar radiation absorbed will be " b_r;sun ¼ aes GD

"   #   # 4 T0 1 T0 4 4 T0 1 T0 4 1 sin a þ aes Gd 1  þ þ 3 TD 3 TD 3 Td 3 Td (4.65)

The sky emits radiation at a temperature of Tsky which, as we have seen, is significantly lower than the ambient temperature. The exergy of radiation emitted per unit area and time, according to Eq. (2.83), is 2 1 T0 4 4 sTsky 1þ 3 Tsky

!4

3 4 T0 5  3 Tsky

(4.66)

The Earth’s surface receives this radiation exergy, which is a cold exergy, following the terminology of Shukuya [36]. Shukuya obtained values for this exergy, depending on the ambient temperature and the relative humidity of the air. Expressing the above equation in terms of the emissivity of the sky we have   1 3 3 þ εsky  ε4sky sT04 3 4

(4.67)

Finally, the exergy flow due to the exchange of long-wave radiation between the exterior surface and the environment (considered together with the sky and

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Exergy Analysis and Thermoeconomics of Buildings

surroundings through the fictitious temperature Tf,sky) can be roughly evaluated by the expression 



2



3  T3 Tes f ;sky

3

4 4 5  Tf4;sky 41  T0  b_r;hv þ b_r;sur ¼ εes s Tes 3 4  T4 Tes f ;sky

(4.68)

Now, the heat that leaves the exterior surface of the envelope is finally exchanged with the environment by convection and long-wave radiation until reaching the ambient temperature. Therefore, the exergy flows that leave the exterior surface by convection and radiation are finally destroyed in the environment, meaning it is a lost exergy so that the previous terms of Eq. (4.63) can be grouped together, finally resulting in the equation b_cd;es þ aes b_r;sun ¼ I_e

(4.69)

In winter, the heat flow and exergy flow have the same direction, while in summer the heat flow is inward and exergy flow, on the contrary, outward. However, in both cases, the conclusion is the same, and all the exergy associated with the heat flow on the exterior surface is finally destroyed.

4.8.3

Examples

Example E.4.8. Let there be a facade formed by a layer of solid moulded brick with mortar joints, 11 cm thick and of thermal resistance 0.25 m2K/W and with an internal lime mortar plastering of 2 cm and thermal resistance 0.03 m2K/W. On a summer day when the outdoor air temperature is 28 C, and the indoor temperature is 24 C, the overall irradiation is 750 W/m2, with the absorptivity of the exterior surface for solar radiation being 0.45 and its emissivity 0.9. The temperature of the exterior surface is 40 C and that of the surrounding area is 32 C. Using the values of the convectionradiation coefficient of the Spanish BTC for exterior and interior surfaces, determine the following per m2 of facade:

(a) (b) (c) (d)

The heat flux by conduction and sun-air temperature. The interior surface temperature and intermediate temperature between the two layers. The exergy flows in the exterior surface and through the interlayer. The rate of exergy destroyed in the interior of the facade.

Solution (a) Carrying out an energy balance on the exterior surface of the facade, in accordance with Eq. (4.59), we have q_cd;es ¼ aes GT þ hcvr;e ðTeq  Tes Þ z aes GT þ hcvr;e ðT0  Tes Þ

Exergy analysis of heat transfer in buildings

299

We use the value of the convection-radiation coefficient of the BTC, according to which, the value to be taken for an exterior vertical surface is hcvr,e ¼ 25 W/m2K. As we will use it later in the exergy calculations, from this data we now calculate the pure convection coefficient. Taking into account that hcvr,e ¼ hcv,e þ hr,e, and that hr;e ¼ 4sεes Tm3 where Tm¼(Tes þ Tsur)/2, we have hr;e ¼ 4sεes Tm4 ¼ 4$5:67$108 $0:9

  313 þ 305 3 W ¼6 2 2 m K

so the convection coefficient is hcv,e ¼ 19 W/m2K. Returning to the energy balance equation, the heat flux by conduction gives q_cd;es ¼ q_cd ¼ 37:5

W m2

The sun-air temperature is Tsa ¼ Teq þ

aes GT aes GT z T0 þ ¼ 41:5 C hcvr;e hcvr;e

(b) The heat of conduction can be worked out using this calculated temperature, since according to Eq. (4.60) we have q_cd;es ¼ q_cd ¼ 25ð41:5  40Þ ¼ 37:5

W m2

As according to the BTC, the interior surface resistance in a vertical enclosure is Ris ¼ 0.13 m2/W, that is, hcvr,is ¼ 7.69 W/m2, the inner surface temperature is q_cd ¼ hcvr;i ðTis  Ti Þ / Tis ¼ 28:9 C while the temperature of the intermediate layer is Tin ¼ Tis þ q_cd Rin ¼ 30:0 C (c) The exergy associated with the heat flow exchanged by convection is     T0 T0 W 1 q_cv;e ¼ 1  hcv;e ðTes  T0 Þ ¼ 8:7 2 m Tes Tes The exergy flow associated with the long-wave radiation exchanged with the sky and surroundings is calculated from the fictitious temperature Tf,sky. Being a vertical facade, we can consider that Fes,sky ¼ 0 and therefore Tf,sky ¼ Tsur ¼ 32 C. Hence, the heat exchanged by long-wave radiation is   4 4 q_r;ðhvþsurÞ ¼ εes s Tes ¼ 48:2 W  Tsur

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Exergy Analysis and Thermoeconomics of Buildings

 3   3  _br;ðskyþsurÞ ¼ q_r;ðskyþsurÞ 1  4T0 Tes  Tsur  ¼ 1:3 W 4  T4 3 Tes m2 sur The exergy of the solar radiation that is absorbed by the exterior surface is ( )  4 4 T0 W _br;sun ¼ aes GT 1 þ 1 T0  ¼ 314 2 3 Tsun 3 Tsun m We have considered that Tsun ¼ 5780 K and the irradiation has not been broken down into its direct and diffuse components. Finally, the exergy flow of conduction on the exterior surface is   T0 W 1 q_ ¼ 1:4 2 m Tes cd;es while the exergy flow associated with conduction in the interlayer is   T0 W q_ ¼ 0:24 W 2 1 m Tin cd (d) The rate of exergy destroyed on the interior of the façade per unit of surface is Tes  Tis W ¼ 1:3 2 d_ cd ¼ T0 q_cd m Tes Tis Example E.4.9.

To calculate the temperature of the sky in cloudless skies, we can use Swinbank’s equation, which states that Tsky ¼ 0:0552T01:5 . Determine: (a) The temperature of a hot black surface that emits the same exergy of radiation as the sky, on a day when T0 ¼ 300 K. (b) And if the ambient temperature is T0 ¼ 250 K.

Solution (a) We calculate the temperature of the sky Tsky ¼ 0:0552T01:5 ¼ 287 K If the exergy of radiation emitted by the sky is the same as that emitted by a black surface of temperature T, then 4 3 3T 4 þ T04  4T0 T 3 ¼ 3Tsky þ T04  4T0 Tsky

and hence T ¼ 310 K

Exergy analysis of heat transfer in buildings

301

Therefore, the ‘cold’ exergy emitted by the sky is the same as that emitted by a hot black surface at a temperature of 310 K. (b) The temperature of the sky is Tsky ¼ 0:0552T01:5 ¼ 218 K 3T 4  4: 250$T 3 ¼ 3: 2184  4: 250$2183

/ T ¼ 280 K

We see that the lower the ambient temperature, the lower is the temperature of the hot surface that emits the same radiation exergy as the sky. Example E.4.10.

The roof of an industrial building consists of a rough concrete slab with dimensions of 10  25 m and 16 cm of thickness. On a winter night, the wind speed is 40 km/h, the ambient air temperature is 2 C, and the temperature of the sky is 23 C. The exterior surface of the roof is at 0 C, while the temperature of the indoor air and internal parititons is 10  C. Determine: (1) The heat transfer through the roof. (2) The flow of exergy associated with that heat flux. (3) The rate of exergy destruction on the exterior surface of the roof.

Solution (1) We shall take an emissivity of 0.94 for the rough concrete. For a wind speed of 40 km/h, the net convection coefficient according to Burberry for a horizontal surface and upward flow is hcv,e ¼ 50.3 W/m2K. According to these values, the heat flux exchanged by the exterior surface of the roof is  4 4  Tsky ¼ 47; 128 W Q_ es ¼ Q_ cv;e þ Q_ r;e ¼ Ahcv;e ðTes  T0 Þ þ Aεes s Tes It is the heat flux lost from the surface of the roof (2) The flow of exergy associated with that heat flux is   T0 _ 1 Qcv;e þ Tes

!   3 3 4 Tes  Tsky _ 271 25; 165 Q 1  T0 4 ¼ 1  r;e 4 3 Tes  Tsky 273   4 2733  2503 þ 1  271 21; 963 2734  2504 3 ¼ 584 W

The heat flow associated with convection involves an exergy flow that leaves the surface. With regards to radiation, although the emission of radiation is greater than the absorption of radiation from the sky, due to the low temperature of the sky, the exergy

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Exergy Analysis and Thermoeconomics of Buildings

associated with the radiation emitted by the sky and absorbed on the surface is greater than the exergy emitted by the surface itself and is associated with heat by convection; hence the negative sign. In effect, the quality factor for the radiation emitted by the

 4

surface is 1 þ 1 3 T04 Tes  4 3ðT0 =Tes Þ ¼ 4:4$104 while for the radiation from the . .  . 4  4 3ðT0 =Tsky Þ ¼ 0:021. sky it is 1 þ 1 3 T04 Tsky (3) All the exergy of the heat flux that reaches the exterior surface by conduction is finally destroyed in the surface itself, in the boundary layer and external environment, so that we have D_ ¼

  T0 _ Qes ¼ 345 W 1 Tes

A surface of 1.3 m2 that is at a temperature of 24 C, with an ambient temperature of 17 C, has an absorptivity of 0.9 for solar radiation and an emissivity of 0.6. It is observed that when the direct and diffuse components of solar radiation are 380 and 470 W/m2, respectively, with direct radiation having an incidence angle of 30 degrees, the surface temperature is 320 K. If the sky temperature is 280 K, determine:

Example E.4.11.

(a) The net heat transfer by radiation to the surface at that moment. (b) The exergy associated with the radiation exchanged.

Solution (a) The absorbed solar radiation is Q_ r;sun ¼ AaðGD cos q þ Gd Þ ¼ 1:3$ 0:9ð380 cos 30 þ 470Þ ¼ 618:5 W

while the heat exchanged by radiation with the sky is  4 4 Q_ r;hv ¼ Aεs Tsky  Tes ¼ 192 W so that the net heat transfer by radiation is  4  Ts4 ¼ 426:5 W Q_ r ¼ AaðGD cos q þ Gd Þ þ Aεs Tsky The exergy associated with the absorbed solar radiation is " B_ r;sun ¼ aGD

"   #   # 4 T0 1 T0 4 4 T0 1 T0 4 þ þ 1 cos q þ aGd 1  3 TD 3 TD 3 Td 3 Td

¼ 335 W

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303

while the exergy of the radiation exchanged with the sky is  3 2 3 Ts3  Tsky 4 5 ¼ 185 W B_ r;hv ¼ Q_ r;hv 41  T0  3 4 Ts4  Tsky Although the emitted radiation to the sky is greater than the absorbed radiation from the sky, due to the exergy of the radiation from the sky being greater than that of the emitted radiation the exergy of the exchanged radiation is positive.

4.9

Exergy exchanged by a building through an opaque envelope

In the previous sections, we obtained expressions to calculate the exergy associated with heat fluxes of conduction, convection and thermal radiation. Likewise, we have highlighted the exergy destruction that takes place in these three mechanisms of exergy transport, undertaking the corresponding exergy balances on the interior and exterior surfaces of a building. The exergy flows are very sensitive to the variations experienced by the RE when the temperatures of these flows and those of the RE do not differ much from each other, as is the case of buildings. This fact must be borne in mind when introducing simplifications in the evaluation of the exergy behaviour of the envelope. There are different methods in the application of exergy analysis to opaque enclosures, with a variable degree of complexity and detail. Below, we present a summary of the different methods, from lower to higher complexity and precision.

4.9.1

Steady-state method

It is the simplest method. The heat transmitted through an envelope is calculated from its thermal transmittance U, by means of the expression Q_ ¼ UAðTi  T0 Þ

(4.70)

where Ti is the indoor air temperature and A the surface of the envelope, C¸engel and Ghajar [15]. For the sizing up of air conditioning equipment, we usually assume that indoor air temperature Ti and exterior temperature T0 are constants, with their values being those corresponding to the design conditions (generally based on the hottest or coldest temperature of the year for that location). In some cases, especially when sizing up equipment whose performance or COP is greatly influenced by the outside temperature, the analysis is usually carried out considering the corresponding average outside temperature for each month, Angelotti and Caputo [37].

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Once the heat transmitted by the opaque envelope has been determined, the exergy associated with this heat is calculated as the sum of the heats transmitted through the different surfaces of the envelope, in accordance with the expression B_ Q ¼

 1

 en T0 X Q_ Ti j¼1 j

(4.71)

Even if a more detailed analysis were carried out, including considering the 8760 hourly values of outside temperature of the climatic year of the locality, it would still be a steady-state method, since the calculation of the energy losses through the envelope using the thermal transmittances does not take into account the thermal inertia of the walls. This method is, therefore, the first approximation and is not valid for a calculation of energy demands or exergy with a certain precision and it is basically for two reasons: • •

Performing a steady-state analysis does not permit taking into account the effect of the inertia of the envelope since by definition it cancels the term for energy variation (exergy) of the envelope in the corresponding balance. As discussed above, exergy flows are more sensitive to changes in the RE when the properties of the system are closer to those of the RE. This circumstance leads to the fact that steadystate analysis, common in studies of power plants or industrial facilities, are not valid for the exergy analysis of buildings in general and of facades or roofs in particular.

4.9.2

Quasi-steady method

It is an intermediate method between the steady-state and the dynamic method. In this method, the energy flows are calculated dynamically, while the exergy flows are evaluated by a steady-state approach during each time step of the simulation, that is, avoiding the possible storage phenomena. Together with the steady-state method, it is one of the methods proposed and used by legislation and regulations for the calculation of energy demand in buildings in many European countries, AENOR [38]. Being a dynamic method in the calculation of heat fluxes, spatial and temporal discretization of the problem is required. Thus, the envelope is represented by a set of nodes j equi-spaced at a distance Dx, forming an RC circuit. The resistance between two consecutive nodes is equal to the thermal resistance to the existing conduction between both. On the other hand, each node concentrates the heat capacity corresponding to the volume element associated with said node. If it is an interior node this element will have a thickness Dx, whereas if it is an exterior (surface) node, it will have a thickness Dx=2.

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305

Figure 4.10 Discretization of the envelope.

Fig. 4.10 represents a wall through a series of nodes connected to each other by a series of thermal resistances with there being in each node a capacitor representing the thermal capacity of the associated layer. Following the symbology used by Shukuya [36] the internal nodes are represented by circles in black, while the nodes representing the interior and exterior surfaces appear as white circles. These nodes are in turn connected to the interior and exterior air and the surfaces with which they exchange radiation, which are represented by white squares. In this way, the differential equation of heat transfer by unidimensional conduction in the non-steady state without heat sources or sinks is   l v2 T vT (4.72) ¼ rc vx2 vt which becomes the equation in finite differences   Tj;nþ1  Tj;n l Tj1;nþ1  2Tj;nþ1 þ Tjþ1;nþ1 ¼ 2 9$c Dx Dt

(4.73)

whose solution in the node j in that moment of time n is Tj,n. When expressing the spatial derivative in finite differences, there are, as we know, two options. Since the nodal temperatures, in general, vary during each time interval, the temperatures in the previous time interval or in the new time interval can be used, as in Eq. (4.73). The first option constitutes what is known as the explicit method and the second is the so-called implicit method.

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In the explicit method, the set of equations for each node is independent of each other, so the numerical resolution is very simple. As a disadvantage, the method imposes limits on the maximum allowed values of distances between nodes ðDxÞ and time interval ðDtÞ, in order to be stable (adimensional Fourier number < 0.5). On the other hand, the implicit method supposes a greater computational effort, since it requires resolving all the nodal temperatures simultaneously for each instance, but it is intrinsically stable regardless of the number of nodes and the time interval Dt chosen, C¸engel and Ghajar [15]. Considering that in many cases the behaviour of the envelope will be simulated for long periods of time, even a whole year, the implicit method for resolution is recommended, as it does not need extremely small time steps. Eq. (4.73), properly reordered, gives for a generic node j the following  kTj1;nþ1 þ ð1 þ 2kÞTj;nþ1  kTjþ1;nþ1 ¼ Tj;n

(4.74)

where k is the adimensional Fourier number, that is k¼

Dt l Dx2 rc

(4.75)

If the wall is divided into M intervals of width Dx, there will exist Mþ1 nodes, see Fig. 4.10. Of all of them, in the extreme nodes (nodes 1 and Mþ1) the boundary conditions are applied and their temperatures are known at all times, as they will have been previously obtained in TRNSYS. Therefore, Eq. (4.73) only needs to be applied in the instant n þ 1 to the M  1 internal nodes. Assuming that all the temperatures in the instant n are known (they have been calculated previously or are initial conditions) and that also temperatures T1,nþ1 and TMþ1,nþ1 are known (they are boundary conditions), the system of M  1 equations with M  1 unknowns is 8 ð1 þ 2kÞT2;nþ1  kT3;nþ1 ¼ T2;n þ kT1;nþ1 > > > > > > > kT2;nþ1 þ ð1 þ 2kÞT3;nþ1  kT4;nþ1 ¼ T3;n > > > > > > < kT3;nþ1 þ ð1 þ 2kÞT4;nþ1  kT5;nþ1 ¼ T4;n (4.76) > > / > > > > > > kTM2;nþ1 þ ð1 þ 2kÞTM1;nþ1  kTM;nþ1 ¼ TM1;n > > > > > : kTM1;nþ1 þ ð1 þ 2kÞTM;nþ1 ¼ TMþ1;n

Exergy analysis of heat transfer in buildings

307

and in matrix form

(4.77) This system written compactly is A$T nþ1 ¼ T n

(4.78)

where the matrix of coefficients A depends solely on the properties of the wall (l, r, c), of the nodal distance Dx and the chosen time step Dt. Once these parameters are set, the matrix is constant throughout the simulation, so the vector of new temperatures Tnþ1 can be easily obtained for any time as T nþ1 ¼ A1 T n

(4.79)

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Once the energy balance is done, we will know the heat flux in successive instants and, of course, the surface temperatures Tis(tk) and Tes(tk). Performing an exergy balance for the total envelope in the instant tk we have _ kÞ Dbðtk Þ ¼ b_q;is ðtk Þ  b_q;es ðtk Þ  dðt

(4.80)

In this method called quasi-steady-state, the term for the variation of the exergy _ k Þ. accumulated in the envelope Dbðtk Þ is grouped with the exergy destruction dðt This then is a term, that following Annex 49 [39] is called exergy consumed, b_cons . Therefore _ k Þ ¼ b_q;is ðtk Þ  b_q;es ðtk Þ b_cons ðtk Þ ¼ Dbðtk Þ þ dðt

(4.81)

Consequently, the exergy consumed in the interval tk is     _bcons ðtk Þ ¼ q_is ðtk Þ 1  T0 ðtk Þ  q_es ðtk Þ 1  T0 ðtk Þ Tis ðtk Þ Tes ðtk Þ

(4.82)

This type of approach is based on a valid approximation only in those systems that do not have a significant storage capacity. However, in many cases, it is not an appropriate method. Taking advantage of the matrix expression of the problem and in order to automate both the calculation of the inverse of the matrix A as well as the resolution of the system of equations for any situation, a code can be implemented in MATLAB. The composition of the envelope (number of layers and thickness, thermal conductivity, density and specific heat of each layer), ambient temperature and interior and exterior surface temperatures are used as input data. These last two are precisely the boundary conditions at the extreme nodes (1 and M þ 1) that allow the resolution of the system of Eq. (4.78). The values of these extreme nodes for each instant of time are obtained by linear interpolation from the time values previously calculated with TRNSYS. For an easier treatment of the results, taking into account that the time step chosen may be, for example, 1 min, the energy and exergy flow values obtained at each instant are subsequently accumulated in hourly values. Finally, it is worth mentioning that, for avoiding possible errors due to the initialization of the internal temperatures in the wall, the calculations can be made with the data corresponding to two full years, taking the values of the second year, as results. The selection of such a large past period is not really necessary, since the values used as initialization of the problem affect, in the worst case, the first 240 h. Proposing a previous period of 1 year is for the simplicity of programming, with the additional computational effort not being excessive. For a laptop with an Intel Core Duo processor at 2.53 GHz and 4 GB of RAM, the simulation time in MATLAB for each case is a few minutes.

Exergy analysis of heat transfer in buildings

4.9.3

309

Simplified dynamic method

Once the energy flows are calculated by the method described in the previous Section 4.10.2, the simplified dynamic method separately considers the exergy stored in the enclosure and the exergy destructions, Torio and Schmidt [39]. Therefore, the consumed exergy includes only the inevitable irreversibilities associated with the temperature difference necessary for heat transfer. The exergy stored in the time interval between tk and tk-1 is " # N X Tj ðtk Þ Dbðtk Þ ¼ rj cj lj Tj ðtk Þ  Tj ðtk1 Þ  T0 ln (4.83) Tj ðtk1 Þ j¼1 From the exergy balance, Eq. (4.9) and taking into account the previous expression, we have that the rate of exergy destroyed in the envelope in the time interval tk is     _ k Þ ¼ q_is ðtk Þ 1  T0 ðtk Þ  q_es ðtk Þ 1  T0 ðtk Þ dðt Tis ðtk Þ Tes ðtk Þ " # (4.84) N X Tj ðtk Þ rj cj lj Tj ðtk Þ  Tj ðtk1 Þ  T0 ðtk Þln  Tj ðtk1 Þ j¼1 As can be observed from the previous expressions, for the evaluation of the stored exergy and the destroyed exergy it is necessary to know the interior temperatures of the wall, at least in each layer (subscript j) and each moment. This necessity represents a problem in many cases. In fact, most of the energy simulation programs for buildings enable knowledge of the energy stored in the wall through the application of the corresponding energy balance. On the other hand, it is not possible to directly obtain the internal temperatures of the wall since it is very common to use the method of transfer functions (CTF), developed by Stephenson and Mitalas [40] for the calculation of the transient heat transfer through it. This is the case for software as popular as EnergyPlus [41] or TRNSYS [42], Klein [43]. An approximate way to solve this problem, proposed by the working group of Annex 49 [39] and Torio [44], has been to replace the real wall with an equivalent homogeneous wall and to approximate its average temperature at every moment Tm(tk) to the average value between the interior and exterior surface temperature, Tis(tk) and Tes(tk), at said moment, that is, Tm(tk) ¼ (Tis(tk)þTes(tk))/2.

4.9.4

Detailed dynamic method

The problem presented by the approximation of the simplified dynamic method described in the preceding paragraphs is that it does not provide the values of internal temperatures of the wall, or at best, approximates them to a linear variation between the two surface temperatures. When calculating the average temperature of the wall in a

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Figure 4.11 (A) Profile of possible temperatures not considered by the simplified dynamic method. (B) Values of the actual average temperature, Tm,dd (black) and the average temperature according to the simplified dynamic method, Tm,sd (blue [grey in print version]).

linear way, this approach can avoid possible maximums and/or minimums of temperature that can occur inside the envelope at certain times of the day. These unconsidered maximums or minimums give rise to an inversion in the direction of the heat fluxes with respect to those obtained with the approximation, see Fig. 4.11a. It could even happen that the actual average temperature of the wall Tm,dd would be greater than the highest of the surface temperatures, Tis or Tes, a situation which is impossible according to the simplified dynamic method hypothesis, see Fig. 4.11b. As for the calculation of exergy balances, it is required to know the accurate internal temperatures of the wall; in the Flores thesis [16], a methodology was proposed that allows them to be calculated, both in homogeneous walls and in those formed by different layers of materials. The calculations are made with MATLAB using a code based on the finite difference method. This method allows the equation of the exergy balance to be solved more precisely, Eq. (4.84), and constitutes what we call the detailed dynamic method. It involves calculating the interior temperatures of the wall, using the surface temperatures obtained with dynamic simulation software, such as TRNSYS, as boundary conditions. The method consists of approximating the differential equation of heat transfer by conduction in the dynamic state to a finite difference equation, obtained from the truncation of the Taylor series, as explained in Section 4.10.2. As Flores explains in his doctoral thesis, this method has been compared with the different existing methods, for a series of cases with different climates, inertias and transmittances. Although in some cases there are hardly any differences, it is in the range of inertias commonly used in construction where the greatest discrepancies in the results are found. For this reason, and given the low computational cost involved, it is advisable to use the detailed dynamic method for the exergy analysis of envelopes.

Exergy analysis of heat transfer in buildings

4.10

311

Indicator of exergy behaviour of a wall

A drawback that characterizes the exergy behaviour of systems is that there is a great variety of coefficients or indicators that reflect the efficiency of their behaviour, as we have already seen in Chapter 1. This drawback arises precisely because of the versatility of exergy analysis, as it can be applied to different disciplines and areas of life. This fact has led to a certain lack of standardization, and the choice of one or the other indicator is often open to individual interpretation, Marmolejo-Correa and Gundersen [45]. Despite this great diversity, there is no an exergy index that can be properly applied to the characterization of facades or roofs. Indeed, the most common indicators such as the universal exergy efficiency, used by authors such as Boelman and Sakulpipatsin [46], Cornelissen and Hirs [47], Torio et al. [23], or the functional efficiency used by authors, such as, Kotas [48] and Tsatsaronis [49], are originally intended for application in industrial processes or power generation facilities. Even when applied to the building sector, as in Favrat et al. [50] or Gonçalves et al. [51] they are not used to evaluate the behaviour of envelopes. The only parameter related a priori to the exergy behaviour of the building envelope found in the bibliography is that proposed by Tronchin and Fabbri [52]. But in the calculation of this parameter, the authors do not take into account the dynamic behaviour of the envelope and do not distinguish between the mechanisms of convection and radiation. This fact and its lack of physical meaning have resulted in it not being used. However, it is necessary to define a parameter that characterizes the exergy behaviour of building envelopes. In order for this parameter to meet the required needs, we must consider the behaviour of the envelope as a dynamic system and, in addition, for a greater ease of application, it would be of value if this parameter did not involve tedious operations, was easy to interpret and did not involve a radical change with respect to what already exists. In his doctoral thesis, Flores [16] defined five different possible parameters. Once the results were analysed for the different walls, climates, etc. he proposed the one that is of most interest from a theoretical and practical point of view. As a starting point, taking the expression proposed by the ISO 9869-1 standard [53], for the ‘in situ’ determination of the thermal resistance of a wall, he defines a dynamic exergy transmittance according to the expression PN ex Udyn

_

j¼1 bq;is;j

¼ PN

j¼1 DTj

! T0;j j¼1 q_is;j 1  Tis;j  PN  j¼1 Ti;j  T0;j

PN ¼

(4.85)

Among the advantages of this proposed parameter are: •

The possibility of being measured ‘in situ’: this parameter can be measured with the same equipment with which the value of the thermal resistance of a wall is determined according to the ISO 9869-1 standard. By means of three temperature probes (air outside, indoor air and

312

•

• • •

Exergy Analysis and Thermoeconomics of Buildings

interior surface) and a heat flux-meter on the interior surface all the terms that appear in Eq. (4.85) can be determined. The difference with respect to the measurement of the thermal transmittance is that, in this case, it is necessary to measure for a whole year, or at least for the heating (or cooling) season, due to the dependence of exergy on the climatic conditions. The other limitations for its experimental determination are the same as in the case of thermal transmittance. It is an alternative to testing: the value of this index can be obtained by simulation of the building. As the variables used (heat flow and temperatures) are the usual output variables in energy simulation programs, it does not require important modifications or the development of complicated codes. Similarity to thermal transmittance: being a similar concept and formula to the thermal transmittance, its use by technicians, or even by administrations, as a control parameter in regulations, would be easy to introduce. ex Ease of interpretation: when comparing two envelopes, the one with the lowest value of Udyn would be the best from an exergy point of view. It considers the dynamic state of the wall: when calculated from the values of heat fluxes and temperatures, it implicitly takes into account both its resistance and its thermal capacity.

A priori someone could raise as a possible drawback that the dynamic exergy transmittance of the same facade gives different values for different climates. This circumstance is unavoidable and inherent in any parameter in which exergy operates, given its dependence on the ambient temperature. However, this drawback could be avoided, if the regulations establish limiting values depending on the locality, in a similar way to what was done in the BTC of 2006 with thermal transmittance, or with energy consumption and demand in the latest version of 2013. The latter proposal could at the same time serve to limit, albeit partially, a building’s energy demand. In fact, once internal temperature levels are set, for example, depending on the outside temperature as stated in the EN 15,026 AENOR 2007 standard [54], the denominator of Eq. (4.85) is constant for a given location. On the other hand, the level of insulation that is currently required and considerations of comfort for the user means that the value of the interior surface temperature moves by very limited values and is close to the indoor air temperature. In this way, establishing a limiting value for ex for a locality, is implicitly limiting the energy demand (exergy) of a building due Udyn to losses through the envelope.

4.10.1

Examples

Example E.4.12.

We want to know the effect of the retrofitting of a façade by an SATE (External Thermal Insulation System). For this, the façade was tested, before and after its renovation, in order to calculate the steady-state and dynamic thermal transmittances, as well as the dynamic exergy transmittance before and after placing the SATE. It consists of a vertical double-layer façade made up, from outside to inside, by 2 cm of mortar plastering, perforated solid brick of 11.5 cm thickness with continuous horizontal and vertical mortar joints, 1 cm of mortar plastering, an air chamber 5 cm wide, single hollow brick 4 cm thick with continuous horizontal and vertical mortar joints, covered with 2 cm of thick plaster and 1 mm thin layer of gypsum plaster.

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313

Solution The façade was tested in a PASLINK test chamber following the procedures described in the document Van Dick, H.A.L. and Van Der Linden, G.P. PASLINK Calibration and component test procedures, TNO, Delf, 1995 developed by the European network PASLINK EEIG. The dimensions of the sample were 2.7  2.7 m (surface area of the sample 7.29 m2) and it was built on an insulating pre-frame, as can be seen in Fig. E.4.1.

Figure E.4.1 Sample of the enclosure and its pre-frame prepared for the test.

Next, a sample of the façade renovated by the SATE was prepared and its dynamic behaviour was tested to calculate its dynamic transmittance and dynamic exergy transmittance. The SATE system consists of rock wool panels 5 cm thick placed on a metal substructure, a 5 cm air chamber, a water barrier film which is permeable to vapour and plates fixed on the outside of the structure. Once the plates were fixed and dried, the reinforcement and levelling plaster was applied with a mortar base incorporating a fibreglass mesh and a stone base plus a finish with acrylic plaster. Fig. E.4.2 shows the façade with the SATE already placed in the test cell.

Figure E.4.2 Sample of the façade with SATE placed in the test chamber.

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.4.3 Effect of SATE on the lag and attenuation of heat wave.

In addition to the instrumentation required by the PASLINK test itself, to characterize the sample, twenty-one PT100 sensors were placed in the different layers of the sample, three Type T thermocouples, five heat flux sensors for contrast and three relative humidity sensors. Fig. E.4.3 represents the difference of temperature between the interior and exterior environment, as well as the heat flux through the façade per unit area, for a day of January in the city of Vitoria-Gasteiz, which is chosen as representative of climatic area D1. The effect of SATE is clearly seen, both in the lag of the heat wave and in its damping. The objective of the tests carried out was to have the necessary data to be able to construct a model of the initial wall and the retrofitted one, which would allow us to know the thermal behaviour for any climatic condition. In this way, the heat gains and losses through the walls can be quantified for any climate and the value of renovation with the SATE can, therefore, be evaluated; in short, the thermal model allows us to understand the thermal behaviour of the façade whatever be the climatic conditions. The thermal model constructed was of the distributed parameter type, that is, an RC model. The heat fluxes on the interior and exterior surfaces of the single hollow brick and solid perforated brick were used as objective functions. The identification system used was based on Monte Carlo and the downhill method, with the idea of finding the vector of resistance and thermal capacities that minimizes the error between the objective function and the equivalent function obtained through the model. The resolution of the equations for the calculation of the resistances and thermal capacities as a function of time was done by the application of the LORD 3.21 software. Both the tools and the calculation procedure were developed by the PASLINK network. In Fig. E.4.4 the simplified scheme of the RC model is shown, both for the non-renovated façade and for the one renovated with the SATE.

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315

Figure E.4.4 RC model of the façade.

Once the models were obtained, the thermal transmittance of both walls was calculated, according to the equation U¼

1 Ris þ Rm þ Res

where Ris and Res are the normalized surface resistances, that is, the values indicated by the TBC in the DB-HE-1 Document and Rm is the sum of the thermal resistances of the different layers of the wall. In a dynamic system, the effect of the capacity of the wall to accumulate heat and the interaction with solar radiation implies that the thermal load associated with the façade differs from that calculated by the use of thermal transmittance. One way of evaluating the effect of the said capacity is using a coefficient that represents the average behaviour, throughout the day, of the thermal gain with respect to the temperature differences between interior and exterior environment. We call this coefficient dynamic transmittance, Udyn and it is obtained by the following expression PN

j¼1 q_is;j

Udyn ¼ PN  j¼1

Ti;j  T0;j



The dynamic exergy transmittance is a sophistication of the previous expression since, instead of considering the heat flux in the inner surface of the envelope, the exergy associated with that heat flux is taken into account. As we have seen, it is calculated from Eq. (4.85).

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In Table E.4.2 the values of the thermal gains and losses are shown per m2 of façade throughout the year for the city of Vitoria-Gasteiz, climatic zone D1, as well as the monthly values of the dynamic thermal transmittance Udyn for the wall before and after being renovated. Fig. E.4.5 shows the values of thermal transmittance U (in steady state) and dynamic transmittance for the tested wall, before and after the renovation, for each month of the year. One can clearly see, that unlike the steady-state U, the dynamic transmittance Udyn varies over the months, increasing significantly in the summer months for the base case. In Fig. E.4.5 the effect of the renovation with the SATE is also recognized, since both the steady-state U as well as the Udyn decrease in a significant way.

Figure E.4.5 Values of U and Udyn of the two façades in Vitoria.

Lastly, in Table E.4.3 and Fig. E.4.6 the values obtained for the dynamic exergy transmittance are shown. Comparing the values with those of the dynamic transmittance we see that the behaviour is qualitatively similar, but naturally, its values are much lower, since now it is the exergy values that appear in the numerator, and these are much smaller than those of the energy.

4.11

Exergy and thermal comfort

The purpose of air conditioning and ventilation is the attainment of thermal comfort conditions; therefore, the definition of a suitable comfort standard is the basis of its design. Given the importance that the method of exergy analysis can have in its application to buildings, it is very important to understand the exergy balance of the human body, in order to appreciate how the heating and cooling demands can be supplied with the highest efficiency, guaranteeing comfortable conditions at all times. We present first a brief summary of the thermal comfort standards, in order to then give an introduction to the application of exergy in this context.

BASE Thermal losses Udyn(kWh/m2 month) 2

Thermal gains (kWh/m month) 2

U Dynamic (W/m K)

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Total

11.22

9.08

7.97

7.22

5.54

4.07

2.99

2.77

3.1

4.61

8.13

11.05

77.75

0.38

0.43

0.74

0.68

0.82

1.02

1.97

2.46

2.45

1.6

0.28

0.26

13.09

1.03

0.97

0.91

0.95

0.95

0.95

1.09

1.19

1.11

0.97

0.94

1.03

4.37

3.59

3.26

2.25

2.25

1.58

1.02

0.83

0.9

1.69

3.21

4.3

29.25

0

0

0

0

0

0.01

0.1

0.07

0.13

0.01

0

0

0.32

0.38

0.36

0.33

0.33

0.33

0.29

0.29

0.23

0.22

0.26

0.35

0.3

Exergy analysis of heat transfer in buildings

Table E.4.2 Gains, losses and dynamic transmittances of the two walls for Vitoria.

BASE D STATE Thermal losses Udyn(kWh/m2 month) 2

Thermal gains (kWh/m month) 2

U Dynamic (W/m K)

317

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.4.6 Dynamic exergy transmittance of the two façades for Vitoria-Gasteiz.

4.11.1

Thermal comfort standards

Currently, the most important thermal comfort standards are the UNE-EN-ISO 7730 (European) [55] and ASHRAE-55 (American) [56] standards. Both standards are based on the assumption that human beings are thermo-regulated machines, which must maintain body temperature while exchanging mass and energy with the environment. Through these balances, we can analyse the influence of the physical parameters of the environment, such as temperature, relative humidity, airspeed and average radiant temperature in relation to the thermal insulation of a person (CLO) and the metabolic activity of an individual (MET). First of all, carrying out a water balance and applying the First Law of Thermodynamics, we obtain a result that determines the load/discharge of energy that the human body experiences in relation to its own thermoregulation mechanisms and which are activated in different modes according to whether the environment is cold, hot or temperate. This energy balance creates a scale of sensations, which later, according to a purely statistical criterion, determines the degrees of dissatisfaction. There are also local discomfort criteria in the cited standards, which qualify the thermal sensation of people and that must be taken into account when designing HVAC systems. These criteria of local discomfort determine the dissatisfaction created by exchanges of heat localized in parts of the human body, which activate the body’s defences, regardless of whether the overall balance is of comfort. This may include possible uncomfortable air currents, asymmetries of radiant temperature with vertical gradients of temperature, situations producing cold feet, etc. In relation to these criteria, there are certain differences between the European and American standards, though not concerning conceptual issues, but that basically the American standard sets ‘comfortable’ as being slightly colder than the European standard. On the other hand, both standards introduce the possibility that human beings have certain inertia in their thermal sensations so that they can assume situations to be comfortable that are not actually in the comfort zone during a period of time.

Exergy analysis of heat transfer in buildings

Table E.4.3 Values of the dynamic exergy transmittance of the two façades for Vitoria-Gasteiz BASE

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Uex dynamic (mW/m2K)

46.0

40.1

25.1

29.2

22.7

16.1

18.5

20.1

18.9

23.1

38.7

42.6

16.9

14.8

9.0

10.1

7.8

4.9

4.9

3.9

3.7

6.2

14.4

16.1

BASE D SATE Uex dynamic (mW/m2K)

319

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Exergy Analysis and Thermoeconomics of Buildings

This circumstance is lightly treated in both standards, and it can be seen that there is a deficit of research on this aspect. The ASHRAE 55 standard even differentiates between cyclic thermal modifications and deviations and ramps, setting temporary acceptance limits for cyclical situations. This standard mentions the concept of adaptive comfort and presents it as an optional method to determine comfort in buildings without air conditioning, in which people have freedom in clothing and have access to the opening of windows and natural means of ventilation. This concept also appears in the European standard UNE-EN 15521, in its annex A, and is defined as informative. This criterion considers variable comfort values depending on the external conditions. The adaptive approach does not yet figure in the aspects that determine the design of buildings and their concepts relative to comfort. However, it is a valuable contribution, which comes from exhaustive statistical studies developed by different authors, among which we should mention Humphreys and Nicol [57]. In short, there are three criteria for thermal comfort, which we could call: static, transient and adaptive. The European standard UNE-EN-ISO 7730 is developed based on Fanger’s postulates [58], through the PMV (Predicted Mean Vote) and PPD (Predicted Percentage of Dissatisfied) indices. The PMV index is applied to humans exposed to constant environmental conditions during a long period in which an invariable metabolic rate is maintained. For its evaluation, the energy conservation equation is used. The resolution of the equation, which requires certain iterative processes, leads to a PMV value that depends on the following parameters PMV ¼ f ðT0 ; pv ; Tmr ; vra ; MET; CLOÞ

(4.86)

where T0 represents the dry bulb temperature of the environment, pv the vapour pressure of the air, Tmr the mean radiant temperature, vra is the residual velocity of the air, MET the individual’s metabolic rate, and CLO an index that represents the insulation of the clothing. The value of PMV obtained from the above equation from the physical parameters mentioned can take values on a scale ranging from ‘e3’ very cold to ‘þ3’ very hot. The range of intermediate values expresses the sensation of comfort, which can be related to a more intuitive interpretation value called PPD (Percentage of Persons Dissatisfied) by means of an equation. The ASHRAE 55 standard uses the ET-DISC (ET Effective Temperature, DISC Discomfort) model. The DISC value represents the relative thermoregulatory stress necessary to reach a state of thermal equilibrium and uses a scale (Cold/Warm/Hot) the same as in the European case. The effective temperature ET is the temperature of an environment with 50% relative humidity in which a person experiences the same amount of losses as in the situation under analysis. The American model determines the heat and vapour flow between the interior of the human organism, the skin and through clothing by using a model based on two concentric cylinders (one represents the skin and the other the clothing) and the use of a two-node calculation module. The model allows us to obtain solutions in time

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321

from an initial moment until stabilization is reached. The output values of this model are used to obtain the ET-DISC values, in addition to other indices, such as SET (Standard Effective Temperature) which represents the thermal stress experienced by the inner cylinder referring to a standard person in a standard environment.

4.11.2 Thermal model of the human body and energy balance Different authors have come up with different models to represent the thermodynamic behaviour of the human body. In the ECBS Annex 49 [39] the human body is considered to be made up of two subsystems: the core and the envelope. The core is a subsystem whose temperature remains constant at approximately 37 C, independently of the variations of temperature and humidity of the ambient air, whereas on the contrary, the envelope is a subsystem highly dependent on those variations. Between both subsystems, there is a variable blood flow dependent on the internal and external conditions of the body, see Fig. 4.12. Other authors like Ferreira and Yanagihara [59] have modelled the human body as a set of 15 cylinders that represent the head, neck, trunk, arms, forearms, hands, thighs, legs and feet. Each cylinder contains a set of tissues, such as skin, fat, muscles, etc. and are interrelated to each other through the bloodstream. Whichever model is used, the energy balance in each of the subsystems that make up the human body is resolved. For this it is necessary to specify first the thermophysical properties of each subsystem, that is, the values of density, specific heat and thermal conductivity. One of the terms of the energy balance is the metabolism M, which is the set of chemical reactions of oxidation that release energy and maintain the processes of life. There are different models like that of Harris and Benedict [60] that correlate metabolic activity with body mass, age and height for each sex. Another term in the energy balance is the heat transferred to the environment by convection and radiation. With hcv being the convection coefficient, hr the linear radiation coefficient of the subsystem under consideration, A the exterior surface of the

Figure 4.12 Thermal model of the human body.

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subsystem, Tskin the surface temperature of the skin and fclo the relationship between the surface covered by clothing and the naked surface, so that for a naked person fclo ¼ 1 (so then the surface temperature of the clothing is that of the person’s skin), we have Q_ ¼ Q_ cv þ Q_ r ¼ A

Tskin  Top 1 Rclo þ fclo ðhcv þ hr Þ

(4.87)

In this equation Top is the operating temperature, that is, a unique temperature that the air and the interior surfaces should have so that an average person exchanges by convection and radiation the same amount of energy that is exchanged in the real situation. This operating temperature is calculated according to the expression Top ¼

hr T r þ hcv Ti hr þ hcv

(4.88)

with T r the average radiant temperature of the surfaces of the enclosure, that is, the unique and uniform temperature of the surfaces with which the heat transfer by radiation with a person located inside is the same as that produced with the real surface 

temperatures. In practice, as hr z hcv the arithmetic mean Top ¼ T r þ Ti 2 is normally used as the operating temperature. The enthalpy flow associated with evaporation from the skin can be calculated by the following expression ps;skin  f0 :ps;0 H_ ev ¼ AW hv ¼ m_ v hv 1 Rev;clo þ fclo hev

(4.89)

where W is the moisture of the skin, which varies between 1 when the skin is completely covered with sweat to 0.06 when there is only vapour diffusion, hev is the equivalent evaporation coefficient, Rev,clo it is the resistance to vapour diffusion of the clothes, ps,skin is the saturation vapour pressure at the temperature of the skin, pv,0 is the saturation pressure in the environment, f0 is the relative humidity of the environment and m_ v , hv are the mass flow rate and the specific enthalpy, respectively, of the vapour generated. Another term in the energy balance is associated with breathing. With m_ res being the mass flow rate of dry breathing air, Tex, uex the temperature and absolute humidity of the expired air and hv,ex the specific enthalpy associated with that expired air, the sensitive and latent losses associated with respiration are   H_ res ¼ m_ res cp;a ðTex  T0 Þ þ m_ res uex hv;ex  u0 hv;0

(4.90) 0

where the mass flow of breathed air is directly linked to the metabolism M .

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323

The variation of the internal energy of the subsystem under consideration is a sum of the metabolism level and the variation due to the change in environmental conditions, that is dU dU ¼ M_ þ jDT dt dt

(4.91)

With W_ being the mechanical power generated by the person, so that for the base metabolism W_ ¼ 0. According to the First Law the following equation must be fulfilled, expressing the internal energy variation of the body over time due to transient environmental conditions   dU j ¼ M_  Q_ cv þ Q_ r þ H_ ev þ H_ res þ W_ dt DT

(4.92)

4.11.3 Exergy balance in the human body A complete study of the energy behaviour of the human body requires the use not only of the First Law, but also of the Second, in order to evaluate the quality of the energy conversion processes that take place in the different organs and systems. Over the years, different models of the exergy behaviour of the human body have been developed, and we highlight the work of Shukuya [61], Iwamatsu and Asada [62], and Mady et al. [63]. Since 2013 there have been numerous works published on the exergy behaviour of the human body, Caliskan [64], Mady et al. [65] among others. In a way similar to what we said for internal energy, the rate of exergy change of the human body is due, on the one hand, to metabolism and, on the other, to the effect of the change of environmental conditions, so that with A being the exergy of the human body, we have dA dA ¼ B_ M þ jDT dt dt

(4.93)

Batato et al. [66] showed that the change of energy due to metabolism and the exergy change are practically identical, so that we can use the approximation M_ z B_ M . The exergy associated with the heat flux exchanged by convection and radiation is B_ Q ¼ 0



0

  T0  _ Qcv þ Q_ r 1 Tskin 00

(4.94)

00

With h , s and h , s the specific enthalpy and entropy of saturated water and saturated vapour respectively at skin temperature, the flow of exergy associated with vapourization on the skin is represented by the following equation B_ ev ¼ m_ v ½ðh00  h0  T0 ðs00  s0 ÞÞ þ m_ v Rv T0 ln

ps;skin pv;0

(4.95)

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Exergy Analysis and Thermoeconomics of Buildings

an expression in which the physical and chemical exergy of the vapour generated on the surface of the skin is taken into account. The exergy flows exchanged by respiration are associated with the inspired and expired air. Obviously, we assume ideal gas behaviour, and for convenience we separate the part of the exergy associated with dry air from that of water vapour, so that we have B_ res ¼ B_ a þ B_ v

(4.96)

where, according to Eq. (3.12) and Eq. (3.92) we have " B_ a ¼ m_ res ð1  uex Þ cp;a



Tex Tex  T0  T0 ln T0



# pa;ex þ Ra T0 ln pa;0

(4.97)

1 pa;ex þ m_ res ð1  uex ÞRa T0 ln 1 þ uex pa;0 " B_ v ¼ m_ res uex

#   Tex pv;ex þ Rv T0 ln cp;v Tex  T0  T0 ln T0 pv;0

þ m_ res uex Rv T0

uex pv;ex ln 1 þ uex pv;0

(4.98)

From the exergy balance in the human body we get that the rate of exergy destruction is     dA _ _ (4.99) D ¼ BM   B_ Q þ B_ ev þ B_ res  W_ dt The exergetic performance of the human body as an energy converting system is expressed by f¼1

D_ jdA=dtj

(4.100)

When the exergy balance is performed in each of the subsystems that are usually considered in the modelling of the human body, it is necessary to consider the exergy associated with arterial and venous blood flows exchanged by each subsystem. By knowing the specific heat of the blood, the corresponding temperatures and mass flows, rates, these exergy flows are calculated by applying Eq. (3.44). In short, calling B_ ar , B_ ven the flow of exergy associated with the flow of arterial and venous blood respectively, through the balance of exergy in the subsystem s we have that    dAs s s s s s D_ ¼ B_ M   B_ Q þ B_ ev þ B_ res  W_ þ ðB_ ar þ B_ ven Þin  ðB_ ar þ B_ ven Þout dt (4.101)

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325

Using this and other similar mathematical models of exergy balance in the human body, we come to some very interesting conclusions. Thus, Ala-Juusela [67] showed that, in the heating period, the minimum exergy consumption of the human body can be achieved at higher average radiant temperatures and lower indoor air temperatures. Therefore, in winter conditions, there is a set of indoor air temperatures between 18 and 20 C and average radiant temperatures between 23 and 25 C for which the consumption of exergy of the human body is minimal so that these conditions of minimum exergy consumption correspond to maximum thermal comfort conditions. These conditions can be achieved with radiant systems (systems of low temperature of heating and high temperature of refrigeration) that provide the energy required to satisfy the demand at a temperature close to the ambient temperature. Likewise, it has become clear that the trunk and the head are the parts of the body in which the greatest exergy destruction takes place and, consequently, they have the lowest efficiencies.

4.12

Energy and exergy demand of a building

To finish this chapter, we will address the calculation of the exergy demand of a building. To do this, we will first recall the essential ideas about the calculation of energy demand, since this is the basis for calculating the exergy demand.

4.12.1 Calculation of energy demand The energy demand for premises is the amount of energy required throughout the year to maintain the premises in the conditions of comfort required by the users. We will review first the distinction between what is gain and what is load, and we will make a brief summary of the existing methods for calculating the demand. It is evident that to calculate the energy (exergy) demand it is necessary to previously define the limits of the system on which the corresponding balance is to be made. This boundary surface corresponds to the interior surfaces of walls, floors and roofs. For a more detailed study, the reader should refer to the abundant literature on this subject, for example in O’Callaghan [68] or Calener [69].

4.12.1.1 Gains (losses) of heat Heat gains (losses) are understood to be the heat fluxes entering (leaving) the control volume defined by the established physical limits. These gains may be of external origin, such as •

•

Gain (loss) of heat by conduction through walls, ceilings, etc. in contact with outside air. Heat gains (losses) through external opaque envelopes are due not only to the temperature difference between the surface of the exterior wall and the ambient air but also due to the solar radiation absorbed. The variations of outside temperature and solar irradiation and the inertia of the walls make the problem dynamic, and the heat transfer equation must be solved for a non-steady system. Gain of incoming solar radiation through windows and skylights.

326

•

•

•

Exergy Analysis and Thermoeconomics of Buildings

The transmission of heat through semi-transparent media is due, on the one hand, to conduction and, on the other, to the incident solar irradiation. The resulting heat flux can be determined from a global energy balance, although for practical reasons both aspects are treated separately and the principle of superposition is applied, Stout and Billings [70] defining what is known as the solar factor. Gain (loss) of heat due to ventilation. Ventilation is the voluntary entry of outside air in order to maintain the quality of indoor air. The resulting gain (loss) of heat is obtained by an energy balance made on the control volume under consideration. Gain (loss) of heat due to infiltration. Unlike ventilation, infiltration is the involuntary input of outside air due to cracks and holes in the building envelope. The flow of infiltration is therefore unknown, but there are approximate experimental methods for its quantification, such as the blower door method, Odriozola [71]. In addition to these gains, there are others, whose common characteristic is that the source of heat is inside the building. Among gains of internal origin is Heat gain due to lighting, occupation and diverse equipment. The instantaneous gain due to lighting is expressed as a function of the installed power, the utilization factor and a characteristic coefficient for each light. The gains due to occupation are due to the exothermic transformations that take place in the human body and depend on the individual, degree of activity, clothing and environmental conditions. The gain is calculated based on the number of occupants and the occupation profile. As for the gain due to equipment such as computers, kitchens, etc. it is calculated analogously to lighting, ASHRAE Fundamentals [72]. Once the equations corresponding to each transfer mechanism have been established to calculate the gains (losses), the next step is to convert those gains into loads and ultimately obtain the thermal demand of the building. Therefore, the thermal load of a space is calculated in two stages: first, instantaneous heat losses (or gains) are calculated, that is to say, the heat fluxes that come out, named as losses, or that come into the defined volume, and in a second stage, from those gains the thermal loads are calculated; finally the demand is worked out.

4.12.1.2 Thermal load and energy demand The heat fluxes of the gains have in general two components: a convective part and a radiant one. The convective part directly affects the indoor air of the zone under consideration, while the radiant part is first absorbed by the surfaces that delimit the zone, to later pass by convection to the air. So, the thermal load corresponding to a zone is understood to be the amount of heat that must be supplied (heating) or extracted (cooling) to maintain the temperature and humidity of the air of the said space constant and equal to a previously fixed value. Fig. 4.13 schematically shows the difference between gain and load. Moisture exchanges contribute significantly to the energy exchanges of buildings, mainly due to the associated phenomena of evaporation and condensation. This is what

Exergy analysis of heat transfer in buildings

327

Figure 4.13 Difference between gain and load.

is called the latent thermal load. By calculating the instantaneous loads, the demand comes from integrating these values over time, which normally will be a year, divided into a heating season and a cooling season. Thus, the integral of thermal loads over time, usually 1 year, is called the thermal demand of the building or the zone under consideration. Next, we will look at some basic ideas on how to calculate that energy demand in any building. According to ISO 13790 (2008), there are two types of methods to calculate this demand: • •

Quasi-steady methods, which calculate the energy balances over a sufficiently long period of time (1 month or the whole season), so that the dynamic effects are taken into account through gain/loss factors that are determined empirically. Dynamic methods, which calculate the energy balances in short periods (typically 1 hour) and which take into account the energy stored and released by the mass of the building.

Numerous national codes are based on the first type of methods. However, due to the software available (TRNSYS, EnergyPlus, etc.) and the possibilities of modern computers, dynamic methods are increasingly used. In turn, dynamic methods can be classified into two groups: direct and indirect methods. •

•

The direct methods form and solve the equations all at once so that in principle the system of equations does not have any restriction as to its character and all the requests are applied simultaneously. It is the most detailed but requires large memory capacity and long execution time. The indirect methods are based on the principle of superposition of the solicitations and the application of laws of convolution, Sanchez [73]. Recall that, in functional analysis, convolution is a mathematical operator that transforms two functions of the same variable (in our case time) into a third, which represents the integral of the product of both, having displaced one of them.

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Exergy Analysis and Thermoeconomics of Buildings

4.12.1.3 Indirect method for calculating energy demand We are going to take a summary of the calculation of energy demand using this second type of methods, on which energy rating software such as CALENER and building simulation software such as TRNSYS and others are based. For a detailed review, consult AICIA [74] or Sala [75]. The indirect method is very interesting because of the reduced calculation effort required and because it provides results broken down by components. Basically, it consists of the determination of the response that would cause a unitary excitation of each one of the present solicitations and the subsequent obtaining of the global response, as superposition of the individual responses. This requires that the equations be linear and the coefficients that appear in them must be constant. Once the instantaneous heat gains (losses) that we have discussed above are calculated, the gains are converted into loads by the response factors, which are transfer functions that calculate the response of the zone under consideration to a unit impulse of heat gain (loss). Each of the components that constitute the gain (loss) has its own response factors, depending on the radiant and convective part and the thermal capacity of the walls and furnishings. Thus, the response factors are different for each room and each component of the thermal load. Since the gains are calculated discretely, for example, from hour to hour, the Z transform method is usually used to calculate the response factors. For the five types of gains to which we have referred above, there are four sets of response factors: conductive response factors, for solar gain, for lighting and for occupation and items of equipment. In this way, the thermal load at the time of calculation is expressed as a function of the load in the preceding hours and the heat gain at the current time and the preceding hours. Carslaw and Jaeger [76], using the Laplace transform of the temperature and radiation excitations, laid the foundations of the response factor method, Mitalas [77] that of the Z transfer functions, Stephenson and Mitalas [78] and Hittle [79] that of the frequency response. These three methods are basically similar, with the objective of determining the coefficients of the transfer function that relate the excitations on the two surfaces of the wall with the resulting heat flux. The difference between the methods lies in the type of excitation used: a triangular impulse the first, a unit slope the second and a unit sine wave the third, of variable frequency and phase shift. An alternative method to solve the non-steady state in multi-layered walls is to solve the resulting differential equations by numerical methods, the most used being the finite difference method, Harnett and Cho [80]. The fundamental problem of these methods is the choice of the numerical scheme and the discretization parameters, mesh size and time interval so that the desired precision is achieved with the minimum calculation effort. The calculation of energy demand is based on the resolution of a system of equations, which comes from applying the energy balances on the exterior surfaces of the building, on the interior surfaces and in the air of each zone. The unknowns are the surface temperatures, which must not be forgotten are variable in time, so that once

Exergy analysis of heat transfer in buildings

329

these are calculated, instantaneous heat fluxes or any temporary integration thereof are obtained. From the energy balance in the exterior surfaces, we have an equation similar to Eq. (4.60) q_cd;es ¼ hcvr ðTsa  Tes Þ

(4.102)

and from the response factors q_cd;es ¼ a0 Tes ðtÞ  bo Tis ðtÞ þ P

(4.103)

and for interior surfaces q_cd;is ¼ b0 Tes ðtÞ  c0 Tis ðtÞ þ Q

(4.104)

where a0, b0, c0 are coefficients of the transfer function and P and Q are associated with temperatures and heat fluxes in previous instants. From Eqs. (4.102) and (4.103) we get Tes(t) and this expression substitutes Tes(t) in Eq. (4.104), thus obtaining qcd,is(t) as a function of Tis(t). In the equations of energy balance on the inner surfaces, we replace q_cd;is ðtÞ by the previous expression, as a function of Tis(t). For a system of N surfaces, we have a system of N equations, with (N þ 2) unknowns, which are the interior surface temperatures Tis, the indoor air temperature Ti and the thermal power supplied or extracted by the air conditioning equipment Q_ dem . We can write an additional equation, which is the sensitive energy balance in the air of the room. Considering a thermal zone, at a given moment that equation will be rcV

N dTi X ¼ Ai hcv;i ðTi  T0 Þ þ rcV_ e ðT0  Ti Þ þ Q_ IS þ Q_ dem dt i¼1

(4.105)

where • • • •

N P

Ai hcv;i ðTi  T0 Þ is the rate of heat exchanged with the interior surfaces.

i¼1

rcV_ e ðT0  Ti Þ is the mass flow rate of outside air that enters the premises (ventilation þ infiltrations). Q_ IS are the convective contributions of internal sources (occupants, lighting and equipment). Q_ dem is the thermal power supplied (or extracted) by the conditioning system.

In short, we have a system of (N þ 1) equations, with (N þ 2) unknowns. There are three ways to solve this problem: (1) Consider a situation in which the air temperature does not vary and therefore dTi/dt ¼ 0. The system of N algebraic equations can be solved and the values of Tis(t) are obtained. Once these are known, we can calculate Q_ dem for each time step Dt. (2) Consider that Q_ dem ¼ 0, so that temperature Ti evolves freely. We will have to solve a system of (N þ 1) equations (N algebraic and one differential) with (N þ 1) unknowns. (3) The most complete solution is to add the equations that characterize the behaviour of the conditioning equipment.

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Exergy Analysis and Thermoeconomics of Buildings

Actually, the heat extracted (added) by the air conditioning system is different from the thermal load, because the internal temperature does not remain constant. This is due to some of the following reasons: • • •

Intentional stops of heating equipment (nights, weekends, holiday periods). Unintended stops (because the comfort conditions have already been reached). The systems do not maintain a temperature but a temperature range (thermostatic band).

4.12.2

Calculation of exergy demand

4.12.2.1 Preliminary comments As we have said, the energy demand is the amount of energy required throughout the year to maintain the premises in the conditions of comfort requested by the users. Similarly, the demand for exergy is the amount of exergy required to maintain the premises in the conditions of comfort requested by the users; it is, therefore, the exergy content of the energy demand. According to the exergy concept discussed in Chapter 2, we could also say that the demand for exergy is the minimum useful work required to satisfy the demand for energy. We know that the energy that is supplied to satisfy the demand must be of the minimum quality required, as otherwise, exergy destruction will take place. For example, this is what will happen when, in order to maintain air at a temperature of 21 C, we use a heating system at 80 C. When more energy is supplied (extracted) than necessary in a room, overheating (sub-cooling) occurs; similarly, the input in excess of exergy causes the destruction of exergy. Therefore, in the ideal situation, the minimum exergy should be supplied; that is, the minimum required to satisfy the conditions of comfort. Any excess exergy that is supplied to the premises will lead to exergy destruction. Once the energy demand is calculated, there are two methods to calculate the exergy demand, as described below. In principle, we could think that the demand for exergy is obtained through the application of exergy balance in the CV that constitutes the space to be conditioned, Eq. (2.53). However, in this equation, two unknowns appear: the demand for exergy and the exergy destroyed. Therefore, the calculation of exergy demand requires starting from the values obtained in the calculation of the energy demand.

4.12.2.2 Simplified method This method was proposed by Schmidt [81]. In the case of radiators or fan heaters, part of the energy demand is supplied by the terminal element of the installation as convection heat and another part is radiation heat, this proportion depending on the type of emitting element. Although the quality factor of one heat and another is different,

Exergy analysis of heat transfer in buildings

331

the energy demand corresponds finally to the convection heat that is exchanged by the air of the premises. In short, the demand for exergy is calculated by the expression   To _ B_ dem ¼ 1  Qdem (4.106) Ti In Section 2.9 of Chapter 2, we explained the meaning of this expression for the different possible values of Ti with respect to T0 and both for heating and cooling. As the average temperature of the interior surfaces of the premises is generally different from that of the indoor air, the operating temperature can also be used Top, ISO 7726 [82] being then the exergy demand   T0 _ _ Qdem (4.107) Bdem ¼ 1  Top This expression does not take into account the fact that part of the demand is due to the need to heat (cool) the ventilation air and that its exergy content does not correspond to the previous expression. In addition, neither the component associated with the pressure nor the chemical component of the exergy has been taken into account. If we consider an air conditioning process in which there is humidification or dehumidification of the air, or if we carry out a study in which indoor air quality arises, then the chemical component is important and should be taken into account. In this regard, refer to Section 3.6.4 of Chapter 3.

4.12.2.3 Detailed method The detailed method, developed by Annex 49 [83] differs from the simplified one, in that it does separate the exergy demand associated with the ventilation air from the rest of the demand. Nevertheless, as the simplified method does not take into account the chemical exergy, and also it does not consider the small difference between the exergy of the convection heat and that of the radiation exchanged between surfaces with small temperature differences. Referring to the case of heating, as we have seen before, the total demand reflects the losses (by transmission through the walls taking into account the inertia, ventilation and infiltration) minus the gains (solar and internal). As discussed in Chapter 2, the quality factor of internal energy at temperature T is less than the quality factor associated with heat at that temperature T. Therefore, to determine the demand for exergy, it will be necessary to evaluate first what part of that demand is needed to heat (cool) the ventilation air, contributing the rest in the form of heat to the operating temperature of the room. Ultimately, to calculate the exergy demand, it is necessary to separate the demand into two components: (1) we determine the exergy needed to condition the ventilation

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air from the outside and mix it with the air of the premises. The exergy variation of the air between the interior and exterior conditions is the minimum exergy that must be provided to condition that air. (2) The rest of the exergy demand, if any, must be supplied as heat at the operating temperature Top. In accordance with the principles outlined above and following the methodology developed by the ECBCS Annex 49, we will present the general equations for the calculation of the exergy demand of premises. These equations can be programmed and coupled to energy simulation software, as has been done with TRNSYS. As we have said, the calculation of exergy demand by the detailed method requires prior knowledge of the energy demand. Once the energy balance is made, the total energy demand Q_ dem is compared first with ventilation losses Q_ vent . If these are less than the total demand, the ventilation air must be heated up to the temperature inside the premises, which implies a minimum contribution of exergy, which can be calculated with the expression  _ _ Bvent ¼ Qvent 1 

  Top T0 ln Top  T0 T0

(4.108)

with Q_ vent being the heat that must be provided to heat the air to the temperature of the premises, which is Q_ vent ¼ m_ vent cp ðTop  T0 Þ

(4.109)

The difference between the total demand and this heat Q_ vent must be provided as heat to the premises, at the temperature Top, so that the complementary exergy to be provided is B_ Q ¼



  T0  _ Qdem  Q_ vent 1 Top

(4.110)

In the case that the total demand is less than the losses by ventilation, the air does not need to be heated up to the temperature Top and no additional heat is required, as this has been given by the internal and solar gains. The temperature at which the air will have to be heated will be DTvent ¼

Q_ dem ðTop  T0 Þ Q_ vent

(4.111)

In short, the set of equations needed to calculate the exergy demand by the detailed method is summarized in the following set of equations   Q_ vent;d ¼ min Q_ dem ; Q_ vent

(4.112)

Exergy analysis of heat transfer in buildings

DTvent ¼

Q_ vent;d ðTop  T0 Þ Q_ vent

Tvent ¼ T0 þ DTvent  _ _ Bvent ¼ Qvent 1 

  T0 Tvent ln Tvent  T0 T0

Q_ ¼ Q_ dem  Q_ vent;d B_ Q ¼



 T0 _ Q 1 Top

333

(4.113) (4.114) (4.115) (4.116) (4.117)

In the case of refrigeration in which T0 > Top all natural energy flows represent unwanted gains, so that Q_ dem > Q_ ven is always going to be fulfilled. Therefore, the ventilation air will always have to be cooled to the temperature Top. In the case of refrigeration in which T0 < Top the need for cooling (energy output) does not represent an exergy demand, but rather is an undesired assignment of exergy. This exergy is given to the building by internal gains and could be somehow collected and used as heat at the temperature Top. In the final report of the ECBCS Annex 49 a comparison of the two calculation methods, simplified and detailed, is made in the case of an office. Different situations are compared, in one case maintaining constants T0 and the energy demand and modifying the level of insulation and air exchanges and in another, maintaining the characteristics of the room but varying the solar irradiation and the outside temperature. In all cases, it was found that the exergy demand is around 10% of the energy demand (obviously depending on T0 and Top). By comparing both methods with each other, the results obtained are quite different, with the demand for exergy calculated by the detailed method being smaller than by the simplified one. This difference becomes larger when the ventilation flow is greater, and Top comes closer to T0. Undoubtedly, the detailed method is more precise, so it should be used when more accurate information is needed, for example, when it comes to optimizing the building’s air conditioning and ventilation systems. Annex 49 recommends using the simplified method, at a preliminary stage, when it comes to analysing the energy supply chain of a building.

4.12.3 Examples Determine the quality factor of the exergy associated with a flow of water at temperature T and the heat quality factor at that temperature, for the temperature values T in Table E.4.4, with T0 ¼ 290 K

Example E.4.13.

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Exergy Analysis and Thermoeconomics of Buildings

Table E.4.4 T values for T0 ¼ 290 K. T(8c) 10 0 10 20 30 40 50 60

Solution The quality factor of energy is the relationship between exergy and energy. In the case of a water mass flow rate m_ the associated exergy is given by Eq. (3.44), so its quality factor is ð2.1Þ FB ¼ 1 

T0 T ln T  T0 T 0

For its part, the quality factor of heat is as we well know ð2.2Þ FQ ¼ 1 

T0 T

Using these expressions and giving values to T we obtain the following Table E.4.5. In order to interpret the results more clearly, we present the absolute values in the table. Table E.4.5 Quality factors. T(8c)

FB

FQ

10

0.95

0.1

0

0.03

0.06

10

0.01

0.02

20

0.01

0.05

30

0.02

0.04

40

0.04

0.07

50

0.05

0.1

60

0.07

0.13

Exergy analysis of heat transfer in buildings

335

We can appreciate that for any value of the temperature, whether it is above or below T0 the inequality FB < FQ is met. Both quality factors only coincide when T ¼ T0, since then its value is zero. Example E.4.14.

Let there be a house in which the losses by heat transfer through the envelope are 5 kW, the losses by ventilation and infiltrations are 3 kW, while the internal gains are 1.2 kW. The temperature of the outside air is 10 C and that of the interior of the house is 20 C. Determine the heating demand and the heating exergy demand. Solution The heating demand is the difference between the gains and losses, so that Qdem ¼ 5 þ 3  1; 2 ¼ 6:8 kW Next, we compare this demand with the losses by ventilation and infiltration, which are 3 kW, evidently less. Therefore, the entire airflow needs to be heated up to the indoor temperature, with the contribution of exergy    T0 Ti B_ vent ¼ 1  ln ¼ 0:05 kW Ti  T0 T0 The difference between the total demand, 6.8 kW and the one due to ventilation, 3 kW, is the heat that must be contributed to the premises, and therefore, the exergy that needs to be provided is    T0  _ Qdem  Q_ vent ¼ 0:13 kW 1 Ti In short, the total demand for exergy is B_ dem ¼ 0:05 þ 0:13 ¼ 0:18 kW so the quality factor of the energy contributed is 2.6%.

Example E.4.15.

In commercial premises, the heat losses through the envelope are 35 kW, the losses by ventilation are 25 kW and by infiltrations are 5 kW, with internal gains of 45 kW. The temperature of the outside air is 3 C and that of the interior of the room is 21 C. Determine the energy and exergy demands. Solution The heating demand for the premises is Q_ dem ¼ 35 þ 25 þ 5  45 ¼ 20 kW Comparing this demand with ventilation losses, we have that Q_ dem < Q_ vent , so that the ventilation airflow will only need to be heated up to a temperature of DTvent ¼

Q_ dem ðTi  T0 Þ ¼ 14:4 K Q_ vent

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Exergy Analysis and Thermoeconomics of Buildings

Tvent ¼ T0 þ DTvent ¼ 289:4 K The exergy needed to heat the ventilation air is    T0 Tvent _ _ Bvent ¼ Qvent 1  ln ¼ 2:28 kW Tvent  T0 T0 The rest of the demand is covered by the internal gains of the commercial premises. The quality factor of the energy contributed to the air of the premises is 9.1%. Example E.4.16.

In an office, the heat inputs through the envelope are 19 kW, those due to infiltrations are 7.6 kW, with internal heat gains of 8.4 kW. The air conditioning of the office is done through a centralized air conditioning system. The outside air temperature is 32 C, with the office temperature at 24 C and the ambient pressure 1 bar. Determine: (a) The airflow rate for the office conditioning. (b) The rate of exergy demand and the quality factor of the energy provided.

Solution (a) The demand for the refrigeration is Q_ dem ¼ 19 þ 7:6 þ 8:4 ¼ 34 kW To calculate the mass airflow rate, we take into account that _ p ðT0  Ti Þ ¼ 34 / mc

m_ ¼ 4:22

kg s

so the air conditioning volume flow rate is _ m_ ¼ V9

3

Ra T0 8:314$305 m ¼ 3:71 / V_ ¼ m_ ¼ 4:22 28:8$100 p0 s

(b) The rate of exergy demand is  B_ dem ¼ Q_ dem 1 

  T0 Ti ln ¼ 0:45 kW Ti  T0 T0

Cooling this airflow of 3.71 m3/s from the ambient temperature to 24  C involves extracting an amount of energy that, per second, is 34 kJ and this means that exergy of 0.45 kW is provided. The minimum electrical power consumed by the refrigerating compression machine to cool that air is 0.45 kW; actually, it is much greater, due to the irreversibilities and consequent exergy destruction. In short, the quality factor of the energy used is 1.3%.

Exergy analysis of heat transfer in buildings

337

Example E.4.17.

Compare the heating exergy demand obtained for a dwelling using the simplified method and the detailed method. Fig. E.4.7 shows a section of the house, consisting of an unheated basement, a ground floor and a first floor, with a total useful area of 280 m2.

Figure E.4.7 Section of the single-family house.

Solution A simulation was carried out with TRNSYS v17 to obtain the heating demand, hour by hour, having used the meteorological data of the city of Bilbao. The monthly cumulative values are presented in Fig. E.4.8. The annual heating demand is 16,187 kWh, the month of maximum demand being January, with a value of 3,132 kWh. As for the exergy, the annual demand is 482 kWh, with the demand in January being 106 kWh. As we can see, the heating energy quality factor is very low, around 3% for the annual demand and slightly higher if we refer to the demand for January.

Figure E.4.8 Energy and exergy demand for heating.

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Exergy Analysis and Thermoeconomics of Buildings

Finally, the demand for heating exergy has been determined by both the simplified and detailed methods of the ECBS Annex 49. The monthly values are shown in Fig. E.4.9 and, as we can see, the values that come from the detailed method are lower than those from the simplified method. By looking at the annual demand, the value is 448 kWh for the detailed method, compared to 563 kWh for the simplified one, which is 23% higher. The exergy demand calculated by the detailed method is always lower than that obtained by the simplified method. The difference is greater when the indoor temperature is closer to the ambient temperature and the ventilation flow rate is higher. In this example, the difference is relatively important, so it is preferable to use the detailed method.

Figure E.4.9 Demand for heating exergy, by the detailed method and the simplified method.

Subscripts 0 s i, e i, f w cv, cd r, lwr, swr sky sun, sur v, a ex dem vent

Environmental state Surface Interior and exterior Initial and final Wall Convection and conduction Radiation, long-wave radiation and short-wave radiation Sky Sun and surroundings Water vapour and dry air Expiration Demand Ventilation

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339

Symbols r V h s T t m_ c Teq Tf Tm Top L A Dx N l R, U ex Udyn, Udyn U Q W d_ 4 u f εi ai ri e_i Gij

Density Volume Specific enthalpy Specific entropy Temperature Time Mass flow rate Specific heat Equivalent temperature Fictitious temperature Mean temperature Operative temperature Thickness Surface Distance Number of layers in a wall; number of surfaces in a room Thermal conductivity Thermal resistance and thermal transmittance Dynamic thermal transmittance and dynamic exergy transmittance Internal energy Heat Work Rate of exergy destruction per unit of area Exergy efficiency Absolute humidity Relative humidity Emissivity of surface i Absorptivity of surface i Reflectivity of surface i Emission power of surface i Gebhart factor of radiant heat exchange between surfaces i and j

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[5] DL n.311/2006, Corrective Provision and Integration to the Legislative Decree 19 Agosto 2005, No. 192, Implementing Directive 2002/91/CE, on the Energy Performance of Buildings (In Italian), 2007. [6] Thermal Regulation, 2012 (in French), http://www.rt-batiment.fr/. [7] The Building Regulations, 2010, 2015 (Internet), http://www.legislation.gov.uk/uksi/ 2010/2214/contents/made. [8] Ministry of Housing, Order FOM/1635/2013, 10 September, Updating Technical Building Code. Basic Document DB-HE: Energy Saving, 17 March, 2013 (in Spanish), approved by Royal Decree 314/2006 (in Spanish), Madrid. [9] S. Ng, K. Low, N. Tioh, Newspaper sandwiched aerated lightweight concrete wall panelsdthermal inertia, transient thermal behavior and surface temperature prediction, Energy and Buildings 43 (7) (2011) 1636e1645. [10] S. Ferrari, Building envelope and heat capacity: Re-discovering the thermal mass for winter energy saving, in: Proceedings of the 2nd PALENC Conference and 28th AIVC Conference on Building Low Energy Cooling and Advanced Ventilation Technologies in the 21st Century, Crete, Greece, 27e29 September, 2007. [11] UNE-EN ISO 13786 (AENOR 2011), 2011. [12] E. Stéphan, R. Cantin, A. Caucheteux, S. Tasca-Guernouti, P. Michel, Experimental assessment of thermal inertia in insulated and non-insulated old limestone buildings, Building and Environment 80 (2014) 241e248. [13] UNE-EN ISO 13786, Thermal Features of the Products and Components of Buildings. Dynamic Thermal Characteristics, Calculation methods, 2011 (in Spanish). [14] P.T. Tsilingiris, Parametric space distribution effects of wall heat capacity and thermal resistance on the dynamic thermal behavior of walls and structures, Energy and Buildings 38 (10) (2006) 1200e1211. [15] Y.A. C¸engel, A.J. Ghajar, Heat and Mass Tranfer: Fundamentals and Applications, fourth ed., McGraw-Hill, New York, 2011. [16] I. Flores, The Method of Exergy Analysis in Buildings. Its Application in the Characterization of the Dynamic Behavior of the Opaque Envelop (In Spanish) (Doctoral Thesis), University of the Basque Country, Bilbao, 2016. [17] W. Choi, R. Ooka, M. Shukuya, Exergy analysis for unsteady-state heat conduction, International Journal of Heat and Mass Transfer 116 (2018) 1124e1142. [18] H. Asan, Investigation of wall’s optimum insulation position from maximum time lag and minimum decrement factor point of view, Energy and Buildings 32 (2) (2000) 197e203. [19] Y.A. C¸engel, Heat Transfer (In Spanish), second ed., McGraw-Hill, Mexico, 2004. [20] N. Ito, K.I. Kimura, Convection Heat Transfer at the Exterior Surface of Buildings Exposed to Natural Wind, J.S:A.E. Transactions, 1968. [21] W.M. Kays, M.E. Crawford, Convective Heat and Mass Transfer, third ed., McGraw-Hill, New York, 1993. [22] B.W. Olesen, Radiant floor heating in theory and practice, ASHRAE Journal 44 (7) (2002) 19e26. [23] H. Torio, A. Angelotti, D. Schmidt, Exergy analysis of renewable energy based climatisation systems for buildings: a critical view, Energy and Buildings 41 (3) (2009) 248e271. [24] F. Incropera, D. DeWitt, Fundamentals of Heat and Mass Transfer, sixth ed., John Wiley & Sons, New York, USA, 2007. [25] J.H. Lienhard, A Heat Transfer Textbook, third ed., Phlogiston Press, Cambridge, MA, USA, 2006.

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[26] R. Petela, Engineering Thermodynamics of Thermal Radiation for Solar Power Utilization, McGraw-Hill, New York, USA, 2010. [27] H.C. Hottel, A.F. Sarofim, Radiative Transfer, McGraw Hill, New York, 1967. [28] E.M. Sparrow, R.D. Cess, Radiative Heat Transfer, Brooks/Cole Publishing, Belmont, California, USA, 1966. [29] B. Gebhart, Heat Transfer, second ed., McGraw-Hill, New York, USA, 1971. [30] J.A. Clark, M.E. Korybalski, Algebraic methods for the calculation of radiation exchange in an enclosure, W€arme- Und Stoff€ubertragung 7 (1) (1974) 31e44. [31] Ministry of Housing, Royal Decree 314/2006 7 March Approving the Technical Building Code, 2006 (in Spanish), B.O.E. 74. [32] J. Brau, Natural Convection in Buildings (In French) (Doctoral Thesis), INSA, Universidad de Lyon, 1980. [33] O. Gliah, B. Kruczek, S.G. Etemad, J. Thibault, The effective sky temperature: an enigmatic concept, Heat and Mass Transfer 47 (9) (2011) 1171e1180. [34] M. Martin, P. Berdahl, Characteristics of infrared sky radiation in the United States, Solar Energy 33 (3) (1984) 321e336.  [35] S. Alvarez, Dynamic analysis of thermal behavior of buildings (in Spanish), Doctoral Thesis, E. S. de Ingenieros Industriales, University of Seville, 1996. [36] M. Shukuya, Exergy. Theory and Applications in the Built Environment, Springer-Verlag, London, 2013. [37] A. Angelotti, P. Caputo, The exergy approach for the evaluation of heating and cooling technologies: first results comparing steady state and dynamic simulations, in: Proceedings of the 2nd PALENC and 28th AIVC Conference: Building Low Energy Cooling and Advanced Ventilation Technologies in the 21st Century, 27e29 September, Crete, Greece, 2007. [38] AENOR, UNE-EN ISO 13790: Energy Efficiency of Buildings. Calculation of Energy Consumption for Heating, AENOR, Madrid, 2008 (in Spanish). [39] H. Torio, D. Schmidt, ECBCS Annex49dLow Exergy Systems for High Performance Buildings and Communities, Annex 49 Final Report, Fraunhofer IBP/IEA, Munich (Germany), 2011. [40] D.G. Stephenson, G. Mitalas, Calculation of heat conduction transfer functions for multilayer slabs, Air Conditioning Engineers Transactions 77 (1971). USA. [41] EnergyPlus Simulation Software, Department of Energy (DOE), National Renewable Energy Laboratory (NREL), 2015. [42] TRNSYS Transient System Simulation Software, Thermal Energy System, Specialist Inc., Madison, USA, 2017. [43] S. Klein, TRNSYS 17: A Transient System Simulation Program, Solar Energy Laboratory, University of Winsconsin, Madison, USA, 2010. http://sel.me.wisc.edu/trnsys. [44] H. Torio, Comparison and Optimization of Building Energy Supply Systems through Exergy Analysis and its Perspectives (Ph.D. thesis), Technical University of Munich, 2012. [45] D. Marmolejo-Correa, T. Gundersen, A comparison of exergy efficiency definitions with focus on low temperature processes, Energy 44 (1) (2012) 477e489. [46] E.C. Boelman, P. Sakulpipatsin, Critical analysis of exergy efficiency definitions applicable to buildings and building services, in: Proceedings of the 21st Conference on Passive and Low Energy Architecture (PLEA) 19e22 September, Eindhoven, The Netherlands, 2004.

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[47] R.L. Cornelissen, G.G. Hirs, Exergetic optimisation of a heat exchanger, Energy Conversion and Management 38 (15e17) (1997) 1567e1576. [48] T.J. Kotas, The Exergy Method of Thermal Plant Analysis, second ed., Krieger Publishing, Florida, USA, 1995. [49] G. Tsatsaronis, Definitions and nomenclature in exergy analysis and exergoeconomics, in: Energy; ECOS 05. 18th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems, ECOS 05, 2007, pp. 249e253, 32(4). [50] D. Favrat, F. Marechal, O. Epelly, The challenge of introducing an exergy indicator in a local law on energy, Energy 33 (2) (2008) 130e136. [51] P. Gonçalves, A. Rodrigues Gaspar, M. Gameiro da Silva, Energy and exergy-based indicators for the energy performance assessment of a hotel building, Energy and Buildings 52 (0) (2012) 181e188. [52] L. Tronchin, K. Fabbri, Analysis of buildings’ energy consumption by means of exergy method, International Journal of Exergy 5 (5e6) (2008) 605e625. [53] ISO 9869-1:2014 Thermal Insulation - Building Elements - In-Situ Measurement of Thermal Resistance and Thermal Transmittance e Part 1: Heat Flow Meter Method. [54] UNE-EN 15026:2007, Hygrothermal Behavior of Components and Elements of Buildings. Assessment of the Moist Transfer through Numerical Simulation, AENOR, (in Spanish) 2010. [55] UNE EN ISO 7730, Ergonomics of the Thermal Environment. Analytical Determination and Interpretation of Thermal Well-Being by Calculating PMV and PVD Indices and Local Thermal Comfort Criteria (in Spanish), (ISO 7730:2005), AENOR, 2006. [56] ANSI/ASHRAE Standard 55, Thermal Environmental Conditions For Human Occupancy, ASHRAE, 2013. [57] M.A. Humphreys, J.F. Nicol, The validity of ISO-PMV for predicting comfort votes in every-day thermal environments, Energy and Buildings 34 (6) (2002) 667e684. [58] P.O. Fanger, Thermal Comfort, Danish Technical Press, Copenhagen, 1970. [59] M.S. Ferreira, J.I. Yanagihara, A transient three-dimensional heat transfer model of the human body, International Communications in Heat and Mass Transfer 36 (2009) 718e724. [60] J.A. Harris, F.C. Benedict, A biometric study of human basal metabolism, Proceedings National Academy Sciences United States America 4 (1981) 370e373. [61] M. Shukuya, M. Saito, K. Isawa, T. Iwamatsu, H. Asada, Working Report of IEA ECBS: human body exergy balance and thermal comfort, in: International Energy Agency, Energy Conservation in Buildings and Community Systems, Annex 49, Low Exergy Systems for High Performance Systems and Communities, Fraunhofer IBP, Germany, 2010. [62] T. Iwamatsu, H. Asada, A calculation tool for human-body exergy balance, in: Newsletter No. 6, IEA ECBCS Annex 49, Low Exergy Systems for High-Performance Buildings and Communities, Fraunhofer Verlag, Stuttgart, Germany, 2009, pp. 4e5. [63] C.E.K. Mady, M.S. Ferreira, J.I. Yanagihara, P.H.N. Saldiva, S. de Oliveira, Modeling the exergy behavior of human body, Energy 45 (2012) 546e553. [64] H. Caliskan, Energetic and exergetic comparison of the human body for the summer season, Energy Conversion and Management 76 (2013) 169e176. [65] C.E.K. Mady, C. Albuquerque, T.L. Fernandes, A.J. Hernandez, P.H.N. Saldiva, J.I. Yanagihara, S. de Oliveira, Exergy performance of human body under physical activities, Energy 62 (2013) 370e378.

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[66] M. Batato, L. Borel, O. Deriaz, E. Jequier, Theoretical and experimental exergetic analysis of the human body (in French), Entropie 26 (1990) 120e130. [67] M. Ala-Juusela, Low Exergy systems for heating and cooling of buildings, Guidebook of IEA ECBS Annex 37 (2003). [68] O’Callaghan, Building for Energy Conservation, Pergamon Press, 1978. [69] Thermal Engineering Group of the School of Engineering, Calener: Reference Manual (in Spanish), University of Seville, 2002. [70] R. Stout, D. Billings, Using Linear Superposition to Solve Multiple Heat Source Transient Thermal Problems, in: ASME-JSME Thermal Engineering And Heat Transfer Conference, Vancouver, Canada, 2007. [71] M. Odriozola, Calculation And Measurement of Air Infiltration in Buildings (in Spanish), University of the Basque Country, Bilbao, 2008. [72] American Society of Heating, Refrigeration and Air Conditioning Engineers, ASHRAE Handbook of Fundamentals, ASHRAE, New York, 2017. [73] J. Sanchez Ramos, Methodology Applied to the Inverse Thermal Characterization of Buildings (in Spanish), Doctoral Thesis, University of Seville, 2015. [74] AICIA, Calculation tool of energy demand. Reference Manual (in Spanish), School of Engineering, University of Seville, 2001. [75] J.M. Sala, Heat Transfer in the Envelop of Buildings in Dynamic Regime (in Spanish), University of the Basque Country, Bilbao, 2011. [76] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. [77] G.P. Mitalas, Calculations of transient heat flow through walls and roofs, ASHRAE Transactions 74 (1978). Parte II. [78] D.G. Stephenson, G.P. Mitalas, Calculation of heat conduction transfer functions for multilayer slabs, ASRAE Transactions 77 (Part II) (1977). [79] D.C. Hittle, Calculating Building Heating and Cooling Loads Using the Frequency Response of Multi-Layered Slabs (Ph.D. thesis), Construction Engineering Research Laboratory, University of Illinois, USA, 1981. [80] J.P. Harnett, Y.I. Cho, Handbook of Heat Transfer, McGraw-Hill, New York, 1998. [81] D. Schmidt, Methodology for the Modelling of Thermally Activated Building Components in Low Exergy Design (Ph.D. thesis), The Royal Institute of Technology, Stockholm, Sweden, 2004. [82] UNE-EN ISO 7726, Ergonomics of Thermal Environments. Instruments for Measuring Physical Magnitudes (in Spanish), AENOR, 2002. [83] ECBCS Annex 49, 2011, Low Exergy Systems For High-Performance Buildings And Communities, 2011. Final Report, www.annex49.com.

Exergy analysis of thermal facilities equipment in buildings (I)

5.1

5

Summary

In this chapter, we will analyse the different components that are part of the heating, domestic hot water (DHW) and air conditioning facilities. For each of these components we will show the conventional equations of conservation of mass and energy and from them exergy balances, as well as the corresponding expressions to characterize their efficiency, both through conventional energy performance and with exergy. We will first consider individual equipment in a steady state, from the end elements of heating and DHW facilities to the generation equipment, either boilers or heat pumps. We will later look at cogeneration facilities, undertaking a review of microcogeneration technologies and then presenting the energy and exergy parameters with which the behaviour of these technologies is characterized. We will end the chapter looking at equipment, such as thermal energy storage systems, that must be analysed as a dynamic system due to its inherent properties.

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00005-9 Copyright © 2020 Elsevier Inc. All rights reserved.

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After a conventional energy analysis in the three phases of loading, storage and discharge, we will characterize its behaviour through exergy analysis, highlighting the usefulness of this analysis and the additional information that it provides.

5.2

Introduction

Exergy analysis is a powerful tool for improving the use of energy in buildings. Reducing losses and exergy destruction and, therefore, increasing efficiency in a system means reducing irreversibilities and, ultimately, using energy in a more efficient way. High exergy efficiency means properly exploiting the utility of energy and ultimately using it in a more rational way. In a building, the demand for heating, air conditioning and DHW depends on a variety of factors, as discussed in Chapter 4. As seen, once the demand for energy is established, since the temperature level is fixed, the demand for exergy is also defined. Therefore, what is being dealt with is the satisfaction of that demand with the lowest exergy consumption and this means making facilities more efficient. The usual analysis methods of energy consumption in buildings are based on the evaluation of primary energy consumption, thus contemplating all stages from the extraction of primary energy to the final demand, going through all stages of the energy chain, DIN 18599, 2007 a1 [1]. This approach aims to reduce the consumption of fossil fuels for a certain demand and maximize the use of renewable energy. However, renewable energy flows are not usually included in the final assessment of primary energy consumption so efficiency in the use of these renewable resources cannot be obtained from this type of analysis. Under this approach, replacing a natural gas boiler with a biomass boiler in a heating installation means significantly reducing the consumption of primary energy (fossil) by replacing it with renewable energy. However, using exergy analysis, we see that since biomass is high-quality energy and the demand for heating is at a temperature close to the environment and, therefore, of low quality, the exergy efficiency of the installation will remain low, surely not more than 10%. This analysis shows us how inappropriate it is to use combustion processes to supply heating demands in buildings. We all agree on the importance of reducing the use of non-renewable energies, but it is also important to use renewable energies in an efficient way. Exergy analysis assesses efficiency in the use of energy, both fossil energy and renewable energy. The objective of exergy analysis applied to the facilities of buildings is to find the most rational use of energy, which implies reducing the consumption of fossil fuels and increasing the efficiency in the energy use of the system considered in its entirety. For this, it will be necessary to adapt the quality levels of the energy supplied to the building demanding it. It is important to highlight the term total system, since, for example, a low-temperature emission system such as a radiant floor, using high-quality energy generation, moves the exergy destruction from the end element to the generation equipment, so with respect to a system with radiators there will be no substantial improvement. A holistic approach is, therefore, necessary.

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347

Figure 5.1 Chain of energy supply in a building.

We will break down the energy supply chain in a building into a set of subsystems. This chain begins with the building envelope, continues with the end elements, energy distribution and storage systems, generation equipment, goes on with the energy vectors (fuel, electricity, thermal energy) that enter the building to meet the demands and ends with primary, renewable and fossil energy, after going through the stages of its corresponding energy chain, see Fig. 5.1. Thus, in a natural gas heating installation we have a series of components that go from the end elements (radiators, underfloor heating, etc.), distribution systems with the pipes, valves, exchangers, to the generation, for example, by condensing boiler and finally, the energy chain of natural gas up to the primary energy. In this, and the following chapter we will analyse the different components that are part of the heating, DHW and air conditioning facilities. For each of these components, we will show the conventional equations of mass conservation and energy conservation and the less used exergy balances, as well as the corresponding expressions to characterize their efficiency, both through conventional energy efficiency and with exergy. Once this information is obtained, the last objective will be to satisfy the final demand with the lowest consumption of energy resources that is economically profitable. In practice, as we will see in Chapter 9 when attempting to achieve energy savings (exergy) in a facility and make it more efficient, there are a number of factors that must be taken into account. • •

•

Not all irreversibilities can be avoided. The technical possibilities for saving exergy are inferior to the theoretical thermodynamic limits. The local exergy savings that can be achieved in each component do not have the same effect on the overall savings of the plant, that is, they are not equivalent. The same decrease in local irreversibility in two different components of an installation leads to different variations in the resources consumption of that installation. Saving opportunities can only be achieved through a detailed study of the fundamental mechanisms that generate the irreversibilities and that give rise to exergy destructions.

5.3

Indoor air

The integral in the time of the heat flux that leaves the end elements of heating facilities is equal in a steady state to the building energy demand. Now, the temperature of the

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emitting elements and that of the indoor air are of course different so that exergy destruction will occur in the indoor air. On the one hand, the heat that comes out of the surface of the emitting element (for example a radiator) is partly convection (around 60%) and the rest is radiation that the radiator yields to the interior room surfaces, which we assume are all at the same temperature, one different from that of the emitting element and which we will designate Tis. This radiation heat, after reflections and absorptions in the different surfaces, finally comes to the indoor air by convection. If we call the average temperature of the emitting element Th, see Section 5.4, the rate of exergy transferred by the heat flux that leaves the surface of said element is
 T0 _ Q 1
Th

(5.1)

Since Ti is the indoor air temperature, the rate of exergy destruction in the boundary layer between the end element and the air is Th
Ti T0 Q_ Th Ti

(5.2)

On the other hand, considering a winter situation, as we saw in Chapter 4, the heat flux that is transferred by conduction from the façade inner surface under consideration towards the external environment, comes from the heat exchange by convection with the indoor air and by long-wave radiation with the rest of the interior surfaces, in addition to the short-wave radiation absorbed from the redistributed solar radiation and from internal emitting sources, such as lamps, etc. As we have said, with Tis being the interior surface temperature of the room walls, the rate of exergy destruction in the boundary layer between the indoor air and the walls is Ti
Tis T0 Q_ Ti Tis

(5.3)

so that the rate of total exergy destruction in the air, the sum of the two previous expressions, is Th
Tis D_ a ¼ T0 Q_ Th Tis

(5.4)

Let us now look at all-air systems, DTIE 9.05, 2010 [2], which, as we will see in the next section, are those that use an air flow, cold or hot, to condition the premises and which are responsible for setting the right temperature and humidity, and for air cleaning. In an all-air system, the conditioning air enters the room through some diffuser before being finally extracted. Since both the temperature, the humidity and the CO2 concentration are different for the input air and extracted air, the exergy

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349

Figure 5.2 All-air system in a room.

balance involves taking into account not only the physical exergy but also the chemical exergy. Consider the schematic in Fig. 5.2. Let 1 be the state of the input air with a temperature T1, humidity u1 and with CO2.1 as the concentration of CO2. The extracted air is in state 2, with corresponding values of temperature, humidity and CO2 concentration. The indoor air is now an open system with an input flow and output flow in states 1 and 2 respectively. Considering that the air state in the room remains constant, the exergy balance in the air leads us to the equation 

m_ a b1 þ bch 1





¼ m_ a b2 þ bch 2






 T0 _ Q þ D_ a þ 1
Ti

(5.5)

where Q_ represents the rate of heat flux exchanged by convection between the air and the inner surface of the walls and which depends on the air temperature and the interior surfaces of those walls, their geometry, etc., all of which is expressed by the convection coefficients. The expressions to calculate b and bch have been presented in Chapter 3, Equation (3.37) and Equation (3.121), respectively.

5.4

End elements

The end elements located in the premises receive the primary flow from the treatment and distribution system and drive the air in the premises under the appropriate

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conditions to counteract the thermal loads of the building. There are various types, as described below: • • • •

All-air systems use an air flow (cold or hot, depending on whether it is cooling or heating) to condition the room, the end elements are the diffusers and grilles of all kinds, and gates for controlling the airflow. All-water systems use a water flow (hot or cold) as a heat transfer fluid that is transported to the premises to be conditioned, where an end unit, radiator or fan coil is responsible for conditioning the room. Air-water systems are a hybrid of the two previous systems so that they consist of fan coils and diffusers that are responsible for providing the ventilation air which has been previously treated. Refrigerant or direct-expansion systems use the refrigerant itself as a means of conditioning the premises. There is a direct-expansion air conditioner in the room that functions as an evaporator of the refrigerant fluid in the case of the cold cycle and as a condenser for heating, Stanfield and Skaves 2016 [3].

5.4.1

Exergy analysis of a radiator

Consider a heating radiator, as shown in the diagram of Fig. 5.3. A water flow rate m_ enters the radiator at the temperature Tin and leaves it at Tout. A part of the heat leaving the radiator goes to the indoor air Q_ and a small fraction of the heat transferred is lost Q_ l . According to the energy balance equation, we can write _ _ _ mcðT in
Tout Þ ¼ Q þ Ql

(5.6)

so we need to know the fraction of heat loss in order to know the heat that is finally given by the radiator to the indoor air. The surface temperature of the radiator is variable from one point to another so that the heat exchanged between the radiator surface and the indoor air can be expressed as a function of the total heat transfer coefficient U, the total surface A and the logarithmic mean temperature difference DTml. In fact, we can consider that the surface temperature of the radiator is the indoor

Figure 5.3 Energy flows in a radiator.

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351

air temperature plus the logarithmic mean temperature difference between the heat transfer fluid and the indoor air, that is Th ¼ Ti þ DTml

(5.7)

where DTml ¼

DTin
DTout DTin ln DTout

(5.8)

with DTin ¼ Tin
Ti and DTout ¼ Tout
Ti. Approximately speaking, DTml can be replaced by the arithmetic mean between the inlet and outlet temperature of the water flow in the radiator. By applying the exergy balance in the radiator, according to Equation (2.54) in Chapter 2 we have
  T0 _ T0 _ _ in
bout Þ ¼ 1
Qþ 1
Ql þ D_ mðb Th Th


(5.9)

where according to Equation (3.44) in Chapter 3 the exergy change of the water flow in the radiator is
 Tin _ Tin
Tout
T0 ln _ in
bout Þ ¼ mc mðb Tout

(5.10)

The exergy destruction is due to two mechanisms: on the one hand, inside the radiator there is a heat flux that is transmitted from the water flow temperature to the surface temperature of the radiator, although this difference of temperatures is very small. In addition, when the water circulates through the radiator, mechanical friction occurs causing corresponding exergy destruction, which is a function of not only the head losses but also of the temperature at which this friction takes place, as seen in Chapter 2. These head losses that occur both in the different radiators of the installation and the distribution pipes are compensated by the contribution of exergy from the circulation pump. Taking into account the exergy accompanying the lost heat, the total irreversibility in the radiator is
 T0 _ I_ ¼ D_ þ 1
Q Th l

(5.11)

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5.4.2

Examples

Example E.5.1. In a heating installation, the average surface temperature of a radiator is 60 C, its surface being 3.8 m2. The convection-radiation coefficient between the indoor air and the radiator is 22 W/m2$K, with the indoor air temperature being 21 C and the ambient air temperature 14 C. Determine:

(a) The rate of heat exergy coming out of the radiator. (b) The rate of exergy destruction in the indoor air.

Solution (a) The heat given by the radiator is the sum of the heat transferred by convection and by radiation. Q_ ¼ Q_ rad þ Q_ conv ¼ hconv
rad $A$ðTh
Ti Þ ¼ 3:26 kW

In this Example E.5.1, we treat the convection and radiation together through an equivalent coefficient of convection-radiation, so that with Th ¼ 333 K, we shall consider the exergy accompanying the heat exchanged to be approximately
 T0 _ _ Q ¼ 0:45 kW BQ ¼ 1
Th b) Undertaking an exergy balance in the indoor air, we have 

T0 _ T0 _ Th
Ti _ Q ¼ 0:37 kW Q
1
Q ¼ T0 D_ a ¼ 1
Th Ti Th $Ti Example E.5.2. The air in a room, which is supposed to be hermetically sealed, is at a temperature of 20 C. The room heating element is a radiant floor, with the water temperature at the floor inlet at 28 C and the outlet at 25 C, and with a flow rate of 405 L/h. The interior surfaces of the walls and ceiling of the room are at an average temperature of 19 C. If the ambient temperature is 8 C, determine the heat given by the radiant floor and the exergy destroyed in the indoor air.

Solution l m3 kg V_ ¼ 405 ¼ 1:12 :10
4 /m_ ¼ 0:112 h s s


 kg r ¼ 1000 3 m

The rate of heat given by the radiant floor is _ in
hout Þ ¼ m$c _ P $ðTin
Tout Þ ¼ 1404 W Q_ ¼ m$ðh To calculate the exergy of the heat flux coming out of the radiator, we first determine the logarithmic mean temperature difference between the water flow in the radiant floor and the indoor air DTlm ¼

DTin
DTout 28
25
 ¼ 7:40 C  ¼
DTin 28
19 ln ln 25
19 DTout

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so that the surface temperature of the radiant floor is approximately Th ¼ Ti þ DTlm ¼ 300:4 K The rate of exergy accompanying the heat flux that comes out of the radiant floor is
 T0 _ Q ¼ 90:7 W 1
Th Undertaking an exergy balance in the indoor air, we have T h
Ti D_ ¼ T0 Q_ ¼ 37 W Th Ti In a room of dimensions 5  4  3 m conditioned by an all-air system, an airflow enters through the intake diffuser at a rate of 1.4 m3/min, a temperature of 20 C and relative humidity of 60%. The extracted air is at 25 C and has a relative humidity of 65%. If the ambient air temperature is 30 C, the pressure is 1012 mbar and the absolute humidity is 16 g/kg dry air, determine:

Example E.5.3.

(a) The water vapor produced in the room. (b) The air enthalpy increase, due to the heat transferred through the walls and by internal gains. (c) The exergy change of the air between the inlet and the extraction.

Solution (a) We first calculate the partial pressure of the vapor in the intake air and extracted air. From the water vapor tables we get ps(20 C) ¼ 23.4 hPa ps(25 C) ¼ 31.7 hPa. According to the definition of relative humidity, we have

f¼

pv /pv in ¼ 14:04 hPa ps ðTÞ

pv; out ¼ 20:60 hPa

The corresponding absolute humidities are u ¼ 0:622

pv g ; / uin ¼ 8:7 kg dry air p
pv

uout ¼ 12:9

g kg dry air

From the intake airflow, we can calculate the mass flow rate, since m_ ha ¼ 9ha V_ ¼

p

g V_ ¼ 27:91 Rha T s

Knowing the mass flow rate of humid air that enters the room, we can calculate the mass flow rate of dry air that enters, which is the same as the one that leaves. m_ ha ¼ m_ a ð1 þ uin Þ /m_ a ¼ 27:67

g dry air s

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By means of a mass balance for the vapor, we have that the rate of water vapor generated in the room m_ v is m_ a uin þ m_ v ¼ m_ a uout /m_ v ¼ m_ a ðuout
uin Þ ¼ 0:12

g s

(b) The air enthalpy increase is

  DH_ ha ¼ m_ a ðhout
hin Þ ¼ m_ a ha;out
ha;in þ uout hv;out
uin hv;in The specific enthalpy of dry air is Z T ha ðTÞ ¼ ha ðTr Þ þ cp;a dT where Tr a reference temperature. Since in the air Tr

conditioning processes we have to calculate enthalpy changes, so that the amount of dry air and water (either in liquid or vapor form) at the inlet of the equipment is the same as at the outlet, we can choose a totally arbitrary reference state for both the dry air and the water. In calculations of a certain precision, the dependence of cp,a on temperature should be taken into account. However, for temperatures up to 100  C, ha ¼ 1.004T kJ/ kg d.a. is approximately satisfied where T is the temperature in  C. With respect to water, the reference state is chosen as the triple point of liquid water, assigning a zero enthalpy to said state. Thus, the vapor enthalpy at temperature T will Z T be hv ¼ lðTPT Þ þ cp;v ðTÞ dT, with the vaporization enthalpy at the triple point TPT

being l(TPT) ¼ 2,500 kJ/kg. Considering that cp,v for the reheated vapour is approximately constant cp,v ¼ 1.86 kJ/kg and since T
TPT z T, we have that hv ¼ 2500 þ 1.86 T (kJ/kg). In short, the heat given to the indoor air is DH_ ha ¼ 437 W (c) To calculate the exergy change of the air we calculate the physical and chemical exergy variation of the air between the inlet and the outlet. The physical exergy is

     bin ¼ ha
ha;0 þ uin hv
hw;0
T0 sa
sa;0 þ uin sv
sw;0

B_ in ¼ m_ a bin

Developing this expression, we obtain Equation (3.37) from Section 3.2.3 in Chapter 3. As at both the inlet and the outlet p ¼ p0, we have bin ¼ 0:170

kJ kg dry air

and for the extracted air bout ¼ 0:043

kJ kg dry air

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355

Therefore, B_ in ¼ m_ a bin ¼ 4:7 W

B_ out ¼ m_ a bout ¼ 1:2 W

According to Equation (3.123), the chemical exergy of the air supplied and the air extracted, per unit mass of dry air, are respectively, bch in ¼ 0:273

J gda

bch out ¼ 0:044

J gda

Multiplying by the mass flow rate of dry air, we have ch B_ in ¼ m_ a bch in ¼ 7:6 W

ch B_ out ¼ m_ a bch out ¼ 1:2 W

In short, the exergy variation of the air is     ch ch B_ in þ B_ in
B_ out þ B_ out ¼ 9:9 W A small vertical steel radiator finished in a black lacquered high gloss surface 0.54 m2 is in a room where the air temperature is 21 C. The walls have an average surface temperature of 18 C, and the ratio between their total surface and that of the radiator is 110. A small fan has been placed in front of the radiator, which multiplies the natural convection coefficient by 6. A water flow of 92 L/h enters the radiator at 64 C, with the outlet temperature being 58 C. Knowing that the radiator emissivity is 0.9, that of the walls is 0.8 and the ambient air temperature is 10 C, determine:

Example E.5.4.

(a) The heat flux transferred by convection and by radiation. (b) The energy and exergy transferred by the water flow to the radiator. (c) The total irreversibility in the radiator.

Solution (a) According to ASHRAE Fundamentals for the convection only coefficient of horizontal heat flux for a room, the value to adopt is hcv ¼ 3.06 W/m2$K. The presence of the fan causes the convection value we use to become hcv ¼ 18.36 W/m2$K. The average surface temperature of the radiator is approximately

Th ¼ Ti þ

Tin
Tout 6 ¼ 334 K ¼ 294 þ DTin 43 ln ln 37 DTout

Therefore, the convection heat transferred is Q_ cv ¼ Ahcv ðTh
Ti Þ ¼ 396 W

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Taking into account that the vision factor between the radiator and the walls is F12 ¼ 1, the radiator emissivity is εh ¼ 0.9 and that of the walls εis ¼ 0.8, the heat exchanged by radiation between the radiator and the walls of the room is   s Th4
Tis4 Q_ r ¼ ¼ 145 W 1
εh 1 1
εis þ þ Ah Ah εh Ais εis (b) The energy given to the radiator by the water flow is

m_ w cp;w ðTin
Tout Þ ¼ 641 W Therefore, there are 100 W that are not transferred by the radiator surface (convection þ radiation) to the interior of the room and which is, therefore, lost heat (15.6%). The exergy transferred by the water flow to the radiator is

 Tin m_ w ðbin
bout Þ ¼ m_ w cp;w ðTin
Tout Þ
T0 cp;w ln ¼ 98 W Tout (c) Grouping the heat exchanged by convection and radiation, considering that the temperature of that heat flux is 334 K and performing an exergy balance in the radiator, we have

m_ w ðbin
bout Þ ¼ B_ Q þ I_ / I_ ¼ 15 W The radiator of a room in which the indoor air temperature is 22 C, gives the air 4 kW of heat, while the water flow enters the radiator at a temperature of 72 C and leaves it at 65 C. Knowing that the radiator’s efficiency is 95%, determine

Example E.5.5.

(a) The heat transferred by the radiator to the indoor air. (b) The exergy of that heat, on two different days, in which the outside air temperature is 0 C and 10 C. (c) The irreversibilities in the radiator when the outside air temperature is 0 C.

Solution (a) Efficiency of 95% means that, of all the heat given by the radiator, only 95% is effective in heating the indoor air. From the expression of the efficiency, we calculate the mass flow rate of the hot water in the radiator

h¼

Q_ m_ w $ðhin
hout Þ

m_ w ¼

Q_ kg ¼ 0:14 h$cw $ðTin
Tout Þ s

where Q_ l ¼ ð1
hÞQ_ h ¼ 21 W is the rate of loss heat.

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357

(b) The radiator average surface temperature is approximately

Th ¼ Ti þ DTlm ¼ Ti þ

DTin
DTout
 ¼ 68:4 C DTin ln DTout

On a day when T0 ¼ 273 K the exergy of that heat flux is

  T0 T0  _ Q
Q_ l ¼ 761 W B_ Q ¼ 1
hQ_ ¼ 1
Th Th and when the outside temperature is T0 ¼ 283 K, then B_ Q ¼ 650 W which represents a 14.6% change with respect to the first value. In this example, we have used a convection-radiation coefficient, so we consider the two heat exchange mechanisms of the radiator together. (c) By performing an exergy balance in the radiator, we can obtain the rate of exergy destruction, which is

m_ w ðbin
bout Þ
B_ Q ¼ I_ As bin
bout ¼ ðhin
hout Þ
T0 ðsin
sout Þ ¼ 5:86

kJ kg

we have that I_ ¼ 59 W. These total irreversibilities in the radiator are the sum of the exergy destruction (internal) plus the exergy accompanying the lost heat, that is to say
 _I ¼ D_ þ 1
T0 Q_ l ¼ 59 W Th so the rate of internal exergy destruction in the radiator is D_ ¼ 55 W.

5.5

Distribution system

The distribution of heat (or cold) from the generation to the end elements is done with pipes through which water circulates or through air ducts. In addition to the pipes and ducts there are a number of auxiliary elements, such as supports, insulation, dilators, joints and other accessories. When selecting the distribution system, compatibility with the fluid being transported must be taken into account, in addition to the pressure

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.4 Heat losses in a distribution pipe.

and the working temperature. The materials used can be metallic (galvanized steel, stainless steel, copper) or thermoplastics (PVC, PVC-C, PE, etc.). Consider a water flow in a pipe through the surface of which there is a heat flux loss to the outside, see Fig. 5.4. We will assume at all times that there is a steady state and that the flow is one-dimensional. Imagine first that the process is internally reversible so that there is no mechanical friction in this flow. The heat that is lost through the outer surface of the pipe insulation leaves at a different temperature than the ambient temperature so that although in the system under consideration there is no internal exergy destruction, there is external destruction. Since the temperature of the pipe and its outer surface T is variable along _ being the heat exchanged in a differential element of pipe length, 1 the flow, with qdL and 2 the water conditions at the inlet and outlet of the pipe of total length L, respectively, for a steady state situation we can write the following exergy balance equation  Z
T0 _ 1
b2 Þ ¼ _ mðb 1
qdL (5.12) T L

where changes in kinetic energy or potential energy have not been taken into account. Therefore, the rate of external exergy destruction will be Z T
T0 _ _ qdL (5.13) De ¼ T0 TTo L

According to what we already mentioned in Chapter 2, we can again observe that the exergy destruction due to thermal irreversibilities is directly proportional to the difference in temperatures that take place in this heat exchange. But also, as already said, we must bear in mind that this destruction is greater when the thermal level of the exchange is lower. We are now going to analyse the real situation when there are internal irreversibilities in the flow process due to the water viscosity. Undertaking an exergy balance we have  Z
T0 _ 1
b2 Þ ¼ _ þ D_ i mðb (5.14) 1
qdL T L

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359

where, as seen in Chapter 2, with wf being the friction work per unit of mass, we have _ 0 D_ i ¼ mT

Z2 1

dwf T0 p1
p2 z m_ T T 9

(5.15)

Considering the internal and external irreversibilities and neglecting the changes of kinetic energy and potential energy in the flow, we have that the decrease in the flow exergy is the sum of the internal and external destructions, that is _ 1
b2 Þ ¼ D_ i þ D_ e ¼ D_ mðb

(5.16)

When carrying out the building simulation with software such as TRNSYS if we want to evaluate the exergy destruction in the distribution system, we must bear in mind that, in this software, the thermal behaviour of flow in a pipe, or conduit, is analysed by considering the pipe divided into segments of varying length and the flow is treated with a piston-like flow approximation, TRNSYS Manual 2014 [4]. It is assumed that the temperature is constant in each section so that the temperature change from one instant to the next is obtained by performing an energy balance in each section (heat given is equal to the enthalpy decrease). The rate of exergy destruction in each section is obtained from Eq. (5.16), which will now be written for the N segments into which the pipeline is divided, that is to say _ kÞ ¼ Dðt

N X j¼1

" m_ w ðtk Þcp;w

Tj ðtk Þ Tj ðtk Þ
Tj ðtk
1 Þ
T0 ðtk Þln Tj ðtk
1 Þ

# (5.17)

As the temperature of each section is not an output of the software, the mean mass temperature Tm of the sections in each time interval is calculated, Torio 2012 [5], and in this way, the exergy destruction rate is calculated according to the following expression _ kÞ ¼ Dðt

5.5.1

N X j¼1

 Tm ðtk Þ m_ w ðtk Þcp;w Tm ðtk Þ
Tm ðtk
1 Þ
T0 ðtk Þln Tm ðtk
1 Þ

(5.18)

Examples

A hot water flow of 2.5 L/s at 60 C moves through a 6 cm diameter pipe. The pipe, which has a length of 20 m and is properly insulated, passes through rooms where the temperature is 20 C. The insulation surface temperature is 30 C and the global convection-radiation coefficient is 5.2 W/m2$K. If the head losses are 2 m w c, and the ambient air temperature is 10 C, determine

Example E.5.6.

(a) The exergy of the lost heat. (b) The rate of internal exergy destruction.

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Solution (a) The heat lost through the pipe is

Q_ ¼

Z _ ¼ pde Lhcv
r ðTes
Ti Þ ¼ 196 W qdL L

The exergy accompanying that heat transferred is 
T0 _ Q ¼ 13 W 1
Tes b) The rate of internal exergy destruction is associated with the head loss, that is, the transformation of the flow mechanical energy into internal energy and heat that is transferred to the outside. According to Equation (2.110) in Chapter 2, since p1
p2/r ¼ 2g J/kg we have

T0 p1
p2 D_ i z m_ ¼ 42 W T 9 Let there be a copper distribution pipe for heating and DHW of 40 m length that is not thermally insulated and whose external diameter is 3 cm. The water flow rate is 0.4 L/s, the water temperature at the pipeline inlet is 70 C and the pipe surface temperature remains constant and equal to 50 C. The head losses are 3 m w c. If the ambient temperature is 15 C, determine:

Example E.5.7.

(a) (b) (c) (d)

The water temperature at the end of the distribution pipe and the heat lost. The exergy of the lost heat. The rate of exergy destruction due to the head losses. The total irreversibility in the pipeline.

Solution (a) The heat flux on the surface of the pipe, per unit area, is

q_ ¼ hðTt
Tm Þ where h is the coefficient of local heat transfer between the water and the inner surface of the pipe, Tt is the temperature in the pipe and Tm the average flow temperature in that section. For the water temperatures and flow velocity of the statement, we consider a convection coefficient h ¼ 1400 W/m2$K. The water temperature decreases along the pipeline, so that, when imposing the condition that Tt is constant, the heat flux must vary. The total rate of heat exchanged by the water flow in the pipe section under consideration is _ in
hout Þ ¼ mc _ p ðTin
Tout Þ Q_ ¼ mðh

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361

so we need to know the temperature at the outlet Tout. Undertaking an energy balance in a differential pipe element, we have the equation _ p dT ¼ hðTt
TÞdA mc where T is the average temperature of the water, which decreases in the direction of flow as a result of heat transfer. By integrating this equation for the length of the pipe, we get ln

Tt
Tout hA ¼
_ p mc Tt
Tin

where A ¼ pDL is the surface of the pipe. So we get   _ p ¼ 50:8 C Tout ¼ Tt
ðTt
Tin Þexp
hA=mc _ p from the above equation leads to the equation that expresses the toRemoving mc tal heat transferred DTout
DTin  ¼ h ADTlm Q_ ¼ h A
DTout ln DTin where DTout ¼ Tt
Tout and also DTin ¼ Tt
Tin. Therefore, the total rate of heat exchanged is Q_ ¼
31:5 kW which obviously, is lost heat. (b) The exergy accompanying that lost heat is


 T0 _ Q ¼ D_ e ¼ 3413 W
1
Tt (c) The water enters at 70 C, and the exit temperature is 50.8 C. We can find the average temperature of the fluid T(x) for any value x of pipe length, since replacing A for pdx in the previous equation of temperature, we have

  _ p TðxÞ ¼ Tt
ðTt
Tin Þexp
hpdx=mc Strictly in the calculation of the internal exergy destruction, we would have to use this variable temperature, for which we would have to consider the internal destruction in a differential length element and then integrate for the total length of the stretch. However, we are going to simplify by considering an average temperature of the water

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Exergy Analysis and Thermoeconomics of Buildings

in the section, equivalent to the arithmetic mean between the inlet temperature and the outlet temperature, that is, T ¼ 333:5 K ð60:4 CÞ. We then get that the rate of exergy destruction associated with the head losses is T0 p1
p2 D_ i z m_ ¼ 10 W 9 T (d) The total irreversibility is the sum of the internal and external exergy destructions and, therefore,

I_ ¼ D_ i þ D_ e ¼ 3423 W A flow of air at a speed of 3 m/s circulates through a conduit with a rectangular section and dimensions of 40  25 cm. A duct section of 15 m in length crosses an external area, with the ambient temperature being 29 C and the pressure at the entrance of the section being 1 bar. The airflow temperature, which is considered equal to that of the duct, at the entrance of the section is 18 C, increasing by 5 C at the outlet and having a pressure loss of 3 mbar. Determine

Example E.5.8.

(a) The rate of heat exchanged and the exergy accompanying that heat. (b) The internal and external rate of exergy destruction.

Solution (a) The mass flow rate of air is

m_ ai ¼ 9AV ¼

p g AV ¼ 370 Rai T s

Assuming that the air has a constant specific heat cp,ai ¼ 1.008 kJ/kg$K, the rate of heat exchanged by the air is Q_ ¼ m_ ai ðhout
hin Þ ¼ 1865 W This is a heat transferred to the air from the environment so the exergy accompanying that heat is zero. (b) As a consequence of this increase in temperature the air exergy decreases since its thermodynamic state approaches that of the environment. The decrease of the exergy thermal component is


   Tin DT _
b c
T
T ln m_ ai bDT ¼ m T ¼ 54 W ai p;ai in out 0 in out Tout This decrease in exergy is due to the exergy that the air yields to the environment associated with the heat transferred from the environment.

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363

The internal exergy destruction associated with head losses, assuming that air behaves like an ideal gas, according to Equation (2.109) in Chapter 2, is. pin D_ i ¼ m_ ai Rai T0 ln ¼ 97 W ps This internal exergy destruction corresponds to the reduction of the mechanical component of the air exergy, that is   pin Dp _ ai Rai T0 ln
b m_ ai bDp out ¼ m in pout Indeed, the exergy decrease due to the heat lost plus the internal exergy destruction coincides with the total decrease in the exergy of the air, since according to Equation (3.12) in Chapter 3, we have


  Tin pin m_ ai ðbin
bout Þ ¼ m_ ai cp;ai Tin
Tout
T0 ln þ Rai T0 ln ¼ 151 W Tout pout

5.6

Three-way valves

In heating and DHW installations, in order to achieve the desired temperature, four-way and three-way valves are often used. We will look at the latter, which have three inputs/outputs and whose function is to mix flows or separate flows into two, in certain determined proportions. When mixing two input flows into a single output, they are called mixers, and when they separate a flow into two outputs, they are called distributors. Fig. 5.5A shows the operation of a mixing valve and Fig. 5.5B its external appearance.

Figure 5.5 (A) Operation of a mixing valve (B) external appearance.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.6 Diagram of a mixing valve in a heating system.

We are going to look at mixing valves, although the type of analysis is the same for the others. Thus, the valve mixes the hot water from the boiler or the DHW tank with the return water and, in this way, an appropriate temperature is obtained in the end elements, see Fig. 5.6. In the mixing of these two water flows at different temperatures there are no energy losses since the process can be considered adiabatic, but there are significant exergy destructions, as we saw in the analysis done in Section 2.17.3.1 of Chapter 2. Calling the mass flow rates m_ 1 and m_ 2 , with T1 and T2 being their respective temperatures, from the mass balance ðm_ 1 þ m_ 2 ¼ m_ 3 Þ and energy balance ðm_ 1 h1 þ m_ 2 h2 ¼ m_ 3 h3 Þ we can find the resulting temperature T3. In general, both T1 and T2 are functions of time, and therefore, also T3. Calling the relationship between these flows x, we have T3 ¼ xT1 þ ð1
xÞT2

(5.19)

The exergy of each flow is calculated by expression (3.44) from Chapter 3. Thus, for the resulting flow 3, the exergy at an instant tk is

 T3 ðtk Þ m_ 3 b3 ðtk Þ ¼ m_ 3 c ðT3 ðtk Þ
T0 ðtk ÞÞ
T0 ðtk Þln T0 ðtk Þ

(5.20)

By means of an exergy balance, we can obtain the rate of exergy destruction in the mixing valve. In effect, the balance is m_ 1 b1 þ m_ 2 b2 ¼ m_ 3 b3 þ D_

(5.21)

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Figure 5.7 Exergy destruction in a mixture of two flows at different temperatures.

Calling s ¼ T2/T1 gives the following expression for the exergy destroyed per unit resulting flow d ¼ T0 ln

x þ sð1
xÞ s1
x

(5.22)

Therefore, whenever we mix two flows of the same fluid at different temperatures, exergy destruction will take place. This exergy destruction will be greater when the temperature difference between the two flows is higher and will also depend on the relationship between the mass flow rates. In Fig. 5.7 we show Eq. (5.22) as a function of s and for different values of the relation between mass flows.

5.7 5.7.1

Heat exchangers Types and characteristics

As the name implies, heat exchangers are devices in which there is a heat exchange between at least two fluids; one of them, the hot fluid, decreases its temperature and gives heat to the other, which is cold, and in this way its temperature increases (or it experiences a phase transition).

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There are numerous types of heat exchangers. Given the relative direction of the two fluid streams, they can be divided basically into two groups: • •

If the two flows cross each other in space, usually forming a right angle, they are said to be cross-flow. This is the case for radiators in cars or the cooling unit of an air conditioning installation. If the two fluid streams move in parallel directions, they are said to be serial heat exchangers. Within this group, there are basically two types: those of co-current or parallel-flow arrangement, when the hot and cold fluids enter at the same end, flow in the same direction, and leave at the same end and the counter-current type, when the two fluids enter at opposite ends, flow in opposite directions, and leave at opposite ends.

There are numerous other types of heat exchangers, Shah and Sekulic 2003 [6], that have special names depending on the role they perform in the facility. Thus, there are condensers, in which condensation of vapor occurs, or evaporators, as they evaporate liquid or more generally saturated liquid-vapor mixtures with a certain quality, etc. The typical temperature profiles for types of exchangers mentioned above are shown in Fig. 5.8. In heating and DHW systems, heat exchangers are basically of two types: plate and shell-and -tube. The most common are plates also termed compact heat exchangers, because they achieve a very large heat transfer surface area per unit volume, and in which the plate represents the heat exchange surface and is produced by cold stamping a metal sheet of homogeneous thickness. The corrugated design of the plates determines their heat transfer characteristics; when the exchanger is closed, the channels are created through which the primary and secondary fluids circulate. The most common material used for the plates is stainless steel. Currently, electro-welded plates are used more and more in these heat exchangers, instead of those with removable plates. They have the disadvantage that they cannot be dismantled, although they have better operating characteristics and are cheaper, so taking into account that the joints must be replaced periodically, in the long term they are more economical.

Figure 5.8 Temperature profiles in some types of heat exchangers.

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The shell-and -tube heat exchangers consist of an interior tubular bundle, through which runs the primary hot water, heated for example by a boiler. The secondary water to be heated circulates through the interior of the housing, which is generally cylindrical. Since the material should not affect the water potability, these heat exchangers are usually made of stainless steel.

5.7.2

Conventional energy analysis

Consider the diagram in Fig. 5.9. Let h be the hot fluid and c the cold fluid and let the inlet and outlet sections be 1 and 2, that is, h1 and h2 for the hot fluid, c1 and c2 for the cold. We choose as CV what is included within the dashed line of Fig. 5.9, that is, the whole of the heat exchanger. Therefore, this CV has two input sections and two output sections. In a steady state, the situation which we are going to analyse, the mass balance says that m_ h1 ¼ m_ h2 and analogously m_ c1 ¼ m_ c2 . Although there is obviously a heat exchange with the exterior, by design, this is very small so that the whole of the heat exchanger can be considered adiabatic. On the other hand, the kinetic and potential energy variations of both flows are generally negligible compared to their enthalpy variations. Taking into account the above, from the energy balance equation we have m_ h hh1 þ m_ c hc1 ¼ m_ h hh2 þ m_ c hc2

(5.23)

which is the same as m_ h ðhh1
hh2 Þ ¼ m_ c ðhc2
hc1 Þ

(5.24)

that is, the enthalpy decrease of the hot fluid is equal to the enthalpy increase of the cold. The objective of a heat exchanger is to accelerate the heat exchange between two flows, without having losses to the outside. In this case, the loss is the heat exchanged with the outside through the exchanger surface. Therefore, an adiabatic heat exchanger will not have losses and, its efficiency, from the point of view of the First Law, would be unity.

Figure 5.9 Scheme of a heat exchanger.

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In practice, one type of problem that arises in the analysis of heat exchangers is the following: completely knowing the physical description of the exchanger, the mass flow rates and the input conditions of the two flows, what will be their respective exit temperatures and, ultimately, what is the rate of heat transfer? It is, therefore, a question of determining the efficiency with respect to the heat transfer of a specific heat exchanger, or determining whether a heat exchanger will perform the function that is assumed. To solve this type of problem Kays and London 1984 [7] developed the method of NTU-Effectiveness. Here, we will only indicate that the effectiveness of a heat exchanger is the quotient between the heat actually exchanged and the maximum that could be exchanged. For its part, the number of transfer units is NTU¼UA/ Cmin, where U is the total heat transfer coefficient, A is the surface area of heat transfer and Cmin is the minimum capacity, that is, the product of the mass flow rate by the specific heat of the fluid for which this value is the lowest. When the problem that arises is that of selecting a heat exchanger that achieves a specified temperature change of a fluid mass flow rate, then, the method of logarithmic mean temperature difference, LMTD, is generally used; in this respect, see a heat transfer text such as C¸engel 2004 [8].

5.7.3

Exergy analysis

Assume that the purpose of the heat exchanger is to heat the cold flow so that the primary is the hot flow and the secondary is the cold flow. The primary flow will decrease the exergy from state h1 to h2, while the secondary will increase its exergy from c1 to c2. Considering the adiabatic heat exchanger and undertaking an exergy balance, we have m_ h ðbh1
bh2 Þ ¼ m_ c ðbc2
bc1 Þ þ D_

(5.25)

Thus, knowing the states at the input and output of the heat exchanger, the above equation allows us to determine the rate of exergy destruction. This destruction is due to the two mechanisms that we have commented on: the temperature difference between the flows and the mechanical friction in both flows. For the case at hand, a heat exchanger with two water flows, we have

  Th1 Tc2 D_ ¼ m_ h c Th1
Th2
T0 ln
m_ c c Tc2
Tc1
T0 ln (5.26) Th2 Tc1 Since the objective of the exchanger is to heat the cold flow, this is its product, and this is done at the expense of the hot flow. In accordance with the definition of efficiency that we have proposed in Chapter 2, the exergy efficiency of the heat exchanger will be 4¼

D_ m_ c ðbc2
bc1 Þ ¼1
m_ h ðbh1
bh2 Þ m_ h ðbh1
bh2 Þ

(5.27)

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Suppose now that the primary is the cold flow and the objective of the heat exchanger is to cool the hot flow of the secondary, which at the exchanger entrance is already below the ambient temperature. This may be the case of the evaporator of a refrigerating machine where the primary is the refrigerant, and the secondary is a water flow that enters at 12  C and is cooled to a temperature of 7  C. As we say, in this case, the objective of the heat exchanger is to cool the secondary at the expense of a temperature increase of the primary, so that the expression for the exergy efficiency will be 4¼

m_ h ðbh2
bh1 Þ mc ðbc1
bc2 Þ

(5.28)

As both the primary and the secondary are below the ambient temperature, the exergy of the primary in state c1 is greater than in state c2, which is at a higher temperature and, therefore, closer to the ambient temperature. As for the secondary flow state h2 is at a lower temperature than state h1; therefore, it is farther from the ambient temperature, and its exergy will be higher, that is, both the numerator and the denominator of Eq. (5.28) are positive. Now let us consider the case of a heat exchanger in which the primary is above the ambient temperature and the secondary below. In this heat exchanger, both the exergy of the primary flow and secondary flow will decrease so that in these conditions the function (thermodynamically) of this equipment is to destroy exergy. This means that this type of heat exchanger should be avoided whenever possible.

5.7.4

Analysis of the mechanisms of irreversibilities

In Section 2.17, we considered the mechanical and thermal irreversibilities separately and obtained corresponding expressions for the calculation of exergy destruction. We will now look at a situation in which both types of irreversibilities occur simultaneously and, for this, we are going to consider a differential element in the heat _ is the rate of heat exchanged between both fluids exchanger of length dL, where qdL in that differential element, see Fig. 5.10. If we call the temperatures of the hot and cold fluids Th and Tc in the volume element of length dL under consideration, the exergy destruction rate is dD_ ¼ T0

w_ fh w_ fc Th
Tc _ þ T0 dL þ T0 dL qdL Th Tc Th Tc

(5.29)

The first term on the right of the equation represents the rate of exergy destruction linked to heat transfer, while the second and third correspond to the internal mechanical irreversibilities, due to the viscosity of both fluids. Of these two mechanisms, undoubtedly, the one that generates the greatest exergy destruction in most situations is the first.

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Figure 5.10 Differential Control Volume in a heat exchanger.

Calling the average thermodynamic temperatures of the two fluids in the heat exchanger Thm and Tcm, Sala et al. 1998 [9], the rate of total exergy destruction in the exchanger is Z Z w_ fh w_ fc Thm
Tcm _ _ Qþ D ¼ T0 dL þ dL (5.30) Thm Tcm Th Tc L

5.7.5

L

Examples

Example E.5.9.

In a counter-current air-water heat exchanger, an airflow mass rate of 0.2 kg/s is cooled from a temperature of 120o C to 30 C at the outlet. The air pressures at the inlet and outlet of the heat exchanger are 1.3 and 1.2 bar respectively, and the areas of the inlet and outlet cross-sections are both 0.1 m2. At the inlet of the heat exchanger, the water pressure is 2.5 bar at a temperature of 20 C, and at the outlet, it is at 95 C and approximately the same pressure. If the ambient temperature is 290 K, determine (a) (b) (c) (d) (e)

The air velocity at the inlet and outlet of the heat exchanger. The rate of heat given by the air and the water mass flow rate. The exergy change of the air and water. The rate of exergy destruction in the heat exchanger. The exergy efficiency of the heat exchanger.

Solution (a) Calculating the air velocity. At the inlet

m_ ai;1 ¼ m_ ai ¼ r1 A1 V1

Exergy analysis of thermal facilities equipment in buildings (I)

Vai;1 ¼

371

m m_ ai m_ ai RT1 ¼ ¼ 1:7 s A1 r1 Mai p1 A1

The air velocity at the outlet is Vai;2 ¼

T2 p1 m m_ ai m_ ai RT2 ¼ ¼ Vai;1 ¼ 1:4 s A2 r2 Mai p2 A2 T1 p2

(b) Considering for air cp,ai ¼ 1.008 kJ/kg$K, the rate of heat given by the air is

Q_ ¼ m_ ai



  1 2 2 hai;1
hai;2 þ Vai;1
Vai;2 ¼ 18:1 kW 2

In this balance, we have maintained the term for the kinetic energy variation to show that it is much smaller than the one corresponding to the enthalpy, so in general, we will not take it into account. To calculate the water mass flow rate, we first determine the change of its specific enthalpy.   kJ hw;2
hw;1 ¼ cw Tw;2
Tw;1 ¼ 313:5 kg The energy balance in the heat exchanger is   kg Q_ ¼ m_ w hw;2
hw;1 /m_ w ¼ 0:058 s (c) The air exergy change is


  T2 p2 _ _ DBai ¼ mai cp:ai T2
T1
T0 ln
Rai ln ¼
2:9 kW T1 p1 while the water exergy change is


 Tw;2 ¼ 2:2 kW DB_ w ¼ m_ w cw Tw;2
Tw;1
T0 ln Tw;1 (d) Undertaking an exergy balance in the heat exchanger, we have

B_ ai;1 þ B_ w;1 ¼ B_ ai;2 þ B_ w;2 þ D_

  /D_ ¼
DB_ ai þ DB_ w ¼ 0:7 kW

(e) The heat exchanger exergy efficiency is

4¼

D_ DB_ w ¼1
¼ 0:75ð75%Þ
DB_ ai
DB_ ai

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Exergy Analysis and Thermoeconomics of Buildings

In a heat exchanger, a water flow rate of 1.4 L/s is heated from a temperature of 25o C to 60 C by partial condensation of a mass flow rate of saturated steam of 0.18 kg/s at 100 C up to a final quality of 0.4. The surface temperature of the heat exchanger has a mean value of 55 C. If T0 ¼ 290 K, determine

Example E.5.10.

(a) (b) (c) (d)

The rate of heat lost to the environment by the heat exchanger. The exergy change of the air and steam. The rate of exergy lost and the rate of exergy destruction. The exergy efficiency of the heat exchanger.

Solution (a) Calling the vapour states at the inlet and outlet of the heat exchanger 1 and 2, with 00 0 h
h ¼ 2256.4 kJ/kg being the vaporization enthalpy at 100 C, the rate of heat given by the steam is

m_ v ð1
x2 Þðh00
h0 Þ ¼ 243:7 kW Calling the water states at the inlet and outlet of the heat exchanger 3 and 4 respectively, the heat that the water flow exchanges is m_ w cw ðT4
T3 Þ ¼ 204:8 kW From the energy balance in the heat exchanger we have that   m_ v ð1
x2 Þ h''
h' ¼ m_ w cw ðT4
T3 Þ þ Q_ l /Q_ l ¼ 38:9 kW (b) The water exergy change is


 T4 _ DBw ¼ m_ w cw T4
T3
ln ¼ 16:4 kW T3

The steam exergy change is

 ð1
x2 Þðh00
h0 Þ DB_ v ¼ m_ v ð1
x2 Þðh00
h0 Þ
T0 ¼ 54:2 kW Tv (c) The rate of lost exergy due to the heat loss, with the surface temperature of the exchanger at Texs ¼ 328 K, is


 T0 _ Ql ¼ 4:5 kW B_ Q ¼ 1
Texs while the rate of exergy destruction is calculated from the exergy balance
 T0 _ _ _ D_ ¼ 33:3 kW _ Ql þ D/ DBv ¼ DBw þ 1
Texs

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(d) The exergy efficiency of the heat exchanger is defined as the relation between the product (increase in the water exergy) with respect to the fuel (decrease in the vapor exergy) which is

4¼

B_ Q þ D_ DB_ w ¼1
l ¼ 30:2% _ DB v DB_ v

If we had used the efficiency based on the First Law, we would have h¼1


5.8 5.8.1

Q_ l 38:9 ¼ 84:0% ¼1
_ 243:7 DH v

Heating and DHW boilers Types and characteristics

The heating boiler is a device in which hot gases resulting from combustion are generated and in which heat exchange takes place between these hot gases and a water flow that is heated. There are different criteria to classify the numerous types of boilers, the most important being the one that refers to the disposition of the fluids. According to this point of view, the boilers are classified into two large groups: fire-tube boilers, see Fig. 5.11 and water-tube boilers. Referring to the boilers that we find in buildings, they can be simple or mixed, depending on whether they work only for heating or heating and DHW, respectively. Heaters are a simple boiler variant, providing only DHW. On the other hand, depending on the type of fuel used we may find solid fuel boilers (firewood, coal or pellets), liquid fuels (gas oil), or gases (butane, propane or natural gas) and, finally, we also have electric boilers.

Figure 5.11 Image of a fire-tube boiler.

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Exergy Analysis and Thermoeconomics of Buildings

The gas boiler is the most used in the current market, due to the fuel characteristics and its availability in most localities. Regarding their placement, there are standing boilers and wall boilers. The first are installed on the floor, while the second are fixed on the wall. According to their operation, they can be automatic or semi-automatic boilers, and according to the flue, we can find pressurized hearth boilers and balanced hearth boilers. An important classification is based on the combustion system, on which the boiler performance depends to a great extent. There are atmospheric and sealed boilers, although today the former is no longer used. The sealed boilers have two concentric pipes to expel the combustion gases to the outside and capture the necessary air for the combustion process in the external environment, which is preheated on entering. For the removal of gases, there is an extractor that guarantees their expulsion to the outside. This arrangement makes the boiler more secure, see Fig. 5.12. On the other hand, depending on the working temperatures we can talk about conventional boilers, low-temperature boilers and condensing boilers. Conventional or standard boilers work at an average temperature between the outgoing and return close to 70 C, to prevent the dew point of the fumes being reached inside, which would cause vapor condensation and the formation of acid compounds. The materials of these boilers are not prepared for condensation, so in centralized installations, they always have a pump or anti-condensation valve to prevent the corrosion of the boiler body when the return temperature is low so that this is usually higher than about 55 C. The main drawback of these boilers is their high fuel consumption since they always produce water at high temperatures. Another drawback is that corrosion will

Figure 5.12 Natural gas sealed boiler.

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375

occur in the body of the boiler if the anti-condensation pump thermostat is not properly regulated. It is clear that the combustion gases temperature in boilers of this type is very high. Generally, these boilers with bodies of sheet steel were installed years ago in centralized installations, as well as in individual systems, so that we find a high percentage of installations of this type. Low-temperature boilers arise from the need for fuel savings and the use of new technologies applied to their manufacture. The main advantage of low-temperature boilers is that they can work with very low return water temperatures (40 C) and that they regulate the temperature depending on the demand. Therefore, they can be adapted to the thermal needs of the building, outputting water at different temperatures depending on the outside temperature, orientation of the building, location, etc. This generates a great energy saving, by not having to maintain the boiler temperature always constant (as is the case of conventional boilers). In addition, if there were no demand for several hours, the burner would work when the temperature dropped to 40  C to compensate for heat losses in the boiler, which prevents sudden starts and stops and reduces losses due to service provision. Among low-temperature boilers, the most interesting are the condensing boilers. The Ecodesign Directive (ErP), transposed into Spanish legislation through Royal Decree 187/2011 [10] and Regulation No. 813/2013 [11], by which the Directive with respect to ecological design requirements applicable to heating appliances and combined heaters was developed, mainly as regards the minimum required seasonal efficiency, mean that the fossil fuel boilers that will be marketed in the coming years will be condensing boilers. So, already at present and in the coming years condensing boilers will be the ones installed. In this type of boiler, part of the water vapor contained in the combustion gases condenses, in order to take advantage of its latent heat and pass it on to the heated water circulating inside the boiler. The question we can ask ourselves is, how can the combustion gases temperature be lowered? The answer can be achieved in two ways: with a large heat exchange surface inside the boiler body and by making the return water temperature as low as possible. Heating oil, with a low sulphur content, conforms to the requirements of the condensation technique, achieving high efficiency and maximum operational safety in the boiler. In any case, natural gas is the fuel par excellence in condensing boilers, being the most commonly used equipment in new heating installations, as well as when modernizing existing facilities, Basic Guide2009 [12]. The dew temperature for diesel oil is about 47  C and about 53  C for natural gas, so to reach these temperatures in the combustion gases requires that the water enters the boiler at a significantly lower temperature. Therefore, the temperature systems 40/30  C offer the maximum energy use, since the working temperatures are always below the dew point. Fig. 5.13 shows a graph that reflects the temperature variation of the outgoing and return water in a radiant floor installation, where it can be seen that the temperatures are lower than the dew point at all times. But even in traditional systems designed to work at high temperature, seasonal efficiency is also considerably increased with the use of condensing boilers. Fig. 5.14 shows the outgoing and return water flow temperature in a heating system

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.13 Outgoing and return flow temperatures in a radiant floor installation.

Figure 5.14 Outgoing and return water flow temperatures in a traditional system in Madrid.

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377

as a function of the outside temperature. As can be seen, for an outdoor temperature above 2  C (83% of hours in Madrid) it is possible to work in condensation with a natural gas boiler and for an outside temperature above 6  C (53% of hours in Madrid) you can work in condensation with a diesel oil boiler. It is interesting to note again that condensing boilers can work at their maximum efficiency even in traditional radiator systems. For this, it is necessary that the temperature to the emitters is not always the maximum, but that it must be modulated throughout the winter and adapted, according to the external conditions, to the demand of each day, VanNorden 2012 [13]. Finally, a few comments on biomass boilers. We must point out that they are beginning to appear in our facilities, with pellets and firewood being the most common fuels for thermal uses in buildings. Wood boilers carry out gasification in a first phase, achieving high efficiencies and relatively low emissions, making them suitable for blocks of houses, schools, etc. Pellet boilers have better efficiency and in all cases are equipped with a backstop that prevents fire at the storage site, IDAE 2012 [14].

5.8.2

Classical energy analysis

In Fig. 5.15 we show the energy flows that cross the limits of the CV representing a boiler. Once the mass balance has been done on the air þ fuel/gas side, the equation m_ a þm_ F ¼ m_ g will be met, which is usually written as m_ a ð1 þ AFÞ ¼ m_ g where AF is the air/fuel ratio. On the water side, the water mass flow rate entering the boiler is the one that also comes out, naturally, when in a steady state. Once these mass balances are done, by applying the First Law, we obtain the following equation

Figure 5.15 Flow of energy in a heating boiler.

m_ F hF þ m_ a ha þ W_ aux ¼ m_ w ðh2
h1 Þ þ m_ g hg þ Q_

(5.31)

where: •

hF is the specific fuel enthalpy, for example, referred to the standard temperature of 25  C, this is

ZTF hF ¼ HHVF þ

cp;F dT 298

(5.32)

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Exergy Analysis and Thermoeconomics of Buildings

hai is the air specific enthalpy, also referred to the standard temperature, so if u is the absolute humidity and T0 the ambient temperature, we have

  hai ¼ cp;ai ðT0
298Þ þ u lð0 CÞ þ cp;v T0
cp;w $298

(5.33)

that is, the sum of the dry air specific enthalpy plus that of water vapor, where l(0 C) is the vaporization enthalpy at 0 C. •

hg is the combustion gases specific enthalpy. Although in modern equipment complete combustion is obtained, in general, we should consider that it is incomplete and that there are, therefore, unburnt fuel elements in the gases. Since h0c;i is the combustion enthalpy of the gases component i and yi its mass fraction, we have

hg ¼ • • •

unb X i

yi h0c;i

þ

Tg X Z j

yj cp;j dT

(5.34)

298

h1,h2 are the water specific enthalpy at the inlet and outlet of the boiler respectively. Q_ is the rate of heat lost through the boiler surface, by convection and radiation. W_ aux is the power of the auxiliaries, such as circulation pumps.

The efficiency of a boiler is defined as the ratio between the energy released to the heated water and the energy supplied, which is the fuel energy, the air combustion energy and the work of the auxiliaries. Generally, this definition does not take into account the sensible enthalpy of the fuel or combustion air as they are practically negligible, nor the work of the auxiliaries. Thus, the instantaneous boiler energy efficiency is h¼

m_ w ðh2
h1 Þ m_ F HHVF

(5.35)

It should be noted that this definition of efficiency requires a prior consensus since it could also refer to the fuel Lower Heating Value, LHVF, in which case its value would obviously be higher. This type of imprecision does not occur when exergy is used. However, as of 26 September 2015, in the EU, the efficiency of boilers must refer to the HHV, so no boiler on the market will have an efficiency greater than 100%, as had been the case with condensing boilers. The above is coherent, since practically all the boilers that we find in the market will be condensing boilers, and therefore, they will already take advantage of the latent heat present in the combustion gases. There are two methods to measure a boiler efficiency. In the so-called direct method, the water flow rate, its temperature at the inlet and outlet of the boiler, as well as the amount of fuel consumed are measured, so that, by applying Eq. (5.35) the efficiency is obtained. It, therefore, requires a water flow meter, two thermocouples in the water line and a fuel meter. In the indirect method, losses are measured. Returning to the energy balance, Eq. (5.31), we approximately have that m_ w ðh2
h1 Þ ¼ m_ F HHVF
m_ g hg
Q_

(5.36)

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and, therefore, the efficiency is h¼1


m_ g hg þ Q_ m_ F HHVF

(5.37)

an expression that is ready for obtaining boiler efficiency by the indirect method or separate losses. Breaking down the combustion gases enthalpy into the sensible part and the chemical part (unburnt) we can distinguish three types of losses, which are referred to the unit of fuel energy, and which are: •

Losses due to the sensitive combustion gases enthalpy

P_ g ¼

m_ g

P R Tg

j 298 yj cp;j dT

m_ F HHVF

(5.38)

The higher the gases temperature (Tg) at the boiler outlet, evidently greater is this term. •

Losses due to unburnt fuel

P_ u ¼

m_ g

P

0 j yj hc;j

m_ F HHVF

(5.39)

These losses occur when the combustion is incomplete and, therefore, unburnt elements appear in the combustion gases (CO, hydrocarbons). With current combustion systems, in heating and DHW boilers these losses are practically zero. •

Losses due to radiation and convection

P_ rc ¼

Q_ m_ F HHVF

(5.40)

This term comes to be of the order of 2%e4% when the boiler operates at full load, varying inversely proportional to the load when operating with partial loads. In short, the boiler efficiency is h¼1


X i

P_ i

(5.41)

To measure the boiler efficiency by the method of separate losses a fuel meter and a gas analyser is needed, which can be used to measure the CO, O2, CO2 concentrations and from these values, the air-fuel ratio can be found. The combustion gases temperature is also measured and, by means of a contact thermometer, the surface temperature of the boiler. Fig. 5.16 shows typical values of losses in a conventional boiler.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.16 Typical values of losses in a conventional boiler.

5.8.3

Instantaneous and seasonal efficiency

The efficiency thus defined is an instantaneous efficiency. However, the European Ecodesign Directive ErP in force since 26 September 2015 and referred to in Chapter 1, establishes a minimum value for the seasonal average efficiency of heating with fuel boilers. This minimum seasonal average efficiency depends on the power level of the boiler, with separate minimum values required for heating and for DHW production, in which case it is defined from an established load profile. The Directive calls for gas boilers (both heating and mixed) with a minimum seasonal efficiency of 86% for powers up to 70 kW and for boilers between 70 and 400 kW, 86%at full load and 94% at 30% of its rated power. These efficiencies are practically impossible to achieve except with condensing boilers, so although the Directive and its Commission Regulations do not require the use of this type of boiler explicitly, the market will drift towards these technologies. It is evident that in a heating installation, much more important than finding the instantaneous efficiency of the generation equipment is to find its seasonal efficiency, that is, the efficiency that the heat generator provides throughout the months of its use and that is a function of the demand curve and the variable operating conditions of the installation. For this reason, the Directive refers to seasonal efficiency, which includes losses during standstill periods, in which the boiler gives off heat to the environment through its envelope until it cools, and also to losses in the gas circuit, due to air circulation, as well as losses when starting due to the pre-purging process. The total of these losses, the sum of the losses through the envelope and by ventilation, are known as losses due to service provision, Rey et al. 2002 [15]. There are, therefore, three periods in the service schedule of a boiler: hours of operation, stoppage and starting. Seasonal efficiency is always lower than that of generation to which we have already referred and decreases as the number of starts and

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stops increases. For this reason, modulating or multi-stage burners are used. So, the most interesting boilers are those with high instantaneous efficiencies throughout the regulation range and with wide ranges of regulation. If we call the rate of boiler losses by radiation and convection during starts and stops P_ rc , the losses due to ventilation in the starts P_ v , the losses due to the pre-purge P_ purg , the operation time during the season top, the stop time tstop and the start time tstrt, it is easy to deduce the relationship between the seasonal efficiency and the instantaneous efficiency of the boiler, worked out as hseason ¼ h


5.8.4

 tstrt   tstop  _ Prc þ P_ v
P_ rc þ P_ purg top top

(5.42)

Exergy analysis

Considering the scheme of Fig. 5.15 again, from the exergy balance, we get the equation m_ F bF þ W_ aux ¼ m_ w ðb2
b1 Þ þ m_ g bg þ B_ Q þ D_

(5.43)

where: • • • •

bF is the fuel (chemical) exergy. b1,b2 is the water exergy at the entrance and exit of the boiler. bg is the (physical þ chemical) exergy of the combustion gases. B_ Q is the exergy of the lost heat, whose value depends on the boiler surface temperature.

If we assume that there is no recovery of the combustion gases exergy, so that this finally is destroyed and we do not take into account the auxiliaries power, the equation for the exergy balance can be written in the following simplified form m_ F bF ¼ m_ w ðb2
b1 Þ þ I_

(5.44)

where I_ is the rate of total exergy destruction, which includes destruction plus losses, these being the flow exergy of the combustion gases leaving the chimney and the exergy of the heat released by the boiler surface. The exergy efficiency, unlike the energy efficiency defined according to Eq. (5.35), reflects the sum of the internal irreversibilities that originate in air and fuel diffusion to form the mixture, in the combustion chemical reactions and in the heat transfer between the combustion gases and water, with external ones associated with combustion gases and heat lost. We define the boiler exergy efficiency according to the expression 4¼

I_ m_ w ðb2
b1 Þ ¼1
m_ F bF m_ F bF

(5.45)

Therefore, the lower the irreversibilities (both internal and external), the higher the value of the efficiency and the closer it will be to unity. This coefficient actually

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Exergy Analysis and Thermoeconomics of Buildings

expresses the boiler degree of thermodynamic perfection, so that if it were perfect, the coefficient would take a unit value. Between this efficiency and that defined according to expression (5.35), there is the following relation
 4 HHV b2
b1 LHV s2
s1 ¼ ¼ 1
T0 h bF h2
h1 bF h2
h1

(5.46)

This relationship can be represented graphically as a function of the water temperature, for a certain boiler that burns a certain fuel. The typical result obtained is that the exergy efficiency is approximately half of the conventional efficiency, which is usually between 0.90 and 0.95 in modern condensing boilers. Fig. 5.17 shows the energy and exergy efficiency curves of a condensing boiler and a conventional hot water boiler. The reason for the great difference observed between both efficiencies is that the exergy efficiency takes into account the significant irreversibilities that take place, which are not considered by the classic energy efficiency. As we have said before, these irreversibilities are basically of two types: chemical, associated with the diffusion and with the combustion reactions, and thermal, due to the temperature differences in the heat exchanges. It is striking that the exergy efficiency of the condensing boiler is lower than that of the conventional boiler. However, this result should not surprise us, since the condensing boiler heats water flow that is at a significantly lower temperature, so although for the same energy supplied it consumes less fuel, the exergy associated with that energy of the water is low. Actually, in order to interpret the significance of condensing boilers with exergy analysis the heating installation as a whole must be considered. In the same way that we defined the seasonal efficiency of a boiler and obtained Eq. (5.42) that relates it to the instantaneous efficiency, we will define a seasonal exergy efficiency. The relationship that links it with the instantaneous exergy efficiency is totally analogous to Eq. (5.42), only that now the losses by ventilation, convection and radiation and by the pre-purge will have to be evaluated as exergy.

Figure 5.17 Energy and exergy efficiency curve of a conventional and a condensing boiler.

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383

In the development of boiler technology, the technical efforts that have been made have led to a significant decrease in irreversibilities and, ultimately, an increase in exergy efficiency. Thus, as we have seen in Section 2.17, the irreversibilities in combustion are reduced by increasing the combustion temperature, and this is achieved by decreasing the heat losses, using the minimum of excess air and preheating it. On the other hand, in order to reduce irreversibilities, the combustion gases temperature must be recovered as much as possible, and this implies lowering the feed water temperature and ultimately arriving at the condensing boiler. In this sense, the significance of the exergy method should not be overestimated, because as we have just said, conventional energy analysis leads to similar conclusions. However, the advantage of the exergy method is that it helps to better understand the situation, by quantifying in each element the irreversibilities that occur in it and, therefore, deciding where to act to achieve improvement in the design and operation of a boiler.

5.8.5

Examples

Example E.5.11.

We are going to compare two heating installations with natural gas boilers, one with a conventional boiler with an efficiency of h ¼ 0.84 and the other with a condensing boiler with h ¼ 0.93 and both with a thermal power of 24 kW. The temperatures of the outgoing and return flow in the conventional boiler are 75 C and 65 C respectively, whereas in the condensing boiler those temperatures are 40 C and 32 C. Both boilers will supply heating to a dwelling in which an indoor temperature of 20 C is maintained, over an ambient temperature of 0 C. The end elements of the conventional boiler are aluminum radiators, while the condensing boiler is connected to a radiant floor. Determine (a) The water flow rate that circulates through the installation and the fuel consumption in both boilers. (b) The exergy efficiency of both boilers. (c) The losses and exergy destructions in the heating installation with the condensing boiler and the overall efficiency of the installation. (d) The same in the installation with the conventional boiler.

Solution (a) Calculating the water flow rate and fuel consumption for the condensing boiler. With P ¼ 24 kW and assuming that for natural gas HHV NG ¼ 50 kJ/g, we have

P ¼ m_ w;cond cw ðT2
T1 Þ/m_ w;cond ¼ 0:72 hCOND ¼

kg s

P g /F ¼ 25:8 kW/ m_ NG; cond ¼ 0:52 F s

For the conventional boiler, we get P ¼ m_ w; conv cw ðT2
T1 Þ/m_ w;conv ¼ 0:57

kg s

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Exergy Analysis and Thermoeconomics of Buildings

P g hCONV ¼ /F ¼ 28:6 kW/ m_ NG; conv ¼ 0:57 F s (b) Assuming that approximately Bch NG ¼ 1:04 LHV condensing boiler exergy efficiency is

NG

and that LHV NG ¼ 0.9 HHVNG, the


 T2 m_ w;cond cw T2
T1
T0 ln T1 4COND ¼ ¼ 11:6 % ch _ BNG; cond

while the conventional boiler exergy efficiency is
 T2 m_ w; conv cw T2
T1
T0 ln T1 4CONV ¼ ¼ 18:1 % ch B_ NG; conv We see that the conventional boiler exergy efficiency is superior to that of the condensing boiler, which at first may seem contradictory. However, the fact that the conventional boiler works with higher water temperatures must be taken into account. (c) In both installations, the final heating destination is to maintain the dwelling temperature at 20 C. We assume that there are no losses in the distribution circuit or the end elements. Therefore, the exergy transferred to the indoor air is


 T0 1
P ¼ 1:64 kW Ti In the condensing boiler installation, the fuel consumed exergy is 1.04$0.9$ 50$0.52 ¼ 24.34 kW. The final exergy transferred to the indoor air is 1.64 kW, so the difference is the irreversibilities, that is, D_ ¼ 22:70 kW. Of this total exergy destruction, in the boiler the rate of destruction is (1e0.116)24.34 ¼ 21.52 kW, which represents 88.4%. The rest of the exergy is destroyed in the other installation components and in the indoor air, which is 24.34e21.52e1.64 ¼ 1.18 kW, which represents 4.8%. The overall installation exergy efficiency is
 T0 1
P Ti 4TCOND ¼ ch ¼ 6:7 % B_ NG; cond (d) In the conventional boiler installation, the fuel exergy is 1.04$0.9$50$0.57 ¼ 26.68 kW, so the rate of total exergy destruction is D_ ¼ 25:04 kW. In the boiler, (1e0.181) 26.68 ¼ 21.85 kW are destroyed, which represents 81.9%. In the other installation components 3.19 kW are destroyed, which is 11.9%.

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The overall installation exergy efficiency is
 T0 1
P Ti 4TCONV ¼ ¼ 6:1% ch B_ NG;conv We see that the overall efficiency in the installation with the condensing boiler is superior to that of the conventional boiler. In this installation, the exergy destruction is displaced to the end elements and the indoor air, since the temperature difference in the heat transfer in those end elements is greater. Example E.5.12.

There is a low-temperature wall-mounted boiler for heating that uses natural gas as fuel. At a given moment, when the ambient temperature is T0 ¼ 273 K, the boiler has an efficiency of 89% and is generating a water flow for heating with a temperature of 52 C and a return temperature of 40 C. Fuel consumption is 16.9 kW (referring to the HHV) with the composition being the following molar percentage: 91% CH4, and the rest C2H6. Knowing that the heat lost by the boiler is 1% of the fuel energy, what is (a) The composition of the gases, knowing that the combustion is carried out with an excess air of 5%. (b) The combustion gases temperature and the mass flow rate of hot water generated. (c) The exergy of the heating water generated. (d) Exergy efficiency and rate of exergy losses and destructions in the boiler.

Solution (a) The combustion reactions that take place are

CH4 þ 2O2 /CO2 þ 2H2 O 7 C2 H6 þ O2 /2CO2 þ 3H2 O 2 Per mole of fuel, the composition of the reactants and that of the products are shown respectively in Table E.5.1 and Table E.5.2 below.

Table E.5.1 Composition of the reactants (moles per mol of fuel). Reac

ni

CH4

0.91

C2H6

0.09

O2

2.24

N2

8.43

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Exergy Analysis and Thermoeconomics of Buildings

Table E.5.2 Composition of the products (moles per mol of fuel). Prod

ni

CO2

1.09

H2O

2.09

O2

0.11

N2

8.43

(b) The boiler energy efficiency is

h¼

m_ w ðh2
h1 Þ ¼ 0:89 m_ F HHVF

Calculating the fuel mass flow rate (in mole/s). With HHVCH4 ¼ 888:5 kJ=mol and HHVC2 H6 ¼ 1557 kJ=mol, we have. mol N_ F ð0:91$888:5 þ 0:09$1557Þ ¼ 16:9/N_ F ¼ 0:018 s Expressing the boiler efficiency as a function of separate losses, gives h ¼ 0:89 ¼ 1


H_ g þ 0:01 F /H_ g ¼ 0:1F ¼ 1:69 kW F

N_ F ½1:09hCO2 ðTg Þ þ 2:09hH2 OðTg Þ þ 0:11hO2 ðTg Þ þ 8:43hN2 ðTg Þ ¼ 1:69 Using the ideal gas tables, we can see that the combustion gases temperature coming out of the boiler is approximately Tg ¼ 332 K. Returning to the expression for efficiency, we get that the mass flow rate of hot water generated is m_ w ¼ h

kg m_ F HHVF ¼ 0:3 s h2
h1

(c) The exergy delivered to the heating water in the boiler is


 Tout B_ out
B_ in ¼ m_ w cw Tout
Tin
T0 ln ¼ 2:17 kW Tin (d) We calculate first the fuel chemical exergy. From Szargut data, we have that bch;0 CH4 ¼ 831:65 kJ=mol and that bch;0 ¼ 1495:84 kJ=mol. Therefore, considering the fuel is an C2 H6 ideal gas mixture, its chemical exergy is bch;0 F ¼ 0:91$831:65 þ 0:09$1; 495:84 þ 8. 314 $ 0.298 $ (0.91ln0.91þ0.09ln0.09) ¼ 890.67 kJ/mol. The exergy efficiency of the boiler is

4¼

B_ out
B_ in ¼ 13:5 % N_ F bch F

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This means that the irreversibilities in the boiler, the sum of the internal exergy destructions and the losses, heat and gases (external irreversibilities) are 13.9 kW, which represents 86.5% of the exergy provided by the fuel. Example E.5.13.

A dwelling has a floor heating system with condensing boiler, whose

energy efficiency is 91%. The water heating flow is 0.7 L/s, with the boiler outlet temperature at 41 C and the return temperature at 34 C. The fuel used is natural gas, which we will assume to be methane, combustion is carried out with 6% of excess air and the gases leave the boiler at a temperature of 52 C. Through the boiler surface there are some heat losses that represent 1% of the fuel consumption, with the average boiler surface temperature of 24 C. Knowing that the atmospheric air is at 5 C, with a relative humidity of 52% and that the pressure is 980 mbar, determine (a) The combustion gases composition at the outlet of the boiler combustion chamber. (b) The heat given to the heating water by the condensation of water vapor from the combustion gases, assuming that these leave the boiler saturated. (c) The boiler exergy efficiency. (d) The exergy losses due to combustion gases, condensate and heat lost. (e) The rate of exergy destruction in the boiler.

Solution (a) Calculating the water vapor generated in the combustion. For this, we first determine the amount of fuel consumed from the boiler efficiency

h¼

g m_ w ðh2
h1 Þ /m_ NG ¼ 0:4 m_ NG HHVNG s

The complete combustion reaction is CH4 þ 2O2 /CO2 þ 2H2 O The combustion gases composition in molar fractions, taking into account the water vapor that accompanies the combustion air, is shown in Table E.5.3. For each mole of fuel 2$1.06 mol of O2 are used, that is, 2$1.06$28.8/ 0.21 ¼ 290.7 g of air, so that for that calculated fuel flow, 290.7$0.4/16 ¼ 7.27 g/s of atmospheric air are needed. The relative humidity of this air is 52%, and the absolute humidity is obtained by application of Equation (3.39) in Chapter 3 and knowing that ps(5 C) ¼ 8.72 mbar. u ¼ 0:622 p f

ps ð5 CÞ
ps

ð5 CÞ

¼ 2:89

g kg d a

As the mass airflow rate is 7.27 g/s, the mass flow rate of dry air is m_ a ð1 þ uÞ ¼ 7:27 /m_ a ¼ 7:25

g s

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Exergy Analysis and Thermoeconomics of Buildings

with the mass flow rate of water vapor being m_ a u ¼ 0:02

g s

The water vapor that appears in the gases coming from the combustion air is 0.02 g/ s, to which we must add the water vapour generated in the combustion which is 2$0.4/ 16.18 ¼ 0.90 g/s, which means a total of 0.92 g/s. The composition of the fumes, in molar fractions, taking into account the water vapour from the air, is shown in Table E.5.3. Table E.5.3 Composition of the combustion gases at the combustion chamber oulet. Prod

mol/s

xi(%)

CO2

1$0.4/16

9.0

H2O

0.02/18 þ 2$0.4/16

18.3

O2

0.12$0.4/16

1.1

N2

7.98$0.4/16

72.6

Total

0.279

100

(b) With ps(52 C) ¼ 12.352 kPa the vapor content of the saturated combustion gases at that temperature is

ps ð52 CÞ ¼ xv p /xv ¼ 12:6$10
3 From this molar fraction we calculate the new composition of the gases, once the vapor has condensed. As the new molar fraction of vapor obtained is nv ¼ 12:6 :10
3 /nv ¼ 0:12 nv þ 9:1 we can calculate the new composition of the combustion gases, at the outlet of the boiler, see Table E.5.4.

Table E.5.4 Composition of the gases after condensing. Prod

ni

xi(%)

CO2

1

10.85

H2O

0.12

1.26

O2

0.12

1.30

N2

7.98

86.59

Total

9.22

100

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389

The mass fraction of vapor in the combustion gases leaving the boiler is obtained through the relationship yv ¼ xv

Mv ¼ 0:76$10
2 Mg

since the apparent molar mass of the combustion gases is Mg ¼

X xi Mi ¼ ð10:85$44 þ 1:26 $18 þ 1:30$32 þ 86:59$28Þ10
2 i

¼ 29:66

g mol

Therefore, since the ratio of the mass flow rates after the condensation and at the entrance of the combustion chamber is 0.884, the vapor mass flow rate in the combustion gases is m_ v ¼ 0:76$10
2 :7:27$ 0:884 ¼ 5:51$10
2 g=s. Adding the water vapor of atmospheric air m_ a u ¼ 0:02g=s with the vapor produced in the combustion 0.4. 36/16 ¼ 0.9 g/s, gives in total 0.92 g/s. Therefore, the amount of vapor that condenses is 0.92e4.88$10
2 ¼ 0.87 g/s. Although the condensation is carried out at a variable temperature, we assume an average temperature from the beginning of the condensation until it ends at 60 C, with the heat given off by the vapor condensation Q_ ¼ m_ COND ðh00
h0 Þ60 C ¼ 2:0 kW (c) As the methane chemical exergy is bch CH4 ¼ 831:65 kJ=mol the boiler exergy efficiency is


 T2 m_ w cw T2
T1
T0 ln T1 4¼ ¼ 10:3 % ch B_ NG

(d) First of all, we calculate the combustion gases physical exergy, using the ideal gas specific heat tables and assuming for the specific calorific values of the ideal gases a mean temperature of 30 C. The value obtained is

m_ NG B_ g ¼ MNG

g X i


 Tg ni cp;i Tg
T0
T0 ln ¼ 25 W T0

Using the Szargut tables the chemical exergy of the combustion gases is obtained, giving m_ NG ch B_ g ¼ MNG

 X  ni bch i þ RT0 lnxi ¼ 416 W i

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Exergy Analysis and Thermoeconomics of Buildings

so that exergy losses due to combustion gases are ch B_ g þ B_ g ¼ 441 W

On the other hand, assuming that the condensates leave the boiler at 52 C, their exergy is B_ COND ¼ m_ COND bw ð52 CÞ ¼ 13 W The rate of heat lost through the boiler surface is Q_ ¼ 0:01$0:4$55; 530 ¼ 222 W and since the temperature is Tbs ¼ 297 K, the exergy of that lost heat is
 T0 _ Q ¼ 14 W 1
Tbs (e) Since the boiler exergy efficiency is 10.3%, it means that the sum of the losses plus the exergy destruction represent 89.7% of the exergy contributed by the fuel, which is 20.79 kW. Therefore I_ ¼ 18; 694 W, with the rate of exergy destruction being

I_ ¼ D_ þ

X i

5.9 5.9.1

L_ i /D_ ¼ 18; 226 W

Heat pumps Types and characteristics

Heat pumps are systems that use a fluid in a thermodynamic cycle, transfer heat from a natural environment, such as atmospheric air, water (from a river or a well) or the soil to another medium at a higher temperature, for example, the indoor air of a building or the water in a DHW tank, etc. requiring a contribution of external energy for their operation. From a thermodynamic point of view, the difference between a heat pump and a refrigerating machine is in the thermal level of the two heat sources with which they work. In a refrigerator, the source from which heat is extracted (useful effect) is at a temperature below the ambient temperature, while the hot source is the ambient temperature. For its part, in a heat pump, the cold source is the environment and the source to which heat is transferred (useful effect) is at a temperature above the ambient temperature. There are a multitude of types of heat pumps and refrigeration machines, depending on whether they are based on chemical phenomena (discontinuous and of little interest) or physical phenomena. These in turn, can be based on a change of state (fusion, sublimation, vapourization), an expansion (air machines, Joule-Thomson effect) and specific effects (Peltier, Ettingshausen, etc.). The systems based on vapourization,

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391

Figure 5.18 Heat pump driven by internal combustion gas engine.

which are of greatest interest, are classified according to how the vapours formed are treated, into absorption machines, mechanical compression machines and vapour ejection machines. By far, the most important type of heat pumps are those using mechanical vapour compression. According to the type of action, there are electric heat pumps in which the compressor is driven by an electric motor and, gas heat pumps in which the action is by means of an internal combustion engine that uses the energy of a fuel, usually, natural gas or sometimes propane, see the operating scheme in Fig. 5.18. Likewise, the useful effect of the heat pump may be the heat production exclusively, but there are also the so-called reversible heat pumps, which can produce cold or heat depending on the time of year, for which an element is used that allows the inversion of the cycle, Kinab et al. 2010 [16]. Manufacturers classify their equipment according to sources among which are those that work in the following groups: •

•

•

When the external source is the ambient air, the group is known as aerothermal heat pumps. If in addition, the interior source is air, then they are air-to-air heat pumps, for example, stand-alone equipment in a business or a domestic conditioner. If the interior source is water, they are air-to-water heat pumps, for example, a chiller or an air-to-water heat pump with underfloor heating. When the external source is continental or marine waters, then the group is known as hydrothermal heat pumps. If the interior source is air, they are water-to-air heat pumps. Inside a building the air is heated (or cooled), extracting (or returning) the heat from (to) a water flow. If the external and interior source is water, then it is a water-to-water heat pump. When the external source is the soil, the heat pumps are called geothermal heat pumps.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.19 Vertical and horizontal layout of pipes buried in the ground.

Geothermal heat pumps have an external water circuit, which exchanges heat with the soil, either in an open loop, in which the water is taken from an aquifer at one point and returned to another located at some distance, or else in a water circuit (sometimes with antifreeze) in a closed loop. In other cases, they make the exchange directly between the refrigerant circuit and the soil (direct expansion). The underground heat exchangers are built by burying polyethylene pipes. Fig. 5.19 shows the two usual arrangements of the pipes, either horizontally at a shallow depth, or in a series of vertical wells, usually 50e100 m in length. The soil is a stable thermal source that regenerates naturally. It has the advantage that, at a few meters deep, its temperature is much more uniform than that of the ambient air. The geothermal heat pump uses the soil to work in more favourable temperature conditions than with the air, but for this, the system needs to be designed correctly, in order for the soil to absorb or yield heat properly. Thus, in a city like Vitoria/Gasteiz, the average temperature of the soil is 14 C, so to heat a building to 21 C, the heat pump has to overcome that difference of 7 C. The air temperature is much more variable than that of the ground, and it reaches values below zero for numerous hours of the winter, so that the temperatures difference to overcome for an aerothermal heat pump is noticeably greater and, therefore, its COP will be less. An important technological challenge for geothermal heat pumps is to limit the phenomenon of thermal damage to the soil, that is, the heat pump exchanging energy with the soil modifies its temperature in a limited and controlled manner, in order to not affect system efficiency. This implies a careful design of the installation, which will have to take into account the energy flows and the thermal characteristics of the ground. Having undertaken this brief presentation of the numerous types of systems we are going to initially perform a global energy analysis of heat pumps. We will consider instantaneous values first, and then we will look at seasonal values. This same approach will continue in the exergy analysis where we will finally look at their main components.

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5.9.2

393

Global energy balance

Let there be a reverse cycle heat pump, where Tc and Th are the cold and hot sources temperatures respectively, see diagram in Fig. 5.20. Since Qh and Qc are the heats exchanged with the hot and cold sources respectively and W the work consumed by the heat pump, we have the equation Qc þ W ¼ Qh

(5.47)

In the heat pump, Tc ¼ T0, with the useful effect being the heat given to the hot source. The coefficient of performance, COP, is defined as the ratio between the heat given to the hot source and the work input. If we use instantaneous values, we define the instantaneous COP, which is COP ¼

Q_ h Q_ ¼1þ c >1 W_ W_

(5.48)

If it is an electrically driven heat pump, see the diagram of Fig. 5.21, this instantaneous COP is expressed referring to the electrical power consumed by the heat pump, and we have COP ¼

Q_ h E_

(5.49)

In the case of a reversible heat pump, operating in the cooling mode, the instantaneous efficiency is expressed by the energy efficiency ratio, EER, which is the quotient between the cooling power and the absorbed electrical power, which is EER ¼

Q_ c E_

Figure 5.20 Conceptual diagram of a heat pump.

(5.50)

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.21 Electrically driven heat pump.

The conditions to which the manufacturers certify the COP and EER of their product are when the equipment is at full load, that is, when the machine is giving 100% of the thermal power that it is capable of supplying. But the reality is that most of the time the heat pump does not work at full load, since it has been sized to give heating when the outside temperature is, for example, 0 C, and will also provide heating when this temperature is 10 C; or if the heat pump desired output is its cooling effect and has been sized for an external temperature of 40 C, it will also work when this temperature is 30 C. Since the COP and EER values are certified with the equipment at full load, many manufacturers prepare their equipment so that they will give good results when they work at 100%, sometimes even at the cost of worse results at partial loads. Therefore, when looking at the efficiency of a unit, both the COP and the EER cannot be considered to be entirely reliable, so they are no longer used. In the case of a gas-driven heat pump, in addition to the heat transferred by the condenser, part of the useful heat is also provided by the motor cooling Q_ m , see the diagram of Fig. 5.22. In that case, the instantaneous COP of the device, which is also called Gas Utilization Efficiency (GUE), is GUE ¼

Q_ h þ Q_ m F_ þ E_ aux

(5.51)

where E_ aux is the consumption of electricity associated with the auxiliaries, such as the pumps/fans needed to transport the heat transferred by the heat pump and F_ is the rate of gas consumption, Quiles and Ginés 2015 [17].

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Figure 5.22 Gas-driven heat pump.

5.9.3

Seasonal average efficiency

To assess the efficiency of a heat pump and evaluate the amount of renewable energy supplied by these technologies, it is necessary to previously know the seasonal performance factor (SPF). The SPF is specifically referred to as the net active seasonal average efficiency (SCOPnet) for electrically driven heat pumps, or the net seasonal primary power-active ratio (SPERnet) for heat-driven heat pumps. For heat pumps in which the desired output is the cooling effect, the seasonal energy efficiency factor (SEER) is defined. To calculate the SCOPnet, follow the UNE-EN 14825:2012 standard [18] and for the SPERnet the UNE-EN 12309:2015 standard should be followed [19]. In the case of a reversible heat pump, operating in cooling mode, the SEER is obtained in accordance with the UNE-EN 14825:2014 standard [20]. These new ratios are more realistic and adequate to describe the energy behaviour of a heat pump in a facility. Without going into the detail of how they are calculated, which is developed in the standards mentioned above, we will say that they take into account the equipment consumption when it is switched off, as well as operating at partial loads (100%, 74%, 47%, 21%), two important aspects that are not considered with the EER and COP coefficients. Therefore, these new parameters are much more reliable than previous ones when it comes to comparing equipment. If only the nominal COP is known, the SCOP can be calculated from this nominal value by using a weighting factor WF, which varies according to the climate zone and another correction factor CF, which depends on the temperature of use or distribution, IDAE 2014 [21]. Once the SPF is known, Directive 2009/28 in Annex VII [22] establishes the amount of aerothermal, geothermal or hydrothermal energy that should be considered

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Exergy Analysis and Thermoeconomics of Buildings

as coming from renewable energies. According to the aforementioned Annex and Decision 2013/114 [23] that developed it, with Qusable being the useful heat provided by the heat pump and calling h the electrical system efficiency, which, in 2010, was set for the EU at a mean value of 45.5%, we have that the primary energy consumed by the heat pump is Qusable SPF$h

(5.52)

For there to be primary energy saving, then Qusable Qusable < SPF$h hc

(5.53)

where hc is the average efficiency of a conventional heating system. If a unit value is assigned to hc, that is to say, all primary energy is used for heating, for there to be primary energy saving as a minimum, then SPF>1/h. Annex VII of Directive 2009/28 states that the only heat pumps that shall be taken into account are those that meet the requirement SPF > 1:15

1 h

(5.54)

For this value of h ¼ 45.5% we get that an electrically driven heat pump must have SPF > 2.5 to be considered as a heating system that uses renewable energy, that is, the minimum SPF must be 2.5. In the case of a gas-driven heat pump, the efficiency h is considered to be unity and, therefore, SPF > 1.15, that is, the minimum SPF must be 1.15. Once a heat pump has been verified as having SPF > 2.5 (SPF > 1.15 if it is gas-driven), the amount of renewable energy supplied by the heat pump is calculated by subtracting from Qusable the non-renewable consumption in the heat pump, finally giving the expression 
1 ERES ¼ Qusable 1
(5.55) SPF As we can see, in the definition of COP, GUE or EER as well as in the seasonal coefficients SCOP, SEER or SPER, the idea of the different qualities of energy is not taken into account. One way to reduce this limitation to some extent is to refer all the energies to primary energy, for which, as we have seen, one of the coefficients modifying the primary energy into the final energy needs to be applied. Now, this conversion coefficient depends on the energy mix of each country, existing as a Recognized Document 2016 in Spain [24]. Thus, referring to primary energy, for an electric heat pump, where WFE is that conversion coefficient for electricity, we can define a COPPE such that COPPE ¼

Q_ h WFE E_

(5.56)

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and for a gas-driven heat pump, where WFF is the gas conversion coefficient COPPE ¼

Q_ h þ Q_ m WFF F_ þ WFE E_

(5.57)

If the gas-driven heat pump is reversible and used in cooling mode, at the same time that the engine cooling heat Q_ m is used for DHW production, the EER of the electrical heat pump system is EER ¼

Q_ c þ Q_ m F_ þ E_

(5.58)

and referred to primary energy EERPE ¼

Q_ c þ Q_ m WFF F_ þ WFE E_

(5.59)

These definitions of efficiency based on primary energy have the advantage that they allow a direct comparison of some systems to others. However, they do not reflect the true thermodynamic quality of the equipment, since they only use the First Law and, therefore, compare energies of different qualities. They are based on a distinction between fossil and renewable energies, in such a way that renewables are not included in the final evaluation, so the efficiency in the use of these energies is not taken into account. In addition, the conversion factors to primary energy vary from country to country and in the same country according to the year and season.

5.9.4

Global exergy balance

Referring again to the diagram of Fig. 5.20 and since if the cold source temperature is T0 the exergy of the heat exchanged is zero, the exergy balance gives
 T0 _ Q þ I_ W_ ¼ 1
(5.60) Th h The rate of irreversibility I_ is the sum of the internal destructions (those that occur in the cycle) and the external destructions (those due to the heat exchanges between the fluid that carries out the thermodynamic cycle and the heat sources). This balance equation tells us that, of the work contributed to the heat pump, one part is the exergy given to the hot source, and the rest is destroyed exergy, as a consequence of the irreversibilities. As we have said before, the heat exchanged with the environment has no associated exergy, We will define the instantaneous exergy efficiency 4 according to the following expression
4¼

 T0 _ Q 1
Th h W_

(5.61)

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and according to the COP definition, we have
4¼

 T0 1
COP Th

(5.62)

Since the maximum COP corresponds to the ideal heat pump, operated according to a Carnot cycle between sources T0 and Th, it is COPmax ¼

Th Th
T0

(5.63)

this means 4¼

I_ COP ¼1
max COP W_

(5.64)

The maximum exergy efficiency is effectively that of the reversible engine, the Carnot heat pump, for which 4 ¼ 1. In a Carnot heat pump, there is no exergy destruction, so that all the exergy provided W_ is given to the hot source. Since the exergy efficiency expresses the quotient between the heat pump COP and the maximum COP, we can also write 4¼

Q_ h max Q_

(5.65)

h

so that the exergy efficiency reflects the relation between the heat given to the hot source and the heat that would be given by the Carnot heat pump that consumed the same work. It can also be interpreted as the relationship between the work that would be consumed by the Carnot heat pump that would give to the hot source the same heat Q_ h and which is really used by the heat pump under consideration. If we refer to the electricity consumption, as in Fig. 5.21, the exergy efficiency is
1
4¼

 T0 _ P Qh I_i Th ¼1
i E_ E_

(5.66)

where now the sum of the irreversibilities will include those of the electric motor, in its conversion of electrical energy into mechanical energy. If we compare the heat pump with other heating alternatives, for example, when the heating is done by the combustion of some fuel, we see that, in this case, all the necessary energy is obtained from the fuel, whose exergy content is very high. There is, thus, significant degradation of energy as a result of the irreversibilities inherent in the combustion process. Something similar can be said about heating by electrical energy, which is of higher quality energy.

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Heating does not require high-quality energy, so when using electricity and fossil fuels, there is significant exergy destruction. Instead of using environmental energy, which is free and whose reserves are practically unlimited, exergy which is valuable and scarce is being used. It is clear that, from an exclusively thermodynamic point of view, the heat pump is the solution, since the energy needed in the heating process is taken in a large part (around 75%) directly from the environment. In a manner similar to what has been said above for energy, more than instantaneous values, it is important to know the seasonal exergy efficiency factor SPxF, which can be interchangeably used whether applied to electrically or thermally- driven heat pumps. This coefficient will be defined as the quotient between the exergy of the useful heat supplied, and the exergy contributed to the machine for its operation, where the compressor consumption must also include that of the circulation system for the heat distribution. If the heat pump is thermally-driven, the fuel exergy used to drive the compressor and the pump/fan will appear in the denominator. For an electrically driven heat pump for heating, by performing an exergy balance across the season, we have Ep=f


 T0 þ Ec ¼ 1
Qusable þ I Tu

(5.67)

where Ep/f refers to the electricity consumed by the pump/fan of the circulation system, Ec is the electricity for the compressor operation, Tu is the temperature of the useful heat generated and I equates to the irreversibilities of the machine, which includes destruction by irreversibilities and the exergy associated with the small heat lost. Therefore, the seasonal exergy efficiency factor SPxF is
 T0 1
Qusable Th SPxF ¼ Ep=f þ Ec

(5.68)

Similar comments can be made when the desired output of the heat pump is its cooling effect. In this case, the useful effect is the exergy given to the cold source, so that, for example, for a gas-driven heat pump, with BF being the fuel exergy consumed in the season and Ep/f the electricity consumption by pumps and fans, the seasonal exergy efficiency will be
 T0
1
Qc Tc SPxF ¼ BF þ Ep=f

5.9.5

Exergy analysis of a vapor-compression cycle

We will apply exergy analysis to each of the four processes of the simple cycle of a vapor-compression heat pump, see Fig. 5.23, in which the basic cycle is represented

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.23 Real cycle of a vapour compression heat pump.

by a T-s diagram. In the evaporator, the absorption of heat takes place from a cold source, the environment. The process is carried out with a temperature difference between the refrigerant fluid and the source, and there are also head losses so that the pressure of state 1 at the outlet of the evaporator is lower than that of state 4 at the inlet. The compression process is adiabatic, but due to the compressor irreversibilities, exergy destruction takes place, so that the entropy at the output of the compressor, state 2, is greater than at the input. Subsequently, there is heat transfer to the hot temperature source Th. This heat transfer is carried out with a temperature difference between the fluid and the hot source, while there are also head losses in the condenser. Finally, an isenthalpic throttling in the expansion valve takes place, a markedly irreversible process, so that the fluid enters the valve in state 3 and exits in state 4. In the analysis that we present below, we will look at the cycle internal irreversibilities. When performing an exergy balance in the evaporator, per unit of refrigerant mass, since the heat is transferred by the environment, its exergy is zero, we have b4
b1 ¼ dev

(5.69)

where dev is the exergy destruction in the evaporator. We can verify that the GouyStodola equation is fulfilled so that with qev being the heat given per unit mass of refrigerant, we have
 qev dev ¼ T0 s1
s4
T0

(5.70)

Due to the irreversibilities in the compressor, the compression is not isentropic. If it were, the state at the output would have the entropy of state 1 and the pressure of 2,

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which we could call state 2s. The specific compression work would be wsc ¼ h2s
h1. However, the compression is performed with a certain isentropic efficiency hs, so that the specific work consumed is wc ¼

h2s
h1 ¼ h2
h1 hs

(5.71)

We can verify that the excess work, wc
wsc does not coincide with the exergy destruction, since wc
w2s ¼ b2
b2s þ dc

(5.72)

This excess exergy between state 2 and 2s is going to be used since the useful effect is precisely the heat given in the condenser. Therefore, isentropic efficiency is not an adequate coefficient to describe the compressor behaviour in the cycle. The situation is different in the case of the refrigerators, since the exergy increase of the refrigerant at the compressor outlet with respect to the ideal compression, b2
b2s, will not be used, given that the next element is the condenser, where heat is released into the atmosphere, and this exergy will degrade. In short, here it would make sense to use the isentropic efficiency, in the same way as the exergy efficiency, to characterize the quality degree of the compression process. In the condenser, the heat given is the useful effect, so that from the exergy decrease of the refrigerant between the input and the output of the condenser one part is the useful effect and the rest is the exergy destroyed by the irreversibilities, which is
 T0 b2
b 3 ¼ 1
(5.73) qu þ dcd Th Finally, in the expansion valve, a throttling isenthalpic process takes place, characterized by being markedly irreversible. The exergy destruction in the valve is b3
b4 ¼ dv ¼ T0 ðs4
s3 Þ

(5.74)

The total exergy destruction is obtained by adding the values from each one of the elementary processes of the heat pump. Therefore, the cycle exergy efficiency is


 T0 P qu di Tu ¼1
i wc wc

1
4¼

(5.75)

If we consider the installation as a whole, it would be necessary to include heat exchanges in the evaporator and condenser, auxiliaries and other sources of exergy destruction, such as mechanical friction in the different components. In short, the total exergy efficiency expresses the relationship between the exergy delivered to the hot source and the total exergy (for example, in the form of electrical energy) contributed to the heat pump.

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Exergy Analysis and Thermoeconomics of Buildings

5.9.6

Examples

Example E.5.14.

Consider an air-to-water heat pump with a scroll-type hermetic compressor and a helical fan. When the ambient air temperature is 0 C, the power consumed by the compressor is 4.2 kW and the total electric power consumed by adding the fan and circulation pump is 4.7 kW. The thermal power is 18 kW in the form of hot water that enters the heat pump condenser at 35 C and leaves at 40 C. The working fluid condenses at a temperature of 45 C and evaporates at
5 C. If the ambient air temperature at the evaporator outlet is
2 C, determine (a) (b) (c) (d)

The rate of heat trabnsfer in the evaporator and the instantaneous COP. The rate of internal exergy destruction in the cycle. The rate of exergy destruction in the heat exchange in the condenser and in the evaporator. The overall exergy efficiency.

Solution (a) According to the definition of instantaneous COP, we have

COP ¼

Q_ h ¼ 4:28 W_

By applying the energy balance in the heat pump, we have Q_ c þ W_ ¼ Q_ h /Q_ c ¼ 13:8 kW (b) From the exergy balance in the heat pump thermodynamic cycle we get


 T0 _ _ Qc þ D_ in /D_ in ¼ 1:65 kW W¼ 1
Tc (c) The above rate of exergy destruction is internal in the cycle. But, in addition, exergy destruction occurs in the evaporator and condenser, due to the temperature differences in the heat exchanges. In the first place, we will look at the condenser and calculate the water mass flow rate that is heated

kg Q_ h ¼ m_ w cw ðTout
Tin Þ/m_ w ¼ 0:86 s Undertaking the exergy balance we get

 T0 _ Tout Qh ¼ m_ w cw Tout
Tin
T0 ln 1
þ D_ cond Th Tin D_ cond ¼ 0:38 kW

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We will now look at the evaporator. The environmental mass airflow rate in the evaporator is kg Q_ c ¼ m_ ai cai ðTin
Tout Þai /m_ ai ¼ 6:84 s Undertaking the exergy balance in the evaporator we get

 T0 _ Tout Qc ¼ m_ ai cai Tout
Tin
T0 ln
1
þ D_ ev Tc Tin D_ ev ¼ 0:21 kW This equation needs an explanation. The refrigerant gives exergy to the environmental air when exchanging heat in the evaporator. In effect, the air enters the evaporator in its ambient state (zero exergy) and leaves at
2 C, with an exergy of 0.05 kW, which is finally destroyed. Therefore, of the whole exergy, 0.26 kW, given up by the refrigerant in the evaporator, 0.05 kW goes to the air (which is exergy that is finally destroyed), and the remaining 0.21 kW is exergy destroyed in the evaporator itself. (d) The overall exergy efficiency of the heat pump is


4¼

m_ w cw

Tout Tout
Tin
T0 ln Tin W_

 ¼ 0:46

Of the exergy contributed to the heat pump only 46% has a useful effect. The rest of the exergy is internal destruction in the cycle (1.65 kW), destruction in heat exchanges in the evaporator and condenser (0.59 kW) and the difference of up to 4.7 kW (2.46 kW) is exergy destruction due to head losses and in the auxiliary equipment. A dwelling is maintained at 20 C by a geothermal heat pump on a winter day in which the outside temperature is 0 C and the ground temperature is 5 C. The hot water produced by the heat pump is sent to a radiant floor at a temperature of 35 C. If the heating output is 12 kW and its COP ¼ 3.2, what is

Example E.5.15.

(a) (b) (c) (d)

The maximum COP. The exergy efficiency. The rate of exergy destruction in the heat pump. The rate of exergy destruction in the heat exchange between the radiant floor and the indoor air.

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Exergy Analysis and Thermoeconomics of Buildings

Solution (a) The COPmax would be that of a reversible heat pump, therefore, operated according to a reverse Carnot cycle, between the soil temperature 5 C, and that of the underfloor heating 35 C. So

COPmax ¼

Trf ¼ 10:27 Trf
Tgr

(b) To calculate the exergy efficiency we need to know the heat extracted from the ground and the mechanical power consumed by the heat pump. From the COP we have

COP ¼

Q_ rf W_

/ W_ ¼

Q_ rf ¼ 3:75 kW COP

Therefore, W_ þ Q_ gr ¼ Q_ rf / Q_ gr ¼ 8:25 kW The heat pump exergy efficiency is then
 T0 _ Qrf 1
Trf
 4¼ ¼ 0:35 T0 _ Qgr þ W_ 1
Tgr This coefficient reflects the thermodynamic quality of the equipment, since, if the heat pump were reversible, its value would be unity. It happens, however, that the exergy extracted from the ground is free, in the sense that nobody pays for it. In this sense, the mechanical power can be considered as the only resource (fuel) and so the exergy efficiency would be
1
4¼

 T0 _ Qrf Trf ¼ 0:36 W_

which could theoretically be greater than unity. (c) By applying the exergy balance in the heat pump, we have



  T0 _ T0 _ Qgr þ W_ ¼ 1
Qrf þ D_ hp / D_ hp ¼ 2:5 kW 1
Tgr Trf

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405

d) The rate of exergy destruction in the heat exchange between the radiant floor and the indoor air is

Trf
Ti _ D_ ¼ T0 Q ¼ 0:54 kW Trf Ti rf Example E.5.16.

A vapor-compression heat pump extracts heat from a well that is containing water at 6 C and gives the heat to a room whose temperature is 21 C. The heat is extracted from the well through a brine circuit with its corresponding circulation pump moving a mass flow rate of 0.56 kg/s, and the heat is transferred to a water circuit in the condenser, with its own circulation pump moving 0.28 kg/s. The water and the brine thermodynamic states are shown in Table E.5.5 and the refrigerant thermodynamic states, which is a freon, are shown in Table E.5.6. The simple vapor-compression cycle has a preheater at the compressor inlet.

Table E.5.5 Brine and water thermodynamic states. State number

p (bar)

T (8C)

h (kJ/kg)

s (kJ/kg$K)

7

2


4.9

8

1.9


8.2

9

10

45.5

192.7

0.651

10

1.8

53.4

224.9

0.751

m (kg/s) 0.56

0.28

Table E.5.6 Thermodynamic states of Freon 502. State number

p (bar)

T (8C)

h (kJ/kg)

x

1

3.4

21.8

365.9

2

23.5

127.7

433

1704

3

23.5

46.2

256.4

1185

4

23.5

30.6

236.3

1121

5

3.4


15.5

236.3

6

3.4


6.6

346

0.34

m (kg/s)

s (kJ/kg$K)

0.052

1640

1143 1569

In Table E 5.5, states 7 and 8 correspond to the brine circuit at the inlet and outlet of the evaporator and states 9 and 10 to the water circuit, at the inlet and outlet of the condenser respectively. The cycle has a preheater at the condenser outlet that preheats the refrigerant after leaving the evaporator outlet and before entering the compressor. In Table E 5.6, state 1 is at the compressor inlet, state 2 at the compressor outlet, state 3 at the outlet of the condenser, state 4 at the preheater outlet, state 5 at the outlet of the expansion valve and state 6 at the evaporator outlet.

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Exergy Analysis and Thermoeconomics of Buildings

The electric power of each motor pump is 60 W with an overall efficiency of 52%, and the efficiency of the compressor drive is 92%. If the ambient conditions are T0 ¼ 275 K, p0 ¼ 1 bar and knowing that the heating power of the heat pump is 9 kW, what is (a) (b) (c) (d) (e) (f)

The rate of heat extracted from the cold source. The instantaneous COP. The rate of heat transferred to the environment by the whole installation. The instantaneous exergy efficiency of the entire installation. The irreversibilities in the main cycle components. The irreversibilities in the whole installation.

Solution (a) If 7 and 8 are the brine states at the entrance and exit to the evaporator, we have

m_ br ðh7
h8 Þ ¼ m_ br

p7
p 8 cbr ðT7
T8 Þ þ 9br



We use the following values for the brine: 9br ¼ 1190 kg/m3and a specific heat of cp,br ¼ 3.06 kJ/kg$K. With this data we have

 ð2
1:9Þ$105 m_ br ðh7
h8 Þ ¼ 0:56 3:06$103 ð
4:9
ð
8:2ÞÞ þ ¼ 5660 W 1190 However, the heat extracted from the cold source is less than this difference in enthalpy since the energy contributed by the brine circulation pump, will have to be subtracted. From the electric power consumed by the brine motor pump a fraction is converted into heat, which is taken by the brine flow. Since εp1 is the drive motor pump efficiency and W_ p1 the electrical power consumed, the part that goes to the brine flow is εp1 W_ p1 ¼ 0:52$60 ¼ 31 W. In short, the heat extracted from the cold source is Q_ c ¼ 5629 W (b) Since m ¼ 0.052 kg/s is the refrigerant mass flow rate, according to the values in Table E.5.6, the compressor electric power is

_ 2
h1 Þ mðh W_ comp ¼ ¼ 3792 W εcomp with the instantaneous heat pump COP being COP ¼

Q_ c Q_ c ¼ ¼ 2:30 _ _ W HP W comp þ W_ p1 þ W_ p2

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407

(c) The rate of heat transferred to the environment by the compressor drive is

Q_ comp ¼ ð1
εcomp ÞW_ comp ¼ 303 W The rate of heat transferred to the environment in the condenser is _ 2
h3 Þ
m_ w ðh10
h9 Þ ¼ 167 W Q_ c ¼ mðh In the brine motor pump, the rate of heat transferred to the environment is Q_ p1 ¼ ð1
εp1 ÞW_ p1 ¼ 29 W and in the water motor pump Q_ p2 ¼ ð1
εp2 ÞW_ p2 ¼ 29 W The rate of heat transferred to the environment in the internal exchanger (preheater) is _ 3
h4 Þ
mðh _ 1
h6 Þ ¼ 10 W Q_ in ¼ mðh Therefore, the rate of total heat transferred to the atmosphere by the installation as a whole is Q_ comp þ Q_ c þ Q_ p1 þ Q_ p2 þ Q_ in ¼ 538 W (d) The instantaneous installation exergy efficiency is




 T0 _ Q 1
Th h
 ¼ 14:6% 4¼ T0 _ Qc W_ comp þ W_ p1 þ W_ p2 þ 1
Tc From a strictly thermodynamic point of view in the denominator of the previous expression, there should be the total resources (in the next chapter we will name them as fuel) used by the heat pump, to which the exergy contributed by the well is added. Now, as this is a free resource which does not have an economical cost, we can define the efficiency according to the expression


 T0 _ Qh 1
Th ¼ 14:9% 4¼ W_ comp þ W_ p1 þ W_ p2

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(e) The irreversibilities in the motor-compressor group are

_ 2
b1 Þ ¼ 1218 W I_comp ¼ W_ comp
mðb since b2
b1 ¼ h2
h1
T0(s2
s1) ¼ 49.5 kJ/kg. In the condenser _ 2
b3 Þ
m_ w ðb10
b9 Þ ¼ 466 W I_c ¼ mðb with b10
b9 ¼ h10
h9
T0 ðs10
s9 Þ ¼ 4:7 kJ=kg and b2
b3 ¼ h2
h3
T0 ðs2
s3 Þ ¼ 34:3 kJ=kg In the expansion valve _ 4
b5 Þ ¼ 315 W I_valv ¼ mðb with b4
b5 ¼ T0 ðs5
s4 Þ ¼ 6:05 kJ=kg In the evaporator _ 5
b6 Þ
m_ br ðb8
b7 Þ ¼ 369 W I_ev ¼ mðb with b5
b6 ¼ h5
h6
T0 ðs5
s6 Þ ¼ 7:45 kJ=kg and for the brine b8
b7 ¼ h8
h7
T0 ðs8
s7 Þ ¼ 0:32 kJ=kg In the internal exchanger _ 3
b4 Þ
mðb _ 1
b6 Þ ¼ 52$2:5
52$0:37 ¼ 111 W I_in ¼ mðb with b3
b4 ¼ h3
h4
T0 ðs3
s4 Þ ¼ 2:5 kJ==kg b1
b6 ¼ h1
h6
T0 ðs1
s6 Þ ¼ 0:37 kJ=kg

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409

f) From the overall exergy balance in the installation we have



  X T0 _ T0 _ _ _ _ Qc þ W comp þ W p1 þ W p2 ¼ 1
Qh þ Ii 1
Tc Th i

Therefore, total irreversibilities are X Ii ¼ 3391 W i

5.10

Cogeneration in buildings

5.10.1 General comments on cogeneration Cogeneration, also known as Combined Heat and Power (CHP), can be defined as the sequential electricity and useful heat generation from the same fuel. Compared with the conventional situation in which electricity is purchased from the grid, and useful thermal energy (useful heat) is generated in the building’s installations by boilers or other thermal equipment, cogeneration involves the simultaneous generation of both products, electricity and useful heat. Cogeneration systems take into account the thermodynamic concept of energy quality. During combustion, a fossil fuel can reach temperatures above 1000 C, and it is a bad use of its energy quality, for example, to utilize it exclusively to generate hot water for heating. On the other hand, cogeneration systems use fuels for high-quality energy generation, such as electric power and, in addition, a low-level thermal energy, but still of service to the user. The increase in the comfort in buildings and the continuous expansion of cities in recent years has doubled the energy consumption of the residential sector and services in Spain, so that, if in 2000, the final energy consumption was 18,700 ktpe, which represented 23.5% of total consumption, it increased to 31.1% in 2015, which meant a total consumption of almost 25,000 ktpe. For reasons of economy and security in the energy supply, this data highlights the need to provide buildings with efficient energy systems. In the conclusions of some European projects, such as TRIGEMED 2003 [25] and SUMMERHEAT 2009 [26], it was highlighted that only a fraction of the cogeneration potential in the EU’s residential-commercial sector had been developed, and there is still a large market to be exploited. A review of the data on the state of cogeneration in Spain, IDAE 2016 [27] reveals that cogeneration is not widespread in the residential sector and services. In fact, in 2015, with a total installed power of 6,018 MW, the installed capacity in the residential and tertiary sectors represented 10% of the total power, while in small-scale cogeneration (typical of residential applications) it was only 36 MW. On the other hand, the 2004 IDAE study indicated a technological potential for the residential and tertiary sectors of 6,414 MWe, so the penetration degree is very small, indicating that there is practically everything to be done.

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Exergy Analysis and Thermoeconomics of Buildings

When the reasons for this situation are analysed, it is easily concluded that investments in cogeneration in buildings show an economic return that is much lower than that of the industry. There are a series of intrinsic problems in this application of cogeneration, such as the high variability of demand, both daily and seasonal, the difficulties in predicting this demand (since it depends on climatic factors and the behaviour of the occupants) and the fact that the potential for installing is lower than in industry, and so arguments concerning economies of scale come into play. However, technologies for small-power cogeneration and micro-cogeneration can provide the energy services demanded in buildings: electricity, DHW, heating and cooling, all with high energy efficiencies, and with the consequent economic benefit and lower environmental impact.

5.10.2

Cogeneration and the energy demand in buildings

Buildings in the residential and tertiary sector (offices, hotels, hospitals, schools, sport centres, shopping centres, etc.) demand final energy in the form of electricity and thermal energy. The electricity demand is due to consumption in lighting, elevators, water pumping, appliances, air-conditioning, etc. while the thermal consumption is for heating, sanitary hot water, pool heating, etc. As we saw in Chapter 1, the building sector is a large consumer of energy resources, so that in Spain in 2015, the final energy consumption of the residential sector accounted for 18.5% of total consumption and the services sector 12.6%, IDAE 2017 [28]. When the owners of a hotel, development, building or home decide to install a cogeneration plant, the electrical installation remains connected to the grid. Due to fluctuations in demand, there will be times when electricity production will be lower than demand, in which case, the deficit will come from the grid, while if production is greater than demand the surplus is sent to the grid. Any interest in sending surpluses into the network depends on the economic conditions and possible legal restrictions. Unfortunately, at present in Spain, in accordance with Royal Decree 900/2015 [29] only Self-Consumption Mode 2 can sell surpluses in the electricity market, at a price quoted by the market at any given hour. Regarding the thermal demand, if this is greater than the cogeneration production, a complementary auxiliary system will be needed, such as an auxiliary boiler, etc. If the thermal demand decreases, the power of the plant can be regulated, or an energy storage system can be used, which allows the plant to be sized more appropriately and even produce electricity in the hours when sales imply a greater profit. The cogeneration fundamentals can be found in the extensive existing bibliography, among which we highlight the works of Polimeros 1981 [30], Marecky 1988 [31], Sala 1995 [32], Horlock 1997 [33] and Petchers 2003 [34]. It is evident that the demands of electricity, heat and cold for buildings represent an opportunity for cogeneration systems capable of producing electricity, heat and cold (coupling absorption chillers) in an efficient and economical way. In the residential and commercial sector in Spain, the thermal demand shows two singular characteristics: (1) a relatively low number of annual hours of heat and cold requirement and (2) reduced periods of maximum demand for heat and cold. These singularities represent a

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411

challenge for the cogeneration system design, that is, in order to define a plant whose total cost (investment and operation) throughout its life cycle is less than that of other energy supply alternatives. In addition to the aspects discussed, there are four good reasons to favour the cogeneration participation in the energy supply facilities in buildings and urban districts in Spain: • • • •

Availability of fuels used (mostly natural gas). Increasing demand for refrigeration. Low penetration currently. In spite of its current state, political support comes from European Directives, which are later transposed into the Member States legislation.

In short, cogeneration can provide high-efficiency systems that save primary energy, contributing to improving energy intensity, the degree of self-sufficiency and security of supply.

5.10.3 Micro-cogeneration technologies The penetration of cogeneration in residential and small and medium tertiary sectors can be carried out with individual systems, semi-centralized or highly centralized systems. As they are current technologies specially adapted for application in buildings, we are going to look at micro-cogeneration facilities. According to Directive 2012/ 27/EU [35], this is the name for those facilities that have a maximum electrical power of 50 kW, although occasionally, this term extends to small-power cogeneration, with a maximum power of 1 MW. Micro-cogeneration facilities use different technologies, and each of them has a series of advantages and disadvantages. We will present below a summary of the most important and currently used technologies.

5.10.3.1 Internal combustion micromotors Alternative internal conmbustion engines are well-known and established technology due to their extensive implementation in the transport sector. Derived from it were engines for stationary applications, either as emergency groups (mainly with diesel engines) or as engines in industrial cogeneration applications. In these applications, the large engines (dozens of MWe) are diesel or diesel oil, while those of lower power (below 10 MWe) are mainly natural gas or other light fuels. At present, there are alternative natural gas engines of small size (from about 5 kWe) suitable for cogeneration applications in the residential sector, which are known as micromotors. An alternative internal combustion engine has up to four recoverable heat sources: exhaust gases, engine cooling water, lubricating oil cooling water and turbocharger cooling water. In micromotors, the latter two are not normally available, although other heat sources, such as from the cooling of the alternator, can be used, Pulkrawek 2004 [36], see Fig. 5.24. Natural gas alternative micromotors are the most suitable option for cogeneration systems in the residential sector since they have a low acquisition cost, are easy to

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Exergy Analysis and Thermoeconomics of Buildings

Figure 5.24 Heat recovery in alternative engines.

install and maintain, have high reliability and efficiency and a low level of emissions. These small motors are normally sold in units fitted with all the heat sources integrated, so that the available heat is delivered in the form of a single hot water stream, with temperatures of up to 110 C. Fig. 5.25 shows the image of a micromotor. Micromotors dissipate heat through cooling water circuits and exhaust gases. Both heat sources are recovered, to finally give all the energy in the form of hot water with the aim for it to be used for heating and DHW.

Figure 5.25 An alternative internal combustion micromotor

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413

Figure 5.26 Schematic of a heating and DHW system with an alternative micromotor. (courtesy of Altare).

Although it is true that alternative micromotors have higher electric efficiencies than microturbines, their use of residual thermal energy is more problematic, since this energy is at a lower temperature and also more distributed (exhaust gases and engine cooling circuits), Caterpillar [37]. As an example, Fig. 5.26 shows the schematic of a micro-cogeneration installation developed by the company Altare for a building containing 130 homes in Madrid. The thermal demand is 193 MWh/year of DHW and 490 MWh/year of heating. It is a centralized installation of two pipes with a 12 kWe and 27 kWt engine and with a 3000 L tank, operating 5700 h/year.

5.10.3.2 Gas microturbines Microturbines had existed since the sixties, when commercial aircraft replaced alternative engines with more reliable and less heavy turbines, to generate the auxiliary energy needed to start the propulsion turbines and other services, such as having light when they are detained in the middle of the airport. They are internal combustion engines, based on the same principle as conventional gas turbines, but simplifying the mechanical elements. In this sense, they have only one moving part in the whole machine, the shaft, with the total absence of lubricating oils and cooling water. The bearings on which the shaft is supported are air bearings, and the operating speed is between 45,000 and 100,000 rpm. As we have said, the microturbine operating mode does not differ much from that of a conventional gas turbine. The main difference is found in the fact of having a regenerator, that is, an internal heat exchanger that preheats the air before it enters the combustion chamber by means of the exhaust gases from the chamber, which gives a marked improvement in the electrical efficiency. In addition, microturbines are characterized by the absence of a differential connected to the alternator. For a detailed

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Figure 5.27 Schematic of a microturbine and its electrical components.

description of microturbines and their mode of operation see Boicea 2014 [38] and Melguizo and Cano 2005 [39]. Due to this, microturbines generate alternating energy at a variable frequency, which is converted to direct current and through an inverter, similar to the one incorporated in photovoltaic systems, it is converted to three-phase alternating current at 400 V and 50 Hz, suitable for low-voltage applications, see the schematic in Fig. 5.27. Finally, the exhaust gases leave the microturbine at approximately 300  C, which provides a useful thermal recovery opportunity for DHW, heating and cooling. The use of microturbines offers a large number of advantages (in comparison with other small-scale energy production technologies) such as • • •

Small number of moving parts, only the microturbine axis. This implies low maintenance and also no consumption of lubricating oil. Reduced weight and size. Thus, establishing a comparison with alternative engines, a 40 kW microturbine weighs about 700 kg, compared to the 2000 kg of an alternative engine. Recoverable thermal energy in the exhaust gases. Unlike alternative engines, gas turbines concentrate waste heat into a single stream at high temperature, simplifying the heat recovery apparatus.

Gas microturbines are highly reliable and efficient for the production of electricity and heat in cogeneration mode, and also, for the air conditioning of buildings that have centralized air conditioning services such as hospitals, hotels, schools, sports clubs, markets, etc. Fig. 5.28 shows the compressor, expander and electric generator of a microturbine. In many buildings, there are boilers for sanitary hot water and heating, in addition to the connection to the electricity grid and, in some cases, emergency equipment to cover power failures. Normally, this emergency equipment is based on alternative diesel-cycle engines. Microturbines can also be used as emergency systems,

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Figure 5.28 Main components of a gas microturbine.

supporting critical loads in case of power failure. In this case, we could eliminate the investment in an emergency generator, so that overall costs would be more favourable. Finally, it should be said that microturbines exhaust gases are generally around 300  C and free of oils. This makes them an ideal system to combine with highefficiency absorption refrigeration equipment (double effect, GAX cycles, etc.) for cold production and also for applications in horticultural greenhouses, where a supply of heat and CO2 with a low level of hydrocarbons is needed. Therefore, one of the most appropriate technological solutions to guarantee energy supply is micro-trigeneration with gas turbines, which offers the possibility of simultaneously generating the electricity, heat and cold necessary for the correct air conditioning of a building throughout the year, with energy savings and supply guarantee.

5.10.3.3 Stirling engines These are alternative external combustion engines with a closed cycle. Unlike alternative internal combustion engines, the engine fluid is not the fuel and air, but a gas (helium or hydrogen) confined in a hermetic enclosure. They have fewer moving parts and no valves, no rockers, no fuel injectors or spark ignition systems, so they require less maintenance and the emission of pollutants is low, Walker1980 [40] and Organ 2014 [41]. The principle of operation is the work done by the expansion and compression of a gas when it is forced to follow a cooling cycle in a cold source, where it contracts, and heating in a hot source, where it expands. A Stirling engine schematic is shown in Fig. 5.29. Its work cycle consists of two isochoric processes (heating and cooling at constant volume) and two isothermic processes (compression and expansion at constant temperature). There is an additional element to the engine, called the regenerator, which is an internal heat exchanger that has the function of absorbing and yielding heat in the processes at constant volume of the cycle. The regenerator consists of a porous medium, with negligible thermal conductivity, which contains a fluid and divides the engine into two zones: one hot and one cold. The fluid moves from the hot zone to the cold zone during the various work cycles, passing through the regenerator.

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Figure 5.29 Schematic of a Stirling engine.

This engine is still under investigation due to the diversity of energy sources that can be used to operate it; as it needs only one heat source external to the cylinder, it is possible to use a wide variety of energy sources, such as solar energy, all types of fuels including biomass, geothermal energy, etc. Great advances have been made in the lower power range, between 0.2 kWe and 9 kWe, and they are especially suitable for the domestic sector, due to the relationship between their electrical and thermal production, since it is usually of the order of 1/6. The most important type of Stirling engine is the alpha type, which has two power pistons, while those of beta and gamma type have a piston and a displacer.

5.10.3.4 Fuel cells Fuel cells are energy converters that directly transform the chemical energy of a fuel into electrical energy, through electrochemical processes and which operate, therefore, without combustion reactions. Their operation is similar to that of batteries, but while these are energy storage devices, fuel cells are converters, that is, they produce electricity from the continuous replenishment of reagents, fuel and oxygen, Otero de Becerra 2010 [42]. Furthermore, while in a battery the electrodes change according to whether it is charged or discharged, in a fuel cell the electrodes are relatively stable. Fig. 5.30 shows the conceptual scheme of a fuel cell. Typical reagents used are hydrogen (on the anode side) and oxygen (on the cathode side). The hydrogen that reaches the anode dissociates into protons and electrons. The protons are driven through the electrolyte to the anode, while the electrons are forced to travel through an external circuit. At the cathode, oxygen molecules react with the protons and electrons to form water. In this case, the only residue left from the use of a fuel cell is water vapor. Fuel cells are classified according to the type of electrolyte used. Thus in polymeric electrolyte cells, also called proton-exchange membrane cells, a polymeric

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Figure 5.30 Operating principle of a fuel cell.

proton-conducting membrane (the electrolyte) separates the anode side from the cathode. This electrolyte can also be phosphoric acid, molten carbonates or a solid oxide. The following Table 5.1 shows the most relevant properties of these different types of cells. As for the electrodes, they are usually made of nickel or carbon nanotubes and are covered with a catalyst, such as platinum or palladium, to achieve greater efficiency. In addition to what we have described so far, which is what we might call the heart of the cell, fuel cells also incorporate a series of complex systems that carry out various functions. Among them are the fuel treatment system, the conditioning system for the Table 5.1 Types of fuel cells. Carrier ion

Types of fuel cells

Acronym

Temperature

Fuel

Oxidant

Proton-exchange membrane

PEFC

80 C

H2 pure

Air without CO

Hþ

Phosphoric acid

PAFC

200 C

H2

Air without CO

Hþ

Molten carbonates

MCFC

650 C

CH4, H2, CO

Air þ CO2

CO¼ 3

Solid oxide

SOFC

950 C

CH4, H2, CO

Air

O¼

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Figure 5.31 Diagram of the different systems of a fuel cell.

electricity produced (where direct current is generated which must be converted to alternating current at 50 Hz), the air management system, the water management system and the thermal energy management system (both for the internal use of the cell, as well as waste heat for its use as a cogeneration system). Fig. 5.31 shows a diagram of those different systems that make up the cell. In the absence of combustion, the cells efficiency is not limited by the Carnot factor, which theoretically can reach very high values. According to what we saw in Chapter 3, the maximum energy conversion from fuel to electricity is limited by the decrease in Gibbs function of the electrochemical reactions which take place in it, in short, by the fuel chemical exergy. Normally, the efficiency that is achieved in this conversion of chemical energy from a fuel into electrical energy is of the order of 50%. In cogeneration applications the efficiency may be lower, since most of the energy not converted to electricity is used as useful heat, reaching very high overall efficiencies. Phosphoric acid fuel cells (PAFC) cover the largest range of cogeneration applications worldwide and can provide overall efficiencies close to 80% (45%e50% electric, with the rest being heat). The largest PAFC fuel cell manufacturer is UTC Power. Molten carbonate fuel cells (MCFC) are also used for identical purposes, and there are prototypes for solid oxide fuel cells (SOFC). Fuel cells offer a series of important advantages, such as high energy efficiency, low level of environmental pollution, modularity, operation flexibility, the possibility of using various fuels, silent operation, reliability and simplicity of installation. The most important drawbacks are their great sensitivity to catalytic poisons and their high current cost, Sorensen 2012 [43].

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5.10.4 Cogeneration with Organic Rankine Cycles (ORC) The Organic Rankine Cycle (ORC) consists of the basic processes of a Rankine cycle, but water is replaced as a working fluid by an organic fluid, which can be a natural hydrocarbon (pentane, propane, butane), a halogenated hydrocarbon (such as R134a, R245fa), silicone oil (hexamethyldisiloxane, octamethylcyclotetrasiloxane) or others. The thermodynamic properties of these fluids allow the ORC cycles to take advantage of medium and low temperature heats in a very efficient way, such as those that occur with solar energy, biomass, geothermal energy, waste heat, etc. for the production of only electricity or, as is more frequent, electricity and useful thermal energy. According to numerous studies conducted, Huang et al. 2013 [44], Dai et al. 2009 [45], the working fluid in an ORC should have a high density, high vaporization enthalpy, high specific thermal capacity at constant pressure, low viscosity, high thermal conductivity, low environmental impact, high temperature stability, low vapor pressures, commercial availability and low cost. In addition, and this property is very important, the saturated vapor curve must be positive or isentropic. With respect to this last property, fluids are classified into three groups: isentropic fluids, wet fluids and dry fluids. The former, such as R11 or R12, have a practically vertical saturated vapor curve in their T-s diagram. Wet fluids, such as water or ammonia, have a negative slope, while dry fluids, such as benzene, toluene, etc. show a positive slope. In ORC cycles, dry fluids are preferable, since in the expansion final stages in the turbine no drops of liquid appear, which diminish its efficiency. The critical point of organic fluids is at a significantly lower temperature and pressure than for water. In current ORC cycles, vapour enters the turbine as saturated or slightly overheated steam. However, there are very interesting advances in the investigation of supercritical cycles, showing higher efficiencies can be achieved, which may make these facilities even more significant, Schuster et al. 2010 [46]. The components of the basic ORC cycle are the evaporator, turbine, condenser and pump. The turbine or expansion device is the most complex component, and its efficiency depends largely on the type of fluid used. Volumetric, scroll or screw tye expanders in the range of powers up to about 150 kW are used, which work inversely to the compressor. Above this power, turbomachines are used. Fig. 5.32 shows a schematic of a biomass boiler that heats a thermal oil, which in turn, gives heat to the organic fluid in the evaporator up to the saturated steam state. In the T-s diagram, the thermodynamic states of the organic fluid are shown, which, as we can see, corresponds to a dry fluid. An installation with a regenerative cycle is shown in Fig. 5.33. The regenerative cycle improves efficiency, preheating the organic fluid that leaves the pump before entering the evaporator. In this way, we take advantage of dry fluids characteristics which leave the turbine at a temperature higher than the condensation temperature, this temperature being used as an internal energy source, thus raising the average thermodynamic temperature of heat input in the cycle and, consequently, increasing the efficiency. This way of carrying out the regeneration is typical of ORC cycles, unlike the water vapor Rankine cycles, in which the regeneration is carried out by means of extractions from the body of the turbine.

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Figure 5.32 Schematic of a basic Organic Rankine Cycle.

Figure 5.33 Schematic of a regenerative Organic Rankine Cycle.

Currently, there are already many manufacturers that have commercial equipment for different applications. According to data for the year 2017 [47], worldwide, the installed capacity until 2016 was 520 MW, of which 80% corresponded to geothermal plants, around 15% to biomass plants and the rest to plants using waste heat.

5.10.5

District heating and cooling

A centralized air conditioning network or heating and cooling network, also known as district heating and cooling, aims to provide different buildings or consumption

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centres with all the thermal energy demanded (heating and cooling, or heating only, or cooling only), generating this energy in a centralized installation which is the generation centre. The buildings are connected to the plant through a distribution network which generally consists of water, controlled and regulated from the generation centre itself, Fogelholm et al. 2008 [48]. An important feature of district heating and cooling is the possibility of using thermal energy storage systems (TES), both for heat and cold. Their usefulness is twofold: they reduce installed power while allowing the continuous operation of equipment, without sudden variations and in an optimum performance regime. This fact implies more economical consumption, higher average efficiency and longer lifespan of the equipment. The difficulty is that, often, storage requires large volumes that must be located within the urban environment, which already have many restrictions on available space for service infrastructure. Heating and cooling networks consist of a generating centre, which is often a cogeneration plant since combining cogeneration with the network is highly efficient. However, depending on the local energy sources, we frequently find plants based on renewable energies such as biomass, geothermal energy, conventional plants supported by solar energy, plants that take advantage of waste heat, heat pumps with conventional boilers, etc. Wiltshire 2016 [49]. Once generated, the thermal energy is distributed to the consumers through a network of thermally insulated pipes, which consists of outgoing and return pipes, Fig. 5.34. The heat transfer fluid used is usually water and sometimes steam. The advantage of steam is that, in addition to heating applications, it can have industrial uses due to its high temperature. As a disadvantage, steam has greater heat losses in transport, precisely because of its high temperature. The water pumping system through the distribution network is designed to overcome the friction head losses, both in the outgoing and return pipes, so that it reaches

Figure 5.34 Schematic of a district heating installation.

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Figure 5.35 Distribution pipes.

the user’s substation under pressure conditions suitable for the service. The main distribution network, see Fig. 5.35, is connected to the heating and DHW users’ systems through heat exchangers or directly: this is what is known as indirect and direct systems. Direct systems operate with outgoing flow temperatures from 85 to 65 C and return from 68 to 34 C, while indirect systems operate at higher temperatures, between 140 and 75 C. There is a control and monitoring centre in the heating and cooling network so that the temperature and pressure control ensures that the system responds adequately to consumer demand at all times. For this purpose, measuring equipment and transmitters are placed at strategic points. The substation, normally placed in the basement or on the ground floor of a user’s building, Fig. 5.36, modifies the state of the thermal energy so that it adapts to the consumer’s requirements, having to satisfy a balance between consumer demand and the thermal energy generated, IEA 2000 [50]. The classic district heating installations, usually linked to thermoelectric power plants, have a strong presence in countries of the North, Central and Eastern Europe, and in other countries such as Russia, China and the United States, where they have proven their energy, economic and environmental worth. In the framework of the European project SUMMERHEAT (2009), studies were carried out in cities of different countries (Germany, Austria, Denmark, France, Poland and the Czech Republic) on the possibility of implementing cooling installations with absorption chillers, which use waste heat from cogeneration plants as an energy source.

Figure 5.36 Substation of a district heating system.

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As regards Spain, in certain places and/or buildings there is a low annual demand for heating. In others, the absence of cold demand during the summer months harms the profitability of district heating and cogeneration projects, since the low installed power and/or a reduced utilization factor slows the investment recovery. On the other hand, the trend towards higher consumption of air conditioning in the building sector has been causing a significant increase in the demand for cold. According to ADHAC (Association of Heating and Cooling Networks) [51], in 2016, in Spain, there were a total of 330 networks, of which 306 were registered, with an installed capacity of 1,219 MW. Of this, 73% was for heating and 27% for cooling. Of the total of networks, most of them (225) used renewable energy, mainly biomass (218), followed by natural gas (41) in number. If we look at it by installed power, the largest percentage corresponds to natural gas (47.4%) followed by renewable (31.4%), then electricity (18.8%) and finally diesel (2.4%). The installed power was distributed as follows: 13% in industry, 35% in the residential sector and 52% in the service sector. The largest number of networks was in Catalonia (91), followed by Castile and Leon (43), with the rest being distributed among the different Autonomous Communities. Together these networks, which totaled 550 km and supplied 4,030 buildings, achieved a CO2 emissions reduction of 180,000 t/year. Some significant facilities are the following: • • • • • •

Molins de Rei (Barcelona): 2.25 MW of heating (IDAE, 2007). Cuellar (Segovia): 6 MW of heating (IDAE, 2007). Sant Pere de Torello (Barcelona): 6 MW of heating (IDAE, 2007). Expo Zaragoza (Zaragoza): 15/20 MW of heating/cooling (DISTRICLIMA, 2012). Central Tanger (Barcelona): 13.4/6.7 MW of heating/cooling (DISTRICLIMA, 2012). Central Forum (Barcelona): 20/15.5 MW of heating/cooling (DISTRICLIMA, 2012).

Directive 2012/17/EU [35] on energy efficiency states that, if a cost-benefit analysis is carried out and it is favourable, the Member States should adopt the appropriate measures to develop an efficient urban heating and cooling infrastructure. In Spain, that Directive has been transposed through Royal Decree 56/2016 [52] that translates almost literally the Directive and points out in its Article 4, the improvement of energy efficiency through district heating and cooling as one of the actions within the Strategic Plan for the Energy Rehabilitation of Buildings. For its part, PAEE 2017e20 [53] reinforces the entry into the market of heating networks, pointing to district air conditioning systems as one of the key elements in the energy efficiency of buildings.

5.10.6 Cogeneration energy parameters We are going to define a series of parameters that allow us to characterize the energy behaviour of a cogeneration plant. Suppose that the cogeneration system is a black box, as shown in Fig. 5.37, that consuming F units of fuel energy simultaneously produces E electricity units and H units of useful thermal energy. We shall define the following parameters: • •

electrical efficiency: hEc ¼ E/F thermal efficiency: hHc ¼ H/F

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Figure 5.37 Cogeneration plant as a black box. • •

overall efficiency: hc¼(E þ H)/F heat-electricity ratio: b ¼ H/E

Therefore, to completely characterize the plant three independent variables among the seven (F,E,H,hEc,hHc,hc,b) need to be known. Another type of energy parameters expresses the comparative advantage of cogeneration over conventional heat and power generation systems. To define them, consider a conventional system that produces the same amounts of electricity and useful thermal energy as the cogeneration plant, see Fig. 5.38. Suppose that E and H have to be supplied to satisfy a consumer’s electrical and thermal demands. The consumer must decide whether to install a cogeneration system or to proceed in a conventional manner by buying electricity from the electric company (which is supposed to have produced it with efficiency hE) and installing a boiler with an energy efficiency hH. The primary energy saving implied by cogeneration will be ES ¼ DF ¼ F 
F ¼ FE þ FH
F ¼

E H þ
F h E hH

(5.76)

Related to this concept, the Fuel Energy Saving Ratio (FESR) is defined as the fuel saving per unit of energy required in the conventional mode, that is FESR ¼

DF F 1 ¼1
¼1
h h E H Ec F þ Hc þ hE hH hE hH

Figure 5.38 Conventional system with the same productions as cogeneration.

(5.77)

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Since it is expressed as a percentage of this index, it is called the Percentage of Energy Saving (PES). If following the nomenclature adopted by Directive 2004/8/ EC [54], we now call CHP Hh instead of H for the thermal energy produced by the cogeneration, CHP Eh instead of E for electricity, hH ¼ RefHh the efficiency of separate generation of thermal energy in the reference installation and hE ¼ RefEh the efficiency of the separate generation of electricity, the PES gives

2

PES ¼ 41


3

1 CHP Hh CHP Eh þ Ref Hh Ref Eh

5100

(5.78)

In Annex III of Directive 2004/8/EC, there are the minimum values that are required of a cogeneration plant for it to be considered as high efficiency. In the case of less than 1 MWe installations, which is the most common in buildings, this value only needs to be greater than zero so that there is primary energy saving. The last parameter that we are going to consider is the equivalent electrical efficiency (EEE), which is specific to the Spanish State and whose definition comes from using a particular criterion when it comes to sharing fuel consumption among the products of the cogeneration system. Specifically, a conventional boiler with efficiency hH would consume the fuel FH ¼ H/hH to produce the useful thermal energy H, so the fuel consumption attributable to the electricity generated in the cogeneration plant can be considered to be FeqE ¼ F
FH

(5.79)

Thus, the equivalent electrical efficiency is defined as

EEE h

E ¼ FeqE

E

H F
hH

¼

hEc h 1
Hc hH

(5.80)

which can also be written as EEE ¼

E E
ES RefEn

(5.81)

This index allows us to compare the electrical efficiency of a CHP plant with the electrical efficiency of a plant that only produces electricity. This direct comparison does not take into account the losses in the electricity transport and distribution. The values of E, F and H are annual values, and therefore, the EEE efficiency is also an annual value and F is expressed referring to fuel LHV. Note how the parameters PES and EEE place special emphasis on finding out if the cogeneration systems transform the energy consumed in useful products (heat/cold and electricity) with greater efficiency than the conventional systems.

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Table 5.2 Minimum values for EEE. P £ 1 MW

Technology and fuel Alternative heat engines. Liquid fuel

56.0%

50.4%

Alternative heat engines. Natural gas and LPG

55.0%

49.5%

Gas turbines. Natural gas and LPG

59.0%

53.1%

In accordance with the Spanish electricity legislation, to be considered a cogenerator and be able to register the plant in the Special Regime and, therefore, have the corresponding rights and obligations, including the right to sell the cogenerated electricity to the network, EEE coefficient needs to be higher than a minimum value. Table 5.2 shows the minimum values in Royal Decree 661/2007 [55]. As can be seen in the table, for installations with electric power P  1 MW, the required EEE min value is 10% lower. To verify compliance with EEE, local and totalizing measurement equipment must be installed for each of the parameters involved (E, F, H). With reference to the environmental aspects, the emissions reduction of CO2 is an environmental criterion that can be calculated directly from the fuel savings, when it is the same for cogeneration and conventional production. In the event that the fuels are different, the decrease will be DCO2 h cFE

E H þ cFH
cF F hE hH

(5.82)

where cFi is the CO2 emission per energy unit of the fuel used. The CertCHP software by AIGUASOL is available in Spain for qualifying the energy efficiency of buildings [56]. According to this software, in order to obtain the Energy Certification for a building, the electricity produced by cogeneration must be subtracted from the total fuel consumption of the cogeneration engine and in a similar way for the CO2 emitted. To conclude, we shall mention that in primary energy savings evaluation in trigeneration plants, Lozano 2010 [57] has conducted some very interesting analysis.

5.10.7

Cogeneration exergy parameters

Once the energy parameters that characterize cogeneration plants have been defined, we can now define similar parameters, but based on exergy. Obviously, we will now define the exergy electric efficiency of a cogeneration plant as the relationship between the electricity generated and the fuel exergy used, so that 4Ec ¼

E BF

(5.83)

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Likewise, the thermal exergy efficiency will be 4Hc ¼

BH BF

(5.84)

where BH is the exergy of the thermal energy produced, so that if hot water is produced it is the hot water exergy increase between the outgoing and the return flow, calculated in accordance with Equation (3.44) in Chapter 3. The sum of these two efficiencies will be the plant overall exergy efficiency, which is 4c ¼ 4Ec þ 4Hc ¼

E þ BH BF

(5.85)

This coefficient really measures the thermodynamic quality of the cogeneration installation. Its value would be unity in the perfect installation, and the better it is it will be closer to that limit value. However, the energy efficiencies in the previous Section do not provide this information and may even give rise to misleading interpretations. In fact, we may find an installation in which the thermal efficiency is high, and the plant overall efficiency is consequently high. However, since the thermal energy generated is of low quality (for example, water at 50 C), the installation might have many irreversibilities, that is, thermodynamically it is a bad installation. The exergy efficiency unequivocally provides us with this information. In Fig. 5.39 we show the energy efficiency and the corresponding exergy efficiency of a microgeneration unit based on a natural gas alternative internal combustion

Figure 5.39 Energy and exergy efficiency of a micromotor (obtained from tests in LCCE).

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engine, of 5.5 kW electrical power. The figure represents the variation of both efficiencies, as a function of the water inlet temperature of the cooling circuit, where T0 ¼ 290 K. As can be seen, for a range of temperatures between 30 and 70  C, the energy efficiency varies between 91.5% and 94%, while the exergy efficiency varies between 30% and 36%. In parallel with the previously defined energy indices, instead of considering the ES, we will now evaluate the ExS, Primary Exergy Saving, which is ExS ¼

E BH þ
BFc 4E 4H

(5.86)

and therefore the Primary Exergy Saving Index is ExSI ¼

ExS BF

(5.87)

In a similar way to the EEE, we can define an Equivalent Electrical Exergy Efficiency EExE according to the expression EExE ¼

E BF


BH 4H

(5.88)

and, therefore, EExE ¼

5.10.8

4Ec 4 1
Hc 4H

(5.89)

Feasibility of cogeneration in buildings

The starting point for any cogeneration project is the realization of a sufficiently rigorous feasibility study, in order to determine which type of installation is best adapted to the consumer, and whether or not this installation is economically profitable. This study usually consists of the following phases: • • • • •

Analysis of the current situation. Forecast of the electric and thermal demands. Energy evaluation. Economic study. Sensitivity analysis.

The potential for cogeneration in the building sector is, as we have said, very high and is a practically untapped sector. However, the profitability of these projects is usually less than that of industrial applications, so it is very important to define the best solution in each case. As we have also commented, the problem with cogeneration

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in buildings is that the thermal demand is very variable, it is difficult to determine with precision and, in addition, the equipment power required is small, much lower than that of the equipment in industrial applications. The high variability of the thermal demand is solved, at least in part, by the use of TES, which cover the gaps between production and demand, as well as operating the equipment at partial load. In Chapter 12 of this book, we will address the problem of optimal sizing for TES. The difficulties in the demand prediction can be solved by means of the use of control systems that program the production based on diverse external readings or by means of predictive algorithms. Finally, the demand small values can be solved by trying to centralize the production for several buildings and if this is not possible, resorting to modular solutions of micro-cogeneration. During the feasibility study we can encounter with three possible situations, Campos et al. 2011 [58]: • • •

That the building exists and there is complete information on consumption and demand (this would be the ideal situation). That the building is a project, in which case, it will be necessary to carry out simulations, through energy simulation software such as TRNSYS, EnergyPlus, etc. to evaluate the thermal demands that it will have when in use. That the building exists, but information about the demand is limited and must be completed with simulations and/or measurements in situ.

The data for the thermal demands (heating, DHW, cooling) can be presented either as a chronological demand curve (CDC) or as a monotonic demand curve (MDC). The CDC provides the demand values chronologically, while the MDC orders the demand values from highest to lowest and allows for the application of rapid sizing methods. Once the demands are known, the essential phase of the study starts, which is the plant design. In this phase, possible technologies (microturbines, micromotors, Stirling engines, etc.) are defined, as well as the plant configuration (number of units, TES, auxiliary equipment, etc.), and the operational strategy, that is, the way of operating and the interaction between the equipments. In the energy systems design, and in particular in the design of cogeneration and trigeneration systems for buildings in the residential-commercial sector, the following factors are involved, Ramos 2012 [59]: • • • • • •

The demand for electric and thermal energy by the consumer. The availability and guarantee of fuels supply, to ensure the functioning of the consumer equipment during its expected useful life. The tariffs and prices of fuels and electricity, applicable in the geographical region where the installation will be located. The commercial availability of different technologies. The choice of the technologies type is subject to the availability of the energy resources they consume. The investment cost of the equipment, taking into account that economies of scale favour investment in larger equipment. The technical characteristics and various parameters, such as its electrical efficiency, the recoverable heat sources temperature, heat/electricity ratio, etc. The electrical efficiency and the heat/electricity ratio determine the economic benefits that come from its operation.

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•

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The legal framework that regulates the cogeneration facilities operation in the electricity market. Each region or country has legal regulations that control the sale of surplus electricity in the market. In Spain, cogeneration facilities are subject to the obligations and advantages of the Special Regime for the production of electrical energy. Environmental legislation on emission limits applicable to facilities that consume fossil fuels should also be considered. The overall strategy of the operation, which is conditioned by: (1) the equipment technical characteristics; (2) the consumer demand profiles for heating, cooling and electricity; (3) fuel and electricity prices; and (4) the possibility of exchanging energy (buying and/or selling electricity) with the market.

The sizing of the cogeneration plant is carried out based on the thermal demand, keeping in mind that the cogeneration will work as a complement to the conventional thermal production method. In conventional design methods, the monotonic heat demand curve provides useful information for choosing the capacity to be installed and calculating the coverage rate, the utilization factor and the use degree of the cogenerated heat. The design must provide a high utilization factor of the installed capacity to favour its amortization. This factor is defined as the quotient between the real annual production and the theoretical maximum annual production; that is, the annual production at nominal load during the 8760 h of the year. It is also advisable to achieve a high coverage rate, which represents the fraction of the user thermal demand served by the cogeneration plant. A very widespread simple method is one that maximizes the coverage rate, that is, the equipment thermal power will be that which maximizes the rectangle area within the MDC, see Fig. 5.40. Unfortunately, in systems with variable demand, such as in buildings, it is not possible to simultaneously maximize the coverage rate and the utilization factor, since when one of them is improved, the other is adversely affected, which makes it difficult to find the optimal design.

Figure 5.40 Monotonic demand curve and maximum coverage rate.

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431

In addition to these conventional design methods, there are other more sophisticated methods, based on mathematical optimization such as integer linear programming (ILP) and others. As we will develop in Chapter 12 of this book, a methodology in the process of synthesis and design of cogeneration systems is as follows, Nemhauser 1999 [60]: •

•

•

In the first place, an energy superstructure is proposed consisting of technologies (candidates) that will compete with each other on the technical (energy benefits) and economic (investment and operation costs) level. From this set of technologies, the combination is chosen whose total cost over the installation life is minimal. In this step, the approximate capacity to install each technology is also determined. Next, the size (rated power) and the amount of equipment to be installed from each selected technology is defined. In this stage, for example, decisions are made on splitting the installed power between several units or installing a single unit. The equipment installed, if there are several units, can be of different models or the same model. Again, from the set of alternatives (equipment configurations) one is selected, the total cost of which throughout its life is minimum. Finally, once the equipment configuration has been determined, feasible operating modes are formulated for the cogeneration system, and from among them, one is chosen that has a minimum operating cost. The optimal operation program is solved for each time interval with which the annual operation is described.

To evaluate the operation cost, we need to bear in mind the fuel cost for the cogeneration plant and the complementary system, income from cogenerated electricity sale, taking into account the complement for efficiency, complement for reactive energy, etc., as well as the maintenance costs of the new plant. Likewise, insurance and financing costs must be taken into account. Once the investment and the expected economic savings have been evaluated, an economic study should be done. For this purpose, the cash flows generated during the plant useful life are usually calculated (approximately 15e20 years). From these cash flows, the profitability indices most commonly used are obtained, such as the internal rate of return (IRR), the net present value (NPV) or the payback period (PB). As a final stage, it is usual to carry out a sensitivity analysis. This type of analysis is used to identify the risks of a project since it identifies the sensitivity degree of the project economy compared to various parameters changes. Usually, the worst case and best case scenarios are defined; in the first case, the parameters usually vary in a very pessimistic context and second, under extremely optimistic assumptions. Both evaluations open a range of possibilities within which the project will be developed. Readers interested in feasibility studies of cogeneration plants can consult Sala 1994 [61].

5.10.9 Examples Example E.5.17.

In a cogeneration facility of a hospital, a gas turbine of 3.2 MW of electrical power consumes 9 MW (referred to the LHV) of natural gas. From the turbine comes a combustion gases flow of 9.2 kg/s at 550 C which are used in a heat recovery boiler until their temperature drops to 115 C, generating a mass flow rate of 1.52 kg/s

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of superheated steam at 6 bar and 200 C, from a water at 60 C. If the ambient temperature is 10 C and assuming that the average specific heat of these combustion gases is cp ¼ 1.02 kJ/kg$K, determine (a) (b) (c) (d)

The energy efficiency of the waste heat recovery boiler and its exergy efficiency. The gas turbine electrical and total efficiencies and the installation total efficiency. The gas turbine exergy efficiency and the installation total exergy efficiency, The irreversibilities in the gas turbine.

Solution (a) From the superheated steam tables, we get that hv ¼ 2850.6 kJ/kg. Assuming a specific heat cp,w ¼ 4.18kJ/(kg$K) for water, we get that the recovery boiler efficiency is

hRB ¼



m_ v ðhv
hw Þ

m_ g hgð550 CÞ
hgð115 CÞ

 ¼ 0:97

This means that 3% of the energy released by the gases in the boiler is not used to generate steam, but is heat lost. From the First Law point of view, this is the boiler efficiency. Now, since the gases enthalpy leaving the boiler is not used and is, therefore, a loss flow (although in reality they are not generated by the boiler), we could define its efficiency as hRB ¼

m_ v ðhv
hw Þ ¼ 0:78 m_ g hgð550 CÞ

To determine the exergy efficiency, we first calculate the exergy change of the water and the gases in the boiler. With sv ¼ 6.968 kJ/(kg$K) and sw ¼ 0.680 kJ/(kg$K), we have m_ v ðbv
bw Þ ¼ m_ v ½hv
hw
T0 ðsv
sw Þ ¼ 1246:8 kW Since Tg,in ¼ 823 K and Tg,out ¼ 388 K the gases exergy change is
   Tg;in m_ g bgð550 CÞ
bgð115 CÞ ¼ m_ g cp;g Tg;in
Tg;out
T0 ln ¼ 2:0851 kW Tg;out The boiler exergy efficiency is then 4RB ¼



m_ v ðbv
bw Þ

m_ g bgð550 CÞ
bgð115 CÞ

 ¼ 0:60ð60%Þ

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This value means that of all the gases exergy change in the boiler, only 60% goes to the water flow to produce steam. The rest (40%) is exergy destruction due mainly to thermal irreversibilities in the heat transfer and the exergy of the heat lost by the boiler surface. In a manner analogous to what we have said concerning energy, assuming that the gases exergy that come out of the boiler is lost exergy, we could define the efficiency according to 4RB ¼

m_ v ðbv
bw Þ ¼ 0:56ð56%Þ m_ g bgð550 CÞ

(b) The gas turbine electrical efficiency is

he;TG ¼

E_ ¼ 35:5 % F_

and the gas turbine total energy efficiency hT;TG ¼

E_ þ H_ g ¼ 91:8 % F_

The whole installation total energy efficiency is hT ¼

E_ þ m_ v ðhv
hw Þ ¼ 79:4 % F_

(c) Bearing in mind that for the natural gas Bch ¼ 1.04 LHV, the gas turbine electric exergy efficiency is

4e;TG ¼

E_ ¼ 34:2% B_ F

and the gas turbine total exergy efficiency is 4TG ¼

E_ þ m_ g bgð550 CÞ ¼ 58:0% B_ F

Since the gas turbine is the equipment that generates the gases that drive the boiler, we could assign the exergy lost by the exhaust gases of the recovery boiler to the turbine itself. Therefore, taking this into account, the gas turbine total exergy efficiency would be

4TG ¼

  E_ þ m_ g bgð550 CÞ
bgð115 CÞ B_ F

¼ 56:5%

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Exergy Analysis and Thermoeconomics of Buildings

The installation exergy efficiency is 4T ¼

E_ þ m_ v ðbv
bw Þ ¼ 47:5% B_ F

(d) By applying the exergy balance in the gas turbine, we have

B_ F ¼ E_ þ B_ gð550 CÞ þ I_TG /I_TG ¼ 3:93 MW which represents 42% of the fuel consumed exergy. Example E.5.18. There is a micro-cogeneration unit consisting of a natural gas internal combustion engine, with heat recovery from the cooling circuit of the casings and gases, a 750-L intermediate storage tank and a heat exchanger to recover the combustion gases enthalpy. The motor drives a water-cooled asynchronous alternator, with a complete electronic regulation apparatus that ensures its perfect operation. The unit produces 5.5 kW electrical power and 15 kW thermal power in the form of hot water that enters the unit at 70 C and leaves at 80 C, with a total efficiency of 95% (referred to the LHV). Assuming that the unit operates 7000 h per year under these conditions and assuming an average ambient temperature of 15 C, determine

a) The percentage of primary energy saving (PES). b) The total irreversibilities in 1 year of operation. c) The energy and exergy efficiency of the unit.

Solution (a) According to Eq. (5.78), for the PES calculation, we need the reference values for the separate production of electricity and thermal energy. According to Commission Decision 21/12/2006 for natural gas fuel, the reference value for the separate production of electricity is RefEh ¼ 52.5%. This basic value is corrected according to the site climatic conditions of the plant and the voltage level of its connection. In our case, the plant is in Biscay (Basque Country), so that the average annual temperature in the range 15  2 C does not need to be corrected. As for the correction factor by voltage level, as it is in the range 0.4e50 kV, the correction factor for self-consumption is 0.925.

On the other hand, in the case of natural gas fuel and with hot water production, the reference value for the separate production of thermal energy is 90%. In accordance with the above, applying Eq. (5.78), we have 2 3 # " 1 1 4 5 PES ¼ 1
100 100 ¼ 1
CHP Hh CHP Eh 15 5:5 þ þ Ref Hh Ref Eh 0:9 0:525 : 0:925 ¼ 3:6% (b) Undertaking an exergy balance in the equipment throughout the year gives



 B_ F
E_
B_ H 7000 ¼ I_

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435

We shall now calculate B_ H , for which we need to know the hot water mass flow rate. Since 15 ¼ m_ w cw ðTout
Tin Þ we have m_ w ¼ 0:36 kg=s, so that B_ H ¼ 0:36$ 4:18ð10  ln363=353Þ ¼ 2:9 kW. From the unit total efficiency we get that 
288 F_ ¼ E_ þ H_ hT ¼ 21:6 kW. Therefore, the fuel exergy consumed is B_ F ¼ 22:4 kW. Returning to the exergy balance equation, we have MWh I_ ¼ 98:28 year (c) The energy efficiency is

h¼

E_ þ H_ ¼ 94:9% F_

However, the exergy efficiency is 4¼

E_ þ B_ H ¼ 37:5 % B_ F

Thus, although apparently, this is a unit in which there are only losses of 5.1%, in reality, 62.5% of the energy contributed (weighted with its quality factor) is not used, being destroyed in the irreversibilities of combustion and heat transfer, or appearing in the flows that are not used, such as the gases that finally escape to the atmosphere and the heat transferred to the environment by the engine and alternator surfaces. Example E.5.19.

A micro-generation unit based on a natural gas alternative internal combustion engine, has a constant electrical power of 5.5 kW. With data collected in a test, the attached Table E.5.7 has been prepared, in which the values of the unit total efficiency are shown, based on the water inlet temperature of the cooling circuit, with the outlet temperature being 74 C and the mass flow rate constant in all cases. Table E.5.7 Total efficiency values. Water inlet T (8C)

hT

30

91.6

40

91.7

50

91.8

60

92.1

70

94.2

Knowing that when the water inlet temperature is 60 C and the ambient temperature is 5 C, the electrical efficiency is 31%, determine

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Exergy Analysis and Thermoeconomics of Buildings

(a) The water mass flow rate of the cooling circuit. (b) The irreversibilities in the unit for different water inlet temperatures.

Solution (a) When the inlet temperature is 60 C, the fuel consumed is

E_ F_ ¼ ¼ 17:74 kW he Next, we calculate the water mass flow rate of the refrigeration circuit hT ¼

E_ þ m_ w cw ðTout
Tin Þ hT F_
E_ kg / m_ w ¼ ¼ 0:18 cw ðTout
Tin Þ s F_

(b) From the exergy balance in the apparatus, we have

  I_ ¼ B_ F
E_ þ B_ where B_ ¼ m_ w cw ðTout
Tin
T0 lnTout =Tin Þ. For different values of the water inlet _ Through the temperature, since the outlet temperature is fixed, we shall calculate B. values of the total efficiency, we can calculate the fuel consumption and, therefore, B_ F and then the irreversibilities, resulting in Table E.5.8 below. Table E.5.8 Results for different temperature values. T (8C)

hT(%)

BF(kW)

B (kW)

I (kW)

I/BF (%)

30

91.6

43.8

17.6

20.7

47.2

40

91.7

35.2

14.9

14.8

42

50

91.8

26.7

11.4

9.8

36.6

60

92.1

18.1

7.1

5.5

30.1

70

94.2

9.4

2.2

1.7

18.3

We can see how, as the return temperature increases, the equipment irreversibilities decrease and the ratio between the irreversibilities and the exergy contributed decreases as well, that is, when the return temperature increases, the unit exergy efficiency increases.

5.10.10 Some final comments on cogeneration The buildings sector is a large consumer of materials and energy resources, and its operation demands final energy, mainly from electricity and thermal energy at low temperatures. These are precisely CHP products, so they are very suitable for this sector.

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The conclusions of several European studies highlight that only a fraction of the cogeneration potential in the EU’s residential-commercial sector has been developed. On the other hand, as we have said, a review of the data on the state of cogeneration in Spain reveals that it is not widespread in the service sector and is practically nonexistent in the residential sector. However, cogeneration has high energy and exergy efficiency, with consequently lower environmental impact. In addition to these thermodynamic aspects, there are other important arguments to favour the cogeneration participation in the supply of energy services in buildings and housing developments in Spain, such as the availability of the fuels used (mainly natural gas), the demand for its products (electricity, heating, DHW and refrigeration) and the current low penetration on the market. Therefore, an adequate economic environment and corresponding political support are required for cogeneration to takeoff in the residential sector. A brief description of district heating technological characteristics has been undertaken. These types of systems are popular in countries of Central, Eastern and Northern Europe, generally linked to thermoelectric power plants, but they have also demonstrated their energy, economic and environmental value in countries such as China or the United States. In the case of Spain, the installed capacity is still small, with biomass being the main fuel for this type of installation and natural gas in second place. Today, there are already cogeneration technologies that are suitably developed for their application in the domestic sector. We have reviewed the most relevant technological characteristics of internal combustion micromotors, which are usually supplied as assembled units, with all the heat sources integrated, so that the available thermal energy is delivered in the form of a hot water single stream. We have seen that gas microturbines incorporate a regenerator in the cycle, which allows them to achieve performances close to those of their larger cousins. Gas microturbines are highly reliable and efficient for the production of electricity and heat in cogeneration mode, and also, for the air conditioning of buildings in trigeneration mode. With regards to the Stirling engine, we have highlighted the versatility of the energy sources that can be used, as it is an external combustion engine, as well as its suitability for the domestic sector, due to its electrical and thermal ratio. Regarding fuel cells, we have highlighted their excellent energy efficiency, as they are not limited by the Carnot factor and the low level of environmental contamination, as there are no combustion reactions. They are also characterized by their modular nature, flexibility of operation, the possibility of using various fuels, silent operation, reliability and simplicity of installation. However, currently, they are not competitive, mainly due to their high price; so we will have to wait some time for their large-scale incorporation into the cogeneration market. We will see in the next chapter that cold generation for air conditioning in trigeneration plants allows for an extension of the operation period of cogeneration equipment, as the demand for cooling and heating do not coincide. Therefore, the conversion of heat into cold, done by absorption or through adsorption machines, can be an excellent solution for cogeneration in buildings. The design process of a cogeneration system includes the selection of the technology type to be used, the size and amount of equipment to be installed and their

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Exergy Analysis and Thermoeconomics of Buildings

operating strategy. This process is conditioned by various factors, such as the demand for energy services, the investment cost of equipment, its energy benefits, etc., as we have discussed in this chapter. Even though it is a complex problem, in practice, analytical procedures have been proposed and used to determine the most relevant characteristics of the systems to be installed. In this chapter, we have shown the method based on the use of the monotonic demand curve. Likewise, reference has been made to more sophisticated mathematical methods that use ILP. The optimization of these systems is carried out by means of adequate computer tools, from their conception (structure determination and equipment configuration) to the optimal real-time control of their operation. Any feasibility study ends with a corresponding economic analysis, so that, based on the expected cash flows, the values of the most common profitability indexes are obtained and the study is concluded, generally, with a sensitivity analysis using the most significant parameters.

5.11 5.11.1

Thermal energy storage systems (TES) Preliminary considerations

A TES stores energy temporarily, for later use. The TES is independent of the equipment that has generated the thermal energy, as well as the fuel used. There are, basically, three types of storage systems: sensitive, latent and thermochemical. In addition, depending on the time scale, we can talk about short-term and long-term TES: the first store energy for hours or days, while long-term or seasonal systems store energy for weeks or months. Sensitive energy TES is based on the change of internal energy that a substance experiences when its temperature varies. The amount of energy that it can store depends on the mass of the material, its specific thermal capacity and the temperature difference between the initial and final state. There is a great variety of sensitive energy TES according to the type of deposit used, which may be tanks, ponds, underground aquifers, the structure of the building itself, so-called thermoactive enclosures, etc. The material used can be solid (concrete, ceramics, the ground itself) or liquid, mainly, in this case, water. Practically, all DHW production facilities are provided with a tank that accumulates hot water. This type of TES is characterized as a robust and reliable technology, but it does have an important disadvantage: the used materials, usually have small specific heats, and consequently, important temperature variations are needed to store significant amounts of energy, Dincer and Rosen 2011 [62]. Latent thermal energy storage systems are based on the internal energy variation of the system when a phase change occurs. The TES absorbs or releases heat when a liquid-liquid, solid-liquid or liquid-gas phase change occurs or vice versa. The most commonly used systems in buildings are based on solid-liquid phase changes. They are known as PCM (Phase Change Materials) TES, with water/ice systems, currently being the most used. There is, currently, an international line of research dedicated to finding new materials that can be used as PCM, see Fig. 5.41.

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439

Figure 5.41 Prototype of TES being tested in the LCCE of Vitoria (Basque Country).

Among the new materials used as PCM are aqueous solutions of salts, fatty acids, hydrated salts, eutectic mixtures, alcohols, etc. Mehling and Cabeza2008 [63]. The main characteristics that differentiate the behaviour of these materials are storage capacity, thermal conductivity, incongruent fusion, subcooling, hysteresis, chemical stability and compatibility with other materials, flammability and fire behaviour. Consult the review carried out by Zalba et al. 2003 [64] or the more recent review by Sharma et al. 2009 [65]. A problem that currently arises in the face of its application is the price. PCM is considered a very promising technology to be applied in buildings for various reasons: • • •

They have a high energy storage density, which reduces the volume occupied by the storage system. This is particularly interesting in buildings, as there is usually little space available. The storage is carried out at a constant temperature, which improves the operation mode of the equipment and reduces thermal losses. TES tanks can take different shapes and sizes, depending on the requirements. On the other hand, in DHW storage tanks, the stratification requires a certain geometry with a certain height.

Thermochemical storage systems are based on the storage and release of energy through reversible chemical reactions. The energy is stored if there is an endothermic chemical reaction and if it is done in the opposite direction, releasing energy, it will be exothermic. Thermochemical energy storage has as its main advantages: its high storage density, above that of sensitive or latent storage, and small losses, due to the possibility of storing at temperatures close to the ambient temperature, Gil et al. 2010 [66]. The biggest drawbacks are the low loading and unloading speeds and the difficulty of finding suitable chemical reactions. It is, currently, in the development phase and cannot be considered as a commercial alternative for application in buildings. The applications for TES can be very varied: solar energy storage during the day for heating in the night hours; seasonal storage of summer heat for use in winter, or on the contrary, cold storage in winter for cooling in summer; its integration into cogeneration

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Exergy Analysis and Thermoeconomics of Buildings

plants, which allows greater flexibility in its mode of operation, etc. Whether for heating, DHW supply or cooling, TES are used when the demand for energy does not coincide with its production in the most favourable economic conditions. Thus, TES can be used in a wide variety of applications and, as we have said, they are designed to operate cyclically, usually in daily cycles but also in seasonal cycles. As indicated by Dincer and Rosen 2011 [67] TES can perform some of the following functions •

•

• • • •

Reduce installed power. Since heating or cooling demands (as well as electricity demand) are variable over time, when demand is low, excess capacity can be stored in a TES to be used when demand increases. This means a lower power can be installed and equipment can have a better load factor. Give greater flexibility to cogeneration plants. Due to the demand variability in a building, one way to adjust the demand to production is through TES. This allows an increase in the operation hours of the cogeneration installation and, consequently, an improvement in its profitability. Move energy purchase to periods of lower cost. A TES user can change the times when they buy energy to times when the cost is lower. Thus, by using electricity in off-peak hours, cold which is produced can be stored and used during the daytime peak hours. Improve the use of renewable energy sources, given that the availability of such sources, such as solar energy, wind power, etc. is intermittent. In addition, TES can be incorporated in both active and passive air conditioning. Increase the reliability of the energy supply system. Integrate them with other functions. So in places where, for security reasons, it is necessary to store fire water, TES can be integrated into a common tank.

5.11.2

Conventional energy analysis

We shall consider a hot water storage tank like the one in Fig. 5.42. The TES is charged by means of a heat exchanger, stores the thermal energy for a period, and this is finally discharged by the same or another heat exchanger. In Fig. 5.42, the three operation phases are shown, and we are going to assume that thermal energy is stored above the ambient temperature and that, at the end of the cycle, the final and initial state of the TES is the same. Performing the energy balance in an instant during the loading period we have dU _ a
hb Þ
Q_ l;1 ¼ mðh dt

Figure 5.42 The three stages in a TES A) load (B) storage (C) discharge.

(5.90)

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441

where Q_ l;1 is the rate of heat given by the TES to the environment during loading. Integrating the above equation for the entire loading period, we have DU1 ¼ Ha
Hb
Ql;1

(5.91)

We can define an energy efficiency for this charging period according to h1 ¼

Ql;1 DU1 ¼1
Ha
Hb Ha
Hb

(5.92)

According to this expression, for an adiabatic TES, obviously, the value of this coefficient is unity. In a similar way for the storage period, the energy balance is
DU2 ¼ Ql;2

(5.93)

We can define the energy efficiency during the storage period as the relationship between the energy accumulated during the loading period plus the energy lost in the storage period with respect to the energy accumulated in the loading, which is h2 ¼

Ql;2 DU1 þ DU2 ¼1
DU1 DU1

(5.94)

An energy balance for the discharging period allows us to write
DU3 ¼ Hd
Hc þ Ql;3

(5.95)

where Hd, Hc are the discharge fluid enthalpy at the outlet and inlet of the TES respectively. Energy efficiency during the discharge period can be defined as h3 ¼

Hd
Hc DU1 þ DU2

(5.96)

and taking into account the energy balance in the storage period, this coefficient is also h3 ¼

Hd
Hc DU1
Ql;2

(5.97)

Finally, considering the set of the three periods, the energy balance gives us 2 ðHa
Hb Þ
4ðHc
Hd Þ þ

3 X j¼1

3 Ql;j 5 ¼ DU

(5.98)

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Exergy Analysis and Thermoeconomics of Buildings

where DU represents the deposit energy change in all three periods, which in the event 3 P Ql;j is the total heat lost, that that the initial and final states coincide will be zero and j¼1

is, the heats lost sum in each of the phases. The overall energy efficiency is, therefore, P3 Hd
Hc j¼1 Ql;j h¼ ¼1
Ha
Hb Ha
Hb

(5.99)

It is easy to verify that the overall energy balance is the sum of the energy balances of each sub-process of loading, storage and discharge. Likewise, the overall efficiency is the product of the other three efficiencies. h¼

3 Y j¼1

hj

(5.100)

It is very common to assume that during the load all the energy transferred by the loading fluid goes to the TES and similarly, during the discharge, the energy transferred by the TES goes to the discharge fluid. These assumptions are reasonable considering that, in general, these heats lost during loading and unloading are much smaller than that lost by the TES during the storage period.

5.11.3

Exergy analysis

As indicated by Dincer and Rosen 2013 [67] there is no single way to compare the efficiency of one TES with another operating in different conditions. Traditionally, a coefficient such as energy efficiency has been used, which, as we have seen, is defined as the ratio between the recovered energy and the total energy supplied to the TES. However, this coefficient is not very suitable, since it does not take into account essential aspects of the TES, such as, for example, if the energy obtained is close to the situation of the TES ideal behaviour, what the length of storage is, or what the value of the temperatures supplied to and obtained from the TES is in relation to the ambient temperature. With conventional energy analysis, all losses are attributed to the heat fluxes that cross the boundaries of the TES (heat outputs or heat inputs). Therefore, the irreversibilities due to internal mixtures in the tank of fluid portions at different temperatures do not appear explicitly. However, an exergy analysis can quantify and distinguish between exergy losses associated with heat flux exchanges (external irreversibilities) and exergy destruction due to the mixing of fluid portions at different temperatures. Therefore, the beneficial stratification effects are valued much more clearly using exergy than with energy. Exergy reflects the heat flux temperature and the heat quality degradation due to the temperature loss. For this reason, exergy analysis is applied in the same way to TES

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443

that store energy above or below the ambient temperature, since the exergy associated with that energy is always positive. However, conventional energy analysis is more difficult to apply, since the energy efficiency definition must be modified from when heat is stored to when cold is stored. From the exergy analysis, the exergy efficiency is defined, which is an index that clearly reflects how far real behaviour moves away from the ideal situation. In addition, as we have said, exergy analysis allows us to identify much more clearly the magnitudes, causes and locations of the losses than traditional analysis. Let us again consider the three stages of the cycle, loading, storage and discharging. By performing the exergy balance per unit of time corresponding to the loading period, we have
 dB T0 _ _ a
bb Þ
1
¼ mðb Ql;1
D_ 1 (5.101) dt Td where dB/dt represents the rate of the tank exergy change, that is, for a tank of constant volume dB dU dS ¼
T0 dt dt dt

(5.102)

with the load flow exergy at the entrance and exit of the heat exchanger being ba,bb and D_ 1 representing the rate of internal exergy destruction due to the irreversibilities in the heat transfer between the load fluid and the tank fluid, as well as due to the mixing of the tank parts that are at higher temperatures with those that are at lower temperatures. Integrating the above equation for the entire loading period, we have DB1 ¼ Ba
Bb
BQ;l1
D1

(5.103)

where D1 represents the internal irreversibilities and BQ,l1 the exergy transferred by heat that is lost through the tank surface. Since the product in the loading process is the tank exergy increase and the resource used is the exergy reduction of the loading fluid, the loading process exergy efficiency is defined as 41 ¼

DB1 I1 ¼1
Ba
Bb Ba
Bb

(5.104)

where I1¼BQ,l1þD1. As can be seen, although the loading process was adiabatic, exergy efficiency is not unity, due to internal irreversibilities. This aspect does not include energy efficiency as we have already mentioned. Similarly, the exergy balance during the storage period means we can write the equation

DB2 ¼

 T0 1
Ql;2 þ D2 ¼ I2 Td

(5.105)

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Exergy Analysis and Thermoeconomics of Buildings

The exergy efficiency for the storage period can be written 42 ¼

DB1
DB2 DB1

(5.106)

and according to the exergy balance equation, this expression is also 42 ¼ 1


I2 DB1

(5.107)

This efficiency expresses the fraction of the exergy accumulated during the load that is maintained in the tank at the end of the storage period. Considering now the discharge period, from the exergy balance we have
 T0
DB3 ¼ Bd
Bc þ 1
Ql;3 þ D3 Td

(5.108)

allowing us to define the exergy efficiency of this period as the relation between the exergy discharged and the exergy accumulated in the TES during the loading and storage, which is 43 ¼

Bd
Bc DB1 þ DB2

(5.109)

which, according to the exergy balance in the storage period, can also be written 43 ¼

Bd
Bc DB1
I2

(5.110)

Performing an overall exergy balance for the whole of the three stages, we have Ba
Bb ¼ ðBd
Bc Þ þ

3
X i¼1

1


 3 X T0 Di Ql;i þ Td;i 1¼1

(5.111)

so that, similarly to what happened in the energy balance, the exergy balance for the overall process is the sum of the exergy balances for each of the three phases. So, the overall exergy efficiency is
P3

4¼

Ii Bd
Bc ¼ 1
i¼1 ¼ 1
Ba
Bb Ba
Bb

1


 P T0 Ql;2 þ 3i¼1 Di Td Ba
Bb

(5.112)

Exergy analysis of thermal facilities equipment in buildings (I)

445

since, as we have said, heat losses are usually not considered in the loading and discharging periods. Evidently, this efficiency is the product of each stage efficiency, which is 4¼

3 Y i¼1

4i

(5.113)

We have seen that energy efficiencies only take into account the losses associated with heat fluxes, but ignore those associated with the temperature degradation. However, the exergy efficiencies weight the heat fluxes as a function of the temperature, so that they take into account the temperature at which the thermal energy is recovered compared to that when it is supplied to the TES. Therefore, the energy efficiencies tend to be optimistic, so that their values are significantly higher than those of the exergy efficiencies, except when the temperature degradation is very small. The study presented in Dincer and Rosen 2013 [67] with respect to the increase in exergy storage capacity in a stratified deposit is very interesting. For this, they consider different temperature profiles with different stratification degrees. In this work, the exergy analysis of a TES is also performed to store cold, as well as another one for seasonal storage. Also very interesting is the work of Campos et al. 2011 [68] in which they consider three different models of stratified tanks. In this paper, it is shown that the ideal stratification model does not satisfy the Second Law since exergy efficiencies are greater than unity. It also shows that the exergy destruction, direct and indirect, has great importance in the viability of a project that incorporates a TES, particularly in the case of cogeneration facilities, in which the electricity cost transferred to the grid is linked to efficiency.

5.11.4 Examples Example E.5.20.

A hot water tank of 3,000 L capacity is in an environment where the temperature is 20 C. The tank is loaded by means of a submerged coil, where a water flow of 5 L/s enters the coil at 75 C and leaves at 68 C for 40 min, such that the water in the tank reaches a temperature of 61 C. The tank stores the energy for a period of 12 h, during which it loses a part of the initially stored energy. The discharge is carried out for 45 min through the same coil, through a water flow also of 5 L/s that enters the coil at 24 C and leaves at 30 C, so that at the end of the cycle, the tank regains its initial state. Determine (a) (b) (c) (d)

The The The The

heat losses during storage and the tank temperature at the end of that stage. energy efficiency of each stage and the overall efficiency of the three stages. loading exergy efficiency. overall exergy efficiency.

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Exergy Analysis and Thermoeconomics of Buildings

Solution (a) Let us assume negligible heat losses during loading and discharging. The energy supplied during loading is

m_ w cw ðTin
Tout ÞDt ¼ 5$4:18ð75
68Þ40$60 ¼ 351; 120 kJ The energy discharged is m_ w cw ðTout
Tin ÞDt ¼ 338; 580 kJ Accordingly, the heat lost in storage is 12,540 kJ, which represents 3.6%. From the energy balance, we obtain the temperature at the end of the storage stage   12; 540 ¼ 60 C DU2 ¼ Md cw Tf 2;d
Ti2;d /Tf 2;d ¼ 61 C 3000$4:18 (b) The energy efficiency in the loading stage is 100% since there is no heat loss, the same as in the discharge stage. The energy efficiency in the storage stage is

h2 ¼

DU1 þ DU2 12; 540 ¼ 96:4% ¼1
351; 120 DU1

and therefore the overall energy efficiency of the three stages is h¼

3 Y j¼1

hj ¼ 96:4%

(c) To calculate the loading exergy efficiency, we first determine the initial tank temperature, before loading. Since the deposit mass is Md ¼ 3,000 kg (assuming 9w ¼ 1 kg/l) the tank temperature change while loading is

Md cw DTd ¼ m_ w cw ðTin
Tout ÞDt /DTd ¼ 28 K so the initial tank temperature is 61e28 ¼ 33  C. The tank exergy change is
 Tf 1;d DB1 ¼ Md cw DTd
T0 ln ¼ 29; 420 kJ Ti1;d Since the duration of the loading period is Dt ¼ 2400 s, the exergy transferred by the loading circuit is
 Tin Dt ¼ 52; 479 kJ Ba
Bb ¼ m_ w cw Tin
Tout
T0 ln Tout

Exergy analysis of thermal facilities equipment in buildings (I)

447

so that the loading exergy efficiency is 41 ¼

DB1 ¼ 56:0% Ba
Bb

(d) To calculate the global exergy efficiency we calculate the storage and discharge stages In the storage stage, the tank cools from 61 C to 60 C, so that the exergy loss is


 Tf 2;d DB2 ¼ Md cw DTd
T0 ln ¼
1523 kJ Ti2;d so the storage exergy efficiency is 42 ¼

DB1 þ DB2 ¼ 94:8% DB1

The exergy transferred to the water circuit in the discharge, which lasts Dt ¼ 2700 s, is
 Tout Bd
Bc ¼ m_ w cw Tout
Tin
T0 ln Dt ¼ 7889 kJ Tin so that the discharging exergy efficiency is 43 ¼

Bd
Bc ¼ 28:3% DB1 þ DB2

Consequently, the overall exergy efficiency is 4¼

3 Bd
Bc Y ¼ 4 ¼ 15:0% Ba
Bb i¼1 i

We see that in the loading and discharging, the energy efficiencies are 100% (there are no heat losses) and that they are nevertheless highly irreversible processes, due to the irreversible heat transfer. In the storage, as it has heat losses, its efficiency is less than 100% (96.4%), and it is nevertheless the stage in which the irreversibilities are fewer since these are due exclusively to the heat exergy that is lost. Finally, we shall indicate that compared to an overall efficiency of 96.4% (only 3.6% losses), the reality is that the efficiency is 15%, which means that 85% of the energy quality is destroyed and, therefore, definitely lost. We see how the conclusions that might be obtained when using only the First Law with regards to this storage system are deeply flawed. Example E.5.21.

In order to reduce the electric power of cooling machines and shift the consumption to cheaper tariff horas, the air conditioning installation of an office

448

Exergy Analysis and Thermoeconomics of Buildings

building has an ice TES. At the beginning of the daily cycle, the TES is completely discharged, so that water is in the liquid state at a temperature of 0 C. When loading, which is carried out completely between 00:00 and 07:00, a mass flow rate of 2.6 kg/s of water/glycol solution at 30% circulates between the tanks containing the storage agent (ice balls) entering the TES at
6 C and leaving at
3 C. Storage takes place during the morning hours, between 07:00 and 13:00, in which a heat flux of 1.2 kW enters the TES, melting part of the ice at the temperature of 0 C. The discharge is carried out from 13:00 by the same mass flow rate, also water/glycol, which now enters at 12 C and leaves at 6 C, thus feeding the consumption circuit through a plate heat exchanger. If the TES state at the end of the daily cycle is the same as the initial state and assuming that there is no heat loss in the loading or discharging, determine (a) (b) (c) (d)

Energy efficiency in the loading and overall efficiency of the storage cycle. The exergy contributed in the loading stage and its exergy efficiency. The storage stage exergy efficiency. The total irreversibilities (destruction and losses) in the storage cycle.

Solution (a) The cold transferred in the loading process is

m_ w
gly cw
gly ðTout
Tin ÞDt ¼ 2:6$3:73ð
3
ð
6ÞÞ7$3600 ¼ 733:17 MJ where for water/glycol at 30% we have used the value cw
gly ¼ 3.73 kJ/kg$K. Once fully loaded, all the water in the liquid phase becomes ice, also at 0 C. The water mass contained in the TES is Md Dhfus ¼ m_ w
gly cw
gly ðTout
Tin ÞDt/Md ¼

733:17 ¼ 2195 kg 334  10
3

where Dhfus ¼ 334 kJ/kg is the ice melting enthalpy at 0 C. Therefore Ha
Hb ¼ DU1 ¼
733.17 MJ. Since there are no ambient heat inputs in the loading, its energy efficiency is h1 ¼ 100%. During storage there are heat inputs of 1.2 kW, so the total heat entering is DU2 ¼ 1.2  6  3.6 ¼ 25.92 MJ. Therefore, the efficiency in the storage stage is h2 ¼

DU1 þ DU2 733:17
25:92 ¼ 96:5% ¼ 733:17 DU1

Loading the TES means extracting heat, and in the storage there is heat input. Finally, the discharge stage is also adiabatic, so that h3 ¼ 100%. In short, the overall efficiency is h ¼ h1 :h2 :h3 ¼ 96:5%

Exergy analysis of thermal facilities equipment in buildings (I)

449

(b) Even if its energy decreases, in the loading stage, exergy is added to the TES, since it is being kept away from equilibrium with the environment. The exergy provided is the decrease in the water/glycol exergy between inlet and outlet, which is


 Tin Ba
Bb ¼ m_ w
gly cw
gly Tin
Tout
T0 ln Dt ¼ 66; 908 kJ Tout The water/glycol receives heat from the TES, and when it is below the ambient temperature the heat flux and exergy have the opposite direction so that the TES when loading is supplied with exergy of 66,908 kJ. Taking into account that the fusion enthalpy at 0 C is Dhfus ¼ 334 kJ/kg, from that exergy the part that arrives at the TES is
 T0 DB1 ¼
Md Dhfus 1
¼ 53; 709 kJ Tc Therefore, the loading exergy efficiency is 41 ¼

DB1 ¼ 80:27% Ba
Bb

(c) Since in the storage q_l;2 ¼ 1:2 kW with Dt ¼ 21,600 s and Ql;2 ¼ q_l;2 Dt the exergy losses are




 T0 DB2 ¼ 1
Ql;2 ¼ 1899 kJ Tc

The storage exergy efficiency is 42 ¼

DB1
DB2 ¼ 96:46% DB1

(d) During the discharge, the water flow temperature is decreased from 12 to 6 C, both below the ambient temperature. However, the enthalpy decrease between input and output implies an increase in exergy. The discharge time is

DU1 þ DU2 ¼ m_ w
gly cw
gly ðTin
Tout ÞDt/Dt ¼

733; 17
25; 92 2:6$3:73ð12
6Þ

¼ 3 h21 min Thus, the exergy yielded in the discharge stage is
 Tout Bd
Bc ¼ m_ w
gly cw
gly Tout
Tin
T0 ln Dt ¼ 27; 400 kJ Tin

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Exergy Analysis and Thermoeconomics of Buildings

Performing an exergy balance in the overall process, we have Ba
Bb ¼ ðBd
Bc Þ þ

3 X i¼1

Ii

/

3 X i¼1

Ii ¼ 39; 508 kJ.

Therefore, the overall exergy efficiency is P3 4¼1


i¼1 Ii

Ba
Bb

¼ 40:9%

With this efficiency, we could calculate the discharge efficiency, since 43 ¼

4 ¼ 52:8% 41 42

Effectively this efficiency is 43¼(Bd
Bc)/(DB1
DB2) ¼ 27,400/(53,709e1,899).

Subscripts 0 a c E, H ev, c, cd F, g, s, u h, c in, out l ld, d m p/f, aux rc, v, purg s

Reference state; ambient state Air Cogeneration Electrical, thermal Evaporator, compressor, condenser Fuel, gas, smoke, unburnt fuel Hot, cold Inlet, outlet Losses Loading, discharge Motor Pumps and fans, auxiliary equipment Radiation and convection, ventilation, pre-purge Surface

Symbols m_ A AF b C CHP Eh

Mass flow rate Surface Air/fuel ratio Specific flow exergy Heat capacity Electrical energy produced by the reference cogeneration plant (Directive 2004/ 8/EC)

Exergy analysis of thermal facilities equipment in buildings (I)

CHP Hh COP D E EEE EER EExE ES ExS FESR GUE h H HHV I L LHV PES Qusable RefEh RefHh s SEER SPF ExSI T Tav Tml U V b h r 4 4Ec,4Hc

451

Thermal energy produced by the reference cogeneration plant (Directive 2004/ 8/EC) Coefficient of performance Exergy destruction Electricity produced by a cogeneration plant Equivalent electrical efficiency Energy efficiency ratio Equivalent electric exergy efficiency Primary energy saving Primary exergy saving Fuel energy saving ratio Gas utilization efficiency Specific enthalpy Thermal energy produced by a cogeneration plant Higher heating value Irreversibilities Total length Lower heating value Percentage of primary energy saving Useful heat Reference electrical generation efficiency Reference thermal generation efficiency Specific entropy Seasonal energy efficiency ratio Seasonal performance factor Primary exergy saving index Temperature Average temperature Logarithmic mean temperature Thermal transmittance Volume Heat-electricity ratio Energy efficiency Density Exergy efficiency Electrical and thermal exergy efficiency of cogeneration

References [1] DIN 18599, Energy Efficiency of Buildings-Calculation of the Net, Final and Primary Energy Demand for Heating, Cooling, Ventilation, Domestic Hot Water and Lighting (in German), Deutsches Institut f€ur Normung, 2007. [2] J.M. Cejudo, F. Domínguez, A. Carrillo, M. Gallardo, DTIE 9.05-Climatisation Systems (in Spanish), ATECYR, 2010. [3] C. Stanfield, D. Skaves, Fundamentals of HVACR, third ed., Air-Conditioning, Heating and Refrigeration Institute, USA, 2016.

452

Exergy Analysis and Thermoeconomics of Buildings

[4] TRNSYS v 17, A TRansient SYstem Simulation Program, Version 17, Solar Energy Laboratory, University of Wisconsin-Madison, USA, 2014. [5] H. Torio, Comparison and Optimization of Building Energy Supply Systems through Exergy Analysis and its Perspectives, PhD Thesis, Fraunhofer Verlag, 2012. [6] R.K. Shah, D.P. Sekulic, Fundamentals of Heat Exchanger Design, John Wiley and Sons, London, 2003. [7] W.M. Kays, L. London, Compact Heat Exchangers, third ed., McGraw-Hill, New York, 1984. [8] Y.A. C¸engel, Heat Transfer (in Spanish), second ed., McGraw-Hill, Mexico, 2003. [9] J.M. Sala, L.M. Lopez, F. Jiménez, V. de la Pe~na, J.J. Eguía, Classical Thermodynamics (in Spanish), Editorial Service University of the Basque Country UPV/EHU, Bilbao, 1998. [10] B.O.E. No. 53, Royal Decree 187/2011, of February 18, on the Establishment of EcoDesign Requirements Applicable to Products Related to Energy, (in Spanish), March 3, 2011. [11] Regulation No. 813/2013 of the Commission of 2 August 2013, by Which Directive 2009/ 125/CE Was Developed with Respect to Heating Appliances and Combined Heaters, 2013. D.O. U.E. 6-9-2013. [12] Basic guide on condensation boilers (in Spanish), Ministry of Economy and Finance, Community of Madrid, Madrid, 2009. [13] R. VanNorden, Understanding Hot Water Heating Systems, Kindle Edit, 2012. [14] IDAE, Biomass and Wastes (in Spanish), Ministry of Industry, Commerce and Tourism, 2012. [15] F.J. Rey, J. San José, V. Eloy, Combustion Technologies. DWH and TF Boilers (in Spanish), Department of Energy Engineering and Fluid Mechanics, University of Valladolid, 2002. [16] E. Kinab, D. Marchio, P. Riviere, A. Zhoughaib, Reversible heat pump model for seasonal performance optimization, Energy and Buildings 42 (2010) 2269e2280. [17] V. Quiles, P. Ginés, DTIE 9.08 Gas Heat Pumps (in Spanish), ATECYR, Madrid, 2015. [18] Standard UNE-EN 14825, Air Conditioners, Liquid Chilling Packages and Heat Pumps, with Electrically Driven Compressors, for Space Heating and Cooling of Premises. Testing and Rating at Part Load Conditions and Calculation of Seasonal Performance (in Spanish), AENOR, 2012. [19] Standard UNE-EN 12309-1, Gas-fired Sorption Appliances for Heating And/or Cooling with a Net Heat Input Not Exceeding 70 kW. Part 1: Terms and Definitions (in Spanish), AENOR, 2015. [20] Standard UNE-EN 14825, Air Conditioners, Liquid Chilling Packages and Heat Pumps, with Electrically-Driven Compressors, for Space Heating and Cooling of Premises. Testing and Rating at Part Load Conditions and Calculation of Seasonal Performance (in Spanish), AENOR, 2014. [21] IDAE, Average Seasonal Performances of Heat Pumps for the Production of Heat in Buildings (in Spanish), Ministry of Industry, Energy and Tourism, 2014. [22] Directive 2009/28/CE of the European Parliament and Council of 23 April 2009 on the Promotion of the Use of Energy from Renewable Sources, 2009. D.O. E.U. 5.6.2009. [23] Commission Decision of 1 March 2009, Establishing the Guidelines for the Calculation by the Member States of Renewable Energy from Heat Pumps of Different Technologies, 2009. D.O.U.E. 6.3.2013. [24] Recognized Document of the RITE, CO2 Emission Factors and Conversion Coefficients for Primary Energy of Different Sources to Final Energy Consumed in the Buildings Sector in Spain (in Spanish), Ministry of Industry, Energy and Tourism and Ministry of Development, 2016.

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[25] TRIGEMED, Promotion of Tri-generation Technologies in the Tertiary Sector in Mediterranean Countries, the Commission of the European Communities, Directorate General for Energy, SAVE Project, 2003. Contract No. 1031/Z/01-130/2001. [26] SUMMERHEAT, Meet Cooling Needs in SUMMER by Applying HEAT from Cogeneration, EU Intelligent Energy Europe Programme EIE-06-194, 2009. [27] IDAE, Statistical Report on Cogeneration (In Spanish), Studies, Reports and Statistics, Ministry of Industry, Commerce and Tourism, Madrid, 2015. [28] IDAE, Detail of the consumption of the Sector Services, Consumption by Energy Uses of the Residential Sector (2010e2015) (in Spansih), Studies, Reports and Statistics, Ministry of Industry, Commerce and Tourism, 2017, 2015. [29] B.O.E. No. 243, 10 October, Royal Decree 900/2015, Which Regulates the Administrative and Economic Conditions for the Supply of Electric Energy for Self-Consumption and Production with Self-Consumption (in Spanish), 2015, pp. 94874e94917. [30] G. Polimeros, Energy Cogeneration Handbook, Criteria for Plant Design, Industrial Press, USA, 1981. [31] J. Marecky, Combined Heat and Power Generating Systems, Peter Peregrinus, Ltd, London, 1988. [32] J.M. Sala, Cogeneration.Thermodynamic, Econmic and Technological Aspects (in Spanish), Editorial Service University of the Basque Country, Bilbao, 1995. [33] J. Horlock, Cogeneration. Combined Heat and Power (CHP). Thermodynamics and Economics, Krieger Publishing Company, USA, 1997. [34] N. Petchers, Combined Heating, Cooling & Power Handbook: Technologies & Applications. An Integrated Approach to Energy Resource Optimization, The Fairmont Press Inc., USA, 2003. [35] Directive 2012/27/EU on Energy Efficiency, Amending Directives 2009/125/EC and 2010/30/EU and Repealing Directives 2004/8/EC and 2006/32/EC. [36] W. Pulkrawek, Engineering Fundamentals of the Internal Combustion Engines, Prentice Hall, USA, 2004. [37] Caterpillar. (http://www.cat.com/power.generation), Waukesha (http://www.dressserwauk esha.com). [38] V.A. Boicea, Essentials of Natural Gas Microturbines, CRC Press, USA, 2013. [39] F.J. Melguizo, A. Cano, The Electrical Distributed Generation with Gas Microturbines (in Spanish), University of Seville, 2005. [40] G. Walker, Stirling Engines, Clarendon Press, United Kingdom, 1980. [41] A.J. Organ, Stirling Cycle Engines: Inner Workings and Design, John Wiley, USA, 2014. [42] J. Otero de Becerra, Hydrogen and Fuel Cells: Current State and Immediate Perspective (in Spanish), National Association of Engineers of ICAI, 2010. [43] B. Sorensen, Hydrogen and Fuel Cells. Emerging Technologies and Applications, Elsevier, Oxford, 2012. [44] Y. Huang, Y.D. Wang, S. Rezvani, D.R. AcIlveen-Wright, M. Anderson, J. Mondol, A. Zacharopoulos, N.J. Hewitt, A techno-economic assessment of biomass fuelled trigeneration system integrated with organic Rankine cycle, Applied Thermal Engineering 53 (2013) 325e331. [45] Y. Dai, J. Wang, L. Gao, Parametric optimization and comparative study of organic Rankine cycle (ORC) for two low grade waste heat recovery, Energy Conversion and Management 50 (2009) 576e582. [46] A. Schuster, S. Karellas, R. Aumann, Efficiency optimization in supercritical organic Rankine cycles, Energy 35 (2010) 1033e1039. [47] ORC World Map, 20/06/2017. http://orc-world-map.org/analysis.html.

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[48] C. Fogelholm, A. Gebremedhin, S. Kim, L. Pedersen, T. Savola, J. Stang, T. Tveit, H. Zinko, 8DCHC-08-02: Improved Cogeneration and Heat Utilization in DH Networks, IEA Implementing Agreement on District Heating and Cooling, Including the Integration of CHP, 2008. [49] R. Wiltshire (Ed.), Advanced District Heating and Cooling (DHC) Systems, Woodhead Publishing Series in Energy, Elsevier, 2016. [50] IEA, District Heating and Cooling Connection Handbook, Program of Research, Development and Demonstration on District Heating and Cooling, IEA, 2000. [51] ADHAC, Association of Companies for Heating and Cooling Networks, Census of Networks, 2016. http://www.adhac.es/. [52] Royal Decree 56/2016, of 12 February, Which Transposes Directive 2012/27/EU of the European Parliament and Council, of 25 October, 2012, Relating to Energy Efficiency, in Relation to Energy Audits, Accreditation of Energy Service Providers and Auditors and Promotion of Energy Supply Efficiency, February 2016. BOE No. 38 11655-11681 16. [53] IDAE, National Action Plan on Energy Efficiency 2017e2020 (in Spanish), Ministry of Industry, Commerce and Tourism, 2017. [54] Directive 2004/EC of the European Parliament and Council of 11 February 2004 on the Promotion of Cogeneration on the Basis of the Demand for Useful Heat in the Internal Energy Market, 2004. D.O.U.E. 21.2. [55] B.O.E. No. 126, Royal Decree 661/2007, of 25 May, Which Regulates the Activity of Production of Electric Power under the Special Regime (in Spanish), May 26, 2007. [56] Aiguasol, CertCHP: Tool for the Energy Certification of Buildings with Microcogeneration (in Spanish), COGEN Spain, 2011. [57] M.A. Lozano, Trigeneration (In Spanish),Master of Research in Energy Efficiency in Industry, Transport and Building of the UPV/EHU, University of Zaragoza, 2010. [58] A. Campos, A. Erkoreka, K. Martin, J.M. Sala, Feasibility of small-scale gas engine-based residential cogeneration in Spain, Energy Policy 39 6 (2011) 3813e3821. [59] J. Ramos, Optimization of the Design and Operation of Cogeneration Systems for the Residential-Commertial Sector (in Spanish), Doctoral Thesis, University of Zaragoza, 2012. [60] G. Nemhauser, L. Wolsey, Integer and Combinatorial Optimization, J. Wiley, USA, 1999. [61] J.M. Sala, Cogeneration in the Residential and Tertiary Sector (In Spanish), Master in Thermal Engineering in Buildings, University of the Basque Country UPV/EHU, 2010. [62] I. Dincer, M.A. Rosen, Thermal Energy Storage: Systems and Applications, second ed., John Wiley & Sons, Ltd, USA, 2011. [63] H. Mehling, L.F. Cabeza, Heat and Cold Storage with PCM. An up to Date Introduction into Basics and Applications, Springer, 2008. [64] B. Zalba, J.M. Marin, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change materials: heat transfer analysis and applications, Applied Thermal Engineering 23 (2003) 251e283. [65] A. Sharma, V.V. Tyagi, C.R. Chen, D. Buddhi, Review on thermal energy storage with phase change materials and applications, Renewable and Sustainable Energy Reviews 13 (2009) 318e345. [66] A. Gil, M. Medrano, I. Martorell, A. Lazaro, P. Dolado, B. Zalba, et al., State of the art on high temperature thermal energy storage for power generation. Part 1dconcepts, materials and modellization, Renewable and Sustainable Energy Reviews 14 (2010) 31e55. [67] I. Dincer, M.A. Rosen, Exergy. Energy, Environment and Sustainable Development, second ed., Elsevier, 2013. [68] A. Camps- Celador, M. Odriozola, J.M. Sala, Implications of the modeling of stratified hot water storage tanks in the simulation of CHP plants, Energy Conversion and Management 52 (2011) 3018e3026.

Exergy analysis of thermal facilities equipment in buildings (II)

6.1

6

Summary

This chapter is a continuation of the previous one. In it, we present the main characteristics of some equipment that forms part of air conditioning and solar energy installations, perform conventional energy analysis and then, exergy analysis, showing in each case the way to calculate the irreversibilities and define the corresponding exergy efficiency. Compression refrigerators are most often used and also the best known, with the simple reverse compression cycle having been analysed in Chapter 5. For this reason, we begin this chapter by looking at absorption refrigerators, describing the simple cycle and showing its energy and exergy analysis. A similar treatment is used for adsorption refrigerators which can use solar energy or waste heat for the production of cold as done in absorption refrigerators. The basic principle of the adsorption/ desorption process and the operation of a single-effect machine is described. Next, the energy and exergy analysis of an air treatment unit with a rotary desiccant dryer will be considered. The chapter continues with an analysis of the basic processes of air conditioning, clearly showing the differences between conventional energy and exergy analysis.

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00006-0 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

We then look at ventilation systems, using exergy to evaluate the advantages and limitations of heat recovery. We finish the chapter looking at systems using solar energy; first, photovoltaic panels, and later applying exergy analysis to thermal collectors for the production of DHW, as well as to mixed panels. As in the previous chapters, a series of examples are given, which serve to reinforce the concepts developed throughout the chapter.

6.2 6.2.1

Absorption refrigerators Types and characteristics

Looking at those procedures that use a change of state to produce cold, we will start with absorption units. Absorption cycles are based on the ability of some substances in the liquid phase to absorb vapours of other substances. It is the case of water absorbing ammonia or some salts such as lithium bromide absorbing water. The first absorption system was invented in 1850 by E. Carré, using water/sulfuric acid as a cooling/absorbent pair. In this regard, the history of the evolution of these engines given by Marcos del Cano 2008 [1] is very interesting. In recent years, due to the possibility of these systems being directly powered by solar energy or residual heat, there has been a resurgence in absorption technology, allowing them to replace compression refrigerators, with a consequent reduction of CO2 emissions linked to electrical energy consumption. Added to this positive effect is the fact that the working fluids in these engines are natural compounds, thus avoiding negative effects on the environment, as opposed to the traditional refrigerants used by mechanical compression engines. The operation of absorption systems using solar energy is popularly known as solar cooling. These systems can help reduce the large spikes in electricity consumption that occur in summer due to the use of air conditioning systems, Kim 2007 [2]. It is also worth noting the spread of the use of absorption units in cogeneration installations for the production of cold, thus optimizing waste heat consumption in cogeneration and giving rise to what is known as trigeneration, that is, the simultaneous production of heat, cold and electrical energy, as seen in Chapter 5. There are different criteria for classifying absorption engines: • • • • •

Depending on the number of effects (number of generators) there are single, double or triple effect engines (one, two or three generators, respectively). According to the refrigerant/absorbent pair used, mainly, there are LiBr/H2O and NH3/H2O systems and also LiNO3/H2O and NaSCN/H2O systems. Depending on the number of stages (number of absorbers); there are single stage, double stage or triple stage systems. According to the condensation system, they may condense using water or air. Depending on the heat source, there are the direct type systems, which use heat provided by combustion gases or those of indirect type, which receive heat through an intermediate fluid and a heat exchanger.

Exergy analysis of thermal facilities equipment in buildings (II)

457

Absorption units, therefore, have characteristics that make them particularly attractive; the possible use of residual heat means that they contribute to improving energy efficiency, and broaden the possibilities of cogeneration, especially in buildings, by extending the hours of operation to the summer months, Wu and Wang 2006 [3]. In addition, they may be associated with the use of renewable energies and, as we have already mentioned, they use substances that do not affect the ozone layer or climate change, Kim and Infante Ferreira 2005 [4]. Absorption engines, capable of producing cold and/or heat, could become an alternative to conventional electricity-driven compression refrigerators. Currently, the most often used are those of simple effect for large powers, but for small powers (at the domestic level) they are not yet competitive compared to electrical powerdriven, so more R&D is needed to improve their efficiency and reduce size and cost. In order to be used in homes, units should be condensed by air, so as to avoid the cooling tower, which is currently ruled out as an element for dwellings.

6.2.2

Simple absorption cycle

In absorption engines, the traditional mechanical compressor is replaced by what is called a thermal compressor formed by two heat and mass exchangers which consist of an absorber (ABS) and a boiler or generator (G), a recuperator (R), a pump and an expansion valve, see Fig. 6.1. The other components in the unit are typical of a refrigerator, that is, the evaporator EVAP, the condenser COND and the throttle valve. The unit exchanges heat with four sources, with these heat exchanges taking place in the generator, absorber, condenser and evaporator. The working fluid is a solution, where, in the case of the LiBr/H2O pair, the absorber is the lithium bromide and the refrigerant the water, while in the NH3/H2O pair, the refrigerant is NH3, Ellington 1957 [5].

Figure 6.1 Conceptual schema of a single effect absorption machine.

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Exergy Analysis and Thermoeconomics of Buildings

Heat is supplied in the generator that boils the solution, thereby separating out the refrigerant vapour. The remaining solution, rich in absorbent, closes the cycle returning to the absorber, while the refrigerant vapour passes to the condenser where it condenses; it is then throttled and reaches the evaporator, where it evaporates with the absorbed heat, in the same way as in a mechanical compression engine. This vapour, at low pressure and temperature, is absorbed exothermically in the absorber by the concentrated solution from the generator. After this brief description of the operation of the cycle, we describe in a little more detail the processes that take place in each of the main components. The condensation (process 1e2) of the refrigerant vapour coming from the generator takes place in the condenser, yielding the condensation heat to the source that is at temperature TCOND. Depending on the prevailing pressure, different condensing temperatures will be available for each refrigerant used. The latent heat of condensation given will be received by the fluid at a lower temperature, usually water, which surrounds the condenser. Next, it passes through the expansion valve (isoenthalpic process 2e3), which has a dual function. On the one hand, it regulates the amount of liquid that enters the evaporator so that, depending on the amount of vapour drawn in by the absorber, the pressure in the evaporator can be kept constant. On the other hand, a reduction of pressure from high in the condenser to low in the evaporator takes place in the valve. The liquid coming from the condenser, at high pressure and high temperature, passes through the valve to a lower pressure, partly vapourizing by taking the necessary heat from the liquid itself, which is subsequently cooled to the lower temperature TEVAP corresponding to the lower pressure. Under these conditions, the refrigerant reaches the evaporator (process 3e4) where it receives heat from the medium to be cooled at temperature TEVAP, which causes its complete evaporation. Depending on the prevailing pressure in the evaporator, different vapourization temperatures will be obtained for each type of fluid used. The refrigerant accesses the absorber in a saturated vapour state, where it is brought into contact with the concentrated solution from the generator, which absorbs the vapour and transforms it into a liquid (heat of condensation) at the same time diluting the solution (heat of dilution). The heat of absorption, some of the heat of condensation plus the heat of dilution, is generally transferred to a cooling water circuit at the temperature TABS. As in the course of operation, the concentrated solution (low in refrigerant) is enriched by absorbing the refrigerant; for continued operation, the absorber needs to be fed with the poor solution coming from the generator, at the same time that the enriched solution is eliminated by sending it to the generator. In the generator, due to the contribution of heat, the refrigerant evaporates and the vapours given off are propelled towards the condenser. During operation, when the refrigerant vapours are given off, the diluted solution (rich in refrigerant) becomes more concentrated and for continued operation, the generator needs to be fed with the rich solution from the absorber, while eliminating the poor solution by sending it to the absorber. As has been said, the dual function of the mechanical compressor is carried out by the absorber (drawing in refrigerant) and the generator (pushing out refrigerant).

Exergy analysis of thermal facilities equipment in buildings (II)

459

Figure 6.2 The appearance of a single effect absorption engine.

We have seen that the solution enriched in the absorber is sent to the generator. To overcome the pressure difference (low pressure in the absorber and high pressure in the boiler) a pump is needed (process 5e6). On the other hand, the poor solution in the generator is sent to the absorber. As the poor solution is in the generator at high pressure, a pressure drop takes place in the regulating valve, taking the pressure down to that of the absorber, thereby fulfilling its regulating function. Fig. 6.2 shows a drawing of an absorption unit with a configuration similar to the units currently on the market. Finally, we see that heat needs to be given in the generator and eliminated in the absorber. As the solution coming from the generator (path to the absorber) arrives hot and the solution coming from the absorber (path to the generator) arrives cold, having a regenerative heat exchanger that raises the temperature of the solution coming from the absorber and decreases that of the solution from the generator is advisable. In this way, both flows near the saturation conditions necessary for absorption and generation, substantially improve the cycle efficiency. We could say that in the absorption refrigeration engine two cycles are carried out: the refrigerant cycle and the solution cycle. The refrigerant cycle starts at the generator and ends at the absorber, passing through the condenser, expansion valve and evaporator. For its part, the solution cycle runs between the absorber and the generator, passing through the circulation pump, regulating valve and regenerative exchanger, Herold et al. 1996 [6]. The two refrigerant/absorbent pairs most used in absorption engines are NH3/H2O and LiBr/ H2O; the first, in applications preferably for cooling, and the second, generally, in air conditioning and heat pumps. In LiBr/H2O absorption systems, since water is the refrigerant, the evaporation temperature must be higher than 0
C, so they work with evaporation temperatures between 4 and 10
C. As the absolute vapour pressure at these temperatures is between 400 and 900 Pa, the specific volume in the evaporator is

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Exergy Analysis and Thermoeconomics of Buildings

very large, of the order of 200 m3/kg. On the other hand, the condenser works with absolute pressures between 4,000 and 10,000 Pa, which implies that the specific volume of the refrigerant is about five times less than that of the evaporator, McNeely 1979 [7]. One of the possible problems with the LiBr/H2O systems is the risk of crystallization of the solution. The crystallization zone is between 65% and 70% concentration of lithium bromide for temperatures between 48 and 105
C. Therefore, the engines are designed to work outside this zone and thus prevent the formation of crystals in the solution. In addition, these solutions are very corrosive in the presence of oxygen, so an inhibitor needs to be added to the solution. The simple effect cycle has undergone several modifications to maximize its energy efficiency through the use of heat exchangers that recover the excess heat in the absorber or the generator. In double-effect refrigeration cycles, the circulation of the solution can be done in various ways, with the flow being in parallel, series and parallel-series. In parallel flow, the solution that leaves the absorber is pumped in suitable proportions to each of the two generators passing through the high- and lowtemperature heat exchangers. The return currents from each generator are mixed before entering the absorber. In series flow, the solution leaving the absorber is pumped directly through the heat exchangers to enter the high-temperature generator. Next, the solution passes to the low-temperature generator and the absorber, previously circulating through each of the heat exchangers in the cycle, see Fig 6.3. Those interested in this type of cycle are advised to consult Marimon 2011 [8]. In addition to those of multiple effect and stages, there are cycles that are called AHX (Absorber Heat eXchange), Ayou et al. 2013 [9], GAX (Generator Absorber eXchange), Zheng et al. 2007 [10] and others.

Figure 6.3 Double effect refrigerator, series flow.

Exergy analysis of thermal facilities equipment in buildings (II)

6.2.3

461

Energy analysis of components

By applying the First Law and the Law of Conservation of Mass in each component, we will obtain the corresponding mass and energy balances. This energy analysis allows us to evaluate the behaviour of the absorption chiller based on the characteristics of its components, the internal conditions and the external conditions of activation and refrigeration. In order to carry out the mass and energy balances, there is a series of diagrams of LiBr/H2O in which the properties that are needed are represented. The PTX (pressure-temperature-concentration) diagram, also called the D€uhring diagram, McNeely 1979 [7], represents the absorption cycle as a function of the saturation pressure of the solution, concentration and temperatures of the solution and the refrigerant. It is the diagram recommended by ASHRAE. The hX diagram (enthalpyconcentration), also called Merkel diagram, McNeely, 1979, allows for the calculation of the enthalpy of the solution as a function of its temperature and concentration. In addition, the diagram of the specific heat of the solution and that of the density of the solution as a function of the concentration are also of interest, Ellington 1957 [5]. For the construction of the thermodynamic model, we need to carry out a mass balance for the refrigerant and another for the solution in each component of the cycle, as well as finding the corresponding energy balance and the equations of the properties of the flows. All these equations will allow us to calculate the thermodynamic properties and the powers exchanged in the components of the absorption system. The model presented below (based on the diagram in Fig. 6.1) is a stationary model, in which the internal conditions of pressure, temperature and rate of mass flow are constant and in which the following hypotheses have also been established: (1) the state of the refrigerant is saturated, (2) the expansion in the valves is isoenthalpic, (3) there is ideal behaviour in the solution pumps (isentropic), and (4) there are no heat losses or head losses in the pipes or in the components.

6.2.3.1

Generator

We shall assume that the refrigerant in state 1, see Fig. 6.1, is pure refrigerant so that for a rate of mass flow of refrigerant m_ r ¼ m_ 1 , the generator is fed with a solution mass flow m_ d ¼ m_ 7 ; returning m_ d m_ r ¼ m_ 8 to the absorber, see Fig. 6.4.

Figure 6.4 Generator.

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Exergy Analysis and Thermoeconomics of Buildings

The mass balance of refrigerant is reflected by the following equation m_ d yABS ¼ m_ r þ ðm_ d  m_ r ÞyG

(6.1)

where yABS and yG are respectively the mass fractions of the refrigerant at the outlet of the absorber (flow 7) and the generator (flow 8). The relationship between the solution mass flow and the refrigerant mass flow can be written as R¼

1  yG m_ d ¼ m_ r yABS  yG

(6.2)

This equation represents the relationship between the rate of solution mass flow moving between the absorber and the generator and the rate of refrigerant mass flow produced in the generator so that for each kg/s of refrigerant, a mass flow of solution m_ d ¼ R is required. Once we evaluate the heat extracted in the evaporator for each unit of mass of refrigerant, qEVAP, and with Q_ EVAP being the thermal load of the system, the rate of mass flow of refrigerant that must circulate through the system is m_ r ¼

Q_ EVAP qEVAP

(6.3)

and therefore, the rate of mass flow of solution will be m_ d ¼ R:m_ r

(6.4)

Undertaking an energy balance gives the equation Q_ G þ m_ d h7  m_ r h1  ðm_ d  m_ r Þh8  Q_ l;G ¼ 0

(6.5)

Assuming the heat losses to the environment are negligible, that is, making Q_ l;G ¼ 0, we finally get Q_ G ¼ m_ r ðh1  h8 Þ þ m_ d ðh8  h7 Þ

6.2.3.2

(6.6)

Absorber

It is the critical component of the system so that its proper functioning depends on its ability to absorb the vapour from the evaporator, Fig. 6.5. From the energy balance we have m_ r h4 þ ðm_ d  m_ r Þh10  m_ d h5  Q_ ABS  Q_ l;ABS ¼ 0

(6.7)

Exergy analysis of thermal facilities equipment in buildings (II)

463

Figure 6.5 Absorber.

Assuming that in the absorber all the heat is transferred to the refrigeration circuit, we get Q_ ABS ¼ m_ r ðh4  h10 Þ þ m_ d ðh10  h5 Þ

6.2.3.3

(6.8)

Heat recuperator

As we have said, the recuperator produces two simultaneous beneficial effects: on the one hand, it brings the diluted solution closer to the boiling point it will reach in the generator, and on the other, it cools the concentrated solution on its return to the absorber, Fig. 6.6.

Figure 6.6 Heat recuperator.

Since the heat received by the cold solution is m_ d ðh7  h6 Þ and the maximum heat that could be exchanged is m_ d ðh8  h6 Þ, h8 being the enthalpy at the temperature T8, the effectiveness of the recuperator is x¼

h7  h6 h8  h6

(6.9)

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Exergy Analysis and Thermoeconomics of Buildings

with the energy recovered being m_ d ðh7  h6 Þ ¼ ðm_ d  m_ r Þðh8  h9 Þ

6.2.3.4

(6.10)

Regulation valve

It produces the reduction of pressure from the high-pressure zone of the cycle to that of the low-pressure zone, Fig. 6.7.

Figure 6.7 Regulation valve.

The energy balance gives us the equation h9 ¼ h10

6.2.3.5

(6.11)

Solution pump

The aim of this pump is to move the solution from the absorber to the generator, Fig. 6.8. Using the energy balance and incorporating the electrical efficiency he of the drive motor gives 1 W_ e ¼ m_ d ðh6  h5 Þ he

6.2.3.6

(6.12)

Condenser

The energy balance in the condenser is Q_ COND ¼ m_ r ðh1  h2 Þ

(6.13)

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465

Figure 6.8 Solution pump.

Figure 6.9 Condenser.

This heat is finally released to the atmosphere, either directly to the air or through a water circuit, Fig. 6.9.

6.2.3.7

Expansion valve

In the isoenthalpic process that takes place in the valve, the refrigerant in the saturated liquid state at the condenser outlet becomes a two-phase liquid-vapour system, at the pressure and temperature of the evaporator, Fig. 6.10. The equation showing the energy balance is h2 ¼ h3

(6.14)

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Exergy Analysis and Thermoeconomics of Buildings

Figure 6.10 Expansion valve.

6.2.3.8

Evaporator

Circulating through the evaporator is the refrigerant, partly as vapour, that does not produce a cooling effect and partly as liquid that evaporates and receives its latent heat from the fluid in which the useful effect of the equipment is produced, Fig. 6.11. The energy balance is Q_ EVAP ¼ m_ r ðh4  h3 Þ

Figure 6.11 Evaporator.

(6.15)

Exergy analysis of thermal facilities equipment in buildings (II)

6.2.3.9

467

Total cycle

Undertaking a global balance of energy for all the elements in the cycle, considering again the schema of Fig. 6.1, we have the equation Q_ G þ Q_ EVAP þ W_ e ¼ Q_ COND þ Q_ ABS

(6.16)

If we ignore the work of the pump and with TG,TEVAP being the temperatures of the generator and evaporator and assuming the same temperature TM for the condenser and the absorber, applying the Second Law to the reversible absorption cycle allows us to write Q_ G Q_ EVA Q_ Q_ þ ¼ ABS þ COND TG TEVAP TM TM

(6.17)

In order to characterize the behaviour of an absorption refrigeration unit, the so-called
energy  efficiency ratio (EER), is used, which
is the ratio between the useful effect Q_ EVAP and the energy needed to produce it Q_ G . For the reversible cycle, and not taking into account the work of the circulation pump, the EERmax is EERmax ¼

   TM TEVAP 1 TG TM  TEVAP

(6.18)

which is the maximum theoretical value. Thus, the EER of the ideal absorption cycle is equal to the product of the thermal efficiency of a Carnot engine cycle between the temperatures of the generator and the absorber/condenser with the energy efficiency coefficient of a Carnot refrigeration cycle between the temperatures of the evaporator and the absorber/condenser, Izquierdo 1996 [11]. Coming back to the real cycle, considering the work of the solution pump, we have EER ¼

Q_ EVAP m_ r ðh4  h3 Þ ¼ _ _ QG þ W e m_ r ðh1  h8 Þ þ m_ d ðh8  h7 Þ þ W_ e

(6.19)

It should be noted that the electrical energy consumed by the solution pump is negligible compared to what is needed in the compression of a vapour, due to the lower specific volume of the solution. If the absorption cycle worked as a heat pump so that the useful effect is the heat given in the condenser and absorber, then the coefficient of performance (COP) is defined according to the expression COP ¼

Q_ ABS þ Q_ COND Q_ G þ W_ e

(6.20)

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Exergy Analysis and Thermoeconomics of Buildings

If we compare with the definition of EER above, we have the relationship COP ¼

6.2.4

Q_ ABS þ Q_ COND Q_ G þ W_ e þ Q_ EVAP Q_ EVAP ¼ ¼1þ ¼ 1 þ EER _ _ _ QG þ W_ e QG þ W_ e QG þ W_ e (6.21)

Exergy analysis of components

To complete the thermodynamic model of the simple cycle described above, we are now going to incorporate the Second Law, including the exergy balance in each component, and finally, defining the exergy efficiency of the equipment as a whole.

6.2.4.1

Generator

Although there are no chemical reactions in any of the components, including the absorber and generator, there is nevertheless a variation in the concentration of the solution in the inputs and outputs of the generator and absorber, which results in a variation in the chemical exergy of these solutions. We will assume that the solutions, both the rich input to the generator and the poor output, are ideal solutions, Sala 206 [12] so that the specific chemical exergy is the sum of the exergy of the two solvent and 2 P solute components for their respective mass fractions yi plus the term RT0 yk lnyk k¼1

representing the mixing exergy. Carrying out a balance of chemical exergy gives ch the chemical exergy variation in the generator DB_ G , as ch DB_ G ¼ ðm_ d

 m_ r Þ RM8 T0

2 X i¼1

!  m_ d RM7 T0

yi lnyi 8

2 X i¼1

! yi lnyi

(6.22) 7

where RM7 and RM8 are the universal constants of the ideal gases divided by the molar mass of the solutions corresponding to flows 7 and 8, respectively, according to Fig. 6.4. From the total exergy balance, that is, the sum of the physical and chemical exergy, and assuming that there is no heat loss, we get that the exergy destruction in the generator is   T0 _ ch _ DG ¼ 1  QG þ m_ r ðb8  b1 Þ þ m_ d ðb7  b8 Þ  DB_ G TG

(6.23)

The exergy destruction in the generator is due to the process of heat transfer supplied to the unit, to the mass transport, which gives rise to the composition variations between the inlet and outlet flows and to the mechanical friction due to the viscosity of the flows.

Exergy analysis of thermal facilities equipment in buildings (II)

6.2.4.2

469

Absorber

Similarly to what happens in the generator, in the absorber, there is also a variation in the chemical exergy of the flows that enter and exit. Following the model of ideal liquid solutions, the chemical exergy variation between the input and output flows in the absorber is ch DB_ ABS ¼ m_ d

RM5 T0

2 X i¼1

!  ðm_ d  m_ r ÞRM10 T0

yi lnyi 5

2 X i¼1

! yi lnyi

(6.24) 10

where RM10 is the universal constant of the ideal gases divided by the molar mass of the solution corresponding to flow 10 and RM5 corresponding to flow 5. The equation of the total exergy balance is written as   T0 ch D_ ABS ¼ m_ r ðb4  b10 Þ þ m_ d ðb10  b5 Þ  DB_ ABS  1  Q_ ABS TABS

(6.25)

which allows us to calculate the exergy destruction in the absorber.

6.2.4.3

Heat recuperator

The irreversibility in the exchange of heat leads to exergy destruction that is calculated according to the equation D_ REC ¼ m_ d ðb6 þ b8  b7  b9 Þ þ m_ r ðb9  b8 Þ

6.2.4.4

(6.26)

Regulation valve

The exergy destruction is D_ RV ¼ ðm_ d  m_ r Þðb9  b10 Þ

6.2.4.5

(6.27)

Solution pump

The exergy destruction in the motor-pump is a result of the following balance equation D_ e ¼ W_ e  m_ d ðb6  b5 Þ

6.2.4.6

(6.28)

Condenser

If the cycle works like a refrigerator, all the heat transferred to the condenser will be part of the external irreversibilities so that the exergy balance can be written as m_ r ðb1  b2 Þ ¼ I_COND

(6.29)

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Exergy Analysis and Thermoeconomics of Buildings

If, on the other hand, it works as a heat pump, the heat given off in the condenser is part of the product of the system so that the equation of balance will now be  _ DCOND ¼ m_ r ðb1  b2 Þ  1 

6.2.4.7

T0 TCOND

 Q_ COND

(6.30)

Expansion valve

The exergy destruction in the expansion valve is D_ EXV ¼ m_ r ðb2  b3 Þ

6.2.4.8

(6.31)

Evaporator

The heat exchanged in the evaporator, operating as a refrigerating engine, is the useful effect of the unit, therefore   T0 _ DEVAP ¼ m_ r ðb3  b4 Þ þ 1  Q_ TEVAP EVAP

(6.32)

By operating as a heat pump, the decrease in exergy between the states 3 and 4 is due to the destruction of exergy, and the flow of exergy exchanged with the evaporator medium, which is zero when the medium temperature is that of the environment; the equation of balance would be written as m_ r ðb3  b4 Þ ¼ I_EVAP

6.2.4.9

(6.33)

Total cycle

Once the exergy destructions in each component are known, we would determine the relative value of these destructions with respect to the total, that is the sum of all of them. The work carried out by Talbi and Agnew 2000 [13] and by Aman et al. 2012 [14] concluded that the largest percentage of exergy destruction takes place in the absorber, around 60%, followed by the generator, with around 20%. Undertaking a global exergy balance for the whole system, we have the equation  1

     T0 _ T0 T0 QG þ W_ e ¼ 1  Q_ EVAP þ 1  Q_ COND TG TEVAP TCOND   X T0 Q_ ABS þ þ 1 D_ j TABS j

(6.34)

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471

The exergy efficiency of the engine working to produce cold is defined as

4CE

  T0 Q_ EVAP  1 TEVAP  ¼  T0 _ Q þ W_ e 1 TG G

(6.35)

When the objective is to function as a heat pump so that the useful effect is the heat given in the condenser and the absorber, the exergy efficiency is defined according to  1 4HP ¼

   T0 _ QCOND þ 1  Q_ ABS TCOND TABS   T0 _ Q þ W_ e 1 TG G T0

(6.36)

By relating to the two given expressions of exergy efficiency, the following relationship is easily checked P

D_ j  4HP ¼ 1 þ 4CE   T0 _ QG þ W_ e 1 TG j

6.2.5

(6.37)

Examples

Example E.6.1. A single-effect absorption refrigerator cools a water flow of 13 L/s from 12 to 7
C in its evaporator. The generator is driven by a flow of hot water of 13.5 L/s that enters the generator at 82
C and leaves at 74
C. In the refrigeration circuit of the absorber and condenser, the water enters at 27
C and leaves at 36
C, finally dissipating this heat in a cooling tower. Assuming that there are no heat losses in the generator and absorber and the ambient temperature is 12
C, determine

(a) The refrigerating power and exergy delivered in the evaporator. (b) The heat and exergy lost in the refrigeration circuit. (c) The EER, EERmax, exergy efficiency of the refrigerator and total exergy destruction.

Solution (a) The cold produced per unit of time, that is, the refrigerating power is Q_ EVAP ¼ m_ w ðhin  hou Þ ¼ 271:7 kW

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Exergy Analysis and Thermoeconomics of Buildings

The exergy transferred to the flow of water that circulates through the evaporator is B_ EVAP ¼ m_ w ½hou  hin  T0 ðsou  sin Þ ¼ 2:4 kW (b) Taking into account the energy balance in the system and assuming the consumption of the pump to be negligible, we have Q_ COND þ Q_ ABS ¼ Q_ G þ Q_ EVAP

The heat supplied to the generator is Q_ G ¼ 13:5$4:18ð82  74Þ ¼ 451:4 kW so that the heat transferred to the condenser and absorber is Q_ COND þ Q_ ABS ¼ 723:1 kW This heat is transferred to the water of the refrigeration circuit. The water mass flow of said circuit is m_ w;CONDþABS ¼

723:1 kg ¼ 19:2 4:18ð36  27Þ s

so that the exergy contributed to the refrigeration circuit that is finally lost is   309 _ Bw ¼ 19:2$4:18 36  27  285 ln ¼ 46:3 kW 300 (c) The EER of the refrigerator is

EER y

Q_ EVAP ¼ 0:60 Q_ G

To calculate the EERmax we assume that the temperature in the evaporator is 3
C below the outlet temperature of the water circuit, that is, TEVAP ¼ 277 K, that the temperature of the generator is 4
C below the water temperature at the output TG ¼ 343 K and that in the condenser and absorber the temperature is 5
C above the outlet temperature of the refrigeration circuit TM ¼ 314 K. With these assumptions the EERmax is EER

max

   TM TEVAP ¼ 1 ¼ 0:63 TG TM  TEVAP

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473

The exergy efficiency of the refrigerator is 4¼

B_ EVAP ¼ 2:8% B_ G

According to this result, 97.2% of the exergy contributed to the generator is lost or destroyed due to irreversibilities. In effect, if we undertake an exergy balance on the whole of the refrigerator we have _ I_ ¼ 81:6 kW B_ G ¼ B_ EVAP þ I/ Example E.6.2.

Let there be a LiBr/H20 single effect absorption refrigerator, as shown in the diagram in Fig. E.6.1. The generator is driven by a flow of hot gases, while the condenser and absorber give heat to the ambient air which is at 35
C. In the evaporator, a flow of water is cooled from 18
C to 12
C. The states and mass flows of the cycle are shown in Table E.6.1. With this information, calculate (a) The heat exchanged in the generator, absorber, condenser and evaporator and the EER of the unit. (b) The exergy destruction in the absorber. (c) The exergy efficiency of the refrigerator.

Figure E.6.1 LiBr/H20 single-effect absorption refrigerator.

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Exergy Analysis and Thermoeconomics of Buildings

Table E.6.1 Thermodynamic data of the states. i

Ti (C)

1

105

hi(kJ/kg)

si(kJ/kg$k)

mi(kg/s)

Xi(%LiBr)

257.63

2.246

0.171

64

2

77.3

194.34

2.274

0.171

64

3

58.5

194.34

2.274

0.171

64

4

47

126.74

2.278

0.184

59.5

5

47.74

128.18

2.282

0.184

59.5

6

70.2

186.9

2.445

0.184

59.5

7

105

2696.9

8.448

0.013

e

8

47

196.3

0.663

0.013

e

9

10

196.3

0.663

0.013

e

10

10

2519.35

8.905

0.013

e

11

372

3624.34

6.307

0.034

e

12

200

2308.09

4.727

0.034

e

Solution (a) The heat given up by the hot gas to the generator is Q_G ¼ ðm_ 1 h1 þ m_ 7 h7 Þ  m_ 6 h6 ¼ 44:72 kW

effectively coinciding with. m_ 11 ðh11  h12 Þ ¼ 44:72 kW The heat given to the air in the absorber is Q_ ABS ¼ ðm_ 3 h3 þ m_ 10 h10 Þ  m_ 4 h4 ¼ 42:66 kJ and in the condenser Q_ COND ¼ m_ 7 ðh7  h8 Þ ¼ 32:50 kW The cold produced in the evaporator is Q_ EVAP ¼ m_ 9 ðh10  h9 Þ ¼ 30:20 kW We can verify that these results are correct through a balance of energy Q_ G þ Q_ EVAP þ W_ p ¼ Q_ COND þ Q_ ABS where the power of the pump is W_ p ¼ m_ 4 ðh5  h4 Þ ¼ 0:27 kW which can be considered negligible compared to the heats exchanged. As we can see, the energy balance is satisfied.

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475

The EER is EER z

Q_ EVAP ¼ 0:67 Q_ G

(b) In the absorber, all the heat transferred to the refrigeration circuit is finally dissipated, and the exergy provided to that refrigeration circuit is destroyed. Therefore, we group that exergy with the destructions in the term for irreversibility, resulting in the following equation for the exergy balance ch m_ 3 ðb3  b4 Þ þ m_ 10 ðb10  b4 Þ  DB_ ABS ¼ I_ABS

Calculating each of the terms on the left of the previous equality m_ 3 ðb3  b4 Þ ¼ 11:77 kW m_ 10 ðb10  b4 Þ ¼ 4:57 kW ch  DB_ ABS ¼ m_ 3 RM;3 T0

X
i

yi lnyi



 m_ 4 RM;4 T0 3

X
i

yi lnyi

 4

¼ 0:78 kW

since Mm3 ¼ 0.64. 86.84 þ 0.36. 18 ¼ 62.0 kg/kmol and Mm4 ¼ 0.595. 86.84 þ 0405. 18 ¼ 58.9 kg/kmol. And so I_ABS ¼ 17:12 kW (c) To calculate the exergy efficiency, we first determine the exergy of the cold produced kg Q_ EVAP ¼ m_ w 4:18ð18  12Þ/m_ w ¼ 1:20 s

The exergy given to the cooled water is DB_ w ¼ 2:09 kW As the exergy contributed to the generator is m_ 11 ðb11  b12 Þ ¼ 28:21 kW the exergy efficiency of the absorption refrigerator is 4¼

6.3

DB_ w ¼ 7:4% m_ 11 ðb11  b12 Þ

Adsorption cooling systems

There are basically two types of heat-activated cooling systems: absorption systems and adsorption systems. The latter is an interesting alternative to vapour compression systems or absorption installations since they can also use waste heat or solar energy as drive energy. The phenomenon of adsorption also has other interesting applications such as oxygen production, IDAE 2010 [15].

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Exergy Analysis and Thermoeconomics of Buildings

6.3.1

Basic principle of adsorption/desorption

The process known as sorption describes the transfer of energy between two subprocesses, adsorption and desorption. Adsorption is a process in which a gas is fixed in a solid medium, usually a porous material, since it must have a large surface per unit mass. It is an exothermic process in which the heat released is due to the condensation of the adsorbate (adsorbed gas) plus the energy generated in the adsorbent-adsorbate junction. At low temperatures, the molecular forces cause the gases to adhere to the surface and then penetrate the crystalline structures of the solid. The process can be reversed by adding heat, as this is an endothermic process that causes the desorption of the gas at high pressure and temperature. Its application in the production of cold goes back to the twenties of the last century, with this type of cooling equipment being quickly replaced by vapour compression. It was towards the eighties of the last century when they became significant again due to their low environmental impact and the use of heat for their operation, which could come from residual heat, for example, in cogeneration installations, or be of solar origin, Gwadera and Kupiek 2011 [16] and Dieng and Wang 2011 [17]. The materials that are used as adsorbents can be of uniform or non-uniform pore size distribution, with the most often used being active carbon, silica gels and zeolites, of which there is a great variety. As an adsorbate, methanol can be used, forming an adsorption pair with active carbon and activated carbon fibres and also water, forming an adsorption pair with zeolites. Of all the adsorbent/adsorbate pairs used, one of the most common is silica gel as adsorbent and water as adsorbate and refrigerant, Solmus et al. 2010 [18].

6.3.2

Operation of a single-effect adsorption system

The basic components needed to perform a single-effect cycle in an adsorption system are shown in Fig. 6.12A while the stages of the cycle are shown in a Dh€uring diagram in Fig. 6.12B. The system consists of an adsorption/desorption chamber, the evaporator, the condenser, the expansion valve and some valves to isolate the adsorption/ desorption chamber. The transformations that make up the basic cycle consist of the following stages: •

•

•

The chamber is isolated from the rest of the components and is supplied with heat from the higher temperature thermal source. Desorption of the gas occurs in the free volume of the chamber, which translates into an increase in pressure. It is, therefore, a stage of compression and heating at constant volume, which ends when the pressure becomes at least equal to that of the condenser, stage A-B of the diagram. Stage BeC, consisting of desorption at constant volume, with the chamber connected to the condenser. It ends when the chamber reaches the maximum temperature TG and the condenser receives a flow of refrigerant vapour, which is then condensed by transfer of heat to the dissipation medium at Tm. This stage is called regeneration since it leaves the chamber ready for a new stage of cold production. Stage CeD of depressurization at constant volume. The chamber is isolated from the rest of the installation and cooled with the dissipation medium of temperature Tm. The adsorption

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477

Figure 6.12 (A) Schema and (B) D€uhring diagram of a single-effect machine.

•

that takes place in the free volume occurs with a drop in pressure. The stage ends when the pressure reaches that of the evaporator. Stage DeA, consisting of the adsorption of the vapours produced in the evaporator, which causes an increase in concentration. It is the cold production stage.

According to what we have described, adsorption systems are in principle intermittent. A solid is loaded with refrigerant vapour at low pressure and temperature; when this phase ends the material must be regenerated (desorption) at high pressure and temperature. The efficiency of the cycle is low and the refrigeration power produced is not continuous. For achieving continuous cooling, at least two adsorbent beds are needed to be operating out of phase so that while one is producing the useful effect (cold), the other is in the regeneration phase. A unit with two adsorption/desorption chambers, connected to the evaporator and condenser by valves, is schematically shown in Fig. 6.13. These chambers contain heat exchangers where hot or cold water circulates, to provide or eliminate the necessary heat.

Figure 6.13 Schema of adsorption engine with two chambers.

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Exergy Analysis and Thermoeconomics of Buildings

We will describe the operation of a machine, which for example, uses zeolites (adsorbate) and water (refrigerant). A flow of water circulates in the evaporator at a higher temperature than the refrigerant (water) which is at low pressure, so the flow is cooled, and this is the useful effect. Typical temperatures used are 12
C at the inlet and 7
C at the outlet. The refrigerant receives this heat and evaporates. The valve that connects the evaporator with chamber I, the one on the left of Fig. 6.13 is open, while the one that connects it with the condenser is closed. Evaporated refrigerant (water vapour) enters the chamber, which is at a slightly lower pressure than the evaporator. The water vapour is adsorbed by the adsorbate that becomes saturated during this adsorption process. Since this process is exothermic, the heat that is finally released to the environment must be dissipated by means of a flow of refrigeration water, usually in a cooling tower. The temperature of this flow usually varies between 24 and 30
C. Meanwhile in the other chamber II, the one on the right, the desorption process takes place to regenerate the adsorbate that is saturated from the previous stage. Since this process is endothermic so a flow of hot water is circulated, which drives the system. The temperature of this flow is usually about 90
C. The valve that connects chamber II with the condenser is then opened, while the valve that connects it with the evaporator is closed. As the pressure in the chamber is slightly higher than that of the condenser, the water vapour that is released from the adsorbate in the desorption process passes to the condenser, where the water vapour condenses yielding heat to the water in the tower circuit. The condensed water vapour passes to the evaporator through the expansion valve, in which the pressure drop takes place. When the adsorbate of chamber I is saturated with water and that of chamber II is dry, the machine automatically reverses the functions of the two chambers. First, the valves that connect both chambers to the evaporator and condenser are closed, and the valves are opened between the two chambers, allowing the pressures to equalize. Next, the hot water from desorption chamber II is circulated through chamber I in order to transfer the residual heat from chamber II and begin the heating process of this chamber. The inversion process of the chambers is completed; the desorption process begins in chamber I and the adsorption process in chamber II, repeating the process. As we see, this is a Tri-Thermic system of cold production, since the machine interacts thermally with three thermal sources: the higher temperature thermal source used in the generator (desorber), the condensing agent, which is also used to extract the heat from the adsorber and, finally, the cold source. In addition to the heat power to be supplied in the desorber and the refrigeration power due to the vapourization of the refrigerant fluid, heat is dissipated to an intermediate level due to condensation and the elimination of heat in the adsorption. In addition to the described single-effect cycle, other types of more complex and efficient adsorption cycles have been designed, among which are the multi-effect cycles, which indicate the number of times that the heat power supplied from the hot source is used in the system and multi-stage cycles, which refer to the number of basic adsorption cycles that make up the system, Raman 2013 [19].

Exergy analysis of thermal facilities equipment in buildings (II)

6.3.3

479

Energy and exergy analysis of an adsorption system

Coming back to Fig. 6.13. According to the schema, we call the states of the heating water at the inlet and outlet in the desorption 1 and 2 respectively and the flow m_ DES ; the states of the cooling water at the inlet and outlet in the adsorption are 3 and 4 and the corresponding flow m_ w . Generally, the same flow of refrigeration water passes first through the adsorption chamber and then through the condenser, so that it will be state 4 at the inlet of the condenser and state 5 at the outlet. The heat released in the desorption process and the heat transferred in the condenser are part of the losses. Finally, m_ EVAP is the flow of water that circulates in the evaporator and that is cooled from the inlet in state 6 to the outlet in state 7. The total heat given in the adsorption and the condenser is Q_ L ¼ m_ w ðh5  h3 Þ

(6.38)

For its part, the energy that is provided to the system for its operation is Q_ DES ¼ m_ DES ðh1  h2 Þ

(6.39)

with the cold produced being Q_ EVAP ¼ m_ EVAP ðh6  h7 Þ

(6.40)

Therefore, the instantaneous EER of the machine is EER ¼

Q_ EVAP m_ EVAP ðh6  h7 Þ ¼ m_ DES ðh1  h2 Þ Q_ DES

(6.41)

In the same way as for other equipment, we will define the EER over a period of operation, the most interesting being the value of the seasonal EER. Looking at the exergy analysis, we see that the exergy contributed by the hot source to perform the desorption is B_ DES ¼ m_ DES ðb1  b2 Þ

(6.42)

with the exergy of the cold produced being B_ EVAP ¼ m_ EVAP ðb7  b6 Þ

(6.43)

so that the exergy efficiency of the adsorption system is 4¼

B_ EVAP m_ EVAP ðb7  b6 Þ ¼ m_ DES ðb1  b2 Þ B_ DES

(6.44)

480

6.3.4

Exergy Analysis and Thermoeconomics of Buildings

Rotary desiccant dryers

In buildings with high internal gains, located in humid climates, there may occur a very significant increase in interior humidity. If a high flow of ventilation is required to avoid an excessive concentration of contaminants, humidity control is essential in addition to temperature control. Conventional systems without humidity control usually have high energy consumption and, of course, do not guarantee thermal comfort. As a solution to this situation, systems that can control the sensitive and latent load separately are very attractive. One option is based on the use of desiccant materials, which can be solid or liquid, although the most common is the former. These solid desiccants are included in air handling units (AHU), usually confined to a cylindrical rotor. These types of systems are called open-cycle desiccant refrigeration systems or rotary desiccant dryer systems, ASHRAE 1996 [20]. Most rotary desiccant dryers contain silica gel or zeolite (molecular sieve) as a drying material, bound to a substrate of glass fibers, paper or sometimes aluminum. The wheel rotates slowly between the process and regeneration flows. The air from the outside to be dehumidified flows between the channels formed and the desiccant impregnated in the structure adsorbs the humidity of the air until it becomes saturated, which increases the vapour pressure of its surface. Thus, the air is dehumidified and heated, since the adsorption heat is released in the adsorption process. As the objective is not only to dehumidify but also to cool, there are other devices in the AHU to bring the air to the required driving conditions, such as sensitive rotary exchangers, cold batteries or evaporative coolers, Fernandez 2015 [21]. As the wheel is rotating, when it enters the regeneration sector, the desiccant is heated by the regeneration air-flow and loses moisture. The regeneration is carried out with air at about 50e60
C, so that this heat can be provided, for example, by means of solar collectors. Once the regeneration stage has been completed, the regenerated desiccant returns to the process zone, where it comes into contact with the external airflow and adsorbs its humidity, Nia et al. 2006 [22]. The applications for the rotary desiccant dryers are diverse: whenever there is a need to reduce internal humidity loads, maintain or lower the specific relative humidity or the dew point and process high latent loads of external air, this technology is of great use. Commercially, rotary desiccant dryer systems are more common in supermarkets, and preservation chambers and freezers. As we have said, in recent years, rotary desiccant dryer systems are being used for air conditioning. Recent changes in regulations have increased the amount of outside air that is required in public buildings. The rooms and conference rooms of hotels or convention centres have large variations of sensitive load. The latent load, on the other hand, is more stable because fresh air is constantly being brought into the building. Conventionally, air conditioning systems control the temperature so quickly that, when they stop, they lead to the formation of condensates in the walls and objects, causing odors and damaging furniture and the structure of the building. In order to counter this situation, the combination of conventional technologies and de-humidification by rotary desiccant dryer, is given as a very attractive

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techno-economic variation. In facilities such as operating rooms and clean rooms, these technologies are used with good results.

6.3.5

Energy analysis of an AHU with a rotary desiccant dryer

Fig. 6.14 shows a typical schema of an AHU with a rotary desiccant dryer. The conditioning system consists of two parts: process and regeneration. In the process, air is taken from the outside (1) and enters the rotary desiccant dryer, where it is dehumidified and heated (2). This hot and dry air passes through the rotary exchanger, where it is cooled with the return air, leaving in state (3), to later go through an evaporative cooling process, where the air temperature decreases at the expense of increasing its humidity until reaching state (4), in which state it is pushed to the building. In the regeneration part, the air extracted from the building (5), at a higher temperature and with a higher moisture content than the air supplied, is cooled and saturated with moisture through evaporative cooling (6), to then pass through the rotary exchanger where it receives heat from the process air, heating up to state (7) and in turn cooling the process air. It is then passed through a heat battery, activated by residual heat, solar energy or a burner to reach the appropriate temperature, which may be between 50 and 60
C; this is state (8). Finally, at this temperature it passes through the rotary desiccant dryer, where it evaporates the moisture from the adsorbent and thus regenerates the wheel, extracting moisture and entering the environment in state (9). Fig. 6.15 shows the air states in a psychrometric diagram. There are a number of comments we can make regarding the progress of the air in this installation: • • •

The air at the outlet (9) is hotter and is more humid than the ambient air (1). The air in the conditioned room (5) is hotter and contains more moisture than the air supplied by the air conditioner, (4). In a steady state, the difference in humidity between the air released into the environment (9) and the ambient air (1) is the amount of water vapour coming from the evaporative coolers and the conditioned space.

Figure 6.14 Diagram of an AHU with rotary desiccant dryer.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 6.15 Psychrometric diagram of the states of the air.

This installation with rotary desiccant dryer exchanges heat and mass with the ambient air and air in the conditioned space. In addition, there are water inlets via the humidifiers. In order to facilitate the analysis, Pons and Kodama 2000 [23] developed a method of converting the open system into a closed one, for which they added two theoretical subsystems so that the total system was a closed one and only exchanged heat. We then carry out the mass and energy balances in each component that makes up the installation. We will use m_ a for the rate of mass flow of dry air and Q_ L for the rate of heat loss fluxes in each piece of equipment that make it up. Rotary desiccant dryer m_ a ðh8  h9 Þ þ m_ a ðh1  h2 Þ  Q_ L;RD ¼ 0

(6.45)

Regenerative heat exchanger m_ a ðh2  h3 Þ  m_ a ðh7  h6 Þ  Q_ L;RHE ¼ 0

(6.46)

Process evaporative cooler m_ a ðu3  u4 Þ þ m_ w;EV ¼ 0

(6.47)

m_ a ðh3  h4 Þ þ m_ w;EV hw  Q_ L;EV ¼ 0

(6.48)

Regeneration evaporative cooler m_ a ðu5  u6 Þ þ m_ w;REV ¼ 0

(6.49)

Exergy analysis of thermal facilities equipment in buildings (II)

m_ a ðh5  h6 Þ þ m_ w;EVR hw  Q_ L;REV ¼ 0

483

(6.50)

Regeneration heat battery
 m_ a ðh7  h8 Þ þ m_ f hf ;in  hf ;ou  Q_ L;RHB ¼ 0

(6.51)

where it is assumed that the heat is supplied to the regeneration battery by a rate of mass flow m_ f that enters the battery with an enthalpy hf,in and comes out with the enthalpy hf,ou. Complete AHU system 
m_ a ðh1  h9 Þ þ m_ a ðh5  h4 Þ þ m_ w;EV þ m_ w;EVR hw
 þ m_ f hf ;in  hf ;ou  Q_ L;AHU ¼ 0

(6.52)

with the total heat lost being Q_ L;AHU ¼ Q_ L:RD þ Q_ L;RHE þ Q_ L;EV þ Q_ L;REV þ Q_ L;RHB

6.3.6

(6.53)

Exergy analysis of an AHU with rotary desiccant dryer

Although there are numerous works of analysis for these components based on the First Law, there are few publications that contemplate exergy analysis. We highlight among others the work of Kodama et al. 2000 [24] which evaluates entropy production due to internal and external irreversibilities and the effect of certain parameters on the generation of entropy. Ogueke 2014 [25] carries out an exergy balance in each of the components of a solar adsorption refrigerator, showing that the greatest destruction of exergy takes place in the adsorption and desorption phases, with exergy efficiencies in the range of 0.08%e1.2%. M. Mujahid 2016 [26] undertakes an exergy analysis of a solar cooling system by adsorption for ventilation, verifying that the adsorption wheel and the solar collector represent 65% of the total exergy destruction. Mandegari 2015 [27] performs an exergy analysis and optimization of an adsorption system with rotary exchanger for dehumidification. We return to the installation of Fig. 6.14, but now applying exergy analysis. The outside air is heated and dehumidified in the rotary desiccant dryer and then cooled in the sensitive regenerator and, by means of evaporative cooling, it is finally released into the room being conditioned. The system can operate in a closed cycle or more frequently in an open cycle with ventilation air. For the regeneration of the desiccant, heat usually needs to be given at temperatures between 60 and 90
C. As all the heat lost in the equipment is part of the irreversibilities, we will group them with the corresponding exergy destructions. By performing exergy balances in each of the components of the installation, we obtain the equations below.

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Exergy Analysis and Thermoeconomics of Buildings

6.3.6.1

Rotary desiccant dryer

Since the air in state 1 is atmospheric air, its physical and chemical exergy are zero. On the other hand, the exergy of state 9 is part of the exergy losses, so that the balance gives the equation m_ a

h

 i b8 þ bch  b2 þ bch ¼ I_RD 8 2

(6.54)

The irreversibilities in the rotary desiccant dryer are due to the heat transfer with a finite temperature gradient, to mass transfer with concentration gradient (actually, a gradient of chemical potential), to the head losses in the two flows and the heat flux lost. Both the process air and regeneration air enter and leave the rotary desiccant dryer with different humidities, and so the variation of their chemical exergy needs to be taken into account.

6.3.6.2

Regenerative heat exchanger

m_ a ðb2  b3 Þ þ m_ a ðb6  b7 Þ ¼ I_RHE

(6.55)

The irreversibilities are thermal, due to the exchange of heat between the flows as well as the heat lost and mechanical, associated with head losses.

6.3.6.3 m_ a

h

6.3.6.4 m_ a

h

Process evaporative cooler  i b3 þ bch  b4 þ bch þ m_ w; EV bw ¼ I_EV 3 4

(6.56)

Regeneration evaporative cooler  i b5 þ bch  b6 þ bch þ m_ w;REV bw ¼ I_REV 5 6

(6.57)

In the humidifiers, the irreversibilities are due to three different mechanisms: the heating or cooling of the water by the air, until it reaches the same temperature as the air, the evaporation of the water and the mixing of the water vapour with the humid air. Of these three mechanisms, the one that generates the greatest exergy destruction is the mixing.

6.3.6.5

Regeneration heat battery


 m_ a ðb7  b8 Þ þ m_ f bf ;in  bf ;ou  I_RHB ¼ 0

(6.58)

Exergy destruction is due to the transfer of heat between two flows of different temperatures.

Exergy analysis of thermal facilities equipment in buildings (II)

6.3.6.6

485

Complete AHU system

The exergy balance of the system is reflected by the following equation m_ a

h

 i

 b5 þ bch  b4 þ bch þ m_ w; EV þ m_ w;REV bw þ m_ f bf ;in  bf ;ou 5 4

¼ I_AHU (6.59) From the exergy balances, the destructions and losses associated with all the irreversibilities due to the adsorption and desorption processes can be obtained, as well as the heat exchanges with temperature jumps and mechanical irreversibilities. Since the goal of the AHU is to provide airflow in state 4, the exergy efficiency can be defined as  P _ m_ a b4 þ bch 4 jI j z1 
 4z
m_ f hf ;in  hf ;ou m_ f hf ;in  hf ;ou

6.3.7

(6.60)

Examples

Let there be an AHU rotary desiccant dryer like the one in Fig. 6.14 in which the outside air in state 1(T1 ¼ T0 ¼ 28
C, f1 ¼ f0 ¼ 80%) leaves the dryer in state 2(T2 ¼ 45
C, u2 ¼ 6 g/kg dry air). It then passes through the rotary exchanger where it leaves in state 3(T3 ¼ 26
C). At the outlet of the evaporative cooler it is in state 4 (u4 ¼ 8 g/kg d a), entering the room to be air conditioned. The return air leaves the room in state 5(T5 ¼ 25
C, u5 ¼ 11 g/kg d a) increasing its humidity in the evaporative cooler to state 6(u6 ¼ 13 g/kg d a). In the heater, a flow of water of 0.64 kg/s enters at 70
C and leaves at 62
C, giving that heat to the air that passes through the rotary desiccant dryer, where it modifies its state and is expelled to the environment in state 9. The rotary desiccant dryer has losses of 6% and the rotary heat exchanger of 4% with respect to the heat supplied. In both evaporative coolers, the water is injected at a temperature of 12
C. Assuming a constant pressure of 1 bar in the whole installation, and with the rate of mass flow of dry air being 1 kg/s, determine Example E.6.3.

(a) The temperature and absolute humidity of the air at the inlet and outlet of each component of the AHU. (b) The irreversibilities in the rotary desiccant dryer and percentage of exergy contributed to the AHU. (c) The irreversibilities in the rotary exchanger. (d) The irreversibilities in the AHU and its exergy efficiency.

Solution (a) In order to simplify the calculations and show the operations that are being carried out, we use a specific heat for dry air of cp,a ¼ 1.004 kJ/kg$K and for water vapour

486

Exergy Analysis and Thermoeconomics of Buildings

cp,v ¼ 1.86 kJ/kg$K. As the vapour pressure at 28
C is ps(28
C) ¼ 37.83 mbar the absolute humidity of the atmospheric air is

u1 ¼ 0:622

ps ð28
CÞ g ¼ 19 1; 000 kg d a  ps ð28
CÞ f1

The states 1(T1 ¼ T0 ¼ 28
C, u1 ¼ u0 ¼ 19 g/kg dry air) and 2(T2 ¼ 45
C, u2 ¼ 6 g/kg d a) are thus defined. The humidity in state 3 is the same as that of 2, therefore 3(T3 ¼ 26
C, u3 ¼ 6 g/kg d a). To determine the temperature in state 4 we undertake a balance of mass and energy in the evaporative process cooler m_ a u3 þ m_ w; EV ¼ m_ a u4 /m_ w; EV ¼ 2

g s


 m_ a h3 þ m_ w;EV hw ¼ m_ a h4 ðT4 Þ/m_ a cp;a T3 þ u3 lð0
CÞ þ cp;v T3 þ m_ w;EV cw Tw


 ¼ m_ a cp;a T4 þ u4 lð0
CÞ þ cp;v T4 meaning that the temperature T4 is T4 ¼ 21:1
C Therefore, the state at the outlet of the evaporative process cooler is 4(T4 ¼ 21.1
C, u4 ¼ 8 g/kg d a). The state of the return air at the outlet of the building is known 5(T5 ¼ 25
C, u5 ¼ 11 g/kg d a). To define the state at the outlet of the evaporative regeneration cooler we need, as before, the mass and energy balances m_ a u5 þ m_ w;REV ¼ m_ a u6 /m_ w;REV ¼ 2

g s

m_ a h5 þ m_ w;REV hw ¼ m_ a h6 ðT6 Þ/T6 ¼ 20:1
C And so 6(T6 ¼ 20.1
C, u6 ¼ 13 g/kg d a). State 7 has the same humidity as state 6 and to know its temperature we carry out an energy balance in the rotary heat exchanger m_ a ðh2  h3 Þ þ m_ a ðh6  h7 Þ  Q_ L;RHE ¼ 0/T7 ¼ 38:2
C _ a ðh2  h3 Þ. So, 7(T7 ¼ 38.2 C, u7 ¼ 13 g/kg d a). The since Q_ L;RHE ¼ 0:04 m humidity of state 8 is the same as that of 7 and to find its temperature we carry out a balance of energy in the heat battery
 m_ a ðh7  h8 Þ þ m_ f hf ;in  hf ;ou  Q_ L; RHB ¼ 0

Exergy analysis of thermal facilities equipment in buildings (II)

487

1:004ðT8  38:3Þ þ 0:013$1:86ðT8  38:3Þ ¼ 0:64$4:18ð70  62Þ/T8 ¼ 59
C Therefore 8(T8 ¼ 59
C, u8 ¼ 13 g/kg d a). Finally, to define state 9 we carry out a balance of mass and energy in the rotary desiccant dryer u8 þ ðu1  u2 Þ ¼ u9 /u9 ¼ 26

g kg d a

m_ a ðh1  h2 Þ þ m_ a ðh8  h9 Þ  Q_ L;RD ¼ 0/T9 ¼ 41:0
C so that 9(T9 ¼ 41.0
C, u9 ¼ 26 g/kg d a). (b) The heat lost plus the exergy destructions are the total irreversibilities of the rotary desiccant dryer. Since for atmospheric air we have b1 ¼ bch 1 ¼ 0, and since the exergy of the air in state 9 forms part of the external irreversibilities, the exergy balance in the rotary desiccant dryer tells us that



 ch m_ a b8 þ bch ¼ I_RD 8  b2 þ b2

Therefore, using the expressions of physical exergy, Eq. (3.37), and chemical exergy, Eq. (3.123), for humid air we have b2 ¼ 0:47

kJ kg d a

bch 2 ¼ 0:84

kJ kg d a

kJ kg d a

bch 8 ¼ 0:15

kJ kg d a

and in state 8. b8 ¼ 1:54

The exergy balance gives I_RD ¼ 0:37 kW The water used in the evaporative coolers is at 12
C. Without taking into account the electricity consumed by the pumps in the installation, we get that the exergy provided to the AHU is
 m_ f bf ;in  bf ;on þ m_ wa EV bw; EV þ m_ w;REV bw;REV ¼ 2:40 kW so the irreversibility in the rotary desiccant dryer represents 15.5%. (c) Undertaking an exergy balance in the rotary exchanger gives m_ a ðb2  b3 Þ þ m_ a ðb6  b7 Þ ¼ I_RHE /I_RHE ¼ 0:46 kW

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Exergy Analysis and Thermoeconomics of Buildings

(d) From the exergy balance in the AHU, we have

 m_ f bf ;in  bf ;ou þ m_ w; EV bw; EV þ m_ w;REV bw;REV þ m_ a b5 þ bch 5
 _ ¼ m_ a b4 þ bch 4 þ I AHU

Calculating the physical and chemical exergy in states 4 and 5, we have b4 ¼ 0:08

kJ kg d a

b5 ¼ 0:015

kJ kg d a

bch 4 ¼ 0:57

kJ kg d a

bch 5 ¼ 0:27

kJ kg d a

Therefore, the  exergy of the air for the air conditioning of the building is m_ a b4 þ bch ¼ 0:65 kW and the total irreversibilities in the AHU are 4 I_AHU ¼ 21:03 kW The object of the AHU is to obtain the airflow in state 4 for the conditioning of the premises; in short, this is its product. Ignoring the exergy of the water in the evaporative coolers, the resource used is the exergy provided by the heat battery, so that exergy efficiency gives  m_ a b4 þ bch 4  ¼ 3% 4¼
m_ f bf ;in  bf ;ou

6.4

Exergy analysis of basic air conditioning processes

For a person to feel comfortable inside a room, among other requirements, the temperature and humidity of the air need to be within a certain range of values. Regarding humidity, comfortable conditions are found in a wide range of values of relative humidity between 30% and 70%, since outside these limits there may be both harmful effects on the health of the occupants and damage done to the materials present in the premises. Likewise, for the operation of certain equipment or storage of certain products, temperature and humidity conditions are required in a well-defined range. However, through heat and mass transfers between the interior of the room and the external environment, as well as by possible internal effects, such as those due to lighting, the people themselves, etc. the temperature and humidity values may depart from desired levels. The state of the air, therefore, needs to be modified to maintain the conditions of thermal comfort that are required. To this end, equipment is available to increase or decrease the temperature and humidity of the air. The actual

Exergy analysis of thermal facilities equipment in buildings (II)

489

processes that air experiences when passing through this equipment can be more or less complicated and, of course, depends on heat and/or mass transfer speeds. However, the study of these transport phenomena is not the objective of this book. As we intend to simply apply thermodynamics, we will consider the different air treatment equipment such as CV i.e. black boxes in which we will first apply mass and energy balances, and then perform exergy balance. All the processes that we will study will be in the steady state and, in addition, barometric pressure will be assumed to be constant. These assumptions are valid in almost all psychrometric processes since the head losses that occur are small if the starting and stopping periods are ignored. In recent years, there have been several studies on the application of exergy analysis in psychrometric processes. Qureshi and Zubair 2003 [28] conducted parametric studies to evaluate the effect of the relation of flow and relative humidity on the efficiency of processes. Marletta 2010 [29] used exergy analysis to evaluate the behaviour of three common air conditioning systems: all air, dual duct and systems with fan coils. Sakulpipatsin et al. 2010 [30] presented an exergy study from the demand of the building to the heat and cold generation and Dincer and Ratlamwala 2013 [31] studied five psychrometric processes using different definitions of exergy efficiency. Likewise, Noro 2015 [32] analysed air conditioning systems based on direct and indirect evaporative cooling from the point of view of exergy.

6.4.1

Sensitive heating or cooling

In a sensitive heating process, heat is supplied to the air without modifying its humidity. This is what happens when air is passed through a hot surface, for example, a heat battery or through an electrical resistance. Sensitive cooling is logically the opposite of heating, but in this case for cooling only, the temperature of the cold surface that comes into contact with the air must be higher than its dew point. As an example, consider a heating process, such as the one shown in Fig. 6.16, between states 1 and 2. Such a heating process is carried out by means of a m_ w mass flow rate of hot water that is cooled from state 3 to state 4 at the outlet of the exchanger.

Figure 6.16 Sensitive air heating.

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Exergy Analysis and Thermoeconomics of Buildings

Both the humidity and the mass flow of dry air is the same in 1 as in 2. Considering the CV of Fig. 6.16, and the heat lost to the exterior as negligible, the energy balance is m_ a ðh2  h1 Þ ¼ m_ w ðh3  h4 Þ

(6.61)

Undertaking an exergy balance gives in the following equation m_ a ðb2  b1 Þ ¼ m_ w ðb3  b4 Þ  D_

(6.62)

where D_ is the rate of exergy destruction. There is considerable discussion in the literature on how to define exergy efficiency in psychrometric processes: Marletta, 2010 [29], Dincer and Ratlamwala 2013 [31], Bejan 2006 [33], Hui and Wong 2011 [34]. In this section, we will continue using the general expression of the efficiency that we saw in Chapter 2, as a relationship between the exergy of the product and the exergy of the contributed resources. For this process, we will consider as product the increase of energy (exergy) of the airflow in heating, while in cooling the product is the decrease of energy (increase of exergy). Therefore, the numerator of the expression will be the energy (exergy) at the outlet minus the energy (exergy) at the inlet, and if it is cooling in reverse, while the resource used is the decrease of the energy (exergy) experienced by the hot water, and if it is cooling, the energy increase (exergy decrease) of the cold water. With this criterion, the energy efficiency of the process is h¼

m_ a ðh2  h1 Þ m_ w ðh3  h4 Þ

(6.63)

Having considered that there is almost no heat lost (it is adiabatic) the energy efficiency is the unit. The exergy efficiency is, however, 4¼

D_ m_ a ðb2  b1 Þ ¼1 m_ w ðb3  b4 Þ m_ w ðb3  b4 Þ

(6.64)

very far from the unit, due to the exergy destruction associated with the irreversibility of heat transfer between both flows of air and water.

6.4.2

Dehumidification by cooling

When the air is cooled below its dew point temperature, vapour condensation is taking place and, consequently, its absolute humidity decreases. Fig. 6.17 shows a schema of a cooling and dehumidification battery, operating by exchanging heat with a flow of cold water or a refrigerant, which is at a temperature below the dew point of the air. Likewise, cooling to a temperature below the dew point can also be achieved by passing the air through a shower of sufficiently cold water, as we will discuss later.

Exergy analysis of thermal facilities equipment in buildings (II)

491

Figure 6.17 Dehumidification by cooling.

Figure 6.18 Dehumidification by cooling in a psychrometric diagram.

The process experienced by the air is shown in a psychrometric diagram in Fig. 6.18. As we can see, the humidity of the air, as well as its dry-bulb temperature and enthalpy decrease, while its relative humidity increases. We may think that the final state 2 should be on the line f ¼ 1, that is, it should be saturated air. However, in reality, this is not achieved as there is no cooling exchanger that is 100% efficient. Not all the air that passes through the exchanger comes into contact with the tubes; what is called the by-pass factor needs to be taken into account, which is defined as the percentage of air that leaves the battery without any change, under the assumption that the rest of the flow has been treated ideally, that is, that it finally reaches the temperature of the battery surface. Let us suppose that the cooling and condensation of the vapor is achieved by a cold water mass flow, or directly from a refrigerant mass flow rate m_ r , that enters the exchanger in state 3 and comes out in state 4. Undertaking a mass balance for water, we have that m_ a u1 ¼ m_ a u2 þ m_ cond

(6.65)

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Exergy Analysis and Thermoeconomics of Buildings

and therefore, the humidity of state 2 is u2 ¼ u 1 

m_ cond m_ a

(6.66)

where m_ cond is the mass flow of condensed water per unit of time. By applying the First Law to the CV of Fig. 6.17 and assuming this to be approximately adiabatic, we get the following equation m_ a ðh1  h2 Þ ¼ m_ r ðh4  h3 Þ þ m_ cond hcond

(6.67)

with hcond being the specific enthalpy of the water that has condensed. Ignoring the enthalpy of the condensate and with Q_ being the rate of heat exchanged in the battery between the air and the refrigerant, the balance of water and energy gives Q_ m_ cond

¼

h1  h2 u 1  u2

(6.68)

We see that the relation between the heat exchanged by the air in the battery and the mass flow of condensate does not depend on the mass flow of circulating air. This quotient between the enthalpy variation and the humidity variation is called the manoeuvering line. On the other hand, another parameter that defines the evolution of air is the so-called sensitive heat factor (SHF), which is defined as the relationship between the variation of enthalpy associated with temperature (sensitive heat) and that associated with the variation of humidity (latent heat). Both the manoeuvering line and the SHF define the evolution experienced by the air, and both parameters are related, Torrella 2014 [35] and Wang 2000 [36]. Looking now to the exergy analysis, undertaking a balance of exergy gives the exergy destruction rate as h  i ch m_ r ðb3  b4 Þ þ m_ a b1 þ bch þ b (6.69)  b  m_ cond bcond ¼ D_ 2 1 2 In this type of process, the refrigerant (or cold water) that enters the battery below the ambient temperature, decreases its exergy, so that b4hs,H0>Hs) the basic processes would be mixing (M), cold battery with recirculation (B0 ) and sensible heating (S), Fig. 6.23d.

Let us suppose, for example, that we combine a heating process with subsequent humidification by water injection, as shown in the diagram of Fig. 6.24. As we have seen, these processes are part of the air treatment in air conditioning units in the winter months, when the outside air is cold and dry. If we use 3 and 4 for the states of the fluid used for heating (which can be hot water) at the input and output to the exchanger, undertaking an energy balance in the CV of the figure we get m_ a ðh2  h1 Þ  m_ w hw ¼ m_ hw ðh3  h4 Þ

Figure 6.24 Heating and subsequent humidification.

(6.81)

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Exergy Analysis and Thermoeconomics of Buildings

with m_ hw being the hot water rate of mass flow in the exchanger. Combining this equation with the one that results from the mass balance for water, we have h2  h1 m_ hw ðh3  h4 Þ þ hw ¼ u2  u1 m_ a ðu2  u1 Þ

(6.82)

Applying the exergy analysis, we have that the exergy destruction in the CV under consideration, referred to as per unit of time, is D_ ¼

h

 i b1 þ bch  b2 þ bch þ m_ hw ðb3  b4 Þ þ m_ w bw 1 2

(6.83)

with the exergy efficiency of the combined process being.

4¼

m_ a

h

 i b2 þ bch  b1 þ bch 2 1

m_ hw ðb3  b4 Þ þ m_ w bw

(6.84)

In their day, Wepfer et al. 1979 [38] made a detailed study of a double-duct installation, obtaining an exergy efficiency that ranges from 3.2% in summer conditions to 11.8% in winter. These results show that there are great possibilities for improving air conditioning processes. Precisely, the detailed assessment of the irreversibilities in each element of the installation allows us to find those places where improvements should be considered as a priority (storage, recovery of waste heat, improvements to the control system, etc.) as well as the possibility of introducing alternative systems, such as heat pumps operating at low temperatures, which eliminate the great exergy destructions that occur in steam boilers or hot water generators.

6.4.6

Examples

Example E.6.4.

In the enclosure of an indoor pool, the air needs to be kept in the following conditions: T ¼ 26
C, f ¼ 0.65, and maximum chlorine concentration ¼ 1.5 mg/m3. The water temperature of the pool is 24
C, its free surface A ¼ 450 m2, and its depth (constant) h ¼ 2 m. The pressure inside the enclosure is the same as the ambient pressure P0 ¼ 1018 mbar and the ambient temperature and humidity are T0 ¼ 5
C and f0 ¼ 0.9. Determine the mass flow rate of renewal air (airflow taken from outside), knowing that (a) The evaporation rate of the pool water can be calculated by the formula: m_ ¼ 25:5 Aðps  pv Þ=ðp0  pv Þ; with m_ expressed in kg/h and A in m2, and with pv being the partial pressure of the vapour in the air, and ps the saturation pressure at the water temperature of the pool. (b) The concentration of chlorine in the pool water, kept constant, is 0.15 g/m3, and assuming that in 24 h the total chlorine content in the water is released to the environment, and the maximum concentration of Cl in the air of the pool is 1.5$106 kg/m3.

Exergy analysis of thermal facilities equipment in buildings (II)

499

(c) Due to the estimated occupancy in such an installation, at least 1.3 renovations per hour of the air in the enclosure, whose volume is V ¼ 4290 m3, are considered necessary.

Solution (a) From the vapour tables we have ps(24
C) ¼ 30.8 mbar, so pv ¼ fps ð26
CÞ ¼ 22:55 mbar

Substituting values in the given formula, we get that the evaporation rate of the water in the pool is m_ ev ¼ 25: 5A

ps  pv kg ¼ 95:10 h p0  pv

For maintaining the state of the air inside the pool enclosure, a renewal of airflow would be needed such that if m_ a is the mass flow rate of dry air, we have m_ a u0 þ m_ ev ¼ m_ a ui where u0 and ui are the absolute humidities of the external and internal air respectively. As ps(5
C) ¼ 8.72 mbar u0 ¼ 0:622 p0 f0

ps ð5
CÞ  ps ð5
CÞ

¼ 4:83

g kg d a

and for the indoor humidity, as ps(26
C) ¼ 34.69 mbar ui ¼ 0:622

34:69 g ¼ 14:10 1018 kg d a  34:69 0:65

Substituting these values gives m_ a ¼

kg m_ ev ¼ 10; 274 h u i  u0

(b) Calculating the airflow needed to maintain that maximum Cl concentration in the pool air. Vpo ¼ A:h ¼ 900 m3

The exit mass flow rate of the Cl of the pool water is m_ Cl ¼

Vpo cCl 900$0:15$103 kg ¼ ¼ 5:62$103 h 24 24

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Exergy Analysis and Thermoeconomics of Buildings

Undertaking a balance in the Cl, the following must be true
 m_ a þ m_ Cl ¼ m_ a 1 þ ymax Cl where yCl is the mass fraction of Cl in the pool air. If we know the air density of the pool, the mass fraction for the maximum concentration condition will be ymax Cl ¼ 1:5$ 106 ri . Calculating the density of the indoor air, per unit mass of dry air vi ¼ ðRa þ ui Rv Þ 9i ¼

Ti ¼ pi

  8:314 8:314 299 m3 þ 0:014 ¼ 0:864 5 28:9 18 kg d a 1:018$10

1 kg d a ¼ 1:157 vi m3

so the maximum mass fraction of Cl in the pool air is 6 ymax Cl ¼ 1:30$10

therefore giving m_ a ¼

kg m_ Cl ¼ 4; 323 h ymax Cl

(c) Let us now see the demands of the renewal air m3 V_ re ¼ 1:3$V ¼ 5; 577 h

It is clear that the higher requirements correspond to the need for maintaining humidity in the pool air, so the dry airflow required is m_ a ¼ 10; 274kg=h. Since the specific volume of the air in the external conditions is v0 ¼ ðRa þ u0 Rv Þ

T0 m3 ¼ 0:794 p0 kg d a

the airflow is m3 V_ ¼ m_ a v0 ¼ 8; 157 h An airflow of 3800 kg/h at 2
C is taken from the outside with a relative humidity of 70%, passing through an electrical resistance where it is heated up to 12
C. Then, that air is mixed with another flow of air at 20
C saturated with humidity, so that the mass flow rate of saturated air is double. With the environmental pressure at 1 bar, determine

Example E.6.5.

Exergy analysis of thermal facilities equipment in buildings (II)

(a) (b) (c) (d) (e)

501

The absolute and relative humidity of the air after passing through the electrical resistance. The heat given in the resistance. The exergy destruction in this heating process. The temperature and relative humidity of the air resulting from the mixture. The exergy destruction in the mixture of the two flows.

Solution (a) Calculating the absolute humidity of the outside air, the atmospheric air, which we call air in state 0. Since ps(2 C) ¼ 7.059 mbar, we have u0 ¼ 0:622 p0 f0

ps ð2
CÞ  ps ð2
CÞ

¼3

g kg d a

After passing through the electrical resistance, the air in state 1 has the same absolute humidity, u1 ¼ u0 ¼ 3 g/kg dry air. The relative humidity is f1 ¼

u1 p0 ¼ 34:2% u1 þ 0:622 ps ð12
CÞ

Before going further, we calculate the mass flow of dry air. m_ a;0 ð1 þ u0 Þ ¼ 3800

kg kg d a /m_ a;0 ¼ 1:050 h s

(b) Applying the energy balance we have Q_ ¼ m_ a;0 ðh1  h0 Þ ¼ 10:6 kW (c) Undertaking an exergy balance and with the electricity consumption in the resistance being _ we have E_ ¼ Q, E_  m_ a;0 ðb1  b0 Þ ¼ D_

Since we consider air as a mixture of ideal gases, dry air and water vapour, of approximately constant specific heats cp,a ¼ 1.004 kJ/(kg$K) and cp,v ¼ 1.86 kJ/ (kg$K) and with the pressure being constant, the change of the physical exergy of the air is


b1  b0 ¼ b1 ¼ cp;a þ u1 cp;v



  T1 kJ ¼ 0:18 T1  T0  T0 ln kg d a T0

which coincides with the exergy of 1, since b0 ¼ 0. Substituting in the exergy balance equation gives D_ ¼ 10:4 kW

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Exergy Analysis and Thermoeconomics of Buildings

This result shows us the highly irreversible nature of this heating process since approximately 98% of the exergy contributed is destroyed. (d) First, we calculate the mass flow rate of the saturated air at 20
C, which we call air 2, and for which we first determine the absolute humidity. Since ps(20
C) ¼ 23.39 mbar and when saturated f2 ¼ 1, we have u2 ¼ 0:622 p0 f2

ps ð20
CÞ  ps

ð20
CÞ

¼ 14:9

g kg d a

As the mass flow rate of air in state 2 is double, we have the relationship m_ a;2 ð1 þ u2 Þ ¼ 2m_ a;0 ð1 þ u0 Þ/m_ a;2 ¼ 2:075

kg s

If the air resulting from the mixture is 3, from the mass balances in the mixing process, we have that m_ a;1 þ m_ a;2 ¼ m_ a;3 /m_ a;3 ¼ 3:125

kg d a s

m_ a;1 u1 þ m_ a;2 u2 ¼ m_ a;3 u3 /u3 ¼ 10:9

g kg d a

To find the temperature resulting from the mixture we carry out the energy balance, which is m_ a;1 h1 þ m_ a;2 h2 ¼ m_ a;3 h3 /T3 ¼ 17:6
C As ps(17.6
C) ¼ 19.4 mbar, the relative humidity is u3 ¼ 0:622 p0 f3

ps ð17:6
CÞ  ps

ð17:6
CÞ

/f3 ¼

p0 u3 0:622 ps ð17:6
CÞ þ u3 ps ð17:6
CÞ

¼ 89% (e) Performing the exergy balance in the mixing process, we have


 _ _ a;2 b2 þ bch _ a;3 b3 þ bch m_ a;1 b1 þ bch 1 þm 2 m 3 ¼D

Calculating the physical and chemical exergy of the air in each state. Using Eq. (3.37) for physical exergy, we have b1 ¼ 0:18

kJ kg d a

b2 ¼ 0:58

kJ kg d a

b3 ¼ 0:44

kJ kg d a

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503

Calculating the chemical exergy for which we use Eq. (3.124). Since state 1 has the same humidity as the ambient air, its chemical exergy is zero. bch 1 ¼0

bch 2 ¼ 1:52

kJ kg d a

bch 3 ¼ 0:53

kJ kg d a

Returning to the balance equation, we have D_ ¼ 1:51 kW In the AHU of an air conditioning installation, a flow of 250 m3/h of outdoor air at 38
C, relative humidity 78% and pressure of 1 bar is mixed with a flow of 70 m3/h of recirculated air at 26
C and relative humidity 60%. The air resulting from the mixture is passed through a cold battery, where it is cooled to a temperature of 15
C. In this battery, the fluid that cools the air is a flow of water that enters the battery at 7
C and leaves at 12
C. As part of the vapour condenses, there is then a moisture separator and finally a heat battery, where a flow of hot water decreases its temperature from 55
C to 45
C, with the final air temperature being 21
C and where the heat losses are 30%. Determine

Example E.6.6.

(a) (b) (c) (d) (e) (f)

The state of the air resulting from the mixture of the two flows. The heat exchanged by the air in the cold battery and the quantity of condensed water. The exergy destruction in the cold battery. The flow of hot water in the heat battery. The exergy destruction in the heat battery. Energy efficiency and exergy efficiency of the AHU and total irreversibilities.

Solution (a) First, we calculate the mass flow of the outside air, state 0, and recirculation air, state 1. The specific volume per unit mass of dry air is obtained from the thermal state equation, since pV ¼ ðma Ra þ mv Rv ÞT/v ¼

V T ¼ ðu þ 0:622ÞRv ma p

Calculating the absolute humidity of the air in states 0 and 1. As ps(38
C) ¼ 66.33 mbar, and ps(26
C) ¼ 33.64 mbar we have u0 ¼ 0:622 p0 f0 u1 ¼ 0:622 p0 f1

ps ð38
CÞ  ps

ð38
CÞ

ps ð26
CÞ  ps

ð26
CÞ

¼ 34

g kg d a

¼ 13

g kg d a

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Exergy Analysis and Thermoeconomics of Buildings

Using the previous expression for the specific volume we have v0 ¼ ðu0 þ 0:622ÞRv

T0 m3 ¼ 0:94 p0 kg d a

v1 ¼ ðu1 þ 0:622ÞRv

T1 m3 ¼ 0:88 p0 kg d a

Therefore, the dry air mass flow rates are m_ a;0 ¼

V_ 0 kg d a ¼ 265:9 h v0

m_ a;1 ¼

V_ 1 kg d a ¼ 79:5 h v1

Once these values are obtained, we calculate the air resulting from the mixture, which we call air in state 2. m_ a;0 þ m_ a;1 ¼ m_ a;2 /m_ a;2 ¼ 345:4

kg d a h

m_ a;0 u0 þ m_ a;1 u1 ¼ m_ a;2 u2 /u2 ¼ 29

g kg d a

m_ a;0 h0 þ m_ a;1 h1 ¼ m_ a;2 h2 /T2 ¼ 35:7
C (b) To calculate the heat exchanged by the air in the cold battery, we first determine the condensed water. Assuming that the bypass factor of the battery is zero, so that all the air is treated ideally and saturated. With 3 being the state of the air at the exit of the battery, since ps(15
C) ¼ 17.06 mbar and f3 ¼ 1 we have u3 ¼ 0:622 p0 f3

ps ð15
CÞ  ps ð15
CÞ

¼ 10:8

g kg d a

Therefore, the amount of condensed water is m_ cond ¼ m_ a;2 ðu2  u3 Þ ¼ 6:29

kg h

From the energy balance we get Q_ cb ¼ m_ a;2 ðh2  h3 Þ  m_ cond hcond and since


m_ a;2 ðh2  h3 Þ  m_ cond hcond ¼ m_ a;2 cp;a T2 þ 2500 þ cp;v T2 u2  
 cp;a T3 þ 2500 þ cp;v T3 u3  m_ cond ccond T3

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505

this means Q_ cb ¼ 6:51  0:11 ¼ 6:40 kW Although the enthalpy of the condensate has been included in this equation, we see that its value is practically negligible compared to the change of the enthalpy of the air. (c) Carrying out an exergy balance in the battery and taking into account that the small exergy of the condensate is lost, we have

 
 ch _ þ b m_ w;c bw;in  bw;ou þ m_ a;2 b2 þ bch  m b ¼ I_cb a;3 3 2 3 Calculating each of the terms on the left of the equality. We first determine the mass flow rate of cold water in the battery  kg Q_ cb ¼ m_ w;c hwð12
CÞ  hwð7
CÞ /m_ w;c ¼ 0:30 s We now calculate the terms of the exergy balance. The exergy change of water in the cold battery is calculated using Eq. (3.43) and the physical exergy of the air using Eq. (3.37) bw;in  bw; ou ¼ 2:11

kJ kg

b2 ¼ 0:009

kJ kg

b3 ¼ 0:92

kJ kg

The specific chemical exergy of the air in states 2 and 3 is calculated by applying Eq. (3.124), resulting in bch 2 ¼ 0:05

kJ kg

bch 3 ¼ 1:49

kJ kg

From the balance equation, we have I_cb ¼ 0:41 kW (c) The humidity of the air at the output of the heat battery, state 4, is the same as in state 3, u4 ¼ 10.8 g/kg da. The heat given to the air in the heat battery is Q_ hb ¼ m_ a;3 ðh4  h3 Þ/Q_ hb ¼ 0:59 kW

with the mass flow rate of hot water being  kg Q_ hb ¼ m_ w; h hwð55
CÞ  hwð45
CÞ /m_ w; h ¼ 50:8 h

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Exergy Analysis and Thermoeconomics of Buildings

(d) From the exergy balance we get
 m_ w; h bw;in  bw;ou þ m_ a;3 ðb3  b4 Þ ¼ I_bc

where
 m_ w;h bw;in  bw; ou ¼ 21:8 W m_ a;3 ðb3  b4 Þ ¼ 40:5 W and therefore I_hb ¼ 62:4 W (e) Under the perspective of the First Law, the resources (F) used in the AHU are the energy provided by the heat battery, the cold supplied in the cold battery and the enthalpy of the recirculation air. We will ignore the enthalpy of the air in state 0, since it is ambient air. And so F ¼ Q_ cb þ Q_ hb þ m_ a;1 h1 ¼ 6:40 þ 0:59 þ 1:31 ¼ 8:30 kW

The goal of the AHU, that is, its product P, is to prepare the airflow in state 4. Therefore P ¼ m_ a;4 h4 ¼ 4:70 kW Therefore, the energy efficiency of the AHU is h¼

P 4:70 ¼ ¼ 56:6% F 8:30

We now determine the exergy efficiency. The exergy contributed to the AHU is    F ¼ m_ w;c bwð7
CÞ  bwð12
CÞ þ m_ w;h bwð55
CÞ  bwð45
CÞ þ m_ a;1 b1 þ bch 1 Calculating each of the terms that form part of the resources used  m_ w;c bwð7
CÞ  bwð12
CÞ ¼ 630 W

 m_ w; h bwð55
CÞ  bwð45
CÞ ¼ 22 W

The physical and chemical exergy of the air in state 1 is b1 ¼ 0:24

 kJ kJ bch /m_ a;1 b1 þ bch ¼ 31 W 1 ¼ 1:17 1 kg d a kg d a

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507

Therefore, the fuel contributed to the AHU is F ¼ 683 W The product of the installation is the flow of air-conditioned generated, this is  P ¼ m_ a;4 b4 þ bch 4 where, applying Eq. (3.37) and Eq. (3.124) we get b4 ¼ 0:49

kJ kg d a

bch 4 ¼ 1:46

kJ kg d a

and so P ¼ 187 W In short, the exergy efficiency of the AHU is 4¼

P ¼ 27:4% F

so that the total irreversibilities of the AHU represent 72.6% of the exergy contributed, that is, 496 W. In a heat exchanger, a vapour flow rate of 20 t/h is condensed with cold water, its state at the inlet corresponding to a wet vapour at 0.056 bar and quality 0.92 and at the outlet, saturated liquid. The refrigeration water flow rate is 330 kg/s and is heated in the exchanger to 28
C. Given the limited availability of water, it must be recirculated, so to cool it, it is passed through a cooling tower with a 60 kW fan, whose operating conditions are as follows: (1) In summer, the air enters the tower at 30
C with a relative humidity of 60%, leaving it at 25
C and with relative humidity of 100%; (2) In winter, air enters the tower at 8
C and relative humidity of 30%, leaving at 17
C with 95% relative humidity. The temperature of the replacement water is 20
C in summer and 8
C in winter. If the temperature of the refrigeration water at the entrance of the exchanger is constant, for both operating conditions, and the ambient pressure is 1 atm, calculate:

Example E.6.7.

(a) The mass airflow rate in the cooling tower and mass flow rate of replacement water in summer and winter. (b) The rate of exergy destruction in the tower in summer. (c) The exergy efficiency of the tower in summer. (d) Th rate of exergy destroyed in the exchanger also in summer. (e) Does it make sense to define the exergy efficiency of the heat exchanger?

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Exergy Analysis and Thermoeconomics of Buildings

Solution. In the following Fig. E.6.2 a schema of the installation is shown.

Figure E.6.2 Schema of the installation.

(a) According to the nomenclature adopted in Fig. E 6.2, carrying out an energy balance in the exchanger, we have
 m_ v hv;1  hv;2 ¼ m_ w ðhI  hIII Þ

From the thermodynamic data for vapour we have hv;2 ¼ 133:9

kJ kg

hv;1 ¼ h0 þ x1 :l ¼ 146:6 þ 0:92$2:418; 1 ¼ 2:371; 2

kJ kg

Since m_ v ¼ 20t=h and m_ w ðhI  hIII Þ ¼ 330$4:18ð28  TIII Þ substituting these values in the balance equation, gives TIII ¼ 19
C. The replacement water is evaporated in the tower so that m_ IV ¼ m_ a ðu1  u0 Þ We do not take into account the kinetic energies of the air and water flows or head losses, so in the energy balance in the tower we do not include the power of the fans. Therefore, from the energy balance in the tower, we have m_ w hI þ m_ a h0 ¼ ½m_ w  m_ a ðu1  u0 ÞhII þ m_ a h1

Exergy analysis of thermal facilities equipment in buildings (II)

509

From the energy balance in the mixing of the return water of the cooling tower with the replacement water we get m_ a ðu1  u0 ÞhIV þ ½m_ w  m_ a ðu1  u0 ÞhII ¼ m_ w hIII Eliminating hII between these two equations, we have m_ a ¼

m_ w ðhI  hIII Þ h1  h0  ðu1  u0 ÞhIV

In summer, since ps(30
C) ¼ 42.42 mbar and ps(25
C) ¼ 31.66 mbar, we have ps ð30
CÞ

u0 ¼ 0; 622 p0 f0

 ps

ð30
CÞ

¼ 16

g kg d a

with the enthalpy of the atmospheric air being
 h0 ¼ cp;a T0 ð
CÞ þ u0 lð0
CÞ þ cp;v T0 ð
CÞ ¼ 71:8

kJ kg d a

For the air at the output of the cooling tower u1 ¼ 0:622 p0 f1

ps ð25
CÞ  ps ð25
CÞ

¼ 20

g kg d a

with its enthalpy being 
h1 ¼ cp;a T1 ð
CÞ þ u1 lð0
CÞ þ cp;v T1 ð
CÞ ¼ 76:2

kJ kg d a

Substituting these values in the previous equation, we have that m_ a ¼ 2:618:6

kg d a s

As v0 ¼ ð0:622 þ u0 ÞRv

T0 m3 ¼ 0:881 p kg d a

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Exergy Analysis and Thermoeconomics of Buildings

this means that the volume airflow rate is m3 V_ 0 ¼ m_ a v0 ¼ 2; 307 s with the replacement water being m_ IV ¼ m_ a ðu1  u0 Þ ¼ 10:5

kg s

Values for winter are solved in a totally analogous way, obtaining the following m_ a ¼ 376:5

kg d a s

m3 V_ 1 ¼ m_ a v1 ¼ 300:8 s

m_ IV ¼ 3:6

kg s

Note that the results obtained are very different. In summer, you need a mass flow rate of air that is more than seven times the mass flow rate that is needed in winter and the replacement water needed is almost three times of that needed in winter. (b) In the cooling tower, the inlet air is atmospheric air, and therefore, its exergy is zero. The air that comes out of the tower has physical and chemical exergy, but that exergy is finally destroyed in the environment so that it forms part of the external irreversibilities (losses). Therefore, undertaking an exergy balance in the tower, we have W_ ven þ m_ w bI  ½m_ w  ðu1  u0 Þm_ a bII ¼ I_CTW

Calculating each of the terms on the left of this equation. For this, we need to previously know the temperature TII. Undertaking a balance of energy in the mixture with the return water, we have 10:5 hIVð20
CÞ þ 319:5 hIIðtII Þ ¼ 330 hIIIð19
CÞ /TII ¼ 18:9
C According to the statement, the replacement water and the ambient air are not in thermodynamic equilibrium, since their temperatures are different. For the calculation of the exergy of the water mass flow rates we choose as ambient temperature the one corresponding to the replacement water, that is, 20
C. We now calculate the specific exergy of the water at the states I and II. As their temperatures are known, through Eq. (3.44) we have bI ¼ 0:45

kJ kg

bII ¼ 0:008

kJ kg

Returning to the equation of exergy balance finally gives I_CTW ¼ 205:9 kW

Exergy analysis of thermal facilities equipment in buildings (II)

511

(c) The objective of the tower is to cool the flow of water that circulates through it, that is, to reduce its exergy, so that the more the water cools (more heat dissipates), the better the operation of the tower. It is, therefore, a dissipative equipment, which only makes sense in that, it is an auxiliary component that serves other productive equipment. Together with the exchanger (condenser) its mission is to condense the vapour mass flow. Therefore, it does not make sense to define an exergy efficiency, as the exergy dissipated in it will be attributed to the productive equipment it serves. (d) From the exergy balance in the heat exchanger, we have m_ v ðbv1  bv2 Þ  m_ w ðbI  bIII Þ ¼ D_ EXC

We calculate the exergy of the saturated liquid-vapour mixture at the entrance of the exchanger   xv1 ðh00  h0 Þ kJ 0  s0 ¼ 165:5 bv1 ¼ h þ xv1 ðh  h Þ  h0  T0 s þ T kg 0

00

0

The exergy of the saturated liquid at the outlet of the exchanger and the exergy change between I and III are obtained by applying Eq. (3.44), giving bv2 ¼ 1:55

kJ kg

bI  bIII ¼ 0:44

kJ kg

Finally, the exergy destruction in the heat exchanger gives D_ EXC ¼ 765:6 kW (e) The objective of the heat exchanger (together with the tower) is to condense vapour, that is, to reduce its exergy. The heat exchanger will form part of an installation in which it is necessary to use the produced condensate, in such a way that the heat exchanger is auxiliary equipment for some other productive equipment. It is, therefore, a dissipative equipment, which must be analysed considering the productive equipment it serves so that, considered in isolation, it does not make sense to define its exergy efficiency.

The atmospheric air of a site is at 38
C with a relative humidity of 78%, and with the ambient pressure being 1 atm. The air needs to be conditioned for the inside of a room at 21
C and with a relative humidity of 51%. To this end, it is passed through a climatization unit in which it is first cooled below its dew point in a cold battery. Then, the saturated air, once the condensed water is separated, is heated in a heat battery, consisting of electrical resistance, up to the desired temperature. The volume flow rate of humid air at the entrance to the AHU is 240 m3/h, calculate

Example E.6.8.

(a) (b) (c) (d)

The states of the air at the inlet and outlet of the cold and heat batteries. The amount of water that condenses per hour. The heat given by the air in the cold battery and heat given to the air in the heat battery. The irreversibilities in the heat battery. Does it make sense to define its exergy efficiency?

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Exergy Analysis and Thermoeconomics of Buildings

Solution. In Fig. E.6.3 a schema of the AHU is shown.

Figure E.6.3 Schema of the AHU. (a) Determining the states of the air at the inlet and outlet of the heat and cold batteries. The absolute humidity in state 0 is u0 ¼ 0:622 p0 f0

ps ð38
CÞ  ps

ð38
CÞ

¼ 34

g kg d a

The absolute humidity in state 2, at the output of the heat battery, is u2 ¼ 0:622 p0 f2

ps ð21
CÞ  ps

ð21
CÞ

¼8

g kg d a

The absolute humidity of states 1 and 2 is the same, and as the relative humidity f1 ¼ 1 we have u2 ¼ u1 ¼ 0:622 p0 1

ps ðT1 Þ  ps ðT1 Þ

¼8

g /ps ðT1 Þ ¼ 12:49 mbar/T1 ¼ 11
C kg d a

(b) Undertaking a mass balance of water between 1 and 2, we have

m_ a u0 þ m_ cond ¼ m_ a u1 /

g m_ cond ¼ u1  u0 ¼ 26 kg d a m_ a

Exergy analysis of thermal facilities equipment in buildings (II)

513

To find the mass flow rate of dry air, we first determine the specific volume of air in state 0 v0 ¼ ðRa þ u0 Rv Þ m_ a ¼

T0 m3 ¼ 0:934 p0 kg d a

V_ 0 kg d a /m_ a ¼ 0:071 s v0

Therefore, the amount of condensate is m_ cond ¼ 1:8

g s

(c) Carrying out a balance of energy in the cold battery, we have Q_ cb ¼ m_ a ðh0  h1 Þ  m_ cond hcond ¼ 6:65 kW

From the energy balance in the heat battery, we get Q_ hb ¼ E_ ¼ m_ a ðh2  h1 Þ ¼ 0:73 kW (d) We assume that all electrical energy is converted into heat that is transferred to the air so that the energy efficiency of the heat battery is 100%. If we analyse the behaviour of the heat battery from an exergy point of view we see that, with the ambient temperature being 38
C, the air in state 1 at the inlet of the battery has a greater exergy than at the exit, since the heat battery brings the state of the air closer to the environmental conditions, and therefore, its exergy decreases. The total irreversibility in the heat battery is D_ bc ¼ E_ ¼ 0:73 kW

From an exergy point of view, we cannot talk about a product of the heat battery, so it does not make sense to define an exergy efficiency. In the AHU of an air conditioning installation, there is a cold battery and a heat battery. The extraction flow is partially recirculated, with the ratio between the recirculated air mass flow and fresh air being 25%. The outside air is at 34
C and 74% relative humidity, with local air conditions at 25
C and 52% relative humidity. The ratio between the latent load of the conditioned room to the sensitive load (associated with dry air) is 1/3. The air enters the heat battery at 14
C and goes to the room at a temperature of 18
C, with the mass flow rate of dry air being 1.2 kg/s. The water temperature at the inlet of the heat battery is 62
C, with a variation of 8
C, while in the cold battery the temperature is 7
C, with a variation of 5
C. Determine

Example E.6.9.

(a) The state of the air after mixing with the recirculated air, at the outlet of the cold battery and the entrance to the premises. (b) The irreversibilities in the mixing process. (c) Overall exergy efficiency of the AHU

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Exergy Analysis and Thermoeconomics of Buildings

Solution (a) We shall use 0 for the state of the outside air, 1 for the recirculated air, 2 for the air resulting from the mixture, 3 for the air to the outlet of the cold battery and input to the heat battery and 4 for the heat battery output, and therefore, the entrance to the site to be conditioned. As ps(34
C) ¼ 53.2 mbar and ps(25
C) ¼ 31.7 mbar the absolute humidity in state 0 and 1 are respectively, u0 ¼ 0:622 p0 f0 u1 ¼ 0:622 p0 f1

ps ð34
CÞ  ps ð34
C Þ ps ð25
C Þ  ps ð25
C Þ

¼ 25

g kg d a

¼ 10

g kg d a

Next, we calculate the mass flow rate of dry air from the outside and the recirculation. We have the equations m_ a;1 ð1 þ u1 Þ kg ¼ 0:25 m_ a;0 þ m_ a;1 ¼ m_ a ¼ 1:2 _ s ma;0 ð1 þ u0 Þ giving m_ a;0 ¼ 0:83

kg d a s

m_ a;1 ¼ 0:37

kg d a s

The state of the air resulting from the mixture, state 2, is obtained by solving the system of the two following equations m_ a;0 h0 þ m_ a;1 h1 ¼ m_ a h2 ðT2 Þ m_ a;0 u0 þ m_ a;1 u1 ¼ m_ a u2 evidently with m_ a ¼ m_ a;0 þ m_ a;1 With the equation of the vapour balance we calculate the humidity in state 2, giving u2 ¼ 22 g/kg d a. We take this result to the energy balance equation, obtaining T2 ¼ 305:3 K ð32:2
CÞ Therefore, the state of the air after mixing is 2(T2 ¼ 32.2
C, u2 ¼ 22 g/kg d a). We now determine the humidity of the air in state 4, at the entrance of the room to be conditioned. According to the relation between the sensitive load and total load, the latent load is one-third of the sensitive load Q_ l ¼ Q_ TOT  Q_ s ¼ Q_ s 3. Writing the energy balance equation for the sensitive load associated with dry air m_ a cp;a T4 þ Q_ s ¼ m_ a cp;a T1 /Q_ s ¼ 8:43 kW

Exergy analysis of thermal facilities equipment in buildings (II)

515

Using the energy balance equation for the latent load gives
 Q_
 m_ a u4 lð0
CÞ þ cp;v T4 þ s ¼ m_ a u1 lð0
CÞ þ cp;v T1 3 u4 ¼

1:2$0:01 ð2500 þ 1:86$25Þ  8:43=3 g /u4 ¼ 9 1:2 ð2500 þ 1:86$18Þ kg d a

Therefore, the state of the air at the inlet to the room is 4(T4 ¼ 18
C, u4 ¼ 9 g/kg d a) and the state of the air at the outlet of the cooling battery is 3(T3 ¼ 14
C, u3 ¼ u4 ¼ 9 g/kg d a). (b) Since in state 0 the exergy of the air is zero, carrying out a balance of exergy in the mixture of the two flows we have

 _ _ a b2 þ bch m_ a;1 b1 þ bch 1 m 2 ¼ I MIX

Calculating each of the terms on the left of the equality. The physical exergy is obtained by applying Eq. (3.37), giving b1 ¼ 138

J kg d a

b2 ¼ 5

J kg d a

The temperature of state 2 is very close to the ambient temperature, and hence, its physical exergy is practically negligible. The chemical exergy is calculated by applying Eq. (3.124), giving bch 1 ¼ 801

J kg d a

bch 2 ¼ 26

J kg d a

Returning to the equation of exergy balance, we get I_MIX ¼ 188 W (c) We calculate first the mass flow rate of cold water in the cold battery. The energy balance is
 m_ a ðh2  h3 Þ ¼ m_ w;cb hcb;in  hcb;ou þ m_ cond hcond

Since the condensate is m_ cond ¼ m_ a ðu2  u3 Þ ¼ 15:6 g=s we get that m_ w;cb ¼ 2:94

kg s

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Exergy Analysis and Thermoeconomics of Buildings

and the mass flow rate of hot water in the heat battery
 kg m_ w;hb hhb;in  hhb;ou ¼ m_ a ðh4  h3 Þ/m_ w;hb ¼ 0:15 s The product of the AHU is the air mass flow rate provided in the conditions of state 4. The fuel is the exergy provided to the cold and heat batteries, as well as that provided by the recirculated air. Therefore, the exergy efficiency of the AHU is  m_ a b4 þ bch 4  4¼

 m_ w;cb bcb;in  bcb;ou þ m_ w;hb bhb;in  bhb;ou þ m_ a;1 b1 þ bch 1 Applying Eq. (3.37) and Eq. (3.124) for the calculation of the physical and chemical exergy of the air in state 4 gives b4 ¼ 0:44

kJ kg d a

bch 4 ¼ 0:93

kJ kg d a

bch 1 ¼ 0:80

kJ kg d a

and for the air in state 1 b1 ¼ 0:14

kJ kg d a

On the other hand, applying Equation (3.44), we find that the exergy provided in the cold battery is
 m_ w;cb bcb;in  bcb;ou ¼ 5:33 kW and in the heat battery
 m_ w;hb bhb;in  bhb;ou ¼ 0:36 kW Coming back to the expression that reflects the exergy efficiency, we finally get 4 ¼ 24:1%

6.5

Ventilation systems

Ventilation is the mechanism through which, in a controlled manner, clean air is provided inside buildings. Ventilation is needed to eliminate the contamination emitted by indoor sources and maintains minimum conditions of sanitation. As a result of

Exergy analysis of thermal facilities equipment in buildings (II)

517

the need to ventilate, there is an increase in energy demand, as indoor air (thermally conditioned but polluted) is replaced by clean outside air without conditioning. To evaluate the energy consumption due to ventilation, in addition to the consumption due to the thermal conditioning of the air, we also need to evaluate due to the operation of the mechanical ventilation system that is installed. It is clear that energy consumption increases with the increase in the demand for ventilation of the dwelling and depends mainly on the severity of the climate in which the building is located and the type of system installed. An analysis of air quality and energy cost in each housing block should be performed to select the system that, fulfilling air quality requirements, operates at the lowest possible cost. Achieving the objectives of air quality and limiting consumption depends on the correct operation of the ventilation system, which in turn depends on proper design and installation and good insulation of the building, Liddament 1996 [39].

6.5.1

Air quality and regulatory development of ventilation in Spain

Poor air quality generates many health problems for building occupants. Thus, the pollutants caused by combustion cause problems related to the respiratory system, fatigue, chest and head pain, and dizziness, among others, World Health Organization 2003 [40]. The presence of Volatile Organic Compounds (VOC) is associated with effects such as irritation of eyes, skin, mucous membranes and respiratory tract, as well as more serious diseases such as asthma and cancer. As for suspended particles, their effects on health are also very broad but can be divided into respiratory and cardiovascular effects, increasing mortality due to exposure. Up to 8000 different compounds have been identified in indoor air, Goodfellow 1998 [41]. These pollutants can be classified according to their origin as pollutants emitted by the occupants, those emitted during domestic activities, those emitted by construction materials and pollution that arrives from the outside. In Spain, since 1957 the preparation of the Basic Building Regulations (Normas Basica de la Edificaci on, NBE in Spanish) has been the responsibility of the Ministry of Housing, following the task developed until then by the Directorate General of Architecture of the Ministry of the Interior. In 1977, the Government approved a unified framework for the Building Regulations, consisting of the Basic Building Standards (Normas Basicas de la Edificaci on, NBE), the Building Technology Standards (Normas Tecnol ogicas de la Edificaci on, NTE) and the Approved Building Solutions (Soluciones Homologadas de la Edificacion, SHE), although the latter was not developed [42]. The Basic Building Regulations (NBE-Spanish) were mandatory, and they defined the minimum requirements to be met by a building. The NBE CT-79. Thermal conditions in buildings standard affected, directly or indirectly, the aspects related to the thermal conditions inside the building, the ventilation and the quality of the indoor air. This standard referred to ventilation, indicating that it is an adequate measure to avoid surface condensation, without making any other comment on aspects related

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Exergy Analysis and Thermoeconomics of Buildings

to indoor air quality, so no particular type of ventilation system was contemplated. For this reason, the renewal of the air in dwellings built under these standards is carried out by infiltration of air and by the opening of windows, which evidently, does not guarantee proper ventilation. On 6 May 2000, the Building Regulation Act (Ley de Ordenacion de la Edificacion, LOE), Law 38/1999 [43], came into force, which aimed to regulate the essential aspects of the construction process. Basically, the necessary conditions were established for the correct development of the building process, in order to guarantee the quality of the building through the fulfillment of some basic requirements. In its second final provision, this law authorized the Government to approve a Technical Building Code (C odigo Técnico de la Edificaci on, CTE). This document established the requirements that buildings must meet in aspects related to safety and habitability. The Regulation of Thermal Installations of Buildings (Reglamento de Instalaciones Térmicas de los Edificios, RITE) approved by Royal Decree 1027/2007 [44] establishes the conditions that must be met by thermal installations in buildings, which aim to maintain thermal and hygienic well-being, through sustainable use of energy, taking into account both economic and environmental aspects. Through Royal Decree 238/2013, of April 5, certain articles and technical instructions in the RITE were modified. The Technical Building Code (CTE in Spanish) was approved by Royal Decree 314/2006, modified by Royal Decree 1371/2007 and corrected by the publication carried out in the Official State Gazette (BOE) of 25 January 2008. One of the great novelties of the CTE came in the Basic Document (Documento Basico DB HS Salubridad in Spanish), which established the requirement of minimum ventilation flows in each site according to their occupation and use. Subsequently, this Basic Document has undergone a series of modifications, the most recent being due to Order FOM/588/2017 [45].

6.5.2

Types of ventilation installations

The need to guarantee a minimum flow of ventilation makes it necessary to install mechanical systems since natural ventilation systems cannot guarantee the minimum required by CTE throughout the year. There are different types of mechanical ventilation systems. A general classification can be found in Russell et al. 2005 [46]: •

•

•

Natural intake and mechanical extraction systems. The extraction is done mechanically, while the air intake occurs due to the pressure difference created by the extraction. The air enters the dry rooms through openings to the outside, crossing the dwelling to be extracted through ports. Mechanical drive systems and natural extraction. The air is pushed into the interior of the dwelling in dry rooms, while the extraction is carried out through the humid rooms in a natural way. This type of system is not very widespread in the case of housing. The pressure inside the dwelling is higher than the outside pressure. Mechanical drive systems and mechanical extraction. The air is mechanically driven into the interior of the house in dry rooms, and the same amount of air is extracted mechanically through the humid rooms. This type of system allows for the inclusion of heat recovery

Exergy analysis of thermal facilities equipment in buildings (II)

•

519

to take advantage of the extraction air energy and reduce the energy load of the thermal conditioning of the dwelling, in addition to having air filters available. On-demand ventilation systems. These are systems that act according to need, which can be according to probes reading CO2, humidity or presence, for example. Depending on the reading made by the probe, the ventilation rate of the dwelling varies.

The simple flow systems (natural admission and mechanical extraction) can be configured in different ways, depending on the installed intake and extraction ports, Millet et al. 1996 [47]. The fixed intake ports have a constant air inlet section, and the flow is defined according to the pressure difference created between the interior and exterior due to the ventilation system itself, wind action and the difference in inside/outside temperature. The self-regulating intake ports keep the ventilation flow constant by modifying its passage section, within a range of pressure difference between the inside and the outside of the house. The hydro-regulating air inlets have a sensor that acts as a function of the relative humidity of the environment: a series of membranes sensitive to moisture vary their length, opening or closing the air passage section. Likewise, the extraction ports can be fixed, self-regulating depending on the pressure difference between the inside and the outside or hygroregulating. In the case of double-flow systems (mechanical impulsion and mechanical extraction), it is necessary to add a network of impulse ducts, in addition to those of the extraction.

6.5.3

Heat recuperators

Heat recuperators are equipment that allow the recovery of part of the energy of the conditioned air of the interior of a premises provided with a system of mechanical ventilation. They consist of a heat exchanger that puts the extracted indoor air in thermal contact with the external air for renewal. In winter, they preheat the cold air from the outside, and in summer they allow it to cool down; they also have some filters that improve the quality of the air. In this way, it is possible to recover a high percentage of the energy used to heat or cool the air inside a room, which would be completely lost without the recuperator. Normally, they come as boxes with some mouthpieces that are installed in the ventilation system, incorporating the fans for impulsion and return, see Fig. 6.25.

Figure 6.25 Appearance of a heat recuperator.

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Exergy Analysis and Thermoeconomics of Buildings

There are three types of recuperators: cross-flow, in which hot and cold air circulate in orthogonal directions to each other so that they cross, parallel flow and rotary flow, which has a rotor with high thermal inertia that rotates driven by a motor. The Technical Code establishes in its Basic Document a mechanical or hybrid ventilation system for dwellings. Therefore, if the ventilation is of the hybrid type, the placement of recuperators cannot be considered, since the intake is not channeled through grids and ducts. However, in the tertiary sector, in those places where the airflow expelled to the outside is higher than 0.5 m3/s, RITE requires having heat recovery units. Consider a heat recuperator in which we use 0 and 1 for the states of the intake air at the inlet and outlet of the recuperator and 2 and 3 for the extracted air states also at the inlet and outlet of the recuperator. Using V_ for the volume airflow rate that is introduced to the building, which we assume is the same as the one that is extracted (the recuperator is balanced), where r0,ri are the densities of the exterior and interior air, respectively, and considering, for example, some winter conditions, from the energy balance we can write the equation _ i ðh2  h3 Þ þ W_ v ¼ Vr _ 0 ðh1  h0 Þ þ Q_ l V9

(6.85)

where the power of the fans W_ v is used to overcome the head losses and Q_ l are the heat losses, which approximately can be considered negligible. The operation of the recuperator is characterized by its effectiveness, ASHRAE 1993 [48], which, as we know, is defined as the heat exchanged with respect to the maximum that could have been exchanged. Considering that the thermal capacity rate for the two airflows is the same, the effectiveness of the recuperator is ε¼

T1  T0 T2  T0

(6.86)

The effectiveness varies from one hour to another, since the outside temperature changes, so it is more attractive to define the average seasonal effectiveness, which will be PH ε i hi (6.87) ε ¼ i¼1 H where hi is the number of hours in which the effectiveness is εi and H is the total number of hours in the period, for example, of heating. Referring now to the definition of efficiency, if we consider that the recuperator is adiabatic since the decrease of enthalpy of the extraction air coincides with the increase of enthalpy of the renovation air, then its energy efficiency would be unity. Now, we can also define the efficiency considering the indoor air energy as the only available, since the energy in state 3 is part of the losses, this is h¼

_ 0 ðh1  h0 Þ _ i h3 þ Q_ l Vr Vr ¼1 _ i h2 þ W_ v _ i h2 þ W_ v Vr Vr

(6.88)

Exergy analysis of thermal facilities equipment in buildings (II)

521

In the same way as for effectiveness, the most interesting value is the average seasonal efficiency, which is calculated in a similar way. On the other hand, undertaking an exergy balance in the recuperator, we have _ i ðb2  b3 Þ þ W_ v ¼ V9 _ 0 ðb1  b0 Þ þ I_rec Vr

(6.89)

where the term I_rec encompasses the exergy associated with the lost heat and the internal exergy destructions, due to the thermal and mechanical irreversibilities. Actually, since the exergy of air in state 3 is finally destroyed, it must be included in the term of irreversibilities, and since state 0 is ambient air, the exergy balance gives _ 2 b2 þ W_ v ¼ Vr _ 0 b1 þ I_T;rec Vr

(6.90)

with the exergy efficiency of the equipment being 4¼

_ 0 b1 I_T;rec Vr ¼1 _ 2 b2 þ W_ v _ 2 b2 þ W_ v Vr Vr

(6.91)

In the same way, as for the effectiveness and energy efficiency, we will calculate the average seasonal exergy efficiency of the recuperator.

6.5.4

Energy and exergy analysis of a ventilation system with heat recovery

We shall look at a mechanical ventilation system with heat recovery for a house. The objective of the analysis that is proposed is to evaluate the saving of primary energy that is achieved, comparing a ventilation system with recovery with a mechanical system without recovery. After the energy analysis, in a second phase, we perform the exergy analysis, in order to highlight the interest of this type of analysis and the additional information that can be obtained. Fig. 6.26A schematically represents the mechanical ventilation system without recuperator, compared to the system with recuperator in Fig. 6.26B. Infiltration airflows, which may differ according to the ventilation system, will not be taken into account in this analysis.

Figure 6.26 Mechanical ventilation (A) without recovery (B) with heat recovery.

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Exergy Analysis and Thermoeconomics of Buildings

If V_ is the ventilation volume airflow rate, and r0 the density of the external dry air, in winter conditions the heat that must be contributed to heat that airflow from the external conditions to the interior temperature of the apartment Ti is
 Q_ ¼ 90 V_ cp;a þ u0 cp;v ðTi  T0 Þ

(6.92)

With ε being the effectiveness of the heat recuperator, assuming that the flow through it is the same for the extracted air as for the renovation air (as happens in a well-balanced system), the temperature at the outlet of the recuperator is T1 ¼ T0 þ εðTi  T0 Þ

(6.93)

Therefore, the thermal energy saving due to this heat recovery is 
ES ¼ 90 V_ cp;a þ u0 cp;v εðTi  T0 Þ

(6.94)

Now, from this saving, the electricity consumption of the fan in the renovation duct (which is not needed in the system without recovery) will have to be subtracted in addition to the head losses in the recuperator that must be overcome by the fan in the extraction duct. With Dp being these pressure losses, the total pressure that the fan must supply to the airflow (sum of the static and dynamic pressure) is Dp ¼ Dpsta þ pdyn ¼ CV_ þ 2

 2 1 V_ 90 2 A

(6.95)

where C is a coefficient, supplied by the equipment manufacturer and A is the internal section of the duct. The power consumed by the fan is therefore 1 _ VDp W_ f ¼ hel;m

(6.96)

where hel,m is the electrical efficiency of the drive motor. Therefore, the net energy saving per unit of time is
 1 _ VDp ESn ¼ 90 V_ cp;a þ u0 cp;v εðTi  T0 Þ  hel;m

(6.97)

More interesting than this value is the Primary Energy Saving that can be obtained. For this, it will be necessary to translate the consumption of electricity to Primary Energy, depending on the energy mix. Regarding the part of thermal energy, to translate it to Primary Energy we will have to take into account the performance of the generation and distribution in the building of the heating system, because if that heat is not recovered, it would have to be contributed by the heating system. Therefore, if we call the performance of the electric system at national level

Exergy analysis of thermal facilities equipment in buildings (II)

523

hel and the performance of the generation and distribution of heating hg, the net saving of primary energy is 
90 V_ cp;a þ u0 cp;v εðTi  T0 Þ 1 _ Vp PESn ¼  hel;m hel hg

(6.98)

Since the effectiveness of the recuperator varies with the ambient temperature, there will be a limit above which environmental temperature will happen that AEPn 0 and kF,r,kZ,r > 1 we have that the following inequality must be met cP;n  cP;n1 .  cP;i  .cP;1

(7.73)

Thermoeconomics and its application to buildings

7.9

605

Exergy cost theory

The Exergy Cost Theory (ECT), developed by Valero et al. 1983 [43], is a cost accounting methodology that evaluates the average costs of all internal flows and products of a system, no matter how complex, either in exergy units or in monetary units. We will present this theory for calculating costs in terms of exergy, and then we will look at the exergoeconomic costs. In order to present the ECT in the simplest way possible, we will develop it not in the most rigorously mathematically way, but in the most appropriate way for the main purpose of this book, which is to encourage technicians in the building sector to use it.

7.9.1

Propositions of Exergy Cost Theory

ECT is based on a series of Propositions, whose systematic application allows for the unequivocal determination of the value of the exergy costs of the flows, fuels and products of the system analysed, Querol et al. 2011 [51]. P1 Exergy cost is a conservative property.

For each component of a system, the sum of the exergy costs of the outflows is equal to the sum of the exergy costs of the inputs. The exergy cost is thus conservative and satisfies equations similar to energy. With A being the incidence matrix of the system formed by n sub-systems and m flows and, therefore, of dimension (n,m) and with B* being the flows exergy cost vector of dimension (m,1), the exergy cost balance for each component of the system is written AB ¼ 0

(7.74)

This matrix equation provides n algebraic equations for calculating the exergy cost of the flows, as many equations as components considered in the system. Since the number of flows is m, we need m independent equations to solve the problem, while in general m > n. If all the components have a single output flow, which is not loss, the problem is solved by applying this Proposition, evidently by knowing the input flows; this is what happens in what we call a sequential system. When, as happens in general, one or more components have more than one output flow, it is necessary to write an additional number of equations for each component equal to the number of output flows minus one. P2 In the absence of external assessment, the exergy cost of the flows entering the installation is equal to its exergy.

When the flow comes from the environment (crosses the control surface of the system analysed) its exergy cost is equal to its exergy; in other words, the unit exergy cost of resources is one. This statement implies that in the analysis of the system we do not take into account what happens outside its limits so that we can write equations of the type Bi ¼ Bi

fi ¼ 1; 2; .eg

(7.75)

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Exergy Analysis and Thermoeconomics of Buildings

that is, as many equations as flows enter the plant. If e is the number of entering flows, we will have e additional equations. If the system under consideration were sequential, with n being the number of components, the number of flows nþ1, as with these two Propositions the system of equations   is closed, and we can resolve the costs calculation. In a general case, if ue ¼ ue;i i¼1;::inis the vector (1,n) where ue,i ¼ Bi and ae is the resources matrix (n,e) where ae ¼ ðaij Þj¼1;::;m i¼1;::;e ¼ dij , P2 can be written in matrix form ae B  ¼ ue

(7.76)

Through these two Propositions, we can write (n þ e) equations, where m is the number of unknowns, so in general, the system of equations is not closed. Let us now refer to two Propositions that are going to be applied to those components that have two or more output flows, that is, they refer to what we call the bifurcations. A component has as many bifurcations as output flows minus one. We will distinguish between internal bifurcations, which are present in equipment with two or more output flows that in turn are inputs of others, and external bifurcations, which are those in which the flows leave the limits of the system to the environment, passing through the boundary surface. We will look in the first place at the internal bifurcations. P3 If an output flow of a component is part of the fuel, the unit exergy cost of that flow is the same as that of the input flow from where it comes.

It is logical that all the costs that take place in the equipment under consideration must be attributed to the product. Therefore, the output flow that is part of the fuel (non-exhausted fuel) must have the same unit exergy cost as the input flow that is part of the same fuel. Consider the system in Fig. 7.4, in which the flows i and j form part of the fuel. According to this P3 we have ki ¼ kj

(7.77)

and, therefore, Bj Bi ¼ Bi Bj

Figure 7.4 Outline of a component in which an output flow is part of the fuel.

(7.78)

Thermoeconomics and its application to buildings

607

If Bi/Bj ¼ xij we get the equation Bi  xij Bj ¼ 0

(7.79)

which relates the exergy costs of the flows i and j, as a result of applying P3 and where xij is the relationship between the exergies of the flows i and j, which is called bifurcation parameter. In order to clarify how to apply this Proposition, let us now consider the generic system in Fig. 7. 5, in which there are three output flows that are part of the fuel (flows that are part of the product are not shown). Since there are three output flows that are part of the fuel, using P3 we can write two equations. One of them is B2 B3 ¼ B2 B3

(7.80)

and, therefore, B2  x23 B3 ¼ 0

(7.81)

Likewise B4 þ B5 B6 þ B7 ¼ B4 þ B5 B6 þ B7

Figure 7.5 Generic system with several output flows that are part of the fuel.

(7.82)

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Exergy Analysis and Thermoeconomics of Buildings

this is   B6 þ B7  xð6þ7Þ=ð4þ5Þ B4 þ B5 ¼ 0

(7.83)

where x(6þ7)/(4þ5)¼(B6þB7)/(B4þB5) Physical meaning of P3 Proposition

In order to better understand the meaning of this Proposition we will apply it to the simple equipment in Fig. 7.6 in which one of the output flows 3 is part of the product, while the fuel of the equipment is the difference (2e4), with this being the product (3e1). Considering that flows 1 and 2 come from outside, the unit exergy cost of both is the unit. According to P3 Proposition, we have B4 B2 ¼ B4 B2

(7.84)

with B1 ¼ B1 and B2 ¼ B2 . Carrying out the cost balance and taking into account the exergy balance gives B3 þ B4 ¼ B1 þ B2 ¼ B3 þ B4 þ D

(7.85)

and, therefore, B3 ¼ B3 þ D

(7.86)

Therefore, P3 Proposition indicates that the exergy destruction in the component is completely assigned to its product so that the cost of the output flow that forms part of the fuel is not modified by the irreversibilities that have occurred in the component. P4 If a component has several products, they will all be assigned the same unit cost, and if a product consists of several flows, they will all have the same unit cost.

Figure 7.6 Component with two output flows, one of them product.

Thermoeconomics and its application to buildings

609

Figure 7.7 Equipment with two output flows that are part of the product.

If in the same sub-system two or more products can be identified, their formation process is the same at the level of aggregation under consideration; therefore, they must be assigned the same cost, proportional to the exergy of each product. The equipment in Fig. 7.7 has two flows i and j that are part of the product, so its unit cost is the same ki ¼ kj

(7.87)

from where Bi  xij Bj ¼ 0

(7.88)

where xij is the relationship between the exergy of the flows. In order to better interpret how to apply this Proposition, consider the generic equipment in Fig. 7. 8, in which flows 8, (10e9) and ((13 þ 14)-(11 þ 12)) are part of the product. According to P4, three auxiliary equations can be written, which are: B8 B10  B9 ¼ B8 B10  B9

Figure 7.8 Generic equipment with several output flows that are part of the product.

(7.89)

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Exergy Analysis and Thermoeconomics of Buildings

     B13 þ B14  B11 þ B12 B8 ¼ ðB13 þ B14 Þ  ðB11 þ B12 Þ B8

(7.90)

B13 B14 ¼ B13 B14

(7.91)

Physical meaning of P4 Proposition

Let us again consider the equipment in Fig. 7.7, in which the two output flows are part of the product. According to Proposition 4, we have   B_ i B_ j ¼ ¼ ki Bi Bj

(7.92)

Undertaking an exergy balance in the equipment and letting the input flow be in we have B_ in ¼ B_ i þ B_ j þ D_

(7.93)

From the exergy costs balance, considering that the input flow to the equipment comes from outside so that its unit exergy cost is the unit and considering the exergy balance reflected by the previous equation, we have   B_ i þ B_ j ¼ B_ in ¼ B_ i þ B_ j þ D_

(7.94)

Therefore, we can write B_ j   B_ i þ B_ i ¼ B_ i þ B_ j þ D_ B_ i

(7.95)

giving finally  B_ i ¼ B_ i þ

B_ i D_ B_ i þ B_ j

(7.96)

and analogously  B_ j ¼ B_ j þ

B_ j D_ _ Bi þ B_ j

(7.97)

These two expressions make it clear to us that P4 states that the exergy destruction that takes place in the equipment must be attributed to the flows that are part of the product in a proportional manner to the exergy of each flow.

Thermoeconomics and its application to buildings

611

P5 When a component has external bifurcations, if the flows are a product, P4 Proposition is applied, and if they are sub-products, losses or residues, the rules established in this P5 Proposition are applied.

We will now look at external bifurcations, which are those that occur in a component with several output flows, when they leave the system, crossing the limiting surface; this is the case that is shown, for example, for the component in Fig. 7.9. If we perform the exergy cost balance, we get the equation

Figure 7.9 Component with an external bifurcation.

B1 þ B2 ¼ Be

(7.98)

Different cases may arise, depending on the type of flows that leave the system: •

If the two flows are product of the equipment, the criterion of P4 will be applied, so that the equation is

B1  x12 B2 ¼ 0 •

(7.99)

One of the flows is a sub-product. Suppose that 1 is the main product and 2 the sub-product. Flow 2 will be assigned a cost equal to what it would have if it were obtained as the main product in an installation whose objective is to obtain that flow and that installation is the best available commercially competitive technology. Let Bsub be the exergy cost in that installation, then

B2 ¼ Bsub

(7.100)

and, therefore, from the cost balance, it follows that B1 ¼ Be  B2 ¼ Be  Bsub

(7.101)

The larger Bsub the lower the cost of the product B1 . Sometimes the sub-product can be bought in the market, as is the case of electric power, steam, etc. in which case it can

612

Exergy Analysis and Thermoeconomics of Buildings

be assigned an exergy cost equal to its exergy and in economic terms, which we will consider later, a cost equal to its price. •

One of the flows is a loss flow. All costs that take place in the equipment are assigned to the flows that form part of the product so that for a loss flow we have

L ¼ 0

(7.102)

and, therefore, P* ¼ F*. Let us consider as an example, a hot water boiler. The boiler product is the increase in enthalpy (exergy) of water, while the lost heat and the enthalpy of the combustion gases appear as loss flows. It seems logical to assign to the boiler product all the costs that take place in it, which implies assigning a zero cost to the loss flows. It must be borne in mind that loss flows are not necessarily formed in the last component through which they pass before entering the environment. Thus, in a single-cycle cogeneration installation, the flow of gases to the atmosphere leaves the recovery boiler. However, where it really was generated was in the combustion chamber of the turbine and it is, therefore, the product of the combustion chamber that is to be penalized by this loss flow, Bejan, Tsatsaronis and Moran 1996 [49]. •

One of the flows is residue. It seems logical that the cost of the resources used for its treatment should be assigned to the productive equipment that has generated it and, therefore, to its final products, in accordance with the productive process of the system under consideration. Therefore, once the residue has been identified, it is necessary to follow its formation process and locate its origin, that is, where it was formed.

To clarify these ideas consider the system in Fig. 7.10. In the main equipment i the product Pi and the residue Ri, are generated, which is taken to the sub-system r for treatment. In this sub-system resources are used with an exergy cost Br .

Figure 7.10 Main equipment and waste treatment equipment.

Thermoeconomics and its application to buildings

613

Carrying out the exergy costs balance in the i eth component we have Fi ¼ Pi þ Ri

(7.103)

while the costs balance in the residue treatment sub-system r leads us to R0 ¼ Ri þ Br

(7.104)

Now, once the residue has been properly treated it becomes a loss flow, so that according to what has been said before we have that R0 ¼ 0 and, therefore, Ri ¼  Br

(7.105)

Returning again to the exergy costs balance in the productive component i, we have Pi ¼ Fi þ Br

(7.106)

Therefore, to the cost of the product must be added the treatment costs needed to send that residue flow to the environment. Thus, in parallel to the product formation process, there is a residue formation process, and to adequately allocate the cost of that residue, its formation process must be followed and its cost assigned to the equipment in which it was generated, Agudelo et al. 2012 [41]. The residual structure has its own components and flows representation, but the connecting arrows go in the direction opposite to the physical flows to make explicitly their negative cost character. We will develop these ideas in more detail in Chapter 8, Section 8.5.

7.9.2

Closure of the system of equations

The Propositions seen above allow us to obtain the necessary equations to close the system. To demonstrate this, we will deduce the general relationship that relates the number of flows m with the number of components n and the numbers b and e of bifurcations and input resource flows to the installation. For any component that we may consider, in relation to the flows we can state the following: • • • •

All component has at least one output flow. In each component, there are as many bifurcations as the number of output flows minus one. The inputs that come from other components have already been computed as outputs or bifurcations of the previous component. In addition, it is necessary to take into account the input flows to the system that come from the outside.

If si is the number of output flows of i-th component from Propositions P3, P4 and P5 we obtain for that component a number of equations equal to si1, so that for the total set we have n X i¼1

ðsi  1Þ ¼

n X i¼1

si  n ¼ m  e  n

(7.107)

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Exergy Analysis and Thermoeconomics of Buildings

Consequently, if the e equations of the input flows are added to the n equations expressing the cost balance in each component and the (men) equations of P3, P4 and P5, a total number of equations equal to m is available, which is the number of flows and, therefore, the system of equations is closed. We have seen that P1 provides n equations, which in matrix form gives Eq. (7.74) and likewise, that of P2 gives the resources matrix, Eq. (7.76). From Propositions 3, 4 and 5 we obtain (mne) additional equations, and to write them in matrix form we construct a distribution matrix ax of dimension [(mne), m], whose rows will have all null elements, except for the following: • • •

Sub-products: Value 1 for the element ai,s relative to the sub-product s generated by the i-th component Residue: Value 1 for the element ai,r relative to the residue r generated in the i-th component. Products: Value þ 1/Bj in the column corresponding to one of the flows and 1/Bk in the one corresponding to the other. Each of the bifurcations will give rise to equations of the form

Bj  xj;k Bk ¼ 0

(7.108)

Finally, we construct the extended matrix Aðm; mÞ, made up of the sub-matrices A(n,m), ae(e,m) and ax(mne,m) in the form A¼

A ae ax

! (7.109)

While the incidence matrix reflects the physical structure of the installation, the matrices ae and ax represent the economic structure. Via the matrices ae and ax we can construct the matrix aex of dimension [(mn),n] formed by the superposition of  ae the two, that is aex h . ax An extended vector Yeðm;1Þ is thus constructed made up of the vector 0 of dimen ue sion (n,1) whose components are zeros and the vector uex ¼ of dimension 0 [(mn),1], with ue being the vector (e,1) whose components are the exergies of the entering flows Be, that is " Ye h

0

#

uex

(7.110)

In this way, the m equations necessary to calculate the exergy cost of the m flows can be written in the following compact form Aðm;mÞ Bðm;1Þ ¼ Yeðm;1Þ

(7.111)

Thermoeconomics and its application to buildings

615

Torres 1991 [52] showed in his Doctoral Thesis that the flow exergy costs of an installation is a unique solution of the previous system of equations. For this, the extended matrix will have to be inverted, finally giving Bðm;1Þ ¼ A1 ðm;mÞ Yeðm;1Þ

(7.112)

Therefore, the exergy costs are determined one-to-one from the input resources and the bifurcation parameters. The criteria for the allocation of costs given by these Propositions, known as FP Propositions, depend solely on the structure of the installation and the productive purpose that has been defined for each component.

7.9.3

Exergy cost of fuel and products of the components

Now that the flow exergy costs have been calculated, we are going to look at the costs of the fuel and products of the equipment. It is understood as exergy cost of the fuel   (product) of a component, and we write it as Fj Pj for the j-th component, the algebraic sum of the exergy costs of the flows that make up the fuel (product) that we are considering. From the exergy cost balance in the generic i-th component we get the equation Pi ¼ Fi þ Li . As we have seen in Section 7.9.1, we assign a zero value to the exergy cost of the loss flows, so that we can write Pi ¼ Fi

(7.113)

 Remembering that ki is the unit consumption in the i-th equipment and with kP;i  being the unit exergy cost of the product and kF;i that of the fuel, this is  kF;i ¼

Fi Fi

(7.114)

 ¼ kP;i

Pi Pi

(7.115)

we can write the above equation as   kP;i ¼ ki kF;i

(7.116)

so that the unit exergy cost of the product of a component is the unit cost of the fuel multiplied by the unit exergy consumption. By taking into account the exergy balance, the increment of .the unit exergy cost in a component could be expressed as  k  ¼ k  I P . kP;i i F;i F;i i

616

Exergy Analysis and Thermoeconomics of Buildings

Referring now to the set of components, with F*,P* being the vectors (n,1) which contain the exergy costs of the fuel and product of each of them, we have F ¼ AF B

(7.117)

and analogously for the products P ¼ AP B

(7.118)

Given that F*P*¼(AFAP)B* ¼ A B* we have that P ¼ F

(7.119)

If kF ; kP are the vectors (n,1) whose components contain the unit exergy costs of fuel and product of each component, it is easy to verify that the following relationship is true kP ¼ K D kF

(7.120)

where KD is the diagonal matrix of exergy unit consumption, defined in Section 7.6.3.

7.9.4

Accumulated exergy cost

In the cost balances that have been established up to this moment, the fact that each component that is integrated in the system is, in turn, a functional product that has its corresponding exergy cost has not been taken into account. For calculating this cost, it would be necessary to know all the materials that make up the equipment, as well as its manufacturing process, and we would then apply the techniques for calculating the exergy cost which we will look at in Chapter 10. Once this cost is known, it would have to be distributed throughout the useful life of the component, and we would thus obtain the exergy amortization of that equipment. Similarly, for maintaining the equipment, additional exergy has to be consumed, which would be the maintenance exergy. If for the set of equipment that makes up the installation we define the vector Y  ¼ Y A þ Y M , sum of exergy and maintenance amortization, P1 proposition is reformulated according to the following equation AB ¼  Y 

(7.121)

Performing this type of analysis involves incorporating exergy costs not only due to the resources consumed in the installation, but also the exergy cost involved in the amortization and maintenance of equipment. In short, using the above algebraic

Thermoeconomics and its application to buildings

617

equation, we calculate the accumulated exergy cost or ecological cost. These accumulated costs are due to the irreversibilities that occur in the manufacture, installation and repair of components. This type of analysis is interesting when we want to evaluate the ecological costs of products used by society since a systematic evaluation of the ecological costs of each asset or service will allow us to assess the viability of our technology, and ultimately, the sustainability of our society. In Chapter 10, we will delve further into these issues. On the other hand, the fuel flows consumed by an installation are rarely composed of non-transformed primary resources. The resources that enter a plant have an exergy cost that is greater than its exergy, since, in its extraction, transportation, storage, processing, etc. it was necessary to incorporate exergy. If we wanted to incorporate these exergy costs into their flows and products, we would write P2 proposition as ext Be ¼ Be þ Bext e , where Be is the exergy used from the primary resource to the installation that will use it. Now, since the exergy that has been used to generate these resources is an external cost, it is not necessary to incorporate it in an exclusive analysis of the installation. In short, it is the vector Y* which incorporates the external information on the exergy costs of the installation. However, we usually focus on the system itself, without worrying about the previous history of the resources and equipment that is using it. We thus separate the system that we are going to analyse from its surroundings, and we ignore the irreversibilities in the stages of transformation of primary resources to final products. There have not been many works undertaken to calculate the accumulated exergy cost of different products. In this respect, it is worth mentioning the work of Szargut 1987 [53]. The works of Boustead and Hancock 1979 [54] should be mentioned as precursors of this concept, as well as those of Leprince et al. 1981 [55] that pursue similar objectives, although with a methodology of analysis based on the First Law.

7.9.5

Exergoeconomic costs

The application of Thermoeconomics for the calculation of exergoeconomic cost (in monetary units) of the flows produced in thermal installations is of great interest since it allows for the correct cost allocation of the intermediate flows and the final products. Thus, in a heating and DHW installation with different generation components, we will have the unit heating cost (cV/kWh), depending on whether it is produced in one boiler or another, or in the heat pump, if there is one; likewise, we will learn the unit DHW cost (cV/kWh or cV/l) depending on whether it is generated in a boiler, or has its origin in solar collectors, etc. It is clear that this information is very interesting, for example, to set the operation mode of the installation so that the costs are minimal. We will call the resources valued in economic terms necessary to obtain a flow in an installation as the exergoeconomic cost of that flow, and we will denote it by the symbol C. It is clear that exergy plays a fundamental role in the thermal installations of

618

Exergy Analysis and Thermoeconomics of Buildings

buildings, so that the exergoeconomic cost of the internal flows and of the installation products will depend as much on the thermodynamic efficiency of the conversion processes of the energy as on the levelized acquisition and maintenance cost of the plant components. Therefore, the exergoeconomic cost of any flow is the sum of two contributions: on the one hand, there is the monetary cost of the resources used in the installation and, on the other hand, the rest of the costs of the installation, such as the capital cost of the components and the maintenance cost. In the same way that we use Bj for the exergy cost of the flow j, we use Cj for the exergoeoconomic cost of said flow, and we will use C as the dimension vector (m,1) whose components contain the economic costs of the flows. Although the term exergoeconomic refers to the fact that the cost is associated with the exergy, in many cases, we will refer to these costs simply as monetary costs. If Zj is the levelized cost of acquisition, depreciation, maintenance, etc. of the j-th component, Z is the vector (n,1) for the set of the n plant components. These equipment acquisition and maintenance costs are external resources, and in a functional diagram can be represented as flows that come directly from the environment of the installation or system under consideration. Likewise, we use Ce for the dimension vector (e,1) that contains the economic costs of the resources entering the plant, Ce,i ¼ cu,iui, and cu,i is the market price of the resource i per unit of exergy. We can construct the vector ℤe of dimension (m,1) that contains the external economic assessments, in an analogous way to Yeðm;1Þ for exergy cost equations, that is ℤe ¼

Z Ce 0

! (7.122)

In this way, in a manner totally analogous to Eq. (7.111), the exergoeconomic costs are calculated by solving the following matrix equation AC ¼ ℤe

(7.123)

We will refer to the exergoeconomic costs per unit of exergy as the unit exergoeconomic costs so that for the flow j we have cj ¼

Cj Bj

(7.124)

Referring the costs to the exergy does not mean that the costs of the material flows are related exclusively to the exergy contained in that flow. There are costs not related to the exergy that can also affect the total cost of a flow. For example, the cost associated with a replacement water flow at the outlet of a treatment unit, an oxygen or

Thermoeconomics and its application to buildings

619

nitrogen flow at the outlet of an air separation unit, etc. When this occurs, the total cost associated with flow j will be given by CjT ¼ Cj þ CjNE

(7.125)

where CjNE refers to the cost not associated with the exergy, Tsatsaronis 1999 [56].

7.9.6

Exergoeconomic costs of fuel and products of components

We will also call exergoeconomic cost of the fuel (product) of a component i as the economic resources needed to obtain the fuel (product) of said component, which we will designate by the symbol CF,i(CP,i). Undertaking a balance of exergoeconomic costs in the ieth equipment, we have CP;i ¼ CF;i þ Zi

(7.126)

In the same way, we will use the term unit exergoeoconomic cost of the fuel (product) of a i-th component which we will designate by cF,i(cP,i) for the quotients cF;i ¼

CF;i Fi

(7.127)

cP;i ¼

CP;i Pi

(7.128)

so that Eq. (7.120) of the cost balance can be written cP;i ¼ cF;i ki þ zP;i

(7.129)

where we have used zP,i ¼ Zi/Pi. By taking into account the exergy balance, the increment of the unit exergoeconomic cost in a component could be expressed as cP,icF,i¼(cF,iIi þ Zi)/Pi. This equation reveals that the unit exergoeconomic cost of the product is always greater than the unit exergoeconomic cost of the fuel and that the difference is calculated in terms of the irreversibility and capital costs. Referring now to all the components, if we use CF,CP for the vectors of dimension (n,1) that collect the costs of each component, in matrix form we have CF ¼ AF C

(7.130)

CP ¼ AP C

(7.131)

If we use cF,cP for the dimension vectors (n,1) that contain the unit costs of the resources and products of each equipment, we have the matrix equation cP P ¼ cF F þ Z

(7.132)

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Exergy Analysis and Thermoeconomics of Buildings

According to the definition of the matrices KD and HD that we saw in 7.6.3, the previous equation can be expressed in the following two ways cF ¼ H D cP  F1 D Z

(7.133)

cP ¼ K D cF þ P1 D Z

(7.134)

or

with the diagonal matrices being FDhdiag(F1,.Fn) and PDhdiag(P1,.Pn).

7.9.7

Examples

Example E.7.9.

Let us refer once again to the schema in Fig. E.7.1 corresponding to the installation of Example E.7.1. From the exergies of the flows, find expressions for: (a) The exergy efficiency of the components and construct the matrices KD and HD (b) The total efficiency of the installation. (c) Write the matrix equation JB ¼ 0

Solution (a) Once the fuel and product of each component have been defined, the respective exergy efficiencies are obtained through Eq. (7.23), giving Table E.7.17.

Table E.7.17 Exergy efficiencies of components.

① ② ③ ④ ⑤ ⑥ ⑦ ⑧

Exergy efficiency 4   B_ 1  B_ 2 B_ 21   B_ 7  B_ 8 B_ 22

      B_ 3  B_ 4 þ B_ 5  B_ 6 B_ 1  B_ 2     B_ 5  B_ 6 B_ 9  B_ 10      B_ 9  B_ 10 þ B_ 23 B_ 15  B_ 16  B_ 19      B_ 7  B_ 8 þ B_ 24 B_ 19  B_ 20     

 B_ 3  B_ 4 B_ 11  B_ 13 þ B_ 12  B_ 14     B_ 17  B_ 18 B_ 15  B_ 16

The diagonal matrix of efficiencies HD(8,8) ¼ diag(41,42, .,48) and the diagonal matrix of unit consumption KD(8,8) ¼ diag(k1,k2,.k8) are shown in Tables E.7.18 and E.7.19 respectively.

B_ 1 B_ 2 B_ 21

HD ¼

e

e

B_ 7 B_ 8 B_ 22

e

e

e e e

e e e

e

e

e

e

e

e

e ðB_3 B_ 4 ÞþðB_5 B_6 Þ

e

e

e

e

e

e

e

e

e

e

B_ 9 B_ 10 B_ 5 B_ 6

e

e

e

e

B_ 15 B_ 16 B_ 19 ðB_9 B_10 ÞþB_23

e

e

e

e ðB_11 B_13 ÞþðB_12 B_14 Þ

e

B_ 1 B_ 2

e e e

e e

e

B_ 19 B_ 20 ðB_7 B_8 ÞþB_24

e

e

e

e

e

e

e

e

e

e

e

e

B_ 3 B_ 4

e

Thermoeconomics and its application to buildings

Table E.7.18 Matrix HD.

e B_ 17 B_ 18 B_ 15 B_ 16

621

622

Table E.7.19 Matrix KD. B_ 21 B_ 1 B_ 2

KD ¼

e e

e

e

e

e

e

e

B_ 22 B_ 7 B_ 8

e

e

e

e

e

e

B_ 1 B_ 2 ðB_3 B_4 ÞþðB_5 B_6 Þ

e

e

e

e

e

e ðB_9 B_10 ÞþB_23

e

e

e

e ðB_7 B_8 ÞþB_ 24

e

e

e

e

e

e

e

e

B_ 5 B_ 6 B_ 9 B_ 10

e

e

e

e

e

e

e

e

e e

e e

e e

e e

B_ 15 B_ 16 B_ 19

e e e

B_ 19 B_ 20

e e

B_ 3 B_ 4 ðB_11 B_13 ÞþðB_12 B_14 Þ

e

e B_ 15 B_ 16 B_ 17 B_ 18

Exergy Analysis and Thermoeconomics of Buildings

e

Thermoeconomics and its application to buildings

623

(b) The total efficiency of the installation is the relationship between the product PT and the total fuel FT, Eq. (7.44), that is, it is the relationship between the product and the fuel at the highest level of aggregation, Fig. E.7.2. 4T ¼

      _ 14 þ B_ 17  B_ 18  B_ 20 _ 12  B0 B_ 11  B_ 13 þ B0 B_ 21 þ B_ 22 þ DB_ 23 þ DB_ 24

(c) According to Eq. (7.34) we construct the matrix J, as presented in Table E.7.20. The matrix equation JB ¼ 0 equals the system of the following eight equations: • ① 0 ¼ k1 B_ 1 þ k1 B_ 2 þ B_ 21 • ② 0 ¼ k2 B_ 7 þ k2 B_ 8 þ B_ 22 • ③ 0 ¼ B_ 1  B_ 2  k3 B_ 3 þ k3 B_ 4  k3 B_ 5 þ k3 B_ 6 • ④ 0 ¼ B_ 5  B_ 6  k4 B_ 9 þ k4 B_ 10 • ⑤ 0 ¼ B_ 9  B_ 10  k5 B_ 15 þ k5 B_ 16 þ k5 B_ 19 þ B_ 24 • ⑥ 0 ¼ B_ 7  B_ 8  k6 B_ 19 þ k6 B_ 20 þ B_ 20 • ⑦ 0 ¼ B_ 3  B_ 4  k7 B_ 11  k7 B_ 12 þ k7 B_ 13 þ k7 B_ 14 • ⑧ 0 ¼ B_ 15  B_ 16  k8 B_ 17 þ k8 B_ 18 Example E.7.10.

Consider again the schema of Fig. E.7.3 corresponding to the installation of Example E.7.2. From the exergies of the flows, find expressions for: (a) The exergy efficiencies of the components and construct the matrices KD and HD (b) The total efficiency of the installation. (c) Write the matrix equation JB ¼ 0

Solution (a) With the fuel and product of each component defined, the exergy efficiency is obtained by applying Eq. (7.23), with the results in Table E.7.21.

The matrix HD is shown in Table E.7.22 and KD in Table E.7.23. (d) The total efficiency of the installation is obtained by applying Eq. (7.44), which refers to the installation at its maximum level of aggregation.

  B_ 21 þ B_ 15  B_ 16 þ B_ 23 4T ¼ _ 25 þ DB _ 26 B_ 22 þ B_ 24 þ DB (e) The matrix J is shown in Table E.7.24. The matrix equation JB ¼ 0 is equivalent to the following system of 10 equations: • S) 0 ¼ k1 B_ 1 þ k1 B_ 2 þ B_ 22  k1 B_ 23  B_ 27 • CC) 0 ¼ k2 B_ 3 þ k2 B_ 4 þ B_ 24  B_ 28 • C) 0 ¼ B_ 1  k4 B_ 2 þ B_ 3  k4 B_ 4  k4 B_ 5 þ B_ 6 • CH) 0 ¼ B_ 5  B_ 6  k5 B_ 7 þ k5 B_ 8 þ B_ 25 • V1)0 ¼ B_ 7  B_ 8  k6 B_ 9 þ k6 B_ 10  k6 B_ 17 þ k6 B_ 18 • V2)0 ¼ B_ 9  B_ 10  k7 B_ 11 þ k7 B_ 12

Table E.7.20 Matrix J. J¼

k1

k1

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

1

e

e

e

e

e

e

e

e

e

e

-k2

k2

e

e

e

e

e

e

e

e

e

e

e

e

e

1

e

e

e

1

1

-k3

k3

-k3

k3

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

1

1

e

e

-k4

k4

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

1

1

e

e

e

e

-k5

k5

e

e

k5

e

e

e

1

e

e

e

e

e

e

e

e

1

1

e

e

e

e

e

e

e

e

e

e

ek6

k6

e

e

e

1

e

e

e

1

1

e

e

e

e

e

e

-k7

-k7

k7

k7

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

1

1

-k8

k8

e

e

e

e

e

e

e

Thermoeconomics and its application to buildings

625

Table E.7.21 Exergy efficiencies of equipment.

S CC C HC V1 V2 HX T V3 D

• • • •

Exergy efficiency 4   B_ 1  B_ 2 B_ 22   B_ 3  B_ 4 /B_ 24    B_ 5 þ B_ 2 þ B_ 4 / B_ 1 þ B_ 3 þ B_ 6     B_ 5  B_ 6 B_ 7  B_ 8     

 B_ 7  B_ 8 B_ 9  B_ 10 þ B_ 17  B_ 18    B_ 11  B_ 12 / B_ 9  B_ 10    B_ 13  B_ 14 / B_ 11  B_ 12      B_ 15  B_ 16 / B_ 13  B_ 14 þ B_ 26    B_ 19  B_ 20 / B_ 17  B_ 18   B_ 21 / B_ 19  B_ 20

HX) 0 ¼ B_ 11  B_ 12  k8 B_ 13 þ k8 B_ 14 T) 0 ¼ B_ 13  B_ 14  k9 B_ 15 þ k9 B_ 16 þ B_ 26 V3) 0 ¼ B_ 17  B_ 18  k10 B_ 19 þ k10 B_ 20 D)0 ¼ B_ 19  B_ 20  k11 B_ 21

Example E.7.11. Consider again the schema of the installation in Fig. 7.1 corresponding to Example E.7.1. Determine:

(a) The exergy costs of the flows. (b) The exergy costs of the fuel and products of the equipment.

Solution (a) To obtain the exergy costs of the flows, we need to solve Eq. (7.111) we show below

Að25;25Þ Bð25;1Þ ¼ Y eð25;1Þ

! A

ae via the matrix ax A(8,25) of Table E.7.1 and the matrices that represent the economic structure ae and ax, as well as the vector Ye(25,1). Table E.7.25 defines the existing bifurcations for the construction of the distribution matrix ax(9,25), defined in P3. It should be noted that, for reasons of space, although the relationship between the exergies of the flows i and j is defined with the nomenclature xij, the bifurcation parameters have been named according to numbering from 1 to 9. However, the second column represents the respective xij. Therefore, we need to construct the extended matrix A ¼

626

Table E.7.22 Matrix HD. B_ 1 B_ 2 B_ 22

HD ¼

e e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e ðB_ 9 B_10 ÞþðB_17 B_18 Þ

e

e

e

e

e

e

e

e

e

e

B_ 11 B_ 12 B_ 9 B_ 10

e

e

e

e

e

e

e

e

e e

e

B_ 5 þB_ 2 þB_ 4 B_ 1 þB_ 3 þB_ 6

e

e

e

B_ 7 B_ 8 B_ 5 B_ 6

e

e

e

e

e e e

e e e

e e e

e e e

B_ 7 B_ 8

e e e

e e

B_ 13 B_ 14 B_ 11 B_ 12

e

B_ 15 B_ 16 ðB_13 B_14 ÞþB_26

e

e

e

e

e

e

e

e

B_ 19 B_ 20 B_ 17 B_ 18

e

e

e

e

e

e

e

e

e

B_ 21 B_ 19 B_ 20

Exergy Analysis and Thermoeconomics of Buildings

e B_ 3 B_ 4 B_ 24

B_ 22 B_ 1 B_ 2

KD ¼

e e e e e

e B_ 24 B_ 3 B_ 4

e e e e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

B_ 1 þB_ 3 þB_ 6 B_ 5 þB_ 2 þB_ 4

e

e

e

e

e

e

e

B_ 5 B_ 6 B_ 7 B_ 8

e

e

e

e

e

e

e

e

e

e

e

B_ 9 B_ 10 B_ 11 B_ 12

e

e

e

e

e ðB_13 B_14 ÞþB_26

e

e

e e e

e e

B_ 7 B_ 8 ðB_9 B_10 ÞþðB_ 17 B_18 Þ

e

e

e

e

e

e

e

B_ 11 B_ 12 B_ 13 B_ 14

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

B_ 17 B_ 18 B_ 19 B_ 20

e

e

e

e

e

e

e

e

e

e

B_ 15 B_ 16

Thermoeconomics and its application to buildings

Table E.7.23 Matrix KD.

B_ 19 B_ 20 B_ 21

627

Table E.7.24 Matrix J.

J¼

k1 k1

e

e

e

e

e

e

e

e

e

e

e

e

e

e e

e

e

e

e

1  k1 e

e

e

1 e

e

k2 k2

e

e

e

e

e

e

e

e

e

e

e

e e

e

e

e

e

e e

1

e

e

e

1

e

e

e

e

e

e

e

e

e

e e

e

e

e

e

e e

e

e

e

e

e

1

k5 k5

e

e

e

e

e

e

e

e e

e

e

e

e

e e

e

1

e

e

e

e

e

e

e

e

e k6 k6

e

e

e

e e

e

e

e

e

e

e

e

e

e e

e

e

e

e

e e

e

e

e

e

e

e

e e

e

e

e

e

e e

e

e

e

e

e

e

e

e

e

e e

e

e

1

e

e

e e

e

e

e

e

e

1 k11 e e

e

e

e

e

e

e

k4 1

k4 k4

e

e

e

e

1

e

e

e

e

e

e

1

1 k6 k6

e

e

e

e

e

e

e

e

1

1 k7 k7

e

e

e

e

e

e

e

e

e

e

1

1 k8 k8

e

e

e

e

e

e

e

e

e

e

e

e

1

1 k9 k9 e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e 1

1 k10 k10 e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e e

e

1

1

1

Thermoeconomics and its application to buildings

629

Table E.7.25 Bifurcation equations. Bifurcations x1.2,25

1. 2. 3.

_

x1 ¼ B_ B25B_ _

1

_

3

_

2

x5.6,3.4

B6 x2 ¼ BB_5  B_

x1,2

x3 ¼ BB_2 1

4.

x5,6

x4 ¼

5.

x9,10

x5 ¼

6.

x7,8

x6 ¼

7.

x12.14,11.13

x7 ¼

8.

x4,3

x8 ¼

9.

x15,16

x9 ¼

4

B_ 6 B_ 5 B_ 10 B_ 9 B_ 8 B_ 7 B_ 12 B_ 14 B_ 11 B_ 13 B_ 4 B_ 3 B_ 16 B_ 15

aX

  B_ 25  B_ 1  B_ 2 $x1 ¼ 0     B_ 5  B_ 6  B_ 3  B_ 4 $x2 ¼ 0 B_ 2 B_ 1 $x3 ¼ 0 B_ 6 B_ 5 $x4 ¼ 0 B_ 10 B_ 9 $x5 ¼ 0 B_ 8 B_ 7 $x6 ¼ 0     B_ 12  B_ 14  B_ 11  B_ 13 $x7 ¼ 0 B_ 4 B_ 3 $x8 ¼ 0 B_ 16 B_ 15 $x9 ¼ 0

Table E.7.26 contains the incoming resources from outside that allows the resources matrix ae(8,25) and the vector Ye(25,1) to be built. There are no sub-products or waste, with the only flow of losses in the 25th row, see Table E.7.5. Since there is no external assessment, we have that Be ¼ Be : Next, the matrix equation is solved, inverting the extended matrix and clearing the vector of the exergy costs of the flows, Eq. (7.106). The results obtained are shown in Table E.7.27. (b) The exergy costs of the fuel and products of the equipment are obtained from the exergy costs of the flows of Table E.7.27, and from the fuel and product matrices, which are reflected in Tables E.7.6 and E.7.7. Using the matrix Eqs. (7.111) and (7.112) we get the results that are shown in Table E.7.28.

The results shown in these Tables are the symbolic expressions of the exergy costs of the flows and those of fuels and products of the equipment. For a given thermodynamic state of the installation, both the bifurcation factors and the exergies of the flows will take specific numerical values. This Example and the next one serve as an introduction to the Symbolic Thermoeconomics that we develop in the next chapter. Example E.7.12. Consider again the schema of the installation in Fig. 7.3 corresponding to Example E.7.2, and determine:

(a) The exergy costs of flows. (b) The exergy costs of the fuel and products of the equipment.

Solution (a) To obtain the exergy costs of the flows, we need to solve Eq. (7.111)

Að28;28Þ Bð28;1Þ ¼ Y eð28;1Þ

630

Table E.7.26 Entrance flows to the installation. Entrances B_ e1 ¼ B_ 21

5.

B_ e5 ¼ B_ 13

2.

B_ e2 ¼ B_ 22

6.

B_ e6 ¼ B_ 14

3.

B_ e3 ¼ B_ 23

7.

B_ e7 ¼ B_ 18

4.

B_ e4 ¼ B_ 24

8.

B_ e8 ¼ B_ 20

Yte

0

0

0

0

0

0

0

0

B_ e1

B_ e2

B_ e3

B_ e4

B_ e5

B_ e6

B_ e7

B_ e8

0

0

0

0

0

0

0

0

0

Exergy Analysis and Thermoeconomics of Buildings

1.

Symbolic expressions of the costs of the flows 1.

B21 B1 ¼ ½ðx1 þ1Þ$ðx 3 1Þ

14.

B14 ¼ B14

2.

B21 $x3 B2 ¼ ½ðx1 þ1Þ$ðx 3 1Þ

15.

B15 ¼

3.

21 B3 ¼ ½ðx1 þ1Þ$ðxB2 1Þ$ðx 8 1Þ

16.

B16 ¼

4.

B21 $x8 B4 ¼ ½ðx1 þ1Þ$ðx 2 1Þ$ðx8 1Þ

17.

B21 $x9 B17 ¼ B18 þ B20 þ B22 þ B23 þ B24 þ ½ðx1 þ1Þ$ðx 2 þ1Þ

5.

B21 $x2 B5 ¼ ½ðx1 þ1Þ$ðx 2 1Þ$ðx8 1Þ

18.

B18 ¼ B18

6.

B21 $x2 $x8 B6 ¼ ½ðx1 þ1Þ$ðx 2 1Þ$ðx8 1Þ

19.

B19 ¼ B20 þ B22 þ B24

7.

22 B7 ¼ ðxB 6 1Þ

20.

B20 ¼ B20

8.

22 $x6 B8 ¼ B ðx6 1Þ

21.

B21 ¼ B21

9.

B21 $x2 B9 ¼ ½ðx1 þ1Þ$ðx 2 1Þ$ðx5 1Þ

22.

B22 ¼ B22

10.

B21 $x2 $x5 B10 ¼ ½ðx1 þ1Þ$ðx 2 1Þ$ðx5 1Þ

23.

B23 ¼ B23

11.

21 B11 ¼ B13 þ ½ðx1 þ1Þ$ðxB2 þ1Þ$ðx 7 þ1Þ

24.

B24 ¼ B24

12.

B21 $x7 B12 ¼ B14 þ ½ðx1 þ1Þ$ðx 2 þ1Þ$ðx7 þ1Þ

25.

B21 $x1 B25 ¼ ðx 1 þ1Þ

13.

B13 ¼ B13



 þ B20 þ B22 þ B23 þ B24 $ðx1 9 1Þ



 9 þ B20 þ B22 þ B23 þ B24 $ðxx 9 1Þ

B21 $x2 ðx1 þ1Þ$ðx2 þ1Þ B21 $x2 ðx1 þ1Þ$ðx2 þ1Þ

Thermoeconomics and its application to buildings

Table E.7.27 Exergy cost expressions of the flows.

631

632

Table E.7.28 Exergy costs of fuel and products. Product

①

 ¼B F① 21

21 P① ¼ xB1 þ1

②

 ¼B F② 22

21 P② ¼ ðxB1 þ1Þ

③

 ¼ B21 F③ x1 þ1

P③ ¼ B22

④

B21 $x2  ¼ F④ ½ðx1 þ1Þ$ðx2 1Þ

B21 $x2 P④ ¼ ½ðx1 þ1Þ$ðx 2 1Þ

⑤

B21 $x2  ¼ F⑤ ½ðx1 þ1Þ$ðx2 1Þ þ B23

B21 $x2 P⑤ ¼ ðx1 þ1Þ$ðx þ B23 2 þ1Þ

⑥

 ¼B F⑤ 22 þ B24

P⑤ ¼ B22 þ B24

⑦

B21  ¼ F⑥ ½ðx1 þ1Þ$ðx2 1Þ

B21 P⑥ ¼ ðx1 þ1Þ$ðx 2 þ1Þ

⑧

B21 $x2  ¼ F⑧ ðx1 þ1Þ$ðx2 þ1Þ þ B20 þ B22 þ B23 þ B24

B21 $x9 P⑧ ¼ B20 þ B22 þ B23 þ B24 þ ½ðx1 þ1Þ$ðx 2 þ1Þ

Exergy Analysis and Thermoeconomics of Buildings

Fuel

Thermoeconomics and its application to buildings

633

! Therefore, we need to construct the extended matrix A ¼

A ae

via the incidence

ax matrix A(10,28), obtained from Table E.7.3 and the matrices that represent the economic structure ae and ax, as well as the vector Ye(28,1). Table E.7.29 defines the existing bifurcations for the construction of the distribution matrix ax(13,28); in this case, the bifurcation parameters have also been named in the second column according to their conventional nomenclature xij. Even so, for reasons of space, they have been renumbered from 1 to 13. Table E.7.30 contains the incoming resources from outside and allows us to build the resources matrix ae(5,28). In this installation, while there are no waste streams or sub-products, there are two loss flows, flows 27 and 28, thus arriving at the vector Ye(28,1). Since there is no external assessment, we have that Be ¼ Be . Next, the matrix equation is solved, inverting the extended matrix and clearing the vector of the exergy costs of the flows, Eq. (7.112). The results obtained are shown in Table E.7.31. (b) The exergy costs of the fuel and products of the equipment are obtained from the exergy costs of flows, Table E.7.31 above, from the fuel and product matrices of the equipment and by applying Eqs. (7.117) and (7.118). The results obtained are shown in Table E.7.32.

In an adiabatic combustion chamber, a fuel mass flow rate of 15 g/s of specific exergy 52.1 MJ/kg is consumed. A flow of hot gases, whose exergy is 120 kW, is produced. This flow is passed through an expander, where an electrical power of 20 kW is produced, leaving a flow of gases still hot with an exergy content of 50 kW, which is used in subsequent processes for DHW production. Determine:

Example E.7.13.

(a) The unit exergy cost and unit exergoeconomic cost (Vc/kWh) of the gases at the combustion chamber outlet. (b) The unit exergy cost and unit exergoeconomic cost (Vc/kWh) of the electricity produced.

Solution (a) Undertaking a balance of exergy costs in the combustion chamber we have  _ Bg;1 ¼ kF B_ F kg;1

We assume that kF ¼ 1, so that from the previous equation we get  ¼ kg;1

B_ F ¼ 6:51 B_ g;1

To calculate the unit exergoeconomic cost, we carry out a balance of economic costs. Previously, to determine the capital cost rate of the combustion chamber, we calculate the annuity factor, which is acc ¼

ið1 þ iÞn ¼ 0:0735 ð1 þ iÞn  1

634

Table E.7.29 Bifurcation equations. Bifurcations x1.2,23

x1 ¼

2.

x1.2,27

x2 ¼

3.

x3.4,28

x3 ¼

4.

x2,5

x4 ¼

5.

x4,5

x5 ¼

6.

x5,6

x6 ¼

7.

x9.10,17.18

x7 ¼

B_ 23

aX    B_ 1  B_ 2 $x1 ¼ 0    B_ 1  B_ 2 $x2 ¼ 0    B_ 3  B_ 4 $x3 ¼ 0

8.

x7,8

9.

x9,10

10.

x11,12

B_ 2 B_ 5 $x4 ¼ 0

11.

x13,14

B_ 4 B_ 5 $x5 ¼ 0

12.

x16,15

B_ 6 B_ 5 $x6 ¼ 0     B_ 9  B_ 10  B_ 17  B_ 18 $x7 ¼ 0

13.

x17,18

B_ 27 B_ 28

Bifurcations

aX

_ x8 ¼ BB_ 7 8 _ x9 ¼ BB_ 9 10 _ x10 ¼ BB_11 12 _ x11 ¼ BB_13 14 _ x12 ¼ BB_16 15 _ x13 ¼ BB_17 18

B_ 7 B_ 8 $x8 ¼ 0 B_ 9 B_ 10 $x9 ¼ 0 B_ 11 B_ 12 $x10 ¼ 0 B_ 13 B_ 14 $x11 ¼ 0 B_ 16 B_ 15 $x12 ¼ 0 B_ 17 B_ 18 $x12 ¼ 0

Exergy Analysis and Thermoeconomics of Buildings

1.

B_ 23 B_ 1 B_ 2 B_ 27 B_ 1 B_ 2 B_ 28 B_ 3 B_ 4 B_ 2 B_ 5 B_ 4 B_ 5 B_ 6 B_ 5 B_ 9 B_ 10 B_ 17 B_ 18

Thermoeconomics and its application to buildings

Table E.7.30 Input flows to the installation. Entrances 1.

B_ e1 ¼ B_ 22

4.

B_ e4 ¼ DB_ 26

2.

B_ e2 ¼ B_ 24

5.

B_ e5 ¼ B_ 16

3.

B_ e3 ¼ DB_ 25

Yte

0

0

0

0

0

0

0

0

0

0

B_ e1

B_ e2

B_ e3

B_ e4

B_ e5

0

0

0

0

0

0

0

0

0

0

0

0

0

635

636

Exergy Analysis and Thermoeconomics of Buildings

Table E.7.31 Symbolic expressions of exergy costs of the flows. Symbolic expressions of exergy costs of the flows 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

1 $ B1 ¼ 1x 6 1 $ B2 ¼ 1x 6

B3

¼

 

_

B_ 24 $x4 x3 þ1

x6 þ1Þ þ B22 $ðxx24þ1

B_ 24 $x4 x3 þ1

$x4 þ Bx222 þ1

_



B_ 24 $ðx5 x6 þ1Þ 1 x3 þ1 1x6 $

1 $ B4 ¼ 1x 6 1 $ B5 ¼ 1x 6 1 $ B6 ¼ 1x 6 1 $ B7 ¼ 1x 8 x8 B8 ¼ 1x $ 8

    

B_ 24 $x5 x3 þ1 B_ 24 x3 þ1 B_ 24 $x6 x3 þ1



_ $x5 þ Bx222 þ1

_

$x5 þ Bx222 þ1







_

$x6 þ Bx222 þ1

B15 ¼ B_ 16 þ x71þ1$

16.

B16 ¼ B_ 16

17.

1 $ B17 ¼ ðx7 þ1Þ$ð1x 12 Þ

18.

 _ 22 þ xB2 þ1

19. 

20.

x12 B18 ¼ ðx7 þ1Þ$ð1x $ 12 Þ 1 $ B19 ¼ ðx7 þ1Þ$ð1x 13 Þ x13 B20 ¼ ðx7 þ1Þ$ð1x $ 13 Þ

B_ 24 x3 þ1

 _ 22 þ xB2 þ1

21.

B21 ¼ x71þ1$

B_ 24 x3 þ1

 _ 22 þ xB2 þ1

22.

B22 ¼ B_ 22

23.

B22 $x1 B23 ¼ ðx 2 þ1Þ

 _ 22 þ xB2 þ1

24.

B24 ¼ B_ 24



25.

B25 ¼ B_ 25



26.

B26 ¼ DB_ 26



27.

B22 $x2 B27 ¼ ðx 2 þ1Þ



28.

B24 $x3 B28 ¼ ðx 3 þ1Þ

x7 B9 ¼ ðx7 þ1Þ$ð1x $ 9Þ



x7 $x9 B10 ¼ ðx7 þ1Þ$ð1x $ 9Þ

B_ 24 x3 þ1



x7 B11 ¼ ðx7 þ1Þ$ð1x $ 10 Þ x7 $x10 B12 ¼ ðx7 þ1Þ$ð1x $ 10 Þ x7 $ B13 ¼ ðx7 þ1Þ$ð1x 11 Þ x7 $x11 $ B14 ¼ ðx7 þ1Þ$ð1x 11 Þ

 _ 22 þ xB2 þ1

B_ 24 x3 þ1



B_ 24 x3 þ1



B_ 24 x3 þ1



B_ 24 x3 þ1



B_ 24 x3 þ1

_

22 þ xB2 þ1

_

22 þ xB2 þ1

_

22 þ xB2 þ1

_

22 þ xB2 þ1



15.



$x7 þ Bx222 þ1



B_ 24 x3 þ1

 _ 22 þ xB2 þ1

B_ 24 x3 þ1

 _ 22 þ xB2 þ1

B_ 24 x3 þ1

 _ 22 þ xB2 þ1

B_ 24 x3 þ1

 _ 22 þ xB2 þ1

  

_

 _ 22 þ xB2 þ1

B_ 24 x3 þ1

_

_

_

Table E.7.32 Exergy costs of fuel and products. Fuel S

FS ¼ B_ 22

CC

 ¼ B_ FCC 24

Product _

_

24 22 PS ¼ ð1x6BÞ$ðx þ xB2 þ1 3 þ1Þ

_



B_ 24 $x7 x3 þ1

_

24 22 PCC ¼ xB3 þ1 þ ð1x6BÞ$ðx 2 þ1Þ

Thermoeconomics and its application to buildings

637

Table E.7.32 Exergy costs of fuel and products.dcont’d Fuel

Product 

C

þx5 þ1Þ FC ¼ ðx41x $ 6

CH

 ¼ B24 þ B22 FCH x3 þ1 x2 þ1

V1

 ¼ B24 þ B22 FV1 x3 þ1 x2 þ1

V2

_

_

_

_

 ¼ x7 $ FV2 x7 þ1

HX



 ¼ x7 $ FHX x7 þ1

B_ 24 x3 þ1

B_ 24 x3 þ1



B_ 24 x3 þ1

 _ 22 þ xB2 þ1

4 þx5 PC ¼ 1þx 1x6 $

V3

 FV3

D



¼

_

_

_

 _ 22 þ xB2 þ1  _ 22 þ xB2 þ1

  _ 24 _ 22 7 PHX ¼ x7xþ1 $ xB3 þ1 þ xB2 þ1



_ 22 þ xB2 þ1



 _ 22 þ xB2 þ1

B_ 24 x3 þ1

_

 _ 22 þ xB2 þ1

24 22 PV1 ¼ xB3 þ1 þ xB2 þ1   _ 24 _ 22 7 PV2 ¼ x7xþ1 $ xB3 þ1 þ xB2 þ1

B_ 24 1 x7 þ1$ x3 þ1

 ¼ 1 $ FD x7 þ1

B_ 24 x3 þ1

24 22 PCH ¼ xB3 þ1 þ xB2 þ1

  _ 24 _ 22 7 þ DB_ 26 $ xB3 þ1 þ xB2 þ1 FT ¼ x7xþ1

T



PT ¼ x71þ1$ PV3



B_ 24 $x7 x3 þ1



¼



_

$x7 þ Bx222 þ1



B_ 24 1 x7 þ1$ x3 þ1

_ 22 þ xB2 þ1



 _ 22 þ xB2 þ1

PD ¼ x71þ1$

B_ 24 x3 þ1

Table E.7.33 Economic data. Combustion chamber

Expansor

Investment

1.2 MV

0.6 MV

Repayment period

20 y

30 y

Hours (h/y)

3500

3500

i (%) 4

so that the capital cost rate of the combustion chamber is aIcc V ¼ 25:2 Zcc ¼ h H The economic costs balance in the combustion chamber gives cg;1 B_ g;1 ¼ cF B_ F þ Z_ cc / cg;1 ¼ 40:5

cV kWh

638

Exergy Analysis and Thermoeconomics of Buildings

To express this cost per energy unit, one would have to know the relation between the energy and exergy of those gases. (b) Undertaking an exergy costs balance in the expander, we have  _  _ Bg;1  kg;2 Bg;2 ke E ¼ kg;1

Since the fuel of the turbine is B_ g;1  B_ g;2 , according to P4 proposition of the  ¼ k  and, therefore, returning to the exergy Exergy Cost Theory, we have that kg;1 g;2 costs balance equation, we get _ _     Bg;1  Bg;2 B_ g;1  B_ g;2 /ke ¼ kg;1 ¼ 22:78 ke E ¼ kg;1 E For the calculation of the exergoeconomic cost, we determine in the first place the capital cost rate of the expansor Z_ exp , which is aexp ¼

ið1 þ iÞn ¼ 0:0578 ð1 þ iÞn  1

Zexp ¼

aIexp V ¼ 9:9 h H

Undertaking the exergoeconomic costs balance in the expander, we have   ce E ¼ cg;1 B_ g;1  B_ g;2 þ Z_ exp / ce ¼ 1:91

V kWh

Example E.7.14.

Consider a cogeneration plant of a large hospital, consisting of a steam boiler and a back-pressure turbine. The boiler produces a mass flow rate of 26.1 kg/s of steam at 40 bar and 400 C, the exergy of the feed water being negligible, as well as the heat lost through its surface. The exergy of the fuel supplied to the boiler is 102 MW, with a unit price of V 8/GJ (exergy) and the exergy of the gases at the boiler outlet is 5.5 MW. The turbine has an isentropic efficiency of 78%, with the back pressure at the output being 7 bar. The investment in the boiler is 0.8 MV and in the turbine 0.6 MV. The number of equivalent hours of operation of the plant per year is 6000, its useful life is 20 years and the annual interest rate is 4%. If the ambient temperature is T0 ¼ 288 K, determine: (a) (b) (c) (d)

The rate of exergy destruction in the boiler. The rate of exergy destruction in the turbine. The cost (Vc/kg) of the steam produced in the boiler. The cost (Vc/MJ) of the work produced in the turbine.

Thermoeconomics and its application to buildings

639

Solution (a) We use 1 for the state of the steam at the outlet of the boiler and 2 for the state after the expansion in the turbine. The exergy of the steam at the boiler outlet is calculated by means of Eq. (3.9) of Chapter 3. From the superheated steam tables we see h1 ¼ 3.213.6 kJ/kg and s1 ¼ 6.769 kJ/kg$K. From the liquid water tables, we have h0 ¼ 63 kJ/kg and s0 ¼ 0.2245 kJ/kg$K. This then gives that

b1 ¼ h1  h0  T0 ðs1  s0 Þ ¼ 1265:8

kJ kg

B_ 1 ¼ m_ 1 b1 ¼ 33:0 MW From the exergy balance in the boiler, we have D_ b ¼ F_ b  B_ 1  L_ b ¼ 63:5 MW (b) According to the definition of isentropic efficiency, we have

hs ¼

h1  h2 ¼ 0:78 h1  h2s

To know h2s, we look in the superheated steam tables for the state of pressure p2 ¼ 7 bar and for the entropy s2s ¼ s1 ¼ 6.769 kJ/kg$K. The enthalpy of this state is h2s ¼ 2799.1 kJ/kg. Returning to the expression of isentropic efficiency, we now calculate the enthalpy of state 2 h2 ¼ h1  hs ðh1  h2s Þ ¼ 2890:3

kJ kg

Therefore, the steam turbine power is W_ ST ¼ m_ 1 ðh1  h2 Þ ¼ 8:44 MW From the exergy balance in the steam turbine, we have FST ¼ B_ 1  B_ 2

PTV ¼ W_ TV

D_ ST ¼ B_ 1  B_ 2  W_ ST and as B_ 1  B_ 2 ¼ 9:61 MW

640

Exergy Analysis and Thermoeconomics of Buildings

we get D_ ST ¼ 1:2 MW (c) To calculate the exergoeconomic cost of the steam produced in the boiler, we carry out an exergoeconomic costs balance in the boiler

c1 B_ 1 ¼ cF;b B_ F;b þ Z_ b We calculate the capital recovery factor for the boiler ab ¼

ið1 þ iÞn 0:04  1:0420 ¼ ¼ 0:0735 n ð1 þ iÞ  1 1:0420  1

so that its capital cost rate is Zb ¼

ab I b V ¼ 9:8 h H

Returning to the equation of the monetary cost balance in the boiler, we have c1 B_ 1 ¼ 81:87

Vc s

Therefore, the unit cost of the steam produced in the boiler is c1 ¼ 2:48

Vc Vc ¼ 3:14 MJ kg

(d) To calculate the monetary cost of the work produced in the steam turbine, we undertake an exergoeconomic costs balance in the turbine.

cST W_ ST ¼ c1 B_ 1  c2 B_ 2 þ Z_ ST Taking into account that the turbine fuel is B_ 1  B_ 2 the following equality is true c1 ¼ c2. We calculate the capital cost rate of the turbine ZST ¼

aST IST V ¼ 7:35 h H

So that

cST ¼

7:35 36 ¼ 2:85 Vc ¼ 10:26 Vc MJ kWh 8:44

2:48 : 9:61 þ

Thermoeconomics and its application to buildings

641

Example E.7.15.

In a double-tube, parallel-flow air-water heat exchanger, a water mass flow rate of 600 kg/h is heated by a gasses mass flow rate of 1.8 kg/s. The inlet temperature of the water flow, which comes from the outside of the installation in which the heat exchanger is a component, is 24 C and that of the gases is 120 C. The product of the heat transfer coefficient for the total surface of the exchanger is 1 kW/K. Assuming that cp,g ¼ 1040 kJ/kg$K and T0 ¼ 290 K, for the gases, determine: (a) The exergy efficiency of the heat exchanger. (b) Total and unit exergy cost of the hot water flow generated in the heat exchanger, in the following two cases: (1) the gases have been generated in a combustion chamber with an exergy efficiency of 4cc ¼ 0.4 and (2) they come from the chimney of a steam boiler.

Solution (a) We know the mass flow rates of the hot and cold fluids, as well as the inlet temperatures, the main objective being to determine the heat transfer between both flows and their respective outlet temperatures. We will use the NTU-effectiveness method presented by Kays and London in 1955. We calculate first the ratios for the thermal capacities of both fluids.

m_ h cp;h ¼ 1:87

kW K

m_ w cp;w ¼ 0:69

kW ¼ Cmin K

  The maximum heat exchanged is Q_ max ¼ Cmin Th;1  Tw;1 and according to the definition of effectiveness, we have ε¼

Q_ Q_ max

Once the effectiveness is known, the exchanged heat is calculated and from it the exit temperatures of both flows. The effectiveness of an exchanger depends on its geometric configuration and the configuration of the flows. In the case of a double-tube, parallel-flow heat exchanger, we have    Cmin 1  exp  NTU 1 þ Cmax ε¼ Cmin 1þ Cmax where NTU is a dimensionless number called the number of transfer units and is expressed as NTU ¼

UA Cmin

642

Exergy Analysis and Thermoeconomics of Buildings

where U is the total heat transfer coefficient and A the transfer surface area of the exchanger. In this Example, we have that NTU ¼ 1.45. Calculating the effectiveness, according to the previous formula, we get ε ¼ 0.627. Therefore, the heat exchanged is Q_ ¼ εQ_ max ¼ 0:627 : 0:696ð120  24Þ ¼ 41:92 kW With the heat exchanged known, we calculate the outlet temperatures of the gases and water.   Q_ ¼ m_ g cp;g 120  Tg;out /Tg;out ¼ 97:6 C   Q_ ¼ m_ w cp;w Tw;out  24 /Tw;out ¼ 84:2  C In the heat exchanger, the product is the exergy increase of the water flowDB_ w while the fuel is the exergy decrease of the gases flow DB_ g . Therefore, the heat exchanger exergy efficiency is given by the expression   Tw;out m_ w cp;w Tw;out  Tw;in  T0 ln Tw;in m_ w Dbw   ¼ 57:3 % 4¼ ¼ Tg;in m_ g Dbg m_ g cp;g Tg;in  Tg;out  T0 ln Tg;out (b) According to P3 proposition, the unit exergy cost of the gases at the inlet of the exchanger is the same as at the outlet. Therefore, the exergy costs balance is

kP DB_ w ¼ kg DB_ g /kP ¼

kg 4

¼ 1:74 kg

As per P2 proposition, the unit exergy cost of the water flow at the exchanger inlet is unity, giving   B_ w;out  Bw;in /kw;out kP DB_ w ¼ kw;out ¼

Bw;in DBw þ kP Bw;out Bw;out

In case (1), the unit exergy cost of the gases is kg ¼

1 ¼ 2:5 4cc

_ w ¼ 4:62 kW we get and, therefore, as B_ w;in ¼ 0:06 kW and B_ w;out ¼ 4:68 kW and DB  kw;out ¼ 4:31/Bw;out ¼ kw B_ w;out ¼ 20:16 kW

Thermoeconomics and its application to buildings

643

In case (2), the flow of gases is a loss flow, so that in the exergy costs balance in the steam boiler, we would consider that its exergy cost is zero, kg ¼ 0 , so that the cost of the boiler fuel would be attributed to the boiler product. Now, considering the whole installation of boiler þ heat exchanger, the fuel of the boiler can be considered to be the combustible minus the flow of hot gases that go to the exchanger, so that the unit exergy cost of both flows is the same and, therefore, kg ¼ 1. This then gives  kw;out ¼

0:06 4:62 þ 1:74 ¼ 1:73/Bw;out ¼ kw B_ w;out ¼ 8:10 kW 4:68 4:68

In a back-pressure steam turbine, a steam flow rate of 3 t/h enters the turbine at 400 C and 0.8 MPa, with the back pressure being 3 bar. Considering that the internal efficiency of the turbine varies between 0.70 and 0.85 in intervals of 0.5, determine: Example E.7.16.

(a) The turbine power in this interval. (b) The variation of the unit exergy consumption. (c) The variation of the exergy cost of the turbine product, if the exergy unit cost of the steam that enters the turbine is 3. (d) The variation of the exergoeconomic cost, if the cost of the steam that enters the turbine is 12 Vc/kWh (exergy), the steam turbine price is of 0.9 MV, it works out to the equivalent of 5000 h per year, its useful life is 30 years and the annual interest rate on the money is 5%.

Solution (a) With 1 being the state at the turbine inlet, from the thermodynamic tables of superheated steam, we get the following values 1(h1 ¼ 3267.7 kJ/kg, s1 ¼ 7.5735 kJ/kg$K). At the pressure of 3 bar and with the entropy value equal to that of state 1, we find state 2s(h2s ¼ 2903.7 kJ/kg,s2s ¼ 7.5735 kJ/kg$K). For an internal efficiency hs ¼ 0.70, the enthalpy of state 2 is calculated at the output of the turbine

h1  h2 ¼ 0:7 h1  h2s

/ h2 ¼ 2994:9

kJ kg

In this state 2, we have that s2 ¼ 7.7523 kJ/kg$K, with a temperature of T2 ¼ 262o C. These calculations are made for the three isentropic efficiency values, with Table E.7.34 showing the enthalpy and entropy of the states at the steam turbine output. The turbine power for each isentropic efficiency value is obtained by applying the equation _ 1  h2 Þ W_ ST ¼ mðh The values are shown in Table E.7.34. (b) The unit exergy consumption of the turbine is

kST ¼

_ 1  h2  T0 ðs1  s2 Þ m½h W_ ST

644

Exergy Analysis and Thermoeconomics of Buildings

with the results again shown in Table E.7.34. (c) Carrying out an exergy costs balance in the turbine we have  _ W ST k1 B_ 1  k2 B_ 2 ¼ kST

and since the fuel of the turbine is the input flow minus the output flow, according to Proposition 3, then k1 ¼ k2 and, therefore,  kST

  3 B_ 1  B_ 2 ¼ ¼ 3kST W_ ST

The results are shown in the Table E.7.34. (d) Calculating the capital recovery factor for the turbine

aST ¼

ið1 þ iÞn ¼ 0:065 ð1 þ iÞn  1

so that the capital cost rate is ZST ¼

aST IST V ¼ 11:7 h H

Carrying out a balance of exergoeconomic costs, we have cST ¼ c1 kST þ

ZST W_ ST

where kST is the unit exergy consumption. The results obtained for the three values of internal turbine efficiency are presented in Table E.7.34. Given that for the mechanical power the energy and exergy coincide, the results of the previous expression are also referred to per unit of energy.

Table E.7.34 Results obtained according to the internal efficiency of the turbine. Intern. Effic. St

h2 (kJ/kg)

s2 (kJ/kg$K)

WST (kW)

kST

kST

cST (cV/kWh)

0.7

2994.9

7.7532

177.3

1.24

3.71

14.87

0.75

2979.7

7.7265

190.0

1.19

3.57

14.30

0.8

2964.5

7.6961

202.7

1.14

3.43

13.72

Thermoeconomics and its application to buildings

645

Example E.7.17. A health centre has an energy facility in which there is a biomass hot water boiler, with an energy efficiency of h ¼ 0.92. The hot water is generated in the boiler at 80 C, using a part of the hot water for heating, with the heating power being 20 kW and the rest for the operation of an absorption refrigerator of coefficient of performance ε ¼ 0.6, which produces 12 kW of cold, cooling a flow of water from 12 C to 7 C. The return temperature of the heating circuit and the circuit for the drive of the absorption refrigerator is the same and equal to 72.5 C. In the heating circuit, a pressure loss of 40 kPa is taking place which is compensated for by a circulation pump. If the ambient temperature T0 ¼ 290 K and using data from Table E.7.35 below, determine:

Table E.7.35 Equipment data and economic data. Equipment

Biomass boiler

Absorption refrigerator

Investment (V)

12,000

18,000

20

20

5600

1200

Repayment period (years) Hours (5000 h/year) i (%)

Cbio (V/kWh)

4

5

(a) The mass flow rate of hot water in the heating circuit and in the drive circuit of the absorption refrigeration unit. (b) The consumption of biomass in kg/h, if the higher heating value of the biomass is HHVbio ¼ 4.85 kWh/kg. (c) The exergy efficiency of the boiler, if the approximate relation bch bio ¼ 1:04 HHVbio is fulfilled for the biomass used. (d) The exergy destruction rate due to head losses in the heating circuit, assuming an average temperature of 75 C in the circuit. (e) Unit exergy cost and cost per unit time of hot water at the boiler outlet, assuming the effect of head losses in the heating circuit to be negligible. (f) Unit exergoeconomic cost (Vc/kWh) of the cold produced.

Solution (a) Let the state at the outlet of the boiler be 1, which coincides with the states of the hot water at the inlet of the heating installation and the absorption refrigerator respectively, the state of the hot water at the outlet of the heating be 2 and the state after the circulation pump be 3, which coincides with the hot water state at the outlet of the absorption refrigerator and with the return to the boiler.

Calculating first the mass flow rates in the heating circuit and in the drive circuit of the absorption refrigerator. Letting m_ w;h and m_ w; c be the mass flow rates in said circuits respectively, we have Ph ¼ m_ w;h cw ðT1  T3 Þ/m_ w;h ¼

20 kg ¼ 0:638 4:18 : 7:5 s

646

Exergy Analysis and Thermoeconomics of Buildings

For the drive circuit of the refrigerator, we have ε¼

Pc 12 kg ¼ 0:638 /m_ w;c ¼ 0:6 : 4:18 : 7:5 s m_ w;c cw ðT1  T3 Þ

therefore m_ w ¼ m_ w;h þ m_ w;c ¼ 1:267

kg s

(b) According to the definition of boiler efficiency, taking into account that 4.85 kWh/ kg ¼ 17,460 kJ/kg, we have

h¼

m_ w cw ðT1  T3 Þ m_ bio HHVbio

/ m_ bio ¼ 2:49

g kg ¼ 8:96 s h

(c) In accordance with the definition of the boiler exergy efficiency, since

  T1 kJ b1  b3 ¼ cw T1  T3  T0 ln ¼ 5:32 kg T3 we have 4¼

m_ w ðb1  b3 Þ ¼ 15:1 % m_ bio bch bio

(d) Considering an average temperature in the heating circuit Tm ¼ 348 K, according to Eq. (2.110), the rate of exergy destruction due to head losses is

T0 Dp ¼ 21:3 W D_ ¼ m_ w Tm 9 (e) To determine the unit exergy cost, we first take into account that the boiler product is the exergy increase of the hot water generated, that is, according to the value previously obtained

B_ 1  B_ 3 ¼ m_ w ðb1  b3 Þ ¼ 6:79 kW  ¼ 1, we have From the exergy costs balance in the boiler and since kbio

    B_ 1  B_ 3 ¼ B_ bio / kP;b ¼ kP;b

B_ bio ¼ 6:66 B_ 1  B_ 3

Thermoeconomics and its application to buildings

647

Once the exergy cost of the boiler product has been calculated, we can determine the exergy cost of the hot water at the boiler outlet. Evidently, we have    k1 B_ 1 ¼ k3 B_ 3 þ kP;b B_ 1  B_ 3 The unit exergy cost of the flows that feed the heating and the refrigerator is the same, and evidently, is the unit exergy cost of the hot water at the outlet of the boiler k1 . Now, it must be true that k1 ¼ k3 , since if we observe the other equipment in the installation, both for the heating and for the refrigeration circuit, the fuel of both circuits is the output flow minus the return flow and, therefore, their unit exergy costs are the same. In fact  k1 ¼ k3 ¼ kP;b ¼ 6:66

k1 B_ 1 ¼ 212:8 kW (f) Undertaking an exergoeconomic costs balance in the boiler we have

  cP;b B_ 1  B_ 3 ¼ cbio B_ bio þ Z_ b Calculating the capital recovery factor ab ¼

ið1 þ iÞn ¼ 0:07358 ð1 þ iÞn  1

and, therefore, the capital cost rate of the boiler is ab Ib cV ¼ 15:76 Z_ b ¼ h Hb From the exergoeconomic costs balance in the boiler, we have cP;b ¼

5$1:04$4:85$8:96 15:76 cV þ ¼ 35:60 6:79 6:79 kWh

Therefore, the exergoeconomic cost of the hot water generated is   c1 B_ 1 ¼ c3 B_ 3 þ cP;b B_ 1  B_ 3 As we have said before, the return to the boiler is part of the fuel, both for the heating and cooling equipment, so we can conclude that these unit exergoeconomic costs are equal. In short c1 ¼ c3 ¼ cP;b ¼ 35:60

cV kWh

648

Exergy Analysis and Thermoeconomics of Buildings

To calculate the cost of cooling, we first determine the capital cost rate of the refrigerator. Given that ar ¼ ab, we have ar Ir Vc Z_ r ¼ ¼ 110:4 h Hr Undertaking a balance of costs, since the product of the refrigeration installation is the exergy of the cold produced B_ c and the fuel is B_ 1  B_ 3 , we have   cc B_ c ¼ c1 B_ 1  B_ 3 þ Z_ r Given that Tc,in ¼ 285 K(12 C) and Tc,ou ¼ 280 K(7 C), the cold water mass flow rate produced is   kg Pc ¼ m_ cw cw Tc;in  Tc;out /m_ cw ¼ 0:57 s and the exergy of the cold produced, which is the product of the installation, is therefore, B_ c ¼ m_ cw cw





Tc;out  Tc;in



Tc;out ¼ 0:32 kW  T0 ln Tc;in

Returning to the exergoeconomic cost balance equation, since B_ 1 B_ 3 ¼ 3:39 kW, we get that the unit cost of the cold produced is cc ¼ 7:20

V kWh

Example E.7.18. Consider an installation in which a geothermal heat pump supplies heating by means of a floor heating system to a residential building, with the thermal power of the pump being 70 kW. The evaporator of the heat pump is hydraulically connected to the geothermal exchanger through a glycol-water circuit, with a flow rate of 9.17 m3/h, which leaves the heat pump at 6 C and returns at 10 C; the average temperature of the ground is 15 C. The head losses in the circuit are 16 mwc with the global coefficient of heat transfer between the soil and the fluid being U ¼ 110 W/m2. The condenser is connected to the hydraulic circuit of the building heating demand, with the water flow rate of this circuit being 11.8 m3/h and the temperatures of the outlet and inlet to the heat pump being 41 C and 35 C respectively. On a day when the ambient temperature is T0 ¼ 273 K, determine:

(a) (b) (c) (d)

The surface of heat exchange with the ground. The COP of the heat pump. The rate of exergy destruction in the ground and in the heat pump. Exergy efficiency of the heat pump.

Thermoeconomics and its application to buildings

649

(e) The cost per kWh of hot water produced, if the price of electricity is 12 Vc/kWh, the investment in the pump is 0.2 MV, the number of equivalent hours per year is 1500 h, its useful life is 20 years and the annual rate of interest on the money is i ¼ 4%

Solution (a) The rate of heat transfer with the ground is

Q_ ¼ m_ gl cp;gl ðTin  Tout Þ ¼ 49:1 kW where we have used the values of cp,gl, rgl corresponding to water-ethylene glycol 30%. Calculating the logarithmic average temperature for the heat exchanger between the glycol water and the ground DT1 ¼ 15  10 ¼ 5 C DTla ¼

DT2 ¼ 15  6 ¼ 9 C

DT1  DT2 ¼ 6:8 C lnðDT1 =DT2 Þ

The surface area of the heat exchanger is Q_ ¼ UA DTla /A ¼ 65:6 m2 (b) The heat transferred by the condenser of the heat pump is

Q_ cond ¼ 82:2 kW so that the power consumed is W_ ¼ Q_ cond  Q_ ¼ 33:1 kW and the instantaneous COP gives COP ¼

Q_ cond ¼ 2:48 W_

(c) If Tgr is the ground temperature, from the exergy balance we get

    T0 _ Q  m_ gl bglð10 CÞ  bglð5 CÞ ¼ D_ gr 1 Tgr

650

Exergy Analysis and Thermoeconomics of Buildings

and, therefore,     273 9:17$1035 283 3:729 10  5  273 ln D_ gr ¼ 1  49:1  ¼ 1:24 kW 288 3600 278 To calculate the rate of exergy destruction in the heat pump, we first determine the power of the circulation pump to overcome the head losses in the hydraulic circuit associated with the ground. Assuming unity efficiency in the pump gives Dp W_ p ¼ m_ gl ¼ 0:41 kW 9gl Undertaking an exergy balance in the heat pump gives     m_ gl bglð10  CÞ  bglð5 CÞ þ W_ þ W_ p  m_ w bwð41 CÞ  bwð35 CÞ ¼ D_ HP so that D_ HP ¼ 24:78 kW (d) The exergy efficiency of the heat pump is

  m_ w bwð41 CÞ  bwð35 CÞ   4HP ¼ W_ þ W_ p þ m_ gl bglð10 CÞ  bglð5 CÞ ¼1

D_  HP  W_ þ W_ p þ m_ gl bglð10 CÞ  bglð5 CÞ

and, therefore, 4HP ¼ 28:8 % (e) Calculating the capital recovery factor for the heat pump

aHP ¼

ið1 þ iÞn ¼ 0:0735 ð1 þ iÞn  1

so that its capital cost rate is ZHP ¼

aHP IHP V ¼ 9:8 h H

Thermoeconomics and its application to buildings

651

The product of the heat pump is the exergy increase in the hydraulic heating circuit, while the fuel is the electrical consumption in the compressor and in the circulation pump. The exergy contributed by the ground is also part of the fuel, but its economic cost is zero. Therefore   ch DB_ h ¼ cel W_ þ W_ b þ ZHP / ch ¼

W_ þ W_ b



m_ w bwð41 CÞ  bwð35 CÞ þ



cel

ZHP

m_ w bwð41 CÞ  bwð35 CÞ



giving ch ¼ 1:38

V kWhex

This unit cost is naturally per unit of exergy. To finally obtain the unit cost per kWh of energy, we should take into account the relationship between the exergyand the energy of the  heating generated. Since 10.04 kW of exergy correspond to m_ w hwð41 CÞ  hwð35 CÞ ¼ 82:21 kW of energy, we have ch ¼ 16:82

7.10

Vc kWh

Other methods of allocating costs

In the previous Sections, we have presented the so-called Exergy Cost Theory (ECT), which aims to calculate the efficiencies and costs in thermal systems. However, in the literature, other methods have been developed that present their own characteristics and have some differences with ECT. Among them are: • • • • • • •

Exergy Economics Approach (EEA), Gaggioli 1983 [57], First Exergoeoconomic Approach (FEA), Tsatsaronis and Winhold 1985 [58], Thermoeconomic Functional Analysis (TFA), Frangopoulos 1983 [34], Engineering Functional Analysis (EFA), Von Spakovsky 1986 [59], Last-In-First-Out Approach (LIFOA), Tsatsaronis and Lin 1990 [60], Structural Theory, Serra 1994 [23], Specific Exergy Costing (SPECO), Lazzaretto and Tsatsaronis 2006 [61].

Given their importance, we will summarize two of these methodologies: Thermoeconomic Functional Analysis (TFA) and SPECO method. Both have the same objective as ECT, that is, the calculation of the exergy and exergoeconomic cost of each of the flows of the system under consideration and in particular of its main products.

652

7.10.1

Exergy Analysis and Thermoeconomics of Buildings

Thermoeconomic Functional Analysis

With respect to the first version of ECT, Functional Thermoeconomic Analysis (FTA) is a more complete theory, since it considers the role of dissipative equipment and takes into account the role of the environment in the installations, from an economic point of view. As in ECT, in TFA the physical model of the system is considered first, that is, the set of equipment that is interrelated through mass and energy flows. This is the type of model with which we usually work since it corresponds to what in the terminology of engineering we call a schematic diagram. If we refer, for example, to a specific heating and DHW installation with geothermal heat pump and natural gas boiler, the physical model will correspond to Fig. 7.11. Likewise, as in ECT, TFA also builds a functional model. A functional model is made up of a series of components, where each one is part of a complex system that performs a certain function, and that is interrelated to the other units of the system. In a similar way to what was said in ECT, in a thermal system each component has a certain function, that is, has a purpose or product, which can be quantified through an extensive magnitude. Thus, the functional model represents the productive structure of the installation. To develop its function, that is, to generate its product, each of the components uses resources from the environment and/or other components. Therefore, the components are connected by means of flows that can be subdivided into resource flows and product flows. Each flow can be a thermodynamic flow or an economic flow, depending on the objective of the analysis. In short, in TFA, the flows with arrows that are drawn correspond to the fuel and products of the equipment. Thus, TFA represents the fuel and product for each component, so that as the products of two or more components sometimes come together to form the fuel of another, fictitious units need to be incorporated to what we call junctions. It can also happen that the product of a component is part of the fuel of other equipment so that it is

Figure 7.11 Physical model of geothermal heat pump installation.

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then distributed among those various components in a virtual unit in which a bifurcation occurs. In some cases these junctions and bifurcations units can be real equipment, as in the case of a three-way valve, etc. but often they are virtual units. In Fig. 7.12, which represents the functional diagram of the installation in Fig. 7.11 the fuel and the product of each component are represented, and different junctions and bifurcations are shown. In this diagram, the relationships between the equipment and the environment are located immediately; thus, how many components are needed to generate the fuel of a component can be seen and, also, how many components its product feeds. The development of this can be found in Chapter 11. Although in ECT all flows are exergy flows, in TFA there is a new topology of virtual flows that are negentropy flows. This type of flow is introduced in order to define the functional product of the dissipative components and to evaluate the role of the environment in the whole installation. To understand its meaning we are going to consider the condenser of a vapour-compression refrigerator. The condenser does not properly have a product expressed in terms of exergy. Its function is to transfer to the environment the entropy accumulated by the operation of the other components in the refrigerator. Therefore, in economic terms, the function of the condenser is to supply the other components with negative entropy that compensates for the one produced in the component under consideration. So, in addition to the electricity used by the refrigerator, another resource needed for its operation is the negentropy that compensates for the increase in entropy in the rest of the components, and this negentropy is supplied by the condenser. Thus, the cost of the condenser is distributed among the other components of the installation, depending on the contribution of the other components to the production of entropy. For example, for the compressor, this contribution will be the ratio between the increase in entropy of the refrigerant in the compressor and the total increase in

Figure 7.12 Functional diagram of the geothermal heat pump installation.

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Exergy Analysis and Thermoeconomics of Buildings

entropy in the set of components in which the entropy of the refrigerant increases (compressor, throttle valve and evaporator). The flow of negentropy produced by the condenser is distributed among all the components of the refrigerator as an additional resource, with an associated cost, which is the cost of investment and operation of the condenser. This concept of negentropy that has been explained with reference to a condenser is applicable to any dissipative equipment. In Chapter 8, Section 8.5.2, we will develop this method in more detail, applying it to a Rankine cycle. This is also the role played by the environment. Think of the chimney of a boiler. An exergy flow comes out of the chimney, since the temperature, pressure and chemical composition of the combustion gases is different from that of the environment. The function of the atmosphere is to redistribute this flow of gases, so that the boiler uses a flow of fresh air. In this way, the environment plays the role of a dissipative component, that is, it closes the entropy cycle, in a way that generates the negentropy that makes it possible for the gases-emitting boiler to take fresh air from the environment. Thus, the environment can be considered as a dissipative component for any energy installation. Therefore, the product of dissipative equipment is the negentropy that it generates. This product is redistributed between the equipment of the installation that generates entropy, proportionally to the entropy generated. The corresponding part of negentropy that each component uses is part of the resources, in this case virtual, that the component uses. The cost of this virtual resource is the corresponding part of the cost of the subsequent dissipative equipment, that is, the cost of the dissipative equipment must be distributed among the equipment that uses the negentropy resource. In Fig. 7.13 we show schematically a dissipative component, in which si is the entropy at the input and so at the output. With m_ being the mass flow rate, the negen_ 0 ðsi  s0 Þ. tropy generated in the equipment is neg ¼ mT As we see in the definition of negentropy, there is a temperature T0. This is so that the units are those of exergy and balances can be done. In short, for dissipative components, negentropy is a product, with an associated cost, while for productive components that generate entropy, negentropy is a necessary resource, with its associated cost. Thus, in the functional diagram of an installation, each unit is crossed by two topologies of flows, resources and products. In turn, these flows can be exergy and negentropy. The resources are the flows of exergy and negentropy input to the component,

Figure 7.13 Negentropy produced in dissipative equipment.

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and there may be more than one resource of both types. Likewise, a component may have a main product and one or more sub-products. Once the functional diagram is constructed, we define the resources of exergy and negentropy and the products (of exergy and negentropy) of each one of the units of the installation. Unit exergoeconomic costs are resolved from the cost balance, with the resulting equation c ¼ Ac þ R

(7.135)

where c is the vector of unit costs, A is the topological matrix of the functional diagram and R is the external evaluation vector, Frangopoulos 1989 [34]. An important aspect to be highlighted is that matrix A refers to the functional diagram and, therefore, includes the equations of the virtual units, junction and bifurcation units, which are the auxiliary equations that are needed to complete the system of equations. Now they appear in a natural way, whereas in ECT, we have seen that once the incidence matrix is built we need to extend it with the auxiliary conditions. Solving the matrix equation, we have c ¼ ½U D  A1 R

(7.136)

If instead of unit exergoeconomic costs we want to use exergy costs, we can modify the external evaluation vector in a convenient way. In TFA the cost of the residual exergy is attributed not only to the last component (as in the first version of ECT) but also among all the components that contribute to its formation. In TFA, the residual exergy flow is used as fuel of a dissipative unit (the environment) that plays the role of closing the entropy cycle, generating a product in the form of a flow of negentropy. This flow of negentropy is distributed as fuel among the rest of the components of the installation that produces entropy. As a result, the cost of the residual exergy flow is distributed among all the components producing entropy. No installation in which there is energy conversion can work without the actuation of the environment. TFA takes into account the environment’s function and internalizes the cost associated with the dissipative effects that take place in it. For an in-depth look at TFA, consult Frangopulos 1987 [62] and Frangopoulos 1992 [63].

7.10.2 SPECO method The SPECO (Specific Exergy Costing) method starts from a different idea for the formulation of the fuel and product of each component. For this, it takes into account the contributions and extractions of exergy that take place in the matter and energy flows. According to this idea, the product is the sum of all the exergies of the output

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flows of the equipment (including the exergy of the flows generated in the equipment itself) plus all exergy increases between input and output (exergy contributions to flows), as long as they correspond to the objective of the component. Similarly, fuel is defined as the sum of all exergy associated with the input flows, plus the exergy decreases between input and output (exergy extractions of the corresponding flows) and minus the exergy increases between input and output that do not correspond to the objective of the component, Lazzaretto and Tsatsaronis 2006 [64]. To obtain the efficiency of a component, the differences in exergy of the material flows between the input and output of the component need to be evaluated. These increases or decreases of exergy must be calculated for all material flows that undergo a change in their physical exergy and in most cases where there is variation of the chemical exergy. There is some exception, for example, in gasifiers, in which the conversion of the chemical exergy of a fuel into physical and chemical exergy through a gasification process takes place. In this case, the chemical exergy of the solid combustible is considered as fuel, while the chemical exergy of the output gas is the product. Thus, exergy contributions and extractions are parts of the product and fuel respectively. The basis of the SPECO method derives from the idea that the productive function of the component depends only on itself and is independent of the presence of the other components in the system. The system interacts with the other components through the contributions and extractions of exergy to and from the mass and energy flows that cross its limits. Therefore, the relation of a component with the rest of the components is the same as that of the physical structure or the flow diagram, since all the productive interactions between the component and the rest of the system are defined within the limits of the component. From the beginning, it is necessary to decide whether the analysis of the components is going to be carried out using the total exergy, or the separate forms of the exergy of the material flows, that is, the thermal, mechanical and chemical exergy. Considering them separately improves the accuracy of the results, but the increase in computational effort is significant, and in many cases, the improvement is marginal and not needed for the main conclusions of the exergoeconomic analysis. SPECO is a general, systematic and unambiguous method for obtaining the exergy efficiencies of any thermal installation and its components. Unlike what happens in ECT, there are no loss flows associated with material flows at the component level since all the material flows that come out of a component are part of the fuel or the product. SPECO provides general criteria for obtaining the necessary auxiliary cost equations, since in general the number of flows is greater than that of the components. In general, for the same definition of fuel and product, all methods provide similar auxiliary equations. In the same way, as in ECT, SPECO also presents a wellstructured matrix formulation of the equations of exergy and monetary costs, but SPECO also extends the matrix formulation for the average costs to the case in which the components of the exergy are broken down. For an in-depth look at the method consult Lazzaretto and Tsatsaronis 2006 [61].

Thermoeconomics and its application to buildings

Subscripts Reference state; ambient state Total Number of components Number of flows Inlet Outlet Related to fuel, products, or losses Sub-product flows Diagonal matrix

0 T n m i e F, P, L sub D

Superscripts D, ext NE *

Inputs, outputs of the system External Not associated with exergy Exergy cost

Scalars r, V h, s b m_ _ W, _ B_ Q, 4j kj yDi yLi ji ri n i H PWF p I A a I0 Vres Z xij neg

Density and volume Specific enthalpy and specific entropy Specific flow exergy Mass flow rate Rate of heat transfer, power and rate of flow exergy Exergy efficiency of j-th component Unit exergy consumption of j-th component Exergy destruction index of i-th equipment Exergy loss index of i-th equipment Fraction of the total destruction of exergy due to equipment i Fuel used in i-th equipment with respect to the total fuel Years Interest rate Equivalent number of hours per year Present Worth Factor Period Investment Annuity Capital recovery factor Investment referred to year zero Residual value Capital and maintenance cost rate Bifurcation parameter Negentropy

657

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Matrices and vectors M H B D a A F P R L HD KD J B* kF , kP F*, P* C cF, cP Z ue ae ax Ye Y Y A Y M c R

Mass flow vector (m,1) Energy flow vector (n,1) Exergy flow vector (m,1) Diagnostic vector (n,1) Global incidence matrix (1,m) Incidence matrix (n,m) Fuel vector (n,1) Product vector (n,1) Residue vector (n,1) Loss vector (n,1) Diagonal matrix of unit exergy efficiency (n,n) Diagonal matrix of unit exergy consumption (n,n) Exergy balance matrix (n,m) Exergy cost vector (m,1) Unit exergy costs vector of components’ fuel(1,n) and of components’ product (1,n) Exergy costs vector of components’ fuel (1,n) and of components’ product (1,n) Monetary (exergoeconomic) costs vector (m,1) Unit exergoeconomic costs vector of components’ fuel (1,n) and of components’ product (1,n) Capital and maintenance cost vector (1,n) Entrance resources vector (1,n) Entrance incidence matrix (n,e) Bifurcation parameters matrix (n,b) Output flows vector (1,n) External information on exergy cost vector (1,n) Exergy amortization cost vector (1,n) Maintenance cost vector (1,n) Unit costs vector External evaluation vector

References [1] W.T. Tutte, Graph Theory, Cambridge University Press, 2001. [2] S. Lipschutz, Lineal Algebra, 2nded., McGraw-Hill, 1992. [3] G. Tsatsaronis, M. Winhold, Exergoeconomic analysis and evaluation of energy conversion plants, part II: analysis of a coal fired steam power plant, Energy 10 (1985) 81e94. [4] C24 CosteXergy- Analysis And Design of Innovative Systems For Low-Exergy In the Built Environment, Cost-European Cooperation in Science and Technology, 2011. [5] [N. Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press, Cambridge, Massachusetts, USA, 1971. [6] J. Keenan, Transactions ASME 54 (1932) 195. [7] M. Benedict, E.P. Gyftopoulos, Economic selection of the components of an air separation process: second law analysis, in: ACS Symposium Series, vol. 122, Washington D.C., 1980, 195e203.

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[8] M. Tribus, R.B. Evans, A Contribution to the Theory of Thermoeconomics, UCLA Report n 62e36, 1962. [9] Y.M. El-Sayed, R.B. Evans, Thermoeconomics and the design of heat systems, Transactions ASME, Journal Engineering for Power 92 (1970) 27. [10] Y.M. El-Sayed, A.J. Aplenc, Application of the thermoeconomic approach to the analysis and optimization of a vapor-compression desalting system, Transactions ASME, Journal Engineering for Power 92 (1970) 17. [11] R.B. Evans, A Proof that Essergy Is the Only Consistent Measure of Potential Work, PhD Thesis, 1969. Dartmouth College, Hanover, New Hampshire, USA. [12] T. Fehring, R.A. Gaggioli, Economics of feedwater heat replacement, Transactions ASME, Journal Engeneering for Power 99 (1977) 482. [13] G.M. Reistad, R.A. Gaggioli, Available-energy costing, in: Thermodynamics: 2nd Law Analysis, Agriculturae Conspectus Scientificus, vol. 122, 1980, 143. [14] R.A. Gaggioli, W.J. Wepfer, Exergy economics, Energy 5 (8e9) (1980) 823. [15] M. Tribus, Y.M. El-Sayed, Thermoeconomic Analysis of an Industrial Process, 1981. DOE/ER10518-2. [16] Z. Rant, Energy-exergy, Strojniski Vestnik 3 (3) (1957) 3. [17] H.B. Baehr, Energy And Exergy, VDI-Verlag, D€usseldorf, 1965 (in German). [18] T. Kotas, The Exergy Method of Thermal Plant Analysis, Elsevier, 1985. [19] G. Tsatsaronis, M. Winhold, Exergoeconomic analysis and evaluation of energyconversion plants-I. A new general methodology, Energy 10 (1) (1985) 69e80. [20] C.A. Frangopoulos, Application of the thermoeconomic functional approach to the CGAM problem, Energy 19 (3) (1994) 323e342. [21] M.R. von Spakovsky, Application of engineering functional analysis to the analysis and optimization of the CGAM problem, Energy 19 (3) (1994) 343e364. [22] A. Valero, M.A. Lozano, L. Serra, C. Torres, Application of the exergetic cost theory to the CGAM problem, Energy 19 (3) (1994) 365. [23] L. Serra, Exergoeconomic optimization of Termal Systems, PhD Thesis, University of Zaragoza, Zaragoza, 1994 (in Spanish). [24] B. Hua, et al., Exergy analysis and optimization of shell-tube heat exchanger and its enhancement, in: S.J. Deng (Ed.), Heat Transfer Enhancement & Energy Conservation, vol. 897, Hemisphere Pub. Co., 1990. [25] B. Hua, R.H. Hu, The exergy analysis and energy integration and optimization for a methanol plant, Petroleum Processing (Special Volume for Energy Conservation) 53 (1992). [26] Q.H. Yin, B. Hua, Optimal synthesis of HEN based on flow exergy dissipation cost and heat transfer enhancement, Journal of Chemical Industry and Engineering 43 (1) (1992). [27] Invited Papers on Exergoeconomic evaluation and optimization of energy systems, Energy 19 (3) (1994) 279e381. [28] A. Lazzaretto, M. Reni, A. Toffolo, V. Verda, Four approaches compared on the TADEUS (thermoeconomic approach to the diagnosis of energy utility systems) test case, Energy 31 (10) (2006) 1586e1613. [29] Y.M. El-Sayed, R.A. Gaggioli, A critical review of second law costing methods. 1. Background and algebraic procedures, Journal of Energy Resources-ASME 111 (1989) 1e7. [30] M.A. Lozano, A. Valero, Theory of the exergetic cost, Energy 18 (1993) 939e960. [31] G. Tsatsaronis, M.J. Moran, Exergy-aided cost minimization, Energy Conversion and Management 38 (1997) 1535e1542.

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[32] G. Tsatsaronis, L. Lin, J. Pisa, Exergy costing in exergoeconomics, Journal of Energy Resources- ASME 115 (1993) 9e16. [33] A. Lazzaretto, G. Tsatsaronis, On the calculation of efficiencies and costs in thermal systems, Proceedings ASME Advanced Energy System Division 39 (1999) 421e430. [34] C.A. Frangopoulos, Thermoeconomical Functional Analysis: A Method for Optimal Design or Improvement of Complex Thermal Systems, PhD Thesis, Georgia Institute of Technology, Atlanta, USA, 1983. [35] M.R. von Spakovsky, R.B. Evans, Engineering functional analysisdparts I, II, Journal Energy Resources-ASME 115 (1993) 86e99. [36] G.J. Klir, An Approach to General Systems Theory, Van Nostrand Reinhold Co., New York, 1969. [37] M. Chandrasekar, F.C. Wong, Thermodynamic systems analysis: I.A graph theoretic approach, Energy 76 (1982) 556e561. [38] C. Torres, A. Valero, V. Rangel, A. Zaleta, On the cost formation process of residues, Energy 33 (2008) 144e152. [39] E.P. Gyftopoulos, G.P. Beretta, Thermodynamics: Foundations and Applications, MIT Press, 2012. [40] J. Santos, M. Nascimento, E. Lora, A. Martinez Reyes, On the negentropy application in thermoeconomics: a fictious or an exergy component flow? International Journal of Thermodynamics 12 (4) (2009) 163e176. [41] A. Agudelo, A. Valero, C. Torres, Allocation of waste cost in thermoeconomic analysis, Energy 45 (2012) 634e643. [42] S. Stecco, G. Manfrida, Second law analysis of composite power plants, in: Proceedings of the 17th IECEC Conference, 1982. Los Angeles. [43] A. Valero, M.A. Lozano, M. Mu~noz, A general theory of exergy saving. Part I: on the exergetic cost. Part II: on the thermoeconomic cost. Part III: energy saving and thermoeconomics, Computer-Aided engineering and energy system. AES 2e3 (1986) 193e198. ASME Book 100236. [44] J. Szargut, Exergy Analysis of Thermal, Chemical and Metallurgical Processes, Hemisphere, New York, 1980. [45] G.M. Reistad, R.A. Gaggioli, Available-energy Costing, in: R.A. Gaggioli (Ed.), Thermodynamics: Second Law Analysis, American Chemical Society, Washington, D. C, 1980. [46] J.W. Wepfer, Applications of available-energy accounting, in: R.A. Gaggioli (Ed.), Thermodynamics: Second Law Analysis, American Chemical Society, Washington, D. C., 1980. [47] K.M. Guthrie, Process Plant Estimating, Evaluation and Control, Craftsman Solana Beach, CA, 1974. [48] E.P. DeGarmo, W.G. Sullivan, J.A. Bontadelli, Engineering Economy, ninth ed., Macmillan, New York, 1992. [49] A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design & Optimization, John Wiley & Sons, Massachusetts, 1996. [50] E.P. DeGarmo, J.R. Canada, G. William, W.G. Sullivan, Engineering Economy, Prentice Hall, 1996. [51] E. Querol, J. García Torrent, A. Camara, J. Ma Montes, Thermoeconomics And Energy Optimization, Universidad Politécnica de Madrid, 2011 (in Spanish). [52] C. Torres, Symbolic Exergoeconomics. Methodology For Thermoeconomic Analysis of Energy Systems, PhD Thesis, Universidad de Zaragoza, 1991 (in Spanish).

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[53] J. Szargut, D.R. Morris, Cumulative exergy consumption and cumulative degree of perfection of chemical processes, Energy Research 11 (1987) 245e261. [54] I. Boustead, G.F. Hancock, Handbook of Industrial Energy Analysis, John Wiley & Sons, New York, 1979. [55] P. Leprince, J.P. Arlie, C. Raimboult, How to calculate the energy content of oil-origin products and their substitutes vegetable and coal-origin (in French), Revue de Institut Français du Petrole 36 (1981) 81e90. [56] G. Tsatsaronis, Design optimization using exergoeconomics, in: A. Bejan, E. Manut (Eds.), Thermodynamic Optimization of Complex Energy Systems, Kluwer Academic Publishers, 1999, 101e115. [57] R.A. Gaggioli, Second law analysis for process and energy engineering, in: R. Gaggioli (Ed.), Efficiency and Costing A.C.S. Symposium Series, vol. 235, 1983, 3e50. [58] G. Tsatsaronis, M. Winhold, Exergoeconomic analysis and evaluation of energy conversion plants, Energy International Journal 10 (1985) 69e94. [59] M.R. Von Spakovsky, A Practical Generalized Analysis Approach to the Optimal Thermoeconomic Design and Improvement of Real-World Thermal Systems, PhD Thesis, Georgia Institute of Technology, 1986. [60] G. Tsatsaronis, L. Lin, On exergy costing in thermoeconomics, in: G. Tsatsaronis, R.A. Bajura, W.F. Kenney, G.M. Reistad (Eds.), Computer-aided Energy Systems Analysis, vol. 21, ASME, Nueva York, 1990, 1e11. [61] A. Lazzaretto, G. Tsatsaronis, On the calculation of efficiencies and costs in thermal systems, in: S.M. Aceves, S. Garimella, R. Peterson (Eds.), Proceedings of the ASME Advanced Energy System Division, vol. 39, ASME, Nueva York, 1999, 413e428. [62] C.A. Frangopoulos, Thermo-economic functional analysis and optimization, Energy 12 (7) (1987) 563e571. [63] C.A. Frangopoulos, Optimal synthesis and operation of thermal systems by the TFA, Journal of Engineering for Gas Turbines and Power 114 (4) (1992) 707e714. [64] A. Lazzaretto, G. Tsatsaronis, SPECO: a systematic and general methodology for calculating efficiencies and costs in thermal systems, Energy 31 (2006) 1257e1289.

Symbolic Thermoeconomics applied to thermal facilities

8.1

8

Summary

In the previous Chapter, ECT was presented which, like the rest of the cost accounting methodologies, is a numerical technique that allows calculating the cost values of the flows by considering their formation process. Indeed, Symbolic Thermoeconomics (ST) is developed during this chapter, and it is explained with functions that relate thermoeconomic variables with some chosen independent variables. If the common real situations are taken into account, two different formulations can be encountered in the ST formulation. In the first case, the independent variables are the external resources used, the bifurcation parameters and the unit consumption of the components; therefore, the thermoeconomic variables are expressed as functions of them. That is called FP formulation, and it is applied in situations in which the facility’s resource consumption is fixed and the production is variable.

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In the second case, called PF formulation, the independent variables are the recirculation parameters, the system products and the components unit consumption; hence, the thermoeconomic variables are expressed as a function of them. This formulation is applied when the system’s total production is fixed and the consumption of resources varies, which depends, clearly, on the components’ irreversibilities. The Chapter finishes by presenting the FP(R) and PF(R) formulations. Those are an extension of the previous ones, but the effects of the residues are included there. The study requires an analysis of residual flows so that their formation process must be known in order to allocate the cost to the products of the facility.

8.2

Introduction

As already learned, Exergy Cost Theory (ECT) works with numerical values; after defining the states of the flows, the exergy destruction values can be obtained as well as the component exergy efficiencies and flow costs, even the intermediate ones or the final products. Cost accounting methodologies, such as ECT, are numerical techniques that allow the calculation of costs in an accurate way; for that, a series of systems of linear equations need to be solved. However, they do not allow the causes of the cost formation process to be identified. Symbolic Thermoeconomics (ST) or Symbolic Exergoeconomics is based on the ECT; it enables general equations that relate the total efficiency of a facility and other thermoeconomic variables as fuel, product, exergy cost, etc. to be obtained with the efficiency of each component which forms it. Working with equations, for example, shows how the variation in the efficiency of a component will affect the total efficiency of the plant. Authors such as Lazaroff and Vulchanova 1985 [1] indicated the interest of working with analytical functions such as the one below 4T ¼ f ð41 ; 42 ; .; 4n ; x1 ; .; xn Þ

(8.1)

where 4T is the overall system efficiency, 41,.,4n reflect the components’ efficiencies and x1,x2,.xn are related to the parameters that represent the structure of the system; as it will be explained later on, these parameters are called bifurcation or recirculation parameters. By means of the conventional methods of thermoeconomic cost accounting, it is possible to know the numerical value of the cost of a system’s product or an intermediate flow; unfortunately, to know the way in which that cost has been obtained cannot be achieved. Conversely, the general solutions are valid for any state of the plant. By combining ECT and Symbolic Computation, the system can be solved in a generic way. In such a case, not only specific numerical values but analytical expressions that relate the costs with the installation’s independent variables can also be obtained. Thus, the interdependence between the parameters are represented and, besides, a thorough study of the thermal systems productive structure can be done.

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In short, working with general equations allows general solutions for general problems to be obtained. Hence, ST is a powerful tool for cost accounting, plant diagnosis and for the synthesis and design of energy systems and installations, Bau et al. 1988 [2], Noor et al. 1990 [3]. For obtaining those general formulas, Cost Accounting Theory (such as ECT) needs to be combined with symbolic computer packages (e.g., Mathematica). Two types of situations appear when ST is applied. In some cases, the resource consumption is already fixed, so depending on the characteristics of the plant, the obtained product can be greater or lower. That situation is known as FP representation or supply-driven model. Expressions relating the system parameters with the consumed resources and a series of parameters of the equipment and structural relationships are, therefore, procured. In other cases, the product of the plant can be established. Thus, a heating facility needs to supply the heating and DHW demand, while an air conditioning installation must supply the cooling demand, etc. In such cases, the different parameters of the plant are expressed in terms of products, equipment characteristics and internal parameters explaining the structure of the plant. This form is called PF representation or demand-driven model. Therefore, the FP representation enables products and costs expressions starting from the required external resources to be obtained. In addition, the costs are given as a function of other (canonical) variables which are the equipment efficiencies and the bifurcation parameters. The PF representation is complementary to the previous one and allows the flows and resources’ consumption expressions from the final products of the plant to be obtained. Symbolic expressions of the flow costs are also obtained from the products and the following canonical variables: equipment efficiencies and recirculation coefficients. Thus, ST allows expressing the thermoeconomic variables of the system flows, that is, the exergy and costs are described depending on the canonical variables of each representation. Obviously, both representations are closely linked and it is possible to move from one to the other. That will be clearly developed during this chapter, and different selected examples will be solved.

8.3

FP representation or supply-driven model

It was marked during the ECT development in Chapter 7 that each component has associated with it an exergy efficiency 4i (or its inverse: a unit exergy consumption ki) and bifurcation parameters xij. According to that, the number of bifurcations of a component is the number of outflows minus one; bifurcation parameter refers to the relationship between the exergies of two outputs. In addition, each element may or may not receive any external resource and ue is used to designate the external resources’ vector (Section 7.9.2). The set of those three parameter types constitutes a vector of m components, that is ce h ðk; x; ue Þ

(8.2)

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The characterization of a system through this set of parameters is called FP representation or supply-driven model. Although ECT permits the numerical values of the flow costs, either exergy costs or exergoeconomic costs, to be calculated by combining ECT with Symbolic Computation not only are the numerical values of particular costs obtained, but analytical expressions that relate the costs with the system canonical variables are also acquired. This will allow the understanding of their interdependence, as well as a deepened analysis of the productive structure to be studied, Torres et al. 1989 [4].

8.3.1

Expressions for the exergy of the flows

In this section, a general method to obtain analytical expressions of the component efficiencies and of the total system will be developed. Then, the costs of the flows and final products will be expressed as a function of the canonical variables; in fact, in this representation, the external resources, the bifurcation coefficients and the equipment efficiencies (or their inverse: unit consumptions) are used. Let us consider the generic installation from Chapter 7, consisting of m flows and n components. KD is the diagonal matrix (n, n) that contains the unit exergy consumption of each component and B is the (m,1) vector of exergy flows shown in Chapter 7, Eq. (7.35). From the exergy balance in every component of the system, the following can be written, Eq. (7.35) here written again JB ¼ 0

(8.3)

where J is the (m,1) matrix that satisfies the equality J ¼ AFKDAP. From ae and ax, matrices from Chapter 7 aex is formed; that is a (mne,n) matrix containing the information about the system input flows as well as the equipment bifurcations. From it and from J, the extended matrix Jx ðm; mÞ is constructed as follows " Jx ¼

J

#

aex

(8.4)

Its regularity is verified, Torres 1991 [5]. By the ae and ax matrices’ definitions, it is fulfilled that ae B ¼ ue

(8.5)

ax B ¼ 0

(8.6)

Recalling the definition of Ye studied in 7.9.2, the following matrix equation is verified Jxðm;mÞ Bðm;1Þ ¼ Yeðm;1Þ

(8.7)

Symbolic Thermoeconomics applied to thermal facilities

667

Since Jx is a regular matrix, its inverse can be obtained, and then the exergies of the flows are B ¼ J1 x Ye

(8.8)

By means of this matrix equation, algebraic expressions relating the exergy of the flows with the set of ce parameters are obtained.

8.3.2

Expressions for the exergy costs and exergoeconomic costs of flows

Similarly to what was stated in the previous section, with vector B* (m, 1) that contains the exergy costs of flows, the following equation from the exergy cost balance in each component can be written as AB ¼ 0

(8.9)

Likewise, with the extended matrix Aðn; nÞ and the Ye vector, the following matricial equation can be found AB ¼ Ye

(8.10)

Reversing the regular matrix A, it turns out that B ¼ A1 Ye

(8.11)

This equation corresponds to Eq. (7.112) from Chapter 7 but, instead of the exergy cost values, costs functions are obtained. In such a way, the exergy costs of the flows are obtained as functions of the canonical variables of the representation, that is, depending on the unit consumptions of the components, the bifurcation coefficients and the external resources. It is interesting to note that B* vector does not depend on the efficiencies (unit consumptions) of the components since the A matrix does not contain the ki variables. This result can be interpreted by verifying that, when KD¼UD, A matrix coincides with J; or what is the same, the exergy cost can be interpreted as the maximum exergy of the flow, once the bifurcation parameters have been set. Similarly, if the C(m, 1) vector that contains the exergoeconomic costs of the flows is considered and recalling the Ze definition of Section 7.9.5, it can be written that AC ¼ ℤe

(8.12)

If A matrix is reversed, the matrix expression for exergoeconomic costs results C ¼ A1 ℤe

(8.13)

A system of m equations is, therefore, available and enables the expressions of exergoeconomic costs of flows to be obtained. Thus, mathematical expressions for the

668

Exergy Analysis and Thermoeconomics of Buildings

Bi ; Bi ; Ci basic thermoeconomic variables of the generic i-th flow have been obtained, as well as any other derived variable, such as ki ; ci . All of them are functions of the canonical variables for this representation. In short, the formulas above (8.8)e(8.13) reveal the analytical expressions of the thermoeconomic variables as a function of the canonical variables which are the equipment efficiencies collected in the KD diagonal matrix, the plant structure expressed through the bifurcation parameters x and the external resources of the system contained in Fe, Ce, Ze vectors.

8.3.3

Expressions for the fuel and product of components

Once the expressions for representing the exergies, exergy costs and exergoeconomic costs of the flows of a system have been obtained, the corresponding expressions for the fuel and product of each component will be attained. An important step forward is initiated since such development will provide more information about the facility’s productive structure and the cost formation process. In addition, it will allow more appropriate expressions for working on the scope of ST to be obtained. Starting from the resource matrix AF and the product matrix AP defined in 7.6.1, it can be said that F ¼ AF B

(8.14)

P ¼ AP B

(8.15)

Regarding exergy costs we have P ¼ F ¼ AP B

(8.16)

Similarly to the previous approach, the APðm;mÞ matrix can be constructed as   AP AP h (8.17) aex as well as the extended P vector which is   P P¼ uex

(8.18)

that verify the relationship AP B ¼ P

(8.19)

This system of m equations has a unique solution, as demonstrated in Torres 1991 [5]. Isolating the B vector from the above equation and substituting it into Eq. (8.14), results as F ¼ AF A1 P P

(8.20)

Symbolic Thermoeconomics applied to thermal facilities

669

By the development of that expression and considering the meaning of generalized inverse matrices, Ronde 1983 [6], it is obtained that ð1Þ

F ¼ AF AP

P þ AF Be

(8.21)

ð1Þ

where AP is the generalized inverse matrix of AP and Be is a (m, 1) vector that represents the external resource flows; so that if ue,i is the only external resource of the facility, then Be,i ¼ ue,i and Be,j(j s i) ¼ 0 for the rest. Therefore, the term AFBe is a (m, 1) vector that represents the external exergy resources entering each component; then it is designated as Fe and is composed by (Be,1,Be,2,.,Be,n). The e subscript means external resource, while the second subscript indicates the involved equipment. ð1Þ If hFPi ¼ AF AP is used to denominate the (n, n) matrix that depends exclusively on ð1Þ the bifurcation parameters contained in AP , the following matrix equation can be written F ¼ Fe þ hFPiP

(8.22)

That expression permits the resources used in each component to be obtained based on the external resources (Fe) and on the product of every jeth component (Pj) in a proportion defined by the coefficients of the hFPi matrix. Therefore, each element of this matrix (yij) can be interpreted as the fraction of the product of ieth component used as a resource in the jeth component, being those yij coefficients function of the n P yij ¼ 1. So, for jeth component it bifurcation parameters and verifying the equality i¼0

can be written Fj ¼ Bej þ y1j P1 þ y2j P2 þ . þ ynj Pn ¼ Bej þ

n X

yij Pi

j ¼ 1; 2; .; n

(8.23)

i¼1

This expression can also be written more compactly as Fj ¼

n X

yij Pi

j ¼ 1; 2; .; n

(8.24)

i¼0

where subscript 0 corresponds to the external environment so that y0jP0 corresponds to B0j ¼ Bej; that is, the fuel fraction of equipment j coming from the external environment. In order to extend the sum to external resources we use the sub-index 0 instead of e. Thus, the total fuel of each equipment j comes from: • •

The external resources of the installation, such as natural gas consumption (in the case of boilers) and electricity (in the case of heat pumps), collected through the vector Fe. The product of each component, in a proportion reflected by the yij coefficients of the hFPi matrix. As stated above, each of these matrix elements can be interpreted as the portion of the product of the ieth equipment becoming a resource of the j-th equipment.

670

Exergy Analysis and Thermoeconomics of Buildings

Table 8.1 Fuel-Product table for an n-component installation. Final product

External resources Process products

Process resources

Total

1

.

j

.

n

B01

.

B0j

.

B0n

P0

.

B1j

.

B1n

P1

«

.

Bij

.

«

.

1

B10

B11

«

«

«

i

Bi0

Bi1

«

«

«

n

Bn0

Bn1

.

Bnj

.

Bnn

F0

F1

.

Fj

.

Fn

Total

.

« Bin

Pi « Pn

Table 8.1 represents the Fuel-Product relationship of a thermal system and describes its productive structure. That is, interrelated production processes are exposed. It can be considered as a specific case of Leontief 1986 [7] input-output table, Fig. 8.1, in which the flows are expressed through exergy. A generic column j in the table satisfies Eq. (8.22), inasmuch as the sum of each column terms is equal to the corresponding column component fuel. From Eq. (8.22) and taking into account the relation F¼KDP we have ðK D  hFPiÞP ¼ Fe

Figure 8.1 Photograph of W. Leontieff (1906e99).

(8.25)

Symbolic Thermoeconomics applied to thermal facilities

671

According to Torres 1991 [5] the (KDhFPi) matrix is strictly dominant diagonal and, therefore, regular, so it can be written as P ¼ hPjFe

(8.26)

where hPj h ðK D  hFPiÞ1 is a matrix operator. Eq. (8.26) enables each component product to be expressed based on the system resources income (Fe), the equipment unit consumption and the system’s functional structure. That is reflected in the hPj matrix operator. From the previous expression, it can immediately be deduced that F ¼ hFjFe

(8.27)

where hFjhKDhPj and hence I ¼ hIjFe

(8.28)

being hIjh(KDUD)hPj. Consequently, every component fuel, product and irreversibility can be expressed as a function of the variables (k,x,ue) by means of the previous (8.26)e(8.28) equations.

8.3.4

Expression of the installation global efficiency

Being PT the installation product (heating, DHW and/or cooling) and FT the resource consumption (fuel and/or electricity), its exergy efficiency is 4T ¼

PT FT

(8.29)

Such an equation will be developed accordingly to express the independent variables of this representation. The total fuel of the system can be expressed as FT ¼ tu Fe where tu is the transpose of the u unit vector (n, 1). Furthermore, from Eq. (8.22) and from the well-known FeP]I relationship, one can get that FT ¼ t uðF  hFPiÞF ¼ t uI þ t uðU D  hFPiÞP

(8.30)

Since FTPT ¼ IT, it can be written that PT ¼ t uðUD  hFPiÞP

(8.31)

If the tu unit transpose vector (1,n) is multiplied by the (UDhFPi) matrix of dimension (n, n) and designated as thPTPihtu(UDhFPi), it can be said that PT ¼ t hPT PiP

(8.32)

672

Exergy Analysis and Thermoeconomics of Buildings

The tPTP transpose vector of dimension (1, n) represents the portion of each component product that becomes part of the total product of the installation. Returning to the system efficiency expression, we have t

4T ¼

hPT PiP t uF e

(8.33)

and finally, taking into account Eq. (8.26) t

4T ¼

hPT PihPjFe t uF e

(8.34)

This equation permits expressing the total system efficiency as a function of every component efficiency, the bifurcation parameters and the input resources by means of an algebraic expression. Following Valero and Alconchel 1987 [8], that equation is known as the universal formula of exergy efficiency of thermal systems. In the Doctoral Thesis by Alconchel 1988 [9] such an expression is applied to obtain the efficiency of a steam cycle.

8.3.5

Expressions for the exergy costs and exergoeconomic costs of fuel and product

Since the fuel cost of a component is the sum of its constituent flow costs, Eq. (8.22) is equally valid for exergy costs and exergoeconomic costs. Therefore, the fuel cost of the generic equipment j is the external resources’ costs (Fe,Ce) which are part of that fuel plus the products’ costs (P*,CP) of the other components multiplied by the yij fraction in which they become part of the i-th fuel. So that Fj ¼ Bej þ

n X

yij Pi

j ¼ 1; 2; .; n

(8.35)

j¼1

CFj ¼ Cej þ

n X

yij Cp;j

j ¼ 1; 2; .; n

(8.36)

j¼1

and in matrix form F ¼ Fe þ hFPiP

(8.37)

CF ¼ Ce þ hFPiCP

(8.38)

where Fe is the (n, 1) exergy cost vector of incoming resources of the system, which, in the absence of external valuation, coincides with its exergies Fe ¼ Fe . Moreover, Ce

Symbolic Thermoeconomics applied to thermal facilities

673

is the vector that contains the exergoeconomic costs of the input resources. If F* ¼ P* is taken into account, one gets that ðUD  hFPiÞP ¼ Fe

(8.39)

If a hP j h ðUD  hFPiÞ1 matrix operator of (n, n) dimension is defined, the following expression for the exergy cost of components’ fuel and product can be obtained as F ¼ P ¼ hP jFe

(8.40)

Henceforth, the exergy costs of components’ fuel and product do not depend on the efficiencies, since the hP*j operator does not contain KD. The corresponding unit costs are obtained by dividing the previous expressions by each component fuel and product. So, for the generic j-th component, it is written as  kF; j¼

 kP; j¼

Fj Fj Pj Pj

¼

¼

t u j hP jF t u j hFjF

e

(8.41)

e

t u j hP jF e t u j hPjF e

(8.42)

being tuj a (n, 1) vector that contains a 1 in the jeth position and 0 in the rest. The exergy cost of the components’ product can also be expressed in terms of the irreversibilities. Indeed, from Eq. (8.40) and isolating Fe from Eq. (8.26) we have P ¼ hP jhPj1 P ¼ hP jðK D  hFPiÞP

(8.43)

and, therefore P ¼ hP jðU D  hFPiÞP þ hP jðK D  U D ÞP

(8.44)

resulting finally in P ¼ P þ hP jI

(8.45)

This expression enables the product cost formation process to be explained. The exergy cost of the components’ product is the sum of its exergy plus the associated irreversibilities in its generation; hence, the matrix hP*j indicates the proportion in which the cost increases due to the irreversibilities of every component. The exergoeconomic costs are now going to be determined. From Eq. (8.38) and (7.126) it is written that ðUD  hFPiÞCP ¼ Ce þ Z

(8.46)

674

Exergy Analysis and Thermoeconomics of Buildings

So the CP vector, gathering the equipment product costs, is CP ¼ hP jðCe þ ZÞ

(8.47)

Therefore, for obtaining the exergy costs, the same matrix operator also relates the product’s exergoeconomic costs to the external resources; in this case, however, those are the fuel costs Ce and the capital cost rates of components, vector Z. Likewise, the components’ fuel costs are CF ¼ CP  Z ¼ hP jCe þ ðhP j  U D ÞZ

(8.48)

According to Eq. (8.32), the system’s total product cost is given by the equation CPT ¼ t hPT PiCP

(8.49)

Considering the hPTPi vector’s transpose expression and substituting it into Eq. (8.49) the following is found CPT ¼ t uðUD  hFPiÞhP jðCe þ ZÞ

(8.50)

and, therefore CPT ¼ t uðCe þ ZÞ

(8.51)

That is, the cost of the total product is the sum of the costs of the external resources or, in other words, it is the sum of the external fuel costs and the capital and maintenance costs of equipment. Similar expressions were published for the first time in Valero and Torres 1988 [10]. This section can be concluded by saying that for the generic thermoeconomic variable X of the fuel and the product of any component, there is a linear operator represented by a regular and positive matrix hXj depending only on the equipment efficiencies k and the bifurcation parameters x, such that it is verified that X ¼ hXjX e

(8.52)

where Xe is a vector that contains the external resources, that is, the system input fuel and the capital and maintenance costs of the equipment. It is also verified, Torres 1991 [5], that those operators have a specific property: if k, x remain fixed and the external resources increase, the fuel, product, irreversibility and costs of all components augment.

8.3.6

Examples

Example E.8.1.

Let us consider a DHW production facility based on a condensing boiler. The system consists of a condensing boiler, a hydraulic compensator, a three-way valve acting according to the demand, a heat exchanger and an accumulation tank. In addition, there are three circulation pumps, one in each of the circuits, see the

Symbolic Thermoeconomics applied to thermal facilities

675

diagram of Fig. E.8.1. Using the FP formulation and without considering residues, the following have been addressed: (a) (b) (c) (d) (e) (f) (g) (h)

Functional analysis of installation flows. Construction of the extended matrix Je and the vector Ye . Symbolic expressions of each flow exergy. Construction of the matrix hFPi. Symbolic expressions of components’ fuel. Symbolic expressions of components’ product. Symbolic expressions of components’ irreversibility. Symbolic expression of the total system efficiency.

Figure E.8.1 Schema of the DHW production facility.

Solution. A total of m ¼ 13 flows and n ¼ 6 components have been considered, see Fig. E.8.2. Circulation pumps have not been taken into account due to their small power. Therefore, the effects of pressure on the water flow exergy values are not considered in the analysis.

Figure E.8.2 Considered components and flows.

(a) The result of the functional analysis is shown in Table E.8.1, which also represents each component unit’s consumption. There is one product on the installation, flow 11, which corresponds to the DHW flow, with associated exergy B_ 11 during the time-step considered.

676

Exergy Analysis and Thermoeconomics of Buildings

Table E.8.1 Functional analysis. n

Fuel

Prod.

kD

Ps

①

Boiler

B_ 13

B_ 1  B_ 2

ðB_ 1 B_2 Þ

0

②

Hydraul. Compens.

B_ 1  B_ 2

B_ 3  B_ 4

B_ 3 B_ 4 B_ 1 B_ 2

0

③

Diverter

B_ 3

B_ 5 þ B_ 6

B_ 5 þB_ 6 B_ 3

0

④

V3V

B_ 6 þ B_ 7

B_ 4

B_ 4 B_ 6 þB_ 7

0

⑤

HX

B_ 5  B_ 7

B_ 8  B_ 9

B_ 8 B_ 9 B_ 5 B_ 7

0

⑥



Tank



B_ 8  B_ 9 þ DB_ 12

B_ 13

B_ 11  B_ 10

B_ 11 B_ 10

ðB_ 8 B_9 ÞþDB_12

B_ 11

Once this functional analysis is done, the construction of matrices AF and AP is immediate. Note that the tank accumulated exergy increase during the analysis period (DB_ 12 ) is considered as fuel, that is, the exergy difference between the initial and final moment of the time-step. (b) The extended matrix Jx and the vector Ye are constructed according to Eq. (8.4) and Eq. (7.110). They are shown below " Jx h

J

#

aex "

Ye h

0

#

uex

The matrix J, which is part of the extended matrix Jx is defined according to J ¼ AFKDAP. It is presented in Table E.8.2.

Table E.8.2 J matrix definition.

J¼

1

2

3

4

5

6

10

11

12

13

k1

k1

0

0

0

0

0

0

0

0

0

0

1

1

1

k2

k2

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

k4

0

1

1

0

0

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

k3 k3

7

8

9

k5

k5

0

0

0

0

1

1

k6

k6

1

0

Symbolic Thermoeconomics applied to thermal facilities

677

The ax bifurcation matrix relates the flow exergies going out of the components. In Table E.8.3 bifurcation parameters are presented (as many as output flows of each component minus 1); due to space reasons, in the second column they are named according to the nomenclature xij, but in the third and fourth columns, and throughout the Example, they are numbered from 1 to 4.

Table E.8.3 Bifurcation parameters. n

xij

Bifurcations

①

x1;2

x1 ¼ BB_ 2

aX

_

B_ 2 B_ 1 $x1 ¼ 0

1

②

x5;6

x2 ¼

③

x5;7

x3 ¼

④

x8;9

x4 ¼

B_ 6 B_ 5 B_ 7 B_ 5 B_ 9 B_ 8

B_ 6 B_ 5 $x2 ¼ 0 B_ 7 B_ 5 $x3 ¼ 0 B_ 9 B_ 8 $x4 ¼ 0

In Table E.8.4 the matrix associated with the bifurcation parameters ax(4,13) is shown. Table E.8.4 ax bifurcation matrix. ax ¼

_

BB_ 2

1

0

0

0

0

0

0

0

0

0

0

0

0

0

_ BB_ 6 5

1

0

0

0

0

0

0

0

0

0

0

0

0

_ BB_ 7 5

1

0

0

0

0

0

0

0

0

_ BB_ 9 8

1

0

0

0

0

1

0

0

0

0

0

0

0

The (3.13) dimension matrix ae contains the coefficients of the incoming flows; besides, the vector Ye (in fact, its transpose) contains the total external resources. Both are reflected in Table E.8.5. Table E.8.5 ae input matrix and Ye vector. ae ¼

t

Ye ¼

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

Be10

0

DBe12

Be13

(c) Once the external fuel (B_ e ), the exergy unit consumptions (ki) and the bifurcation parameters that define the physical system are known, the symbolic expressions of components fuel are obtained. Eq. (8.8) is used for the resolution and the results are collected in Table E.8.6.

678

Exergy Analysis and Thermoeconomics of Buildings

Table E.8.6 Symbolic expressions of flows. FP representation.

9.

Flows symbolic expressions fk; x; Be g  B_ 1 ¼ B_ e13 ½k1 $ð1 x1 Þ  B_ 2 ¼ B_ e13 $x1 ½k1 $ð1  x1 Þ  B_ 3 ¼ B_ e13 $k3 $k4 $ð1 þ x2 Þ ½k1 $k2 $½x2 þ x3  k3 $k4 $ð1 þ x2 Þ  B_ 4 ¼ B_ e13 $ðx2 þ x3 Þ ½k1 $k2 $½x2 þ x3  k3 $k4 $ð1 þ x2 Þ  B_ 5 ¼ B_ e13 $k4 ½k1 $k2 $½x2 þ x3  k3 $k4 $ð1 þ x2 Þ  B_ 6 ¼ B_ e13 $k4 $x2 ½k1 $k2 $½x2 þ x3  k3 $k4 $ð1 þ x2 Þ  B_ 7 ¼ B_ e13 $k4 $x3 ½k1 $k2 $½x2 þ x3  k3 $k4 $ð1 þ x2 Þ  B_ 8 ¼ B_ e13 $k4 $ð1  x3 Þ ½ðx4  1Þ$k1 $k2 $½x2 þ x3  k3 $k4 $k5 ð1 þ x2 Þ  B_ 9 ¼ B_ e13 $x4 $k4 $ð1  x3 Þ ½ðx4  1Þ$k1 $k2 $½x2 þ x3  k3 $k4 $k5 ð1 þ x2 Þ

10.

B_ 10 ¼ B_ e10

1. 2. 3. 4. 5. 6. 7. 8.

11.

  B_ 11 ¼ B_ e10 þ B_ e12 k6  B_ e13 $k4 $ð1  x3 Þ k6 $k1 $k2 $½x2 þ x3  k3 $k4 $k5 ð1 þ x2 Þ

12.

DB_ 12 ¼ B_ e12

13.

B_ 13 ¼ B_ e13

(d) The previous matrices are used for the construction of the matrix hFPi, taking into account ð1Þ the relation hFPi ¼ AF AP , see Table E.8.7. Table E.8.7 hFPi matrix. t

hPT Pi [

hFPi ¼

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

x2 þx3 x2 þ1 1x3 x2 þ1

0

It is verified that the boiler product is entirely transformed into the fuel of the discharge manifold and something similar happens with the hydraulic compensator and the three-way 3 diverter. From the total product of the diverter, however, the portion xx22þx þ1 goes out to V3V, and the remaining part goes to the exchanger. The total product of the heat exchanger is also transformed into the tank fuel. It can also be seen that the total product of the tank becomes entirely part of the total product of the installation (last term of vector PTP). (e) From Tables E.8.3 and E.8.6, and by using the F ¼ AFB relation, the symbolic expressions of components’ fuel are obtained, see Table E.8.8.

Symbolic Thermoeconomics applied to thermal facilities

679

Table E.8.8 Symbolic expressions of components’ fuel. FP representation. Fuels symbolic expression ①

F1 ¼ B_ e13

②

F2 ¼ Bke13 1

③

2 F3 ¼ B_ e13 $k3 $k4 $k1 $k2 $½x2 þx1þx 3 k3 $k4 $ð1þx2 Þ

_

þx3 Þ F4 ¼ B_ e13 $k4 $k1 $k2 $½x2 þxðx32k 3 $k4 $ð1þx2 Þ

④

3 F5 ¼ B_ e13 $k4 $k1 $k2 $½x2 þx1x 3 k3 $k4 $ð1þx2 Þ

⑤

3 _ F6 ¼ B_ e13 $k4 $k1 $k2 $½x2 þx31x k3 $k4 $k5 ð1þx2 Þ þ Be12

⑥

(f ) Similarly, using the P ¼ APB relationship, symbolic expressions of the components’ product are obtained, see Table E.8.9. Table E.8.9 Symbolic expressions of components’ product. FP representation. Products’ symbolic expressions _

①

P1 ¼ Bke13 1

②

4 $ð1þx2 Þðx2 þx3 Þ P2 ¼ B_ e13 $k1 $kk32$k $½x2 þx3 k3 $k4 $ð1þx2 Þ

2 P3 ¼ B_ e13 $k4 $k1 $k2 $½x2 þx1þx 3 k3 $k4 $ð1þx2 Þ

③

þx3 P4 ¼ B_ e13 $k1 $k2 $½x2 þxx32k 3 $k4 $ð1þx2 Þ

④

3 P5 ¼ B_ e13 $k4 $k1 $k2 $½x2 þx1x 3 k3 $k4 $ð1þx2 Þ

⑤

_ 3 P6 ¼ Bke12  B_ e13 $k4 $k6 $k1 $k2 $½x2 þx1x 6 3 k3 $k4 $k5 ð1þx2 Þ

⑥

(g) The corresponding expressions for the components’ irreversibility are obtained subtracting the previous expressions, since I ¼ FeP. The results are shown in Table E.8.10. Table E.8.10 Irreversibility symbolic expressions. FP representation.

① ②

Irreversibilities’ symbolic expressions   I1 ¼ B_ e13 $ 1  k11 I2 ¼ B_ e13 $

 1 k1

4 $ð1þx2 Þðx2 þx3 Þ  k1 $kk32$k $½x2 þx3 k3 $k4 $ð1þx2 Þ



③

2 $ðk3  1Þ I3 ¼ B_ e13 $k4 $½k1 $k2 $½x2 þx1þx 3 k3 $k4 $ð1þx2 Þ

④

þx3 Þ $ðk4  1Þ I4 ¼ B_ e13 $½k1 $k2 $½x2 þxðx32k 3 $k4 $ð1þx2 Þ   1 1 3 $  I5 ¼ B_ e13 $k4 $k1x ½x2 þx3 k3 $k4 $ð1þx2 Þ ½x2 þx3 k3 $k4 $k5 ð1þx2 Þ 1 $k2

⑤ ⑥

    3 _ e12 $ 1  1 þ B I6 ¼ B_ e13 $k4 $k1 $k2 $½x2 þx1x k6 3 k3 $k4 $ð1þx2 Þ

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Exergy Analysis and Thermoeconomics of Buildings

(h) The total efficiency of the installation is _ 1  x3  Be12  B_ e13 $k4 $ _ _ B11  B10 PT k6 k6 $k1 $k2 $½x2 þ x3  k3 $k4 $k5 ð1 þ x2 Þ 4T ¼ ¼ ¼ FT B_ e12 þ B_ e13 DB_ 12 þ B_ 13 

Representation PF or demand-driven model

8.4

As seen before, from ECT and through the ST application, symbolic expressions of the thermoeconomic variables of the system can be obtained. So far, expressions in the FP representation have been obtained, that is, a representation in which any thermoeconomic variable is a function of the equipment efficiencies, the exergy bifurcation parameters and the facility external resources. At this moment, a representation in which the thermoeconomic variables are represented according to the system’s total product, us, the equipment efficiencies, k, and parameters reflecting the plant structure in a different way than bifurcation coefficients (called recirculation parameters) will be presented. Recirculation of a component is the number of entering flows minus one, and the relation between the exergy of those inflows is known as recirculation parameter r. The bases of this representation are found in Valero and Torres 1990 [11]. Therefore, in this PF representation, the set of canonical variables form the vector cs such that cs h ðk; r; us Þ

8.4.1

(8.53)

Expressions for the exergies of flows

The equation JB ¼ 0 comes out from the exergy balance at each component. Then, n equations with m unknowns are obtained. Since the system products us are known, s auxiliary equations can be added. If as is the matrix (s, m) that contains the coefficients of these equations, we have as B ¼ u s

(8.54)

where us is a vector (s, 1) containing the installation total product. Therefore, additional (mns) equations are needed to close the system. Those equations are obtained from the functional classification of the flows, that is, from each component’s productive purpose concept. In fact, if in any u component the unit exergy consumption ku and the exergy of the output flows are known, the total input flows can be out in P P B j ¼ ku B i . determinate, since j

i

If the equipment had only one input flow, it would be univocally determined, but if it has eu > 1 entries, (eu1) additional equations are needed to specify them. These equations are obtained by means of the so-called recirculation parameters. As said, recirculation in a component is the number of inflows minus one. So, if a component

Symbolic Thermoeconomics applied to thermal facilities

681

u has entering flows eu and all are fuel, the recirculation parameters (eu1) are defined as rij ¼ Bi/Bj, verifying the following equation Bi  rij Bj ¼ 0

(8.55)

If the input flow j belongs to the product of the equipment, where h is an output flow that is also part of the product, then rjh ¼ Bj/Bh, and the next equation would be verified as Bj  rjh Bh ¼ 0

(8.56)

So for each component with input flows eu the recirculation parameters (eu1) can be defined. Inasmuch as all the flows are the inputs of some equipment, except for the final products, the total number of system recirculations is n X

ðeu  1Þ ¼

u¼1

n X

eu  n ¼ m  s  n

(8.57)

u¼1

and, therefore, it coincides with the number of additional equations necessary to calculate the installation exergy flows. If ar is denoted to the [(mns), n] matrix containing the recirculation equation coefficients, it is fulfilled that ar B ¼ 0

(8.58) .

Note that for the recirculation parameters the inequality rij s Bi Bj is ascertained, so arB* ¼ 0 is not fulfilled. In principle, it could be thought that exergy costs could not be obtained by this representation. In theory, this is logical, since the exergy cost of a flow is defined as the amount of ue resources necessary to produce it, and it does not make sense to express it in terms of the products of the installation us. However, the recirculation parameters can be expressed as a function of ce variables, since the exergy of the flows can be expressed in terms of them, so that rij ¼

Bi fi ðk; x; ue Þ ¼ rðk; x; ue Þ ¼ Bj fj ðk; x; ue Þ

(8.59)

In the same way, the bifurcation parameters of the FP representation can be expressed as a function of cs variables. Consequently, in any system, from the set of canonical variables ce, the thermoeconomic variables can be expressed as a function of the set of canonical variables cs and vice versa. Through the as and ar matrices, a asr matrix of dimension (mn, n) can be constructed by the superposition of both. Likewise, if usr is the (mn, 1) vector such   us that usr h , in that case 0 asr B ¼ usr

(8.60)

682

Exergy Analysis and Thermoeconomics of Buildings

In the same way, as in the FP representation, the matrix J can be extended to a square matrix Jr of dimension (m, m), expanding it with the matrix asr such that     J 0 Jr h . If the vector Ys h containing the exergy of total product flows asr usr is constructed, then the following matrix equation holds Jr B ¼ Ys

(8.61)

Since Jr is a regular matrix, Torres 1991 [5], its inverse can be obtained and, therefore, B ¼ J1 r Ys

(8.62)

The exergy flow formulas or symbolic expressions are thereby obtained. The Ys vector contains the total product of the installation (us) and the matrix Jr gathers the components unit consumptions (ki) and the recirculation parameters (rij). By that way, through Eq. (8.62) the flow exergies are represented according to the recirculation parameters, the components efficiencies and the exergy of the final products.

8.4.2

Expressions for the fuel and product of components

Similarly to 8.3.3, the equations for the fuel and product of the components will be obtained in the PF formulation. If the extended matrix AFðm;mÞ is built such that " AF h

AF

#

asr

(8.63)

and the Frðm;1Þ expanded vector is defined as " Fr h

F

#

asr

(8.64)

the following equation is obtained AF B ¼ F r

(8.65)

From Eq. (8.61) and using the previous equation Jr A1 F Ar ¼ Ys is achieved. Developing this expression and calling • • •

Bs to the (m, 1) vector that contains the total costs of the system’s product, so that Bsihusi if the flow i is part of the total (final) product and otherwise Bsih0. PshAPBs to the vector that depends only on us and describes the obtained total product from each equipment. hPFi to the (n, n) matrix that depends exclusively on the r recirculation parameters.

Symbolic Thermoeconomics applied to thermal facilities

683

In Torres 1991 [5], the obtainment of the following expression is shown P ¼ Ps þ hPFiF

(8.66)

and in algebraic notation Pi ¼ Bie þ

n X

Bij

(8.67)

j¼1

where Bij represents the product portion of ieth component that is part of the jeth component fuel and Bie refers to the part of the i-th component product that is part of the system total product (hence the subscript e refers to the external environment, being the environment another component that interacts with the installation). So, this expression shows that the destiny of each component’s product can be: • •

The total product of the installation Ps. The fuel of other equipment, in a proportion indicated by the hPFi matrix components.

Indeed, each qij element of the hPFi matrix depends on the recirculation parameters and can be interpreted as the fraction of the jeth component resources coming from n P ieth component, that is, qij ¼ Bij/Fj. Furthermore, the condition qij ¼ 1 is verified. j¼1

Hence, the product of the generic equipment i is Pi ¼ Bie þ

n X

qij Fj

i ¼ 1; 2; .; n

(8.68)

j¼1

or in a more compact way and being the subscript 0 assigned to the outside environment, it can also be written Pi ¼

n X

qij Fj

i ¼ 1; 2; .; n

(8.69)

j¼0

By means of those equations, the components’ product is related to the total product and the other components’ fuel, through the recirculation exergy ratios qij from hPFi. In turn, those coefficients can be related to each component product, so that qij ¼

Bij Bij Pj 1 ¼ ¼ kij kj Fj Pj Fj

(8.70)

and, hence kij ¼ qij kj

(8.71)

684

Exergy Analysis and Thermoeconomics of Buildings

The kij coefficient represents the amount of resources coming from i needed to produce a unit product of jeth component. Those are called exergy marginal consumptions and verify the condition n X

kij ¼ kj

(8.72)

i¼0

A hKPi matrix can be defined by the formed kij elements, such that hKPi ¼ hPFiK D

(8.73)

Returning to Eq. (8.66) the following matrix equation can be obtained P ¼ PS þ hKPiP

(8.74)

and in components form Pi ¼ Bi0 þ

n X

kij Pj

(8.75)

j¼1

If F¼KDP is taken into account, compact equations of components fuel, product and irreversibility can be obtained, depending on the final products, the equipment efficiency and the recirculation parameters. Indeed P ¼ jPiPS

(8.76)

being jPi h ðU D  KPÞ1 the matrix operator. Likewise, F ¼ jFiPS

(8.77)

with. jFi ¼ K D jPi ¼ ðH D  PFÞ1 Equally, for the irreversibility, it results I ¼ jIiPS

(8.78)

being jIi¼(KDUD)jPi the matrix operator. The total consumption of installation resources is FT ¼

n X

k0j Pj

(8.79)

j¼1

and expressed in matrix form depending on the system product, it is FT ¼ t ke jPiPS

(8.80)

wheretke¼(k01,k02,.,k0n) is a vector that contains the marginal exergy consumption of the system-input resources.

Symbolic Thermoeconomics applied to thermal facilities

8.4.3

685

Expression of the installation global efficiency

As shown in 8.3.4, the exergy efficiency of a facility is 4T ¼

PT FT

(8.81)

Such expression will now be developed in the PF formulation. The total product can be expressed as PT ¼ tuPS, so from Eq. (8.66) and considering FeP]I, it can be written as PT ¼ t uðP  hPFiFÞ ¼ t uI þ t uðU D  hPFiÞF

(8.82)

Being tuI ¼ IT and as FTPT¼IT, FT ¼ tu(Ps þ I) is obtained or equivalently, using the above Eq. (8.82) we have PT þ IT ¼ FT ¼ t uðU D  hPFiÞF

(8.83)

If we establish the identity tu(UDhPFi)hthFTFi it results in FT ¼ t hFT FiF

(8.84)

The thFTFi transpose vector of dimension (n, 1) represents the portion of each component fuel that comes out from the total fuel of the installation. Accordingly, the obtained expression of the installation global efficiency is 4T ¼ t

t uP

S

hFT FiF

(8.85)

and, finally, if Eq. (8.77) is considered, the expression results in 4T ¼ t

t uP

S

hFT FijFiPS

(8.86)

This is the total system efficiency equation based on the independent variables of the PF representation.

8.4.4

Expressions for the exergy costs and exergoeconomic costs of fuel and product

It has been previously developed that the marginal exergy consumption of j-th component (kij) represents the resources (fuel) coming from the i-th component required to obtain a unit of product of the j-th component. Therefore, the sum of resources

686

Exergy Analysis and Thermoeconomics of Buildings

from other equipment ( exergy consumption,

n P

kij ) together with those from outside (k0j) is equal to the unit

i¼1 n P

kij ¼ kj . In the particular case that the fuel of the component

i¼0

does not have any external contribution, this is, the outside resources  (electricity  and n P fuels) are not part of the fuel of that component, the equality k0j ¼ 1  kij ¼ 0 is i¼1

valid. Therefore, it can be said that the unit product cost of jeth component is equal to the marginal external exergy consumption (k0j) multiplied by its unit cost (external cost) plus the exergy marginal consumption from the other components (kij) multiplied by their respective unit costs, that is to say  kP;j ¼ k0j kF e; j þ

n X

 kij kP;i

(8.87)

i¼1

where kF e j is the unit cost of the external resources entering in component j. A (n, 1) dimension vector can be defined so that it contains the first term of the previous equation, that is  ke;j ¼ k0j kF e; j

(8.88)

represents the contribution of the system’s external resources to the product unit cost of jeth component. So, Eq. (8.87) can be written in matrix form as follows kP ¼ ke þ t hKPikP

(8.89)

With kF e j ¼ 1 in the absence of external evaluation, the equality ke ¼ hFT Fi is complied. From Eq. (8.89), the matrix notation of the product exergy costs of the components can be expressed based on the system’s external resources unit costs, since ðU D  t hKPiÞkP ¼ ke

(8.90)

and, therefore, it can be written kP ¼ t jPike

(8.91)

where the linear operator t jPi h ðU D  t hKPiÞ1 was introduced. Eq. (8.91) reflects the product unit exergy costs of the equipment relying on the independent variables in the PF representation. Once the expressions for the unit exergy costs of the products are obtained, fuel unit costs are deduced from kP ¼ K D kF .

Symbolic Thermoeconomics applied to thermal facilities

687

Even though, those fuel costs can also be directly obtained in a similar way to the product costs, but with the hPFi matrix instead. Indeed, part of the fuel of j-th compoP nent comes from every product of the i-th component multiplied by the fraction qij i   P and the remaining q0j ¼ 1  qij comes from the external fuel of the plant. i¼1

Therefore, the unit fuel cost of jeth component will be the sum of the system’s external resources constituting such fuel multiplied by its unit costs plus the fraction of fuel coming from the internal components’ products multiplied by their unit costs, this is  kF;j ¼ q0j kF e ;j þ

n X

 qij kP;i

(8.92)

i¼1

Multiplying both sides of the above equation by KD, Eq. (8.92) can be written in matrix form as K D kF ¼ ke þ K D t hPFikP

(8.93)

and taking into account that kF ¼ K D kP , it results in kF ¼ t jFike

(8.94)

Where the matrix operatortjFiist jFi h ðK D  t hPFiÞ1 . Similarly, expressions for the exergoeconomic costs will be obtained next in such a way that the fuel and the product unit exergoeconomic costs will depend on the external resource costs and capital costs of the components. They are similar to Eq. (8.89), but the capital cost rates of components are now considered. Hence, it can be written as cP ¼ ce þ t hKPicP þ H D zP

(8.95)

where zP ¼ P1 D Z refers to the capital cost rate of components per unit of product and ce is connected to the monetary costs vector of external resources so that for the jeth component the expression for c0,j becomes c0;j ¼ 1 

n X

! kij cFe;i ¼ k0j cFe;j

(8.96)

i¼1

where cFe,j is the unit economic cost of external resources of the j-th component. According to Eq. (8.95) ðUD  t hKPiÞcP ¼ ce þ H D zP

(8.97)

688

Exergy Analysis and Thermoeconomics of Buildings

And isolating the product unit cost vector, it is finally obtained that cP ¼ t jPiðce þ H D zP Þ

(8.98)

If the unit economic costs of components’ fuel are regarded, by Eq. (7.133) it is obtained that cF ¼ H D cP  zF ¼ H D t jPiðce þ H D zP Þ  zF

(8.99)

t t where zF ¼ F1 D Z. When jFi ¼ HD jPi, it results

cF ¼ t jFiðce þ H D zP Þ  zF

(8.100)

Ultimately, the cost of the system’s final product will be given by the expression CPT ¼ tcPPS. From this expression and using the preceding equations, it is shown in Torres 1991 [5] that, as expected, the total product cost is CPT ¼ t ce F þ t uZ

(8.101)

and, therefore, the cost of the installation product is the sum of the total fuel cost and the capital cost of the components. Torres 1987 [12] developed a ST model with interesting applications for thermal system simulations, Torres et al. 1989 [13]. The first ST work applied in buildings appears in Picallo et al. 2016 [14].

8.4.5

Relationship between FP and PF representations

Until here, two types of thermal system representations were developed, each of them being characterized by a set of m canonic variables. On the one hand, the FP representation informs about the products’ obtainment and the costs of the used resources, so that the flow of information is going in the same direction as that of the productive process. On the other hand, the PF representation permits formulas to be obtained that associate the exergy of flows, the total fuel, the component’s fuel and product unit costs, etc. with the system’s final products. Therefore, the flow of information in the PF representation goes in the opposite direction, so that, if the product of the system is known, it is possible to determine the required resources to obtain the internal products and their costs. Both representations are complementary and provide a complete picture of the production process and cost formation. Torres’s doctoral thesis [5] shows that they are closely linked and we can move from one representation to another by using the hFPi and hPFi matrixes. In effect, the variables are related by yijPj ¼ qjiFi expression and in matrix form is hPFi ¼ PD $t hPFi$F1 D

(8.102)

Symbolic Thermoeconomics applied to thermal facilities

689

By means of the exergy marginal consumptions, the above relation can also be written as yijPj ¼ kjiPi. In matrix form, such a relationship is t

hFPi ¼ PD hKPiP1 D

(8.103)

The operators in the FP representation can be passed to the PF representation and vice versa. Thus, the relationship between the hP j h ðU D  hFPiÞ1 operator at the FP representation and the operator jPi h ðUD  hKPiÞ1 at the PF representation is hP j ¼ PD t jPiP1 D

(8.104)

Using Eq. (8.104), a result that will be used in the next chapter is obtained. We refer now to the previously deduced Eq. (8.45) as it allows an explanation of the cost formation process of the componentsproducts. By unit of product, that equation becomes  kP ¼ u þ P1 D hP jI and being substituted into Eq. (8.104), it is kP ¼ u þ t jPiP1 D I

(8.105)

Taking into account that the irreversibility vector is I ¼ PD ðK D  U D Þu

(8.106)

if this expression is replaced with Eq.(8.105) and according to the definition of the irreversibility operator jIi, seen in 8.4.2, it results in kP ¼ u þ t jIiu

(8.107)

and in scalar form  kP;j ¼1 þ

n X

fij

(8.108)

i¼1

This result is an alternative way to evaluate the unit exergy cost of the product as a sum of the contributions of components’ irreversibilities. The term fij represents the irreversibility occurring in ieth component when obtaining a unit of product in j-th component.

8.4.6

Examples

Example E.8.2. We refer to the same installation considered in Example E.8.1, that is to say, a DHW production facility with a condensing boiler. The system consists of a condensing boiler, a hydraulic compensator, a three-way valve acting according to the demand, a heat exchanger and an accumulation tank. In addition, there are three

690

Exergy Analysis and Thermoeconomics of Buildings

circulation pumps, one in each of the circuits, see the diagram of Figure E.8.1. Using the PF formulation and without considering residues, the factors considered are: Functional analysis of the flows. Construction of the Jr extended matrix and the Ys vector. Symbolic expression of each flow exergy. Construction of the hPFi matrix. Symbolic expressions of components’ fuel. Symbolic expressions of components’ product. Symbolic expressions of components’ irreversibilities. Symbolic expression of the total system’s efficiency. Symbolic expressions of unit exergy costs of components’ fuel and unit exergy cost of components’ product. ( j) Symbolic expressions of unit exergoeconomic costs of components’ fuel and unit exergoeconomic costs of components’ product. (k) Expression of the facility’s total cost.

(a) (b) (c) (d) (e) (f ) (g) (h) (i)

Solution (a) The facility’s functional analysis is done in Example E.8.1 and shown in Table E.8.1.

For the construction of the Ys vector and the Jr extended matrix, Section 8.3.1 formulas are taken into account, such as " # J Jr h asr " Ys h

0

#

usr

The J matrix, defined according to the following equation J ¼ AFKDAP, is the same as that in Table E.8.2. The ar recirculation matrix relates the exergies of the entering flows to the equipment. In Table E.8.11, the component recirculation parameters are shown for those components having more than one inflow (there are as many parameters as inputs to the equipment minus 1), and in Table E.8.12, the recirculation matrix with dimension (6,13) is presented. Table E.8.11 Recirculation parameters. n

Recirculations

①

r1;2

r1 ¼

②

r3;4

r2 ¼

③

r6;7

r3 ¼

④

r8;9

r4 ¼

⑤

r10;11

r5 ¼

⑥

r8:9;12

r6 ¼

B_ 2 B_ 1 B_ 4 B_ 3 B_ 7 B_ 6 B_ 9 B_ 8 B_ 10 B_ 11 B_ 8 B_ 9 DB_ 12

ar B_ 2 B_ 1 $r1 ¼ 0 B_ 4 B_ 3 $r2 ¼ 0 B_ 7 B_ 6 $r3 ¼ 0 B_ 9 B_ 8 $r4 ¼ 0 B_ 10 B_ 11 $r5 ¼ 0   _ 12 $r6 ¼ 0 B_ 8  B_ 9 DB

Symbolic Thermoeconomics applied to thermal facilities

691

Table E.8.12 ar recirculations matrix. ar ¼

_

BB_ 2

1

0

0

0

0

0

0

0

0

0

0

0

0

0

_ BB_ 4 3

1

0

0

0

0

0

0

0

0

0

0

0

0

_ BB_ 7 6

1

0

0

0

0

0

0

0

0

_ BB_ 9 8

1

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

1

0

_ BB_ 10 11

0 ðB_8



0

0

B_ 9 Þ DB_ 12

0

The as(1,13) matrix, which contains the coefficients of the outgoing flows, and the Ys transpose vector, which contains the exergy of the total product flows, are reflected in Table E.8.13.

t

Table E.8.13 as output matrix and transpose of Ys vector. as ¼ t

0

Ys ¼

0

0

0

0

0

0 0

0

0

0

0

0

0

1

0

0

0

0

1

0

0

0

0

0

0

(b) If the exergy of the output flows (B_ s ), the exergy unit consumptions (ki) and the recirculations that define the system structure (rr) are known, the symbolic expressions of the flows are obtained. For that, Eq. (8.62) reproduced below should be solved " B_ ¼

J asr

#1

2

3 0ð6; 1Þ 6 7 6 uS ð1; 1Þ 7 4 5 0ð6; 1Þ

(c) The symbolic expressions of the exergy of each flow are presented in Table E.8.14.

Table E.8.14 Symbolic expressions of the flows exergy. Flows symbolic expressions fk; r; Bs g _

1.

B ð1r2 Þ B_ 1 ¼ r6 $k2 $k3 $ð1r $ k5 $k6 $ s11 1 Þ ð1k3 $k4 $r2 Þ ð1þr6 Þ

2.

B ð1r2 Þ $ k5 $k6 $ s11 B_ 2 ¼ r1 $r6 $k2 $k3 $ð1r 1 Þ ð1k3 $k4 $r2 Þ ð1þr6 Þ

3.

Bs11 6 B_ 3 ¼ r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

4.

Bs11 6 B_ 4 ¼ r2 $r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

5.

Bs11 $r2 ð1þr3 Þ$k5 $k6 $ð1þr3 Þ$ð1þr B_ 5 ¼ r5 $½k3 $k4ð1k 3 $k4 $r2 Þ 6Þ

_

_

_

_

Continued

692

Exergy Analysis and Thermoeconomics of Buildings

Table E.8.14 Symbolic expressions of the flows exergy.dcont’d Flows symbolic expressions fk; r; Bs g _

6.

Bs11 6 B_ 6 ¼ r2 $r6 $k3 $k4 ð1kk53 $k $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ

7.

Bs11 6 B_ 7 ¼ r3 $r2 $r6 $k3 $k4 ð1kk53 $k $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ

8.

Bs11 B_ 8 ¼ r6 $k6 $ð1r4 Þ$ð1þr 6Þ

9.

Bs11 B_ 9 ¼ r4 $k6 $ð1r4 Þ$ð1þr 6Þ

10.

Bs11 B_ 10 ¼ r5 $1r 5

11.

Bs11 B_ 11 ¼ 1r 5

12.

s11 DB_ 12 ¼ k6 $1þr 6

13.

B 2 $k3 $ð1r2 Þ $ s11 B_ 13 ¼ r6 $k1 $k5 $k6 $kð1k 3 $k4 $r2 Þ ð1þr6 Þ

_

_ _

_

_

B_

_

(d) The matrix hPFi with dimension (6.6) depends exclusively on the recirculation parameters r and is presented in Table E.8.15. Table E.8.15 hPFi matrix. t

hFT Fi [

hPFi ¼

1

0

0

0

0

1 1Dr6

0

1

0

0

0

0

0

0

1  r2

0

0

0

0

0

0

1

1

0

0

0

r2

0

0

0

0

0

0

0

0

r6 ð1þr6 Þ

0

0

0

0

0

0

It can be verified that the sum of each column

n P j¼1

ðPFij þFT Fj Þ, is equal to the unit.

When analysing the hPFi matrix, it is seen that the fuel of the hydraulic compensator comes entirely from the product of the boiler. However, the fuel of the diverter, equipment 3, consists of the products of two different components: the fraction F3$(1r2) comes from the product of the hydraulic compensator (P2) and the remaining fraction, F3$r2, from the product (P4) of the three-way valve V3V. It may seem strange since the output of the V3V component is not physically directed to the separator; however, at

Symbolic Thermoeconomics applied to thermal facilities

693

the production level, it works as a recirculation of equipment input 3. The product of the diverter supplies the fuel (F4) to V3V and the heat exchanger (F5). The fraction r6 F6 $1þr of the fuel in the tank is the product P5 of the heat exchanger, and the remain6 1 comes from the outside, which corresponds to the input ing fraction hFT Fi6 ¼ F6 $1þr 6 cold-water network. On the other hand, in the boiler, all the fuel is supplied from outside hFTFi1 ¼ 1, which justifies why the first column of matrix hPFi is zero. Therefore, the PF representation offers the information of the required resources for obtaining the final product of the components, while the FP representation enables the data of the components’ product obtained from the incoming resources. As seen, both representations are closely related, and it can be passed from one to the other through the hFPi and hPFi matrices. According to Eq. (8.102) hPFi ¼ PD $t hPFi$F1 D where PD and FD are the diagonal matrices (6.6) that contain the values of the product and fuel of the component. This equation allows relating the recirculation and bifurcation parameters in both representations. With qij the elements of the hPFi matrix and yji the elements of the hFPi matrix, both matrices are related according to the previous equation, that is qij ¼

Pi $yji Fj

For this specific example, the relations are y21 ¼

F2 $q12 P1

y32 ¼

F3 $q23 P2

y43 ¼

F4 $q34 P3

y53 ¼

F5 $q35 P3

y34 ¼

F3 $q43 P4

y65 ¼

F6 $q56 P5

(e) The symbolic expressions of the components’ fuel are obtained by means of equation F ¼ AF$B and the results are shown in Table E.8.16.

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Exergy Analysis and Thermoeconomics of Buildings

Table E.8.16 Symbolic expressions of the components’ fuel. Fuels symbolic expressions ① ② ③ ④ ⑤ ⑥

B_

2 $k3 $ð1r2 Þ $ s11 F1 ¼ k1 $k7 $B_ s15 þ r6 $k5 $k6 $kð1k 3 $k4 $r2 Þ ð1þr6 Þ

B_

s11 6 F2 ¼ r6 $k2 $k3 $ð1  r2 Þ$ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

B_

s11 6 F3 ¼ r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

B_

s11 6 F4 ¼ r2 $r6 $k3 $k4 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

  B_ s11 6 F5 ¼ ðr5 $½k3 $k4 $r2  ð1 þ r3 Þ  r3 $r2 $r6 $k3 $k4 Þ$ ð1kk53 $k $ $k4 $r2 Þ ð1þr3 Þ$ð1þr6 Þ B_

B_

s11 s11 þ k6 $1þr F6 ¼ ðr6  r4 Þ$k6 $ð1r4 Þ$ð1þr 6 6Þ

(f) The symbolic expressions of the components’ product are obtained by means of equation P ¼ AP$B and the results are shown in Table E.8.17. Table E.8.17 Symbolic expressions of the components’ product. Products symbolic expressions ① ② ③ ④ ⑤ ⑥

B_

s11 6 P1 ¼ r6 $k2 $k3 $ð1  r2 Þ$ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

B_

s11 6 P2 ¼ r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ$ð1  r2 Þ

B_

s11 6 P3 ¼ ðr5 $½k3 $k4 $r2  ð1 þ r3 Þ þ r2 $r6 $k3 $k4 Þ$ð1kk53 $k $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ

B_

s11 6 P4 ¼ r2 $r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

B_

s11 P5 ¼ ðr6  r4 Þ$k6 $ð1r4 Þ$ð1þr 6Þ

P6 ¼ B_ s11

(g) The symbolic expressions for the components’ irreversibility are obtained by means of equation I ¼ FeP and the results are shown in Table E.8.18. Table E.8.18 Symbolic expressions of the components’ irreversibility. Irreversibilities symbolic expressions ① ②

_

B 2 $k3 $ð1r2 Þ $ s11 $ðk1 1Þ I1 ¼ k1 $k7 $B_ s15 þ r6 $k1 $k5 $k6 $kð1k 3 $k4 $r2 Þ ð1þr6 Þ B_

s11 6 I2 ¼ r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ$ðk2 1Þ

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Table E.8.18 Symbolic expressions of the components’ irreversibility.dcont’d Irreversibilities symbolic expressions B_

③

s11 6 I3 ¼ ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ$ðr6 $k3 $ð1 r2 $k4 Þ r5 $½k3 $k4 $r2  ð1 þ r3 ÞÞ

B_

④

s11 6 I4 ¼ r2 $r6 $k3 $ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ$ðk4 1Þ

⑤



I5 ¼ ðr5 $½k3 $k4 $r2  ð1 þ r3 Þ  r3 $r2 $r6 $k3 $k4 Þ$

B_ s11 k5 $k6 ð1k3 $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ



B_ s11 ðr6  r4 Þ$k6 $ ð1  r4 Þ$ð1 þ r6 Þ _

_

Bs11 Bs11 þ k6 $1þr  B_ s11 I6 ¼ ðr6  r4 Þ$k6 $ð1r4 Þ$ð1þr 6 6Þ

⑥

(h) The facility’s whole efficiency is obtained from Eq. (8.85), the example being

4T ¼

  B_ 11  B_ 10 PT ¼ ¼ FT DB_ 12 þ B_ 13



k6 $

B_ s11

 B_ s11 k2 $k3 $ð1  r2 Þ $ 1 þ r6 $k1 $k5 $ ð1  k3 $kd4 $r2 Þ 1 þ r6

(i) The symbolic expressions of the unit exergy costs of the components’ fuel are obtained from Eq. (8.94) and those of the components’ product through Eq. (8.91). The results are shown in Tables E.8.19 and E.8.20 respectively.

Table E.8.19 Unit exergy costs of components’ fuel. Fuels’ unit exergy costs ①

kF 1 ¼ 1

②

kF 2 ¼ k1

③

ð1r2 Þ kF 3 ¼ ð1k $k2 $k1 3 $k4 $r2 Þ

④

k3 $ð1r2 Þ kF 4 ¼ ð1k $k2 $k1 3 $k4 $r2 Þ

⑤

k3 $ð1r2 Þ kF 5 ¼ ð1k $k2 $k1 3 $k4 $r2 Þ

⑥

k6 $r6 k6 $r6 k5 $k3 $ð1r2 Þ  ð1þr $ $k2 $k1 kF 6 ¼ 1  ð1þr 6Þ 6 Þ ð1k3 $k4 $r2 Þ

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Exergy Analysis and Thermoeconomics of Buildings

Table E.8.20 Unit exergy costs of components’ product. Products unit exergy costs ①

kp1 ¼ k1

②

kp2 ¼ k2 $k1

③

ð1r2 Þ$k3 kp3 ¼ ð1k $k2 $k1 3 $k4 $r2 Þ

④

ð1r2 Þ$k3 kp4 ¼ k4 $ð1k $k2 $k1 3 $k4 $r2 Þ

⑤

ð1r2 Þ$k3 kp5 ¼ k5 $ð1k $k2 $k1 3 $k4 $r2 Þ

⑥

ð1r2 Þ$k3 k6 $r6 k6 kp6 ¼ ð1þr $k5 $ð1k $k2 $k1 þ ð1þr 6Þ 3 $k4 $r2 Þ 6Þ

(j) The exergoeconomic unit costs of the components’ fuel are obtained by Eq. (8.100) and shown in Table E.8.21. Table E.8.21 Unit exergoeconomic costs of the components’ fuel. Fuels unit exergoeconomic costs ①

cF1 ¼ cNG

②

cF2 ¼ cP1

③

cF3 ¼ ð1  r2 Þ$cP2 þ r2 $cP4

④

cF4 ¼ cP3

⑤

cF5 ¼ cF3

⑥

1 $c þ r6 $c cF6 ¼ ð1þr w ð1þr6 Þ P5 6Þ

(k) The exergoeconomic costs of the components’ product, as seen, can be broken down into two components: those due to external resources, ceP ¼ t jPice and the capital cost rate of the components cZP ¼ t jPiHD zP . The corresponding symbolic expressions are obtained by applying Eq. (8.98). The results are shown in Tables E.8.22 and E.8.23 respectively. Table E.8.22 Product unit exergoeconomic costs associated to the external resources. Product unit exergoeconomic costs associated to external resources ①

cep1 ¼ k1 $cNG

②

cep2 ¼ k2 $k1 $cNG

③

ð1r2 Þ$k3 cep3 ¼ ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

④

ð1r2 Þ$k3 cep4 ¼ k4 $ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

⑤

ð1r2 Þ$k3 cep5 ¼ k5 $ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

⑥

ð1r2 Þ$k3 k6 $r6 k6 cep6 ¼ ð1þr $k5 $ð1k $k2 $k1 $cNG þ ð1þr $cw 6Þ 3 $k4 $r2 Þ 6Þ

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Table E.8.23 Unit exergoeconomic costs of the products associated to the capital cost rate. Product unit exergoeconomic costs associated with investment ①

czp1 ¼ z1

②

czp2 ¼ k2 $z1 þ z2

③

2 Þ$ðk2 $z1 þz2 þr2 $z4 Þ czp3 ¼ z3 þk3 $ð1r ð1k3 $k4 $r2 Þ

④

2 Þ$ðk2 $k3 $z1 þk3 $z2 þz3 Þ czp4 ¼ z4 þk4 $ð1rð1k 3 $k4 $r2 Þ

⑤

3 $z1 þk3 $z2 þz3 þr2 $k3 $z4 Þ czp5 ¼ z5 þ k5 $ð1r2 Þ$ðk2 $k ð1k3 $k4 $r2 Þ

⑥

k6 $r6 z5 þk5 $ð1r2 Þ$ðk2 $k3 $z1 þk3 $z2 þz3 þr2 $k3 $z4 Þ czp6 ¼ z6 þ ð1þr $ ð1k3 $k4 $r2 Þ 6Þ

(l) Finally, the cost of the final product of the installation, which in this case is DHW, is given by the CPT ¼ tcPPS expression, or applying Eq. (8.101), resulting in CPDHW ¼ P6 $cF6 ¼ B_ s11 $

8.5

1 r6 $cw þ $cP5 ð1 þ r6 Þ ð1 þ r6 Þ

FP and PF representations with residues

As shown in Chapter 7, in thermal installations, in addition to the product, frequently unwanted flows appear, which have exergy content but are not used in the facility or any other part. Therefore, that exergy is destroyed outside the facility, due to external irreversibilities. Those types of flows are known as losses and are represented with the L symbol; they are due to the equipment’s technical limitations. This is the case of the boiler’s combustion gases in a heating system or the heat dissipated in the condensers of air conditioning facilities. It has also been shown that ECT proposes assigning a zero cost to those flows so that the cost of resources and the capital cost of the equipment is assigned to the product. It has also been commented that this zero cost allocation should not necessarily be made on the equipment from which the loss flow comes out, but on the equipment that has generated it. Thus, in a cogeneration facility with an alternative motor and a recovery boiler for hot water production, the gases coming out from the boiler have not been generated in there but in the alternative engine. Therefore, instead of accounting them as a boiler loss, the most reasonable criterion is to consider them to be part of the product of the alternative engine (with a minus sign). Then, in addition to the electricity produced, the product of the alternative engine is the enthalpy of the gases at the engine output minus its enthalpy at the exit of the boiler. Moreover, in thermal installations, there are often dissipative components, that is, equipment in which a product’s proper definition cannot be done, but they are required to serve a series of productive equipment. This is the case of the condenser in a refrigerating machine, or the throttle valve in a refrigeration unit, or the condenser of a power plant, etc.

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Exergy Analysis and Thermoeconomics of Buildings

Besides, in a facility, unwanted flows can be produced in such a state that they cannot be sent to the environment, since there are legal restrictions, because of the contaminant character associated with their chemical composition, due to their temperature, etc. Those types of flows are known as residues. That is the case of biomass boiler fumes, which require some cyclones to separate the dragging solid particles or the case of the used oils in various equipment, etc. It is, therefore, necessary to have additional auxiliary equipment, which is responsible for treating those flows before sending them into the environment. The auxiliary equipment needs the contribution of additional resources to turn the residue flows into loss flows. Let us use ST to obtain the equations that define the product costs, taking into account the costs of residues. The ST extension is called the FP(R) model, since it is an extension of the FP model developed in 8.3, but residues are now included. The other extension is the PF(R) model, which is the extension of the PF representation with residues included. First, an analysis of the residue formation process will be carried out, and a summary of the negentropy method that is referred to in Chapter 7 will be given as a method used to assign costs to dissipative equipment.

8.5.1

The process of residues cost formation

The generation of residues implies an additional consumption of resources and, therefore, we are interested in how much that consumption is. In short, how much the exergy and monetary costs of the residues are. That exergy cost of residues (its formation cost plus the cost of the resources used in its elimination) must be distributed among the components’ products that have contributed to its generation, in accordance with the production structure of the installation. Therefore, those costs impact the final product costs. In essence, once the residues are identified, their formation processes should be analysed in order to locate them from their origins. In such a way, the residue costs can be correctly calculated and included in the costs of the final products. In Chapter 7 it was shown that, in accordance with the Proposition 5 of ECT, if a component generates residues, the exergy cost of the product is equal to the fuel cost plus the cost associated with the residue, so that: P* ¼ F*þR*. Hence, two chains intervene in the cost formation process of the product: a direct chain of product formation and another chain of residue formation.

Figure 8.2 Schema with two productive and one-residue treatment components.

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699

Those ideas will be developed here a bit more, using the monetary costs. For that, the schema of Fig. 8.2 is used. It is similar to Fig. 7.10 of the previous chapter, where a productive structure of an i-th productive component that is also generating residues is drawn; in addition, an r-th equipment is used to eliminate the generated residue of the productive component turning it into a loss, Torres et al.2008 [15]. The exergoeconomic cost balance of the i-th generic equipment leads to the following equation Cij þ Cir ¼ CFi þ Zi

(8.109)

where Cij is the cost of the flow, which being part of the i-th component’s product is fuel of j-th equipment. Cir is the cost of the residue generated in the i-th component. Furthermore, the cost balance at the r-th component is Cpr ¼ Cir þ Cer

(8.110)

where Cer refers to the cost of eliminating the residue, which includes the cost of the resources used in r plus the capital cost of the necessary equipment. Because of the required treatment, the residue is transformed into a loss flow and then Cpr ¼ 0, so Cir ¼ Cer. Applying the balance equation to the two-component system inside the dashed line, we get Cij ¼ CFi þ Zi þ Cer

(8.111)

As the product of i-th component is the flow going to j, it results in Cpi ¼ Cij ¼ CFi þ Zi þ Cer

(8.112)

This equation expresses that the cost of the product of a component is the cost of the resources used (fuel and capital) plus the cost of the generated residue. If instead of a residue a loss flow was generated, then Cer ¼ 0. In a general case as the one represented in Figure 8.2, the residue dissipated in the r-th treatment unit has its origin in several components, so that the cost of the residue Cer is broken down into several costs, one for each component that contributes to its formation, it is Cer ¼

X Cir

(8.113)

i

where Cir is the cost of the residue treated in the r-th treatment equipment, which has been generated in the ieth productive component.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 8.3 Schema of a productive component linked to two residue treatment components.

On the other hand, the i-th component, in turn, can generate more than one residue flow, see Fig. 8.3, which are treated in several treatment components r1 and r2 so that the total cost of the residues that must be attributed to the productive i-th component is R X

CiR ¼

Cir

(8.114)

r¼1

where the sum is extended to the equipment in which the residues generated in i-th component are treated. Returning to Eq. (8.112), the product cost of the i-th component is CPi ¼ CFi þ Zi þ CiR

(8.115)

Thus, the cost of the residues is allocated to the product of the equipment which generated it. At this point, a criterion needs to be established to determine the Cir values, that is, to set up some distribution coefficients, so that Cir h jir Cer resulting

P

(8.116)

jir ¼ 1. In this respect, different distribution criteria have been

i

established: • •

One criterion is to divide the residue costs (and the losses of the dissipative component as well) proportionally to the entropy generated in each equipment. That criterion is used by the negentropy method that will be developed in the next paragraph 8.5.2. Torres et al. 2008 [15] initially proposed a very simple criterion, based on the exergy flows of the dissipative component such as

Symbolic Thermoeconomics applied to thermal facilities

jir ¼

Bir Fr

701

(8.117)

where Bir is the flow exergy coming from the i-th productive component, which is treated in the r-th equipment and Fr is the fuel of that equipment. Hence, they are directly obtained from the productive diagram of the installation. • •

Seyyedi et al. 2010 [16] proposed a similar method. Recently, Agudelo et al. 2012 [17] proposed a more sophisticated method which takes into account the extent to which every productive component contributes to the cost of each residue. The method considers whether a component that generates a residue also supplies resources to other components. It means that the responsibility for the residue also falls on those later components, since they indirectly determine the amount of residue generated by demanding resources for their operation.

8.5.2

The negentropy method

As stated, Thermoeconomics proposed different methods for the allocation of the dissipative component costs and for the cost of cleaning the residues. Unfortunately, that is a problem that has not yet been definitively resolved. One of the first methods proposed is based on the concept of negentropy, which has been briefly referred to in Chapter 7. Likewise, it has been used mainly in systems based on thermodynamic cycles, Frangopoulos 1987 [18], Lozano et al. 1993 [19], Lozano and Valero 1993 [20] and von Spakovsky 1994 [21]. The negentropy method will be briefly developed by applying it to the Rankine cycle of Fig. 8.4. The installation consists of 4 components (boiler, steam turbine, condenser and feeding pump) and the number of flows considered is equal to 9.

Figure 8.4 Components and flows of the Rankine cycle.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 8.5 T-s diagram of Rankine Cycle.

In principle, the condenser product is the dissipated heat exergy, so that P3]B9¼BQ0. However, that flow is a loss, since the exergy of that flow is finally destroyed in the environment. Therefore, it must be assigned to the other productive components of the installation. If the condenser function is analysed, it is seen that, even if the entropy flow in the rest of the components increases, it decreases in the condenser. So, to observe that entropy reduction compensates the rise in the other components, see the Rankine cycle in the T-s diagram of Fig. 8.5. Because of that, the negentropy method proposes that the fuel of each productive component (in this case, the remaining three components) should increase in a fraction according to the product of the condenser. That growth should be proportional to each component’s entropy increase Frangopoulos 2004 [22]. For that, some coefficients are defined, which are the ratio between the considered component entropy increase and the condenser decrease in entropy. So, for example, for the boiler, it is r25 ¼

s5  s2 s3  s4

(8.118)

The same is done for the other two productive components. Consequently, the heat exergy dissipated in the condenser can be written as BQ0 ¼ ð925 þ 932 þ 954 ÞB9

(8.119)

Accordingly, the negentropy method proposes that the fuel of each productive component increases by a fraction of the condenser product; that should be proportional to the entropy increase of each component. Thus, referring in the first place to

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703

the boiler, since the exergy cost of the fuel is no longer B1 but B1 þ r25 B9 , the exergy cost balance is B2  B5 ¼ B1 þ r25 B9

(8.120)

where, in the absence of external valuation, B1 ¼ B1 is verified. Therefore, the fuel in the boiler has increased by a fraction related to the dissipated heat in the condenser, proportional to the boiler’s entropy increase. In a similar way, the cost balance in the turbo-alternator is B6 þ B7 þ B8 ¼ B2  B3 þ r32 B9

(8.121)

and according to the Fuel-Product Propositions of the ECT, the following equations are also fulfilled k2 ¼ k3

(8.122)

k6 ¼ k7 ¼ k8

(8.123)

If the corresponding balance of costs is applied in the feeding pump, we have B5  B4 ¼ B7 þ r54 B9

(8.124)

and, finally, the cost balance equation in the condenser is B9 ¼ B6 þ B3  B4

(8.125)

where also k4 ¼ k3 is verified. The system of equations is in this way closed, since there are 9 equations with 9 unknowns. Thus, the exergy cost of each flow can be obtained. It can, therefore, be considered that the objective of a dissipative component is to produce negentropy in order to compensate for the entropy increase occurring in the other system components. The method has been applied in the case of a dissipative component with a residual heat which is a loss flow. If instead of loss, the component would generate a residue, the costs of the equipment should be distributed among the productive components, proportionally to the entropy generated in each one. However, the method of negentropy is limited for open systems, Santos et al. 2008 [23]. In addition, the residues are related, not with their entropy content, but with the damage that they can cause or with the inability to turn them into something useful. Besides, when negentropy is used as a fictitious flow to assign costs, inconsistencies may appear in the calculation of the costs, since unit exergy costs may appear with values less than unity. That can happen because the exergy loss is considered as a resource and negentropy as a product, Santos et al. 2009 [24]. In order to overcome those difficulties, Santos developed what is called the H and S method, Santos 2009 [25].

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Exergy Analysis and Thermoeconomics of Buildings

The previous FP and PF formulations do not include residues, so they are going to be extended next to contemplate the appearance of residue flows. First, the expansion of the FP formulation FP(R) covering residue flows will be presented, and the symbolic expressions for fuel and product, as well as for exergy and thermoeconomic costs will be obtained. Afterwards, the extended PF formulation PF(R) will be developed and the expressions for exergy and exergoeconomic costs of the components’ fuel and product will be obtained.

8.5.3

FP(R) formulation

For developing this model, the exergoeconomic costs are going to be used and the equations to obtain the symbolic expressions of components’ fuel, product and residue costs will be obtained. As an extension of Eq. (8.22) the following expression permits the resources used in each component to be obtained based on the external resources (Fe), on the hFPi matrix (n, n) whose coefficients are the cost distribution ratios of the productive component yij and on hRPi a new (n, n) dimension matrix whose coefficients rrj are the cost distribution ratios for the dissipative or residue treatment components F ¼ Fe þ hFPiP þ hRPiP

(8.126)

From Eq. (8.126) and taking into account the relation F¼KDP we have ðK D  hFPi  hRPiÞP ¼ Fe

(8.127)



e h ðK D  hFPi  hRPiÞ1 the above equation If we define the matrix operator P can be written as

e Fe P¼ P

(8.128)

From the previous expression, it can immediately be deduced that

e Fe F¼ F

(8.129)





e h KD P e and, hence, where F

I ¼ eI Fe

(8.130)





e . We can check the similarity with Eq. (8.26), (8.27) results in eI h ðK D  UD Þ P and (8.28) but now we incorporate the effect of residues.

8.5.3.1

Exergy costs and exergoeconomic costs

Eq. (8.46), or its equivalent Eq. (8.47), enable the components’ product in this formulation to be obtained. If Eq.(8.114) is taken into account, the fact that a component can

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705

generate more than one residue is considered. Besides, Eq. (8.116) contemplated the residues cost distribution coefficients. Hence, returning to Eq. (8.46), we get ðUD  hFPi  hRPiÞCP ¼ Ce þ Z

(8.131)

This linear system of equations allows the cost of each component’s product to be determined simultaneously. For the i-th component the above equation becomes X X CPi  yij CPj  rrj CPj ¼ Cei þ Zi (8.132) j

r



e matrix Isolating the costs of the components’ product and calling and using the P operator, Eq. (8.131) can be written as

e ðCe þ ZÞ CP ¼ P (8.133) Once the costs of the products of the different components have been obtained, the costs of the components’ fuel used and that of the residues can be immediately obtained. In fact, in matrix form for the fuel, we get CF ¼ Ce þ hFPiCP

(8.134)

and for the residues CR ¼ hRPiCP

(8.135)

In order to analyse in more detail the cost formation process and to evaluate the effect of residues on the product costs, the previously obtained Eq. (8.131) will again be referred to. Substituting the expression of residue costs Eq. (8.135) into Eq. (8.131), we get ðUD  hFPiÞCP ¼ Ce þ Z þ CR

(8.136)

Thus, the residue costs allocated to each productive component can be interpreted as an additional external resource necessary to compensate the residues’ cost formation. Therefore, the costs of the components’ products can be expressed as follows CP ¼ hP jðCe þ Z þ CR Þ

(8.137)

where hP*j is the matrix operator hP j ¼ ðU D  hFPiÞ1 defined in Section 8.3.5 and depends exclusively on the productive component’s distribution coefficients. In short, the above equation allows decomposing the cost of the products on its three contributions: the costs of external resources, capital costs and the costs of residues, which is CP ¼ CeP þ CzP þ CrP

(8.138)

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Exergy Analysis and Thermoeconomics of Buildings

Those relationships refer to the exergoeconomic costs. From a computational point of view, exergy costs can be considered as a particular type of monetary costs, when the cost of external resources is equal to exergy (Ce,i ¼ Be,i) and the capital costs do not appear (Zi ¼ 0). Accordingly, if Eq. (8.131) is referred to exergy costs we have ðU D  hFPi  hRPiÞBP ¼ Be

(8.139)

and Eq. (8.132) becomes   r BP ¼ hP j Be þ BR ¼ Be P þ BP

(8.140)

Torres and Valero 2015 [26] demonstrated that the products’ exergy costs due to external resources can be written as follows  Be P ¼ P þ hP jI

(8.141)

This expression reflects that this exergy cost of the products is the sum of their exergy plus the irreversibilities accumulated throughout their formation process. It can, therefore, be considered as the exergy cost of the products due to the components’ internal irreversibility of the facility.

8.5.4

PF(R) formulation

The previous PF formulation equations are now extended to include the residues. Thus, Eq. (8.74) can now be written as Pi ¼ Bi0 þ

n X

Bij þ

j¼1

n X

Rij

(8.142)

j¼1

where Rij is that part of the i-th equipment product that crosses the system limits as a residue. Using the already defined kij coefficients and introducing the qij coefficients that represent the marginal consumptions of residue exergy, the previous equation becomes Pi ¼ Bi0 þ

n X ðkij þ qij ÞPj

(8.143)

j¼1

and in matrix notation P ¼ PS þ hKPiP þ hKRiP

(8.144)

where hKRi is a (n,n) matrix whose components are the exergy marginal consumption associated with residues. Analogously to Eq. (8.76), it can be written as

 P ¼ e P Ps

(8.145)

Symbolic Thermoeconomics applied to thermal facilities

707

 where the matrix operator e P has been introduced, such that



e P ¼ ðUD  hKPi  hKRiÞ1

(8.146)

Eq. (8.145) permits the symbolic expression of the component’s product to be obtained according to the canonical variables of this representation. Those variables are the system product, the recirculation parameters, the components unit consumptions and the unit consumptions connected to residues.

 Likewise, the components’ fuel can be expressed according to the F ¼ e F Ps equa 

  P . Similarly, substituting the F and P tion, where the operator e F is e F ¼ K D e





 P . expressions, it is easily deduced that I ¼ eI Ps where eI ¼ ðK D  UD Þ e

8.5.4.1

Exergy costs and exergoeconomic costs

Following the same sequence as in Section 8.4.4, unit exergy costs can be decomposed among contributions associated with external resources ke P and now also with residues kr , so that p r kP ¼ ke P þ kP

(8.147)

where the costs due to external resources are obtained by the matrix equation ke; P ¼ t



 

e t

e;

e Pi $ke and those associated with the residues by kr; P ¼ R $kp , where R is the following matrix operator, see the work of Torres and Valero 2015 [26].



e R ¼ ðUD  jRiÞ1  U D

;

jRi ¼ hKRi$jPi

(8.148)

In short, the total cost of the components’ product can be written compactly as t

kP

  ¼ e P $ ke

(8.149)

t

 where the e P operator contains the resource and residue matrices. Analogously to Eq. (8.92), the unit exergy costs of the components’ fuel are kF ¼ ke þ t hPFi$kP

(8.150)

Finally, we refer to exergoeconomic costs. In such a case, the costs of the components’ product are divided into three parts: the external resources ceP , the part related to capital and maintenance costs czP and the one related to residue generation crP , so that cP ¼ ceP þ czP þ crP

(8.151)

 giving ceP ¼ t jPi$ce , czP ¼ t jPi$zp and crP ¼ e R $ ceP . From the unit exergoeconomic t

708

Exergy Analysis and Thermoeconomics of Buildings

costs of the product, the fuel unit costs can be obtained by means of the following relation cF ¼ ce þ t hPFi$cP

(8.152)

Figure 8.6 Summary of the FP(R) and PF(R) symbolic representations.

8.5.5

Examples

Example E.8.3.

We refer to the same facility as in Example E.8.1 but, in this case, the PF(R) formulation is used. That is to say, it is about a DHW production facility using a condensing boiler. The system consists of a boiler, a hydraulic compensator,

Symbolic Thermoeconomics applied to thermal facilities

709

a three-way valve acting according to the demand, a heat exchanger and an accumulation tank. In addition, there are three circulation pumps, one in each of the circuits, see the diagram of Fig. E.8.1. Using the PF(R) formulation, the questions are: Functional analysis of the installation flows. Construction of the Jr extended matrix and the Ys vector. Symbolic expression of each flow exergy. Construction of the hPFi,hKPi and hKR imatrixes. Symbolic expression of the total system’s efficiency. Symbolic expressions of unit exergy costs of the components’ product, associated to external resources and residues. (g) Symbolic expressions of unit exergy costs of fuel components. (h) Symbolic expressions of unit exergoeconomic costs of the components’ product, associated to external resources, components’ investment and residues. (i) Symbolic expressions of unit exergoeconomic costs of components’ fuel.

(a) (b) (c) (d) (e) (f)

Solution The components considered for the analysis are shown in Fig. E.8. 3, as well as the nomenclature assigned to the flows. In total, 15 flows are considered, with a product of the installation (B_ 11 ) and one dissipative component, which is the chimney, with a loss flow (B_ 15 ).

Figure E.8.3 Components and flows of the facility.

(a) Table E.8.24 shows the results of the functional analysis, as well as the unit exergy consumption and the total product of the plant. Compared to the previous examples, a dissipative component appears, which is the chimney. It has a loss flow (B_ 14 ) associated with the combustion gases exiting through the chimney (B_ 15 is the corresponding exergy loss before being emitted to the atmosphere).

710

Exergy Analysis and Thermoeconomics of Buildings

Table E.8.24 Results of the functional analysis. n

Fuel

PROD.

Resid.

k

Ps

Rs

①

Boiler

B_ 13

B_ 1  B_ 2

B_ 14

ðB_1 B_2 ÞþB_14

0

-

②

Hydraul. Compens.

B_ 1  B_ 2

B_ 3  B_ 4

-

0

-

③

Diverter

B_ 3

B_ 5 þ B_ 6

-

0

-

④

V3V

B_ 6 þ B_ 7

B_ 4

-

0

-

⑤

HX

B_ 8  B_ 9

-

0

-

⑥

Tank

B_ 5  B_ 7   B_ 8  B_ 9

B_ 11  B_ 10

-

B_ 11

-

B_ 15

-

0

B_ 15

B_ 13 B_ 3 B_ 4 B_ 1 B_ 2 B_ 5 þB_ 6 B_ 3 B_ 4 B_ 6 þB_ 7 B_ 8 B_ 9 B_ 5 B_ 7

B_ 11 B_ 10

ðB_8 B_9 ÞþDB_12

þDB_ 12 ⑦

B_ 14

Chimney

B_ 15 B_ 14

The changes due to the incorporation of the chimney have been highlighted. Once this functional analysis is done, the construction of matrices AF and AP is immediate. (b) Table E.8.25 shows the Jr extended matrix (15.15) and the Ys extended vector. Table E.8.25 J extended matrix’. 1 J¼

as ¼

ar ¼

2

k1 k1

5

6

7

8

0

0

0

0

0

0

0

0

0

k3 k3 0

k2 k2

9

10

11

12

13

14

15

0

0

0

0

1

k1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

k6

k6

1

0

0

0

0

0

0

0

1

k7

1

0

0

1

0

0

0

0

k4

0

1

1

0

0

0

0

1

0

1

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

0

0

k5 k5

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

_ BB_ 2 1

1

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

_ BB_ 4 3

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

_ BB_ 7 6

1

0

0

0

0

0

0

0

0

0

0

_ BB_ 9 8

1

0

0

0

0

0

0

0 0 ðB_8 B_9 Þ  DB_ 0

0

0

0

0

0

0

Ys ¼

4

1

0

t

3

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

1

0

_ BB_ 10 11

0

12

0

0

0

0

0

0

1

Symbolic Thermoeconomics applied to thermal facilities

711

Note that the recirculation equations coincide with those of Table E.8.11; this happens because the incorporation of the chimney adds an outgoing flow in the boiler (not an entrance) so that the recirculations are maintained. However, when the seventh component is added, two new flows are added, B_ 14 and B_ 15 , so two additional equations are needed. These additional equations are, on the one hand, the exergy balance RES in component 7 and, on the other hand, a new residual output flow B_ s ¼ B_ 15 , so the as matrix will now have (2,15) dimension. Table E.8.25 shows the J extended matrix which is the result of composing the matrix J with ar and as matrices. (c) By solving Eq. (8.62), the symbolic expressions of the flow exergies are obtained. They are based on the unit exergy consumptions of the equipment, the recirculation parameters and the output flows of the installation. The expressions obtained are reflected in Table E.8.26.

Table E.8.26 Symbolic expressions of flow exergies. Flow exergies symbolic expressions _

1.

Bs11 k5 $k6 2Þ B_ 1 ¼ r6 $k2 $k3 $ð1r ð1r1 Þ$ð1k3 $k4 $r2 Þ$ð1þr6 Þ

2.

Bs11 k5 $k6 2Þ B_ 2 ¼ r1 $r6 $k2 $k3 $ð1r ð1r1 Þ$ð1k3 $k4 $r2 Þ$ð1þr6 Þ

3.

Bs11 6 B_ 3 ¼ r6 $k3 ð1kk53 $k $k4 $r2 Þ$ð1þr6 Þ

4.

B_ 4 ¼ r2 $r6 $k3

5.

Bs11 2 ð1þr3 Þ$kd5 $kd6 $ð1þr3 Þ$ð1þr B_ 5 ¼ r5 $½k3 $k4 $rð1k 3 $k4 $r2 Þ 6Þ

6.

Bs11 6 B_ 6 ¼ r2 $r6 $k3 $k4 ð1kk53 $k $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ

7.

Bs11 6 B_ 7 ¼ r3 $r2 $r6 $k3 $k4 ð1kk53 $k $k4 $r2 Þ$ð1þr3 Þ$ð1þr6 Þ

8.

Bs11 B_ 8 ¼ r6 $k6 $ð1r4 Þ$ð1þr 6Þ

9.

Bs11 B_ 9 ¼ r4 $k6 $ð1r4 Þ$ð1þr 6Þ

10.

Bs11 B_ 10 ¼ r5 $1r 5

11.

Bs11 B_ 11 ¼ 1r 5

12.

s11 DB_ 12 ¼ k6 $1þr 6

13.

B 2 $k3 $ð1r2 Þ $ s11 B_ 13 ¼ k1 $k7 $B_ s15 þ r6 $k1 $k5 $k6 $kð1k 3 $k4 $r2 Þ ð1þr6 Þ

14.

B_ 14 ¼ k7 $B_ s15

15.

B_ 15 ¼ B_ s15

_

_

B_ s11 k5 $k6 ð1k3 $k4 $r2 Þ$ð1þr6 Þ _

_

_

_ _

_

_

B_

_

712

Exergy Analysis and Thermoeconomics of Buildings

(d) In order to obtain the exergy costs of components’ fuel and product, it is necessary to previously build the hPFi, hKPi and hKRi matrices. This last matrix, of elements rr,i, represents the amount of residues coming from the i-th equipment needed to produce a product unit. The matrices obtained are shown in Tables E.8.27, E.8.28 and E.8.29. Table E.8.27 hPFi matrix. t

hFT Fi [

hFPi ¼

1

0

0

0

0

1 1Dr6

0

0

1

0

0

0

0

1

0

0

1  r2

0

0

0

0

0

0

0

1

1

0

0

0

0

r2

0

0

0

0 0

0

0

0

0

0

r6 ð1þr6 Þ

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Table E.8.28 hKPi matrix. ke T [

k1

0

0

0

0

k6 1Dr6

0

hKPi ¼

0

k2

0

0

0

0

k7

0

0

k3 $ð1  r2 Þ

0

0

0

0

0

0

0

k4

k5

0

0

0

0

k3 $r2

0

0

0

0 0

0

0

0

0

0

k6 $r6 ð1þr6 Þ

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Table E.8.29 hKRi matrix. hKRi[

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

B_ 15 ðB_1 B_2 ÞþB_14

0

0

0

0

0

0

Symbolic Thermoeconomics applied to thermal facilities

713

(e) Applying Eq. (8.86) the expression of the facility’s overall exergy efficiency is obtained, which expresses it in terms of the components’ unit consumptions, the recirculation parameters and the system products. The obtained result is presented below

  B_ 11  B_ 10 PT 4T ¼ ¼ FT DB_ 12 þ B_ 13 ¼

k1 $k7 $B_ s15 þ k6 $



B_ s11

B_ s11 k2 $k3 $ð1  r2 Þ $ 1 þ r6 $k1 $k5 $ ð1  k3 $k4 $r2 Þ 1 þ r6



(f) From the previous matrices the unit product exergy costs are obtained. These costs are decomposed into those associated with external resources and those associated with residues (in this case, flow 14), hence, the total product exergy cost is the sum of both. The results are shown in Tables E.8.30 and E.8.31. Table E.8.30 Unit exergy costs of components’ fuel associated to external resources. Fuels’ unit exergy costs ①

kF 1 ¼ 1

②

kF 2 ¼

③

ð1r2 Þ kF 3 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

④

ð1r2 Þ$k3 kF 4 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

⑤

ð1r2 Þ$k3 kF 5 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

⑥

k6 $r6 k6 $r6 ð1r2 Þ$k3 $k5 kF 6 ¼ 1  ð1þr  ð1þr $ $ k2 $k1 6Þ 6 Þ ð1k3 $k4 $r2 Þ ð1r7;1 $kd7 Þ

⑦

kF 7 ¼

k1

ð1r7;1 $kd7 Þ k2 $k1 k2 $k1 k2 $k1

k1

ð1r7;1 $kd7 Þ

Table E.8.31 Unit exergy costs of components’ product associated to residues. P unit exergetic cost associated with residues ①

¼ kpr; 1

②

kpr; ¼ k2 $ 2

③

ð1r2 Þ$k3 kpr; ¼ ð1k $k2 $ 1r7;1 $k $kpe; 3 3 $k4 $r2 Þ ð 7;1 7 Þ 7

④

ð1r2 Þ$k3 kpr; ¼ k4 $ð1k $k2 $ 4 3 $k4 $r2 Þ

ð1r7;1 $k7 Þ

⑤

ð1r2 Þ$k3 kpr; ¼ k5 $ð1k $k2 $ 5 3 $k4 $r2 Þ

ð1r7;1 $k7 Þ

r7;1

ð1r7;1 $k7 Þ r7;1

$kpe; 7

ð1r7;1 $k7 Þ

$kpe; 7 r

r7;1

$kpe; 7

r7;1

$kpe; 7 Continued

714

Exergy Analysis and Thermoeconomics of Buildings

Table E.8.31 Unit exergy costs of components’ product associated to residues.dcont’d P unit exergetic cost associated with residues ⑥

ð1r2 Þ$k3 k6 $r6 kpr; ¼ ð1þr $k5 $ð1k $k2 $ 6 6Þ 3 $k4 $r2 Þ

⑦

kpr; ¼ 7

r7;1

ð1r7;1 $k7 Þ

r7;1

ð1r7;1 $k7 Þ

$kpe; 7

$kpe; 7

The r7,1 term represents the component of row 7 and column 1 of thehKRi matrix that is, r7;1 ¼ 

B_ 15  _ B1  B_ 12 þ B_ 14

(g) By means of Eq. (8.150), the unit exergy costs of components’ fuel are obtained. Table E.8.32 shows the expressions obtained for these costs. Table E.8.32 Unit exergy costs of components’ fuel. Fuels unit exergy costs ①

kF 1 ¼ 1

②

kF 2 ¼

③

ð1r2 Þ kF 3 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

④

ð1r2 Þ$k3 kF 4 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

⑤

ð1r2 Þ$k3 kF 5 ¼ ð1k $ 3 $k4 $r2 Þ

ð1r7;1 $kd7 Þ

⑥

k6 $r6 k6 $r6 ð1r2 Þ$k3 $k5 kF 6 ¼ 1  ð1þr  ð1þr $ $ 6Þ 6 Þ ð1k3 $k4 $r2 Þ

⑦

kF 7 ¼

k1

ð1r7;1 $kd7 Þ k2 $k1 k2 $k1 k2 $k1

k2 $k1

ð1r7;1 $kd7 Þ

k1

ð1r7;1 $kd7 Þ

(h) The exergoeconomic costs are associated with the following three sub-components: external resources, equipment investment and maintenance and the generated residues. By means of Eq. (8.151) the corresponding symbolic expressions are obtained. The results are shown in Tables E.8.33, E.8.34 and E.8.35. Table E.8.33 Unit exergy costs of components’ product associated to external resources. P unit exergy costs associated with external resources ①

cep1 ¼ k1 $cNG

②

cep2 ¼ k2 $k1 $cNG

③

ð1r2 Þ$k3 cep3 ¼ ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

④

ð1r2 Þ$k3 cep4 ¼ k4 $ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

Symbolic Thermoeconomics applied to thermal facilities

715

Table E.8.33 Unit exergy costs of components’ product associated to external resources.dcont’d P unit exergy costs associated with external resources ⑤

ð1r2 Þ$k3 cep5 ¼ k5 $ð1k $k2 $k1 $cNG 3 $k4 $r2 Þ

⑥

ð1r2 Þ$k3 k6 $r6 k6 cep6 ¼ ð1þr $k5 $ð1k $k2 $k1 $cNG þ ð1þr $cw 6Þ 3 $k4 $r2 Þ 6Þ

⑦

cep7 ¼ k7 $k1 $cNG

Table E.8.34 Unit exergy costs of components’ product associated to investment. P unit exergy costs associated to investment ①

czp1 ¼ z1

②

czp2 ¼ k2 $z1 þ z2

③

2 Þ$ðk2 $z1 þz2 þr2 $z4 Þ czp3 ¼ z3 þk3 $ð1r ð1k3 $k4 $r2 Þ

④

2 Þ$ðk2 $k3 $z1 þk3 $z2 þz3 Þ czp4 ¼ z4 þk4 $ð1rð1k 3 $k4 $r2 Þ

⑤

3 $z1 þk3 $z2 þz3 þr2 $k3 $z4 Þ czp5 ¼ z5 þ k5 $ð1r2 Þ$ðk2 $k ð1k3 $k4 $r2 Þ

⑥ ⑦

z þkd5 $ð1r2 Þ$ðk2 $k3 $z1 þk3 $z2 þz3 þr2 $k3 $z4 Þ ð1k3 $k4 $r2 Þ

k6 $r6 5 $ czp6 ¼ z6 þ ð1þr 6Þ

czp7 ¼ k7 $z1

Table E.8.35 Unit exergy costs of components’ product associated to residues. P unit exergy costs associated to residues ①

crp1 ¼

②

crp2 ¼ k2 $ 1b7;1 $k $k1 $cNG ð 7;1 7 Þ

③

ð1r2 Þ$k3 crp3 ¼ ð1k $k2 $ 3 $k4 $r2 Þ

④

ð1r2 Þ$k3 crp4 ¼ k4 $ð1k $k2 $ 3 $k4 $r2 Þ

⑤

ð1r2 Þ$k3 $k2 $ crp5 ¼ k5 $ð1k 3 $k4 $r2 Þ

⑥

ð1r2 Þ$k3 k6 $r6 $k5 $ð1k $k2 $ crp6 ¼ ð1þr 6Þ 3 $k4 $r2 Þ

⑦

crp7 ¼

b7;1

ð1b7;1 $k7 Þ

$k1 $cNG

b

b7;1

ð1b7;1 $k7 Þ

b7;1

ð1b7;1 $k7 Þ

$k1 $cNG

$k1 $cNG

b7;1

ð1b7;1 $k7 Þ b7;1

ð1b7;1 $k7 Þ

$k1 $cNG

$k1 $cNG b7;1

ð1b7;1 $k7 Þ

$k1 $cNG

716

Exergy Analysis and Thermoeconomics of Buildings

(i) Finally, by applying Eq. (8.152), the exergoeconomic costs of the components’ fuel are calculated. The expressions obtained are reflected in Table E.8.36. Table E.8.36 Unit exergoeconomic costs of components’ fuel. Fuel’s exergoeconomic unit costs ①

cF1 ¼ cNG

②

cF2 ¼ cP1

③

cF3 ¼ ð1  r2 Þ$cP2 þ r2 $cP4

④

cF4 ¼ cP3

⑤

cF5 ¼ cF3

⑥

1 $c þ r6 $c cF6 ¼ ð1þr w ð1þr6 Þ P5 6Þ

⑦

cF7 ¼ cP1

8.6

Symbolic Thermoeconomics in thermal installations analysis

Two representations FP and PF have been developed along with the chapter (the FP(R) and PF(R) models are an extension of them, including residues). Those representations reflect the system structure from the productive process perspective and, therefore, permit the analysing of the cost formation process and components’ efficiency. The use of FP or PF representation will depend on the type of problem to be solved. The {ce} variables are adequate to determine the final products, by knowing the consumed total fuel. On the contrary, the {cs} variables enable the total fuel consumption to be obtained when the system’s total product is fixed. However, those structural representations do not contain any information about the equipment thermodynamics, so that the functions obtained are independent of the system’s physical characteristics. Thus, from a thermodynamic point of view, two facilities that are different can have the same productive structure and, consequently, the same ST formulae. ST permits describing a series of functions of the system’s thermoeconomic properties, using as independent variables the so-called canonical variables ({ce} or {cs}) depending on the chosen formulation. Those formulas indicate the functional dependence between the different structural parameters and allow the costs to be accounted for once the exergy of the flows are known. Therefore, those ST models are the most adequate, if the need is to determine the system’s product costs or the variation of the overall system efficiency when the efficiency of one component is modified. However, ST models have a clear limitation, since the structural parameters do not contain any information about the thermodynamic behaviour of the system. In other words, they are disconnected from their physical reality. For that reason, to use these models, some type of procedure should be available to relate the structural parameters with the thermodynamic ones.

Symbolic Thermoeconomics applied to thermal facilities

717

In a thermodynamic model, the physical and morphological parameters of the installation are used as control variables. Through functions of those parameters, the rest of the thermodynamic properties of the flows and components are determined, such as flow exergies, efficiencies, etc. To do this, thermodynamic properties that relate the flows intensive properties (pressure, temperature, composition) with the extensive ones (volume, entropy, enthalpy, etc.) must be used; besides, mass and energy balances need to be applied. In addition, heat transfer, mass and movement laws provide the laws that relate the flow’s and component’s thermodynamic properties with their morphological parameters. Both types of models are required for thermal system analysis: structural and thermodynamic. The objective is to predict the system’s behaviour and calculate the flows’ and equipments’ thermoeconomic properties. This is done from the physical and morphological parameters that characterize it, such as pressures, mass flows, temperatures, etc. In such a case, the parameters to act on (design variables) are localized. So, two levels of variables exist: • •

Design variables, designated as {s}. Structural variables {ce} or {cs}.

Thermodynamics provides tools to express structural variables, such as recirculation parameters, exergy performances, etc., depending on the design variables. That is, it allows defining the k ¼ fk(s), r ¼ fr(s) and x ¼ fx(s) functions. Thus, by means of the thermodynamic model, the values of the structural variables are determined for certain values of the physical variables. From there, by applying the structural model, thermoeconomic variables of flows and component are obtained. In short, as mentioned, thermal system analysis requires the use of two types of models: thermodynamic and structural. Lastly, it should be indicated that various symbolic computer programs are currently on the market, which can be installed on personal computers. Among them REDUCE [27] and MATHEMATICA [28] are highlighted. Valero et al. [29] present a set of programs developed in REDUCE to obtain symbolic expressions of thermoeconomic variables.

Nomenclature Superscript 0 T n m e, x, r F, P, L, r

Subscript e, r, z

Reference state, environment Total Number of components Number of flows System inlets, bifurcations, recirculations Fuel, product, loss, residue

Useful product, residue, fixed costs

718

Exergy Analysis and Thermoeconomics of Buildings

Scalars

r, V h, s,b m_ _ W, _ B_ Q, 4j kj xij rij jir uej usj

Density, volume Specific enthalpy, specific entropy, specific flow exergy Mass flow rate Heat flow rate, work flow rate, exergy flow rate Exergy efficiency of j-th component Unit exergy consumption of j-th component Bifurcation parameters in FP representation Recirculation parameters in PF representation Residue distribution parameters External resources of j-th component in FP representation Output product of j-th component in PF representation

Matrices and vectors B B*,F*,P*,R* kF ,kP C CF,CP Ze J ae as ax ar A, AF , AP Fr Jx , Ye Jr , Ys hFPi hPFi hKPi t PTP t FTF hFj,P, hIj jFi,jIi,jPi

 

e P , e R

Flow exergy vector (m,1) Exergy flow costs vector(m,1), fuel costs vector(n,1), product costs vector(n,1), residue costs vector(n,1) Unit exergy costs of components’ fuel vector(n,1), unit exergy costs of components’ product vector (n,1) Flow exergoeconomic costs vector(m,1) Fuel exergoeconomic costs vector (n,1), product exergoeconomic costs vector (n,1) Capital and maintenence components’ costs vector(n,1) Matrix (n,m) which contains the exergy balances Matrix (e,m) which contains the input flows Matrix (s,m) which contains the output flows Matrix (mne,m) which contains the bifurcation parameters Matrix (mns,m) which contains the recirculation parameters Extended incidence matrix (m,m), fuel incidence matrix(m,m), product incidence matrix(m,m) Extended fuel vector (m,1) Extended matrix of Jx(m,m) and external assessment vector(m,1)in FP representation Extended matrix of Jr(m,m), external assessment vector(m,1)in PF representation Matrix (n,n)which contains the bifurcation ratios in FP representation Matrix(n,n)which contains the recirculation ratios in PF representation Matrix (n,n) which contains the unitary consumptions Portion of each component product in the output product vector (1,n) Portion of each component fuel coming from the external fuel vector (1,n) Matrix operators(n,n) in FP representation Matrix operators(n,n) in PF representation Matrix operators (n,n) in PF(R) representation

Symbolic Thermoeconomics applied to thermal facilities

719

References [1] J. Lazaroff, B. Vulchanova, Thermodynamic analysis of industrial energy systems, Parts: I,II;II, Hungarian Journal of Industrial Chemistry Veszprem 13 (1985) 379e395, 457-480. [2] H.H. Bau, T. Herbert, M.M. Yovanovich, Symbolic Computation in Fluid Mechanics and Heat Transfer, HTD-Vol 105, 1988. ASME Book G00483. [3] A.K. Noor, I. Elishakoff, G. Hulbert, Symbolic Computations and Their Impact on Mechanics, PVP-Vol205, 1990. ASME Book G00584. [4] C. Torres, A. Valero, C. Cortés, Application of Symbolic Exergoeconomics to Thermal Systems Simulation, 1989, pp. 75e84. AES Vol-9/HTD Vol-124, ASME Book H00527. [5] C. Torres, Symbolic Thermoeconomics. Methodology for the Thermoeconomic Analysis of Termal Systems (In Spanish), Ph D thesis, University of Zaragoza, 1991. [6] C.A. Ronde, Special Applications of the Theory of Generalized Matrix Inversion, John Hopkins, 1983. [7] W.W. Leontief, Input-Output Economics, second ed., Oxford University Press, Nueva York, 1986. [8] A. Valero, J.A. Alconchel, Towards a universal formula of efficiency. Proceedings of the IV International Symposium on Second Law Analysis of Thermal Systems, 1987. ASME Book 100236, Roma. [9] J.A. Alconchel, Exergy Modeling of Steam Cycles in Power Plants (In Spanish), Ph D thesis, University of Zaragoza, 1988. [10] A. Valero, C. Torres, Algebraic Thermodynamics of Energy Systems. Approaches to the Design and Optimization of Thermal Systems, 1988. AES VOl-7, ASME Book G00452. [11] A. Valero, C. Torres, On causality in organized energy systems. Part II: Symbolic Exergoeconomics, in: Proceedings of the Symposium: A Future for Energy, Pergamon Press, Florencia, 1990, pp. 393e401. [12] C. Torres, COSTEX, User Guide (In Spanish), Department of Mechanical Engineering, University of Zaragoza, 1987. [13] C. Torres, A. Valero, C. Cortés, Application of Symbolic Exergoeconomics to Thermal System Simulation, Simulation of Thermal Energy Systems, 1989, pp. 75e84. AES Vol-9/ HTD Vol-124, ASME Book H00527. [14] A. Picallo, C. Escudero, I. Flores, J.M. Sala, Symbolic thermoeconomics in building energy supply systems, Energy and Buildings 127 (2016) 561e570. [15] C. Torres, A. Valero, V. Rangel, A. Zaleta, On the cost formation process of residues, Energy 33 (2) (2008) 144e152. [16] S.M. Seyyedi, H. Ajam, S. Farahat, A new criterion for the allocation of residues cost in exergoeconomic analysis of energy systems, Energy 35 (8) (2010) 3474e3482. [17] A. Agudelo, A. Valero, C. Torres, Allocation of residue cost in thermoeconomic analysis, Energy 45 (2012) 634e643. [18] C.A. Frangopoulos, Thermo-economic functional. Analysis and optimization, Energy 12 (7) (1987) 563e571. [19] M.A. Lozano, A. Valero, L. Serra, Theory of exergetic cost and thermoeconomic optimization, in: J. Szargut, Z. Kolenda, G. Tsatsaronis, A. Ziebik (Eds.), Energy Systems and Ecology, Cracow, Polonia, vol. 1, 1993, pp. 339e350. [20] M.A. Lozano, A. Valero, Thermoeconomic Analysis of a Gas Turbine Cogeneration System, 1993, 312e320. ASME Book, No. H00874, WAM, AES 30. [21] M.R. von Spakovsky, Application of engineering functional analysis to the analysis and optimization of the CGAM problem, Energy 19 (3) (1994) 343e364.

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[22] C. Frangopoulos, Thermoeconomic functional analysis, in: C.A. Frangopulos (Ed.), Exergy, Energy System and Optimization, Encyclopedia of Life Support System (EOLSS), vol. II, EOLSS Publishers, Oxford, 2004. [23] J. Santos, M. Nascimiento, E. Lora, M. Martinez, On the productive structure for the residues cost allocation in a gas turbine cogeneration system, Proceedings of ECOS 2008 (2008) 641, 48, Cracovia, Polonia. [24] J. Santos, M. Nascimiento, E. Lora, M. Martinez, On the negentropy application in thermoeconomics: a fictious or an exergy component flow? International Journal of Thermodynamics 12 (4) (2009) 163e176. [25] J. Santos, Negentropy Application in the Termoeconomic Modeling of Systems (In Portuguese), Ph D thesis, Federal University of Itajuba, Itajuba, Brasil, 2009. [26] C. Torres, A. Valero, ThermoeconomicAnalysis, University of Zaragoza, 2015. [27] Reduce User’s Manual, Rand Corporation, 1987. [28] Mathematica 11, Wolfram, 2017. [29] A. Valero, D. Wimmert, C. Torres, Symbcost: A Program for Symbolic Computation of Exergoeconomic Cost Parameters, Computer- Aided Energy Systems Analysis, 1990. AES-Vol. 12, ASME Book G00568.

Operational diagnosis of thermal installations in buildings

9.1

9

Summary

Thermal installations in buildings, especially those of a certain age, are not usually energy optimized, so that their correct operation and adequate maintenance management can produce significant improvements in performance and, ultimately, reduce energy consumption. In order to optimize the operational mode of installation, its operational state needs to be known, and an adequate methodology needs to be chosen to explain the causes of abnormal increases in fuel consumption, thus allowing satisfactory decisions to be made. All this is included under the concept of energy diagnosis. This chapter presents, in the first place, some general ideas about energy diagnosis of installations, which aim to uncover and interpret the anomalous functioning of installation equipment and to evaluate the effect that each component has on additional fuel consumption. Next, thermoeconomic diagnosis is presented, which is based on setting a productive formulation expressed in terms of exergy for each component.

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00009-6 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

By applying Symbolic Thermoeconomics developed in the previous chapter and the Theory of Exergy Cost, the production structure of the installation can be generated, perfectly locating the origin of the resources consumed by each component, as well as the destination of its product. The impact on fuel consumption due to anomalies in the equipment is then given, developing the methodology of malfunctions and dysfunctions. After revealing the limitations of this theory, in the final part of the chapter, the method of characteristic equations is given, which complements the previous method and serves to detect the origin of anomalies in the equipment, with the significance of using both diagnostic methodologies being highlighted, given their complementary nature. The chapter ends with an introduction to a method that enables to discriminate the origin of the exergy destruction known as Theory of Advanced Exergy, in which a distinction is made between avoidable exergy destruction and unavoidable exergy destruction that is due to technical limitations. Likewise, these irreversibilities in the components may be intrinsic to them (endogenous) or may be a consequence of interrelationships between them, which we call exogenous irreversibilities.

9.2

Introduction to energy diagnosis

Recent technological advances, both in the design of equipment and in everything related to control, have opened up great possibilities for the improvement of energy efficiency, as well as in the use of renewables for thermal installations in buildings. But as already highlighted by Le Goff 1982 [1], the possibilities of saving energy depend on the level of decision-making of the persons or entities that address the problem. The higher this level of decision-making the greater the possible savings. Thus, to improve the performance of an installation, options range from engineering, which can propose new technologies, more efficient equipment and better integration of processes with structural and control modifications to maintenance activities and manual control adjustements. A thermal installation in a building is a dynamic system whose operation depends on conditions that can be modified by the plant operator (such as the temperature of hot water that is produced, DHW storage temperature, etc.), other non-modifiable conditions (environmental conditions, fuel characteristics), as well as conditions associated with the deterioration of equipment. Control and maintenance actions must be carried out on a regular basis in order to preserve plant efficiency and achieve greater readiness of equipment. These actions are of two types, depending on whether they are executed before (preventive) or after (corrective) the equipment shows signs of deterioration. Corrective actions aim to improve the efficiency of the installation when changes in the behaviour of the equipment have been detected. Therefore, in order to take corrective action, the causes of the abnormal increase in fuel consumption in the installation and the contribution of each cause to this increase in consumption must be discovered. For this, an energy diagnosis needs to be performed. In this chapter, we are not going

Operational diagnosis of thermal installations in buildings

723

to refer to mechanical diagnostic procedures that identify the mechanical state of the equipment through vibration measurements, acoustic analysis, etc. While energy diagnostic methodologies aim to analyse the anomalies that cause a decrease in the efficiency of systems, mechanical diagnosis aims to predict possible future failures. Energy diagnosis of installations is, therefore, a methodology to discover anomalies through monitoring of operating conditions, by means of the data received from the instrumentation of the installation. Its objective is to discover and interpret the abnormal functioning of equipment and to evaluate the additional consumption of resources due to these abnormalities. It is based on precise knowledge of the operating state of the installation and its comparison with respect to an optimum operational reference state. Fig. 9.1 shows the main diagram of a well-monitored heating and DHW installation. As we have said before, variations in the efficiency of a component in an installation can be due to different causes: some are external, such as variations in environmental conditions, in total production or change of fuel quality, and others are internal to the installation, and may be intrinsic, due to anomalies caused by the deterioration of the components or induced, due to variations in the operation of the equipment as a result of interactions with other equipment and the intervention of the control system. The objective of the diagnosis is to detect and locate intrinsic anomalies. But this objective is usually very difficult to accomplish, since an anomaly that takes place in any particular component affects the efficiency of the rest of the components, through interactions between components that are interrelated by mass and energy flows. In addition, there is the intervention of the control system, which will try to restore the prefixed values (set points). Thus, the true origin of the anomaly is hidden by the consequently induced effects. The reference state represents the maximum saving in the consumption of global resources for the installation, which can be achieved by carrying out pertinent actions to repair the defective behaviour of the equipment. Therefore, the reference state

Figure 9.1 Sensors in a heating and DHW installation.

724

Exergy Analysis and Thermoeconomics of Buildings

should not be confused with the designed state of the installation, which is defined by the manufacturers of the equipment for certain environmental and production conditions, and which we call nominal. The reference state is characterized by the absence of anomalies in the equipment but can be defined for any environmental or production condition. Following Lozano 1987 [2], we can say that the operational diagnosis of an installation is the way to discover and interpret the signs of a malfunction in equipment and to quantify its effects on the additional consumption of resources. Therefore, it deals with knowing where, how and what part of the resources used can be saved, while keeping the quantity and specifications of the products constant (heating, DHW, etc.). Due to the possibilities offered by the Internet and the affordable prices of sensors, it is now common for the energy installations of buildings to be continuously monitored. The establishment of a diagnostic method will require: • • • •

A data acquisition system. The appropriate instrumentation must be available, with a corresponding data acquisition system, which includes the filtering of the data, consistency tests and storage. Definition of the operating status. A calculation procedure that allows for the continuous determination of the real operating status of the installation needs to be established, and this should be as accurate as possible according to the instrumentation available. Definition of the reference state. The aim is to define a validated model of the installation that represents its reference status for any mode of operation, environmental conditions and different characteristics of the fuel used. Effect on the consumption of global resources. The objective is to obtain the effects on the consumption of global resources caused by each one of the variations in the efficiency parameters in relation to the value they take in the reference state.

Since diagnosis requires the comparison of the real operating state with respect to a reference state, a predictive model of the installation is needed. The equations needed to obtain the operating status of the plant are the mass and energy balances together with the relationships of thermodynamic properties. In addition, the model allows for the calculation of the efficiency parameters of the equipment, which serve to quantitatively evaluate its operation, such as effectiveness in the heat exchangers, polytropic performance in the fans, etc. Since the model must be predictive, in addition to mass and energy balances, it must also include kinetic laws, to characterize any feasible operating regime. On the other hand, since the diagnosis is a study of incremental magnitudes of small value (the real state with respect to the reference state), an analysis of the uncertainties in the diagnostic results is necessary. However, an energy diagnosis can be undertaken without having to know the kinetics of the energy transformation processes. These are the diagnostic methods based on Thermoeconomics, which consist of generating the production structure of the installation and deducing the impact on fuel consumption caused by equipment anomalies. In this respect, the works of Lozano et al. 1994 [3] and Valero et al. 1996 [4] are to be highlighted. Energy diagnostic methodologies are used to detect the problems of equipment deterioration during operation and to know in advance the savings that can be achieved in the consumption of global resources when solving these problems, in order to

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prioritize maintenance actions. Among the possible operational strategies, it will be the operator of the plant who must establish the optimal operational strategy, according to economic, safety and environmental protection criteria. The establishment of a diagnostic system will make it possible to establish recommendations for modifying operational strategies, maintenance actions and the replacement of components. Due to the complex interrelationships that may exist between the components of an installation, it is not easy to locate and quantify the effect produced by each component on the loss of performance of an installation. The diagnosis must evaluate the effect of any deviation from the operational parameters of each component in the total cost of operation.

9.3

Thermoeconomic diagnosis

As we have seen in previous chapters, exergy analysis of a system allows us to locate and calculate the irreversibilities in each component and thus identify the component in which the irreversibilities are greatest. This information is very interesting, but it is not enough when the objective is to improve the energy efficiency (energy saving) of an installation since we must keep in mind that not all irreversibilities are avoidable. The technical possibilities of exergy saving are always lower than the theoretical limits established by Thermodynamics since they are restricted by technical and/or economic considerations and also depend on the level of decision-making. The exergy destroyed in each component together with that delivered to the environment (losses) make up the irreversibility of that component and is a measure of its efficiency. Obviously, it is not technically feasible to avoid all irreversibility, only that fraction due to the difference between the operational state and the reference state can be avoided. That is, one can avoid the irreversibility that is attributable to the improper operation of equipment, which is known as technical saving. Therefore, unlike conventional exergy analysis, Thermoeconomics considers for comparison purposes, an installation state in which none of the components has anomalies. We have already said that this installation state is called the reference state and possible savings are determined by comparing the real installation with the reference installation. Diagnosis based on Thermoeconomics belongs to the group of methodologies based on energy monitoring and covers a wide spectrum of methods and techniques. Thermoeconomic diagnosis has its foundation in the productive function of each component within the whole installation and in the exergy of the flows. Through Thermoeconomics, this functionality of the equipment is established, that is to say, the productive structure of the installation. This productive structure will not only explain the productive function of each component but will also allow us to find the authentic formation process of the products cost. The behaviour of each component is described by general parameters that represent the consumption of resources that come from other equipment or the environment, in order to achieve its productive aim. The modification of these parameters, which represent the efficiency of the equipment, gives rise to the change in consumption of global resources.

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Exergy Analysis and Thermoeconomics of Buildings

As we will see later, very intuitively, a loss or destruction of exergy has a different effect on the additional consumption of fuel (resources) necessary to produce the same product depending on its location in the energy chain, so that the closer it is to the final product of the installation the greater will be the overconsumption (the impact) of fuel (resource).Thermoeconomic diagnosis of an installation operation aims to discover and interpret the abnormal operation of the equipment and quantify its effect in terms of increased consumption of resources. In short, like any other energy diagnostic methodology, thermoeconomic diagnosis locates and evaluates the increase in the consumption of resources due to anomalies in the equipment of the installation. Likewise, as we have indicated previously, thermoeconomic diagnosis is based on a comparison of two operating conditions: the real operation condition and the one corresponding to the reference, in which there are no anomalies in the equipment. In order to facilitate this comparison, external causes that may affect the modification of the installation efficiency need to be eliminated, such as (a) the variation of the total production (b) the modification of environmental conditions and (c) the variation in fuel characteristics. In this way, the variations in the efficiency depend only on the internal anomalies. Thermoeconomics allows for the quantification of the global effect of the deterioration of a component in the installation, that is, the amount of additional consumption of resources due to the variation of the irreversibilities (lost and destroyed exergy) in each component in relation to the reference state, attributable to internal causes, that is to say, assuming that the production of the installation, the weather conditions and the characteristics of the fuel are kept constant. The parameter that relates this local variation to the global impact is the exergy cost of the fuel supplied to the component. The application of thermoeconomic diagnosis on an installation can have two different aims. One of these, which is the most important and known as a direct problem, is the detection of a possible anomaly and its location. The second objective, known as an inverse problem, consists of the quantification of the effect of the anomalies, that is, in the evaluation of the increase in resources consumption that this anomaly implies. Therefore, as the two main aims of diagnosis are the location of the origins of the anomalies and the quantification of their cost (both at component and installation level as a whole), if we want to correctly quantify the cost of the anomalies we must be very strict in the evaluation of exergy consumption throughout the process. Fig. 9.2 shows an operator performing maintenance work on an air conditioning installation. In recent years, different diagnostic methods have been developed based on the Second Law and Thermoeconomics. The contribution due to the component with an anomaly in the variation of total fuel consumption is shown in the so-called impact on fuel formula, presented first by Valero et al. 1990 [5] and later developed by Reini et al. 1995 [6], Torres et al. 1999 [7] and Lozano and Valero 1999 [8], among others. In order to overcome the problem of separating the effects due to the intrinsic anomalies from the induced ones, the theory of malfunctions and dysfunctions was developed by Torres et al. [7] and the zooming strategy by Verda 2002 [9,10]. However, according to Lazzaretto and Toffolo 2006 [11], these methodologies are effective for assessing the impact of anomalies but are not effective for identifying intrinsic anomalies, so they propose a method based on characteristic functions, which we will refer to later.

Operational diagnosis of thermal installations in buildings

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Figure 9.2 Maintenance operations in an air conditioning installation.

We must also highlight the methodology developed by Tsatsaronis and Morosuk 2012 [12] which is called Advanced Exergy, and we will comment on this at the end of the chapter. According to Tsatsaronis costs are more appropriate for quantifying the effects of the anomalies than locating the causes of the anomalies. These methods began to be implemented in thermoelectric plants to detect deviations in operation with respect to previously programmed production objectives. Remiro’s Doctoral Thesis 2005 [13] and the publications in which the different thermoeconomic diagnostic methodologies are compared, Pacheco-Ibarra 2011 [14] and Us
on and Valero 2011 [15] are significant in this respect. Regarding thermal installations in buildings, it is worth noting the publication by Piacentino 2013 [16] as he uses thermoeconomic diagnosis to detect single or multiple failures in air conditioning installations and to quantify their impact on the increase in energy consumption. Along the same lines, Piacentino and Catrini 2016 [17] investigated the sensitivity of diagnostic techniques on the parameters that have the most significant influence on the exergy efficiency of the evaporator of a refrigerating machine for air conditioning. The work of Picallo et al. 2016 [18] can also be found in the field of heating installations. In any case, on no occasion to date has thermoeconomic diagnosis been applied to building installations. This chapter aims to present the bases of these diagnostic methodologies and to make them accessible to the building sector, in order to understand their potential and significance for greater efficiency and better performance of thermal installations.

9.3.1

Intrinsic anomalies and induced anomalies

At this point, we are going to make a distinction between what we will call intrinsic anomaly and induced anomaly. When there is an anomaly in a component, for

728

Exergy Analysis and Thermoeconomics of Buildings

example, fouling of a heat exchanger, excessive heat losses in a pipe due to poor insulation, etc., an increase in the irreversibilities of the equipment takes place. This increase in irreversibility that is directly linked to the problems of deterioration of the equipment during its operation, we will call as intrinsic anomaly. However, when an intrinsic anomaly occurs in a component, the operating conditions of the rest of the equipment are altered, so that they no longer work in the conditions corresponding to those of the reference state. These types of anomalies we will call induced anomalies. Once the anomalies have been detected and the direct problem solved, if there is more than one intrinsic anomaly, the resolution of the inverse problem allows the incidence of each anomaly on the impact on fuel to be found and, ultimately, the increase in the operating cost of the installation. Therefore, the intrinsic anomaly that has the greatest effect on the fuel consumption increase of the installation is the first that should be eliminated, if that is economically appropriate to be done. All thermoeconomic diagnostic methods are based on the idea that the effect of an anomaly on a component is the variation of the specific consumption of the resources used by that equipment, this specific consumption being the relationship between the exergy associated with the resources and the product of the equipment. Since these specific consumptions of exergy (and other indicators that are also used) take values that are a consequence of the anomaly, that is, they are dependent variables, it is not possible to use them to distinguish between intrinsic and induced anomalies. Precisely, one of the biggest problems of thermoeconomic diagnosis is differentiating between the two types of anomalies.

9.4

Exergy indicators. Impact on fuel

Different indicators based on exergy have been used to quantify the effects of equipment anomalies. One of them is the variation of the irreversibility DIi between the real and reference conditions, so that when the production of the plant is kept constant n X i¼1

DIi ¼ DFT

(9.1)

must be verified so that each term DIi can be interpreted as the effect of the anomaly of equipment i on the increase of the total consumption of resources in the installation. Another indicator proposed by Reini and Taccani 2002 [19] is based on the index ri defined in Section 7.7.1 and which is the quotient of the equipment fuel Fi and the total fuel of the installation FT. Comparing the real operating conditions with the reference conditions, the authors proposed using the following indicator X X Pi  Fi  D½ri ð4i  1Þ ¼ D D4T ¼ FT i i

(9.2)

Operational diagnosis of thermal installations in buildings

729

A part of the variation of the irreversibility between the real conditions and the reference conditions is due to the variation of the exergy unit consumption of each component, while the rest is due to the variation of its product. Therefore, Valero et al. 1990 [20] separated the variation of irreversibility into two components, DIDk and DIDP, so that DI ¼ DIDk þ DIDP ¼ Dk P þ ðk  1ÞDP

(9.3)

Likewise, other authors such as Lazzaretto et al. 1998 [21] analysed the effectiveness of these indicators when representing the impact of equipment anomalies. The use of the indicators, in all cases, showed that the same increase in irreversibility occurring in different components has a different effect on the increase of resources needed to obtain the same product from the installation. It means that irreversibilities have different costs, depending on the position of the equipment in the structure of the installation. As the idea is of great importance, we will develop it later. A widely used indicator that adequately reflects the effect of anomalies is what is called the impact on fuel, Valero et al. 1996 [5]. The impact on fuel is defined as the difference between the consumption of resources of the real installation and that of the reference, that is, the installation without anomalies in the equipment and with the same total production   DFT ¼ FT ðxÞ  FT0 x0

(9.4)

where FT(x) is the total resource consumption (fuel and electricity, that is, total fuel) of the installation   under the real operating conditions and x are the independent variables, while FT0 x0 refers to the reference conditions. This increase in resources can be broken down into the sum of the irreversibilities that take place in each component, that is, DFT ¼ DIT ¼

n  X j¼1

n   X Ij ðxÞ  Ij x0 ¼ DIj

(9.5)

j¼1

However, as we said before and will check now, the local exergy savings that can be achieved in each component are not equivalent, that is, the same variation of irreversibility in two different components gives rise to different variations in the total fuel consumption of the installation. We saw in Chapter 8 that kij is a marginal exergy consumption, which represents the quantity of resources (the exergy) necessary from i-th component to obtain the unit of n P kij ¼ kj . By using a thermoeproduct in j-th component and verifying the condition i¼0

conomic model of the installation, we can calculate the marginal exergy consumptions, exergy unit consumptions and all other thermoeconomic variables. These variables can be calculated for an installation under operating conditions and then can be compared with the corresponding values under reference conditions.

730

Exergy Analysis and Thermoeconomics of Buildings

It usually happens that there are several components that experience a deterioration of behaviour in an installation with respect to the reference conditions; consequently, their efficiencies diminish and their unit exergy consumptions increase. Thus the variation of the marginal exergy consumption kij is   Dkij ¼ kij ðxÞ  kij x0

(9.6)

where, as we have said before, x represents the value of the variables under real n P k0j Pj conditions and x0 under reference conditions. We saw in Chapter 8 that FT ¼ j¼1

and in vector form FT ¼ tkeP, where tkeh(k01,k02,.k0n) is a (n,1) vector whose elements contain the marginal consumption of the resources exergy that enter the installation. Therefore, comparing the real with the reference operation we have DFT ¼ Dt ke P0 þ t ke DP

(9.7)

In the development that follows, we will use the PF representation of Symbolic Thermoeconomics that we saw in Chapter 8, since it is the one that best adapts to the objectives of this chapter. Keeping in mind Eq. (8.74), the variation of the equipment products that make up the installation can be expressed as a function of the unit consumption variation according to the equation DP ¼ DPs þ DhKPiP0 þ hKPiDP

(9.8)

and therefore, using the matrix operator jPi that we saw in Chapter 8, we have   DP ¼ jPi DPs þ DhKPiP0

(9.9)

Considering that there is no variation in the installation total production and therefore DPs ¼ 0, substituting Eq. (9.9) into Eq. (9.7) and taking into account Eq. (8.91), the increase in the total fuel consumption is given by the expression   DFT ¼ Dt ke þ t kP DhKPi P0

(9.10)

and in scalar form DFT ¼

 n  n X X  kP;j Dkji P0i Dk0i þ i¼1

(9.11)

j¼1

This equation, known as Impact on Fuel, expresses the additional resource consumption DFT as the sum of the contributions due to the unit consumption increases

Operational diagnosis of thermal installations in buildings

731

of each component. Looking at the equation, we see that there is no equivalence between the irreversibilities of the components of an installation, since the more advanced the equipment in the energy chain, the greater the increase in the consumption of resources. Indeed, an increase in the marginal consumption of exergy of a component in the quantity Dkji P0i implies an additional consumption of external  Dk P0 where we see that the unit exergy cost of the j-th equipment resources of kP;j ji i appears and this exergy cost increases the closer the equipment is to the end of the energy chain. We see therefore that, in order to evaluate the impact on fuel in the installation, we need to know the components products under reference conditions, the unit exergy cost of those products and the increase between the reference and operating conditions of the exergy marginal consumption of each component in the installation. For this, we must have a thermodynamic model of the installation, in addition to the fuel-product functional model. Eq. (9.10) was obtained considering that the product of the plant remains constant. If between the reference and the real state there were a variation of the plant product DPs then the impact on fuel would be   DFT ¼ Dt ke þ t kP DhKPi P0 þ t kP DPs

(9.12)

As pointed out by Torres and Valero 1999 [22], this formula allows for the calculation of the value of the total impact on fuel in an exact way in which the products of each component refer to the reference conditions and the unit costs of the products refer to the operating conditions. Expressed in scalar form, we have  n  n n X X X   DFT ¼ kP$j Dkji P0i þ kP;i DPs;i Dk0i þ i¼1

j¼1

(9.13)

i¼1

Therefore, each component contributes to the total impact on fuel if its unit exergy consumption varies or as well if its product forms part of the total product of the installation and also varies. Thus, the contribution of the equipment i to the total fuel consumption of the installation is   n X   DFTi ¼ Dk0i þ kP; j Dkji P0i þ kP;i DPs;i

(9.14)

j¼1

Instead of referring to exergy units, if the impact on fuel is expressed in monetary costs, the increase in the total economic cost associated with the anomalies is similar to that of Eq. (9.4), which is   DCFT ¼ CFT ðxÞ  CF0 T x0

(9.15)

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Exergy Analysis and Thermoeconomics of Buildings

If the monetary cost coming from the outside per unit of product is c0j ¼ C0j/Pj, we n P c0j Pj and therefore, the previous expression gives can write CFT ¼ j¼1

DCFT ¼ Dt ce P0 þ t ce DP

(9.16)

Developing in a similar way to the previous equations, but now with exergoeconomic costs, we have DCFT ¼ ðDt ce þ t cp DhKPiÞP0

(9.17)

and considering the variation of the installation total product, gives DCFT ¼ ðDt ce þ t cp $DhKPiÞP0 þ t cp DPs

9.5

(9.18)

Diagnosis through malfunctions and dysfunctions

In the previous section, we have seen that there is no direct relationship between the increase in the irreversibility of a component and the consequent increase in the consumption of resources of the installation. The closer the equipment is to the end of the  or c energy chain, the greater is the cost of that irreversibility (since the values of kP;j P,j are larger) and, consequently, the equipment’s impact on fuel is greater. On the other hand, the deterioration of a component forces other components to adapt to the new operating conditions, and consequently, their irreversibilities are modified. Using the technique of malfunctions and dysfunctions analysis (MD) which is presented below, Torres and Valero2015 [23], we will separate the impact on fuel due to the increase in unit exergy consumption of the equipment itself from that caused by the variation of the equipment product. Before proceeding further, it is worth remembering that the total fuel consumed by the installation is the sum of the total product plus the total irreversibilities, so that, as we have seen in Chapter 8, we have FT ¼ tu$ (I þ Ps). In addition, as we have said, we will use the PF representation, so that from the product of the installation we determine the increase in resources consumed and costs.

9.5.1

Malfunctions and dysfunctions

When there is a variation in the behaviour of a i-th component in the installation, and consequently, any of the canonical variables cs(ki,rji,usi) corresponding to that equipment is modified not only does an increase in irreversibility occur due to the anomaly or malfunction in the equipment, but this malfunction also forces the other components to readjust to the new situation in order to maintain production conditions and consequently, their irreversibilities will also increase.

Operational diagnosis of thermal installations in buildings

733

Comparing the real operating conditions with those of reference, the impact on fuel due to the sum of the increase in the irreversibilities in the equipment as a consequence of the anomalies plus that due to the variation of the installation total production is    DFT ¼ t u ðI þ Ps Þ  I0 þ P0s ¼ t uðDI þ DPs Þ

(9.19)

Taking into account that I]FeP and therefore I¼(KDUD)P we have    DI ¼ ðK D  U D ÞP  K 0D  U D P0 ¼ DK D P0 þ ðK D  U D ÞDP

(9.20)

where P0 refers to the product of the components under the reference conditions. From the previous expression we see that we can distinguish two types of irreversibilities: •

Those due to an increase in the marginal consumption of the equipment exergy called malfunctions (endogenous irreversibilities). Thus, the malfunction in the i-th equipment due to an increase in the exergy marginal consumption from the j-th equipment is

MFji ¼ Dkji P0i

(9.21)

with the total malfunction in the i-th equipment being MFi ¼ Dki P0i ¼

n X j¼0

MFji

fi ¼ 1; 2; .ng

(9.22)

and in matrix form for the n components in the installation MF ¼ DK D P0 •

(9.23)

The so-called dysfunctions (exogenous irreversibilities), which take place in a component as a consequence of the malfunctions of other components, since these malfunctions force the equipment to consume more resources in order to obtain the additional production required by the other components. Thus, the dysfunction in the i-th equipment is

DFi ¼ ðki  1ÞDPi

(9.24)

Therefore, malfunctions are due to the anomalous behaviour of equipment while dysfunctions have their origin in how equipment adapts to maintain the installation total production. In matrix form, for all the equipment in the installation, the dysfunctions vector is DF ¼ ðK D  U D ÞDP

(9.25)

A variation of the parameters csj in different components j gives rise to a sum of P terms DFij in equipment i due to the dysfunction produced by the variation of those j

734

Exergy Analysis and Thermoeconomics of Buildings

parameters and which are a consequence of the very structure of the installation under consideration. The fundamental point of this analysis is to calculate the dysfunction DFij, that is, the increase of irreversibility in equipment i due to the malfunction of equipment j, so that the increase of irreversibility of a component is the sum of its malfunction plus the dysfunctions that are generated in it due to the malfunctions of other components. It is, therefore, an analysis of the production process of the upstream installation, that is, how the malfunction of a component affects the previous equipment in the production process of the installation analysed. In order to look in depth into the causes and effects of irreversibilities, we will consider new expressions that allow us to evaluate the impact of a malfunction on the fuel and its effect, that is, the dysfunctions in the rest of the equipment. Since, as we have Eq. (9.8) and using the matrix operator jPi we have obtained Eq. (9.9), substituting this equation into Eq. (9.25) and remembering that jIi ¼ ðK D  U D ÞjPi we have   DF ¼ jIi DhKPiP0 þ DPs

(9.26)

Therefore, the increase of irreversibility, Eq. (9.20), can be expressed as a function of the marginal exergy consumption variation according to the following equation   DI ¼ DK D P þ jIi DhKPiP0 þ DPs

(9.27)

In scalar form the above equation is DIi ¼

n X j¼0

Dkji P0i þ

n X j;h¼1

fih Dkhj P0j þ

n X j¼1

fij DP0sj ;

fi ¼ 1; 2; .; ng

(9.28)

where fih are the coefficients of the irreversibility matrix operator jIi. The first member on the right of the previous expression corresponds to the malfunction in equipment i and the rest to the dysfunction. In effect, if we use DFij for the increase of irreversibility in the i-th component due to the malfunctions in jeth component, we have DFij ¼

n X h¼1

fih Dkhj P0j

(9.29)

and using DFi0 for the increase of irreversibility in the i-th equipment due to the variation of the total production of the plant, we have DFi0 ¼

n X j¼1

fij DP0sj

(9.30)

We see that the coefficients fih that appear in these expressions reflect the effect of the malfunction on the dysfunction and depend only on the state of the plant. They are

Operational diagnosis of thermal installations in buildings

735

the irreversibility operator coefficients jIi in the real operating conditions. Thus, a malfunction Dkhj P0j in the j-th component generates a dysfunction in the i-th component proportional to the coefficients fih, which represent the weight of the malfunction effect. The dysfunction generated depends on these coefficients and the increase in the exergy marginal consumption generated. Therefore, dysfunctions cannot be corrected in themselves, we can only decrease the malfunction that has generated them. We see that the calculation of the impact on fuel is obtained from the malfunction of each component and the effect that the malfunctions of other components have on it. Thus, considering the generic i-th component, if we add the malfunction of the equipment MFi with the dysfunctions that Pare generated in said component due to the malfunctions of the other equipment DFij the increase of irreversibility DIi in j equipment i is obtained, and this is DIi ¼ MFi þ

n X j¼1

DFij

(9.31)

Adding for all the components, together with the increment of total product DPs, we obtain the increase in fuel, Eq. (9.19) DFT ¼

n X i¼1

ðDIi þ DPsi Þ ¼

n  X i¼1

MFi þ

n X j¼1

 DFij þ DFi0

(9.32)

In order to better understand the origin of the increases in irreversibility, we are going to use a matrix notation. To do this, we define the malfunctions matrix [MF] as a dimensional (n,n) matrix such that ½MF h DhKPiP0D where P0D is the diagonal (n,n) matrix containing the products of equipment P0i in the reference state. From this matrix, the vector MF that contains the malfunctions of each component can be expressed as t

MF ¼ Dt ke P0D þ t u½MF

(9.33)

where Dt ke P0D ¼ MF0 represents the vector of malfunctions associated with the increase of exergy consumption of external resources. Likewise, we define the dysfunctions matrix as [DF]hjIi[MF] of (n,n) dimension and the dysfunction vector associated with the variation of the installation total production as DF0hjIiDPs. According to these expressions, the vector DI containing the increase of irreversibility in each component can be written DI ¼ MF þ ½DFu þ DF0

(9.34)

Therefore, this equation tells us that the increase of irreversibility in a component is the sum of the malfunction in the component plus the dysfunctions generated in the

736

Exergy Analysis and Thermoeconomics of Buildings

other components due to that malfunction, plus the dysfunction due to the increase in the installation production. So, for the i eth component we have DIi ¼ MFi þ

n X j¼1

DFij þ DFi0

(9.35)

In short, according to Eq. (9.32), the impact on fuel can be written in terms of malfunctions and dysfunctions according to the following equation  n  n X X DFij þ DFi0 DFT ¼ MFi þ i¼1

9.5.2

(9.36)

j¼1

Cost of malfunctions

In Section 9.4 we obtained Eq. (9.12) which expresses the additional resource consumption of an installation, which we call impact on fuel, as the sum of the contributions due to the increases in unit consumption of each of the components and that due to the increase in the installation total product. According to this equation, a malfunction in the ieth component implies an additional consumption of external resources n P  Dk P0 . We will call this expression the cost of malfunction that is given by kP; ji i j j¼0

MFi since it is the malfunction multiplied by the unit cost of the additional resources required. As we can see, the impact on fuel can be broken down into two components: one of them reflects the costs of malfunctions, Valero and Torres 2009 [24], due to the variation of exergy marginal unit consumptions. So, for the i-th component that term is MFi ¼

n X j¼0

MFji ¼

n X j¼0

 kP;j Dkji P0i

(9.37)

where in the summation the exterior has been included, that is, the term DtkeP0. The other term is the impact on fuel due to the variation of the plant total product, which is MF0 ¼

n X i¼1

0 kP;i DPsi

(9.38)

The total impact on fuel is, therefore, the sum of the cost of the malfunctions in each component, due to both terms and so DFT ¼

n X i¼0

MFi

(9.39)

Operational diagnosis of thermal installations in buildings

737

In Chapter 8 we obtained the expression kP ¼ u þ t jIiu, and in scalar form n P  ¼1þ fhj which is an alternative way of expressing the product unit exergy kP;j h¼1

cost of a component as a sum of the contributions of the irreversibilities in the different components, since fhj represents the irreversibility generated in the j-th component per unit of product of the h-th component. The cost of the malfunction MFji can, therefore, be expressed as MFji

¼

1þ

n X h¼1

! fhj Dkji P0i

(9.40)

which according to Eq. (9.22) and Eq. (9.29) allows us to write MFi ¼ MFi þ

n X j¼1

DFji

(9.41)

with the cost of the malfunction associated with the variation of the installation total product being MF0 ¼ DPs þ

n X h¼1

DFh0

(9.42)

verifying Eq. (9.39). The cost of a malfunction is, therefore, the sum of the malfunction and the dysfunctions it causes, so these indices are of great interest in the diagnosis of installations. We see that the calculation of the impact on fuel can be broken down in two different ways. One way is that which we saw in the previous Section 9.5.1, starting with the malfunction of the i-th component and the effect that the malfunctions of other equipment have on it, Eq. (9.36). The other way is the one developed in this Section, through the cost of the malfunctions, which represents the malfunction in the component and the total of the dysfunctions that are generated in the other components, precisely due to the malfunction in the component under consideration. Thus, referring to the generic i-th component, the sum of the malfunction MFi plus the dysfunctions that are generated in the other components due to the malfunction in said equipment i, n P DFji , is given by Eq. (9.41), reflecting Eq. (9.42) the effect due to the variation j¼1

of the installation total production. We are now going to use the matrices [MF] and [DF] that we previously introduced. The malfunctions cost vector can be written MF ¼ t ½MF þ t u½DF

(9.43)

738

Exergy Analysis and Thermoeconomics of Buildings

with the malfunction cost associated with the variation of the total product being MF0 ¼ DPs þ t uDF0

(9.44)

These expressions are reflected in Table 9.1 which shows the two possible ways of breaking down the calculation of the impact on fuel, either through the costs of the malfunctions or through the increase of the irreversibilities in each component. In effect, that the cost of the malfunction in each component is the sum of its own malfunction and the disfunctions that it causes in the other components can be verified, due to the changes in the components’ mode of operation (reading vertically). Likewise, the increase of irreversibility in each component (reading horizontally) is the sum of the malfunction in the component plus the dysfunctions generated in the component due to malfunctions in the other components of the plant. The total impact on fuel can be obtained as the sum of the costs of malfunctions (reading vertically) or as the increases of total product and irreversibilities in each component (reading horizontally). In order to evaluate the importance of the cost of malfunction in relation to the impact on fuel, Picallo et al. 2017 [18] propose using the following two indices: jMFi ¼

9.5.3

MFi DFT

jMF0;i ¼

 MF0;i

(9.45)

DFT

Inclusion of residues in the diagnosis

So far we have not considered the effect of residues in the diagnosis. We have seen that the impact on fuel is given by Eq. (9.7), so substituting into this expression Eq. (8.76) gives DFT ¼ Dt ke P0 þ t ke DjPiPs þ t ke jPiDPs

(9.46)

Table 9.1 Break down of impact on fuel. DPs

MF1

.

D

MFj

.

MFn

DPs

D

D

MF1

DF10

DF11

.

DF1j

.

DF1n

DI1

.

.

.

.

.

.

.

.

DFi0

DFi1

.

DFij

.

DFin

.

.

.

.

.

.

.

.

MFn

DFn0

DFn1

.

DFnj

.

DFnn

DIn

.

MFn

MFi

þ

¼ S

MF0

¼

¼ MF1

.

MFj

DIi

¼ ¼

DFT

Operational diagnosis of thermal installations in buildings

739

Recalling as we saw in Chapter 8 that kP ¼ t jPike the above equation gives us DFT ¼ Dt ke P0 þ t ke DjPiPs þ t kP DPs

(9.47)

But, as we have seen in Chapter 8, in an installation, we can generally find flows that are residues, so there will be a variation in the impact on fuel due to the variation

e in the residues exergy consumption. Taking

 into account the definition of P operator,

e Eq. (8.146), developing its increase D P , after some matrix transformations, Rangel 2005 [25], gives DFT ¼ Dt ke P0 þ t kP ðDhKPi þ DhKRiÞP0 þ t kP DPs

(9.48)

Let us discuss the meaning of each of the terms on the right of the previous equation: • • • •

DtkeP0 is the impact on fuel due to the variation in unit exergy consumption of external resources, that is, the flows that come from the external environment. t  kP DhKPiP0 represents the impact on fuel due to the variation in the resources unit consumption of the components due to malfunctions and whose exergy cost is given by the resources unit exergy cost used up. t  kP DhKRiP0 stands for the impact on fuel due to the variation in the residues unit consumption , or rather, the resources cost consumed in order to generate the residues. t  kP DPs is the impact on fuel due to the increment of the installation total product.

In component form, the above equation is written as DFT ¼

n X n X i¼1

j¼0

 n X   k0i þ kP;j ðDkji þ Dqji Þ P0i þ kP;i DPs;i

(9.49)

i¼1

In short, this equation tells us that the increase of irreversibility in any i-th component in the installation is due to the variation in the exergy unit consumption of the resources and the increase in the marginal consumption due to the residues, which n P is reflected by Dqji P0i . As we saw in 9.5.1 this is what we call malfunction in the j¼0

i-th component, only now considering the residues we can distinguish two types of malfunctions or endogenous irreversibilities: •

Internal malfunction in the i-th component is the increase of irreversibility in the component due to the variation of the exergy marginal consumptions of the fuel coming from the other components in the installation

MFjiin ¼

n X j¼0

Dkji P0i

(9.50)

740

•

Exergy Analysis and Thermoeconomics of Buildings

External malfunction is due to the variation in the exergy marginal consumption in the generation of residues, which is

MFjiex ¼

n X j¼0

Dqji P0i

(9.51)

In addition to the malfunctions, there are the dysfunctions that, as we saw, are the increase in irreversibility in the components due to the local variation of its production caused by the malfunctions of the other components in the installation. When there are residues, the dysfunction of the i-th component is DFi ¼ ðki  1ÞDPi þ

n X j¼0

qji DPi

(9.52)

and in matrix form DF ¼ ðK D  U D  hKRiÞDP

(9.53)

In a similar way to what was done in 9.4.1 we can express the dysfunctions as a function of the coefficients of the irreversibility matrix operator jIi and of the residue operator coefficients jRi defined in Chapter 8. After a series of matrix operations, Rangel 2005 [25], we have DF ¼ ðjIi þ jRiÞðDhKPi þ DhKRiÞP0

(9.54)

and written in scalar form DFj ¼

n  X i;h¼1

 in  ex fjh þ jjh MFhi þ MFhi

(9.55)

This equation is telling us that a malfunction in equipment i generates a dysfunction in equipment j proportional to the coefficients (fjhþjjh) where the first coefficients are those of the irreversibility matrix operator jIi and the second coefficients are those of the residue operator jRi both evaluated in the real operating conditions of the installation. In short, these coefficients reflect the weight of the malfunction effect on the impact on fuel and, as we see, depend on the unit consumption of the equipment. We have seen that the other way to calculate the impact on fuel is through the cost of malfunctions, the cost of a malfunction in a component being the sum of the malfunction and the dysfunctions generated by it. We have also seen that the cost of malfunctions is calculated by multiplying the component malfunction by the unit exergy cost of the resources used. Therefore, the cost of an internal malfunction in the i-th component will be MFiin ¼

n X j¼0

 in in kP; j MFji ¼ MFi þ

n  X h¼1

 fhj þ jhj MFjiin

(9.56)

Operational diagnosis of thermal installations in buildings

741

while for an external malfunction MFiex ¼

n X j¼0

 ex ex kP; j MFji ¼ MFi þ

n  X h¼1

 fhj þ jhj MFjiex

(9.57)

with the impact on the fuel being expressed in terms of the costs of the malfunctions according to the following expression DFT ¼

9.5.4

n  X  MFiin þ MFiex

(9.58)

i¼1

Intrinsic and induced malfunctions

The first diagnostic problem is the so-called direct problem, that is, to detect if there are anomalies present and determine in which components they are located. Generally, the detection of whether there are anomalies or not is a simple problem, since, if production remains constant, the increase in irreversibility in one or more components will cause an impact on fuel consumption (resources). Thus, the manager of the installation can verify the correct operation by comparing the consumptions in the operational and reference conditions. Once an anomaly has been verified, the next step is to locate the component where the anomaly has occurred. As we have seen before, with this objective, different indices can be used, Stoppato and Lazzaretto 1996 [26], Torres and Valero 1999 [23], and others. If a component has an intrinsic anomaly, its impact on fuel is other than zero, but other components also contribute, due to the presence of dysfunctions and other types of malfunctions that are generated in the components on which we will comment on now. Indeed, the methodology of malfunctions/dysfunctions that we have shown in the previous Sections 9.5.1 to 9.5.3 contemplates the increase in exergy consumption of the equipment due to its deterioration, which we have called malfunction and its effect on the equipment located upstream, which must adapt their operation to maintain production conditions; consequently, there is an increase in their irreversibilities which we have called dysfunction. The deterioration of a component, which causes a variation in its unit consumption, we will call intrinsic malfunction. But an intrinsic malfunction, in addition to dysfunctions, also modifies downstream equipment in the production process, since the conditions of entry into these components have varied, also modifying to a greater or lesser degree their efficiency and this will affect the equipment in the installation. Consequently, when there is an intrinsic malfunction, in addition to the dysfunctions, induced malfunctions are generated in the other equipment, which can have a very significant effect on the overall behaviour of the installation. In fact, when an intrinsic malfunction occurs in an i-th component, the operating conditions of the rest of the components in the installation are modified. As a consequence, the different components, in which there are no intrinsic malfunctions, are operating outside of their design conditions (reference) and, consequently, there is a

742

Exergy Analysis and Thermoeconomics of Buildings

variation in their efficiencies and in their unit exergy consumptions, which gives rise to the presence of malfunctions, but which will not now be intrinsic but induced by the intrinsic malfunction in the i-th component. In Section 9.4 we have seen different indicators for quantifying the effects of equipment anomalies. However, the indicators (the ratios DFi/DFT, or MFi/I0, etc.) help us to locate the intrinsic anomalies only in some cases. They occur when induced malfunctions are small with respect to intrinsic malfunctions. However, it may happen that the maximum value of the indicator is present in a component that only has induced malfunctions, as a result of the component’s product being raised or because of a high unit cost of the resources used by the component. There is, therefore, a problem, which is to be able to discern the intrinsic malfunctions from the induced. The increase in the unit consumption of exergy of a component can be due to different causes, not necessarily to an intrinsic malfunction. Thus, change of environmental conditions, in the quality of the fuel, operation at partial load or the intervention of the control system can cause changes in the behaviour and efficiency of the equipment. In short, the MD method that we have just presented is not sufficient to determine the origin of the malfunctions and to discriminate the intrinsic ones from the induced. We will now look at a method to eliminate induced malfunctions due to the control system. Subsequently, in Section 9.6 we will look at a different thermoeconomic diagnostic method, based on the characteristic functions of the equipment, which tries to discriminate between intrinsic and induced malfunctions.

9.5.5

Filtering malfunctions due to the control system

The effect of an anomaly on a component generally causes variations in the thermodynamic properties of the flows, but the control system imposes certain restrictions on the propagation of that intrinsic malfunction. For example, if the performance of a hot water boiler decreases the outlet temperature will decrease, but the control system orders the burning of more fuel, in order to keep that temperature constant. There is a cause-effect relationship between the malfunction and the intervention of the regulation system. The set values and demands represent restrictions that must be maintained by the control system, regardless of what happens in the installation. These restrictions modify the natural propagation of the effects of the malfunctions, generating other induced malfunctions and dysfunctions, which makes it very difficult if not impossible to locate the original anomaly. In the example of the boiler, the natural effect of the anomaly is the decrease in temperature of the hot water generated, but once the control system intervenes, the value of that temperature is recovered. Therefore, to filter these effects and detect the origin of the malfunctions, the idea is to eliminate the effects of the total product variation of the installation and the set values. For this, both in the reference conditions and in real operation, the control system must act in the same way. For this purpose, an artificial condition is defined, consisting of the installation being in real operating conditions but the regulation system acting in the same way as it would under the reference conditions, Verda 2001 [27]. In this condition,

Operational diagnosis of thermal installations in buildings

743

which is called the free condition, the installation has the same anomalies as in the real operating conditions, but the control system works in the same way as in the reference conditions, so that the propagation of the malfunctions is natural. Therefore, the comparison between reference and free conditions does not include malfunctions induced by the control system.

Figure 9.3 The three conditions of operation in thermoeconomic diagnosis.

Fig. 9.3 shows the characteristics of the three operating conditions of the installation: reference, real operation and free conditions. The reference and real operation conditions are characterized by the same values of production and the same parameters, but if the system has anomalies, the control works differently. The reference and free conditions have the same control, but the restrictions are different. The fact that the same control gives rise to different behaviours in the two modes of operation is due to the presence of malfunctions in the free condition. The free condition cannot be obtained in a real installation since the parameters of the control system cannot be modified at will, and the demands are fixed by the user, so it has to be obtained theoretically. There are two ways to do it: one of them is based on modelling the plant through a Taylor development when each parameter of the control system is modified, Us
on and Valero 2010 [28]. This Taylor development can be applied to obtain the thermodynamic properties related to the free condition or directly to obtain the exergy unit consumptions or other thermoeconomic quantities. The other method is to simulate the operating condition and the free condition using a TRNSYStype software, with the free condition maintaining the real state of the plant but with the control corresponding to the reference state, Picallo et al. 2016 [18]. The method developed by Orozco et al. 2016 [29] is also very interesting, incorporating neural networks.

9.5.6

Impact on fuel expressed in exergoeconomic costs

In Section 9.4 we defined the impact on fuel and we expressed it in terms of the increase in exergy consumed by the installation. At the end of that Section, Eq. (9.15) to Eq.(9.18), we have obtained some expressions for the impact on fuel in monetary

744

Exergy Analysis and Thermoeconomics of Buildings

units. Now we are going to deepen in that development using exergoeconomic costs but taking into account the effect of the control system.. We are going to deduce the expression for the calculation of the impact on fuel in economic terms in an analysis in which the free condition that we saw previously is used. As we saw, the economic impact is the difference between the fuel total cost under real operating conditions and reference conditions, which is DCFT ¼ CFT  CF0T

(9.59)

On the one hand,

there is a cost associated with the intervention of the control control system DC FT which represents the cost generated to maintain the thermodynamic parameters within an operational range; that is, the difference in cost between the real operating situation and the free condition. On the other hand, there is the cost related to the anomalies

DCanom FT

which represents the added cost due to

malfunctions in the equipment; that is obtained by diagnosis. Thus, Eq. (9.59) can be broken down into two components



free 0 control  C þ DC anom þ C DCT ¼ CFT  CFfree FT ¼ DC FT FT FT T

(9.60)

Thus, the economic impact can be summarized as 0 B B DCFT ¼ B @

Control system Y

Anomalies þ

DCFcontrol T

Y DCFanom T

1 C C C A

(9.61)

The cost related to the intervention of the control system is obtained by applying  Eq. (9.59) between the real condition (CFT) and the free condition CFfree T t

¼ CFT  CFfree ¼ t cF $FT  cF free $Ffree DCFcontrol T T T

(9.62)

where cF is the unit economic cost of fuel in each condition. The economic cost associated with the anomalies is calculated following the same procedure as in Eq. (9.7); in this case, however, the terms for unit exergy costs of external resources (DcFk0 and cFk0 ) are used instead of their unit consumption. Knowing that DP ¼ PeP0 t

t

free 0 0 0 DCFanom ¼ cfree F $FT  cF $FT ¼ DcFk0 $P þ cFk0 $DP T

(9.63)

Operational diagnosis of thermal installations in buildings

745

If the expression of DP from Eq. (9.9) is introduced between the free and reference conditions, DCFanom ¼ ðDcFk0 þ cFk0 $jPiDhKPiÞ$P0 þ cFk0 $jPi$DPs T

(9.64)

  Analogous to the equation DFT ¼ t u$ MF þ MF0 that is obtained from Eqs (9.43) and (9.44), the economic impact related to the anomalies can be divided between the exergoeconomic cost due to malfunctions (CMF ) and that produced by the variation of the final product between the free and reference conditions (CMF0 ), which is: DCFanom ¼ CMF þ CMF0 . That way we have that T t

CMF ¼ ðDcFk0 þ cFk0 $jPi$DhKPiÞ$P0

(9.65)

t

CMF0 ¼ cFk0 $jPi$DPs

(9.66)

9.5.7

The problem of intrinsic malfunctions detection

Diagnosis is the art of discovering and understanding the causes of malfunctions and quantifying their effects. It is, therefore, a task of great complexity, since there are many factors involved. As we have already said, when the behaviour of a component is modified, it may be due not only to an intrinsic malfunction, but also to the variation of the external conditions, or the control system, etc. In the previous Section we have seen how the effect of the control system can be solved, although, in any case, the main problem of the diagnosis remains which is to identify and quantify the intrinsic malfunctions. The type of malfunction is related to the effect that the operational parameters of the installation have on the equipment efficiency. If a parameter is local, the effect of its variation will only occur on the equipment with which it is associated. Now, if the parameter is global, it is not associated with a single component, so its variation will cause intrinsic malfunctions in several components in the installation. Therefore, the thermoeconomic diagnosis will depend on the choice of operating parameters and the level of aggregation of the productive structure. A choice of model that makes most of the operational parameters local will increase the potential of the thermoeconomic diagnosis. It is clear that the method of malfunctions/dysfunctions that we have presented is not adequate for determining the origin of the malfunctions. Exergy consumptions are not the control parameters with which the installation operates, given that the true control variables are pressures, temperatures and flow rates. The question is whether the impact on fuel or any other index can be expressed in terms of those control variables. For this, we would need to be able to express the increases of the exergy unit consumption as a sum of the control variables contributions. This requires having a simulator of the installation or additional information to that provided by thermoeconomic analysis. Precisely, the method of characteristic functions that we will see in Section 9.6 tries to solve this problem.

746

9.5.8

Exergy Analysis and Thermoeconomics of Buildings

Examples

Inverse problem with an anomaly. Heating and DHW installation Consider an experimental installation for heating and DHW located in the Laboratory for Quality Control ofr Buildings (LCCE) of the Basque Government. The heat generated for heating, which corresponds to a 16 tenement building located in Bilbao, is dissipated in a fan coil with a three-way valve. The installation consists of a Baxiroca 24 BIOS/28F condensing boiler, which, working in the high-temperature mode, has an energy efficiency of 97% (the exergy efficiency is 17%). The other components of the installation are a hydraulic compensator, a 1000 L DHW tank, a plate heat exchanger, three-way valves and three circulation pumps, see Fig. E.9.1. Example E.9.1.

Figure E.9.1 Diagram of the heating and DHW installation.

The control of the installation is such that the DHW has priority over the heating. The equipment is activated or deactivated depending on the temperature of the DHW tank (T21) and the heating demand profile. If the tank temperature is lower than 62 C, the boiler is activated until 70 C is reached. When the temperature difference of the plate heat exchanger primary input is greater than 7 C, the DHW production is activated and if the difference is less than 4 C, the three-way valve, located just in front of the plate heat exchanger, sends the hot water flow to the compensator. The demand for heating is a function of the outside and is activated temperature

_ within a certain time limit. When there is demand Qheating the return temperature to the boiler decreases, and if it falls below 60 C the boiler is activated. The threeway valve associated with the DHW production is adjusted to supply the water mass flow rateðm_ DHW Þ at the temperature TDHW ¼ 55 C.

Operational diagnosis of thermal installations in buildings

747

In order to develop the example, an anomaly is introduced in the radiator system (RS), consisting of a 10% reduction in its energy efficiency, meaning this efficiency the ratio between the useful heat supplied by the radiators and the enthalpy variation of the heating water at the entrance and exit of the radiator system. The objective of this example is to determine the malfunction and dysfunction in each component, the cost of malfunctions, the dysfunctions that this malfunction generates in the other equipment and the economic cost due to the intrinsic malfunction that we have introduced in the radiator system. Solution. The heating demand was obtained by TRNSYS v17, using Type 56 and 1 h intervals, considering a level of occupancy of the typical homes of the Basque Country. The demand for DHW was calculated using the Task 26 DHW [E1] program. In Fig. E.9.2 the profile of heating and DHW demand for 5 days of January are shown.

Figure E.9.2 Demand profiles of heating and DHW for 5 days in January.

For the analysis, a total of 13 components and 24 flows were taken into account, as canbe seen  in Fig. E.9.3. Consider that two resources   enter from the exterior: natural gas B_ 20 and the contribution due to the tank DB_ 21 , which is the difference between the initial and final exergy of the tank in the period under consideration. Both are represented by dotted arrows in Fig. E.9.3. The grated indicate   the final  arrows products generated by the installation, that is, heating B_ 19 and DHW B_ 23 . The three circulation pumps were not considered in the analysis, due to their small power. If this were not so, it would be convenient to break down the physical exergy into its two thermal and mechanical components, which undoubtedly would make the analysis more precise, but we would considerably complicate the presentation of the example. Therefore, the calculations do not contain the effect of the pressure on the values of the physical exergy of the water flows.

748

Exergy Analysis and Thermoeconomics of Buildings

Figure E.9.3 Physical structure of the installation.

Definition of the free condition. For the reasons stated, the intervention of the control system must be cancelled to obtain the free condition. Fig. E.9.4 represents the process followed in TRNSYS v17. The REF index refers to the reference condition and FREE to the free condition (see FAULT incorporated in the lower part of the figure). It also shows the connections between components and the control system. For the operating conditions, we apply the same control strategy as in the reference conditions and in this way we define the free condition. Effect of total production variation There are two products from the installation: heating and DHW. The heating corresponds to the demand required by the users, so the heating produced for the 0 free condition and the reference is the same Q_ heat ¼ Q_ heat , since both the environmental conditions and the internal comfort conditions for both states are the same and therefore DPs,heat ¼ 0. However, the DHW production corresponds to the water mass flow rate demanded ðm_ DHW Þ at the specified temperature (TDHW ¼ 55 C). These conditions are obtained by means of the three-way valve V3, which mixes the cold water flow of the network ðm_ nw ; Tnw Þ with the hot water from the storage tank ðm_ hw ; T18 Þ. Therefore, the DHW production is Q_ DHW ¼ m_ DHW $cp $ðTDHW  Tnw Þ ¼ m_ hw $cp $ðT18  T0 Þ þ m_ nw $cp $ðTnw  T0 Þ ¼ H_ 18 þ H_ 24 _ 18 is the water flow enthalpy from the tank and H _ 24 that of the water flow where H from the network. For obtaining the free condition, the control system forces valve V3 to act in the same way as in the reference condition and therefore m_ hw ¼ m_ 0hw and m_ nw ¼ m_ 0nw . However, since the hot water temperature at the tank outlet is a function of the tank

749

Figure E.9.4 Obtaining the free condition.

Operational diagnosis of thermal installations in buildings

750

Exergy Analysis and Thermoeconomics of Buildings

temperature, that is, T18 ¼ T18(T21) and due to the anomaly introduced in the installation, the instantaneous tank temperature is different in the two conditions, that is, 0 . Therefore, since H_ s H 0 , there is a variation in the total DHW producT18 s T18 18 18 tion and so DPs,DHW s 0. In short, in this installation in which there are two products, only one of them can remain the same for the free and reference conditions, while the other varies. Using TRSYS v17, the three conditions of the installation are simulated throughout the year: the real condition (with the anomaly introduced in the radiator system), the reference condition (without any anomaly) and the free condition (according to the comments made previously). The accumulated exergy values for each of the flows and the entire heating period are collected in Table E.9.1. Table E.9.1 Accumulated exergy values of each of the flows. [MJ]

B1

B2

B3

B4

B5

B6

B7

B8

B9

B10

B11

Reference

29.1

23.4

102.4

97.4

13.4

89.0

11.1

2.3

1.8

12.9

84.5

Free

29.1

22.9

85.8

80.3

13.1

72.7

10.9

2.2

1.8

12.7

67.7

Real

29.1

23.0

101.7

96.3

17.0

84.7

15.3

1.7

1.3

16.6

79.7

B12

B13

B14

B15

B16

B17

B18

B19

B20

B21

B22

B23

B24

54.6

34.5

30.0

2.2

1.7

0.0

0.4

1.0

34.2

0.0

0.0

0.3

0.0

38.7

34.0

29.1

2.2

1.7

0.0

0.4

1.0

37.2

0.0

0.0

0.2

0.0

52.3

32.3

27.5

1.6

1.3

0.0

0.4

1.0

36.0

0.0

0.0

0.3

0.0

In order to demonstrate that the study is dynamic, Fig. E.9.5 shows the simulated exergy consumption of natural gas in the condensing boiler for 5 days in January. As shown, the blue dotted and red grated lines refer to the reference and free conditions (it is checked that the boiler is activated and deactivated in the same instants, see the horizontal axis); the full green line, on the other hand, corresponds to the operating condition (the boiler is activated when the control system intervenes).

Figure E.9.5 Consumption of the boiler for 5 days in January for the three conditions.

Operational diagnosis of thermal installations in buildings

751

Table E.9.2 shows the diagnosis results according to Eq. (9.32). The columns of the table show the final product variation DPs, the values of the malfunctions (MF0i þ MFi), Eq. (9.33), where the malfunctions MF0i correspond to the first term on the right of said equation and the dysfunctions (DF0i þ DFi), Eq. (9.26), of each component. The sum of the last four columns corresponds to the irreversibility increase DI, Eq. (9.34), that is, the part of the impact on fuel associated with the anomaly. The values of FT0 and FTfree correspond to the total consumption of resources (fuel) in the reference state and in the free condition respectively. The difference between these values, as well as the sum of all the cells in Table E.9.2, shown in Eq. (9.32) matches the impact on fuel DFTanom ¼ 3:010 MJ: Table E.9.2 Diagnosis DFT ¼ DIþDPS [MJ]. DI MF

DF

DPs

MF0i

MFi

DF0i

DFi

①

CB

e

147

e

1250

3640

②

HC

e

e

12

26

78

③

D1

e

e

e

e

e

④

V1

e

e

e

e

e

⑤

M1

e

e

2

e

e

⑥

HX

e

e

e

e

e

⑦

V2

e

e

e

e

e

⑧

M2

e

e

39

2

9

⑨

M3

e

e

59

5

29

⑩

RS

e

e

382

e

e

⑪

T

e

e

e

29

29

⑫

V3

105

e

180

77

e

⑬

D2

e

2

e

e

e

FT0 ½MJ ¼ FTfree ½MJ ¼

34,174 37,184

Analysing the results obtained, we can make the following comments: •

•

DPs in the RS component is zero, and there is a negative value in V3 for the total product variation ½DPs12 ¼ 105 MJ. This result confirms what was previously affirmed, that is, that there is no variation in the heating production, while there is a reduction in the DHW production due to the presence of the anomaly in the free condition. If we refer to the MF malfunction vector, we observe that the malfunction affects mainly the RS component in which the anomaly exists [MF10 ¼ 382 MJ], but the malfunction is also significant in the boiler [MF1 ¼ 147 MJ]. For a clearer interpretation of this result, MF must be broken down into the malfunctions due to exergy consumption variation MFi and

752

• •

Exergy Analysis and Thermoeconomics of Buildings

to external resources variation, MF0,i, Eq. (9.33). Thus, the boiler CB is affected mainly by the variation in consumption of external resources [MF0,1 ¼ 147 MJ]. The components located upstream of the anomaly (HC [MF2 ¼ 12 MJ], M2 [MF8 ¼ 39 MJ], M3 [MF9 ¼ 59 MJ]) also exhibit malfunctions. In all cases, these are induced malfunctions. The component most affected by the malfunctions of the other components is the first component in the energy transformation chain, that is, the boiler CB with [DF1 ¼ 2390 MJ]. There are components with negative dysfunction values, such as M3 [DF5 ¼ 9 MJ] or V3 [DF12 ¼ 77 MJ], which are related to the decrease in the DHW production.

In order to delve into the origin of the dysfunctions, Table E.9.3 shows the dysfunction matrix, as defined in Section 9.5.1. Table E.9.3 Dysfunction matrix DF0

½DF

① e1250 e

e61 e330

e

12

2

e

204 345 2240 e6 1234 e

②

e26

e

e

e7

e

e

e

e

4

7

48

e

26

e

③

e

e

e

e

e

e

e

e

e

e

e

e

e

e

④

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑤

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑥

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑦

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑧

e2

e

e

e16

e

e

e

e

e

1

4

e

2

e

⑨

e5

e

e

e42

e

e

e

e

e4

2

10

e

5

e

⑩

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑪

e29

e

e

e

e

e

e

e

e

e

e

e

29

e

⑫

e77

e

e

e

e

e

e

e

e

e

e

e

e

e

⑬

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⓪

①

②

③

④

⑤

⑥

⑦

⑧

⑨

⑩

⑪

⑫

⑬

With respect to this table, we can make the following comments: •

P The sum of each line DFij corresponds to the total dysfunction generated in the i-th j component which matches the corresponding element in Table E.9.2. For example, the   P DF1j ¼ 3640 MJ are the dysfunctions that appear in CB) and is sum of the first line ( j

•

equal to the corresponding element of Table E.9.2 [DF1 ¼ 3640 MJ]. Using this table the effects induced in the i-th component caused by a malfunction in the j-th component can be visualized. For example, [DF1,8 ¼ 204 MJ] corresponds to the CB dysfunction arising from M2.

Using Eq. (9.43) and Eq. (9.44), the malfunctions costs are obtained, see Table E.9.4. The last two columns show the values of the indices whose objective

Operational diagnosis of thermal installations in buildings

753

is the identification of the importance of the malfunction cost in relation to the impact on fuel, Eq. (9.45). Table E.9.4 Diagnosis DFT ¼

P

MFi ½MJ and indices.

MF*

MF0

jMF

jMF0

①

CB

147

e

5%

e

②

HC

73

e

2%

e

③

D1

396

e

13%

e

④

V1

e

e

e

e

⑤

M1

e

e

e

e

⑥

HX

e

e

e

e

⑦

V2

e

e

e

e

⑧

M2

244

e

8%

e

⑨

M3

413

e

14%

e

⑩

RS

2683

e

89%

e

⑪

T

e

e

e

e

⑫

V3

1481

1487

49%

50%

⑬

D2

2

e

e

e

DFTAnom

½MJ ¼

3010

According to the values obtained, some comments can be made. • •

•

•

The malfunction cost of the components that do not have malfunctions and which do not induce dysfunctions in other components  is zero.    Some malfunction costs are negative MF2 ¼ 73 MJ and MF3 ¼ 396 MJ . It is because the dysfunctions induced by these components in the rest are negative, which means that they cause a decrease in local production in other components, compared with the reference condition. h i The component with the largest index jMFi is RS jMF10 ¼ 89% . This result implies that 89% of the extra fuel consumption is due to the anomaly of the radiator system, which in turn causes an increase in consumption in other components [5% in CB, 8% in M2, 14% in M3 and 49% in V3] and a decrease in others [-2% in HC, 13% h in D1], due toi induced effects.

 Likewise, V3 involves a consumption reduction of 50% jMF0;12 ¼ 50% simply because a fraction of the additional consumption of fuel gives rise to a decrease in production in the free condition.

The results of Table E.9.2 and Table E.9.4 are represented graphically in Fig. E.9.6 and Fig. E.9.7, respectively. Fig E.9.6 shows the malfunctions, dysfunctions and the total product variation between the free and reference conditions. It can be seen that the boiler CB is the component with the greatest dysfunction. Fig E.9.7 shows the impact on fuel depending on the malfunctions costs and shows that RS is mainly responsible for the increase in fuel.

754

Exergy Analysis and Thermoeconomics of Buildings

Figure E.9.6 MF and DF of the components.

Figure E.9.7 MF cost in the components.

Finally, Table E.9.5 shows the results obtained for the exergoeconomic costs associated with the malfunctions, through Eqs. (9. 65) and (9. 66). With respect to this table, we can make the following comments: •

As might be expected, the RS component that contains the intrinsic anomaly is the one that has the largest exergoeconomic cost associated with the cost of its malfunction ½CMF11 ¼ 147 V. • During the heating period, the economic cost due to the presence of the anomaly goes up to [DCF ¼ 164 V]. This cost is the sum of the contribution of each component, according to the index jMF  , that is, V8 due to the induced malfunction in CB, -V22 in D1, V23 in M3, etc. [E.1] A. Picallo, J.M. Sala, E. Iribar, M. Odriozola, L. del Portillo, Application of the malfunction thermoeconomic diagnosis to a dynamic heating and DHW facility for fault detection, Energy and Buildings 135 (2017) 385e397.

Operational diagnosis of thermal installations in buildings

755

Table E.9.5 Economic costs of malfunctions. CMF ½V

CMF0 ½V

①

CB

8

e

②

HC

4

e

③

D1

22

e

④

V1

e

e

⑤

M1

e

e

⑥

HX

e

e

⑦

V2

e

e

⑧

M2

13

e

⑨

M3

23

e

⑩

RS

147

e

⑪

T

e

e

⑫

V3

⑬

D2

81

82

e

e

DCFAnom T

164V

Inverse problem with two anomalies. Heating and DHW installation We refer again to the installation previously described in Example E.9.1. Two anomalies are now incorporated into the system: one of them is in the RS radiator system consisting of a 10% decrease in its efficiency, and the other is in the HX heat exchanger, where there is now a 35% decrease in its heat transfer coefficient. Solution. In the same way, as in the previous example, calculations of the exergy of the flows for the operating conditions (real state with faults), free conditions and for the reference state are made. The accumulated values for the heating season are represented in Table E.9.6. However, only the values are shown for the free condition (which will be the reference used) and the real condition with anomalies; since the purpose of this example is to exclusively work the MF and DF theory related to failures. The results of the analysis of malfunctions and dysfunctions are presented in Table E.9.7. The first column represents the component, with its corresponding number. The second column corresponds to the malfunction, and then the expanded matrix of dysfunctions appears, in which the dysfunctions associated with the consumption of external resources DFi0 and those due to other components DFij are shown. The last column corresponds to the total product variation of the installation. Example E.9.2.

756

Table E.9.6 Accumulated values of the flows exergy during the heating period. [GJ]

B1

B2

B3

B4

B5

B6

B7

B8

B9

B10

B11

FREE

122.9

100.1

372.3

351.8

192.0

180.3

153.3

38.9

29.8

182.9

169.2

REAL

122.9

99.2

369.8

348.4

190.7

179.1

151.9

38.8

29.8

181.7

166.7

B13

B14

B15

B16

B17

B18

B19

B20

B21

B22

B23

B24

57.6

122.7

111.6

37.2

28.3

0.2

6.5

2.3

149.1

0.04

0.2

5.8

0.03

57.7

121.4

109.2

36.2

27.5

0.2

6.4

2.3

155.3

0.05

0.2

5.6

0.03

Exergy Analysis and Thermoeconomics of Buildings

B12

MF and DF diagnosis DPS

MF

DF0

①

1214

1396

e

557

24

e

e

1255

e

486

e

6617

34

21

e

e

②

450

9

e

e

80

e

e

48

e

52

e

480

104

e

e

e

③

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

④

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑤

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑥

206

12

e

e

e

e

e

e

e

e

e

e

10

e

e

e

⑦

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑧

136

14

e

e

87

e

e

32

e

23

e

15

25

e

e

e

⑨

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑩

1093

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑪

40

6

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⑫

1

15

e

e

e

e

e

e

e

e

e

e

e

e

e

129

⑬

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

⓪

①

②

③

④

⑤

⑥

⑦

⑧

⑨

⑩

⑪

⑫

⑬

[DF]

Operational diagnosis of thermal installations in buildings

Table E.9.7 MF and DF values.

757

758

Exergy Analysis and Thermoeconomics of Buildings

In view of these results we can make the following comments: •

• • • • •

The components with the highest values of malfunctions are those that contain the anomalies (HX and RS, MF6 ¼ 206 MJ and MF10 ¼ 1093 MJ, respectively). However, these values correspond to intrinsic and induced malfunctions, and so no immediate conclusions can be drawn. Precisely, due to the propagation of induced effects, other components also have malfunctions ([MF1 ¼ 1214 MJ], [MF2 ¼ 450 MJ], [MF8 ¼ 136 MJ], [MF11 ¼ 40 MJ] and [MF12 ¼ 1 MJ]). Malfunctions usually cause dysfunctions. These effects are mostly experienced by equipment upstream from the anomaly site. So the boiler CB is the component that experiences the greatest dysfunctions [DF1 ¼ DF1,2þDF1,3þDF1,6þDF1,10þDF1,11þDF1,12 ¼ 6.702 MJ]. For its part, the RS component is the one that induces the greatest amount of dysfunctions [DF1,10þDF2,10þDF6,10þDF8,10 ¼ 7864 MJ].   P The dysfunctions generated by HX DFi;6 ¼ 1239 MJ are notable but do not have as i

much effect because this equipment is located at the beginning of the energy chain. According to Eq. (9.32) the sum for all components reflects the impact on fuel as a consequence of the intrinsic anomalies, that is, DFT ¼ 6296 MJ.

9.6

Method of characteristic curves

Both intrinsic and induced malfunctions are effects of deterioration or failures that occur in one or more components in the installation. Now, the most direct effect of the appearance of an anomaly in a component is the modification of the functional relationships between the thermodynamic properties of the mass and energy flows that interpose in the operation of that component, as well as in the rest of the equipment. These functional relationships are called characteristic functions or characteristic curves (CC) and can be of very different types, depending on the equipment in question. Thus, characteristic functions are the models of heat transfer in heat exchangers, pressure drop in filters and operating charts in compressors, etc. The modification of a characteristic curve causes a variation in the behaviour of the equipment, and this causes the so-called intrinsic malfunctions to appear. In a component where an intrinsic anomaly occurs, the mass and energy flows change. Due to the interactions between the components, this change in the characteristic curve of one component affects the operation of the others, which react to these changes according to their characteristic curves. In short, the modifications caused by an intrinsic malfunction are spread throughout the installation and cause induced malfunctions in components that had no anomaly. As we have said previously, these induced effects will probably also alter the operation of the very component in which the anomaly occurred, according to the new characteristic curve which has changed due to that intrinsic anomaly. The interactions between components are precisely the obstacle to identifying the sources of malfunctions. The procedure described in Section 9.4, distinguishing between the MF malfunctions (the rate of irreversibility due to the variation in specific

Operational diagnosis of thermal installations in buildings

759

exergy consumption Dk) and DF dysfunctions (the rate of irreversibility due to the product variation DP of the component considered), does not make it possible to clearly distinguish between intrinsic and induced effects, except when the specific consumption curves are flat. For this reason, Lazzaretto and Toffolo 2006 [30,31] considered that malfunctions should not be considered as clues that reveal the causes of a deteriorated global performance. They propose that the changes in the characteristic curves of the equipment should serve as a guide for the sources identification of the deteriorated operation, provided that the real and reference operating conditions are adequately compared.

9.6.1

Discrimination between the intrinsic and the induced malfunctions

As we have said, the location of the components affected by intrinsic malfunctions is based on the knowledge of their behaviour, that is, on the availability of the characteristic curves in the reference conditions. The characteristic curves of a component consist a set of relations that express any thermodynamic property that reflects the behaviour of the component, for example, its efficiency, as a function of a set of properties that interpose the operation. Thus, the operation point in the reference condition satisfies the following equation for the generic i-thequipment

ref ref ref ref pref ¼ f ; c ; .c c i i i;1 i;2 i;k

(9.67)

The property p can be any property that characterizes the processes that take place in the component. As we have said, it can be the isentropic efficiency of a compressor, the output temperatures in heat exchangers, the pressure drop in a filter, etc. Exergy or thermoeconomic properties can also be used; for example, the unit exergy consumption of the component. It may be of interest to use the irreversibility in the component as a property pi, since it has the advantage that any anomaly causes an increase in irreversibility in relation to the reference and, therefore, the indicator will always have a positive value in the case of intrinsic malfunction. The properties ck must be a set of independent properties that characterize the behaviour of the component, so that the characteristic curves firef and their derivatives have to be defined as functions of ci,k. Therefore, the most natural choice is the set of thermodynamic properties (mass flow rate, pressure, temperature, composition) with a number equal to the number of degrees of freedom. The anomalies cause a change in operation, from the reference conditions to the real conditions. When there is an intrinsic anomaly in a component, the rest of the equipment that do not have intrinsic anomalies continue working along their reference characteristic curves, but at different points of operation of those curves, due to the induced effects. Therefore, those real points of operation belong to their corresponding characteristic curves of reference. On the contrary, the real point of operation of the component affected by some intrinsic anomaly does not belong on the characteristic curve of reference, see Fig. 9.4.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 9.4 Actual and reference operating point for equipment (A) without intrinsic anomalies (B) with intrinsic anomalies.

To check if a malfunction is intrinsic or induced, where Ini is the indicator used, in the equation of the reference characteristic curve we put the values of the properties corresponding to the real state and calculate the expression



ref real real real real real ; c ; ::; c ; c ; ::; c Ini ¼ fireal creal  f c i;1 i;2 i;k i;1 i;2 i;k i

(9.68)

If this expression is equal to zero, the point of operation corresponding to the real operation is found on the reference characteristic curve; if not, some anomaly has altered the relation firef giving rise to a degraded characteristic curve fireal . As such, the quantity Ini is the indicator to check the type of malfunction: if Ini s 0 the component is affected by some intrinsic anomaly, on the contrary, if Ini ¼ 0, the component will only be affected by induced effects, Toffolo and Lazzaretto 2007 [30]. real creal ; creal ; ::; creal the indiTaking into account Eq. (9.67) and that preal ¼ f i i i;1 i;2 i;k cator Ini can be expressed as follows h



i ref ref ref ref real  p  f Ini ¼ preal c  f c i i;k i i i i;k

(9.69)

where the term in brackets can be developed according to the following expression firef

" #



X vf ref ref ref real i ck  fi ck ¼ vck k

cref k

 cref creal k k

(9.70)

For each component, an approximate value of these derivatives can be obtained by knowing a number l of points of operation near the reference state. These operating conditions are obtained by imposing different combinations of the parameters of the control system, and/or modifying the external conditions and/or introducing anomalies

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in other components, for which a simulation of the installation will be needed. The values of the derivatives are obtained by solving the following system of equations % $  l vf ref D ck vck

¼ Dl p

(9.71)

cref k

Returning to Eq. (9.69) we finally have Ini ¼ preal i



pref i

$ % X vf ref i  vck k

cref i;k

Dci;k

(9.72)

This formulation can be interpreted as the result of a virtual restoration of the reference state so that the point of operation is brought from the real operation condition to the reference condition. Insisting on what has been said above, if the point of operation coincides with the reference point, the malfunction of the component is an induced effect and in that case Ini ¼ 0, neglecting the approximation introduced with the linearization of the characteristic curve, see Fig. 9.5a. On the other hand, if there is an intrinsic malfunction in the component, since the point of operation does not belong on the reference characteristic curve, the point of operation on the reference curve is not recovered, since it belongs to a different curve. Consequently, the index Ini will have a non-zero value, see Fig. 9.5b, and this is the cause of the malfunctions induced, either by the modification of external conditions, interaction between components or by adjustments of the control system.

Figure 9.5 Restoration of the reference state with and without anomalies.

As we have said before, in the theory proposed by Verda, a third state (the free state) is considered in addition to the reference and real state, obtained by calculation and in which the characteristic curves of the equipment are those of the real state (including

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Exergy Analysis and Thermoeconomics of Buildings

anomalies if they exist), but the variables governed by the control system are set to values as if they were in the reference state. In this way, the malfunctions causes are sought by comparing the free state and the reference state, thus eliminating the effect introduced by the control system. In summary, even in the case of equipment that does not have an intrinsic anomaly, if the efficiency curve is not completely flat, deterioration is induced in its behaviour that can be evaluated through its characteristic curve. If there is an intrinsic anomaly, the characteristic curve is also modified. Let us finally consider that the indicator used is the unit exergy consumption k. For the generic i-th component two exergy consumptions can be considered: one in the reference state kiref and the other when anomalies are present, kireal . Due to the induced effects, the independent thermodynamic properties will be different in the reference conditions than in the operating conditions. As a result, the increase in the exergy unit consumption Dki can be divided into intrinsic variations Dki,int and induced variations Dki,ind. Indeed, in the same way that we saw in Eq. (9.69) the unit consumption real  k ref can be written variation Dki ¼ ki;real i;ref



ref ref ref ref real real  ki;ref ¼ ki;real  ki;real  ki;ref Dki ¼ ki;real þ ki;real

(9.73)

real represents the real unit consumption for the real independent variables, where ki;real ref ki;real the unit consumption on the reference curve for the value of the real variables, etc. Therefore, we can write



ref real  ki;real Dki;int ¼ ki;real

(9.74)



ref ref  ki;ref Dki;ind ¼ ki;real

(9.75)

This separation between the intrinsic and induced component is observed using Fig. 9.4. We see how in (a) it is true that Dki,int ¼ 0, while in (b) both Dki,int and Dki,ind are other than zero. Consequently, the malfunction of the equipment can be expressed as the sum of the intrinsic and induced malfunctions, which is MFi ¼

X int

MFi;int þ

X X X MFi;ind ¼ Dki;int P0i þ Dki;ind P0i ind

int

(9.76)

ind

This method has diverse applications. Worth mentioning is the publication by Lazzaretto 2004 [32] which uses irreversibility as an indicator and applies the method to the diagnosis of a combined cycle, while Xu et al. 2016 [33] undertook the diagnosis of a 330 MW plant, using a plant simulator.

9.6.2

Examples

We will refer again to the heating and DHW installation in Fig. E.9.1. We are going to build the characteristic curves of some of its components. Since for the diagnosis we

Operational diagnosis of thermal installations in buildings

763

use TRNSYS v17 in the simulations, we will use the same models that this software uses to build the characteristic curves. Example E.9.3.

Characteristic curve of a heat exchanger Construct the characteristic curve of the heat exchanger in Fig. E.9.8.

Figure E.9.8 Heat exchanger.

Solution. Since the fuel of the heat exchanger is B_ 8  B_ 9 and the product is B_ 15  B_ 16 the unit exergy consumption of the heat exchanger is kHX ¼

B_ 8  B_ 9 B_ 15  B_ 16

The exergy for the i-th flow of water is   Ti _ Bi ¼ m_ cp Ti  T0  T0 ln T0 The independent variables (sHX) chosen for the heat exchanger are: the  primary and  secondary input temperatures (T8,T16), the mass flowrates m_ prim ; m_ sec , the ambient temperature (T0) and the global coefficient of heat transfer UA. Therefore, the exchanger outlet temperatures (T9,T15) depend on these variables. Since the objective is to determine the exchanger outlet temperatures of which the transfer surface is known, the method used is that of Effectiveness-Number of Transfer Units, εNTU. For this, we must first determine whether the maximum thermal capacity corresponds to the primary or secondary. If Cprim ¼ m_ prim :cp and Csec ¼ m_ sec :cp we will call Cmax ¼ maxðCprim ; Csec Þ Cmin ¼ minðCprim ; Csec Þ

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Exergy Analysis and Thermoeconomics of Buildings

The effectiveness of the heat exchanger depends on the geometric configuration, as well as on the configuration of the flow. For the plate heat exchanger in the installation, the expression obtained for effectiveness is    UA Cmin 1  exp  1 C C  min  max  ε¼ Cmin UA Cmin 1 exp  1 Cmin Cmax Cmax From the effectiveness, the exit temperatures are determined, which are in turn the entry temperatures for M1 and T. These temperatures are ! Cmin T9 ¼ T8  ε$ ðT8  T16 Þ Cprim   Cmin T15 ¼ T16  ε$ ðT8  T16 Þ Csec If the exit temperatures are known the unit exergy consumption kHX can be calculated. In Fig. E.9.9, its values are represented graphically, when one of the independent variables changes and the rest remain constant. The graphs in Fig. E.9.9 have been constructed for the following values: UA ¼ 133,888 kJ/hK, m_ prim ¼ 1:920kg=h , m_ sec ¼ 1860kg=h keeping constant two of the three temperatures T16 ¼ 35 C, T0 ¼ 15 C and T8 ¼ 75 C, with the third one appearing on the horizontal axis.

Figure E.9.9 Characteristic curve of the heat exchanger relative to a variable change. Example E.9.4.

Characteristic curve of a boiler Construct the characteristic curve of the condensing boiler in Fig. E.9.10, which is part of the experimental installation of the LCCE.

Operational diagnosis of thermal installations in buildings

765

Figure E.9.10 Boiler.

Solution. The Type chosen in the TRNSYS v17 library to build the characteristic curve is Type 700, which corresponds to a boiler. We will assume that it works at high temperature (60e80 C) so that it behaves like a conventional high-performance boiler. The energy efficiency of the boiler is hC ¼

E_ 1  E_ 2 E_ 20

and the specific exergy consumption is kC ¼

B_ 20 _ B1  B_ 2

The exergy for the water flows i ¼ 1, 2 is calculated by Eq. (3.44), while the exergy of the natural gas is obtained from Eq. (3.136), that is, B_ 20 ¼ m_ NG fICVNG where f is the correlation coefficient that for natural gas takes the average value of 1.04. The independent variables (sC) chosen for the boiler are the inlet temperature (T1), _ and the ambient the mass flow rate of the water to be heated ðm_ 1 ¼ m_ 2 ¼ mÞ  temperature (T0). Also, known parameters are defined as the maximum power E_ MAX , the set temperature at which hot water is produced (Tset), the energy efficiency curve ðhC ðDT; m_ 1 ÞÞ and the minimum power  at which it can work. The boiler outlet temperature (T2) and the required fuel E_ 20 depend on these variables. There are two main states for the boiler: there is no mass flow rate (boiler off), or there is circulating flow (boiler on). In the first case, the model establishes the outlet  equal to that of the inlet (T2 ¼ T1) and the consumption is zero temperature _ 20 ¼ 0 . In the second state, the model first calculates the required energy E   E_ req to raise the water temperature to the set temperature.

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Exergy Analysis and Thermoeconomics of Buildings

If E_ req is negative, it means that the inlet temperature is higher than the set temper_ ature; therefore, the boiler behaves as if it is switched off.  If Ereq is  between 0 and the maximum power, the energy transferred to the water E_ 2  E_ 1 will be E_ req . The boiler is internally controlled, in such a way that it adapts the consumption to obtain the hot water at T2 ¼ Tset, operating at partial load (PLR), so that the consumption will be E_ req ¼ PLR E_ MAX . If E_ req is greater than E_ MAX , it means that the energy input would exceed   the power of the boiler. In this case, the energy transferred to the water E_ 2  E_ 1 is E_ MAX , so that the partial load coefficient will be the unit (PLR ¼ 1) and the outlet temperature _ p . Once the energy is T2 ¼ T1 þ E_ MAX mc transferred to the water is known in all   cases, the fuel consumption is E_ 20 ¼ E_ 2  E_ 1 hc and in this way kC is obtained as a function of the independent variables. Fig. E.9.11 shows the values of kc, when one of the independent variables T1 varies, and the others remain constant for the following values: m_ ¼ 1:062 kg=s , T0 ¼ 15 C, E_ MAX ¼ 28 kW and Tset ¼ 75 C.

Figure E.9.11 Characteristic curve of the boiler with respect to the variable T1.

Inverse problem with several anomalies. Heating and DHW installation We consider again the installation of Example E.9.1, to which the two anomalies of Example E.9.2 are incorporated. As we have said, one of them is in the RS radiator system, with a 10% decrease in its efficiency and the other is in the HX heat exchanger, with a 35% decrease in its heat transfer coefficient. The objective of this example is to solve the discrimination problem of intrinsic anomalies by means of the method of characteristic equations in parallel with the method of malfunctions and dysfunctions. Example E.9.5.

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Solution. Since 13 components have been considered, 13 characteristic curves must be defined. For achieving this, the different Types existing in TRNSYS v 17 were used, the characteristic curves of two of these components having been shown in the two previous examples. The simulation of the installation was carried out hour by hour, with the demand profiles that have been represented in Fig. E.9.2. The cumulative values of the exergy of the flows in the reference conditions and for the state with the two anomalies introduced in the equipment described above are presented in Table E.9.6. In order not to include external induced anomalies (such as control intervention, changes in external conditions, etc.), the reference state coincides with the free condition. When there are several anomalies in an installation, the anomaly in one of the i-th components leads to the unit consumption variation in the component itself Dki,int (intrinsic malfunction) and in the rest of the j-th equipment (j ¼ 1,n, j s i) it leads to induced malfunctions Dkj,ind as well as a variation in its products DPj (dysfunctions). The objective is to discriminate between these induced malfunctions and dysfunctions, in order to evaluate the increase in the resources consumption due to the intrinsic malfunction of the i-th component. By using the MD method, the extra consumption of resources associated with the increase in the products of the j eth equipment can be obtained through the dysfunctions DFji but additional information is needed to evaluate the effect of the other induced malfunctions. Complementing the MD diagnosis with that of the CC diagnosis, the component with the most important intrinsic malfunction can be identified, that which causes the greatest impact on fuel. Once this intrinsic malfunction is eliminated, the analysis is carried out again by applying the MD method a second time. The impact on fuel calculated in the first analysis DFT1 less the impact on fuel made in the second DFT2 (when the main anomaly has been eliminated) is the fuel saving obtained when that anomaly has been eliminated, that is to say DFsav ¼ DFT1  DFT2 st

1 On the other hand, this fuel saving is the sum of the intrinsic malfunction MFi;int   P 1st P ind;1st plus the effects induced in that first analysis DFji þ MFji plus the total j

j

product variation of the plant DP1;2 s and the dysfunction that is generated between both states. In this way, induced malfunctions can be calculated. The method can be repeated as many times as intrinsic malfunctions exist and the inverse diagnosis problem solved, see Fig E.9.12. For more details of the method see Picallo et al. 2016 [E.1]. The values obtained are presented in Table E.9.8. This table refers to the first analysis, which contains the two malfunctions, and then the second is presented, which has 1st the intrinsic malfunctions the most influential malfunction removed. In column MFint

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.9.12 MD and CC combined methodology for locating malfunctions.

Table E.9.8 MF, DF values deduced using the characteristic curves method. Characteristic curves st MF1int

MF1ind

st

DF1

st

①

CB

e

1214

6467

②

HC

e

450

500

③

D1

e

e

e

④

V1

e

e

e

⑤

M1

e

e

e

⑥

HX

323

117

22

⑦

V2

e

e

e

⑧

M2

e

136

42

⑨

M3

e

e

e

⑩

RS

1212

119

e

⑪

T

e

40

6

⑫

V3

e

1

15

⑬

D2

e

e

e

Operational diagnosis of thermal installations in buildings

769

st

1 represents the values of the induced malfuncare represented, while column MFind tions, as the characteristic curves of the components are not represented by horizontal lines. The sum of both columns corresponds to the total malfunctions of each component, while the last column represents the dysfunctions. In view of the table we can make the following comments:

•

•

The method of the characteristic equations allows us to distinguish between the intrinsic malfunctions and the induced malfunctions. Thus, the table shows that the components with the h i h i 1st ¼ 323 MJ and MF 1st intrinsic malfunctions are MF6;int ¼ 1212 MJ corresponding to 10;int the HX and RS components, respectively. However, this methodology does not allow for the identification of the origin of each of the st dysfunctions, since only the total dysfunctions DFi1 can be calculated for each component.

Since we identify two components with intrinsic malfunctions, the next step is to eliminate the intrinsic malfunction of greatest weight (that of RS). Once that intrinsic malfunction has been eliminated, and this component is brought back to the reference conditions, we perform the simulation again, in order to evaluate the decrease in the impact on fuel between the first and the second simulations. Table E.9.9 shows the results obtained by applying the method of characteristic equations to this second simulation. In view of the table we can make the following comments: Table E.9.9 MF, DF and Ps deduced using the method of characteristic curves in the second simulation. MF and DF diagnosis

Characteristic curves nd MF2int

nd MF2ind

DF20

nd

DF2

nd

DP2s

nd

①

CB

e

2048

754

2197

e

②

HC

e

143

1

82

e

③

D1

e

e

e

e

e

④

V1

e

e

e

e

e

⑤

M1

e

e

e

e

e

⑥

HX

317

118

6

9

e

⑦

V2

e

e

e

e

e

⑧

M2

e

45

11

59

e

⑨

M3

e

e

e

e

e

⑩

RS

e

18

e

e

e

⑪

T

e

33

12

e

e

⑫

V3

e

1

10

e

76

⑬

D2

e

e

e

e

e

770

•

• • • •

Exergy Analysis and Thermoeconomics of Buildings

Since the anomaly in RS has been eliminated, only the anomaly in HX is present, highlighting 2nd ¼ 317 MJ. As we can see, this intrinsic anomthe malfunction in the heat exchanger MF6;int aly varies slightly with respect to the previous situation, as the operating conditions of the equipment are slightly modified. 2nd is still important. In fact, since the fault is in HX, the final DHW production is still DFi;0   state, and this has an impact on the consumption reduction lower the reference P than 2nd ¼ 792 MJ . DFi;0 i Since the number of intrinsic anomalies has been reduced, the total production variation nd DP2sDHW is closer to zero. nd The impact on fuel due to the existence of the two intrinsic anomalies is DFT2 ¼  590 MJ: In short, the saving obtained by the elimination of the anomaly in RS is: DFsav ¼ 6886 MJ.

The general results corresponding to the anomalies whichPwere deliberately caused P are collected in Table E.9.10. The rows MFint, MFind and DF are the intrinsic and induced malfunctions and the dysfunctions of the components with anomalies; while row DF0 þ DPs indicates the effects of the anomalies on the final production. Finally, DFanomaly summarizes the impact on fuel of each anomaly. Table E.9.10 General results of the diagnosis. RS anomaly

HX anomaly

MFint P MFind P DF

1212

317

695

1270

7082

1230

DF0þDPs

714

867

DFanomaly

6886

590

Thus, the anomaly in RS generates an extra consumption of 6886 MJ of which 7599 MJ are due to the anomaly proper, and the remaining 714 MJ are due to the decrease in the final product. On the other hand, the anomaly in HX generates an overconsumption of 590 MJ (underconsumption in this case), of which 277 MJ are due to the anomaly in the heat exchanger and the remaining 867 MJ are explained by the reduction in the DHW production. [E.1] A. Picallo, J M Sala, C. Escudero, A comparative analysis of two thermoeconomic diagnosis methodologies in a building heating and DHW facility, Energy and Buildings 146 (2017) 160e171.

9.7

Advanced exergy theory

As we know, by combining the Theory of Exergy with Economics we can determine the cost of destroyed exergy in any installation. This information, which could not be obtained with a conventional energy analysis, provides the installation operator (and of course the designer) with very useful information, since by being evaluated and

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identified the costs of inefficiencies they can be reduced, allowing the optimization of the installation, both in the operational phase and for a later redesign. Thermoeconomics is, therefore, a powerful tool, but the truth is that it is rarely used among building professionals and in particular by installation engineers. We know that the exergy destruction in each component in an installation is due not only to the inefficiencies of the equipment under consideration but also the inefficiencies of the other equipment. In Section 9.5, this is what we call dysfunctions and induced malfunctions. Therefore, the interactions between components need to be thoroughly understood. We present below the fundamentals of a theory that decomposes the origin of exergy destructions and treats those interactions in a different way, known as Advanced Exergy Theory (AET), and which was proposed by Tsatsaronis1999 [34] and Tsatsaronis and Park 2002 [35].

9.7.1

Avoidable and unavoidable exergy destruction and costs

For a given state of technology, due to existing physical and economic constraints, a part of the exergy destruction that occurs in a component is unavoidable. Thus, in a heat exchanger, the reduction to zero of the irreversibilities associated with heat transfer would imply an infinite surface, so that there is a minimum temperature jump below which it is not economically interesting to reduce the irreversibility. In a boiler, there are a series of processes that are highly irreversible, such as diffusion processes, chemical reactions of combustion and heat transfer, so there is a minimum exergy destruction that is obviously not zero. Therefore, for each i-th component of an installation there are irreversibilities that cannot be reduced, even using the best technologies available on the market, due to physical, technological or economic limitations. This part of the exergy destruction UN we call unavoidable exergy destruction D_ i , with the remaining part being the avoidAV able exergy destruction D_ i . Thus, the exergy destruction in an i-th component can be broken down into two components AV UN D_ i ¼ D_ i þ D_ i

(9.77)

Taking this division into account, we can define the modified exergy performance of a component i focusing on the part of the exergy destruction that is avoidable, so that 4i ¼

P_ i

UN F_ i  D_ i

¼1

AV D_ i UN F_ i  D_ i

(9.78)

It is first necessary to determine the unavoidable part of the exergy destruction. Following Tsatsaronis and Park 2002 [35] for this we consider Fig. 9.6 which repre  sents the relation between the investment cost per zP;i ¼ Z_ i P_ i   unit of product versus the exergy destruction per unit of product dP;i ¼ D_ i P_ i , so that, according to the definition of exergy efficiency this exergy destruction is dP,i¼(14i)/4i.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 9.6 Relationship between investment cost and exergy destruction in equipment.

The shaded area in Fig. 9. 6 represents the variation range of investment costs due to uncertainty and the various designs that may exist on the market for a specific component. As shown in the figure, the unit investment cost zP,i increases as exergy destruction decreases (efficiency increases). It is the behaviour shown by the vast majority of equipment. If there is a component where zP,i decreases as the efficiency 4i increases there would be no dilemma since among all the possible designs we would choose the most efficient equipment. The equipment would simultaneously present the lowest values for the cost of fuel per unit of product cF,iki and the lowest unit investment cost zP,i, so that according to the cost balance equation cP,i ¼ cF,iki þ zP,i the unit cost of the product would be minimal. Due to the technical limitations imposed by the cost of the materials and/or the manufacturing process, there is a maximum value of the exergy efficiency that cannot be exceeded, even if the investment cost continued to increase. As shown in the figure,   UN this situation defines the unavoidable exergy destruction per unit of product D_ P_ . i

In practice, this term is determined by selecting the most representative thermodynamic parameters of equipment i and looking for the maximum performance on the market. For example, for a hot water boiler, we could define the power and the flow temperature and using these two parameters search among the boilers of different manufacturers that boiler which has the maximum exergy efficiency. It is evident that this way of acting implies more or less arbitrary decisions.   UN Similarly, the unavoidable unit investment cost Z_ P_ i is obtained by searching among the most inefficient components and extrapolating a version of the equipment i that does not exist on the market due to the extremely high fuel costs per unit of   UN   UN product ðcF kÞ . Once the terms D_ P_ and Z_ P_ have been estimated, the uni

i

i

avoidable exergy destruction and the unavoidable costs of equipment on the market

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(corresponding for example to design point A in Fig. 9. 6) are obtained by the following equations  UN D_ UN _ _ DA ¼ PA P_ i

UN UN C_ D;A ¼ cF;i ki D_ A

 UN D_ UN _ _ Z A ¼ PA P_ i

(9.79)

Once the unavoidable costs are known, the avoidable costs are calculated by subtracting the unavoidable costs from the total costs and so AV UN C_ D;A ¼ C_ D;A  C_ D;A

AV UN Z_ A ¼ Z_ A  Z_ A

(9.80)

This breakdown of costs into avoidable costs and unavoidable costs is of great

AV AV interest. The sum of the avoidable costs C_ D;A þ Z_ A characterizes the potential   to reduce equipment costs much better than the sum of the total costs C_ D;A þ Z_ A since it is the avoidable costs that should be minimized, Tsatsaronis and Moran 1997 [36].

9.7.2

Endogenous and exogenous exergy destruction

As we saw in Chapter 2, when we analysed the mechanisms of irreversibility, all real processes are irreversible. By reducing the exergy destruction in a component we improve the performance of that equipment and ultimately the installation. However, as we have said, keeping in mind the physical, technical and economic limitations that exist, only a part of the exergy destruction can be avoided. In addition, due to the interrelationships of the equipment in an installation, there is a part that may be due to the irreversibilities of the other equipment, so it might be of interest to try to improve other components and not precisely the one which produces the greatest exergy destruction. All of this is pointing out to us that it is important to know the origin of exergy destructions in each component in the installation. In Advanced Exergy Theory (AET), the limits of each component are considered to be at the temperature of the reference environment and, therefore, there are no exergy losses associated with heat flow losses. The exergy losses appear when the installation as a whole is considered. Thus, the exergy efficiency of any component i in the installation is 4i ¼ 1 

D_ i F_ i

(9.81)

If D_ i ¼ T0 m_ i sg;i is the exergy destruction in the i-th equipment we see that it has two different origins: one depends on the inefficiencies of the equipment itself (expressed through the exergy destruction sg,i), while the other depends on the structure of the system and the inefficiencies of the other equipment (expressed basically through the variations of m_ i ). Taking into account these ideas, AET breaks down the

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Exergy Analysis and Thermoeconomics of Buildings

exergy destruction D_ i into two components, endogenous and exogenous destruction, so that EN EX D_ i ¼ D_ i þ D_ i

(9.82) EN

The endogenous exergy destruction D_ i , is the part of the total exergy destruction in the i-th component due exclusively to the irreversibilities in the equipment itself, when the rest of the equipment in the installation operates in an ideal way, with efficiencies of 100%. It is therefore evident that the endogenous exergy destruction is associated with the inefficiencies that take place in the equipment itself. The exogEX enous exergy destruction D_ i , is the difference between the total destruction in the component and the endogenous destruction, so it is due to the inefficiencies in the i-th component as a consequence of the inefficiencies in the rest of the equipment. We see that these concepts are similar to those we saw in previous Sections in relation to intrinsic and induced malfunctions and dysfunctions. To clearly understand the meaning of these concepts, we will refer to the sequential installation in Fig. 7.3 and present the analysis made by Tsatsaronis and Moran 1997 [36]. It is a sequential system consisting of three components, which we will now call equipment A, B and C, so that the product of the first component A is the fuel of the second B and so on, with the total product of the installation, which is the product of equipment C, being constant. Considering that there are no exergy losses, the exergy balance of the installation is F_ T ¼ P_ T þ D_ A þ D_ B þ D_ C

(9.83)

For component C, taking into account that P_ C ¼ P_ T the exergy destruction is   1 D_ C ¼  1 P_ T (9.84) 4C According to this expression, it is evident that the exergy destruction in C only depends on its irreversibilities. Therefore, the exergy destruction in this equipment EN is the destruction of endogenous exergy D_ C ¼ D_ C . However, carrying out an exergy balance for equipment B, gives   1 D_ B ¼  1 4C P_ T (9.85) 4B According to this expression, the exergy destruction in equipment B depends on equipment B and also on equipment C. Therefore, the exergy destruction in this equipment has one part which is endogenous and another that is exogenous. Likewise, carrying out an exergy balance in equipment A, gives   1 _ DA ¼  1 4B 4C P_ T (9.86) 4A

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so the exergy destruction in equipment A depends on the irreversibilities in equipment A, and also those of B and C. If the other two components worked ideally, that is, 4B ¼ 4C ¼ 1 then the exergy destruction in A would be the endogenous exergy destruction. Many works have been published which undertake the breakdown of exergy destruction into endogenous and exogenous components. The so-called thermodynamic method has been applied in refrigeration cycles, with the work of Morosuk and Tsatsaronis 2006 [37], and Tsatsaronis et al. 2006 [38,39] being noteworthy. For installations that have combustion reactions, some more appropriate methods have been developed, such as the graphics method devised by Kelly 2008 [40]. Due to the difficulties that arise in the breakdown of the endogenous and exogenous components, a method called the breakdown method has recently been devised that significantly reduces the computational time and effort required and which is based on the idea that the concept of exergy is independent of the facility structure, Penkhun and Tsatsaronis 2017 [41].

9.7.3

Applications of Advanced Exergy Theory

Once we have introduced the concepts of endogenous and exogenous, and avoidable and unavoidable exergy, we can combine them with each other. In this way, for any i-th component in an installation, we will distinguish between the avoidable endogeAV;EN nous part of exergy destruction D_ i which can be reduced by improving the efficiency of the i eth component, the avoidable exogenous part of the exergy destrucAV;EX tion D_ i which can be reduced by improving the efficiency of the remaining components and of course by improving the efficiency in the i-th component itself, UN;EN the unavoidable endogenous part of exergy destruction D_ i which cannot be reduced because of technical limitations for the i-th component and the unavoidable UN;EX exogenous part of exergy destruction D_ i that cannot be reduced because of technical limitations in the other components. Table 9.2 shows the four categories of exergy destruction and their characteristics and Fig. 9.7 shows the breakdown of the exergy destruction into its various categories. Table 9.2 Characteristics of the four types of exergy destruction. Endogenous

Exogenous

Avoidable

May be reduced through improvements in the efficiency of component considered

May be reduced by structural optimization of the general system or improvements in the efficiency of the other components

Unavoidable

Cannot be reduced due to technical and process limitations of component considered

Cannot be reduced due to technical and process limitations in the other component of the system

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Figure 9.7 Schematic representation of the types of exergy destruction.

In the same way as for the exergy destruction, the costs associated with the exergy destruction are broken down into four components: costs of the avoidable endogenous

AV;EN AV;EN part of exergy destruction C_ D;i ¼ cF;i D_ i , costs of the avoidable exogenous

AV;EX AV;EX ¼ cF;i D_ i , costs of the unavoidable part of the exergy destruction C_ D;i

UN;AN UN;EN ¼ cF;i D_ i and finally costs of endogenous part of exergy destruction C_ D;i

UN;EX UN;EX ¼ cF;i D_ i . the unavoidable exogenous part of exergy destruction C_ D;i EN _ The endogenous capital and maintenance cost Z i is the cost of the i-th component

EX if the other components in the installation work ideally, while the exogenous cost Z_ i is the additional cost that must be invested in the i eth component due to the exergy destruction in the other components. Combining these costs with the avoidable and unavoidable costs that we saw above, we find four types of investment costs: avoidable AV;EN endogenous capital investment costs Z_ i , avoidable exogenous capital investment AV;EX UN;EN , unavoidable endogenous capital investment costs Z_ i and unavoidcosts Z_ i UN;EX able exogenous capital investment costs Z_ i . Fig. 9.8 shows a diagram of the breakdown of investment costs, Tsatsaronis 2007 [42].

Figure 9.8 Diagram of the breakdown of investment cost.

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There are many publications in which AET has been used. We would highlight its application to combined cycles, in Tsatsaronis and Pisa 1994 [43] and Petrakopoulo et al. 2012 [44], to a new electricity generation system, Tsatsaronis and Morosuk 2010 [45], and in supercritical plants, Wang et al. 2012 [46]. Although far fewer, there are also relatively recent publications in which this method is applied in the building sector. The work by Wang et al. 2012 [46], the exergy analysis of energy consumed in a building from primary energy, by Accikalp et al. 2014 [47,48], and its application to a trigeneration plant, by Accikalp et al. 2014 [49] all deserve to be highlighted.

9.7.4

Examples

Let us consider an experimental installation for heating and DHW production located in the Laboratory for the Quality Control of Buildings (LCCE) of the Basque Government. It consists of a Stirling micro-cogeneration engine with an electric power of 1 kW and a thermal power in the form of hot water between 3.7 and 5 kW, which can provide additional thermal power of 20 kW by means of an auxiliary boiler. There is also a 28 kW condensing boiler for hot water. The DHW branch has a plate heat exchanger and a deposit of 1000 L. The heat generated for heating is dissipated in a fan coil with a three-way valve. The installation also has a hydraulic compensator, circulation pumps and distribution pipes, and 120 sensors that record the temperatures, pressures and flow rates of the different flows over time, see the diagram in Fig E.9.13.

Example E.9.6.

Figure E.9.13 Diagram of the installation.

The control of the installation is such that the Stirling has priority over the boiler so that it is the first component to activate when the temperature of the DHW tank drops below 60 C and until it reaches 70 C, or when there is heating demand. The auxiliary boiler will start working when, while the Stirling engine and the condensing boiler are on, the return temperature drops below 60 C.

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Using the TRNSYS software, the heating and DHW demand profile for three terraced houses located in Vitoria was calculated. These calculated demand profiles are reproduced faithfully by the installation control system, acting on the DHW valve and the three-way valve associated with the fan coil. With the data collected in a trial conducted over 4 days, determine Equipment under consideration and functional analysis. Percentage of exergy destruction in each component. Avoidable and unavoidable exergy destruction. Endogenous and exogenous exergy destruction. Avoidable endogenous and avoidable exogenous exergy destruction and unavoidable endogenous and unavoidable exogenous exergy destruction in each component. (f) Distribution of the avoidable endogenous and exogenous exergy destruction and unavoidable endogenous and unavoidable exogenous exergy destruction throughout the whole of the installation.

(a) (b) (c) (d) (e)

Solution. (a) Fig. E.9.13 shows an outline of the installation. The figure also shows the equipment under consideration for the analysis, according to the criteria given below.

Before starting the analysis, the equipment to be considered needs to be chosen, and the functional analysis needs to be performed on each of them. Some components need to be considered together with others in order to assign them a productive process. For example, the outgoing manifold and the return manifold considered individually do not have a productive purpose, but if we consider them together, as a single component (equipment C), their productive purpose is the heating and DHW supply. Something similar happens with the separator and mixer (equipment V1) and with the threeway valve and the mixer, (equipment V2 and V3). Considered together they have a product which consists of DHW and heating supply, DHW only and heating only, respectively. In this way, we have selected the equipment that appears in Table E.9.10. Table E.9.10 List of equipment considered for analysis. Name

Description

S

Stirling cogeneration engine

CB

Condensing boiler

ITF

CB inlet temperature controller

C

Outgoing and return manifold

HC

Hydraulic compensator

V1

DHW and heating mixer and separator

V2

HX mixer and separator

HX

Heat exchanger

V3

Heating mixer and separator

T

Thermal energy storage

FC

Fan Coil

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Once the equipment has been selected, using the experimental data from the trial, a grey box model was built for each one of them. To this end, we used the TYPE of TRNSYS that was considered most appropriate, and when incorporating the test data, parameters were adjusted to the model, so that the final model incorporates the inertias and describes the real behaviour of the equipment. This was done by integrating TRNSYS with MATLAB. This development can be found in greater detail in Picallo et al. 2017 [E.2]. Fig. E.9.14 shows the integration mode of these two pieces of software obtaining the model in the case of two components, the round-trip manifold (C), and the heat exchanger (HX).

Figure E.9.14 C and HX models obtained using TRNSYS and MATLAB. (b) Performing an exergy balance in each component gives the exergy destruction. Fig. E.9.15 shows the percentage of destruction in each component with respect to the total destruction. As can be seen in the equipment where there is combustion, the highest percentages are 27% for the Stirling engine and 46% for the condensing boiler. These differences are explained, on the one hand, because the condensing boiler has greater power and on the other, because the Stirling engine has a significantly better efficiency, as it simultaneously produces electricity and hot water. (c) Unavoidable exergy destruction is calculated for each component considering it in isolation and assuming the most favourable conditions. These conditions involve small temperature differences in heat transfer and small head losses, producing the same amount of product. We see, therefore, that the definition of these conditions is to some extent arbitrary and depends on the criteria and experience of the analyst. We will now detail the criteria that were used for each component in the installation. • C/V1/V2/V3: Irreversibilities in these components are due to the mixture of flows with different temperatures and pressures. Therefore, it can be assumed that the control system acts in such a way that these differences are avoided so that the unavoidable destruction can be considered to be zero.

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Figure E.9.15 Percentages of exergy destruction in the equipment. • • • •

•

AuxCB: The objective of this equipment is to guarantee adequate temperature at the inlet of the condensing boiler. Therefore, all irreversibilities can be avoided if this flow is in the proper state. D: Unavoidable exergy destruction is defined by the selection of the fan-coil with the highest efficiency in the market. HX: Unavoidable exergy destruction will correspond to an adiabatic heat exchanger, with minimum head losses and selecting the minimum temperature difference between the average thermodynamic temperature of the hot flow and the cold flow. HC/T: Since the greatest irreversibility in the tanks is due to the mixing of the hot and cold flows, tanks with the highest stratification and without heat losses should be sought. Although they have an important effect on the irreversibilities, both the filling and emptying temperatures are fixed, as well as the filling and emptying process, which is established by the DHW demand profile. S/CB: As we have said, the components in which combustion takes place are the ones that have the greatest exergy destruction. The causes of irreversibility are friction, diffusion, mixing, chemical reactions and heat transfer. Unavoidable exergy destruction is obtained by considering small head losses in the combustion chamber, complete combustion with the theoretical air (although this increases the adiabatic combustion temperature) and a minimum temperature difference in the heat transfer between the gases and the water.

For maintaining these conditions, the unavoidable exergy destruction of each component was calculated. Once this has been calculated, the avoidable exergy destruction is obtained by subtracting the unavoidable exergy destruction already calculated from the total exergy destruction. Fig. E.9.16 shows the values obtained for DUN and DAV i i for each component during the period of the test.

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Figure E.9.16 Avoidable and unavoidable exergy destruction in each component. (d) The endogenous exergy destruction in equipment is part of the total exergy destruction that is due exclusively to the irreversibilities in that equipment. In order to calculate it, the recently developed method, known as the breakdown method, has been used, which consists in calculating the endogenous exergy destruction of a component, idealizing the behaviour of the rest of the installation’s equipment, while maintaining constant production. Fig. E.9.17 shows the application of the breakdown method for the calculation of the endogenous exergy destruction in the Stirling engine S, in the component V2, in the hydraulic compensator HC and in the plate heat exchanger HX.

Once DEN i has been calculated for each component, the exogenous exergy destruction is calculated as the difference between the total exergy destruction and endogenous exergy destruction, which is, EN DEX i ¼ Di  Di

Fig. E.9.18 shows the endogenous and exogenous irreversibilities of each of the components in the installation. As can be seen, the exogenous irreversibility decreases the closer the component is to the end of the energy chain. It is explained by the fact that, for a fixed production of heating and DHW, the equipment that is at the beginning of the energy chain needs to produce more to overcome the irreversibilities of the equipment that is further along the chain and therefore, will generate more irreversibilities. It is of interest to know the effect of each component in the calculation of exogenous irreversibilities, for which, scenarios are drawn up in which two components work with their real efficiency and the rest of the equipment functions under ideal conditions, that is, with unit efficiency. In this way, the exergy destruction induced in the i-th equipment is calculated because the need to adapt to the irreversibilities

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Figure E.9.17 Application of the breakdown method.

Figure E.9.18 Endogenous and exogenous exergy destruction in each component in the installation.

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that occur in equipment k, DEX k/i . This calculation was made by subtracting the exergy destruction in the previous step from the new exergy destruction D0i when all equipment except equipment i is ideal, which is 0 EN DEX k/i ¼ Di  Di

Fig. E.9.19 shows the contribution of other equipment in the exogenous exergy destruction of each component.

Figure E.9.19 Exogenous exergy destruction in each component due to other equipment.

Once the exergy destruction due to each of the other components in the installation, n P DEX k/i has been calculated for equipment i, the effects induced when more than

k¼1;k s i

two components are considered must be taken into account. This is the term that is known as mexogenous exergy destruction and is calculated by subtracting the previous sum from the exogenous exergy destruction, which is DMEX ¼ DEX i i 

n X k¼1;k s i

DEX k/i

(e) Once the avoidable and unavoidable, endogenous and exogenous exergy destructions have been calculated, we combine them to obtain, for each component: the reduction in exergy destruction that can be introduced by improvements in the equipment DAV;EN ; the reduction i in exergy destruction that can be made by improvements in the other components and the structure of the installation DAV;EX ; the unavoidable exergy destruction because of the i equipment itself DiUN;EN and that due to the structural restrictions of the installation and to the technical limitations of the other equipment DUN,EX Fig. E.9.20 shows the results obtained for each component.

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Figure E.9.20 Distribution of exergy destruction in the equipment. (f) Finally, Fig. E.9.21 gives the percentages of the four types of exergy destruction in the installation as a whole. As can be seen, 76% of the exergy destruction is unavoidable, of which 30% is due to the limitations of the equipment and 46% to the structural restrictions in the interrelations of the equipment.

Figure E.9.21 Percentages of the types of exergy destruction in the installation. [E.2] A. Picallo, J M Sala, G Tsatsaronis, S. Sayadi. Dynamic Advanced Exergy Analysis in Building Heating Systems. Dynamic Modelling, Avoidable/Unavoidable, Endogenous/ Exogenous and Mexogenous Exergy Destruction Assessment

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Subscripts T e in s n, m

Total Inputs to the system Internal External Number of components, number of flows in the system

Superscripts ref, real 0 free control, anom UN, AV EN, EX

Reference state and real state Environmental state Free condition Intervention of the control system, anomalies Unavoidable, avoidable Endogenous, exogenous

Scalars DFT 4j 4j kj kij rij usj x jMFi fih jji p Ini MFi DFij

Impact on fuel Exergy efficiency of j-thcomponent Modified exergy efficiency of j-th component Unit exergy consumption of j-th component Marginal exergy consumption Recirculation parameters, PF formulation Product output of j-th component, PF formulation Independent variables Coefficients of malfunction impact Coefficients of jIi matrix operator Coefficients of jRi matrix operator Characterization property of the processes Indicator Malfunction of the i-th component Dysfunction generated by the j-th component on the i-th component

Matrices and vectors F, P, I, R, D kF , kP C, CF, CP Z MF

Vectors of Fuel, Product, Irreversibility, Residue and Destruction of dimension (n,1) Unit exergy costs vector of fuels (n,1) and products (n,1) Exergoeconomic costs vector of flows (m,1), fuels (n,1) and products (n,1) Investment and maintenance costs vector (n,1) Malfunctions vector (n,1)

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DF MF* [MF] [DF] hPFi hKPi t hFT Fi jIi, jPi, jRi

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Dysfunctions vector (n,1) Malfunction costs vector (n,1) Malfunctions matrix (n,n) Dysfunctions matrix (n,n) Matrix (n,n) whose elements are the recirculation coefficients rij Matrix (n,n) whose elements are the marginal exergy consumptions kij Transpose vector of external fuel portion of each component(1,n) Matrix operators (n,n), PF formulation

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Section D Sustainability and exergy in buildings

Sustainability and exergy in buildings

10.1

10

Summary

In this chapter, we will highlight the importance of using exergy to evaluate the sustainability of buildings and their facilities. In accordance with the knowledge we have already acquired, we know that the exergy method is a powerful tool for promoting the most efficient use of resources, since it can be used to locate and quantify the true magnitude of losses and residues. We will begin the chapter with some considerations concerning sustainability, presenting the need to analyse products and services throughout their life cycle, giving an introduction to externalities and raising the problem of limitations on resources. We will then undertake a brief review of different tools for the analysis of sustainability, from Energy Content and Carbon Footprints to Life Cycle Assessment (LCA). We then justify the idea that the exergy method is of great help when evaluating sustainability since it can serve as an indicator to characterize the depletion of resources, whether they be energy resources or raw materials, as well as to characterize emissions. We will further present the exergy tools that have been developed for this purpose and end the chapter with an example in which we apply exergoenvironmental analysis to a cogeneration installation. Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00010-2 Copyright © 2020 Elsevier Inc. All rights reserved.

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Considerations concerning sustainability

Throughout its history, humanity has selected energy systems based on two fundamental parameters: technical availability and economic viability. Only in recent years has a new variable been considered that determines the acceptance or rejection of an energy system, that variable being the environmental impact that the energy’s use may cause. In the current energy setting, this new factor is acquiring an ever-increasing weight, to the point that it is already a decisive parameter when evaluating and comparing the different sources and technologies that will shape the energy future of many countries, Martinez-Val 2004 [1]. One of the most characteristic aspects of industrialized countries is the consumption of goods and services. The production and consumption of these goods and services have an important impact on nature that until recently was practically ignored. Nowadays, the degradation of the environment has given rise to the development of an environmental conscience in society and its environmental implications, UNDP 2000 [2]. It is important to bear in mind that products that apparently give the same service can, however, be radically different if there is an accountability of the environmental costs of their raw materials, their production, transport and use. In the seventies and eighties, efforts in the field of energy were aimed at improving the efficiency of its use and of transformations up to its final use, as well as in the utilization of new energy sources. However, in the mid-nineties concern began to turn towards the protection of the environment, and the search for energy systems that had a lower environmental impact. Analysis methods were developed that took into account not only the energy consumption (exergy) and economic profitability but also began to place importance on aspects such as the scarcity of energy sources, as well as the degradation of the environment. These effects related to the scarcity of resources and environmental impact began to be considered, not only during the phase of use of the product considered but also throughout its entire life cycle, from its design, construction and use, to the end of its useful life with the corresponding recycling of materials. Thus, at the end of the nineties, matters of sustainability began to be introduced in the design and operation of energy systems. Nowadays, the idea is being established that the resolution of environmental problems involves taking into consideration the global character of the environment. Overall, actions aimed at improving the environment and human activity, based on scenarios that contemplate specific and local aspects, are doomed to fail in the long term, since they do not optimize resources and may even be counterproductive. Without a global analysis what is achieved is the transfer of environmental load (amount of pollutant that reaches the environment or amount of resources extracted from it) or its effects but not its reduction. This transfer can occur between facilities, geographical areas, temporal spaces, between environmental goods (air, water, soil) or between impact categories (acidification, toxicity, destruction of the ozone layer, etc.). An example of displacement of environmental impacts is that produced in the state of California, where, in an attempt to reduce photochemical fog, manufacturers were

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pressured to use methyl chloroform, which is not active in that sense, but which is a potent destroyer of the ozone layer. If we consider, for example, the purification of wastewater, it seems obvious that it is beneficial for the environment, but to what extent? This purification involves the consumption of energy (generated elsewhere through polluting processes), the use of chemical products (whose production processes also contaminate), the emission of certain gases into the atmosphere and the creation of certain sludges. Consequently, in our studies and projects, we must expand our horizons to consider the environment in both a temporal and global way. In short, in a broad sense, we must consider the whole of human society and its environment, that is, we must contemplate the concept of sustainability. Already in 1987, the well-known Brundtland Report [3] established that sustainable development is development that meets the needs of the present generation without compromising the ability of future generations to meet their needs. We present below a series of basic concepts needed to tackle the complex problem of sustainability.

10.2.1 Life cycle Current evidence seems to indicate that human activities are affecting the chemical composition of the Earth and its energy balances, with consequences that may be catastrophic, as indicated by what we call climate change. Therefore, the analysis and design of systems, and in particular of buildings, should be expanded through space and time, considering the entire ecosystem as the system to be analysed and the life cycle as the relevant time scale. Therefore, it is necessary to consider that a building has a limited life and the effects associated with the end of its useful life must be included, since the demolition of the building can have important repercussions, with regards to whether or not it has recyclable materials. In addition to these repercussions at the end of the chain, the initial effects must also be taken into account, that is, the environmental impact, consumption of resources and energy associated with the materials needed to raise the building. With regards to energy conversion facilities in general and in particular those of buildings, global analysis of the whole life cycle is the only way of being able to compare different technologies, and this is despite subjective aspects that may be incorporated into the methodology. In fact, the only way to evaluate renewable energies is through these life cycle methodologies. Thus, a photovoltaic system does not generate emissions in its operational phase, so that the life cycle is the only way to account for emissions, since these can only occur in the preparation phases of the semiconductor material and the manufacturing of the modules, as well as the effects associated with the rest of the elements, that is, the supports, the electronics, integration in the building, etc., Dones and Frischknecht 1998 [4]. By taking this perspective into account, a powerful, systematic and objective tool is needed that can evaluate the environmental impact of the products and that includes all the stages of their life cycle, as well as all their possible effects without geographical, functional or temporal limits. Life Cycle Assessment (LCA), Heijungs 1990 [5] has

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emerged as just such a tool and, although some methodological aspects are still being developed, companies and public administrations are successfully applying it to design products, improve processes and plan medium- and long-term environmental strategies. LCA is a fairly recent technique, which has been developed since the early nineties, even though its origins go back to the seventies when energy analysis of products began, Kl€ opffer and Grahl 2014 [6]. The methodology continues to be developed today, with many complex issues that are the subject of discussion among experts yet to be resolved, mainly in relation to impact analysis.

10.2.2

Environmental externalities

Since the sixties, there has been a growing general concern about the degradation of the environment, as a consequence of emissions caused mainly by fuels. Since then, the effects of acidifiers, chemical compounds such as CFCs and fungicides that damage the ozone layer, and Greenhouse Gases (GHG) have been of great interest. This is reflected in recent trends, particularly in the emphasis on sustainable development and the use of market mechanisms for environmental regulation. The damage that pollution produces in the environment translates into costs that fall on society and which are not reflected in the market economy. These are called external costs. In economic terms, an external cost or externality appears when the social or economic activities of one group of people have an impact on another group, and that impact is not fully accounted for by the first group. The source of externalities lies in the absence of ownership of many goods, such as the air we breathe. The existence of these costs implies an inefficiency in the economy and poor distribution of resources. There are several reasons for the growing interest in the quantification and monetization of generated environmental impacts: • • • • •

The need to integrate environmental aspects when selecting between different materials and energy technologies. The need to evaluate the costs and benefits of stricter environmental standards. The increase in attention paid to the use of economic instruments in environmental policy. The need to develop general indicators of the environmental behaviour of different technologies to allow for comparison between them. The existence of various political initiatives to achieve a greater impact of market mechanisms in the energy sector (privatizations, subsidy limitation, liberalization of the energy market, etc.).

Monetization allows the internal costs and environmental costs to be put on the same basis, which makes it possible to compare them and also to compare the different energy alternatives, something that cannot be achieved with the use of other tools, see Fig. 10.1. All these issues are reflected in recent legislation at the European level. The Maastricht Treaty of 1993 [7] introduced the principle of sustainable economic development, respecting the environment, as the main objective of the European Union, and the Fifth Environmental Action Programme clearly indicates the need for an analysis

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Figure 10.1 Monetization of environmental costs.

of externalities and their economic valuation. It is in this European framework that an important project was developed with the aim of developing a methodology for the analysis of external costs and applying it to the energy sector within the EU. The so-called ExternE Project 2005 [8] was a huge advance over previous work on the calculation of externalities, developing a much more reliable methodology. In the United States, there is a greater tradition for the monetary valuation of impact on the environment and health, and in the use of legislative instruments to internalize external costs in decision-making, especially in the energy sector. The best example of the potential use of the results of externalities analysis in the United States is the requirement made by several state energy commissions to include externalities in their planning and decision making. Trade in SO2 emissions is another example of the possible use of the results. Although there is a consensus regarding the definition of external costs, there is less clarity when defining its limits, so that the determination of externalities is very complicated. It can be divided into three groups for simplicity, according to the criteria laid down by Owen 2004 [9]. • • •

Hidden costs supported by governments. Costs of damage caused to health and the environment, excluding global warming. Costs of global warming of the Earth.

The first category includes the cost of regulatory and inspection bodies (generally small-scale) and the cost of subsidies received by the energy industry, which are not so small; for example, the government expenditure on research in the nuclear field also falls into this category. In any case, what concerns us here are the other categories. The second category can be a significant percentage of total external costs depending on the fuel used. It comprises a wide variety of external effects, from that caused by acid rain, damage to health caused by sulphur and nitrogen oxides, the toxicity of

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heavy metals, etc. Other costs included in this category are accidents in the energy industry, in coal mines, on oil rigs, in nuclear power plants, etc. The probability of a nuclear accident is extremely low, but the multiplying of this probability by the enormously high value of the damage caused, results in very high cost. The third category is the most controversial and important. Estimates of the economic implications of global warming are very large in the studies which have been carried out to date, although the range of values found is very broad, OECD 2015 [10]. Despite the progress made, there are enormous difficulties in the analysis of external costs, and there are great uncertainties in their estimation. For most pollutants, the damage caused on a global scale is not known with precision, and furthermore, the interactions between the different pollutants at that scale are very complex. However, this does not mean that these costs are less real, and their existence must, therefore, be recognized by governments when considering possible energy options and use of materials. There are a series of facts that we must take into account: • • •

Natural resources are limited, so we must preserve natural systems (soil, water, air and biological diversity). There are limits on the capacity of the planet to regenerate, and it seems that we are surpassing or have already exceeded those limits. In addition, we must consider that economic development is not a panacea that justifies the reduction of environmental quality.

The problem may be that prices reflect the marginal costs of production so that externalities need to be internalized in such a way that prices reflect the marginal costs of social opportunity, Sciubba and Frankl 2009 [11].

10.2.3

Social externalities

According to classical economists, Hicks 1946 [12], the concept of growth is associated with an increase in the amount of matter and energy used that make possible the economic activities of production and consumption of goods and services. Since the environment in which we live is finite, it seems clear that unlimited growth is not possible. By bearing in mind the social aspects, growth at the expense of consumption of geological capital must be limited by the cost imposed on future generations. A unit of resource (for example, 1 kg of any material) that today has a monetary value V will have, after n years and considering a constant interest rate i, a value V(1 þ i)n. It is clear that we cannot assure our descendants that, for each unit of a resource we use today, we will be able to generate the V(1 þ i)n value of the same resource for future use. In addition, economic growth requires extra space for humans and their activities, which implies that the space of other species is invaded. Continuous expansion of the human economy is incompatible with the maintenance of ecological systems and biodiversity. Economic growth, environmental protection and social equality should

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be interdependent, although very often policies attempting to achieve those objectives are in conflict. Finally, it should be pointed out that we must make a clear distinction between growth and development. Growth, which is generally expressed through Gross Domestic Product, implies a higher consumption of natural resources and is, therefore, not sustainable in a finite environment. On the other hand, development implies a qualitative improvement and, therefore, does not need an increase in the consumption of materials and energy over the capacities of regeneration and absorption by the environment. So, paraphrasing Sciubba and Frankl, sustainable development is development without growth.

10.2.4 Limitation of resources All materials, minerals and fossil fuels that we use are included in the term resources. The extraction of resources is responsible for a large number of environmental problems, the main ones being: •

•

Effects associated with mining and the purification of extracted minerals. Aspects related to environmental pollution include the production of waste, the emission of polluting substances and the loads associated with the production of the energy needed to extract the resources. Effects associated with the reduction in the availability of resources.

In referring specifically to this second aspect, there are still several issues that need to be considered, Heijungs 1997 [13]: • • •

Depletion of reserves. Loss of options for future generations. An increase in the environmental impact of mining in the future because easily accessible resources are the first to be exhausted.

The term reserves is, of course, controversial in itself. Guineé and Heijungs 1995 [14] gave several different definitions of what can be understood by reserves, since it is not clear whether the total reserves of the geosphere should be considered, or only the reserves capable of being extracted from a technological point of view, or only the reserves capable of being extracted from the point of view of economic profitability, or a number of other viable definitions. These concepts may alter over time, although, generally, the concept of the extractable geological reserve is currently used. Quantification of depletion is done in terms of elements or compounds depending on what is relevant for the depletion. For example, with respect to aluminium what matters is the amount of the Al element present in the mineral, regardless of the mineral’s composition. With fossil fuels what matters is the chemical composition, which is what determines their convertibility into energy (natural gas is considered to be a resource, but not carbon or hydrogen). With regards to wood, which is a natural resource of great importance in construction, excessive logging leads to deforestation, with enormous effects, Fig. 10.2.

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Figure 10.2 Logging.

Authors such as Huppes 1993 [15] argue that the depletion of energy resources is not problematic, due to the fact that the discovery of new deposits of fossil fuels is still increasing and the greater potential for their substitution with clean energies. However, this substitution is a very long-term process and may never be completely successful, so it is better to have a conservative view, apart from the fact that relying on this substitution is an unfair obligation on future generations. To conclude this introduction, it is worth remembering the three rules of economist H Daly [16] on the limits of sustainability. For a renewable resource, the consumption rate should not be higher than the regeneration rate. For a non-renewable resource, the sustainable consumption rate should not exceed the rate at which a renewable resource, sustainably used, could replace it. Finally, for a pollutant, the emission rate should not be higher than the rate at which this pollutant can be recycled, absorbed or neutralized in its sink. These are the limit conditions of the economic-social model that we need.

10.3

Sustainability in buildings

Today’s society and its standard of living and well-being are intimately linked to the consumption of large amounts of material and energy resources. An important part of these resources is consumed in the tertiary sector (residential and services) which, together with transport, form the so-called diffuse sectors. The measures that need to be carried out to limit energy consumption in these sectors are more complex to implement than in the case of industry. Buildings, throughout their construction, use and demolition, are the origin of a large amount of environmental impact, due to the energy used to provide them with necessary services, as well as the materials used in their construction. They effect the thinning of the ozone layer, as a result of the use of various chemical products,

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such as CFCs, HCFCs, etc., and climate change, due to significant CO2 emissions, both in the construction phase and during their lifespan. A building uses energy throughout its life, from its construction to its demolition. The consumption of energy during the life of a building is broken down into two components: direct energy and indirect energy. Direct energy is used in construction, use, renovation and demolition, while indirect energy is used by the building during the development of the materials that go into making it up, both in the building’s envelope and technical facilities, Adalberth 1997 [17]. The building sector plays a very important role in the consumption of natural resources and emissions into the atmosphere. A large number of environmental problems are caused or directly related to the intensive use of materials, water and conventional energy sources needed for the construction and use of buildings. Currently, as we saw in Chapter 1, the contribution of buildings to total energy consumption worldwide is 40%, while they are responsible for about 50% of materials used and 50% of waste generated. Unlike what happens with the products of industries with industrial processes in series, construction forms part of an industry that performs its processes in situ, in the place where the building stands. Once the work is finished, building activity moves to a new space, with a limited temporary stay. In addition, unlike industrial products, which have a short and intense life cycle, construction products exist for an extended period. However, once demolition starts, it is difficult to separate components, which makes reuse or even recycling difficult, and although these components are mostly inert materials, they occupy a large amount of space in landfills.

10.3.1 What is sustainable construction? Given these considerations, the question that arises is: what does sustainable building really consist of? Many terms appear in connection with this concept such as bioclimatism, renewable materials, recycled materials, solar energy, water reuse, waste management, etc., and they are, of course, related to each other. In buildings, we use some resources (fuel), and the buildings have a utility (product). After its useful life, the building is demolished, and some materials that appear to have lost their usefulness (waste) are returned to the environment. Strictly speaking, sustainability means keeping natural capital constant, which implies returning resources to the same level at which we found them, that is, closing material cycles, Fig. 10.3. Regarding energy, we know that during the life cycle of a building there are a series of irreversibilities that give rise to a corresponding exergy destruction, which is irretrievable. Therefore, although we talk about material cycles, it does not make sense to talk about an energy cycle, precisely because of that irretrievable destruction. For its part, closing material cycles require energy consumption, adequate technology and a society that is interested in carrying out these processes of cycle closure. This closing of the material cycles entails a radical demand on our technical systems, and in general, we do not have the capacity to do so. Consider that, for example, closing the material cycle of fossil fuels would involve collecting the products of combustion and using them to re-form the molecular chains of the original hydrocarbons.

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Figure 10.3 The strict meaning of sustainability.

The biosphere is the means we have available to face the challenge of closing material cycles. In effect, the biosphere is able to collect CO2 and water and transform it back into fuel, but solar energy and the correct surface need to be available for this to happen. Therefore, the absorption of waste by the biosphere and its renewal into resources is limited by the amount of land available. Precisely, when we speak of renewable materials we refer to materials with a cycle closed by the biosphere, while a non-renewable material does not enter this biosphere circuit and its cycle needs to be managed by our technical systems. As the closing of the material cycles is a necessary condition for sustainability, the material flows that circulate through buildings need to be known, as well as the actions that need to be undertaken for their closure. According to data provided by Cuchí 2012 [18] for a house in Catalonia, the flows of the main materials per inhabitant and day are 3 kg of construction materials, 2 kg of CO2 associated with energy consumption, 1.70 kg of household waste and 168 kg of water. There are a series of actions that must be undertaken in order to move towards sustainable building, such as: • • • •

Proper management of waste for recycling. Replacement of materials that have greatest impact. Increase in the use of renewable materials. Increase in recycling of materials.

With regard to water consumption, in order to move towards sustainable building, we must reduce the impact on the environment caused by its consumption, through actions such as: • • • •

Improving the efficiency of water use. Recycling of water, depending on the quality needed for each use. Collection of water in the building itself. Improvement of water quality when it is returned to the environment.

Finally, with regard to energy consumption, moving towards sustainable building implies putting into practice the conclusions that we have reached throughout this book and which can be summarized in the following points: • •

Use energy sources appropriate to the needs of each use (adjust the quality of the energy). Increase efficiency in the use of energy (reduce irreversibilities).

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Use strategies to take advantage of local energy sources. Take advantage of solar energy and other renewable energies.

As we see, sustainable construction should be understood as traditional construction, but with considerable responsibility for the environment. A sustainable building has to maximize energy efficiency and comfort while producing the least environmental impact. This implies an analysis of the different alternatives in the construction process, looking for one that favours the minimization of resource depletion, that prevents environmental degradation and provides a healthy environment, both inside buildings and in their surroundings. Therefore, the term sustainable construction encompasses, not only the buildings themselves, but also takes into account their environment and how they behave to form cities. By definition, a sustainable building or eco-building interacts intimately with its surroundings. In such buildings, natural phenomena such as natural ventilation, daylight, passive heating and cooling and renewable energies are integrated into a thermally insulated envelope with efficient installations. Therefore, attention must be paid to the interaction between the occupants, the building, the climate and the environment. These aspects are evident in the design of new buildings, but it is equally important to consider them in the renovation of existing buildings. Following Lanting 1996 [19] we list in broad terms the requirements that sustainable buildings must meet: • • • • • •

Consume a minimum amount of energy and water throughout its life. Make efficient use of raw materials (materials that do not harm the environment, renewable materials). Generate minimum amounts of waste and pollution throughout its life (durability and recyclability). Use of minimum land and integrate into the natural environment. Adapt to the current and future needs of the users (flexibility, adaptability and quality of the site). Create a healthy indoor environment.

Focusing on energy, the reduction of its consumption in buildings is a key element for the improvement of energy efficiency and ultimately for sustainability. For this, the way forward will be to reduce demand, introducing new forms of energy use, maximizing the use of renewable energy sources and promoting the extensive use of ICT for monitoring and control of all functions and systems. In recent years, efforts to maximize energy efficiency in buildings have focused, on the one hand, on improving the elements of the enclosure (facades, windows, roofs) and on the other hand on the installations (heating, ventilation, cooling and lighting). Significant progress has been made, although there are still important opportunities for improvement. However, this idea has reached its limits, since the behaviour of each element depends to a large extent on the system of which it is a part, so that, for example, a heat pump depends not only on the equipment as such but also on the heating and cooling system as a whole. But considering the different systems independently is not enough. Buildings function as a whole and, therefore, it is necessary to consider them in an integral way, simultaneously contemplating the different details, such as architectural and structural aspects, the use of energy, the environmental quality of indoor air, noise, etc. These issues are developed in Section 1.11 of chapter 1.

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In this chapter, we are going to apply the Laws of Thermodynamics and show the role of the impact of human activities on natural resources and the environment. Thermodynamics can be used to analyse systems that involve interactions between ecological, economic, industrial and social processes, which are, therefore, multidisciplinary. It makes excellent contributions to the analysis of these systems, provided that their limits are well defined and that the analysis focuses on the transformations of matter and energy.

10.4

Conventional methodologies for the analysis of sustainability

Current evidence indicates that the actions of humans are modifying the chemical and energy balances of planet Earth, that is to say, that natural cycles are being affected by human interference. Nowadays there is a noteworthy international debate attempting to evaluate the latest consequences of this interference, as well as trying to find ways to mitigate those consequences. Precisely, it is the engineers and architects who have a remarkable capacity to reduce this human influence on the evolution of the state of planet Earth. To address this situation, we must expand the temporal and spatial horizon in our studies and projects, as previously stated. We, therefore, need adequate methodologies to carry out this type of extensive analysis. These methodologies, which allow a sustainability analysis of any system, must meet a series of requirements, such as: • • • •

They should cover the entire period from the “cradle to the grave” of the system and likewise should take into account its useful lifespan. They must be able to quantify environmental externalities. They should provide congruent results when applied to comparable contexts. They must be able to evaluate social externalities.

Taking into account the meaning of exergy, one more requirement that we need to add is that we must also assess the exergy destruction, in the processes of both energy and materials conversion. Precisely for this purpose, various methodologies have been developed in recent years that use exergy and which will be put forward in the final part of this chapter. Next, we will briefly describe some of the conventional methodologies, devoting more attention to LCA. Each of these methodologies collects, structures and evaluates information according to various aspects, which in many cases are complementary to each other, SETAC1999 [20]. As to which of these methodologies is the best, one cannot give a definitive answer, since it depends on our needs and the proposed objectives.

10.4.1

Analysis of environmental risks

Environmental risks caused by specific or diffuse sources of emissions are evaluated with this tool. Risks for human health in the workplace are also evaluated, UNE

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Standard 150. 008 [21]. It is a tool that has an analytical approach, with probability criteria for estimating risks. It is generally used to evaluate the levels of concentration and/or periods of exposure to a certain hazardous substance in the environment, in order to know if it is below acceptable levels of risk or not.

10.4.2 Environmental impact assessment Environmental Impact Assessment (EIA) is a tool oriented towards the management of the territory, which is used to investigate environmental changes caused by constructions such as roads, industrial plants, etc. It considers environmental effects during the construction period, as well as those that occur during the operation phase, and is a requirement for obtaining a construction or operation licence. EIA allows for the determination of whether or not the project or activity is responsible for the environmental effects it generates, through the application of mitigation, repair and/or compensation measures. In general, EIA data is detailed with respect to a specific impact and usually takes into account the duration and concentration of the pollutants emitted by assessing their impact on the environment, Allpe Medio Ambiente 2016 [22].

10.4.3 Carbon footprint A Carbon Footprint is defined as the objective quantification of greenhouse gases (GHG) issued directly or indirectly by products, services, companies, countries, etc., and whose results are reproducible and verifiable by third parties. There are different methodologies for calculating carbon footprints, the best known being the GHG Protocol [23] and the British standard PAS 2050: 2011 [24]. In Spain, the Ministry of Agriculture, Food and Environment published an official guide in 2014 [25]. In addition, there are several other methods, such as the one based on ISO 14,064 [26], the 2006 IPCC Guidelines [27], etc. The Global Warming Potential (GWP), which expresses the warming potential of a given gas over a period of time (generally 100 years) in comparison with the warming potential of the same volume of CO2 during the same time, is defined to make the effects of the different gases comparable. This is known as CO2 equivalent. Thus, the CO2 equivalent of methane over 100 years is 25, that of nitrous oxide is 298, while that of a fluorinated gas such as HFC23 is 14,800. The conversion factors are associated with the characteristics of each gas and also depend on the time in which the gases reside in the atmosphere. For assessing the carbon footprint, all sources of GHG emissions need to be identified along with the conversion factors to be used.

10.4.4 Environmental product declaration Environmental Product Declaration (EPD) consist of quantified environmental information concerning the cycle of the products (and services) in order to allow a comparison between products that perform the same function. They began to be used in 1997 by the Swedish industry; in 1998, the first EPD published in the world

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on electricity from hydraulic sources appeared, and in recent years their increase has been exceptional, The International EPD System 2012 [28]. EPD is based on an independent verification of LCA data and, are therefore, an ideal tool for making decisions based on the environmental impact of the life cycle of goods and services. They make comparisons possible through the so-called Product Category Rules (PCR), which describe the details by product for data collection, calculation methodology and presentation of results according to the LCA scheme. UNE EN 15,804:2012 [29] is a standardized PCR at European level for the realization of EPD in the construction sector. In Spain, we have the AENOR Global EPD programme, valid for any type of product/service and which has three published PCRs: steel, ceramic coating and cement. There is also the EPD programme, valid exclusively for construction products and based on UNE EN 15,804. The programme is operated by the Association of Quantity Surveyors, Technical Architects and Construction Engineers of Barcelona.

10.4.5

Environmental audit

Environmental Audit consists of carrying out physical inspections at certain points to verify legal compliance, and identify responsibilities and important risks, ISO 14,010: 1996 [30]. The audit is focussed on the activity that is being reviewed and not on the retrospective or prospective data of the process. There are also other methodologies for environmental management, such as Environmental Behaviour Assessment, Flow Analysis, Matter and Energy Analysis, Product Line Analysis, etc. We are going to focus, however, on two methodologies that are of the greatest interest to us, mainly because they are the starting point for other methodologies that use exergy.

10.4.6

Cumulative energy content

Cumulative Energy Content (EC), also simply called Energy Content, is a method that was proposed as mere energy accounting in the seventies and which evolved into a method of systematic analysis in the eighties, Herendeen et al. 1981 [31]. The main characteristics of the method are: • • • • • •

The energy value of the materials in the Earth’s crust, before their extraction, is considered to be zero. The energy of a certain product is the value of the energy accumulated in each of the stages necessary for its final use, that is, the EC accumulates the energy needed for the extraction, preprocessing, transportation, manufacturing and distribution, which goes into a product. Recycling reduces the energy content and must be taken into account. The environmental effects are taken into account considering the energy needed for total cleaning. The EC of a product is the sum of the energy contents of each of its constituents, including environmental effects. Labour and capital costs are taken into account but measured in monetary units.

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The calculation of the EC can be done using two different methodologies: macroeconomic and microeconomic. The macroeconomic methodology is based on the use of tables of industrial exchanges or input-output tables. It requires an accurate energy analysis of production processes and a good knowledge of national accounting. It has the advantage of being a general calculation method for all complex systems. On the other hand, in the microeconomic or technical methodology, the different stages of product manufacturing are considered, and the quantities and forms of energy brought into play are evaluated. It is very complicated for systems that involve several manufacturing processes, with diverse technologies and materials. Cumulative Energy Content has notable deficiencies that limit the possibilities of its application since the environmental impact of a product or service cannot be estimated only in terms of its EC so that it only makes sense in combination with other methods. Its main limitations are: • • • •

It does not take into account the intrinsic energy content of the materials in the Earth’s crust. It does not distinguish the quality of energies. Regarding environmental effects, it only considers the energy needed in the final part of the cycle, so that effects due to mining are not taken into account. For capital and labour, the cost is expressed in monetary units, while the rest is expressed in units of energy.

10.4.7 Life cycle assessment (LCA) The first agreed definition of Life Cycle Assessment (LCA) was given by the Society of Environmental Toxicology and Chemistry (SETAC), a leading association in its methodological development, Consoli et al. 1993 [32]. LCA provides a complete view of the environmental impact and consumption of resources of a given product. The information it provides, combined with trends in technological development, can be used to forecast the environmental profiles of possible future scenarios. The methodology of LCA is regulated by the standards ISO 14,040 [33], ISO 14,041 [34] and ISO 14,042 [35]. In the ISO 14,040 standard, a definition is given: “LCA is a technique for assessing the environmental aspects and potential impacts associated with a product by: compiling an inventory of relevant inputs and outputs of a product system, evaluating the potential environmental impacts associated with those inputs and outputs and interpreting the results of the inventory analysis and impact assessment phases in relation to the objectives of the study”. We give a summary of this methodology of environmental analysis below, there being abundant bibliography in this regard, such as Curran 2015 [36] or Kl€ opffer and Grahl 2014 [37].

10.4.7.1 LCA stages LCA must be carried out in four interrelated work phases, which follow a more or less defined sequence, although sometimes it is possible to carry out a not so ambitious study, avoiding some of them. Fig. 10.4 shows the LCA phases that interact with each other.

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Figure 10.4 Phases of LCA.

10.4.7.1.1

Definition of objectives and scope

10.4.7.1.2

Life Cycle Inventory

This first phase should include both the exact definition of the objectives and the scope and depth of the study, to determine the purpose for which the results obtained and the conclusions drawn will be used. In the scope of the study, the functional unit, its limits, necessary data, hypotheses and limitations must be defined. The boundaries of the system, both geographic and temporal, must be clearly established, as well as any assumptions made. The functional unit (FU) is defined as the system from which all the inputs and outputs are referenced in phase two, Life Cycle Inventory (LCI). An example of FU for the life-cycle of a house may be: construction, use for 60 years and end of the useful life of a detached house of 140 m2 built surface in Bilbao. If, for example, we wish to compare two exterior paints, we can take FU as the amount of paint needed to maintain one square metre of wall in good condition for 10 years. In this way, two paints A and B of different characteristics can be compared.

Life Cycle Inventory (LCI) is the next phase of LCA and corresponds to the inventory of environmental loads, that is, the identification and quantification of all flows of materials, energy, water and contaminants entering and leaving the system. Its result will be an extensive table consisting of all the system interactions with the environment; they are direct interactions with the environment, not with the technosphere. These interactions, which are called loads, can be inputs (consumption of natural resources) or outputs (emissions to the atmosphere, water and soil during the entire life cycle of the product). Although many LCAs involve managing complex systems, there are precise guidelines on how to proceed, SETAC1993 [32]. Considering all input and output flows may be really impossible; ISO 14,041, under the heading of Relevant and Irrelevant Processes, recommends that the economic importance and/or the estimate of the relative contribution to the environmental

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impacts produced be taken as a basis. In addition, the validity time, the geographical area and the technology that the inventory includes needs to be set and its level of reliability and representativeness must be established. A database is needed in order to carry out an inventory. On this basis, there is a large number of fundamental inventories already completed, such as, for example, the inventory of 1 kg of steel, of 1 TJ of thermal energy in a natural gas furnace, of 1 km per kg in transport by truck, etc. Without the existence of this multitude of fundamental inventories, the undertaking of any LCA is unfeasible. As an example, in Fig. 10.5 the production inventory of 1000 kg of aluminum is shown.

10.4.7.1.3

Impact assessment

Once the inventory has been done, the quantities of matter, energy, emissions and waste produced have been determined, but their impacts have not yet been related to the different compartments of the environment. Then the next LCA phase starts, which is the Impact Assessment, in which the inventory data is linked to the damages caused by the inventoried substances, through characterization factors. Impact analysis techniques help convert the result of the inventory (a table of hundreds of pieces of data referring to different amounts of environmental loads at all stages of the process) into a list of a few pieces of data interpreted according to their ability to affect the environment. This consists of a technical phase, considered mandatory by the methodology, and of an optional phase of a political nature. The process is generally carried out in several steps, called: classification, characterization and normalization. In each of these steps, the data coming from the inventory is manipulated, reducing them successively in quantity or complication and facilitating their interpretation. However, this simplification has its price: compared to the objectivity of the inventory data (within the margins of error that it has), each new step in the simplification incorporates a certain subjectivity, so that when we reach the end of the process we may find a single number or environmental index to describe the system (assessment stage), easy to interpret, but very subjective.

Figure 10.5 Life Cycle Inventory for the production of 1000 kg of aluminum.

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Exergy Analysis and Thermoeconomics of Buildings

In the classification, the data obtained in the inventory phase is classified by impact categories, taking into account which impacts can potentially cause. Once classified, the flows are converted into impacts, and the characterization phase starts, in which the flows assigned to a particular category are quantified using a common unit for that category, through characterization factors. The analysis is carried out in a series of impact categories, such as ozone depletion, acidification, eutrophication, toxicity or depletion of resources. Keep in mind that the same emission can generate different impact categories. Thus, CFC emissions are responsible for the disappearance of the ozone layer and at the same time have a significant influence as GHG. On the other hand, different emissions may contribute to the same environmental impact with different values. Consoli et al. 1993 [32] define characterization as a stage in which a quantitative analysis takes place and where the aggregation of impacts within defined categories is possible. Once the impact categories have been defined, quantitative results are obtained through characterization models, with the results expressed by means of indicators. For example, within the greenhouse effect impact category, if an equivalence factor of 1 is assigned to CO2, methane is assigned a factor of 11. This characterization is based on the concept of GWP. In other impact categories, other equivalence criteria between emissions are obviously used. So, therefore, for the greenhouse effect, the effect index is calculated: Greenhouse Effect ¼

X i

ðGWPi  Emissioni Þ

(10.1)

This quantification and aggregation should be based as much as possible on scientific knowledge. The definition of the characterization factors (or equivalence factors) suitable for human and ecological toxicity is one of the biggest problems faced by LCA, Guineé and Heijungs1993 [14]. ISO 14,042 recommends that the characterization model should take into account the complexity of the mechanisms, spatial and temporal characteristics and the dose-response type. An optional step within the characterization is the normalization of the indices of each category. The indices obtained after the characterization determine the contribution to well-known environmental problems. The meaning of the resulting numbers, however, is far from obvious. Such indices can gain meaning if we convert them into relative contributions to the different problems through normalization. At this point, Guineé 1994 [38] proposed dividing the indices of the different effects between the total amount of these same indices, for a certain area and a certain period of time. The result of this stage would be called normalized environmental profile. The characterization (and normalization) results in an environmental profile (normalized), which as far as possible is the product of empirical knowledge concerning economic and environmental processes.

Sustainability and exergy in buildings

10.4.7.1.4

809

Evaluation and interpretation of results

After the previous phases, a valuation is made for both the comparison of products and their improvement. At this stage, the results are interpreted, taking into account the defined objectives and scope, the hypotheses and limitations, etc. In the comparison of goods or services, the category indices of the environmental profiles of the different products have to be compared with others, while with regards to the improvement of products, it is necessary to determine which aspects should preferably be improved. The valuation is the quantitative or qualitative stage in which the relative importance of the different impact categories is weighted. It consists of the weighted aggregation of the indices of the different impact categories. Multiple methods of valuation have been developed, some based on monetization and others on the distance to a goal. The principle of monetization is to attribute monetary values to each impact category, Lindeijer 1996 [39], considering economic mechanisms as a correct guide for weighting. The most developed monetization methods are the EPS system and the Tellus method. In the methods based on the distance to the objective, pollution standards or environmental quality objectives are used to perform the weighting of the impact categories. The general form of application of these methods is the multiplication of the normalized indices by a quotient between the current impacts and the objective impacts. The Eco-Indicator 95 method, or the Eco-Indicator 99 method, Preconsultants 2000 [40], corresponds to this philosophy of analysis based on scientific criteria as far as possible, constituting a reproducible and widely accepted methodology. Despite being a very complete method of analysis, LCA has important limitations, since all LCA involves certain hypotheses and subjective evaluations that must be clearly reflected. As the results depend on these hypotheses, one must be very cautious in the use of the results. Finally, it should be noted that LCA does not include economic aspects, so for decision making other indices need to be used, not included in LCA. The stages in an LCA require the handling of a large amount of data from inventories, followed by numerous calculations that are applied to characterization factors, category indices, etc. At present, there are a number of computer applications in the commercial field. When deciding on one of these programmes, one must take into account the inventories that they include (if they are specific to the area in which we wish to use them), as well as the quality in the management of the data, mainly the flexibility in the use, updating, substitution, etc., of the data in the inventories and the reliability of the calculations made. The lack of traceability of some construction products revealed the need to have applications with appropriate inventories to cover the wide range of materials and construction processes. Some of them were developed as a result of specific research programmes, with objectives associated with the project, and were only later commercialized. Table 10.1 shows a selection of the most representative programmes, indicating the organization that created it, the object and the country of origin.

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Exergy Analysis and Thermoeconomics of Buildings

Table 10.1 Software for the LCA of construction products. Software

Organization

Object

Country

ATHENA

ATHENA sustainable materials institute

Materials and construction systems

Canada

BDA

ATHENA sustainable materials institute

Databases

Canada

EcoQuantum

PRé consultants

Construction systems

Holland

ENVEST

BRE-British research establishment

Construction systems

United Kingdom

EQUITY

Centre scientifique et technique du batiment

Construction systems

France

LCA-house

VTT-building technology

Construction systems

Finland

10.4.8

Examples

Calculation of the EC of a flat roof We shall calculate the EC of a flat roof. The roof corresponds to a development of 79 council houses and annexes located in Bilbao-La Vieja. The plot forms part of the new area that emerged after connecting El Casco Viejo with Miribilla continuing from the San Ant on Bridge, see Fig. E.10.1.

Example E.10.1.

Figure E.10.1 Housing development with flat roof.

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We will refer the study to 1 m2 of roof surface with a useful life of 80 years (functional unit). We will assess heat losses through the roof during winters, but we will not consider the monetary costs of capital and labour. Fig. E.10.2 shows a section of the flat roof, which is composed of the following layers, from the outside to the inside.

Figure E.10.2 Section of the flat roof. • • • • •

Gravel protection layer 8 cm thick. Polyester separation layer. Extruded polystyrene insulation layer of 5 cm. Waterproofing with double asphalt cloth of 6 cm thickness. Standardization with 10 cm expanded clay mortar.

Solution. First of all, the inventory of all the components necessary to build the roof and then the energy consumed in transporting the materials to work must be defined. After this, consumption must be taken into account during the assembly phase and the use phase of the component to be studied and finally recycling and depositing in a landfill. Regarding the gravel protection layer, the origin of the gravel is unknown, so the generic process of the Ecoinvent database “Gravel, unspecified at the mine” was taken as a model. As the quantity of gravel used to manufacture one square metre of roof needs to be known, the common density of the gravel, which is 2000 kg/m3, was used. Since the thickness of the gravel layer is 8 cm, 0.08 m3 per m2 of roofing is needed, which means a total of 180 kg. The insulation layer is 5 cm so that with the density of the extruded polystyrene being 35 kg/m3, 1.75 kg is required. The “Polystyrene, extruded (XPS) at plant” process was selected as a model from the Ecoinvent database. Insulating materials,

812

Exergy Analysis and Thermoeconomics of Buildings

such as extruded polystyrene, consume a considerable amount of energy in their manufacture, although this energy is more than compensated for by the reduction of energy they provide in the use phase of the building, in this case, in its application in the roof. Given the impossibility of finding a process that serves as an approximate model for double asphalt, it was necessary to create our own, from the raw materials and energy needed in its manufacture, as well as the waste that this process produces both in the atmosphere and in the water and soil. The data was taken from the ATHENA report A LifeCcycle Inventory of selected commercial roofing products. The process was created with the name SBS Impermeable Membrane. There is a double asphalt cloth of 6 cm thickness on the roof and the weight of the asphalt sheet was found to be 4 kg from the TEXA manufacturer’s catalogue. In the managed databases there was no process that could represent the expanded clay mortar layer, so a new one was created called Expanded Clay Mortar, composed of expanded clay (49% by weight), Portland cement (7%) and water (44%). As the thickness of the layer is 10 cm, for each m2 of cover 220 kg is needed. Below, Table E.10.1 shows the approximate inventory of materials transport from the production plant to the construction site. Most of the distance data has been taken from the approximate average distances for the EU provided by Ecoinvent, although some data was taken directly from the distance between the nearest factory and the construction site. Table E.10.1 Transport of materials to the site. Material

Weight (kg)

Distance (km)

Data source

TRANSPORT (tkm)

Gravel

160

20

Ecoinvent

3.2

Extruded polystyrene

1.75

230

Basf iberica Tudela

0.4

Waterproofing

4

50

Ecoinvent

0.2

Leveling mortar

220

20

Ecoinvent

4.4

Total

82025

For the transportation of all materials, the “20e28-ton transport lorry, fleet average” process was selected. This process includes the 20e28-ton truck operating sub-processes, its production and disposal and the construction, maintenance and elimination of the road. In order to evaluate the heat losses through the roof, a model of the building was built using the DesignBuilder software tool (EnergyPlus), and a dynamic thermal simulation was carried out. For this, DOY-E’s climatological data in the TMY archives for Bilbao, and the thermal conductivities and thicknesses data returned for the roof in the project were used. Annual losses through the roof of 28 kWh/m2 were generated. When analysing only the roof and not the entire building, heat losses through the corresponding roof during the months of September to May of each relevant year were considered in the use phase. From the Ecoinvent database, a heat generation process was chosen using a natural gas boiler “Heat, natural gas, at boiler modulating”.

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Finally, in the demolition and waste treatment phase, all activities that have the purpose of the final dismantling of the roof and the treatment of the corresponding waste generated were included. Both the energy resources used during the demolition and the transportation from the site to the landfill were examined, considering that all the waste generated is taken to a controlled landfill. In Table E.10.2 and Fig. E.10.3 the results obtained are shown. The use phase accounts for 78% of energy consumption, which as can be seen in Fig. E.10.3 comes almost entirely from fossil resources.

Table E.10.2 EC results for the flat roof (MJ/eq).a Impact category

Totala

Construction of the roof

Use phase

Transport to construction

Waste scenario

Total

6370.0

1367.4

4972.8

26.8

2.9

Non renewable. Fossil

6190.3

1272.2

4890.1

25.1

2.9

Non renewable. Nuclear

143.6

76.8

65.3

1.4

0.1

11.9

8.6

3.2

0.0

0.0

Renewable wind, solar, geotherm

1.8

0.6

1.2

0.0

0.0

Renewable. Water

22.3

9.0

13.0

0.3

0.1

Renewable. Biomass

a

Energy units per FU, that is, per square meter of flat roof.

Figure E.10.3 EC results for the flat roof.

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Exergy Analysis and Thermoeconomics of Buildings

Example E.10.2.

LCA of an inclined roof We shall now undertake the LCA of a sloping roof using the SimaPro software. The roof corresponds to a housing development in Muskiz (Basque Country), see Fig. E.10.4. The sloping roof, Fig. E.10.5, is composed of the following layers, from the outside to the inside:

Figure E.10.4 Housing development in Muskiz (Basque Country). • • • •

American asphalt plate 0.5 cm thick. Mortar of 4 cm thickness. Reinforced concrete layer 22 cm thick. Projected rock wool mortar 3 cm thick.

Figure E.10.5 Detail of the sloping roof.

Solution. Given the impossibility of modelling the American asphalt plate as a database process, a ceramic tile was taken from the Ecoinvent database as a representative process: “Roof tile, at plant”. The weight of this layer per FU, 1 m2 of cover, is 11 kg since this is indicated in the catalogue by the distributor “Bricomart” (Valencia). The mortar compressing layer consists of a conventional Portland cement mortar. Since the

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thickness of the layer is 4 cm and its density is 1200 kg/m3, the mass of mortar is 48 kg/FU. The “Cement mortar at plant” process was selected from the Ecoinvent database. As indicated in the project report, the concrete to be used in this roof must be HA-25/B/20/I with B400S quality steel. It is considered to be reinforced concrete with an approximate density of 2400 kg/m3, resulting in a mass of 582 kg/UF. In order to model this type of concrete, a process was created in Simapro from structural concrete and corrugated steel bars with the name Concrete Roof. Given the impossibility of modelling the wool mortar with a database process, the representative process taken was “Rock wool at plant” with a density of 250 kg/m3, resulting in a mass of 7.5 kg/FU. The approximate inventory for the transport was carried out analogously to the previous Example E.10.1 for the flat roof, obtaining the results that are shown in Table E.10.3. Table E.10.3 Transport of materials to the site. Material

Weight (kg)

Distance (km)

Data source

Transport (tkm)

Gravel

11

50

Ecoinvent

0.55

Extruded polystyrene

48

20

Ecoinvent

0.96

Waterproofing

550

20

Ecoinvent

Leveling mortar

7.5

230

Rockwool international A.S. (Caparroso, Navarra) Total

11 1.72 14.23

In order to evaluate the heat losses through the sloping roof, a model of the building was built using the DesignBuilder software tool (EnergyPlus), and a dynamic thermal simulation was carried out. For this, DOY-E’s climatological data in the TMY archives for Bilbao, and the thermal conductivities and thicknesses data returned for the sloping roof in the project were used, resulting in annual losses through the roof of 22 kWh/FU. The Eco-Indicator 99 method was used, which reduces all environmental impact results by weighting coefficients to a single value known as the Eco-indicator. The Eco-Indicator is a number that tells us the environmental impact of the roof from the LCI data. The higher the indicator, the greater the environmental impact. There are three types of damages: •

Damage to human health. This refers to the number of diseases that a person suffers throughout their life and the average duration. This concept is expressed in a unit known as “DALY” (sum of years of life lost and of years lived disabled, a term also used by the World Bank and WHO).

816

•

•

Exergy Analysis and Thermoeconomics of Buildings

Damage to the quality of the environment. This refers to the loss of species diversity in a specific area and at a specific time. Among the effects considered are eco-toxicity, acidification and eutrophication, and land use (these will constitute the impact categories associated with this type of damage). Damage to resources. It takes into account that, as the natural resources of the land are extracted, their extraction supposes an increasing consumption of energy. The damage is measured as the surplus energy needed for future extractions (MJ).

The Eco-indicator 99 method allows for the selecting of different perspectives that assess the contribution of each damage category to the final value in a different way: •

• •

Hierarchical (H): This corresponds to a perspective in which it is considered that a suitable environmental policy can avoid problems, both in the short and long term. In this perspective, the following weighting is done: • Damage to human health: 40% • Damage to the environment: 40% • Damage to resources: 20% Individualist (I): Short-term problems are considered, and nature is viewed as something robust and able to adapt. Equal (E): Problems are considered as being very long term, and nature perceived as something fragile for which we must take responsibility. In this case, damage to the environment contributes 50% of the indicator value.

In this Example, a hierarchical perspective was used (the method most used in this type of analysis), in which the values of the weighting coefficients are those indicated above. The results obtained are shown below in Fig. E.10.6. As we can see, the use phase is the one that has the greatest impact among all stages of the life cycle (62.7%), with the contribution of the construction phase being smaller (35.5%). The remaining impact is attributable to transport to the site and the future demolition of the building.

Figure E.10.6 Points of each stage of the inclined roof example.

Sustainability and exergy in buildings

10.5

817

Exergy and sustainability

For the sustainable development of society in general and of the building sector in particular, a sustainable supply of natural resources is needed. This statement has important consequences since it implies a supply of long-term resources at a reasonable cost and the need for them to be used in the most efficient way possible. In this way, the benefits of the use of these resources are maximized and negative impacts, such as environmental damage, are minimized. Most natural assets are finite, so their efficient use contributes to development over a longer period of time. This efficient use must be kept in mind even with resources that are readily available and cheap at a given time. By taking these ideas into account, exergy is presented as an essential concept and the exergy method as a powerful tool to promote the most efficient use of resources, since it allows for the location and quantification of the true magnitude of losses. In addition, as we have seen, the exergy method reveals if it is possible or not and how possible it is, to design more efficient energy systems, reducing inefficiencies in existing systems. Thus, exergy analysis provides us with the knowledge of how effective and balanced a society is with regard to the consumption of its physical resources. This information can be used to identify areas in which technical and other improvements can be made, as well as to indicate the priorities that should be assigned to improvement measures. Establishing a comparison between different societies in the world and analysing the international system can be of great importance, if we really are serious in our efforts to achieve a distribution of resources in a fairer world. While the exergy of a material or form of energy is a measure of its utility, it is also a measure of its potential to originate a change, that is, exergy can provide a basis for measuring the potential of an energy or a material to cause an impact on the environment. We know that exergy is a measure of the imbalance of a system with the environment. A material found in nature or created artificially, in imbalance with the environment, can be considered a natural resource and its value as a resource is associated with its reactivity (in the case of fuels) or its composition (in the case of minerals). The degradation of resources reduces their exergy and ultimately reflects damage to the environment. Polluting emissions, inasmuch as they are not in equilibrium with the environment, have the potential to cause a change, and the exergy of these emissions represents a potential to modify the environment. This change is associated with damage to health, buildings, etc., and also interferes with the exergy of solar radiation, causing problems such as climate change. Increasing efficiency generally reduces environmental impact and has implications for sustainability since it extends the useful life of natural resource reserves, Rosen 2008 [41].

10.5.1 Exergy as a method of resources characterization It is clear that the resources we use to improve our standard of living play an important role in any discussion about sustainable behaviour. It is important to know the

818

Exergy Analysis and Thermoeconomics of Buildings

availability of these resources, how efficiently they are used, when they will be exhausted and, in addition, how to assign those resources among the different species and generations on the planet. In this regard, Thermodynamics can be very valuable in the accounting of resources and the provision of criteria for the allocation of costs. Traditionally, natural resources are usually divided into energy resources and raw materials. This separation, however, is nothing more than an approximation. Oil, for example, is considered to be an energy resource and wood, a raw material. However, oil is used in the production of many useful materials, such as plastics, insulation, etc., and wood can be used as fuel. Likewise, the amount of extra insulation used in the construction of a building must be compared with the energy savings achieved in the use phase of the building. Therefore, it would be convenient to consider both resources jointly. Natural resources, energy and raw materials, are presented either as flows or as deposits. Thus, the flow of solar radiation, water flows and wind flows are natural flows. A natural flow has a limited size, but usually lasts a long period of time. However, oil and fossil fuels are presented as deposits, so that a deposit can give rise to a flow if it is gradually used. In turn, deposits can be classified as dead or live deposits, a classification that depends on the time they take to accumulate when regenerating. Natural flows and live deposits constitute what we call renewable resources. Energy resources (oil, natural gas, coal, solar radiation, wind, etc.) can obviously be added depending on the energy but exergy is more suitable than energy for the description of these resources, due to the factor of quality. But it is also true that exergy can characterize not only energy resources, but also non-energy resources. Exergy carries information, within itself, on the difference in concentration between the extracted raw materials and the geosphere, so that the greater the difference between the concentration of a substance in the reference environment and the deposit from which the raw material is extracted, the greater will be the exergy. Thus, the factor that determines the quality of material resources through exergy is the dispersion term (the greater the dispersion, the lower the exergy). On the other hand, if a mineral deposit of high concentration (high exergy) is depleted, other reserves of exergy (those of fuels) can be used for the exploitation of poorer deposits. This justifies the value of exergy as an interchangeable indicator of energy and nonenergy resources. The exergy content of energy resources is obtained by simply multiplying their energy content by the quality factor that is applied to the energy form in question, Dincer 2002 [42]. Material resources are measured in units of mass, volume, etc. To express them in exergy units simply multiply their quantity by a factor, which corresponds to the specific chemical exergy, as we saw in Chapter 3. In this way, the balance of resources that are usually broken down into energy and raw material balances are integrated into a single balance. When we spoke about the depletion of resources as an environmental problem, the loss of choice for future generations and the greater contamination that will occur in the future as a result of having to extract increasingly dispersed minerals were cited as problems. Exergy gives an accurate measure of this problem, since the smaller

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the exergy of the minerals, the greater the exergy needed to extract them. Thus, two copper mines may contain the same amount of copper, but if the concentration is different, the amount of exergy within the mineral (which is inversely proportional to the exergy needed to process it) will be lower when its concentration is lower. Nature has made available to man resources whose formation has taken thousands and thousands of years, and the Sun has provided (and continues to provide) the exergy necessary for the formation of these high exergy resources (for example, fossil fuels). The current extraction rate of natural resources is vastly superior to that of their regeneration, which is the root of the depletion problem and results in a progressive consumption of the exergy of natural resources. Fig. 10.6 shows a map of the places in the world where natural gas reserves exist. In the case of energy resources, although the chemical exergy is not related at all to the greater or lesser availability of a given resource, it represents a valid criterion for its characterization, since it describes the equivalence between resources. The case of non-energy resources is different; although in fossil fuels the exergy is determined primarily by its molecular form, in a resource such as iron, what is of interest are the Fe atoms themselves. But, obviously, the amount of iron on the Earth remains constant. There is change only in the concentration and the molecular structure to which the atoms are associated. So, when we speak of depletion, what exactly is used up or consumed? We have already seen that, given a sufficient amount of exergy, it is always possible to acquire the desired amount and the desired concentration of a mineral. This leads to the conclusion that exergy is the limiting factor. However, the weakness of exergy as a characterization of depletion resides in the fact that it does not properly represent the scarcity of resources. For example, iron ore can have a very high concentration in a deposit and, although iron is a fairly common element in nature, this high concentration can give rise to a high exergy value and, therefore, to the factor of the iron characterization. On the other hand, if we consider a

Figure 10.6 Natural gas reserves in the world.

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Exergy Analysis and Thermoeconomics of Buildings

scarce element, such as gold, if a deposit of low concentration is exploited, a low exergy value may result even in spite of the low gold content in the Earth’s crust. Therefore, gold has a low characterization factor because it is an extremely scarce resource. This seems to show some weakness in the characterization criterion based on exergy, Gaudreau et al. 2009 [43]. In summary, the use of exergy to describe resources does not take into account aspects related to extractable reserves or the current rate of consumption, so that the problem of depletion is observed from a purely energetic perspective. In energy resources, exergy has a clear meaning, while in non-energy resources what is measured is the exergy necessary to acquire the concentration in the exploited deposit starting from the average concentration in the geosphere. The first systematic efforts to use exergy as a generic measure for all resources (long before the occurrence of LCA) were carried out by Wall 1977 [44], who tried to describe the exergy flows in the Swedish economy, Wall 1987 [45]. Later the same author applied these ideas to the economy of Japan, Wall 1990 [46] and Italy, Wall et al. 1994 [47] and other authors did the same for the economy of the United Kingdom, Gaspartos et al. 2012 [48,49], of China, Chen and Chen 2009 [50], etc. Although Wall’s ideas were a driver for exergy accounting of non-energy resources, he incorporated imprecise exergy calculations in his work. In this context, the book by Valero and Valero 2014 [51] on exergy and the limited nature of mineral resources, in which they present a detailed cradle to grave analysis of the mineral resources of the Earth, is noteworthy. Their reflections on the fact that the growth of the exploitation of minerals on Earth in the last 120 years is an exponential function and that new materials (such as In, Te, Pt, etc.) are the basis of the new green economy are very interesting. On the other hand, recycling of materials and critical elements is almost nil, but even if we recycled 100%, it would still not be enough since the demand rises faster for many metals. The authors of this interesting work tell us that the social and environmental impact of mining continues to increase, and although the mining sector contributes only 0.5% worldwide to direct employment and 0.9% to Gross Product, mining consumes between 8% and 10% of global energy and is responsible for 13% of global SO2 emissions. These authors believe that global mineral production will require exponentially increasing amounts of energy that will affect Earth’s climate much more than today. Therefore, they recommend that it is time for humanity to manage its nonrenewable resources intelligently. Finally, it should be noted that until recently exergy was a forgotten concept in buildings and their thermal installations. However, as we have seen in previous chapters, if we use exergy to characterize the energy efficiency of a building as the relationship between the exergy demand (for example, for heating) and the resources used to satisfy it, we find values that hover around 6%. This indicates that if we had not looked at exergy, we would not have been aware of the enormous irreversibilities that take place in buildings and, consequently, these great environmental problems and their solutions would have remained hidden, Kilkis 2010 [52]. Therefore, in recent years several exergy indexes have been developed to evaluate the behaviour of sustainable buildings, Schmidt 2009 [53].

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10.5.2 Exergy as a method of emissions characterization Exergy can not only be used as a measure of the inputs to a system but can also characterize the outputs. We know that most of the time exergy is lost as heat at low temperature, which heat is rarely harmful to the environment. But, sometimes, it is lost in the form of chemically reactive materials, which are part of the type of flows that we called residue in Chapter 8. These residues, after a proper treatment, are sent to the environment and constitute not only unused exergy but chemical species in imbalance with the environment and which can cause pollution problems, see Fig. 10.7. In short, it can be said that pollutants are susceptible to being classified as such because they have exergy. Ayres et al. 1996 [54], therefore, proposed to characterize the emissions of pollutants according to their exergy, since this gives a measure of the distance to the equilibrium of these pollutants and, therefore, of their reactivity. Thus, exergy serves as a criterion to characterize in an LCA not only the inputs to the system (resources) but also the outputs (emissions). This form of characterization has the advantage of being applicable to all emissions, which eliminates the problem of comparing different impacts, Ayres et al. 1998 [55]. Although it seems a contradiction, exergy in the form of a resource is of value, whereas, in the form of emission it is detrimental because of its ability to produce environmental damage. To understand this point well, we must assess whether this exergy is limited or not. The resources found in the environment are restricted precisely due to their exergy, while exergy emissions to the environment can freely interact with it in an uncontrolled way, Rosen 2002 [56]. It is clear that exergy cannot be used as the only tool for the characterization of emissions. First, exergy does not measure the reactivity of a material flow, that is, the physical reactivity (for example, due to thermal imbalance) nor the chemical reactivity. This has a component related to the concentration difference, a concentration gradient that gives rise to diffusion processes not associated with environmental

Figure 10.7 Emission of gases to the atmosphere.

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Exergy Analysis and Thermoeconomics of Buildings

problems. Thus, the diffusion of CO2 concentrated in fumes down to the concentration in the atmosphere is not in itself a problem. But, although we referred to the chemical exergy associated with the existence of chemical species different from those present in the RE, this exergy cannot be indicative of the toxicity or the dangers of an emission. We know that any method of impact analysis in an LCA must be based on the perniciousness of the emissions. It is clear that Thermodynamics alone cannot determine the dangers of an emission and that other aspects that have to do with chemical kinetics, biology, geology, etc. must be considered.

10.6

Exergy methodologies for the analysis of sustainability

Different tools have been developed that use exergy to evaluate the sustainability of energy systems. In most cases, this is an extension of conventional methods, to which exergy analysis has been added, in order to assess the exergy destruction in the conversion processes of matter and energy. Below are the most relevant characteristics of some of the more interesting methods.

10.6.1

Cumulative exergy content

This is an extension and refinement of the Cumulative Energy Content method, shown in Section 10.4.6. Szargut et al. 1988 [57] introduced the concept of Cumulative Exergy Content (CExC) which, for a given product, includes exergy consumption in all stages of its production process, from raw materials to the final product. This concept corrects the defects of the Cumulative Energy Content method, which does not take into account non-energy resources and does not allow an assessment of the degree of thermodynamic perfection of the production processes. Since the exergy is cumulative, for a flow that undergoes a series of thermodynamic transformations, the accumulated exergy value is an adequate measure of the quantity and quality of the energy exchanges that this flow has experienced. Therefore, Szargut et al. proposed characterizing each goods or service with its corresponding CExC, obtained from the sum of the exergy contributed to the different flows involved in its manufacture, from the exergy of the raw materials that constitute the initial entry to the process. The CExC values can be calculated separately for each particular type of primary exergy so that they can contain only the sum of the non-renewable primary exergy, or refer to the totality of the primary exergy. This last case is generally considered since it is impossible to distinguish between the irreversibilities associated with renewable and non-renewable energies. There are two methods to calculate CExC that we can call sequential and simultaneous. The sequential method (process analysis) begins at the final stage of the manufacturing of the product under consideration, and the exergy used throughout the intermediate processes (manufacturing of products and manufacturing of the

Sustainability and exergy in buildings

823

machines and equipment used) is accumulated until reaching the first phase of raw materials extraction from natural resources. It allows for the analysis of a single product each time and can be applied when the consumptions in the first phases of the product manufacturing are small and can be neglected. Fig. 10.8 shows a diagram of the energy and manufacturing chains of the equipment on which this method is based. The simultaneous method is more general and complex since it requires the simultaneous formulation and solution of the set of balance equations for the different useful products of the sector considered. These balances are based on the fact that the CExC assignable to the useful products comes from the sum of the CExC that characterize the materials used, the semi-finished products and the energy vectors employed. Szargut defined the cumulative degree of perfection of a process (CDP) as the quotient between the exergy of a product and the total exergy used in the production of said product, and undertook the calculation of this value for a good number of products and fuels, Szargut 1987 [58]. For example, in the production of 1 kg of cast iron, raw materials provide an exergy of 1.2 MJ and the energy used has an exergy of 49.84 MJ, with the exergy content of 1 kg of cast iron being 8.2 MJ, which gives rise to a CDP of 16.1%. In almost all products, the predominance of fuel exergy over raw materials exergy can be seen. At least in the initial approach of this method, labour is not taken into account, and both capital and environmental costs are expressed in monetary terms. The method can be applied to any technological chain and with different levels of aggregation. As an alternative to what is proposed in this method, the limits of the system can be moved up to solar radiation. This implies that conversion from primary energy to solar radiation should be included for all systems. This type of analysis is proposed in methodologies such as the so-called Exergy Cumulative Ecological Consumption (ExCEC),

Figure 10.8 Energy and manufacturing chains of equipment for a product.

824

Exergy Analysis and Thermoeconomics of Buildings

Extended Exergy Analysis (EExA), Sciubba 2001 [59] or Emergy Analysis, about which a few comments will be made below. However, moving all the processes to the last energy source implies increasing the imprecision of the data used and this is precisely one of the biggest criticisms of this type of analysis.

10.6.2

Emergy analysis

Emergy Analysis (EmA) is a method that quantitatively expresses the value of all products based on equivalent solar energy. It was developed by Professor Odum of the University of Florida, 1971 [60]. Odum considered the biosphere as the source of resources and environmental services and that this came from solar energy. All natural resources are expressed in terms of the equivalent solar radiation (direct and indirect) required for their formation, and this is precisely the concept of emergy. Analysis by emergy can discern the energy quality of biosphere flows; for example, 1 kJ of grass is not the same as 1 kJ of meat. Energy transformations originate hierarchies, similar to hierarchies in food chains in ecosystems. The application of EmA to biological systems provides an interesting insight into the complex energy cascades of the biosphere. However, its applications in the world of engineering are limited by the numerous hypotheses and simplifications that need to be made.

10.6.3

Exergy life cycle assessment

Exergy analysis and LCA were developed separately. In Section 10.4.7 we presented a summary of the LCA phases, and we saw that it is a tool that can be used to minimize the environmental impact of the products analysed. Now, this tool can be made more powerful if it is used in combination with exergy analysis. For achieving sustainable development, the exergy destruction in the use of natural resources must be minimized to such an extent that the supply of exergy to future generations is assured and that no harm is done to the environment. Exergy Life Cycle Assessment (ELCA) is a method proposed by Cornelissen in 1997 [61]. It can be defined as an extension of exergy analysis to the entire life cycle of the products analysed, presenting a structure similar to that of LCA. In effect, the definition of objectives and the scope is the same, but the inventory phase is more complete in ELCA, since for each of the production stages the mass and energy balances need to be closed, before calculating the flow exergies and undertaking exergy balances. ELCA examines the flow exergies and serves to identify irreversibilities in the various stages of a product life cycle. It gives the total irreversibility of the life cycle, with the aim of reducing the exergy destruction and thus improve the efficiency of the processes. The improvement analysis can be done incorporating Thermoeconomics, that is, taking into account the monetary costs. The emissions of pollutants are considered as simple exergy losses so that the toxicity or the polluting potential of this waste is not taken into account.

Sustainability and exergy in buildings

825

Its advantages with respect to LCA are the same as those of CExC with respect to CEC, that is, considering the exergy instead of the energy allows a correct evaluation of the resources and their final use since the exergy, sustainability and the environmental impact are related to each other. Evidently, ELCA also has the limitations that we commented on with respect to LCA in Section 10.4.7. In a reversible process, there is no depletion of resources or emissions to the environment, since the exergy of the fuel and the product are equal. However, in real processes, in general, there are exergy destructions and emissions so that the exergy of fuel (resources) is always greater than that of the product. Cornelissen introduced a variation in the ELCA concept in order to take polluting emissions into account. The method consists of completing the process so that the exergy of the emissions is cancelled, through separation and transformation processes. These separations and transformations suppose an additional exergy expense, which is the exergy consumption that is assigned to the different emissions. With this method, which he called ZeroELCA, the environmental problems associated with emissions are incorporated in a certain way and not only the depletion of resources. It is, therefore, a question of characterizing the emissions according to the exergy necessary for them to have zero exergy. Actually a process is considered sustainable when the level of emissions is below the minimum threshold. Therefore, instead of zero exergy emissions, the aim is to achieve sustainable emission levels, or more properly, an exergy level sufficiently low to ensure an acceptable level of sustainable development. In our opinion, this method presents two difficulties. In the first place, there are only defined processes for the sustainable reduction of certain very localized emissions, but how do we calculate, for example, the exergy required to reduce the problem of methane emissions due to natural gas leakages during transport? On the other hand, as already mentioned above, the exergy needed to reduce emissions is not related in principle to the toxicity or dangerousness of those emissions. This can frequently lead to incorrect results since a less toxic emission would be more influential in the result, if its elimination is very costly in terms of exergy when compared to another very toxic emission whose elimination would require little exergy.

10.6.4 Extended exergy accounting Extended Exergy Accounting (EEA) is similar to ELCA with the difference that now the three factors of production (capital, labour and materials) are expressed in terms of their exergy value. The time interval for calculating these exergy flows covers the entire life of the installation, from the extraction of raw materials, construction, use and demolition phase, Sciubba 2003 [62]. Although it is money (capital) and not energy which is the main parameter for evaluating human activities, we must bear in mind that the economic system is only a portion of the ecosystem and that it is maintained thanks to the flows of materials and energy that come from the ecosystem. This is precisely the point of view that justifies EEA, which on the contrary considers exergy for the quantification of these flows.

826

Exergy Analysis and Thermoeconomics of Buildings

The treatment of environmental externalities in EEA is similar to what we saw in Section 10.6.3 for Zero-ELCA. Let us consider a process in which residue is produced, that is, flows with chemical compounds that are not present in the RE and at a pressure and temperature different from those of the RE. To achieve zero environmental impact these flows must be brought to a thermal and chemical equilibrium with the RE, so the additional process necessary for these output flows to have zero exergy, will require the consumption of energy, of raw materials, labour and equipment. These additional consumptions of exergy should be assigned to the product of the main process so that the overall efficiency of the process will be lower, Sciubba 2012 [63].

10.6.5

Exergoenvironmental analysis

Finally, we will devote greater attention to the method known as Exergoenvironmental Analysis (AExA) which is an extension of Thermoeconomics taking into account environmental aspects, by internalizing the external costs caused by polluting emissions. It is based on the idea that exergy constitutes a rational basis not only for allocating costs but also for evaluating environmental impacts and inefficiencies in the systems. The point of view of Thermoeconomics is modified so that a problem of economic valuation becomes one of ecological evaluation. To this end, a methodology has been developed that combines Thermoeconomics with a method of environmental impact assessment, such as LCA. The advantage of using LCA is that, on the one hand, it takes into account the complete life cycle of the system and on the other that the impacts on the environment are directly determined by environmental models. A series of environmental loads occur in the life cycle of any system, but in a system with several products we need to distinguish which environmental loads correspond to which products. This question is framed within a methodological problem that exists in LCA, called allocation of loads (or just allocation). The allocation of loads is far from simple in most cases and there has been much discussion about the methodology to be followed. Due to a lack of thermodynamic evaluation, LCA is not capable of allocating environmental impacts generated in an installation to each of the components that go into making it up. If the physical causes of the environmental loads are determined and associated with the different products of the installation, what we are doing is eliminating the allocation problem since, by breaking the system up into smaller sub-systems, we can trace the creation process of environmental loads. In principle, a method such as Thermoeconomics, which serves to distribute the economic costs of fuel and investment, can also serve as a basis for the allocation of environmental costs. The allocation of costs based on exergy is a rigorous way of calculating product costs (but not market value); in this way, the inefficiencies of the installations, which are responsible for the consumption of resources and the origin of the costs, can be identified, allocated, quantified and attributed. The calculation of exergy costs, therefore, serves as a parameter for allocating environmental loads among the products of the plant. Thus arises exergoenvironmental analysis which combines exergy analysis with an environmental assessment method such as LCA, Meyer et al. 2009 [64].

Sustainability and exergy in buildings

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Figure 10.9 Analogy between exergoeconomic analysis and exergoenvironmental analysis.

In AExA, the problem of calculating exergoeconomic costs turns into a problem of ecological evaluation. The analogy between Exergoeconomic Analysis and Exergoenvironmental Analysis is shown in Fig. 10.9. The allocation of environmental impact to the flows is done in a similar way to the allocation of exergy costs (and exergoeconomic costs) in Thermoeconomics. In this way, the exergoenvironmental cost of a flow i, A_ i , is defined as the environmental impact associated with the generation of that flow, expressed, for example, in Eco-Indicator points per unit of time (Pts/s). Likewise, the specific exergoenvironmental cost of an i-th flow, ai, is defined as the environmental impact associated with the generation of that i-th flow per exergy unit and is expressed, for example, in Pts/GJ. Evidently, the environmental impact of flow A_ i is the product of the specific environmental impact with the flow exergy, that is, A_ i ¼ ai B_ i . The methodology of AExA, basically, consists of three stages: in the first, exergy analysis of the system is carried out. In the second, LCA of the installation and of each one of the incoming flows coming from the outside is undertaken, using an impact quantification method, for example, based on Eco-Indicator 99. In the third stage, the environmental impact obtained from LCA is allocated to each of the flows using the Thermoeconomics Propositions, thus calculating the exergoenvironmental properties of each flow and performing the corresponding exergoenvironmental analysis. As an example, consider an installation made up of different components and let k be the component in Fig. 10.10. For a flow i in the k-th equipment the environmental impact of the mass flow rate m_ i is A_ i;k ¼ ai;k B_ i ¼ ai;k m_ i bi

(10.2)

828

Exergy Analysis and Thermoeconomics of Buildings

Figure 10.10 Balance of environmental impact on equipment k.

The environmental impacts associated with heat and work flows will, respectively, be A_ Q;k ¼ aQ;k B_ Q

(10.3)

A_ W;k ¼ aW;k W_

(10.4)

Sometimes, as we saw in Chapter 3, it may be useful to break down the exergy into its physical and chemical components. In this case, the exergoenvironmental cost is also broken into two components: one associated with physical exergy and the other ch ph ch with chemical exergy, that is, A_ i;k ¼ A_ i;k þ A_ i;k ¼ ach B_ i þ aph B_ i . By applying i;k

i;k

LCA we can obtain the environmental impacts of the flows that enter the facility from the exterior. The environmental impacts associated with the components will be obtained by applying LCA to each of them. The impacts associated with each one of the phases is taken into account, that is, construction (including manufacturing, transport and placement), operation and maintenance, and dismantling at the end of its useful life. Thus, the environmental impact for the k-th equipment is CONS OM DIS Y_ k ¼ Y_ k þ Y_ k þ Y_ k

(10.5)

The values of the environmental impacts corresponding to the internal flows and products of the system are obtained from functional analysis and by applying the Thermoeconomics Propositions that we saw in Chapter 7. The balance of exergoenvironmental costs in each component is obtained by equaling the sum of the exergoenvironmental costs of the inflows plus the associated costs of the equipment with the exergoenvironmental costs of the outflows. Thus, for equipment k in Fig. 10.10 we have in  X j¼1

aj B_ j



þ Y_ k ¼ k;in

out  X j¼1

aj B_ j

 k;out

(10.6)

Sustainability and exergy in buildings

829

For example, if we consider the exchanger in Fig. 10.11 from the environmental impact balance we get the following equation. a1 B_ 1 þ a3 B_ 3 þ Y_ EX ¼ a2 B_ 2 þ a4 B_ 4

(10.7)

In order to obtain the necessary m equations in the system of m flows, the Fuel and Product Propositions are also applied, both for internal and external bifurcations that we saw in Chapter 7, but now, instead of referring to the exergy costs or exergoeconomic costs we refer to the exergoenvironmental costs. For example, if in the exchanger of Fig. 10.11 the fuel is F ¼ B_ 3  B_ 4 , we have that a3 ¼ a4.

Figure 10.11 Heat exchanger.

This results in a system of m equations, the unknowns now being aj as the value of each flow. As with the exergy and monetary costs, in the case of dissipative systems, the environmental costs associated with the irreversibilities and the equipment (construction, operation and maintenance) must be distributed among the products of the equipment which they serve, according to criteria similar to that given earlier. In a similar way to Thermoeconomics, a series of exergoenvironmental properties can be defined. Thus, the fuel specific environmental cost for the i-th component is aF;i ¼

A_ F;i B_ F;i

(10.8)

and that of the product aP;i ¼

A_ P;i B_ P;i

(10.9)

830

Exergy Analysis and Thermoeconomics of Buildings

As we saw for exergy costs and exergoeconomic costs these impacts grow as the equipment under consideration comes closer to the final product of the installation, since it is incorporating the environmental impacts of the flows that preceded it. The relative difference of exergoenvironmental cost in an i-th component is ra;i ¼

aP;i  aF;i aF;i

(10.10)

We can also define the exergoenvironmental factor, so that fa;i ¼

Y_ i _ Y i þ A_ D;i

(10.11)

There are several publications in which the AExA methodology has been used. In the building sector, it has been used in the analysis of heating systems, Y€ucer and Hepbasli2014 [65], for an ORC in a trigeneration installation, Ahmadi et al. 2012 [66], for a geothermal heat pump-based system, Akbulut et al. 2016 [67], etc. Likewise, in the same way that we saw in Chapter 9, where the foundations of the Advanced Exergy Theory were given, the Advanced Exergoenvironmental Theory has been developed in a totally analogous manner. In this regard, we can highlight the publications of Renzo et al. 2009 [68], or the publication on power plants by Petrakopoulo et al. 2012 [69]. To conclude, we can say that the objective of all these methodologies is to generate information that can be used to improve the design and/or the operation mode of installations, and reducing the environmental impact of the installation as a whole. However, we must point out that all the methods we have presented for analysing environmental impact are largely incomplete. They are based on statistical data, economic impact models of the different alternatives, cost estimates, etc. Despite these difficulties and the fact that there is no one method that can be considered as definitive, they are a valuable aid to decision-making. Although there are many unresolved problems, there have been great advances in recent years, and there is no doubt that the use of any of the methodological tools given here allows us to make more accurate decisions than if we did not have them.

10.6.6 E.10.3.

Examples

Exergoenvironmental analysis of a cogeneration plant Let us consider a cogeneration plant with alternative internal combustion engines that burn natural gas, and whose exhaust fumes are directed to a recovery boiler, where steam is generated for the needs of a hospital. In addition, part of the heat from the cooling motors is also recovered for the production of hot water. The objective of this Example E.10.3 is to show how to perform Exergoenvironmental Analysis of the installation and comment on the results obtained. Solution. The Example will be developed in two parts. In the first, LCA is carried out and the results obtained are presented, using Eco-Indicator 95. Next, the application of

Sustainability and exergy in buildings

831

Exergoenvironmental Analysis method will be shown and the results finally obtained will be presented (Fig. E.10.7).

Figure E.10.7 Schematic of the cogeneration plant.

LCA of the installation LCA on the plant was first carried out. The inventory was carried out following the methodology developed by the ETH, so that ready-made modules of, for example, 1 kg of cast iron, 1 kg of concrete, 1 kg of rock wool sent to landfill, etc. were incorporated. Obviously, electrical energy is used to make 1 kg of cast iron (among other forms of energy), so in order to complete the inventory of this material, it is necessary to first start the inventory with the forms of energy used. And conversely, at some point in its process chain, any form of energy has the use of cast iron (among many other materials). There is, therefore, a recursion in the generation of the inventory, which is solved by the ETH through the use of software prepared for this purpose, and based on the matrix calculation results in the final inventory of all the modules, considering only the interactions with the environment and not with the technosphere. Given that electrical and thermal energy is produced in the cogeneration plant at the same time, and environmental loads will have to be distributed according to various criteria, 1 TJ of natural gas (with reference to the LHV) burned in the engines was used as a FU to begin and from there, FUs of 1 TJ of electrical energy and 1 TJ of thermal energy were taken. These same units were also used to compare conventional forms of generation. The reason for using TJ comes from the order of magnitude of most loads, which would be very small in the case of using a unit such as kWh.

832

Exergy Analysis and Thermoeconomics of Buildings

Most of the data used in the LCI of the cogeneration plant are taken from the inventory of the energy systems life cycle developed by ETH. This inventory is a very important database. In addition to this information, inventories of all materials, fuels, transportation, processes, etc. needed to carry out LCA on the cogeneration plant were used. Some data was also obtained from the LCA of alternative gas engines carried out at the University of Utrecht, which, due to their specific nature were considered more suitable. The inventory was carefully done for all the equipment, even breaking up each equipment into parts. Thus, for example, the motor-generators were divided into motor, alternator and bedplate, apart from the foundations. The total inventory resulted from grouping together the inventory of the different components (infrastructure), with the oil inventory of the engines, natural gas (pre-combustion inventory, which includes all the environmental loads that occur during the exploitation of deposits, the fuel preparation and its transport) and the inventory of the emissions produced during the plant operation (combustion). Adding together the results of the four inventories into which the life cycle of the cogeneration plant was separated, a final inventory was obtained, whose summary is shown in Table E.10.4. As we already know, after the inventory, further analysis needs to be carried out. The reason is that these emissions (of substances) and extractions (of resources), as they are listed in the inventory, have no meaning in and of themselves. The problems Table E.10.4 Inventory of the cogeneration plant life cycle (for 1 TJ of natural gas). Energy resources Oil gas

23.86 Nm3

Mine gas

2.58 kg

Wood

0.0037 t

Potential energy of water

0.00041 TJ

Raw brown coal

73.26 kg

Raw coal

317.0 kg

Raw natural gas

33,342.4 Nm3

Raw oil

0.351 t

Natural mineral uranium

0.0053 kg Air emissions

CO2

71,954.8 kg

CO

287.10 kg

SOx as SO2

14.84 kg

Nox as NO2

236.55 kg

CH4

719.66 kg

NMVOC

308.13 kg

Aromatics

10.2386 kg

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Table E.10.4 Inventory of the cogeneration plant life cycle (for 1 TJ of natural gas).dcont’d Air emissions PAH

0.0004 kg

Partículas

15.978 kg

Cadmium

0.0001 kg

Lead

0.0029 kg

Manganese

0.0108 kg

Rest of metals

0.02060 kg

Radionuclides

490.0729 kg Raw materials (non-energy) resources

Bauxite

6602 kg

Bentonite

6930 kg

Lead

0.223 kg

Chrome

0.727 kg

Iron

251.5 kg

Limestone

135.7 kg

Copper

2.167 kg

Nickel

0.639 kg

Silver

0.00110 kg

Zinc

0.10107 kg

Tin

0.00397 kg

Titanium

0.1 kg Water spills

Ion chloride

19.01 kg

Sulphates as SO4

5.97 kg

Ammonia as N

0.027 kg

Fats and oils

2.136 kg

Aromatics

0.128 kg

Ion Ba

0.103 kg

Ion Cr3þ

0.0106 kg

Ion Ni

0.0029 kg

Ion Pb

0.0070 kg

Ion Hg

0.00012 kg

Radionuclides

8.119.5 kg

834

Exergy Analysis and Thermoeconomics of Buildings

caused by these emissions and extractions are what is important. As we have said, there are different methodologies, although here we show the results obtained with Eco-Indicator 95, an impact analysis method with great acceptance and that was born with the aim of being a valid method at European level. The method is implemented in the SimaPro software, which was used to carry out this LCA and which is well-established in companies. In Table E.10 5, the impact values in each category are shown for the four inventories under consideration and in graphic form in Fig. E.10.8. In Fig. E.10.9 the percentage of each stage in the value of the final indicator is shown. Table E.10.5 Valuation of each stage of the life cycle (for 1 TJ of natural gas). Natural gas

Category

Infraestruc.

Oil

Combustion

Total

Greenhouse effect

0.065

0.004

2.886

12.291

15.246

Ozone layer destruction

0.021

0.033

0.185

Acidification

0.31

0.016

2.587

13.061

15.974

Eutrophication

0.012

0.002

0.445

3.575

4.034

Heavy metals

1.276

0.041

3.858

0.005

5.181

Carcinogenicity

0.463

0.021

2.094

9.287

11.865

Winter smog

0.192

0.676

0.733

0.027

1.629

Summer smog

0.021

0.023

1.718

3.518

5.280

Eco-indicator 95

2.361

0.817

14.506

41.764

0

Figure E.10.8 Contribution to each effect of the parts of the life cycle.

0.239

59.45

Sustainability and exergy in buildings

835

Figure E.10.9 Percentage of each stage in the final indicator.

Fig. E.10.10 shows the relative contribution of each effect category in each of the four stages in which it has been divided to make the inventory.

Figure E.10.10 Relative contribution of each effect in the parts of the life cycle.

Exergoenvironmental Analysis The exergoenvironmental cost is an extension of the concept of exergoeconomic cost and is the method that we have used to allocate the environmental loads to the flows in the energy plant. A flow has an associated environmental cost, just as it has an associated monetary cost or an associated exergy cost. As we have said, for the allocation of loads we will apply the propositions from the Exergy Cost Theory (ECT) established in Chapter 7.

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Exergy Analysis and Thermoeconomics of Buildings

Obviously, in the cogeneration plant under study, the relative importance of the environmental loads associated with the equipment is much lower than that associated with the preparation and combustion of natural gas, although there are some impact categories for which its importance is relevant, as is the case of heavy metals. The inclusion of the environmental loads associated with the equipment in the balance of each sub-system is a way of giving priority to the functionality of each component or flow (for example, the engine oil), thus avoiding, as much as possible, allocation based on physical parameters. In the plant studied, we defined 9 components and 21 flows. The definition of components comes from functional criteria. In the definition of the flows, the heat dissipated to the atmosphere by radiation and convection in the equipment was disregarded, except in the air coolers, which are components whose function is precisely to dissipate heat. The components and flows under consideration are presented in Table E.10.6., and are also numbered in Fig. E.10.11. Next, and to apply the

Table E.10.6 Sub-systems and flows considered in the cogeneration plant. Subsystems 1

Internal combustion engines

2

Electrical generators

3

Medium voltage installation

4

Power transformer

5

Auxiliary services transformer

6

Waste heat boiler

7

Mixing valve

8

Air coolers

9

Plate heat exchangers Flows

1

Natural gas

2

Shaft power

3

Electric power in alternator terminals

4

Engine exhaust gases

5

Refrigerated water, high temperature circuit

6

Exit refrigeration water of engines, high temperature circuit

7

Return refrigeration water to engines, low temperature circuit

8

Exit refrigeration water of engines, low temperature circuit

Sustainability and exergy in buildings

Table E.10.6 Sub-systems and flows considered in the cogeneration plant.dcont’d Flows 9

Combustion gases to the atmosphere

10

Water supply to the boiler

11

Steam

12

Return of condensates

13

Replacement water

14

Electric power to power transformer

15

Electric power to auxiliary services transformer

16

Electric power produced

17

Electric power to auxiliary services

18

Exit refrigeration water from plate exchangers

19

Exit hot water from the tar preheater

20

Return hot water to the tar preheater

21

Energy dissipated in air coolers

Figure E.10.11 Sub-systems and flows in the diagram.

837

838

Exergy Analysis and Thermoeconomics of Buildings

Propositions of Environmental Exergoeconomics, the functional analysis is done, and the flows are classified as Fuel, Product and Losses, as we saw in Chapter 7. Each flow is assigned an exergoenvironmental cost, that is, an entire environmental inventory expressed for example in Pts/GJ, or as a vector of as many components as there are environmental loads considered in the inventory. As we have said, the calculations were made referring to 1 TJ of natural gas burned in the engines, so that we call: a1: unit exergoenvironmental cost associated with the preparation and combustion of 1 TJ of natural gas and so on up to a21, which is the exergoenvironmental cost associated with flow 21, energy dissipated in the air-coolers. With regards to the equipment, the nomenclature adopted is: YM: environmental impact associated with the engines corresponding to 1 TJ of natural gas; YA: the same for the oil; YOC: civil work; YV: ventilation; YBT: Low voltage installation; YAE: air coolers; YAL: alternators; YMT: Medium voltage installation; YTP: power transformer; YTA: auxiliary services transformer; YC: heat recovery boiler; YI: heat exchangers; YP: pre-heater. Although the exergoenvironmental cost associated with natural gas is known, we will consider it as an unknown for consistency with the equations established in ECT, finally adding an equation corresponding to the external valuation of this cost. In order to better understand the meaning of the equations, we present them one by one, instead of using matrix language. Undertaking an exergoenvironmental costs balance in each component gives the following system of equations 8 > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > :

ð1Þ

a1 B_ 1 þ a17 B_ 17 þ Y_ M þ Y_ A þ Y_ OC þ Y_ V þ Y_ BT     ¼ a2 B_ 2 þ a4 B_ 4 þ a6 B_ 6  a5 B_ 5 þ a8 B_ 8  a7 B_ 7

ð2Þ

a2 B_ 2 þ Y_ AL ¼ a3 B_ 3

ð3Þ

a3 B_ 3 þ Y_ MT ¼ a14 B_ 14 þ a15 B_ 15

ð4Þ

a14 B_ 14 þ Y_ TP ¼ a16 B_ 16

ð5Þ ð6Þ ð7Þ ð8Þ ð9Þ



a15 B_ 15 þ Y_ TA ¼ a17 B_ 17    a4 B_ 4  a9 B_ 9 þ Y_ C ¼ a11 B_ 11  a10 B_ 10

a12 B_ 12 þ a13 B_ 13 ¼ a10 B_ 10     a8 B_ 8  a7 B_ 7 þ a6 B_ 6  a5 B_ 5 þ Y_ AE ¼ a21 B_ 21     a20 B_ 20  a19 B_ 19 þ Y_ I þ Y_ P ¼ a6 6  a18 B_ 18

This system of equations simply means that all the loads associated with the inputs to a system must be allocated to the outputs. According to Proposition 3 of Chapter 7, for any fuel with input and output, the environmental loads per exergy unit of the incoming flow are equal to the loads per exergy unit of the outflow, so we can write the following equations

Sustainability and exergy in buildings

839

8 ð10Þ a19 ¼ a20 > > > > > < ð11Þ a7 ¼ a8 > > ð12Þ > > > : ð13Þ

a5 ¼ a6 a4 ¼ a9

Likewise, according to Proposition 4, since in a component with several products, all have the same unit environmental loads (per exergy unit), we have the equations 8 > > ð14Þ a4 ¼ a2 > > > > > > a8 B8  a7 B7 > > > ð15Þ ¼ a2 > < B8  B7 > > a6 B6  a5 B5 > > ¼ a2 > > ð16Þ B6  B5 > > > > > > : ð17Þ a15 ¼ a14 With respect to loss flows, we find flow 9, gases to the atmosphere through the chimney and flow 21, energy dissipated by the air coolers. Undertaking the same considerations as when speaking of exergy costs, according to Proposition 5 we obtain equations 18 and 19, which are (

ð18Þ

a9 ¼ 0

ð19Þ

a21 ¼ 0

When carrying out the external evaluation of the replacement water (flow 13), we assign a zero exergy cost and, at the same time, a zero exergoenvironmental cost. This flow of water, however, is associated with environmental loads due to the resource itself, those associated with electricity used in pumping, etc. However, given its small magnitude, we will assume that the exergy cost and the eco-vector associated with this flow have a zero value. Finally, we have as a last equation the exergoenvironmental cost of natural gas, which as we have said, includes what happened upstream with the gas, so that in the absence of external valuation we would assign a zero value. Therefore, we can write the last two equations (

ð20Þ

a13 ¼ 0

ð21Þ

a1 ¼ aGN

Thus, we complete a system of 21 equations with 21 unknowns, which are the exergoenvironmental unit costs. As was mentioned in the calculation of the exergy

840

Exergy Analysis and Thermoeconomics of Buildings

cost, flows 9 and 21 are losses of exergy, so that as they are not useful products, their associated exergoenvironmental costs must be zero, since all environmental loads must be shared among the useful products. The inventory, as well as the analysis phase, was carried out on the basis of 1 TJ of natural gas consumed in the engines. The results obtained per energy unit of product are 117.68 Pts/TJ for electricity and 55.08 Pts/TJ for thermal energy. This calculation was also carried out without taking into account the impact due to the equipment of the installation, in which case the results obtained were 116.92 Pts/TJ and 53.08 Pts/TJ of electrical and thermal energy, respectively. We see then that the effect of the equipment on the total value of the Eco-Indicator is around 4%, so this greater complexity is not justified, meaning that the calculation of the environmental impact of the flows could have been made without taking into account the equipment effect.

Superscripts CONS, OM, DIS ch ph

Construction, operation and maintenance, dismantling Chemical Physical

Symbols m_ b ai A_ i aF,k aP,k n i ai,k Y_ k A_ Q;k A_ W;k A_ D;k ra,k fa,k

Mass flow rate Specific flow exergy Environmental impact of the i-th flow per exergy unit Environmental impact of the i-th flow Environmental impact of the equipment k fuel per exergy unit Environmental impact of the equipment k product per exergy unit Number of years Annual interest rate Environmental impact of the ieth flow on equipment k per exergy unit Rate of environmental impact associated with investment in equipment k Rate of environmental impact associated with heat flow in equipment k Rate of environmental impact associated with workflow in equipment k Rate of environmental impact associated to the exergy destruction in equipment k Relative difference of environmental impact in equipment k Exergoenvironmental factor of equipment k

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[3] Brundtland Report, Our Common Future, World Commission for Environment and Development, United Nations, 1987. [4] R. Dones, R. Frischknecht, Life-cycle assessment of photovoltaic systems: results of Swiss studies on energy chains, Progress in Photovoltaics: Research and Applications 6 (1998) 117e125. [5] R. Heijungs, Environmental Life Cycle Assessment Manual, NOH, Leiden, 1992. [6] W. Kl€opffer, B. Grahl, Life Cycle Assessment. A Guide to Best Practice, Wiley-VCH, Weinheim, Germany, 2014. [7] Maastricht Treaty on the European Union, Eur-Lex, 1992. [8] E. Extern, External costs of energy, in: P. Bickel, R. Friedrich (Eds.), ExternE Methodology, 2005 Update, IER University of Stuttgart, Germany, 2005. [9] A.D. Owen, Environmental externalities, market distortions and the economics of renewable energy technologies, Energy Journal 25 (3) (2004) 127e156. [10] OECD, The Economic Consequences of Climatic Change, OECD Publishing, Paris, 2015. [11] E. Sciubba, P. Frankl, Life-cycle, environmental and social considerations- sustainability, in: Exergy, Energy Systems Analysis and Optimization, vol. 3, EOLSS Publishers, UNESCO, Frangopulos, Ch, 2009. [12] J.R. Hicks, Value and Capital, Oxford University Press, USA, 1946. [13] R. Heijungs, J. Guineé, G. Huppes, Impact Categories for Natural Resources and Land Use, 1997. CML report 138. Leiden. [14] J.B. Guineé, R. Heijungs, A proposal for the definition of resource equivalency factors for use in product life-cycle assessment, Environmental Toxicology and Chemistry 14 (5) (1995) 917e925. [15] G. Huppes, Macro-Environmental Policy: Principles and Design, PhD Thesis, University of Leiden, Leiden, 1993. [16] H. Daly, Economy, Ecology And Ethics, Economic Culture Fund of Spain, 2013 (in Spanish). [17] K. Adalberth, Energy use during the life-cycle of buildings: a method, Building and Environment 33 (4) (1997) 317e320. [18] A. Cuchí, What Is Sustainable Construction? Vallés School of Architecture, Polytechnic University of Catalonia, 2003 (in Spanish). [19] R. Lanting, Sustainable Construction in the Netherlands - a perspective to the year 2010, in: Working Paper for CIB W82 Future Studies in Construction, TNO Bouw Publication number 96-BKR- P007, 1996. [20] SETAC, Life Cycle Assessment and Conceptually Related Programs, Society for Environmental Toxicology and Chemistry, Europe Working Group, 1999. [21] UNE 150008, Analysis And Evaluation of Environmental Risk, AENOR, 2008 (in Spanish). [22] Allpe Medio Ambiente, Environmental Impact Research, 2016 (in Spanish), Madrid. [23] Greenhouse Gas (GHG) Protocol, World Resources Institute and World Building Council of Sustainable Development, www.ghgprotocol.org. [24] PAS 2050:2011, Specification For the Assessment of the Life Cycle Greenhouse Gas Emissions of Goods and Services, BSI, 2011. [25] Royal Decree 163/2014, of March 14, through Which Is Created the Registry of Carbon Footprint, Compensation and Carbon Dioxide Absorption Projects, Spanish Ministry of Agriculture, Food and Environment, 2014 (in Spanish). [26] ISO 14064-1:2006 Greenhouse gases – Part 1: specification with guidance at the organization level for quantification and reporting of greenhouse gas emissions and removals, 2006.

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[27] IPCC, IPCC Guidelines for National Inventories of Greenhouse Gases, 5 vols, 2006. [28] The International EPD System, Sweden, www.environdec.com. [29] UNE EN 15804, Sustainability in Construction, Environmental Product Declarations, 2012. [30] ISO 14010:1996, Guidelines for Environmental Auditing-General Principles, International Organization for Standardization, 1996. [31] R. Herendeen, C. Ford, B. Hannon, The energy cost of living, Energy 6 (1981) 1433e1450. [32] F. Consoli, D. Allen, I. Boustead, N. de Oude, J. Fava, B. Franklin, R. Quay, R. Parrish, R. Perriman, D. Postlethwaite, J. Seguin, B. Vigon, Guidelines for Life-Cycle Assessment: A ‘Code of Practice’, SETAC- Europe, Brussels, 1993. [33] UNE EN ISO 14040:1996, Environmental Management, Life Cycle Assessment. Principles And Frame of Reference, 1996. [34] UNE EN ISO 14041:1996, Environmental Management. Life Cycle Assessment. Definition Of the Objective and Scope and Life Cycle Inventory, 1996 (ISO 14041:1998). [35] UNE EN ISO 14042:2002, Environmental Management. Life Cycle Assessment. Impact Assessment of the Life Cycle, 2002 (ISO 14042:2000). [36] M.A. Curran (Ed.), Life Cycle Assessment Student Handbook, J. Wiley, 2015. [37] W. Kl€opffer, B. Grahl, Life Cycle Assessment (LCA). A Guide to Best Practice, J. Wiley, 2014. [38] J.B. Guineé, Review of classification and characterization methodologies, in: Integrating Impact Assessment into LCA, SETAC, Brussels, 1994. [39] E. Lindeijer, Normalisation and valuation, in: Towards a Methodology for Life Cycle Impact Assessment, SETAC-Europe, Brussels, 1996. [40] Pré Consultants, The Eco-Indicator 99 e A Damage Oriented Method for Life Cycle Impact Assessment, Manual for Designers, 2000. [41] M.A. Rosen, Exergy as a tool for sustainability, in: 3rd IASME/WSEAS International Conference on Energy & Sustainability, University of Cambridge, 2008. [42] I. Dincer, The role of exergy in energy policy making, Energy Policy 30 (2002) 137e149. [43] K. Gaudreau, R.A. Fraser, S. Murphy, The tenous use of exergy as a measure of resource value or waste impact, Sustainability 1 (2009) 1444e1463. [44] G. Wall, Exergy e a Useful Concept within Resource Accounting, Report, Physical Resource Theory, 1977. Chalmers, Gothenburg, Sweden. [45] G. Wall, Exergy conversion in the Swedish society, Resources and Energy 9 (1987) 55e73. [46] G. Wall, Exergy conversion in the Japanese society, Energy 15 (5) (1990) 435e444. [47] G. Wall, E. Sciubba, V. Naso, Exergy use in the Italian society, Energy 19 (1994) 12. [48] A. Gasparatos, M. El-Haram, M. Horner, Assessing the sustainability of the UK society using thermodynamic concepts: Part 1, Renewable and Sustainable Energy Reviews 13 (2009) 1074e1081. [49] A. Gasparatos, M. El-Haram, M. Horner, Assessing the sustainability of the UK society using thermodynamic concepts: Part 2, Renewable and Sustainable Energy Reviews 13 (2009) 956e970. [50] G.Q. Chen, B. Chen, Extended-exergy analysis of the Chinese society, Energy 34 (2009) 1127e1144. [51] A. Valero, A. Valero, Thanathia: The Destiny of the Earth’s Mineral Resources: A Cradle to Cradle Thermodynamic Assessement, World Scientific, 2014.

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[52] B. Kilkis, Exergy aspects of operative temperature and its implications on sustainable building performance. Raising Effciency to New Levels, ASHARE Transactions, New Mexico, 2010. [53] D. Schmidt, Low exergy systems for high eperformance buildings and communities, Energy and Buildings 41 (2009) 331e336. [54] R.U. Ayres, L.W. Ayres, K. Martinas, Eco-Thermodynamics: Exergy and Life Cycle Assessment, INSEAD, Working Papers, 96/19/EPS, 1996. Fontainebleau, France. [55] R.U. Ayres, L.W. Ayres, K. Martinas, Exergy, waste accounting and life-cycle analysis, Energy 23 (5) (1998) 355e363. [56] M.A. Rosen, Assessing energy technologies and environmental impacts with the principles of thermodynamics, Applied Energy 72 (2002) 427e441. [57] J. Szargut, D.R. Morris, F.R. Steward, Exergy Analysis of Thermal, Chemical and Metallurgical Processes, Hemisphere, 1988. [58] J. Szargut, Analysis of cumulative exergy consumption, International Journal of Energy Research 11 (4) (1987) 541e547. [59] E. Sciubba, Beyond thermo-economics? The concept of extended exergy accounting and its application to the analysis and design of thermal systems, International Journal of Exergy 1 (1) (2001). [60] H.T. Odum, Environment, Power and Society, John Wiley & Sons, 1971. [61] R.L. Cornelissen, Thermodynamics and Sustainable Development. The Use of Exergy Analysis and the Reduction of Irreversibility, Ph. D Thesis, University of Twente, The Netherlands, 1997. [62] E. Sciubba, Extended exergy accounting applied to energy recovery from waste: the concept of total recycling, Energy 28 (2003) 1315e1334. [63] E. Sciubba, A thermodynamically correct treatment of externalities with an exergy-based numeraire, Sustainability 4 (2012) 933e957. [64] L. Meyer, G. Tsatsaronis, J. Buchgeister, L. Schebek, Exergoenvironmental analysis for evaluation of the environmental impact of energy conversion systems, Energy 34 (2009) 75e89. [65] C.T. Y€ucer, A. Hepbasli, Exergoeconomic and enviroeconomic analyses of a building heating system using SPECO and Lowex methods, Energy and Buildings 73 (2014) 1e6. [66] P. Ahmadi, I. Dincer, M.A. Rosen, Exergo-environmental analysis of an integrated organic Rankine cycle for trigeneration, Energy Conversion and Management 64 (2012) 447e453. [67] U. Akbulut, Z. Utlu, O. Kincay, Exergoenvironmental and exergoeconomic analyses of a vertical type ground source heat pump integrated wall cooling system, Applied Thermal Engineering 102 (2016) 904e921. [68] L. Meyer, R. Castillo, J. Buchgeister, G. Tsatsaronis, Application of exergoeconomic and exergoenvironmental analysis to an SOFC system with an allothermal biomass gasifier, International Journal of Thermodynamics 12 (4) (2009) 177e186. [69] F. Petrakopoulou, G. Tsatsaronis, T. Morosuk, C. Paitazoglou, Environmental evaluation of a power plant using conventional and advanced exergy-based methods, Energy 45 (2012) 23e30.

Application of exergecoeconomic and exergoenvironmental analysis to several cases of building thermal installations

11.1

11

Overview

This Chapter aims to put into practice the concepts developed in the previous Chapters to apply them in some facilities. Four thermal installations have been selected with the intention of covering a wide range of facilities in building energy supply systems. We first consider a conventional heating and DHW facility with boilers and then we continue with more complex ones, such as the cogeneration plant of a block of dwellings or the trigeneration of a hospital. In all cases, the same structure has been followed: first, the building or buildings are described, and their geometry, as well as the characteristics of the envelope, the occupation factor and the climatic characteristics are defined. These data allow the heat, DHW and refrigeration demands to be obtained by simulation. After defining the energy supply facility, either a simulation of the facility is performed or the Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00011-4 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

monitored data are collected to calculate the hourly values of each energy and exergy flow; from here, the seasonal or annual accumulated values are obtained. Once the functional analysis is carried out, using Symbolic Thermoeconomics (ST), the fuel and product of each component are defined. Besides their energy and exergy efficiencies, exergy costs, exergoeconomic costs and the CO2 emissions are calculated. The purpose of this Chapter is to show how to apply Thermoeconomics in different types of facilities, pointing out the difficulties that may arise and the valuable information that can be obtained so that the Chapter aims to be a compendium of the methodology presented in the previous Chapters through its application in four specific cases.

11.2

Introduction

As said in Chapter 1, the building envelope design must be carried out in parallel with its thermal facility, in order to achieve the one that best adapts to the external conditions. In such a way, it is possible to reduce the heating and cooling demands to the minimum. Passive systems are the envelope components that use the environment potentials such as the sun, wind and other natural resources to illuminate, ventilate and heat or cool the building. However, in winter, an installation is required to maintain comfort, preferably a low-temperature one, Fenercom 2017 [1]. On the other hand, in summer, moderate thermal conditions can be achieved with night ventilation, the placement of appropriate shading devices, the reduction of internal gains and through the use of insulating materials with adequate thermal capacities; in this way, cold sources without very low-temperatures can be used for cooling. However, in order to achieve comfortable conditions, a cooling facility is often necessary. The whole of the HVAC system (Heating, Ventilation and Air Conditioning) can be divided into two components: the conditioned space, which is the component consuming the energy; and the conditioning system, which transforms the different energy sources into the appropriate forms and supplies the required services to the conditioned space. A conventional thermodynamic analysis of an HVAC system begins with data collection, which is basically, temperatures and flow rates. Before proceeding with the analysis, these data must be validated, and for such aim, a series of tests are done. By using these data, and the corresponding tables, diagrams or software of the working substances, the thermodynamic properties of the flows taking part in the system are obtained. Next, the mass and energy balances are performed and, thus, some unknown values are obtained or the consistency of the available values is simply checked. Usually, the behaviour of buildings’ thermal systems is characterized by applying the First Law of Thermodynamics. If the performance of the equipment is thus defined, only the energy flow losses (heat, enthalpy) transferred to the environment and not used are contemplated. However, as repeatedly said in several Chapters, the

Application of exergecoeconomic and exergoenvironmental analysis

847

energy balance does not enable the true inefficiencies of the equipment to be identified, so analyses linked exclusively to the First Law lead to conclusions that may be erroneous. In addition, the true losses, which are the irreversibilities, are not quantified. Hence, this justifies the interest of going a step further and proceeding with the exergy analysis. Consequently, once the mass and energy balances have been duly validated, the exergy analysis should be carried out. Only the quantification of the exergy lost to the environment, and the components’ exergy destructions permit the real losses to be evaluated. Additionally, exergy efficiency is the most appropriate parameter to compare the energy performance of different equipment and even entire installations, regardless of whether they have different utilities or that they are made up of equipment with very different characteristics. The flows are grouped by functional analysis, by means of AF and AP matrices. Once the fuel and product of each component are known, that is, the flow exergies that are a part of the fuel and product is calculated, the exergy efficiency of each component is immediately obtained. The ST application allows the linkages between the components to be analysed and to relate them in terms of unit exergy consumptions. In this way, as shown in Chapter 9, a component efficiency variation can be analysed when the internal or external parameters of the other components vary; that is, it can be quantified how much each component influences the others and the facility as a whole. Thereafter, the exergy costs of the flows (the vector k*) and the fuel and product exergy cost of each component (the vectors k
F and k
P ) are calculated in order to know how these unit costs increase along with the energy chain development, starting from generation up until consumption. Likewise, the unit economic costs are consecutively determined, both of the flows (vector c) and the components fuel and product unit costs (vectors cF and cP respectively). Undoubtedly, the most interesting values are the costs of the system’s total product, that is, the unit cost (per kWh) of heating, cooling, DHW and electricity (if cogeneration exists). For calculating these costs, it is necessary to know the used resource prices (natural gas, electricity, other fuels, etc.), as well as the equipment investment cost and other economic data (useful life, rate of interest, etc.), as shown in Chapter 7. Finally, the ideas presented in Chapter 10 are applied in order to make the exergoenvironmental analysis and to calculate the environmental impact of each flow. The most interesting results are associated with the system’s total products (heating, DHW, air conditioning and electricity). Among the different impact categories, only the CO2 emissions are assessed in this Chapter. In addition, the environmental impact due to the equipments’ manufacturing would not be taken into account. As it is known, its effect on the system’s product environmental impact is very small and, besides, its calculation would require information that is lacking, or an LCA should need to be performed for each component. Therefore, the exergoenvironmental costs would correspond exclusively to the CO2 emissions of the system resources (fuel and electricity). Both the unit prices and the CO2 emissions of the used resources are shown in Table 11.1.

848

Exergy Analysis and Thermoeconomics of Buildings

Table 11.1 Unit prices and CO2 emissions of used resources. Cost

Emissions

Resources

[cV/kWh]

[gCO2/kWh]

Electricity

21.81

649

Natural gas

5.274

204

Gasoil

9.43

287

Biomass

4.1

0

As mentioned, four representative heating, DWH and air conditioning facilities have been selected. They cover a wide spectrum, from a heating and DHW boilers facility for dwellings to a trigeneration plant for a hospital. In all cases, the methodology is the same, having followed the steps described above and whose foundations have been developed in the previous Chapters; they are outlined in Table 11.2. Before proceeding with the system analysis, the heating, DHW and air conditioning demands of each case need to be determined. These demands were obtained through the building dynamic simulations with TRNSYS v17, except in one case, where real data were obtained from the monitoring system. Once the demands have been calculated, the facility simulation is performed, also with TRNSYS v17, obtaining for each time interval set (in some cases every 7 min, in others hourly intervals) the data of involved flows, temperatures and pressures. From these values, the energy and exergy of the flows are calculated, and the accumulated annual or seasonal values are obtained, which are the ones presented in the Chapter. Likewise, the seasonal energy and exergy efficiency values of the equipment and the global values are presented, as well as the seasonal unit costs of the flows and mainly of the considered system products, both in exergy and monetary terms. Finally, the environmental impact measured in CO2 emissions associated with each flow and in particular with the system
s products is presented.

Table 11.2 Methodology for thermal systems analysis. 1 Physical diagram of the installation/ Selection of components and flows. Definition of the incidence matrix A. 2 Application of Thermoeconomics / Productive and dissipative components. Construction of matrices and vectors AF;AP;F;P;kD. Determination of the interrelations between the components. 3 Energy analysis/ Mass and energy balances. Component efficiencies. 4 Exergy analysis/ Calculation of flow exergies and exergy destructions. Exergy efficiencies. 5 Exergy costs calculation/ Vectorsk
; k
F ; k
P 6 Exergoeconomic costs calculation/ Vectors c;cF;cP 7 CO2 emission impacts calculation / Vectors aF;aP

Application of exergecoeconomic and exergoenvironmental analysis

849

It must be indicated that the four cases have been developed using ST in the PF representation shown in Chapter 8. This PF formulation is the most appropriate since it allows determining the necessary resources to obtain the system production objective, as well as calculate the flows’ unit costs from the external resources unit costs. In that way, in all cases, the products of the installation are fixed since the respective DHW, heating and/or cooling demands have to be met. However, for simplicity reasons, matrix has been obtained from the FP and PF representations’ relationship. After all, the construction of the matrix is the one that has a simpler and more direct physical meaning. Therefore, although the study has been done under the PF demand-driven model, the independent input variables were the system’s total resources, the bifurcations (in components with more than one output) and each component’s unit consumption. Once that has been done, the PF representation was attained through the relations between both representations shown in Chapter 8. Afterwards, each selected system results are detailed. In addition to the individual conclusions of each case, the following can be considered as a general conclusion: even when dealing with relatively complex systems, by applying Thermoeconomics, it is relatively easy to determine where the irreversibilities take place, quantify them and value their cost, both in energy, monetary and environmental units. In such a way, valuable information is provided to know where to act in order to improve the facility’s efficiency.

11.3

Case 1: heating and DHW facility with natural gas boilers

11.3.1 Description of the building and its thermal facility Case 1 is a set of four buildings with 566 dwellings. Two of those blocks contain 108 dwellings each, a third one has 190 and the fourth block has 160, see Fig. 11.1. This set of buildings is located in Bilbao (Basque Country), and the type of construction is characteristic of the seventies. The heating and DHW facility is centralized, so that it meets the demands of the four blocks. It consists of three gasoil boilers: two of them (C1 and C2), with a nominal power of 2325 kW each, work in cascade and cover the heating demand, and the third one (C3), with 1162 kW, supplies the DHW. The hot water generated in the boilers is grouped into a collector that distributes it to the heating and DHW distribution circuits. The heating circuit configuration is a ring divided into four branches, one for each block, and the substation of the building heating supply is on each ground floor. There are two branches in the DHW circuit, one for the two high blocks and the other for the other two low ones. The DHW supplied to the low blocks is accumulated in a 4000 L tank (T3) and that of the high blocks in two parallel 3500 L/each tanks (T1 and T2). Two heat exchangers (HXa and HXb) connect the generation circuit with the accumulation tanks.

850

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.1 Four blocks of dwellings with a centralized heating system.

Fig. 11.2 shows a schematic of the DHW distribution system, in which the inputs to the substations (H1, H2, H3 and H4) are indicated. In Fig. 11.3 the components are reordered and labeled. The heating control is carried out by means of three-way valves (Sc1-4, Mc1-4) whose objective is to supply water flow at the setpoint temperature. This temperature

Figure 11.2 Schematic of the DHW distribution system.

Application of exergecoeconomic and exergoenvironmental analysis

851

Figure 11.3 Simplification of the schema and symbols used for the considered components.

is a function of the outside temperature so that when it is 5 C, the heating setpoint temperature is 75 C and if the outside temperature increases to 15 C, the setpoint temperature decreases linearly up to 60 C. The heating circuit boilers operate in cascade, generating at 80  C and modulating that temperature up to 60%. With regard to the DHW, the boilers operation is controlled according to the average accumulation temperature of the tanks, which must be 65 C. The small boiler works as a base, while the other two operate when a minimum storage temperature cannot be maintained. Table 11.3 shows the various components that have been considered, with their abbreviation; hence, there are 27 components. Fig. 11.4 shows the simplified schema used for the analysis, indicating the numbering of the flows. The inflows and outflows of each component can be detected, whereas the flows coming from outside are shown with dotted arrows. Flows E55, DE56 and DE57 represent the exergy variation in the tanks associated with the accumulated energy variation and DE58 is the one associated with the hydraulic compensator. Table 11.4 summarizes the number of components, total number of flows, number of inflows and outflows, bifurcations and recirculations, verifying the equalities m ¼ n þ e þ b and m ¼ n þ s þ r. To finish this section, Fig. 11.5 schematically shows the energy chain: it goes from the heat generation in the boilers, through the accumulation groups and distribution pipes until the final heating radiators and the DHW consumption. The nomenclature used in this image is the following: HP (heat production); C (heat collector); H/DHW (division into heating and DHW branches); h4/d2 (4 heating branches in each residential block andDHW separation in high and low floors); h4/dT2 (heating distributed in the four blocks and secondary with DHW accumulation in the upper and lower floors); D (heat distribution: the four blocks heating demands

852

Exergy Analysis and Thermoeconomics of Buildings

Table 11.3 Numbering and symbols of the considered components. Considered components n

Symbol

Description

n

Symbol

Description

1

C1

Boiler 1

15

Sb

DHW diverter low floors

2

C2

Boiler 2

16

H1

Block I heating

3

C3

Boiler 3

17

H2

Block II heating

4

C

Hydraulic compensator

18

H3

Block III heating

5

Sab

High/low floors DHW diverter

19

H4

Block IV heating

6

Mab

High/low floors DHW mixer

20

Mc1

Block I heating mixer

7

HXa

High floors heat exchanger

21

Sc1

Block I heating diverter

8

HXb

Low floors heat exchanger

22

Mc2

Block II heating mixer

9

T1

High floors tank 1

23

Sc2

Block II heating diverter

10

T2

High floors tank 2

24

Mc3

Block III heating mixer

11

T3

Low floors tank

25

Sc3

Block III heating diverter

12

DHWa

High floors DHW exit mixer

26

Mc4

Block IV heating mixer

13

Sa

High floors DHW diverter

27

Sc4

Block IV heating diverter

14

DHWb

Low floors DHW exit mixer

are H_ I , H_ II , H_ III and H_ IV whereas DHWL and DHWH are the DHW demands in the low and high blocks respectively).

11.3.2

Heating and DHW demands

The heating demand was calculated by dynamic simulation with software TRNSYS v17 [2]. To do this, the occupation conditions, setpoint temperatures, ventilation rates, infiltrations, etc., were previously specified. According to the hourly simulation results, the annual heating demand is 704.9 MWh, (600.5 MWh corresponds to the dwelling demand and the remaining part to locals); the peak heating demand is 538.8 kW. The monthly profile is shown in Fig. 11.6. The DHW demand was calculated based on the daily and monthly multiplying factors defined in Annex A of the Institute for Energy Diversification and Saving (IDAE) of the Spanish government; besides, the daily DHW consumption set by IDAE (28 L/ person) for multi-family dwellings [3] was considered. The number of people per

Application of exergecoeconomic and exergoenvironmental analysis

853

Figure 11.4 Numbering of flows. Table 11.4 Summary of components and flows. Physical determination Components

n

27

Flows

m

59

Inflows

e

9

Outflows

s

6

Bifurcations

b

23

Recirculations

r

26

Figure 11.5 Energy chain of the facility.

854

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.6 Monthly heating demand profile.

dwelling was established according to the minimum occupancy values defined in BTC, so that single-room dwellings are occupied by 1.5 people and those of two and three rooms by 3 and 4 people, respectively. This demand was calculated taking into account a 60  C accumulation temperature that guarantees the Legionella prevention, as fixed by RD 865/2003 [4]. Additionally, monthly average water network temperatures were considered. These temperatures are established in BTC according to the city location, in this case, Bilbao. Annual DHW demand is 289.6 MWh distributed over the months as shown in Fig. 11.7.

11.3.3

Functional analysis

Each one of the considered 27 components has a series of input and output flows, which are reflected through the A incidence matrix of dimension (27,59). After that, the functional analysis can be performed, and the flows are grouped into fuel F and product P; the AF and AP matrices are built in such a way, both with dimensions of (27,59). Due to the space they occupy, these matrices are not presented as such; instead, the physical structure and productive structure are collected using tables, see Table 11.5. Thus, on the left side of Table 11.5, (A) the corresponding numbers

Figure 11.7 Average monthly DHW demand and average monthly network water temperature.

Physical structure

Productive structure

Input

Output

Fuel

Product

C1

2 þ 52

1

[52]

[1e2]

C1

C2

4 þ 53

3

[53]

[3e4]

C2

C3

6 þ 54

5

[54]

[5e6]

C3

C

1 þ 3 þ 5 þ 8 þ 27 þ 29 þ 31 þ 33 þ 58

2 þ 4 þ 6 þ 7 þ 26 þ 28 þ 30 þ 32

Sab

7

9 þ 11

[7]

[9] þ [11]

Sab

Mab

10 þ 12

8

[10] þ [12]

[8]

Mab

Hxa

9 þ 15

10 þ 13

[9e10]

[13e15]

Hxa

HXb

11 þ 17

12 þ 16

[11e12]

[16e17]

HXb

T1

13 þ 56 þ 59

14 þ 15

[13e15]þ[56]

[14e59]

T1

T2

14 þ 20 þ 55

18 þ 59

[14e59] þ [55]

[18e20]

T2

T3

16 þ 24 þ 57

17 þ 22

[16e17] þ [57]

[22e24]

T3

DHWa

18 þ 19

38

[18]þ[19]

[38]

DHWa

Sa

21

19 þ 20

[21]

[19] þ [20]

Sa

DHWb

22 þ 23

39

[22] þ [23]

[39]

DHWb

Sb

25

23 þ 24

[25]

[23] þ [24]

Sb

H1

40

34 þ 41

[40e41]

[34]

H1

H2

43

35 þ 44

[43e44]

[35]

H2

[1] þ [3] þ [5] þ [8] þ [27] þ [29] þ [31] þ [33] þ [58]

[2] þ [4] þ [6] þ [7] þ [26] þ [28] þ [30] þ [32]

C

855

Continued

Application of exergecoeconomic and exergoenvironmental analysis

Table 11.5 (A) Physical structure and (B) Productive structure of the facility.

Physical structure

856

Table 11.5 (A) Physical structure and (B) Productive structure of the facility.dcont’d Productive structure

Output

Fuel

Product

H3

46

36 þ 47

[46e47]

[36]

H3

H4

49

37 þ 50

[49e50]

[37]

H4

Mc1

26 þ 42

40

[26] þ [42]

[40]

Mc1

Sc1

41

27 þ 42

[41]

[27] þ [42]

Sc1

Mc2

28 þ 45

43

[28] þ [45]

[43]

Mc2

Sc2

44

29 þ 45

[44]

[29] þ [45]

Sc2

Mc3

30 þ 48

46

[30] þ [48]

[46]

Mc3

Sc3

47

31 þ 48

[47]

[31] þ [48]

Sc3

Mc4

32 þ 51

49

[32] þ [51]

[49]

Mc4

Sc4

50

33 þ 51

[50]

[33] þ [51]

Sc4

Exergy Analysis and Thermoeconomics of Buildings

Input

Application of exergecoeconomic and exergoenvironmental analysis

857

of the flows entering and leaving the equipment are gathered, whereas, on the right side, the flow numbers that are part of F and P are indicated.

11.3.4 Energy analysis The simulation of the facility was carried out using TRNSYS v17 dynamic simulation software, with a time interval of 7 min. According to the existing schedule, the plant operates providing heating between November and May and in the 2-10 pm time interval. The heating demand is activated whenever the outside temperature or its average during the last 18 h is less than 15 C. Outside temperatures were obtained from the Meteonorm database. In addition, the results obtained by simulation were contrasted with the monthly gasoil consumption during the period 2010e13. Table 11.6 shows the accumulated energy values of the components
fuel and product corresponding to a simulated year. These values were obtained from the energy values in each time interval and added throughout the year. The quotient between both values gives the average energy efficiency of each component. Table 11.6 Seasonal energy efficiency of components. Energy [MWh] h[%]

Fuel

Product

C1

2110

1792

C2

e

e

C3

89

75

C

1867

1858

100

Sab

3803

3802

100

Mab

3483

3483

100

Hxa

185

185

100

HXb

135

134

99

T1

57

45

79

T2

128

121

94

T3

134

125

93

DHWa

215

217

100

Sa

49

49

100

DHWb

161

162

100

Sb

36

36

100

H1

416

398

96

H2

146

142

98

85 e 85

Continued

858

Exergy Analysis and Thermoeconomics of Buildings

Table 11.6 Seasonal energy efficiency of components.dcont’d Energy [MWh] h[%]

Fuel

Product

H3

126

122

97

H4

413

408

99

Mc1

6867

6695

97

Sc1

6284

6286

100

Mc2

3876

3812

98

Sc2

3669

3671

100

Mc3

3901

3816

98

Sc3

3693

3695

100

Mc4

5775

5635

98

Sc4

5227

5229

100

It can be seen that boiler C2 does not turn on during the whole season (), so it is a component that only responds for safety reasons, and that shows the facility oversizing. The components related to the energy distribution, such as the mixing and separating valves, have hardly any energy losses and are associated with an efficiency close to unity (hSci,Mci w1). The considered losses for the tank efficiency calculation
are heat losses and, therefore, tanks also reach high efficiencies hTi w 90% . In addition, the high energy efficiency of high-temperature radiators should be noted, since they are close to 100% (hHi >97%). If the total product (heating and DHW) is divided by the consumed total fuel (gasoil in the boilers and cold water), the average annual performance of the system is obtained, which turns out to be 62%. If the production and consumption corresponding to heating and DHW are considered separately, a seasonal heating efficiency of 60% and an average annual DHW efficiency of 70% turn up, see Table 11.7.

11.3.5

Exergy analysis

Similarly, the exergy values of each of the flows in the facility were calculated and the cumulative total values were obtained; the results are reflected in Table 11.8. By taking Table 11.7 Summary of annual energy efficiency. Energy efficiency Total

62%

Heating

60%

DHW

70%

Accumulated exergy values [MWh]

[MWh]

[MWh]

[MWh]

[MWh]

[MWh]

B1

B2

B3

B4

B5

B6

B7

B8

B9

B10

B11

B12

1355.08

1021.05

0.00

0.00

37.50

24.32

311.71

253.09

112.07

79.53

199.41

173.72

B13

B14

B15

B16

B17

B18

B19

B20

B21

B22

B23

B24

48.64

39.19

22.58

78.55

55.36

14.15

0.03

0.10

0.13

12.05

0.03

0.07

B25

B26

B27

B28

B29

B30

B31

B32

B33

B34

B35

B36

0.10

282.79

186.38

111.04

76.98

107.51

73.25

250.15

160.05

15.76

5.55

4.71

B37

B38

B39

B40

B41

B42

B43

B44

B45

B46

B47

B48

15.81

11.10

8.50

484.89

422.34

236.26

276.56

254.69

177.90

277.27

258.48

185.44

B49

B50

B51

B52

B53

B54

B55

B56

B57

B58

B59

407.84

346.35

186.60

2255.16

0.00

94.82

0.01

0.06

0.01

0.00

8.05

Application of exergecoeconomic and exergoenvironmental analysis

Table 11.8 Values of the accumulated exergy for each flow during the study period.

859

860

Exergy Analysis and Thermoeconomics of Buildings

into account the fuel and product definitions of each component (Table 11.3), the average annual exergy efficiencies of the components were calculated as well, see Table 11.9. Table 11.9 Seasonal exergy efficiency of components. Exergy [MWh] 4[%]

Fuel

Product

C1

2257

334

C2

e

e

C3

95

13

14

C

347

313

90

Sab

312

312

100

Mab

253

200

79

Hxa

33

26

79

HXb

27

23

88

T1

10

6

62

T2

17

8

48

T3

24

12

51

DHWa

14

11

78

Sa

0.1

0.1

100

DHWb

12

9

Sb

0.1

0.1

100

H1

67

16

23

H2

25

6

22

H3

22

5

21

H4

67

16

24

Mc1

519

485

93

Sc1

422

423

100

Mc2

289

277

96

Sc2

255

255

100

Mc3

293

277

95

Sc3

259

259

100

Mc4

437

408

93

Sc4

346

347

100

15 e

75

Application of exergecoeconomic and exergoenvironmental analysis

861

As seen, the greatest exergy destructions take place in the boilers. In fact, although having high energy efficiencies hC1 ¼ 85% and hC3 ¼ 85%, their exergy efficiencies are low, 4C1 ¼ 15% and 4C3. ¼ 14%. Therefore, even though the boilers are apparently very efficient components, the reality is that great exergy destructions are taking place due to the nature of the combustion processes. In other words, the used technological option is not the most appropriate from the strictly thermodynamic point of view, due to the high irreversibility of the diffusion processes, combustion reactions and heat transfer taking place in the boilers. Likewise, storage tanks also have high energy efficiencies hT1 ¼ 79%, hT2 ¼ 94% and hT3. ¼ 93%, while their respective exergy efficiencies 4T1 ¼ 62%, 4T2 ¼ 48% and 4T3. ¼ 51% are noticeably lower. This is mainly due to the irreversibilities caused in the mixture of flows at different temperatures, which are not valued by the First Law. The exergy efficiency reduction with respect to the energy in the mixing components is justified in the same way; a mixture takes place between different temperature flows. The diverters, however, have 100% exergy and energy efficiencies. There are also great destructions in the heating terminal components (in which the indoor air is also included). Their seasonal exergy efficiencies are 4H1 ¼ 23%, 4H2 ¼ 22%, 4H3. ¼ 21% and 4H4. ¼ 24%. These low values show the lack of adequacy between the radiator surface temperatures, which are fed by circuit water at a temperature range of w8060 C and the indoor air temperature which is at w20 C. Obviously, these values are significantly higher in low-temperature systems, such as radiant floors. Finally, the global (seasonal) exergy heating efficiency was calculated, considering all the energy chain from the gasoil to the indoor air. Likewise, the annual exergy efficiency for DHW was obtained, considering the total DHW energy chain. The summarized results are presented in Table 11.10 where the low exergy efficiency values, compared to energy efficiencies, are easily observed. Those low values show the existing wide margin for the system’s energy efficiency improvement, which is representative of the conventional heating and DHW systems in our country. As a summary, in Fig. 11.8 the energy and exergy profiles of the system energy transformation chain, from primary energy to outdoor environment, are depicted. The following stages are schematically presented: • • •

Primary energy (PE): primary energy resources, in this case, gasoil. Heat production (HP) in boilers: hot water obtained by combustion. Heat collector (C): intermediate stage to collect the hot water.

Table 11.10 Summary of annual exergy efficiency. Exergy efficiency Total

3%

Heating

2.3%

DHW

3.5%

862

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.8 Energy and exergy profile in the system energy chain. • • • • • •

Division between heating and DHW (H/DHW): branching for the demand distribution according to the use. Heating branch for the four blocks and DHW separation between low- and high-floor plans (h4/d2) for distribution by buildings and floors. Heating distribution and DHW accumulation in deposits for low and high plants (h4/dT2). Heating and DHW consumption (D) in the terminal equipment, radiators for heating and taps for DHW. Indoor air (IA). Dissipation in the external environment (Env).

Fig. 11.8 allows the enormous difference between both profiles to be identified at a glance. It can be seen that although the energy losses are small in the whole chain, great exergy destruction in the generation occurs. It should also be noted that the energy transferred to the environment has zero exergy so that the profile ends by cutting the abscissa axis.

11.3.6

Exergy costs

From the values of flow exergies and considering the previously described productive structure, the unit exergy costs of fuel and product, k
F and k
P are calculated. The results are presented in Table 11.11 in which each component exergy destruction (kP
i  kF
i ) corresponds to the irreversibilities taking place in it. In the absence of an external evaluation, the unit exergy costs associated with external recourses are equal to unity. In this case, these resources are the used gasoil in the boilers (C1 and C3) and the cold water entering into the DHW storage tanks (T1, T2 and T3). As can be seen, the unit costs of the fuel of those last chain equipments are not equal to unity, because in addition to the water from the network, other flows from the heat exchangers (HXa and HXb) also form part of the fuel, so that the cost is the weighted average of those flow costs. Among the values provided in Table 11.11, the most interesting are underlined: they are those which correspond to the unit exergy costs of heating in each block

Application of exergecoeconomic and exergoenvironmental analysis

863

Table 11.11 Unit exergy costs of each component
s fuel and product. Unit exergy cost [e] k
F C1 C2

1.00 e

k
P 6.75 e

k
F

k
P

Sb

1.00

1.00

H1

10.88

43.20

C3

1.00

7.19

H2

10.76

42.44

C

9.43

9.58

H3

11.19

44.64

Sab

9.58

9.58

H4

10.82

42.07

Mab

9.58

9.59

Mc1

10.17

10.88

Hxa

9.58

11.97

Sc1

10.88

10.88

HXb

9.58

10.62

Mc2

10.30

10.76

T1

11.99

10.02

Sc2

10.76

10.76

T2

10.02

22.20

Mc3

10.59

11.19

T3

10.62

20.55

Sc3

11.19

11.18

DHWa

22.00

28.11

Mc4

10.10

10.82

1.00

1.00

Sc4

10.82

10.81

20.39

28.96

Sa DHWb

and those which refer to the DHW. As seen, slight differences appear between the four heating unit costs, but on average the value is 43.1; that is, 43.1 exergy units are needed to provide a heating exergy unit. This, in short, means that the seasonal heating exergy efficiency is 2.3% (as shown in Table 11.10). For DHW, there is also a small difference according to the branch, but on an average it is 28.5, which means that the average annual exergy efficiency in DHW production is, as seen before, 3.5%.

11.3.7 Exergoeconomic costs The costs calculation in monetary units (exergoeconomic costs) is analogous to that of exergy costs. However, in addition to the resource costs, the capital cost rate and maintenance of components must be considered. Table 11.12 shows the costs of the system’s equipment, according to the project data, together with the unit prices of the resources and other economic data. Table 11.13 shows the costs of fuel and product of each component. The cost of the product has been separated into two components:czP reflects the unit levelized cost of acquisition, maintenance, etc. and, ceP is the cost associated with the resources (gasoil and cold water). Since the pumps have not been considered in the analysis, the electricity cost has not been included in the final cost.

864

Exergy Analysis and Thermoeconomics of Buildings

Table 11.12 Acquisition cost of components and other economic data. Tariffs Gasoil [cV/kWh]

9.12

Cold water [V/m3]

0.52 Economic data

Effective interest rate

0.05

Useful life of the facility (y)

20

Acquisition and start-up costs [V] C1

49,046

Sb

9,190

C2

49,046

H1

9,828

C3

46.979

H2

7,339

C

9,828

H3

7,339

Sab

2,289

H4

9,828

Mab

2,000

Mc1

1,145

Hxa

5.808

Sc1

1,000

HXb

5,808

Mc2

1,145

T1

8,576

Sc2

1,000

T2

8,576

Mc3

1,145

T3

9,052

Sc3

1,000

DHWa

5,214

Mc4

1,145

Sa

5,214

Sc4

1,000

DHWb

9,190

The results were obtained per exergy unit and are shown in Table 11.13; if instead energy unit costs were used, the relationship between energy and exergy for each flow would have to be considered. It is verified that the exergoeconomic costs increase as the energy chain progresses until reaching the final components, which are precisely those underlined. Some of them reflect the unit costs of the blocks’ heating (I, II, III and IV) and the others reflect the DHW costs in the lower and upper floors, separated into costs due to resources and costs related to the investement (the investment cost of C2 appears with a very big value since this component nearly never enters into operation). Finally, Table 11.14 summarizes the unit exergoeconomic costs for the products of the installation, that is, the heating cost per kWh (in energy) for each block and the DHW unit cost for the upper and lower floors, as well as the total annual costs and annual costs per dwelling. Because the facility does not yet have energy meters or

Application of exergecoeconomic and exergoenvironmental analysis

865

Table 11.13 Fuel and product unit exergoeconomic costs of each component. Unit exergoeconomic costs[cV/kWh] n

czP

ceP

cF

n

czP

ceP

cF

C1

9.07

61.22

1.55

Sb

0.15

0.15

974.91

C2

9.07

9.07

516172.79

H1

106.84

391.72

38.90

C3

9.07

65.23

37.51

H2

105.78

384.78

46.18

C

92.41

86.83

7.10

H3

110.01

404.74

50.36

Sab

93.94

86.90

7.19

H4

106.21

381.50

38.07

Mab

94.08

86.95

7.27

Mc1

99.79

98.69

8.15

Hxa

94.08

108.54

11.32

Sc1

106.84

98.62

8.17

HXb

94.08

96.26

10.60

Mc2

101.20

97.60

8.18

T1

120.12

90.84

12.38

Sc2

105.78

97.52

8.22

T2

103.25

201.33

33.85

Mc3

104.08

101.50

8.52

T3

106.91

186.30

28.46

Sc3

110.01

101.41

8.55

DHWa

236.82

254.85

52.74

Mc4

99.16

98.11

8.11

0.15

0.15

407.27

Sc4

106.21

98.02

8.13

221.01

262.48

62.85

Sa DHWb

Table 11.14 Heating and DHW exergoeconomic costs. Final product costs cV/kWh

V/y

V/dw$y

DHW high

14.15

30,697

110

DHW low

17.08

27,664

100

Heating block I

17.06

67,865

357

Heating block II

16.79

23,911

221

Heating block III

17.51

21,442

199

Heating block IV

16.26

66,346

349

cost distributors, IDAE 2007 [5], Ziemele et al. 2015 [6], the unit cost per dwelling was obtained dividing the total cost by the number of households, as all they have the same surface. If the cost is allocated through this methodology, those systems that generate more irreversibilities are penalized, that is to say, the components with higher exergy destructions. In this way, installations that make the best use of the different levels of energy quality are benefited, because they adapt better to the building’s needs.

866

11.3.8

Exergy Analysis and Thermoeconomics of Buildings

Impact on CO2 emissions

Finally, Table 11.15 includes the environmental impact of components’ fuel and product, exclusively due to the CO2 emissions associated with the consumed gasoil. In the elaboration of such Table, the impact due to the equipment manufacturing has not been taken into account, since its effect is very small and, in addition, the necessary data are not available, Kallenberger and Althaus 2009 [7]. As seen in Table 11.15, Sa and Sb network cold water valves have zero emissions, since they are not linked to any external resources with any CO2 emissions, but only to the network water inlet. Heating produces an average unit emission of 0.46 kg CO2/kWh energy (11.83 kg CO2/kWh exergy) and a seasonal total of 495 t CO2, which is underlined and separated for each of the four blocks. The DHW production represents an average unit emission of 0.41 kg CO2/kWh energy (7.9 kg CO2/kWh exergy) and an annual emission of 154 t CO2, which is also underlined and broken down between the upper and lower floors. The sum of both values corresponds to the total CO2 emitted in the gasoil combustion, since, electricity generation and CO2 emissions corresponding to the system’s equipment manufacturing and its dismantling were not considered.

11.4 11.4.1

Case 2: heating and DHW facility with geothermal heat pump Description of the building and its thermal facility

In case 2, the facility under analysis covers the heating and DHW demands of a building with 26 social housing units in Durango, see Fig. 11.9. It is composed of five floors plus a penthouse for dwellings and two underground floors, for garages and storage rooms, with high-quality architectural design and provided with a radiant floor heating system. The thermal facility consists of a water-to-water geothermal heat pump with 68 kW of nominal power. It was dimensioned for supplying the building base heating and DHW demands using subsoil heat. As such, the low geothermal enthalpy that is renewable and clean, apart from being a good alternative to supply energy, was taken advantage of, Llopis and Rodrigo [8]. There is also an auxiliary generation system, consisting of a natural gas condensation boiler, with 120 kW nominal power and an efficiency of 97.5%. It is dimensioned to be able to supply the totality of the demand in the case where the geothermal system is temporarily out of use. The heat pump condenser feeds the primary circuit and gives the produced hot water to a 2000 L inertial tank. Such hot water is used to cover the building heating demand or to supply heat to the primary circuit of the DHW storage tank. The heating system works against the inertial tank, in order to avoid an excessive number of starts and stops of the heat pump. The DHW accumulation is done through two 2000 L deposits each. Thus, the geothermal heat pump is the main generator that feeds a radiant floor and a low-temperature storage tank that serves as DHW support.

Application of exergecoeconomic and exergoenvironmental analysis

867

Table 11.15 CO2 emissions associated with the components’ product and fuel. Impact on CO2 emissions [kgCO2/kWhex] aF

aP 1.86

[tCO2] AF

AP

C1

0.28

C2

e

C3

0.28

1.99

26

26

C

2.60

2.64

5572

5572

Sab

2.64

2.64

824

824

Mab

2.64

2.65

670

670

Hxa

2.64

3.30

86

86

HXb

2.64

2.93

68

68

T1

3.31

2.76

86

86

T2

2.77

6.13

86

86

T3

2.93

5.67

68

68

DHWa

6.07

7.76

86

86

Sa

0

0

0

0

DHWb

5.62

7.99

68

68

Sb

0

0

0

0

H1

3.00

11.92

188

188

H2

2.97

11.71

65

65

H3

3.09

12.32

58

58

H4

2.99

11.61

184

184

Mc1

2.81

3.00

1456

1456

Sc1

3.00

3.00

1269

1269

Mc2

2.84

2.97

821

821

Sc2

2.97

2.97

757

757

Mc3

2.92

3.09

856

856

Sc3

3.09

3.09

798

798

Mc4

2.79

2.99

1218

1218

Sc4

2.99

2.99

1034

1034

e

622 e

622 e

Those underlined values correspond to the final products of the installation (heating, DHW, electricity). They are then considered the most important values of each table.

868

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.9 Building with geothermal heat pump.

That DHW demand is covered by the condensing boiler, which operates at high temperature to reach the required setpoint, Best 2008 [9]. The control is carried out through a three-way modulation valve controlled by the regulation system, whose position varies according to the users’ needs and the weather conditions. The facility has numerous sensors that provide the necessary signals to control and guarantee its correct operation, as well as to monitor its operating status allowing, therefore, detailed energy monitoring to take place. Depending on the location of the flow and the monitored equipment, the data record is made in different periods: in general, the temperature values within the distribution circuit are collected every 15 min and those of the DHW circuit every hour, although there are calorimeters that extract daily values. In Fig. 11.10 the schematic of the installation is depicted, while Fig. 11.11 shows the simplified schema for the analysis. As seen, the equipment has been numbered and reorganized, in order to visually separate the generation, the distribution and the energy supply sections. As shown in Table 11.16, 18 components were considered, and their assigned numbers and abbreviations are exposed. In Fig. 11.12 the considered 50 flows for the thermodynamic study are numbered. As seen, some are highlighted with double arrows: flows D19, D20 and D33 correspond to the energy variation (exergy) accumulated in the deposits; 17 is the DHW return; 12 refers to the cold water inlet from the network; natural gas input into the boiler is 39; 41 assumes the electricity consumption of the heat pump; 42 refers to the obtained heat from the ground; 36 is the heating return. Dotted arrows correspond to flows 15, 35 and 43e49 and represent the electricity pumps consumption. Two

Application of exergecoeconomic and exergoenvironmental analysis

869

Figure 11.10 Schematic of the facility.

Figure 11.11 Reorganization of the schema and symbols of the considered components.

flows are drawn fatter, which correspond to the facility’s final products: flow 16 is DHW, and 34 is heating. As a summary, Table 11.17 shows the total number of components and flows and the external inputs and outputs, as well as the recirculations and the internal number of bifurcations.

870

Exergy Analysis and Thermoeconomics of Buildings

Table 11.16 Numbering, symbols and brief descriptions of the considered components. Considered components n

Symbol

Description

n

Symbol

Description

①

C

Boiler

⑩

HX2

DHW HP heat exchanger þ prim. pump

②

I1

Boiler impulsion manifold þ impul. pumps

⑪

HX3

Boiler heating heat exchanger

③

R1

Boiler return manifold

⑫

I2

Heating HP impulsion manifold þ secondary pump.

④

HX1

DHW boiler heat exchanger þ second. pump

⑬

R2

HP heat return diverter

⑤

T1

Tank 1

⑭

T3

Tank 3

⑥

T2

Tank 2

⑮

H

Heating preparation

⑦

DHW

V4V DHW

⑯

H/D

Heat/DHW collector

⑧

V1

V3V return DHW

⑰

V3

V3V ACS/heating þ HP

⑨

G

Geothermal circuit þ ground pump

⑱

HP

Heat pump

Figure 11.12 Numbered flows.

Application of exergecoeconomic and exergoenvironmental analysis

871

Table 11.17 Summary of components and flows. Physical determination Components

n

18

Flows

m

49

Inflows

e

18

Outflows

s

2

Bifurcations

b

13

Recirculations

r

29

11.4.2 Heating and DHW demands As previously stated, the facility has a monitoring system with numerous sensors allowing the collection of numerous data and the subsequent real data analysis. The electricity consumption in the heat pump, fuel consumption in the boiler and the values of temperature and mass flow rates were collected every quarter of an hour from June to November. Once these data were processed, the hourly energy values and exergy of each flow were calculated, which are the basis for a dynamic analysis of the plant operation. Fig. 11.13 shows the contribution of each generation unit, boiler and heat pump in DHW production. Besides, Fig. 11.14 depicts the contribution to heating. The boiler contributes more in DHW production, while in heating, the largest share comes from the heat pump. However, taking into account the studied period (JuneeNovember), DHW consumption is significantly higher than that required for heating, so, as will be demonstrated later, the boiler’s contribution share is bigger than that of the heat pump.

11.4.3 Functional analysis In Table 11.18, (A) the physical structure of the system is shown, while in Table 11.18, (B) its productive structure is reflected; therefore, the flows that are fuel and those that

Figure 11.13 DHW contribution from each of the heating generation units.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 11.14 Heating contribution from each generation unit.

Table 11.18 (A) Physical structure and (B) Productive structure of the facility. Physical structure

Productive structure

Inputs

Outputs

Fuels

Products

C

39 þ 40

1

[39]

[1e40]

C

I1

1 þ 43þ44

2þ3

[1]þ[43]þ[44]

[2]þ[3]

I1

R1

4þ5

40

[4]þ[5]

[40]

R1

HX1

2 þ 7þ45

6þ4

[2e4]þ[45]

[6e7]

HX1

T1

6 þ 8þ18 þ 19

7 þ 14

[6e7]þ[19]

[14-8-18]

T1

T2

10 þ 11þ20

8þ9

[20]þ[9e10]

[8e11]

T2

DHW

13 þ 14þ17

16 þ 18

[14e18]

[16-13-17]

DHW

V1

12

11 þ 13

[12]

[11]þ[13]

V1

G

37 þ 42þ35

38

[42]þ[35]

[38e37]

G

HX2

9 þ 21þ48

10 þ 22

[21e22]þ[48]

[9e10]

HX2

HX3

3 þ 28þ46

5 þ 26

[3e5]þ[46]

[30e28]

HX3

I2

25 þ 30

26

[25]þ[30]

[26]

I2

R2

27

28 þ 29

[27]

[28]þ[29]

R2

T3

26 þ 32þ33

27 þ 31

[26e27]þ[33]

[31e32]

T3

H

31 þ 36þ49

32 þ 34

[31e32]þ[49]

[34e36]

H

H/D

24

21 þ 25

[24]

[21]þ[25]

H/D

V3

22 þ 29þ15

23

[22]þ[29]þ[15]

[23]

V3

HP

23 þ 38þ41

24 þ 37

[41]þ[38e37]

[24e23]

HP

Application of exergecoeconomic and exergoenvironmental analysis

873

make up the product of each component are gathered according to their corresponding numbering. The functional classification of the flows is shown in Fig. 11.15, which represents the productive structure (fuel-product diagram) of the facility. As can be seen, a series of virtual components appear, which are the junction components (rhombuses) where the flows (fuel or product) are joined and the bifurcation components (circumferences) where the flows are separated, so that the arrows entering and exiting from each equipment represent its fuel and product respectively. For creating such a diagram, matrix and vector were used, as shown in Table 11.19. In this way, the resources of each component coming from different products can be detected: rij element of the matrix represents the percentage of the total resource of component j coming from component i. Thus, the sum of the P elements of each column rij is the unit where row 0 ( vector) is included in i external resources. Thus, for example, 4% of the total that sum which contains the resource of equipment 2 (impulsion manifold and pumps) comes from outside (r02, electricity for pumps), 56% comes from the boiler
s product (r12) and the rest (r32 ¼ 40%) comes from the recirculation of the return collector.

11.4.4 Energy analysis From the system data collected, the energy of each flow was calculated for each hour in the JuneeNovember period. The accumulated results are presented in Table 11.20, which reflects the energy associated with the fuel and the product of each component during the period, as well as its average energy efficiency. The heat pump has a seasonal COP of 4, while the boiler has also a high energy efficiency, with a 97% value.

11.4.5 Exergy analysis Similarly to the energy calculations, the exergy of the flows are calculated every hour from the values obtained from the monitored flows using the expressions from Chapter 3. Table 11.21 contains the cumulative exergy values of each flow during the considered period, while Table 11.22 is analogous to Table 11.20 and reflects each component
s fuel and product expressed in exergy terms (its quotient represents the seasonal exergy efficiency). Therefore, when passing from energy to exergy, the values of the component efficiencies, especially those related to the combustion equipment, are completely modified. Thus, while the energy efficiency of the boiler is hC ¼ 97%, its exergy efficiency results in 4C ¼ 7%. Something similar happens when flows are mixed at different temperatures: although energy efficiencies are usually close to unity, as it happens, for example, in the case of tanks and three-way valves (hT1 ¼ 83% and hH ¼ 98%), their exergy efficiencies are significantly lower (4T1 ¼ 43% and 4H ¼ 78%). However, the exergy destruction effect due to mixing is hardly noticed in manifolds R1 and I2. This is due to the control system intervention since most of

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.15 Fuel-Product diagram of the facility.

874

F TF ¼

¼

1

1

2

1

0.04

4

4

5

6

0.04

0.00

0.02

7

8

9

10

11

12

1

1

0.12

0.53

0.00

13

14

15

16

17

18

0.01

0.22

0.00

0.25

0.91

0.56 1.00

2 3

3

0.96

0.47

0.40 1.00

5

0.96

6

0.03

7 0.01

8

0.09

9 10

0.98 0.01

11

1.00

12

1.01

0.09

13

Application of exergecoeconomic and exergoenvironmental analysis

Table 11.19 Extended matrix in the PF representation.

0.54 0.78

14 15 16

0.88

0.90

0.21 0.24

18

0.76

875

17

876

Exergy Analysis and Thermoeconomics of Buildings

Table 11.20 Seasonal energy efficiency of components. Energy [kWh] h[%]

Fuel

Product

C

13,721

13,310

97

I1

25,635

25,635

100

R1

12,326

12,326

100

HX1

13,296

11,966

90

T1

11,966

9,930

83

T2

1,736

1,061

61

DHW

11,136

11,136

100

V1

9,331

9,331

100

G

2,244

1,626

72

HX2

1,758

1,738

99

HX3

13

12

89

I2

1,506

1,506

100

R2

1,199

1,199

100

T3

307

252

82

H

258

252

98

H/D

4,757

4,757

100

V3

2,704

2,704

100

HP

513

2,054

400

Table 11.21 Accumulated exergy values for each flow during the season. Accumulated exergy in flows [kWh] B1

B2

B3

B4

B5

B6

B7

B8

B9

B10

1613

1591

23

652

20

1013

169

37

118

28

B11

B12

B13

B14

B15

B16

B17

B18

B19

B20

10

10

0

705

16

705

303

303

1

2

B21

B22

B23

B24

B25

B26

B27

B28

B29

B30

129

13

44

192

63

70

37

6

31

7

B31

B32

B33

B34

B35

B36

B37

B38

B39

B40

157

136

0

157

22

136

19

70

14,290

671

B41

B42

B43

B44

B45

B46

B47

B48

B49

513

2

76

2

35

2

3

17

6

Application of exergecoeconomic and exergoenvironmental analysis

877

Table 11.22 Seasonal exergy efficiency of components. Exergy [kWh] 4[%]

Fuel

Product

C

14,290

942

I1

1,613

1,613

100

R1

673

671

100

HX1

938

844

90

T1

844

365

43

T2

92

27

30

DHW

402

402

100

V1

303

303

100

G

10

10

100

HX2

116

90

77

HX3

2

1

51

I2

70

70

100

R2

37

37

100

T3

32

21

65

H

27

21

78

H/D

192

192

100

V3

44

43

99

HP

513

148

29

7

the time only one flow enters those manifolds so that the output is, therefore, the input (there is no mixing of two different flows). For the heat pump, although by definition its COP is higher than unity, its exergy efficiency is significantly lower than one, since the product of the heat pump is lowquality thermal energy, while its fuel is electricity. In this case, the average exergy efficiency in the period is 4BC ¼ 29%.

11.4.6 Exergy costs From the exergy values of the flows and considering the previously described productive structure, exergy costs and the unit costs of the components’ fuel and product (k
F and k
P ) are calculated. The values obtained are presented in Table 11.23. As known, see Eq. (7.120), the exergy destruction in each component is identified by the difference between the cost of the product and the cost of the fuel, that is, for the

878

Exergy Analysis and Thermoeconomics of Buildings

Table 11.23 Unit exergy costs of the components’ fuel and product. Unit exergy cost [e] k
F

k
P

k
F

k
P

C

1.00

15.17

HX2

3.49

5.17

I1

14.58

15.28

HX3

7.75

32.20

R1

15.28

15.31

I2

4.32

4.32

HX1

14.77

17.02

R2

4.32

4.32

T1

17.00

39.40

T3

4.34

6.73

T2

5.09

17.08

H

5.44

7.02

36.94

36.94

H/D

3.85

3.85

V1

1.00

1.00

V3

3.34

4.57

G

1.00

0.47

HP

0.95

3.63

DHW

i-th component is equal to kP
i  kF
i . As expected, high exergy destructions arise in the boiler. Likewise, it can be seen how the upstream components influence the subsequent ones since the costs increase as the irreversibilities are accumulated. Therefore, the unit exergy cost of heating has a value of 7.02; similarly, DHW has 36.94. This difference in costs is, above all, due to the equipment used to satisfy those demands, see Fig. 11.13 and Fig. 11.14. DHW is supplied by the boiler (component with great irreversibilities) whereas heating is done by means of the heat pump. Because of that, more irreversibilities are accumulated in the DHW branch, so the unit exergy cost with respect to heating is bigger. Likewise, the number of intermediary components between generation and emission is greater. Besides, the exergy destructions at the DHW accumulation tanks must also be considered. Unlike the great exergy destructions occurring in the high-temperature radiators, in radiant floors, the irreversibilities between the indoor air and the heating terminal are significantly lower (kF
H kP
H ¼ 1; 58). If the heating and DHW demands were constant and any of the equipment suffered a degradation (an increase in its unit exergy consumption), this would be reflected in the rest of the equipment and especially in those located upstream from the faulty component. That implies that this equipment would require, in the new situation, more resources to be able to overcome the increase in unit consumption in order to maintain the same product.

11.4.7

Exergoeconomic costs

The calculation of the exergoeconomic costs is similar to that of exergy costs, but in this case, the price of the used resources, such as, natural gas, electricity and network water, as well as the levelized acquisition and maintenance costs of the equipment need to be considered. The costs due exclusively to the resources have been calculated and

Application of exergecoeconomic and exergoenvironmental analysis

879

Table 11.24 Prices of resources and investment costs. Tariffs Electricity [cV/kWh]

12.21

Natural gas [cV/kWh]

4.94

Cold water [V/m3]

0.52 Economic Data

Effective interest rate

0.05

Useful life of the facility (y)

20

Acquisition and start-up costs [V] C

17,046

HX2

493

I1

251

HX3

493

R1

768

I2

946

HX1

601

R2

946

T1

4601

T3

1284

T2

4594

H

1756

DHW

295

H/D

245

V1

629

V3

1099

G

982

HP

11,845

they are represented by the ceP vector; the total exergoeconomic costs have also been assessed, that is, taking into account the acquistion and maintenance costs. Table 11.24 shows the prices of the resources and the investment costs of the system equipment. Fig. 11.16 depicts the unit economic cost variation of heating and DHW (in grated line) along the energy supply chain, due to external resources, referred to exergy

Figure 11.16 Evolution of the heating unit economic cost and the heating profile along the system: per exergy unit (A) and per energy unit (B).

880

Exergy Analysis and Thermoeconomics of Buildings

(A) and energy (B). The figure also shows the energy and exergy profiles (in full line) of the entire energy chain, from primary energy (P.E.), generation (Gen.), collectors (Col.), distribution system (Dist.) and storage (Stor.) to the terminal elements (Emis.). It is verified that, as expected, the unit cost increases as the exergy(energy) decreases. Note the different order of magnitude of the unit exergoeconomic costs referred to exergy with respect to the ones referred to energy. On the other hand, even though the energy profile slope is relatively low (few losses), the exergy curve presents a pronounced reduction in the generation part, since, as shown in Fig. 11.13 and Fig. 11.14 and Table 11.22, the boiler percentage in the total exergy destruction is much higher than that of the heat pump (86% versus 14%). Therefore, at a global level, the irreversibilities in the boiler are of great influence. Table 11.25 shows the unit exergoeconomic costs of the fuel and product of each component; these costs are broken down in a part due to the external resources consumption and the other to investement costs. The DHW unit cost is 396.13 cV/kWhex which corresponds to 14.3 cV/kWhen, 201.94 cV/kWhex (7.29 cV/kWhen) due to consumption of resources and the balance 194.19 cV/kWhex (7.01 cV/kWhen) to investment. Likewise, the total heating unit cost is 733.87 cV/kWh (60.33 cV/kWhen), with 118.62 cV/kWhex due to external resources (9.75 cV/kWhen) and 615.25 cV/kWhex (50.58 cV/kWhen) to investement cost. If the unit exergoeconomic costs are compared with the unit exergy costs (Table 11.23), the reduction in the difference between the heating and DHW cost values can be surprising. Nevertheless it can be explained Pex Pex because in addition to the disparity between energy qualities PDHW < Pheat en en , the fixed costs DHW

heat

added by investment are remarkable, since heating is barely activated during the study period, and then these acquisition costs are more relevant, and such fact is easily seen with exergy analysis.

Table 11.25 Unit exergoeconomic costs (per exergy unit) of each component. Unit exergoeconomic costs [cV/kWh] n

czP

ceP

cF

n

cF

ceP

czP

C

5.07

76.95

31.84

HX2

230.88

95.79

252.26

I1

110.27

77.32

38.02

HX3

66.05

177.02

887.52

R1

115.34

77.48

40.11

I2

280.65

75.21

229.29

HX1

112.00

85.94

44.52

R2

304.50

75.21

273.70

T1

130.33

198.94

125.25

T3

306.10

117.21

466.28

T2

341.33

315.09

1125.73

H

457.67

118.62

615.25

DHW

394.84

201.94

194.19

H/D

258.30

73.47

187.08

V1

0.00

0.00

112.00

V3

243.82

77.28

294.77

G

21.81

10.33

33.66

HP

23.83

72.35

152.42

Application of exergecoeconomic and exergoenvironmental analysis

881

Table 11.26 Heating and DHW exergoeconomic costs. Final costs cV/kWh

V/period

V/dwelling$period

DHW

14.30

1597

61

Heating

60.33

183

7

The average DHW and heating costs during the study period (JuneeNovember) are shown in Table 11.26; the total DHW cost per dwelling during those months is 61V, with 7V being the heating cost per dwelling.

11.4.8 Impact on CO2 emissions Table 11.27 shows the unit environmental costs referred to CO2 emissions, for the components’ fuel and product, as well as the total CO2 emissions throughout the period. As said, the obtained values reflect only the impact due to the used external resources, natural gas and electricity; but, do not take into account the impact associated with the equipment, since this information implies having an LCA available for each component. Finally, the unit heating emissions are 0.29 kgCO2/kWhex (0.02 kgCO2/kWhen), resulting in 0.07 t CO2 total emissions during the period. Referring to DHW, the unit emission is 0.27 kgCO2/kWhex (0.01 kgCO2/kWhen), which represents 3.06 t CO2 total emissions for the entire period. For these calculations, only the emissions due to the natural gas combustion and those associated with the electricity consumption were taken into account, for which the Document on CO2 Emission Factors [10] was used.

11.5

Case 3: heating and DHW facility with boiler and CHP

11.5.1 Description of the building and its thermal facility Case 3 is an nZEB building composed of 171 social housing units, one private property, three commercial shops and linked urbanization. There are eight floors, two basements and a commercial area, and it is located in Vitoria-Gasteiz (Basque Country), see Fig. 11.17, Tecmared Group 2017 [11]. The dwellings have linked 176 storage rooms located in the floor below deck and a garage situated on two basement floors with 184 spaces. The boiler room and the electric transformation center are located on the ground floor. The central heating production system covers the heating and DHW demands through an 80/60 C hot water circuit. It consists of two high-performance natural gas boilers working in cascade, with adjustable useful power between 320 and

882

Exergy Analysis and Thermoeconomics of Buildings

Table 11.27 CO2 emissions associated with the components product and fuel. Impact on CO2 emissions [kgCO2/kWhex] aF

[tCO2]

aP

AF

Ap

C

0.20

0.21

2.80

2.80

I1

0.19

0.19

4.81

4.81

R1

0.16

0.16

2.01

2.01

HX1

0.21

0.23

2.80

2.80

T1

0.23

0.28

2.80

2.80

T2

0.15

0.24

0.26

0.26

DHW

0.27

0.27

3.06

3.06

V1

0.00

0.00

0.00

0.00

G

0.01

0.01

0.02

0.02

HX2

0.15

0.15

0.26

0.26

HX3

0.49

0.58

0.01

0.01

I2

0.10

0.10

0.16

0.16

R2

0.07

0.07

0.08

0.08

T3

0.24

0.29

0.07

0.07

H

0.29

0.29

0.07

0.07

H/D

0.09

0.09

0.42

0.42

V3

0.04

0.04

0.10

0.10

HP

0.31

0.16

0.32

0.32

500 kW each and 92.7% energy efficiency at full load and 95.2% when the load is 30%. Instead of providing 30% of the DHW (climatic zone I) by means of solar panels, two cogeneration engines have been installed, with 5.5 kW electrical power and 12.5 kW thermal power each. The cogeneration engines work against a 3000 L inertia tank through a heat exchanger, Gelegenis and Axaopoulos, 2015 [12]. The integration of the inertial tank allows the simultaneous charge and discharge. The flows coming from the inertia tank and boilers are directed to a discharge manifold from which the water is distributed to the heating and DHW circuits. This hot water flow passes through a heat exchanger, so that the secondary circuit is connected to a 3000-L DHW storage tank. In addition to the combustion equipment, the building has a series of PV panels located under the windows on the south facade, with a peak power of 33.5 kW, Abella 2005 [13].

Application of exergecoeconomic and exergoenvironmental analysis

883

Figure 11.17 nZEB building in Vitoria-Gasteiz (Basque Country).

The operation of the facility gives the priority to the two engines, for both DHW and heating. They are designed to supply 90% of the DHW demand. The engines start operating whenever there is a demand, either DHW or heating, because they are the most advantageous systems since they simultaneously produce electrical energy and heat. When the demand exceeds the production of the alternative engines, the boilers start functioning since an external control turns on the boilers when the engines cannot supply all the demand. The engines do not have additional external control, in as much their shutdown is internally implemented if the return temperature is higher than 73 C. In its standard configuration, the boilers have a control for partial load modulation in accordance with the return temperature. The hot water is produced at 80 C. As the maximum demand is around 600 kW and each of the boilers is capable of supplying 500 kW, the secondary boiler hardly operates during the whole year, only during the demand peaks. The principal boiler works in a load range from 0 to 1, while the second is put into operation when the demand exceeds 500 kW and, therefore, works in a very low partial load. The simplified hydraulic schema of the installation is shown in Fig. 11.18, in which all the equipment considered has been listed and numbered. Table 11.28 shows the selected components, with its numbering and the designated symbols. For each component, the input and output internal flows are defined, as well as the flows exchanged with the environment. In Fig. 11.19, the installation schematic prepared for the analysis is presented with the numbered flows. Table 11.29 is a summary including the number of considered components, the total number of flows, the number of system inputs and outputs and the number of bifurcations and recirculations. The m ¼ n þ e þ r, m ¼ n þ e þ b and m ¼ n þ s þ r equalities are fulfilled, so that the system of equations that allows the flow costs to be calculated is closed.

884

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.18 Numbering and symbols of the considered components in the simplified schema. Table 11.28 Numbering, symbols and brief descriptions of the considered components. Considered components n

Symbol

Description

1

C1

Cogeneration group 1

2

C2

Cogeneration group 2

3

M1

Cogeneration impulsi
on mixer

4

D1

5

n

Symbol

Description

8

B2

Boiler group 2

9

HC

Hydraulic compensator

10

H

Heating emissor þ heating pump

Cogeneration return diverter þ cog pump

11

HX2

DHW heat exchanger þ HX primary pump

HX1

Cog heat exchanger þ cog tank pump

12

T2

DHW tank þ DHW HX secundary pump

6

T1

Cogeneration tank þ distribution pump

13

DHW

DHW emissor

7

B1

Boiler group 1

The geometric model of the building was built in AutoCad, and later TRNSYS v17 was used to perform the simulation of heating and DHW demands. Then, the thermal installation was simulated using the Simulation Studio interface of TRNSYS. For this, the components that best represent the system were selected from the wide accessible

Application of exergecoeconomic and exergoenvironmental analysis

885

Figure 11.19 Numbering of the considered flows.

Table 11.29 Summary of components and flows. Physical determination Components

n

13

Flows

m

41

Inflows

e

7

Outflows

s

4

Bifurcations

b

21

Recirculations

r

24

library. The simulation was performed throughout the year with the Vitoria-Gasteiz meteorological data. The model in TRNSYS is shown in Fig. 11.20. The flow rates and temperatures of each flow were obtained throughout the 8760 h simulation period. These data are the basis of the analysis presented below.

11.5.2 Heating and DHW demands As said, an hour-by-hour simulation was carried out, to obtain the heating and DHW demand profiles shown in Fig. 11.21. The DHW demand profile was obtained using the same hypotheses from Section 11.3.2.

886

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.20 Model of the thermal installation in TRNSY.

Figure 11.21 Heating and DHW demands during the year.

11.5.3

Functional analysis

In Table 11.30 (A) the physical structure of the plant is presented, or what is the same, the flows that enter and leave each component. In Table 11.30 (B) the productive structure is shown, that is, each component
s fuel and product, according to the functional analysis accomplished. The total product of the system is heating, B_ 27 , DHW, ðB_ 31  B_ 32 Þ, and the generated net electricity, which is the sum of the electricity generated in the two engines minus the consumptions of the pumps, ðB_ 6 þ B_ 13 Þ. The installation total resources consist of the fuel consumption in the boilers plus the consumption in the engines ðB_ 41 þ B_ 10 þ B_ 16 þ B_ 19 Þ because as mentioned, the pumps are fed directly from the cogenerated electricity.

Physical structure

Productive structure

Inputs

Outputs

Fuels

Products

C1

3 þ 41

1þ6

[41]

[1e3]þ[6]

C1

C2

4 þ 10

2 þ 1þ13 þ 24þ34 þ 35 þ36 þ 37þ38 þ 39þ40

[10]

[2e4]þ[13]þ[24]þ [34]þ[35]þ[36]þ[37] þ[38] þ[39]þ[40]

C2

M1

1þ2

5

[1]þ[2]

[5]

M1

D1

7 þ 34

3þ4

[7]þ[34]

[3]þ[4]

D1

HX1

5 þ 9þ35

7þ8

[5e7]þ[35]

[8e9]

HX1

T1

8 þ 11þ21 þ 24

9 þ 12

[8e9]þ[11]þ[24]

[12e21]

T1

B1

15 þ 16þ36

14

[16]þ[36]

[14e15]

B1

B2

18 þ 19þ37

17

[19]þ[37]

[17e18]

B2

HC

12 þ 14þ17 þ 22þ25

15 þ 18þ20 þ 21þ23

[12]þ[14]þ[17]þ[22]þ[25]

[15]þ[18]þ[20]þ[21]þ[23]

HC

H

20 þ 38

22 þ 27

[20e22]þ[38]

[27]

H

HX2

23 þ 28þ39

25 þ 26

[23e25]þ[39]

[26e28]

HX2

T2

26 þ 29þ33 þ 40

28 þ 30

[26e28]þ[29]þ[40]

[30e33]

T2

DHW

30 þ 32

31 þ 33

[30e33]

[31e32]

DHW

Application of exergecoeconomic and exergoenvironmental analysis

Table 11.30 (A) Physical structure and (B) Productive structure of the facility.

887

888

11.5.4

Exergy Analysis and Thermoeconomics of Buildings

Energy analysis

In Table 11.31 (A) the yearly accumulated energy values of the components’ fuel and product are presented. The quotient of these values gives the annual average energy efficiency, which appears in the right column. Similar energy efficiency values from the previous cases are observed. Distribution system components, such as separators, mixers, hydraulic compensators and heat exchangers have very high energy efficiencies (in some cases even reaching 100%, if they are considered approximately adiabatic). Likewise, the tank efficiencies are close to unity, while the combustion engines have lower energy efficiencies, but also high hgen>80%. The circulation pumps were grouped together with different thermal equipment. If they were individually analysed, the mechanical energy variation of the flow (the water specific volume multiplied by the increase in pressure between inlet and outlet) should be considered as a product of the pump, and the fuel should be the consumed electricity.

11.5.5

Exergy analysis

Similarly, using the equations seen in Chapter 3, the exergy of each flow was calculated hourly over the year and cumulated, see Table 11.32. From these values, the exergy of the equipment
s fuel and product can be calculated, and the average annual exergy efficiency can be obtained, see Table 11.31 (B), the column on the right. It is noteworthy that, although the average energy efficiency of the boilers hB ¼ 92% is higher than that of the cogeneration engines hC ¼ 80%, its exergy efficiency 4B ¼ 15% is significantly lower than 4C ¼ 36%. Thus, it may seem that from the First Law viewpoint boilers are more efficient: however, the reality is that cogeneration engines perform better. After all, one of the products of the cogeneration is electricity, and it is high-quality energy. Considering the facility as a whole and referring to electricity generation, the annual electrical efficiency was 39.8% and the electrical exergy efficiency 38.3%. On the other hand, the annual energy efficiency in the heating and DHW generation was 86.4%, and the exergy efficiency was 8.2%. Finally, the total energy efficiency of the facility throughout the year was 89.4%, and the exergy efficiency was 7.1%.

11.5.6

Exergy costs

Knowing the exergies of the flows and taking into account the productive structure, the unit exergy costs vector of the components
fuel and product is calculated (k
F and k
P ). Table 11.33 shows the obtained average annual values. As it is known, the exergy destruction in each i-th component is identified with the difference between
P and the fuel cost k
F . Natural gas is the resource used in the the product cost kP;i i F;i i boiler and cogeneration engines, and its unit exergy cost was considered equal to 1. However, since pumps are supplied with the cogenerated electricity, its exergy cost is

equal to kF;pump ¼ kP;cog .

Application of exergecoeconomic and exergoenvironmental analysis

889

Table 11.31 (A) Yearly energy efficiency and (B) yearly exergy efficiency of components. Energy [kWh] h[%]

Fuel

Product

C1

56,358

44,962

80

C2

58,056

45,426

78

M1

1,218,898

1,218,898

100

D1

1,165,613

1,159,401

99

HX1

61,330

60,109

98

T1

60,434

57,978

96

B1

837,763

768,894

92

B2

79,315

72,902

92

HC

16,642,400

16,635,432

100

H

600,469

599,120

100

HX2

294,871

294,151

99

T2

295,005

289,954

98

DHW

289,954

289,873

100

Fuel

Product

4 [%]

C1

58,612

20,983

36

C2

60,378

21,443

36

M1

105,835

105,835

100

D1

100,773

94,301

94

HX1

131.07

11,109

85

T1

11,647

10,563

91

B1

871,182

141,006

16

B2

82,483

12,717

15

HC

1,351,061

1,336,877

99

H

108,690

25,447

23

HX2

43,947

41,051

93

T2

42,133

24,525

58

DHW

24,525

19,849

81

Exergy [kWh]

890

Table 11.32 Annual accumulated exergy values for each flow. Accumulated exergy in flows

[kWh]

B2

B3

B4

B5

B6

B7

B8

B9

B10

52,917

52,918

47,151

47,151

105,835

15,217

94,242

208,984

197,875

60,378

B11

B12

B13

B14

B15

B16

B17

B18

B19

B20

34

72,849

1038

549,567

408,561

868,882

26,711

13,994

82,385

744,949

B21

B22

B23

B24

B25

B26

B27

B28

B29

B30

[kWh]

62,286

637,707

107,086

572

64,226

101,517

25,447

60,466

5

24,778

B31

B32

B33

B34

B35

B36

B37

B38

B39

B40

B41

20,172

323

253

6531

1514

2299

99

1448

1087

1087

58,612

Exergy Analysis and Thermoeconomics of Buildings

[kWh]

B1

Application of exergecoeconomic and exergoenvironmental analysis

891

Table 11.33 Unit exergy costs of each component
fuel and product. Unit exergy cost [e] k
F

k
P

k
F

k
P

C1

1.00

2.79

B2

1.00

6.50

C2

1.00

2.82

HC

6.69

6.76

M1

4.38

4.38

H

6.71

28.65

D1

4.28

4.57

HX2

6.66

7.13

HX1

4.20

4.95

T2

7.02

12.06

T1

4.86

5.36

DHW

12.06

14.90

B1

1.00

6.21

Considering the table, it is worth highlighting the remarkable increase in the unit
cost between the fuel and product of the heat emitting device, going from kF;H ¼ 6:71
to kP;H ¼ 28:65. This is because in such component the indoor air was included, and therefore, its product is the heat given to the indoor air (which is at a temperature close to the environment Top) and not the heat at the surface temperature of the

radiators. Nevertheless, the unit cost of the fuel is kF;DHW > kF;H since, as in the previous case, DHW generation crosses more equipment and therefore accumulates more irreversibilities and increases its unit exergy cost. Finally, the heating unit exergy cost is 28.65, that of DHW is 14.9 and that of cogenerated electricity varies slightly from one engine to another, with a value close to 2.8.

11.5.7 Exergoeconomic costs In Table 11.34 (A) the purchase prices of electricity from the grid, natural gas and water are presented, as well as other economic data, such as the useful life of the facility and the interest rate. In Table 11.34 (B) the equipment acquisition costs are shown, according to the data obtained from the project. Consequently, the exergoeconomic costs of the flows were calculated, as well as the costs of each component
s fuel and product. Table 11.35 gathers the unit costs (per unit of exergy) of each component
s fuel and product, having separated the total cost into two components: one due to the used resources, and the other indirect cost due to the investment in the equipment. Table 11.36 shows the heating and DHW annual average unit costs and the cogenerated electricity unit cost, as well as the building’s annual cost and the cost per dwelling, referred to energy. Then, the savings obtained with the cogenerated electricity are shown in Table 11.37, resulting from subtracting the cogenerated electricity cost from the purchase cost if it had been purchased directly from the electrical grid. In spite of a relatively low number of the engines’ operating hours (1477 h/year for the two

892

Exergy Analysis and Thermoeconomics of Buildings

Table 11.34 Prices of resources and investment costs. Tariffs Electricity [cV/kWh]

22.33

Natural gas [cV/kWh]

5.43

Cold water [V/m3]

0.52 Economic data

Effective interest rate

0.05

Useful life of the facility (y)

20

Acquisition and start-up costs [V] C1

20,148

B2

21,713

C2

20,148

HC

1640

M1

7679

H

6502

D1

8184

HX2

2531

HX1

1720

T2

6084

T1

6216

DHW

21,280

B1

21,713

Table 11.35 Unit exergoeconomic costs of each component
s fuel and product. Unit exergoeconomic costs [(cV/kWh)] n

cF

ceP

czP

n

cF

C1

5.07

14.17

10.11

B2

5.09

32.92

18.05

C2

5.07

14.28

9.89

HC

40.08

34.20

6.32

M1

51.35

22.19

29.92

H

40.30

144.93

29.90

D1

50.30

23.17

31.50

HX2

40.12

36.08

7.51

HX1

48.89

25.11

34.20

T2

43.10

61.03

15.62

T1

57.75

27.18

42.70

ACS

76.65

75.41

30.59

B1

5.12

31.40

1.78

ceP

czP

Application of exergecoeconomic and exergoenvironmental analysis

893

Table 11.36 Unit costs of system products and annual total costs. Final products costs[cV/kWhen] ceP

czP

V/year

V/dwe

Heating

6.16

1.27

45.174 V

257 V

DHW

5.16

2.09

23.278 V

132 V

Electricity

6.68

4.69

14.516 V

82 V

Table 11.37 Savings with self-produced electricity. Savings [V/a~ no] Total Network purchase cost

6737

Cogenerated cost

3512

Yearly saving

3226

engines), there are notable savings; after all, the electricity purchased from the network (22.33 cV/kWh) is replaced by that which is produced by the engines (11.37 cV/kWh). Consequently, not only are energy savings obtained with the cogeneration micromotors, since they present a greater exergy efficiency than boilers, but they are also economically attractive, even though micromotors require relatively high investments in the beginning.

11.5.8 Impact on CO2 emissions Following the same methodology as in the previous cases, the environmental impact is calculated by evaluating the CO2 emissions linked to each flow, as well as that of each component
s fuel and product. As in the previous cases, emissions associated with the manufacturing of the equipment were not considered. In Table 11.38 only the CO2 Table 11.38 Unit CO2 emissions from the system products and total emissions. Impact on CO2 emissions [kgCO2/kWhen]

[tCO2]

Heating

0.24

142.66

DHW

0.20

57.90

Electricity

0.26

23.34

894

Exergy Analysis and Thermoeconomics of Buildings

emissions associated with each of the three products of the facility are presented, together with the annual emissions. Obviously, the sum of these emissions corresponds to those due to the natural gas combustion in boilers and microengines.

11.6 11.6.1

Case 4: trigeneration facility of a hospital Description of the building and its facility

The following facility refers to a hospital with 1000 beds, located in Bilbao, see Fig. 11.22. Hospitals are characterized by being large thermal and electrical energy consumers; so in recent years a growing concern has been developing for improving their thermal system efficiencies and reducing their energy costs, Fenercom 2010 [14]. Therefore, it is very common to find in hospitals high-efficiency heat and cold generation facilities, such as trigeneration plants. The heat generation system of this hospital consists of two natural gas boilers, one with a nominal power of 3448 kW, which can modulate from 1200 kW (Boiler 1), and the other of 3000 kW, which modulates from 1500 kW (Boiler 2). In addition, there are two cogeneration engines powered by natural gas with an electrical power of 1056 kWe (Cog. 1 and Cog. 2). The produced electricity is sent to the electrical grid, except for what is required for auxiliary equipment self-consumption. Likewise, the thermal energy generated by the engines is recovered through four heat exchangers. The equipment operates according to the thermal demand; first, the engines are turned on and subsequently the boilers. Cold production is carried out by means of two water chillers of single-effect absorption cycles, one of 650 kW (York) and the other of 1000 kW (Broad); both

Figure 11.22 Hospital buildings in Bilbao (Basque Country).

Application of exergecoeconomic and exergoenvironmental analysis

895

powered by hot water, Catalog 2016 [15]. The operation of the latter is subject to the established schedules of the cogeneration engines. Additionally, there are four aircooled chillers, two of 705.4 and 792.5 kW (McQ and Quay 2) and another two of 974 kW (RTHC and RTAC). These chillers are condensed by air, not by water, to minimize the risks of appearance and proliferation of the Legionella bacteria [15]. In the installation, there are also five cooling towers. Consequently, since the facility of this hospital is so complex, it was necessary to reorganize the equipment according to the performed function; therefore, the schematic of Fig. 11.23 was finally achieved. Distribution lines exit from the generation subgroup, which supply hot water and cold water to the different components. Some of these lines gather in a manifold for hot water (upper right part of Fig. 11.23) and others for cold water (low right part of Fig. 11.23). The distribution of hot water is carried out from the hot water manifold and the DHW distribution, conversely, is done by means of a heat exchanger (see rectangle in dotted line on the right upper part of Fig. 11.23). In addition, the cold water distribution is carried out directly from each collector. In spite of the already introduced simplifications, there are still numerous components in the schema of Fig. 11.23. However, the difficulty lies in adequately grouping the equipment in subsystems, rather than in the considered number, since a greater number of components does not imply a higher mathematical complexity if the analysis is performed by applying ST. For making this idea clear, the study was carried out in two ways: • •

In an exhaustive way: considering 57 components (where five correspond to each cooling tower, that is, dissipative equipment) and 126 flows. In a more simplified or compact way: considering 17 equipment groups (where two groups are the dissipative equipment) and 63 flows.

The number of chosen components depends to a great extent on the plant monitoring system; so, the more sensors there are, the greater the detail of the dynamic representation will be. However, in order to reduce the amount of data, a thermoeconomic study can be done in two stages: in the first one, a compacted analysis is made, by grouping units in different groups, and this way, the subset of the greatest influence on cost, on destruction of exergy, etc. is detected. In the second stage, the detailed study of the identified subgroup is carried out. In addition, if a greater precision is still desired, the ST application can be focused on a subgroup of that specific set or simply on a component. Therefore, by breaking down the components, the required level of detail is reached. The higher the level of disaggregation, the better the understanding of the cost formation process is. For space reasons, the results for the simplest (compact) case of the two studied are here presented. Table 11.39 shows the considered components (15 productive and 2 dissipative), the used symbols and the denomination of the selected subgroups. As mentioned, two rows were added for the representation of the dissipative components (T1 and T2). These two components do not follow any productive objective but have the purpose of dissipating energy to guarantee the correct functioning of the

Exergy Analysis and Thermoeconomics of Buildings

Figure 11.23 Schematic of the facility.

896

Application of exergecoeconomic and exergoenvironmental analysis

897

Table 11.39 Numbering, symbols and brief descriptions of the considered components. Considered components n

Symbol

Description

n

Symbol

Description

1

B1

Boiler group 1

10

RTHC

RTHC cooling group

2

B2

Boiler group 2

11

RTAC

RTAC cooling group

3

C1

Cogeneration group 1

12

McQ

McQ cooling group

4

C2

Cogeneration group 2

13

Q

Quay2 cooling group

5

Dist

Distribution group

14

BROAD

Broad cooling group

6

DHWgen

DHW generation group

15

Cold

Cooling dissipation group

7

Heat

Heating group

16

T1

Cooling towers group 1

8

DHW

DHW group

17

T2

Cooling towers group 2

9

Y

York cooling group

rest of the equipment. In effect, the cooling towers are needed for cooling the water flow of the condensation circuit and that of the cooling circuit engines. As done in the rest of the cases, the entering and outgoing flows of each component are defined. Table 11.40 presents a summary for the thermodynamic study, which also reflects the number of dissipative components and the number of residue flows. Figure 11.24 shows the grouping of the equipment and the installation schema is presented in Fig. 11.25. The flows are also listed there, being m ¼ 63.

11.6.2 Functional analysis The facility physical structure is shown in Table 11.41 (A). Likewise, once the functional analysis was carried out, the flows that pertain to the fuel and product of each Table 11.40 Summary of components and flows. Physical determination Components

n

15

Flows

m

63

Inflows

e

20

Outflows

s

7

Bifurcations

b

26

Recirculations

r

39

Dissipative comp.

nD

2

Residue flows

sR

2

898 Exergy Analysis and Thermoeconomics of Buildings

Figure 11.24 Composition of the components involved in the facility.

Application of exergecoeconomic and exergoenvironmental analysis

Figure 11.25 Numbering and symbols of the considered components and flows. 899

Table 11.41 (A) Physical structure and (B) Productive structure of the facility. 900

Physical structure

Productive structure

Inputs

Outputs

Fuels

Products

B1

48 þ 1þ4

2þ3

[48]þ[2e1]

[3e4]

B1

B2

49 þ 6

5

[49]

[5e6]

B2

C1

50 þ 8

7 þ 56

[50]

[7e8]þ[56]

C1

C2

51 þ 10

9 þ 57

[51]

[9e10]þ[57]

C2

Dist

2þ3þ5þ7þ9þ 12 þ 16 þ 17 þ 18

1 þ 4 þ 6 þ 8 þ 10 þ 11 þ 13 þ 14 þ 15

DHWgen

13 þ 32

12

Heat

10 þ 20 þ 24 þ25 þ 26 þ 31

18 þ 19 þ 21 þ 22 þ 23

DHW

19 þ 30 þ 27 þ 28

20 þ 29

[19e20] þ [30]

[29-27-28]

DHW

Y

15 þ 34

16 þ 33 þ 59

[15e16]

[33e34] þ [59]

Y

RTHC

52 þ 36

35

[52]

[35e36]

RTHC

RTAC

53 þ 38

37

[53]

[37e38]

RTAC

McQ

54 þ 40

39

[54]

[39e40]

McQ

Q

55 þ 42

41

[55]

[41e42]

Q

BROAD

14 þ 44

17 þ 43 þ 58

[14e17]

[43e44] þ [58]

BROAD

Cold

33 þ 35 þ 37 þ 39

46 þ 34 þ 36 þ 38 þ 40 þ 42 þ 44

[46e45]

Cold

T1

59 þ 61

63

[59] þ [61]

[63]

T1

T2

58 þ 60

62

[58] þ [60]

[62]

T2

[2] þ [3] þ [5] þ [7] þ [9] þ [12] þ [16] þ [17] þ [18] [13]þ[32] [11] þ [20] þ [24] þ [25] þ [26] þ [31]

[12] [18] þ [19] þ [21] þ [22] þ [23]

Dist DHWgen Heat Exergy Analysis and Thermoeconomics of Buildings

[33e34] þ [35e36] þ [37e38] þ [39e40] þ [41e42] þ [43e44] þ[47]

[1] þ [4] þ [6] þ [8] þ [10] þ [11] þ [13] þ [14] þ'[15]

Application of exergecoeconomic and exergoenvironmental analysis

901

group were defined, that is, the productive structure is defined and is presented in the right part of Table 11.41 (B).

11.6.3 Energy analysis According to the thermodynamic parameters of components, Table 11.42 was filled, which shows the energy accumulated values throughout the year of each component
s fuel and product, as well as their average energy efficiencies. The conclusions obtained from this Table 11.42 are similar to those seen in the previous cases. The units with combustion processes have high energy efficiencies, with boilers having slightly higher values than those of the cogeneration equipment (hBi ¼ 91%, hCi ¼ 89%.) Referring to cold production, absorption refrigerators have energy efficiency ratios of EERY ¼ 0.71 and EERBROAD ¼ 0.73, while for absorption chillers these coefficients are, in all cases, greater than unity (COPRTHC ¼ 2.97,COPRTAC ¼ 1.29,COPMcQ ¼ 3.15,COPQ ¼ 3.15). It does not make Table 11.42 Seasonal energy efficiencies of components. Energy [MWh]

ɳ [%]

Fuel

Product

B1

5,887

5,405

92

B2

6,146

5,562

91

C1

8,256

7,365

89

C2

8,125

7,231

89

Dist

293,041

290,724

99

DHWgen

75,362

73,325

97

Heat

202,182

200,058

99

DHW

18,411

15,189

83

Y

2,032

1,443

71

RTHC

793

2,354

297

RTAC

705

912

129

McQ

309

972

315

Q

309

972

315

BROAD

4,907

3,603

73

Cold

8,779

3,038

35

T1

5,985

5,985

e

T2

8,624

8,624

e

902

Exergy Analysis and Thermoeconomics of Buildings

sense to define efficiencies for dissipative components since they have no productive purpose. If the installation as a whole is analysed, considering the production of each component, the average energy efficiency for heating was found to be 94%, 92% for DHW, 24% for electricity and the ratio between the produced cold and the resources consumprion in the cooling machines was found to be 2.13.

11.6.4

Exergy analysis

The value of each flow exergy was calculated with the equations of Chapter 3. In Table 11.43, the exergy of the fuel and product of each component and their average annual exergy efficiencies are shown. As in the previous cases, high exergy destructions appear in the equipment in which combustion reactions take place. Likewise, it is verified that the exergy efficiencies of the engines are significantly higher than

Table 11.43 Seasonal exergy efficiency of components. Exergy [MWh] Fuel

Product

4 [%]

B1

6,030

896

15

B2

6,392

919

14

C1

8,586

2,909

34

C2

8,450

2,883

34

Dist

19,319

18,680

97

DHWgen

6,185

6,041

98

Heat

12,201

11,226

92

DHW

2,398

892

37

Y

346

76

22

RTHC

793

124

16

RTAC

705

48

7

McQ

309

51

17

Q

309

51

17

BROAD

815

190

23

Cold

652

352

54

T1

320

320

e

T2

461

461

e

Application of exergecoeconomic and exergoenvironmental analysis

903

that of the boilers, due to the fact that one of their products is electricity, while as seen before, their energy efficiencies are lower. In this case, for the installation as a whole, the average exergy efficiency for heating is 6%, for DHW is 3%, for electricity 11% and for cold production 24%. Therefore, the values are significantly lower than the respective average energy efficiencies. As previously mentioned, in order to obtain more information from ST, the analysis can be performed with a higher disaggregation level. Thus, to know in detail which mechanism is contributing the most in the irreversibilities of the combustion components, the system can be subdivided into a series of subsystems as follows: air and fuel inlet, mixture, combustion reactions and gas-water heat transfer. In this way, it is possible to determine exactly where the greatest destructions are generated and to understand better the cost formation process.

11.6.5 Exergy costs Table 11.44 presents the average unit exergy costs of each component
s fuel and product, underlining (as in the previous cases) the final heating cost, the DHW cost, the electricity cost and the cooling unit exergy cost. In this case, since there are dissipative devices that introduce residues costs, a third column has been included kpr;
. This column represents the unit extra consumption required due to the presence of dissipative equipment; that is, because of the need for heat dissipation in cooling devices. Consequently, it only affects the costs of the cooling circuit groups. Likewise, in the absence of external valuation, the unit exergy costs associated with external resources are equal to unity. In this case, this resource is natural gas used in boilers and alternative engines, while electricity is the resource of compression Table 11.44 Unit exergy costs of each component
s fuel and product. Unit exergy costs[e] k
F

ke:
P

kr:
P

B1

1.01

6.77

0

RTHC

1.00

6.38

0

B2

1.00

6.95

0

RTAC

1.00

14.66

0

C1

1.00

2.95

0

McQ

1.00

6.02

0

C2

1.00

2.93

0

Q

1.00

6.02

0

Dist

3.17

3.27

0

BROAD

3.27

6.70

8.66

DHWgen

2.04

2.09

0

Cold

9.91

11.06

7.29

Heat

2.80

3.05

0

T1

8.32

2.87

5.45

DHW

3.03

8.15

0

T2

7.49

3.58

3.92

Y

3.27

5.14

12.06

k
F

ke:
P

kr:
P

904

Exergy Analysis and Thermoeconomics of Buildings


(Y and BROAD) accumurefrigerators. It can be seen that the absorption chillers kFi late all the irreversibilities up to the entrance of that equipment, so their cost is equal to that of hot water. Besides, it is observed that boiler B1 has a fuel unit cost slightly greater than unity (kF
B1 ¼ 1'01) because it is associated with a heat recovery (which has a cost because it is an intermediate flow). This makes its product cost less than that of the other boiler B2 (kP
B1 < kP
B2 ) due to a greater exergy efficiency. According to Table 11.44, the DHW unit exergy cost is 80 15, or what is the same, 1 kWh of DHW production requires 80 15 kWh of exergy. On the other hand, the heating unit exergy cost is 30 05, while that of the cold is 180 35. Taking into account the different origins of the cold, the exergy annual average unit exergy cost of the cold produced by the chillers is 70 7, and that produced by the absorption units is 120 04 respectively. Besides, the unit exergy cost of electricity is 20 94.

11.6.6

Exergoeconomic costs

In Table 11.45 (A) the tariffs for natural gas and electricity are presented, which are the same as in the other cases, as well as the facility useful life and the interest rates.

Table 11.45 Resources prices and investment costs. Tariffs Electricity [cV/kWh]

12.21

Natural gas [cV/kWh]

4.94

Cold water [V/m3]

0.52 Economic data

Effective interest rate

0.05

Facility useful life (y)

20 Acquisition and start-up costs [V]

Heat/DHW

Cold

B1

75,000

Y

90,000

B2

65,000

RTHC

105,000

C1

715,575

RTAC

100,000

C2

715.575

McQ

121,565

Heat

5000

Q

121,565

DHW

30,155

BROAD

122,921

Cold

43,194

Application of exergecoeconomic and exergoenvironmental analysis

905

Table 11.46 Unit costs of the final products of the facility. Economic costs[cV/kWh] per energy unit ceP

crP

czP

c

Heat

0.64

0

0.01

0.65

DHW

1.80

0

0.03

1.83

Cold

17.43

4.56

0.37

22.35

Elec

5.92

0

0.17

6.09

Table 11.47 Unit and total CO2 emissions of the products of the facility. CO2 emissions [kgCO2/kWhen] Heat

0.02

DHW

0.07

Cold

0.70

Elec

0.23

Table 11.45 (B) includes the investment costs of the subgroups forming the installation, in accordance with the data provided by the hospital’s maintenance service. Table 11.46 shows the unit costs of the final products (per unit of energy). These costs have been broken down into its three fractions: those due to resources, the part associated with the dissipation and those related to the equipment investment.

11.6.7 Impact on CO2 emissions Finally, the CO2 emissions associated with each flow were calculated due exclusively to the used resources, which are electricity and natural gas. The unit CO2 emissions of the installation
s products are presented in Table 11.47.

Subscript F, P n m e,s,b,r

Fuel, product Number of components Number of flows Number of entries to the system, exits, bifurcations and recirculations

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Exergy Analysis and Thermoeconomics of Buildings

Superscript e,r,z

Costs due to external resources, residues and acquisition and maintenance

Scalars hj 4j ri,j

Energy efficiency of component j Exergy efficiency of component j Component of the extended matrix

Matrices and vectors F, P AF,AP B k
F , k
P cF, cP aF, aP

t FTF

Fuel vector (n,1) and product vector (n,1) Fuel matrix(n,m) and product matrix (n,m) Flow exergy vector (m,1) Unit exergy cost vector of fuel(1,n) and product (1,n) Unit exergoeconomic cost vector of fuel (1,n) and product (1,n) Unit exergoenvironmental cost vector of fuel(1,n) and product (1,n) Matrix (n,n) which contains the bifurcation parameters in the FP representation Matrix (n,n) which contains the recirculation parameters in the PF representation Portion of each component’s fuel coming from the external fuel vector (1,n)

References [1] FENERCOM, Radiant Floor Guide, Energy Foundation of the Community of Madrid, 2017 (in Spanish). [2] TRNSYS V18, TRNsient SYStem Simulation Program, University of WisconsinMadison, 2017. [3] Spanish Government. Conditions of Acceptance of Alternative Procedures to LIDER and CALENER (in Spanish). Ministry of Industry. Tourism and Commerce. [4] Royal Decree 865/2003, of July 4, Which Establishes Sanitary Hygienic Criteria for the Prevention and Control of Legionellosis (in Spanish). [5] IDAE, Technical Guide to Accounting for Consumption, Savings and Energy Efficiency in Air Conditioning, Institute for the Diversification and Saving of Energy, Madrid, 2007 (in Spanish). [6] J. Ziemele, I. Pakere, D. Blumberga, G. Zogla, Economy of heat cost allocation in apartment buildings, Energy Procedia 72 (2015) 87e94. [7] D. Kallenberger, H.-J. Althaus, Relevance of simplifications in LCA of building components, Building and Environment 44 (4) (2009) 818e825. [8] G. Llopis, V. Rodrigo, Geothermal Energy Guide, Fenercom, Energy Foundation of the Community of Madrid, 2009 (in Spanish).

Application of exergecoeconomic and exergoenvironmental analysis

907

[9] Best, Execution Project, Heating and DHW Centralized Installation in Building of 26 Dwellings of Official Protection in Durango, Bilbao Energy Solutions Trends, 2008 (in Spanish). [10] Recognized Document of RITE, Emission Factors of CO2 and Coefficients of Passage to Primary Energy of Different Sources of Final Energy Consumed in Buildings, Ministry of Industry, Energy and Tourism and Ministry of Development, 2016 (in Spanish). [11] Tecmared Group, Evaluating the New Indicator System to Define Nearly Zero Energy Consumption Buildings in Spain, 7o Workshop Eecn, Madrid, 2017 (in Spanish). [12] J. Gelegenis, P. Axaopoulos, Residential cogeneration of heat and power: a promising way to sustainability, a challenging way for tutors, International Journal Of Higher Education And Sustainability 1 (1) (2015) 19e39. [13] M.A. Abella, Photovoltaic Systems. Introduction to the Design and Dimensioning of Photovoltaic Solar Energy Installations, S.A.P.T. Technical Publications edition, 2005 (in Spanish). [14] Fenercom, Energy Savings and Efficiency Guide in Hospitals, Energy Foundation of the Community of Madrid, Madrid, 2010 (in Spanish). [15] Water Chillers by Absorption Cycle, Manufacturers Catalog, 2016 (in Spanish).

Section E Design and thermoeconomics in buildings

Design and optimization of the envelope and thermal installations of buildings

12.1

12

Summary

The envelope and thermal installations of buildings allow interior comfort conditions to be maintained while consuming natural and economic resources and thus generating an impact on the environment. Therefore, their design optimization, both with regard to the envelope and the facilities, is a very important task, since it allows the demands of heating, DHW and cooling to be met by minimizing the consumption of resources and adverse effects on the environment. In this chapter, we present basic ideas concerning thermal systems design. After an introduction, we will look at the physico-mathematical models necessary for the behaviour simulation of thermal systems. We will then present the optimization mathematical problem, defining the objective function, the independent or design variables and the constraints, both equality and inequality constraints. In summary, reference is made to the mathematical optimization methods, highlighting linear and non-linear programming methods of continuous and discrete variables that are most commonly used. Once these principles have been established, we highlight the importance of Thermoeconomics in the thermal installations design and make a distinction between two

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00012-6 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

basic methods: the method based on multipliers and the approximation method proposed by Tsatsaronis. Several consistent examples are presented concerning the thermal storage system in a micro-cogeneration installation of a residential building and the optimal sizing of a tri-generation installation in a hospital. We will later look at the case of existing installations, in which the objective is to optimize their operating mode, with an example being developed in detail. Finally, we will present a series of considerations on the energy renovation of buildings and undertake a review of the existing legislation. A summary of the existing computer tools for the renovation optimization will be given, presenting a model in which Thermoeconomics is applied in the definition of the actions to be taken, taking into account the actions that refer to both the envelope and the installations.

12.2

Introduction

Although it is not properly a definition, we can say that designing a thermal system entails specifying the characteristics of the set of components that go into making it up, in order to achieve the desired objective. In the field of engineering, we can see that there were heat engines from the earliest times, such as Hero’s engine, and that already in the 1400s, water-powered machines were used to ventilate mines and irrigate fields. In 1600, hydraulic pump technology was known, while the development of heat engines took place with the invention of the steam engine during the Industrial Revolution. At that time, the design basis was trial and error. In addition, each designer used the ideas of others, usually introducing small modifications in their design. This ensured that the new equipment worked as expected since as we have said, they were minimal variants of other designs whose operation was already known so that the small improvements introduced guaranteed a niche in the market. However, basic science and its application in the world of engineering and technology have advanced rapidly in the last 200 years. Scientific knowledge of Thermodynamics and Heat Transfer means the design process can be approached more systematically than a simple trial and error basis. In the thirties and forties of the last century, scientists and engineers began to apply analytical tools, and consequently, these tools have become better known, and their application has spread very quickly. Simultaneously, the development of computers has made it possible to use increasingly powerful analytical tools, allowing a large number of calculations to be carried out with enormous speeds. But what is meant by the design of a system and, in particular, of a thermal system? Basically, it is the application of Thermodynamics, Heat Transfer, Mass Transfer, Fluid Mechanics and Cost data into the definition and subsequent manufacture of the set of components that make up the system. In general, a system involves a large number of components and, therefore, the complete specification of each of them and how they are interrelated is necessary. A fundamental step in the process of designing a system is to precisely and quantitatively define the functions expected of it, that is, to formulate the design specifications. Thus, in a hot water boiler, the function is to produce a water flow

Design and optimization of the envelope and thermal installations of buildings

913

at a certain temperature; in a refrigeration equipment, the function is to generate a cooling capacity to the requested temperature; in a ventilated facade, in addition to the protection and aesthetics functions, the energy demand of the building should be reduced, etc. In general, there are different models and brands of the same component that can perform the same function, so it is necessary to make a selection, and we must choose, for example, the right heat exchanger among the many commercially available types, etc. Nowadays, the task of designing and manufacturing is more demanding, since it is not only a matter of achieving that main objective but also of doing so with the greatest positive effects (performance, social benefits, economic benefit, etc.) and the least adverse effects (environmental impact, costs, etc.). Among the possible systems, which meet the technical specifications, there will be one that will be the optimal system. The term optimal can be used with different criteria: minimum cost, maximum reliability, maximum performance, etc. These factors should be known as a function of a series of parameters, such as size, materials used, range of operation, transport and installation costs, etc. The complexity of the energy systems and processes is such that achieving an optimum (the maximum or the minimum depending on the chosen criterion) cannot be accomplished in an effective way without the application of mathematical procedures known as optimization. In order for these to be applied, it is first necessary to build a model as close to reality as possible, which describes the functioning of the system. In some design processes, the model construction is carried out following the sequential method. The system is subdivided into a series of components, where each one is a block whose input data is the output of other equipment that has already been calculated. However, due to the complexity that generally exists, the simultaneous method is used in which the equations that govern the behaviour of each subsystem are formulated and solved simultaneously. The system of equations is generally non-linear, and there are usually several solutions, some preferable to others, Stoecker 1971 [1]. In the design and optimization of energy systems, the so-called classical or academic situation is that in which the problem considered is well defined in relation to the data and objectives, and the solution is obtained by certain methods and algorithms. However, in the real world, there are many problems in which the objectives are not well defined, the data is incomplete and those problems are sometimes not expressed quantitatively but qualitatively. In addition, energy systems have an effect on human health, on natural ecosystems and, in a broad sense, on the environment. It is, therefore, necessary to design systems that take into account these impacts, both in society and in the environment. Today, we have powerful methodological tools, such as the ones referred to in Chapter 10, which allow us to internalize these externalities and evaluate their implications, both locally and globally. The oil embargoes of the 1970s focused attention on the efficient use of energy, emphasizing this aspect in the systems design. Until then, these considerations had not been taken into account, being seen as unimportant. As a consequence, courses

914

Exergy Analysis and Thermoeconomics of Buildings

on thermal systems design were developed in universities, Stoecker 1971 [1], Boehm 1987 [2], Janna 1993 [3] and Bejan 1996 [4]. Also worth noting is the methodology developed by Linnhoff 1993 [5] known as the pinch method, used mainly in the recovery of waste heat from industrial plants. In addition, attention was focused on concepts that had been developed before, such as exergy, since it provided a uniform basis for comparison between very diverse processes, Moran 1982 [6]. Specifically referring to thermal installations, their design involves answering questions such as the following: • • • • •

If the heating, DHW and cooling demands are known, what is the best type of system? What is the best configuration, that is, what are the best components and their interconnections? What are the best technical characteristics of each component (power, size, materials, etc.)? What are the best flow rates, pressures and temperatures of the different fluids? What is the best operation point at each moment?

On the other hand, when there is already an installation, consisting of different components to meet demand, other questions must be answered, such as: • •

What equipment should be operated and with what load? How the operation and maintenance of each component should be planned?

12.3

Modelling and simulation

A model of a thermal system consists of a description of its behaviour, both under normal operating conditions and under unforeseen conditions. Such a description is usually translated into a system of equations that, once given some initial data, are solved to provide the values of the variables that describe the physics of the phenomena contemplated in the model. In short, a model consists of an operator U (which we can call the transfer function) that acts on the inputs INi(i ¼ 1,2,.,in) to obtain the corresponding values of the outputs OUTj(j ¼ 1,2,.,out), that is OUT ¼ PðINÞ

(12.1)

where the operator P can be algebraic, differential, integro-differential, etc. The form of this operator determines the number and type of the initial and boundary conditions. Therefore, and according to Sciubba 2009 [7], a model solution requires an exact knowledge of the inputs (information that is supplied to the model), a knowledge of the physical and functional behaviour of the components or processes (which means finding a mathematical representation of its transfer function) and finally, solving Eq. (12.1). As we said before, in an ideal situation, the inputs are unequivocally specified, the outputs defined perfectly and the physical and operational constraints known precisely. This type of situation is not usual in reality and rather belongs to what can be called academic context. Generally, the objectives of the model are well defined, but the data is incomplete and often expressed qualitatively, and the

Design and optimization of the envelope and thermal installations of buildings

915

constraints are specified inaccurately. The solution of these problems requires the experience and intuition of the architect or engineer, in addition to an analogy with other situations. Whatever the complexity of a process, it is always feasible to break it down into processes that are simpler to simulate, so that the physical description of a complex process is equivalent to that of several simpler subprocesses that are interconnected. Once the processes have been simulated, it is possible to recover the complete process. This is how modular simulators appear so that by integrating different components, the model of a complex system can be constructed; software like Simulink or GateCycle have this modular structure. The model should be closed; that is, it should not require any hypothesis external to the theory. Sometimes, since physics is complex, semi-empirical coefficients are needed to close the model in a mathematical sense. As we improve the understanding level of the phenomena under consideration, we refine the model, and so it becomes more precise, meaning that modelling is a dynamic concept. A model must respect the conservation laws such as those of mass and energy, angular momentum, etc. It should be based on the smallest possible number of independent variables, consistent with the reality complexity that it is going to simulate and should be formulated in the simplest mathematical way, but without neglecting to take into account the effects that may be important. In addition, it should avoid empirical constants and, if possible, it should be formulated in a dimensionless way. Fig. 12.1 shows the Kubik intelligent building of Tecnalia in Bilbao for testing construction elements. Thermal systems modelling entails developing thermophysical property models of the different substances that are involved. These models must include the most important properties (such as enthalpy, entropy, specific heat, etc.) as a function of the independent variables, which are generally the most easily measured (pressure, temperature, composition and physical state). Two types of components can appear in a model: passive and active. The function of the active components is to exchange energy with the flows with which they interact.

Figure 12.1 Kubik intelligent building of Tecnalia in Bilbao (Spain).

916

Exergy Analysis and Thermoeconomics of Buildings

This is the case of heat exchangers, circulation pumps, air chambers in ventilated facades, boilers, etc. In contrast, passive components do not have this function of exchanging energy and include pipes, valves, tanks, structural elements of the envelope, etc. These components are modelled based on the mass and energy conservation and by considering the dissipative effects that take place in them. The active components are more difficult to model than the passive ones since the energy exchange mechanisms with the flows can often be complex, as is the case of heat transfer in the air chamber of a ventilated facade, or combustion in a boiler. The laws of mass and energy conservation must be complemented with a model that relates the physico-chemical process with a series of design parameters, which very frequently involves the use of dimensionless parameters. Once the model is built, the simulation consists of obtaining the numerical values of its outputs (with the values of the inputs already known). A simulator is a computer package that has all the necessary capabilities to perform these calculations. It can be said that building modelling, both of their envelope components and their thermal installations, is at a mature phase. However, new constructive solutions and new equipment that needs to be modelled are continually appearing on the market. There are models to simulate equipment in non-stationary regimes, such as while starting-up and stopping, as well as in conditions which were not contemplated during design. However, it is necessary to have more data on the dynamic behaviour of the constructive solutions, and of the installations and their components, as well as to spread the knowledge of these mathematical methods among the professionals of the sector. Fig. 12.2 shows the distribution system of the experimental installation of the Basque Government Building Quality Control Laboratory (LCCE) for testing new equipment and components of thermal installations in buildings. A fundamental aspect of the models is their proper contrast. Once a model is constructed, the results obtained as outputs need to be compared with the observed facts, or with the results of another already contrasted model, in order to verify that the simulation results are correct. If the results are not accurate, the model will need to be re-formulated.

Figure 12.2 Distribution system of the experimental installation in the LCCE in Vitoria (Basque Country).

Design and optimization of the envelope and thermal installations of buildings

12.4

917

Stages in the thermal systems design process

The preliminary activity before the design process of a thermal system is data analysis. Using the most relevant data or through the appropriate statistical treatment of the data set, the appropriate information is extracted. Thus, in the case of thermal installations design for buildings, the preliminary phase consists of determining the demands, that is to say, in defining the heating, DHW and cooling profiles. From this point onwards, the design process can be considered as three levels: •

Synthesis. This phase involves defining the components and their interconnections.

The term synthesis implies the selection of energy technologies that will make up the productive structure of the energy system. The synthesis of the system requires the simultaneous integration of all the subsystems that make it up, so it entails the evaluation of a large number of different alternatives: it is the stage that requires the most ingenuity in the design process. Likewise, it is the most complex and difficult stage to systematize, but it is also the stage that involves the greatest advances in the final system definition. Thus, in the design of a building thermal installation, this stage aims to define what technologies will be installed and with what capacity, so that the technical characteristics of the equipment are described with average values for a range of commercial models. One way to resolve this stage of synthesis, which we will see later in this chapter, is to define a superstructure for the installation, that is, to contemplate the whole set of possible technological alternatives. In this way, in the subsequent design stage, the optimization process will eliminate those technologies that do not meet the optimization criteria that have been adopted. If, for example, a ventilated facade was to be designed in this phase, the type of facade should be defined so that, depending on its ability to take advantage of solar radiation, a choice between an opaque or glazed exterior facade, or a mixed configuration, with glazed outer sheet and opaque interior, would be needed. With regards to the support system for the outer sheet, it would be necessary to decide if it will be supported by the internal slabs and structure pillars of the building or if it will be hung. The air chamber can be configured so as to be a ventilated facade with a single air chamber or a mechanism with louvres centred on the chamber, and which can be divided into two sub-chambers according to climatic conditions. When taking into account the way the facade is to be divided over the height of the building, a facade divided by floors may be chosen, or a continuous facade over the entire envelope. Also, with regards to the use of the air flow in the chamber, a facade of the type with external air curtain or internal air curtain, or facade with air supply, air extraction or a sealed air chamber can be considered. •

Design. In this phase, the characteristics of the components that make up the system, and the properties of the fluids with which there is energy exchange, are defined.

In the case of the design phase of a building thermal installation, the technical characteristics (specifications) of the equipment and the properties of the fluids entering

918

Exergy Analysis and Thermoeconomics of Buildings

and leaving each component are defined under rated conditions. Obviously, the design includes the synthesis and involves answering the question: what size and number of components will be installed for each technology? The design task is often based on selecting the most suitable equipment from that available on the market. In this phase, equipment models are built, and from them, the installation model is constructed, and the resulting equations are solved to evaluate how it would behave. Returning to the example of the ventilated facade, or any other constructive element, the mathematical model of its thermal behaviour is built, using, for example, the type of model of concentrated parameters for the base wall. We usually build finite volume models to characterize the behaviour of the air chamber, and once this is known, it is incorporated into the concentrated parameter models. In this phase, the materials to be used in the external and internal sheet, the type and thickness of the insulation layer, the air chamber thickness, construction details for the support system of the outer sheet, etc. are selected. Thus, after constructing the model and solving the resulting equations (analysis), a valuation (objective function) is assigned to the system, which can be cost, safety, energy consumption, environmental impact, or a combination of them, to make a systematic search (optimization) of the system which improves the evaluation, within the range of operating conditions. •

Operation. Given a system, after carrying out the synthesis and design, in this phase, the optimal operation mode is defined.

In the case of an installation, the objective is to define powers, mass flow rates, temperatures, etc., that optimize the operating mode according to the established optimization criteria. In short, it is a matter of answering the question: what is the best operation programme for the equipment? The operation determines the energy flows produced and consumed by the equipment, and ultimately, the energy billing. In simple problems (with regular demand for energy services, constant prices of energy exchanges, etc.), once the data analysis has been carried out, it can be passed directly to the design (selection of equipment to be installed and operation strategy to be used). But in large buildings, residential neighbourhoods and urban districts, the problem of synthesis must not be overlooked, that is, selecting the envelope types and energy installations to be installed, looking for the best use of local energy resources, the best energy integration in its operation, the suitability of gathering together demand from different consumers to smooth out demand, etc. According to the above and following Westerberg and Stephanopoulos 1979 [8] we can show that the activities that make up the design process are those shown in Fig. 12.3. In the example of the ventilated facade, once its model has been built, it is incorporated into the whole building model. Any dynamic building simulation software, preferably of the TRNSYS type, can be used since it allows the designed model developed for the ventilated facade to be incorporated (by creating a new TYPE) with the rest of the standard type models that the software has. The results are analysed, comparing the demands of the initial building with respect to those obtained after applying the new facade model. Thus, depending on the reduction of energy demands and costs, a parametric optimization is carried out until the final design of the target facade is defined.

Design and optimization of the envelope and thermal installations of buildings

919

Figure 12.3 Activities in the design process.

To conclude, in a situation where the aim is complete optimization, each level must be considered in relation to the other two levels. That is, the objective is to complete the synthesis of the system, define the characteristics of the components and establish the operation strategy that supposes the optimum, in accordance with the criteria established.

12.4.1 The problem of synthesis Of the three stages of the design process, undoubtedly, the most difficult is that of the synthesis. Nowadays, this phase is usually carried out based on the experience and knowledge of the engineer or architect, so the question is whether it can be replaced by an automated procedure that, with the appropriate software, allows for the synthesis of the best system. Maybe in the coming years, the application of Artificial Intelligence will enable us to take giant strides in this sense. While the optimization problem of design and operation can be effectively dealt with by the methods available, the methodology for the synthesis optimization is at an early stage. Some methods have been developed for specific problems, such as the heat exchangers network optimization, Linnhoff 1993 [5]. However, to date, no method has been developed that deals with the synthesis in a general way. The different methods that have appeared in the literature concerning synthesis can be classified into three types: •

Heuristic methods. These are based on the experience of the engineer or architect, who generates a series of possible configurations. From an initial configuration and through the application of certain rules, for example, based on exergy analysis, other possible configurations are obtained. For each accep configuration, an indicator is evaluated, and the configuration that presents the best value for the indicator is selected.

920

•

•

Exergy Analysis and Thermoeconomics of Buildings

Methods based on objectives. In these methods, the principles of Thermodynamics and other sciences are applied to obtain the objectives of the optimal configuration. These objectives correspond to the maximum and minimum values of the best configuration, and this allows the exclusion of numerous possible configurations, thus reducing the size of the search. Methods based on a superstructure. These methods start with a superstructure, which includes all possible equipment and its interconnections, Lozano and Ramos, 2010 [9]. Next, the objective function is defined, and the optimization problem is formulated. The solution leads to the optimal configuration, which must inevitably be contained within the initial superstructure. The difficulty with this method is that the optimization problem can be very large, so that the mathematical algorithms available today may not be able to solve it. In Example E.12.5 we present an application of this method.

The only task that till date has not been automated is precisely that of synthesis, that is, the conceptual definition of systems. As we have said before, this automation will surely be implemented in the near future through the application of Artificial Intelligence techniques by expert systems.

12.5

Mathematical formulation of optimization

The first stage in an optimization problem is the precise definition of the system limits to be optimized. In this sense, all the equipment or subsystems that significantly affect the behaviour of the system must be included, and once the limits have been defined, the criteria under which the optimization will be carried out needs to be established. According to Frangopoulos 2012 [10], optimization is the process of finding the values of variables that minimize (or maximize) the objective function. Sometimes the word optimization is used to refer to the installation improvement, but they are different concepts. The definition of the objective function depends on the optimization criterion used since it can be economical, technological or environmental. Thus, in the thermal installation of a building, the objective function can be economical (expressed, for example, by minimizing the fuel cost), technological (maximizing the plant efficiency) or environmental (minimizing CO2 emissions, etc.). In addition, multiobjective optimization methods have been developed, Collette and Siarry 2004 [11], which seek to achieve two or more objectives simultaneously. In this case, the obtained optimum does not satisfy each objective individually, so that the solution that is achieved is a compromise between the various objectives. Each component and the system as a whole, are subject to requirements that are defined by external conditions, such as environmental pressure and temperature, the natural gas price, etc., which we call parameters. On the other hand, the variables are modified during the optimization process; of these, some do not depend on other variables, so they are called independent variables or design variables. An essential element in the formulation of an optimization problem is the selection of independent variables, which characterize the possible design options. The optimization objective is to precisely determine the optimal values of the independent variables, while the

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rest of the variables are linked to them through equations and these we call dependent variables. In addition to optimizing the objective function (finding the maximum or minimum), generally in an optimization problem, there are ties between the variables or limitations on them. Some are due to the model equations, others to the permissible range of variation, others due to the rules of operation, etc.; these ties are called constraints. Mathematically, the optimization problem is expressed as follows: Minimize f ðxÞ

with respect to ½xðx1 ; .; xn Þ; 

(12.2)

subject to the constraints. hj ðxÞ

j ¼ 1; 2; .; m < n

gk ðxÞ  0

k ¼ 1; 2; .; p

(12.3) (12.4)

where x is the vector of independent variables. Expression (12. 2) also covers maximization, since minf(x,w,z) ¼ max[f(x,w,z)]. The optimization objective is to determine the values of the independent variables, so if the number of equality constraints is greater than the total number of variables, the problem is overdetermined, and optimization makes no sense. In a complete optimization problem (that is synthesis, design and operation) we must distinguish between three sets of variables: •

• •

{z} is the set of independent variables associated with synthesis. There is a series of variables of this type for each component, indicating whether or not the component is in the optimal configuration. Among them are the binary variables (0, 1), with a zero indicating the nonexistence of that component in the final configuration. {w} is the set of independent variables of the design optimization (rated capacities of the components, mass flows, pressures and temperatures of the flows, etc.). {o} is the vector of independent variables for the optimization of the operation (load factors of the components, mass flow rates, pressures and temperatures of the flows, etc.).

The decision variables are chosen so that they can be used to choose the operation point of the system, its size and economic valuation. It is generally preferable to use thermodynamic properties (pressures, temperatures, flow rates, efficiencies, etc.) that must be able to represent all possible operation points. However, other variables can be chosen related to geometry, type of materials, etc. The objective function f(x) can be fuel consumption, exergy destruction, the total cost over the useful lifetime, etc. The equality constraints hj(x) make up the system simulation model (energy balances, exergy balances, economic considerations, etc.). The vector of the decision variables is restricted to take values in a hyperplane, with dimensions equal to the number of decision variables. Therefore, these constraints are very strict, since the decision variables are compelled to belong to the hyperplane whose equation is the constraint. The inequality constraints gk(x) reflect the operation limits, security requirements, regulations, etc. The decision variables are restricted to

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Exergy Analysis and Thermoeconomics of Buildings

Figure 12.4 Equality and inequality constraints.

being above or below a hyperplane, of dimensions equal to the number of decision variables. These types of constraints are obviously much less restrictive than those of equality, see Fig. 12.4. The constraint equations can also be limits on the variables, that is, LLi  xi  ULi, so that the variable xi must be limited between an upper limit value ULi and a lower limit value LLi in the optimization process. These types of constraints are very interesting since by reducing the variation range of the decision variables we narrow down the problem and reduce the calculation time. In mathematical terms, the limits of the variables are different from the constraint equations. The latter binds variables together and restricts the possibilities of their relative changes, while the limits are extreme values imposed on the possibility of a variable change. The restrictions, equalities and inequalities reflect the design characteristics and the conditions that the system and its components must meet to satisfy the requirements of available materials, financial resources, government regulations, operability, safety, etc. The set of these restrictions makes up the system model, which can be built at the level of each component in order to integrate them later and establish the global model of the whole system. It is worth emphasizing that the equality constraints come from thermodynamic and cost equations, as well as boundary equations. Among these equations are mass and energy balances in each component, as well as relationships associated with the design, such as the efficiency of the components, etc. Inequality constraints specify the limits of the components operation, limits on the availability of resources or requirements of maximum and minimum production. In this way, these constraints impose the thermodynamic consistency of the optimization routine results, for example, pressures that cannot be negative, temperature values that cannot exceed certain limits, etc. In addition, they take into account the technological structure of the installation and, in some cases, impose limits on economic values (for example, a limited budget). In the case of complex optimization problems, that is, with a large number of decision variables and, in general, when the function to be optimized is not convex, there is always the risk that the optimization routine will find a local minimum, in place of the

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Figure 12.5 Local and global minimum.

global minimum, Fig. 12.5. For avoiding this problem, there are some algorithms that are adaptive; that is, they can modify the slope of the gradient around the local minimum. A practical way to solve this local minimum problem is to use different initial values of the decision variable vector x0. If the optimization result, that is, the optimal value of the decision variables vector xOPT is always the same, one can practically guarantee that the global minimum has been found. It is clear that simplifications are introduced in all models. The more the model faithfully reflects reality, the closer the calculated optimum will be to the real optimum. If the model built is adequate, the calculated optimum will undoubtedly be better than that based exclusively on experience. The solution of an optimization problem, which, in general, is a non-linear problem, requires the use of an optimization routine. There are several calculation routines on the market, depending on the type of problem, such as MATLAB, LINGO, etc.

12.5.1 Mathematical background We will first look at the case of when the variables to be optimized are continuous. As we have seen in the previous Section, the optimization problem consists of minimizing an objective function subject to a series of constraints, Eq. (12.2). Note that maxf(x) ¼ minf(x) and also that gk(x)0 ¼ gk(x)0. According to the so-called first-order necessary conditions (Kuhn-Tucker) if x* is a local minimum of the problem then there are some multipliers l ¼ [l1,l2,.,lm], one for each equality constraint and some multipliers m ¼ [m1,m2,.,mp], one for each inequality constraint, such that the following conditions are met. vf ðx Þ X vhj ðx Þ X vgk ðx Þ þ lj þ mk ¼0 vxi vxi vxi j k mk gk ðx Þ ¼ 0

k ¼ 1; 2; .; p

i ¼ 1; 2; .; n

(12.5)

(12.6)

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Exergy Analysis and Thermoeconomics of Buildings

This set of equations are the optimal conditions and, therefore, allow us to obtain the optimal values of the independent variables and thus solve the problem. For a detailed study of the mathematical aspects, see Diwekar 2003 [12] and Winston 2005 [13]. In the particular case in which there are only equality constraints, the optimal conditions are vf ðx Þ X vhj ðx Þ þ lj vxi vxi j

i ¼ 1; 2; .; n

hj ðxÞ ¼ 0 j ¼ 1; 2; .; m < n

(12.7)

(12.8)

The optimization problem calls for solving the (m þ n) equations, and calculating the m variables xi and the n multipliers lj. We see that if we define what is called the Lagrangian function Lðx; lÞ ¼ f ðxÞ þ

X j

lj hj ðxÞ

(12.9)

and set the optimum conditions without constraints for this function we get the optimal conditions defined above. Up to this point, we have looked at the case in which all the design variables are continuous variables. But in numerous problems, we also find other types of variables, which are binary, where the variable can take the values (1,0), which can mean being YES (ON)/NO (OFF). These types of variables are used to express whether a component is present or not in the installation, or that at any given time the equipment is working or not. If y ¼ [y1,y2,.yq] is the set of binary variables, the optimization problem is formulated now as minf ðx; yÞ

  x ¼ ½x1 ; x2 ; ::; xn  y ¼ y1 ; y2 ; .; yq

(12.10)

subject to hj ðx; yÞ ¼ 0 j ¼ 1; 2; .; m < n

(12.11)

gk ðx; yÞ  0 k ¼ 1; 2; .p

(12.12)

12.6

Different mathematical optimization methods

In a conventional situation, the objective is to define an acceptable design, that is to say, an installation or a building envelop that satisfies the technical requirements. For example, in a building that has a certain demand for heating and DHW, the conventional design tries to define an installation that satisfies those demands.

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However, there is always more than one acceptable installation, that is, one that satisfies those demands and in fact, there may be better designs than what is achieved with conventional methods. The optimization role is precisely to reveal the best installation (for certain criteria and restrictions) and the best operation mode, without the designer having to analyse and evaluate one by one the multitude of possible solutions. The optimization application to the design and operation will thus increase the quality of the systems, reduce their operating costs, save energy and materials, comply with environmental requirements and save time for the designer. The development of mathematical optimization methods begins with the works of Newton, Euler, Lagrange and Cauchy. Likewise, the development of differential calculation methods applied to optimization is due to the publications of Newton and Leibniz. Despite these early contributions, there was little progress until the middle of the last century when the emergence of computers made it possible to implement optimization methods. There are various ways to solve the different types of optimization problems so that distinct methods have been developed that adapt to each type of problem. These methods, known as mathematical programming methods, are classified according to different criteria. The objective function can depend on a single decision variable or several, it can be continuous or discontinuous, and it can be linear or non-linear. On the other hand, constraints can be expressed as linear or non-linear equations, and the decision variables can be continuous, discrete or a combination of both. According to these ideas, the following mathematical optimization methods can be established, Frangopoulos 2011 [14]: •

•

Direct or Search Methods. This is the name given to those methods in which the optimization is achieved without the use of derivatives, that is, the search for the end-point is done by comparing the values of the function at different test points. The calculation can be random or systematic, with the second type of method being more efficient. If the objective function is continuous, the optimum cannot be found; it can only be approximated after a finite number of searches. Indirect or Calculus Methods. These are applied to problems with continuous and differentiable functions. The necessary condition for a local maximum or minimum is that the first derivative is equal to zero. If all the derivatives of the function up to (n1) are equal to zero and the nth derivative is non-zero, the sufficient condition for a local minimum is that the derivative is positive. On the contrary, if it is less than zero, it is a local maximum.

These necessary and sufficient conditions extend to optimization problems with numerous decision variables, in principle without ties. If equality constraints are introduced, the Lagrange multipliers theory allows for the necessary and sufficient conditions to be obtained. If inequality constraints are considered, the Kuhn-Tucker conditions appear. The analytical application of necessary and sufficient conditions is only possible in very simple problems. In most real cases, the functions are not continuous and differentiable, and the application of numerical methods is necessary. Several algorithms have been developed, the most efficient being the Generalized Gradient method and the Sequential Quadratic Programming method.

926

•

• • •

•

• • •

Exergy Analysis and Thermoeconomics of Buildings

Linear, Non-linear, Quadratic and Geometric Programming Methods. This classification is made according to the nature of the equations that appear. If they are all linear functions of the independent variables, the method is called Linear Programming, and if even only one is non-linear the method is said to be a Non-Linear Programming problem. If the functions can be expressed as polynomials of the independent variables, the method is called Dynamic Programming, and it is said to be Quadratic Programming when the problem is non-linear, and the functions are quadratic. Integer and Continuous Programming. If some of the independent variables in the problem are discrete, it is said to be an Integer Programming problem, whereas if all the independent variables can take any value, then it is a Continuous Programming problem. Deterministic and Stochastic Programming. If all the independent variables are deterministic, it is said to be a Deterministic Programming problem, while if all or some of the variables are random, then we speak of Stochastic Programming. Decomposition Programming. This is the term used if the functions that appear in the problem, both the objective function and the constraints, can be separated as sums of functions, each according to its independent variables. We will refer in more detail to this type of method in the following Section, because of its application in thermal installations and because it allows problems to be solved that, otherwise, could be beyond reach. Uni-objective and Multi-objective Programming. It may be that the optimization is done with a single objective (to minimize the cost) or that there are several simultaneous objectives (to minimize cost and CO2 emissions). In the case of Multi-objective Programming, there is usually no single value of the independent variables that satisfies the different objectives, so a compromise is needed, which is usually subjective. Calculus of Variations. This method is applied when the objective is not to find a value of the independent variables, but a function that optimizes an integral. An example could be finding a car speed on a trip so that fuel consumption is minimal. Dynamic Programming. This concerns optimizing, as in the previous case, a function, but now the function is discrete, or it is a continuous function that is discretized. Artificial Intelligence. To conclude, we must point out that in recent years, the methods that are known as Artificial Intelligence (AI) have increasingly had a more relevant role in the design and control of thermal systems. Within AI there are different techniques such as neural networks, fuzzy systems, genetic algorithms, etc., although, in the field of thermal engineering, it is expert systems which are of most interest. For a study of AI fundamentals see Goodfellow et al. 2016 [15], while for thermal applications, the pioneering work of Paoletti and Sciubba, 1997 [16] is worth noting.

12.6.1

Decomposition methods in complex problems

A very complex and highly dynamic problem with a large number of degrees of freedom can become a solvable problem if the original problem is broken into a series of problems of less complexity, so that the solution of these small problems approaches the solution of the original. The decomposition can be done at a conceptual level, in time, or at a physical level and we will look at them below. From a conceptual point of view, optimization covers the three levels discussed, that is, synthesis, design and operation. Thus, at the operation level, the system is optimized with respect to the operational (control) variables for a specific structure (synthesis/design) over a load profile, in order to determine the optimal operating

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mode for that profile. The results are integrated over time and are introduced at the synthesis level. At this level, a new configuration (synthesis) is selected based on the optimization of the objective function with respect to the synthesis variables. The results of this optimization are passed to the design level where, for the given configuration, the objective function is maximized (or minimized) with respect to the design variables. In this way, an iterative process is established that moves back and forth between the three levels, until finally a global optimum for the objective function is reached. This type of decomposition allows for the chain solving of a set of simpler optimization problems than the original problem, although the computational effort may be very large, Frangopoulos 1990 [17]. A variant of this type of decomposition, which avoids having to go back and forth, completely separates the synthesis/design from the operation. The synthesis/design is optimized for the most demanding load, and environmental conditions and the optimal solution and a series of feasible solutions are defined near the optimum. These feasible solutions are optimized for all operating conditions outside the rated conditions, before selecting the optimal solution. Decomposition in time consists of dividing the problem of operational optimization into a series of quasi-stationary subproblems, each of them corresponding to a time interval. These sub-problems are optimized individually (provided that it can be assumed that the operation in that interval does not affect the operation in other intervals) with respect to the operational (control) variables and the results are overlapped over all the time intervals, Frangopoulos et al. 2009 [18]. Unlike the previous decomposition types, physical decomposition refers to the problem in which the system is separated into a series of sub-systems, each of which constitutes a sub-problem within the context of the global system optimization. For each of the sub-systems, a set of disjoint variables is established with respect to which each sub-system is optimized. In addition, there is another set of variables at the system level with respect to which the problem is optimized at the global level. In the method known as local-global optimization (LGO), the optimum of each sub-system is found for its variables and the set of global system variables. In this way, the combination of these optima gives us the global optimum of the system. In the method known as iterative local-global optimization (ILGO), it is not necessary to find that optimum for each sub-system. ILGO uses information from shadow prices (derived from the function optimum with respect to its variables) in such a way that it moves along the optimum response surfaces of the sub-systems reaching the system optimum, Mu~ noz and von Sapkovsky 2001 [19]. There are numerous occasions in which this type of method can be used in the field of thermal installations in buildings. Thus, with reference to the operation mode of an air conditioning system, since the demands of a building are variable over time, the optimization is done by decomposing the season into a series of time intervals. The set of optimums in each time interval defines the optimal functioning for the season, except when there is interdependence between the intervals, as happens in installations using energy storage. We will return to the physical decomposition later, using the so-called Thermoeconomic Isolation Principle.

928

12.7

Exergy Analysis and Thermoeconomics of Buildings

Optimization in the design of thermal installations in buildings

In spite of the existence of the numerous mathematical optimization methods that we have commented on in the previous Section, the reality is that its use in the design of thermal installations in buildings is very limited. This is due to various reasons, such as the effort that must be made to develop the system model, the need for optimization software, the lack of adequate correlation between the design variables and the cost of the components, the requirement for training in various disciplines such as in the field of engineering, economics and optimization theory, etc. Another important aspect is the optimization of the operation mode. It requires the appropriate hardware and software for monitoring the installation and the control system performance. Fast algorithms and procedures are needed in order to apply on-line optimization. Fortunately, nowadays, with the introduction of home automation in buildings, more and more algorithms are being used that allow the management of facilities in the most efficient way, Newman 2013 [20]. However, the design and operation optimization of thermal installations in buildings and in particular, cogeneration installations, both in the residential and tertiary sector, is of great interest. This is mainly due to the variability of thermal and electrical demands, market prices, the legal framework of cogeneration and the regulations on energy efficiency in buildings. It happens that when the normative or operational restrictions do not have the same time basis, the optimization becomes more complex since the annual optimal operation does not adjust to the seasonal optima sum. This occurs precisely in building installations, where the operational restrictions have a seasonal basis and many of the legal restrictions, in particular for cogeneration, are applied on an annual basis (minimum efficiency required, minimum saving of primary energy, etc.). If, in addition, the thermal installation has a thermal storage system integrated, the optimization complexity increases considerably, due to the introduction of an additional optimization variable which the thermal storage level entails. This fact means that the optimal functioning at a specific moment totally depends on the plant operation in the previous instants, so that it is not possible to separately study each of the hours of the time horizon under consideration (decomposition in time), which leads to a substantial increase in the number of possible solutions, Bischi et al. 2014 [21]. The high number of decision variables differs depending on whether the phase considered in the optimization problem is the synthesis of the system, its design or its operation. With the exception of equipment manufacturers, the objective set by a professional in the sector is not going to be that of designing a new boiler or a new heat pump, but instead, by using commercial equipment, will be in each case, the defining of the installation that satisfies the demands with minimum cost, or minimum CO2 emissions, etc. In general, in an industrial plant, there are two types of components: those from the catalogue and components specially designed for a specific application, such as heat exchangers, waste heat boilers, etc. However, in building installations,

Design and optimization of the envelope and thermal installations of buildings

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with some exceptions, we always find components from the catalogue, which are selected from the manufacturer’s files, such as pumps, boilers, etc., the geometric parameters of which have already been optimized by the manufacturer. Thus, in installations design, the objective is to select that equipment which meets the technical specifications and suchlike, and whose thermodynamic efficiencies justify the investment costs. Therefore, the installation synthesis involves the selection of the technologies that make it up (condensing boilers, heat pumps, micro-cogeneration, etc.), as well as the interconnections between them. For this, as we have seen, one of the methods consists of the designing of a superstructure, considering all the possible technologies to be installed and the possible interconnections between them. Once the technologies to install are known, the design optimization focuses on the dimensioning of the equipment (size and amount of equipment), starting from its technical characteristics and the investment cost (economic optimization) or emissions generated in its manufacture and use (environmental optimization). Finally, the operation is optimized according to energy resources consumption, cost or environmental damage. In the last few decades, in publications on the design of thermal installations in buildings, several methods have been proposed, from heuristics to mathematical programming methods, either Mixed Integer Linear Programming (MILP), Frangioni et al. 2009 [22], or Mixed Integer Non-Linear Programming (MINLP), which we have previously described briefly. Nowadays, thanks to the great improvement in the existing software for solving MILP problems, a frequently used method is to convert the original MINLP problem into an MILP by approximating the non-linear constraints to linear constraints, Li and Shahidehpour 2005 [23]. In recent years, several publications have appeared on the use of MILP mathematical programming for the optimization of synthesis, design and operation of cogeneration and trigeneration systems, such as Lozano et al. 2010 [24], Costa and Fichera 2014 [25] among others. This is due to the possibility offered by this method of solving large problems with multiple variables through a horizontal algorithm, where the synthesis, design and operation variables are treated in a similar way and at the same level. The thermal systems optimization usually has a uni-objective approach, to minimize the overall cost or maximize the energy saving. However, there is a growing need to achieve more efficient systems that are both economically profitable and respectful of the environment. However, achieving these objectives is not an easy task, since they are generally in conflict, so it is necessary to define a multiobjective optimization model that simultaneously considers the different criteria. Different multi-objective methods proposed for the optimization of cogeneration and trigeneration systems can be found in the literature, see Kavvadias and Maroulis 2010 [26], Fazlollahi et al. 2012 [27].

12.7.1 Simple optimization problems Before properly addressing the design problem of a thermal installation we will consider a series of simple optimization problems that will serve as a starting point to tackle the general problem.

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12.7.2

Equipment selection with optimal efficiency

Consider the case of an isolated component, which can be a condensing boiler, a plate heat exchanger, a heat pump, etc. This involves selecting from the set of condensing boilers in the catalogues, or plate exchangers, etc., the equipment that generates the product with the lowest economic cost. If cF is the unit cost of the fuel used, kF the equipment unit consumption and zP the investment unit cost, from the costs balance, Eq. (7.129) of Chapter 7, we have the equation. cP ¼ cF k þ kZ

(12.13)

and taking into account the exergy balance, we can also write the previous equation as cP  cF ¼

cF I þ Z P

(12.14)

This equation clearly shows that the product unit cost is always greater than the fuel cost, due to the cost of the irreversibilities and the investment and maintenence cost. As has been said, the goal is to define the equipment that minimizes the product unit cost. The parameter k is, of course, the efficiency function, since k ¼ 1/4, we also need to know how the investment cost varies with efficiency. Although in the next Section 12.7.4 we will refer to the equipment cost functions, we are now going to use a function that was proposed by Lozano, of the type.  zP ¼ z0P

þ

z1P

4 max 4 4

n (12.15)

where the coefficients z0P and z1P and the exponent n are adjusted for each component, with 4max being the maximum efficiency that component could have. This equation has the form, which reflects the variation of investment cost with performance, that we expect the function to have. Indeed, on the one hand, the investment increases with increasing efficiency (at least in a range where the optimal performance is found) and on the other hand, no matter how much we increase the investment, we will not be able to find commercial equipment that exceeds a certain efficiency limit 4max due to technological reasons. Fig. 12.6 graphically represents Eq. (12.13), that is, the typical variation of the product unit cost with the efficiency. Therefore, we have the function that links the product unit cost with the efficiency. cP ð4Þ ¼ cF kð4Þ þ kZ ð4Þ

(12.16)

So to find the equipment that minimizes this cost, we will have to make dcP/d4 ¼ 0, meaning that the optimal efficiency is 4max

4OPT ¼ 1þ

4max kZ1 n cF

!

1 1þn

(12.17)

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Figure 12.6 Variation of the product unit cost with efficiency.

12.7.3 Choosing the best alternative In this example, we are going to compare two possible alternatives, in order to select the one that is the best, from an economic point of view. Let us suppose that, for example, we need to satisfy the heating demand and we have two options: to produce that demand with a natural gas condensing boiler or with an air-to-water heat pump. If Pn is the equipment rated power and futhe annual utilization factor, the number of equivalent hours operating at full load is 8760 fu, so that the equipment production will be 8760 Pnfu, for example, in kWh/year. If I is the investment required, the investment cost per product unit is zP ¼ a I/(8760 Pnfu). Calling zPu the investment and maintenance equipment cost per product unit and for a utilization factor fu ¼ 1, the boiler technology, which we will call A, will be better than the heat pump B, if the inequality ðcP ÞA  ðcP ÞB is met, that is,     cF zPu cF zPu þ þ  4 fu A 4 fu B

(12.18)

We, therefore, see that, for a given utilization factor, only when the three conditions are fulfilled simultaneously (that the fuel is the cheapest, the efficiency is the highest and the investment is the lowest) can we be assured that one technology is better than the other. Otherwise, it is necessary to calculate the product unit cost and check which of the two costs is the lowest, according to inequality (12.18).

12.7.4 Equipment cost functions In the objective function to be minimized, both Zi(x), the investment and maintenance cost of component i, and Cf(x), cost of external resources must be functions of the

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decision variables. We need, therefore, functions that express the equipment cost according to the design variables. Keep in mind that this is not an analysis of an existing installation, in which each component has a fixed cost, but that the investment cost now is a function of the design variables. In the optimization, it is useful to express this capital cost as a flow cost (V/s) which includes the investment cost plus the maintenance cost. Considering a residual value of zero, as we saw in Chapter 7, Equation (7.57), this capital cost is expressed as follows. Zi ðxÞ ¼ f

Ii ðxÞ:a H:s

(12.19)

where Ii(x) is the investment cost of equipment i, a is the capital recovery factor, f is the maintenance factor, H is the number of equivalent hours of operation in the year (which as we have seen depends on the utilization factor) and s ¼ 3600 is the number of seconds in an hour. The investment cost Ii(x) is linked through a functional relationship with the decision variables vector, which are the selected thermodynamic variables that reflect its operation (temperatures, pressure ratios, efficiencies, etc.), as well as the equipment geometric variables. In the specialized literature, different models have been proposed to reflect the equipment cost based on thermodynamic design parameters. In Section 12.7.1, we have used an investment cost function related to the equipment performance. Authors, such as Szargut and Maczek 1964 [28], proposed cost functions that increase with the production capacity and with the reduction of the specific exergy consumptions (or increase in efficiency), proposing relationships of the type 

ki;0 Zi ¼ Zi0 þ bi ki  ki;0

ai

g

Pi i

(12.20)

where ki is the unit consumption, Pi is the component product (power), Zi,0 is the independent cost part of the product and bi, ai, gi are parameters. Both production and unit consumption are functions of the design variables. According to other authors, such as Tsatsaronis 1982 [29], the investment and maintenance costs are functions of the type Z¼

a þb In

(12.21)

where {a, b, n} are constant characteristics of the equipment type and its capacity, and I is the investment. Other authors such as Levi 1984 [30] proposed cost functions of the type Zi ¼ ca;i Ai

(12.22)

Design and optimization of the envelope and thermal installations of buildings

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where ca,i is the manufacturing unit cost and Ai is a characteristic dimension of the component that is expressed as a function of the thermodynamic variables xj and a series of parameters mi and aj proper to each component, according to the Cobbe Douglas production function Ai ¼ mi

Y a xj j

(12.23)

j

Generally, in order to identify the optimal mode of operation, thermodynamic properties are usually employed as independent variables and are used to express the cost Ii of a device. They can be variables that reflect the size, such as flow, power, heat transfer, etc., or variables that show efficiency, such as head losses, isentropic performance, temperature difference in heat transfer, etc. Currently, functions Ii(x) can be obtained in books, such as Turton et al. 2009 [31] or in journals, such as the Chemical International Journal. The costs can be updated using the MSEC (Marshall and Swift Equipment Cost Index) or the CEPC (Chemical Engineering Plant Index). On the other hand, there is the external resources cost Cf(x) also expressed as a flow cost (V/s) depending on the decision variables, which as we have said, will usually be thermodynamic properties. In the particular case of fuel, we have Cf ðxÞ ¼ cf m_ f ðxÞHHVf

(12.24)

where cf is the unit cost (V/kg), m_ f ðxÞ is the fuel consumption rate (kg/s), expressed as a function of the decision variables and HHVf is the higher heating value of the fuel under consideration, for example, in (kJ/kg).

12.7.5 Optimization of thermal installations operation mode A thermal installation in a building can produce different products, such as electricity (cogeneration), heating, DHW and cooling for air conditioning. For a given installation, under certain technical, environmental and economic conditions and at every moment, the question is: what is the best operation mode? By operation mode, we understand the flow properties (pressure, temperature, composition, mass flow) and equipment (power, etc.) over time. The degrees of freedom increase if the installation can also import or export energy, as is the case with electricity in cogeneration installations. Different criteria can be used for optimization. For example, we can try to optimize the overall exergy efficiency, so that the optimization will provide operating conditions within established restrictions, resulting in maximum exergy efficiency. However, by not taking costs into account, this operation mode can lead to high operating costs. Similarly, defining the operation mode with the lowest operating costs can result in excessively low exergy efficiency. The operation mode that minimizes fuel consumption, or that minimizes operating costs, etc., can be found. It is also possible to use a parameter that takes into account both costs and efficiency, such as the products unit cost of the plant.

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Exergy Analysis and Thermoeconomics of Buildings

The problem of optimizing the operation can be considered at a certain moment, minf(x), or more generally, in a period of time, which may be a day, a month, a year, or throughout the installation useful life, which is Z minFðxÞ ¼ min

f ðxÞdt

(12.25)

t

Often, the integration period can be considered broken down into N intervals of duration Dtn(n ¼ 1,2,.N) with stationary conditions in each interval. In that case, the integral can be replaced by the summation minf ðxÞ ¼ min

N X n¼1

fn ðxn ÞDtn

(12.26)

If the operation in each time interval does not influence and is not affected by the operation in other intervals, the decomposition can be applied in time, which we mentioned in Section 12.6.1. If, on the other hand, there is an interdependence between the time intervals, as occurs in facilities where TES is present, then it is necessary to apply dynamic programming techniques, Lew and Mauch 2007 [32].

12.7.6

Solution of the optimization problem

Once the decision variables have been defined, the model that links the dependent variables to the decision variables is built, and the equipment costs in terms of the design variables are known, the design problem consists of finding the value of the decision variables that minimize the objective function, which is usually total cost, that is, the sum of the operation cost and investment cost. In solving the problem, one has to keep in mind that the mathematical routine that resolves it does not know anything about physics or economics. Therefore, there are restrictions that may seem evident, for example, that the water temperature at the boiler outlet is higher than at the inlet, but which, in the case of boiler design, it is necessary to impose. There are different commercial optimization programmes, which will have to be chosen depending on the type of problem posed. Working with continuous variables can be used, for example, the Optimization Toolbox of MATLAB [33]. Once the optimization problem is solved, we will find that there is no equipment on the market that has exactly those parameters. Then, we can proceed in two ways. One is the heuristic way to look in the manufacturers’ catalogues for equipment that has characteristics as close as possible to the result obtained from optimization. But there is another more precise way, which consists of using what is called the branch and bound method, Brassard and Bratley [34] which leads us to an optimal final solution, with the equipment that exists on the market. Likewise, the resulting cost of the optimization comes from a cost function that is not the equipment real cost on the market. The specific equipment is defined using the branch and bound algorithm, and the actual cost is then obtained.

Design and optimization of the envelope and thermal installations of buildings

935

The optimal design is obtained for a certain scenario, defined by the imposition of values on a series of technical and economic parameters. If the scenario is modified, the optimal point is also modified. For this reason, it is important to assess how the design would be modified when some parameters of the scenario are modified, for example, if the fuel price varies, the interest on money is different, etc. This is what is called conductiong a sensitivity analysis.

12.7.7 Examples Example E.12.1.

From the data in the manufacturer’s catalogues, obtain the investment cost of natural gas condensing boilers and low-temperature boilers according to their rated power. Solution. Fig. E.12.1 shows the relationship between the investment cost of natural gas condensing boilers and the rated thermal power, obtained from the catalogue data [E.1] and [E.2]. It can be observed that the set of points follows a linear trend, with the adjustment function and the R2 regression coefficient indicated in Fig. E.12.1. From the same source, the annual maintenance cost of the condensing boilers was obtained, which is approximately 9.5% of the initial investment. The costs related to the combustion exhaust system were not considered.

Figure E.12.1 Price of condensing boilers as a function of rated power.

Therefore, the cost of a condensing boiler, Ccb(P) expressed in V, based on its rated thermal power in kW, is Ccb ðPÞ ¼ 39:42 P þ 8771:6 For low-temperature boilers, the investment cost has also been plotted against its rated thermal power, resulting in a set of points that can be adjusted to a linear function,

936

Exergy Analysis and Thermoeconomics of Buildings

Fig. E.12.2. The annual maintenance cost of these boilers, as with condensing boilers, was estimated to be approximately 9.5% of the initial investment.

Figure E.12.2 Price of low-temperature boilers as a function of rated power.

It follows, therefore, that the cost of a low-temperature boiler, Clb(P) expressed in V, based on its rated thermal power in kW, is Clb ðPÞ ¼ 15:16P þ 4064:7 [E.1] Institute of Construction Technology (Spain) ITeC, http://itec.es/nouBedec.e/ [E.2] CYPE Engineers, Software for Architecture, Engineering and Construction (in Spanish) http://www.generadordeprecios.info/ Example E.12.2.

From the data in the manufacturers` catalogues, obtain the investment cost of pellet biomass hot water boiler installations as a function of rated thermal power. Solution. The calculation of the economic cost of a biomass boiler installation requires the defining of the fuel storage system used, as well as the boiler feeding system. Basically, the storage types for fuels of small and standardized granulometry (such as pellets), used in residential building installations, can be divided into two types: prefabricated ground silos and prefabricated underground silos. For determining the storage system cost, it is necessary to know its volume. This was calculated bearing in mind that the minimum storage volume required by RITE [E.3] for newly constructed buildings is that corresponding to 2 weeks of maximum fuel consumption. In the case of pellets and a horizontal floor tank, the volume required for storage of 1 week is equivalent to 0.019 m3 per kW of installed power. The system for feeding the boiler varies depending on the storage type, employing a flexible corkscrew in the case of the ground tank, and a pneumatic system for drawing

Design and optimization of the envelope and thermal installations of buildings

937

up pellets in the case of a buried silo. Fig. E.12.3 shows the investment carried out for the installation of biomass boilers according to their rated power, which includes both the boiler price, the storage system and feeding system. According to the data obtained from the market and from [E.4], the installation cost in the case of a buried silo is slightly higher than the ground tank. The set of points obtained, independently of the storage and feeding systems used, can be adjusted to a linear function.

Figure E.12.3 Price of biomass boilers as a function of rated power.

It follows, therefore, that the cost of a biomass boiler, Cbiob(P) expressed in V, based on its rated thermal power in kW, is Cbiob ðPÞ ¼ 197:61:P þ 14504 In order to know the influence of the storage and feeding systems prices, their contribution to the global investment cost was evaluated. It was found that this contribution is greater in low power boilers and for the buried silo storage system. On the other hand, the annual maintenance cost of a pellet boiler installation is approximately 4% of the total investment, that is, the maintenance factor is B ¼ 1.04 [E.5]. [E.3] AVEBIOM, Recognized Document: New performance correction curve with the partial load factor for biomass boilers (in Spanish), 2011. [E.4] IDAE, Technical Guide for biomass installations for buildings (in Spanish), Ministry of Industry, Tourism and Commerce, Madrid, 2009. [E.5] Institute of Construction Technology (Spain) ITeC, http://itec.es/nouBedec.e/ Example E.12.3.

From the market data, obtain the storage tanks investment cost according to the storage volume. Solution. The investment cost of the storage tanks with respect to the storage volume is adjusted to a potential function of the form axn, as shown in Fig. E.12.4.

938

Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.4 Price of storage tanks depending on the storage volume.

As this is a non-linear equation, a linear approximation was carried out by sections. In linearization by sections, the x-axis (volume) is divided into different sections, and an expression of the type ax þ b is obtained for each of them. The coefficients a and b of each section for the curve of Fig. E.12.4 are those shown in Table E.12.1. Table E.12.1 Linearization coefficients in three sections for storage tanks. Volumen (l)

a

b

0-500

3.1635

0

500-1000

1.7601

701.69

1000-5000

1.1036

1358.3

Example E.12.4. Optimal integration of a TES in a micro-CHP installation in a residential building This Example refers to a building of 36 flats of social housing located in Bilbao. Let us consider that the micro-cogeneration engine has already been previously defined, as well as the auxiliary boiler. The objective of Example E.12.4 is to define the TES and its integration within the installation so that, among the different possible configurations, the investment and operation costs are optimized (minimized). The full development of the Example is found in Pérez Iribarren 2015 [E.6]. Here, we present the fundamental aspects, with the objective that the reader understands the interest in this type of optimization problem and the difficulties that arise. Solution. The technical, economic and environmental viability of cogeneration installations in the residential sector is closely linked to the correct sizing not only of the microCHP equipment but also of the storage system. In this Example, we present the design optimization of a thermal energy storage system (TES) and its integration in the micro-cogeneration installation. In general, the cogeneration unit covers the base demand, while the auxiliary boilers satisfy the remaining thermal demand. These boilers can be replaced in part by a TES, which is charged when demand is low and discharged at peak demand, increasing the

Design and optimization of the envelope and thermal installations of buildings

939

hours number of cogeneration operation. As we know, the demand for heat in the tertiary and residential sector is characterized by being variable in time, so the use of TES allows for the reduction of the negative effects of that demand variability, Arteconi et al. 2012 [E.7]. Engineers, generally, use approximate methods for sizing the TES, assuming that the tank minimum volume to be installed is equivalent to the energy stored during 1 hour of the micro-cogeneration equipment continuous operation, FENERCOM 2012 [E.8]. However, approximate methods lead, in many cases, to inadequate dimensioning, which can result in oversizing, with the consequent increase in investment and occupied space that this entails, as well as greater heat losses and a decrease in the primary energy saving. Thermal and electrical demands First, the thermal and electrical demands of the proposed building were determined. Heating demand was obtained through the dynamic simulation software TRNSYS v 17 and the typical meteorological year (TMY). The demand for DHW was calculated from daily and monthly multiplying factors that determine its profile, IDAE 2011 [E.9], and the network average temperature and the consumption in litres/(person day) were estimated using the 2013 CTE [E.10]. The demand for electricity was defined by daily profiles and considering an annual electricity consumption of 3,500 kWh for a dwelling in Bizkaia (Basque Country). Fig. E.12.5 shows the electricity consumption profile on a typical winter and summer day. An optimization simulating the installation hour by hour, which considers the demands variability and other factors would require a high computational time. This time increases linearly with the number of constraints and exponentially with the number of integer variables, with an optimization problem of these characteristics being almost impossible to solve in a reasonable time. Furthermore, keep in mind that not all restrictions apply for the same time basis. For example, it may happen that the operating conditions of one particular hour depend on those of the previous hour. Thus, the TES charge state depends on the previous hour; this is also the case for starting and stopping the engine, for the minimum operating time required by some equipment, etc. In addition, there are restrictions that may have an annual basis, such as legal requirements as the equivalent electrical efficiency (Spanish legislation), the minimum percentage of primary energy to be saved, etc. The use of restrictions of different time bases means that the annual optimal conditions do not correspond to the superposition of the optimal schedules, which would considerably reduce the calculation time. All this makes it necessary to reduce the problem size by selecting a few representative days of the year, typical days, so that through a series of typical days, the annual demand profiles can be reproduced. However, there is no rule to determine the number of required typical days, nor to select these typical days so that they represent the annual values of the model appropriately, although different methods have been proposed, Domínguez-Mu~ noz et al. 2011 [E.11]. In this Example, a typical day was chosen for each of the months, which represents the said month days, also adding the day of maximum heating demand, which, in itself, is considered a representative day. As a result, 13 typical days were selected

940

Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.5 Electrical demand daily profile.

to represent the demand for heating and 12 typical days for the rest of the demands (DHW and electricity demand), as well as for weather conditions, such as ambient temperature or solar radiation. In the case of the month that includes the maximum heating demand day, two typical days were considered: the peak demand day and the typical day that represents the rest of the days in the month, which was defined as the month average day without including the maximum demand. The typical day of each month corresponds to the average vector (centroid) of all the days of the selected month. The selection of the centroid method (average day) as a representative day is justified by Chebyshev’s theorem, from which it is concluded that the gravity centre is the element that presents the minimum distance with respect to the rest of the elements. The proposed method preserves the demand peak for the plant sizing and synthesis, as well as the total annual demand. It was found that the monotonic heating demand curve obtained by the typical days and the result of using TMY practically coincide, so the proposed method is considered valid. Installation characteristics This is a micro-CHP installation with a condensing boiler. The micro-CHP unit is an alternative internal combustion engine that has a thermal and electrical rated power of 12.5 and 5.5 kW, respectively, with a rated natural gas consumption of 20.5 kW. This equipment operates at full load, without the modulation possibility. The boiler power will depend on the TES and its integration mode in the installation. The selection of a condensing boiler for these temperatures is justified, in addition to economic reasons, by the Royal Decree 238/2013 high level requirements for the efficiency, which are only met with the condensing boilers. From this micro-CHP unit, different plant configurations were considered based on the TES integration mode, so that the TES and boiler dimensioning can be compared based on the behaviour of the storage system for each of the configurations. The sizing and operation of the proposed configurations were optimized according to an economic criterion, considering that the thermal demand is completely satisfied and that the electricity generated is consumed in the building. To this end, Mixed Linear

Design and optimization of the envelope and thermal installations of buildings

941

Programming (MILP) algorithms were used, so it was necessary to linearize all the nonlinear functions that were found when modelling the plant operation. With the objective of having a greater efficiency in the use of primary energy, a time horizon of 24 h was considered, since an optimization in a daily time horizon allows for better use of primary energy and a higher Equivalent Electric Efficiency (EEE). TES integration Four different configurations were analysed according to the TES integration. Configuration 0 corresponds to the cogeneration engine operation without storage, while configurations 1, 2 and 3 analysed different integrations and strategies for storage in the TES, see Figs. E.12.6eE.12.8. The auxiliary boiler rated power was obtained by solving the optimization problem, from which the existing relationship between the storage integration mode, the storage volume and the boiler power to be installed is established.

Figure E.12.6 Configuration 0 without storage.

A

Figure E.12.7 Configuration 1 with storage in the return.

942

Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.8 Configurations 2 and 3 with intermediate storage.

Economic and environmental data For carrying out an economic analysis, the electricity and natural gas tariffs were defined, as well as the initial investment for the equipment and its maintenance. The electricity purchase price corresponds to that of the fixed tariff of last resort, which, on the dates in which the Example was developed, established a value of 12.41 cV/kWh, while the natural gas price for the end user was 5.73 cV/kWh. Likewise, a maintenance cost of 2.5 cV/kWhe was considered for the cogeneration equipment, SenerTec [E.12]. It should be noted that in the investment costs, only the cost of the equipment to be sized was taken into account, as the rest of component costs is constant in all the configurations. Therefore, from the market data, we used the linear cost-volume relationship of the storage system that we developed in Example E.12.3 and the linear cost-rated power relationship of the condensing boiler, which we saw in Example E.12.1. Objective function The objective function to be minimized is the total cost CTOT that includes the annual investment cost of the components to be sized CINV, the variable cost due to the energy CEN and other operation and maintenance costs of the plant components COM, which is CTOT ¼ CINV þ CEN þ COM The annual investment cost CINV was calculated as the product of the capital recovery factor a and the investment of each component added over the components, that is, the condensing boiler and the TES. Obviously, the cogeneration engine cost and the rest of the components were not taken into account, since they are the same in all cases. Likewise, the boiler maintenance cost and that of the TES was included, which, for these components, is a function of the investment cost. Then COM¼COMTES þ COMB, and, in this case, we have COMTES ¼ 2:1 % CINV TES

Design and optimization of the envelope and thermal installations of buildings

943

COMB ¼ 9:5 % CINV B with the investment cost being CINV ¼

X ak I k k

where the factor ak is calculated by the expression (7.55) of Chapter 7. The interest rate considered was that in force in the year 2015 in which this Example was developed, which was considered to be 5%, while the assumed useful life was 15 years. With d being the typical day and h the hour, cF the fuel unit cost, FB and FICE the fuel consumption in the boiler and engine, respectively, cE the electricity price and EDEM and EICE the electricity demand and the electricity generated by the engine, respectively, then the energy cost on day d and hour h is CEN ðd; hÞ ¼ cF ½FB ðd; hÞ þ FICE ðd; hÞ þ cE ðd; hÞ½EDEM ðd; hÞ  EICE ðd; hÞ so that EDEMEICE ¼ ENTW. Therefore, since ndt(d) is the number of days in the year of a typical day d, the total annual energy cost plus that of other operation and maintenance costs is CEN þ COM ¼

XX d

h

½CEN ðd; hÞ þ COM ðd; hÞndt ðdÞ

The group of equality and inequality constraints (linear, and if not linearized) are obtained from the energy balance of each component, their capacity and production limits and compliance with current regulations. Below are the technical restrictions for each of the components to be installed and the legal restrictions to be considered. Technical and legal constraints Since the microcogeneration engine operates only at full load, the total fuel consumed is calculated as the product of the nominal consumption FICE and a binary variable ICE(d,h), which is responsible for indicating whether at that instant h of the day d the engine is running or not, that is, FICE(d,h) ¼ ICE(d,h)FICE. The thermal and electrical outputs of the microcogeneration equipment are calculated from the thermal and electrical efficiencies respectively. EICE ðd; hÞ ¼ FICE ðd; hÞhel QICE ðd; hÞ ¼ FICE ðd; hÞhQ In the model developed in Pérez Iribarren 2015 [E.6], the decrease in efficiency during the start-up period of the engine, both cold and warm, was taken into account and was applied both to the heat production and to the electricity. To this end, the model developed by ANNEX 42 2007 [E.13] in the IEAeECBCS program (International Energy Agency’s Energy and Buildings Communities Program) was used.

944

Exergy Analysis and Thermoeconomics of Buildings

For the TES, the four proposed configurations were analysed. In the case of configuration 0 in which no TES is installed, the heat generated by the engine is the useful heat QICE(d,h) ¼ QICE,U(d,h). Of the other three configurations, we will present only the equations that result from configuration 1, with the TES in return. Undertaking an energy balance at point A of Fig. E.12.8, at the connection of the TES with the engine thermal production, with QCHR(d,h) being the energy charged and QDIS(d,h) the energy discharged by the TES in the hour h of day d, we have QICE ðd; hÞ þ QDIS ðd; hÞ ¼ QCHR ðd; hÞ þ QICE;U ðd; hÞ On the other hand, the heat stored in the TES at each instant QTES(d,h) is obtained from the energy balance in the tank, where the losses QLOSS(d,h) are calculated as 1% of the accumulated heat in the previous instant, that is, QLOSS ¼ 0.01QSTRG(d,h1). This percentage of losses depends of course on the type and thickness of insulation, diameter-height ratio and storage temperature. Therefore QSTRG ðd; hÞ ¼ QSTRG ðd; h  1Þ þ QCHR ðd; hÞ  QDIS ðd; hÞ  QLOSS ðd; hÞ As in this configuration, the charging and discharging cannot occur simultaneously, it is necessary to use binary variables so that when one occurs, the other does not and vice versa. If CHR(d,h) and DIS(d,h) are those binary variables, then the following must be satisfied CHRðd; hÞ þ DISðd; hÞ  1 On the other hand, when the tank charging occurs CHR(d,h) ¼ 1, the energy charged in the TES at that instant QCHR(d,h) must be equal to or lower than the heat generated by the engine, that is QCHR ðd; hÞ  CHRðd; hÞQICE ðd; hÞ Because both CHR(d,h) and QICE(d,h) are variable at each instant, their product function is not linear. The linearization of this product was carried out using the Big M method, whose basis and development is presented in Winston and Goldberg 2004 [E.14]. In the case that the TES is discharged, DIS(d,h) ¼ 1, the heat released at that moment cannot be greater than the heat stored in the tank at the previous moment and, therefore, QDIS ðd; hÞ  DISðd; hÞQSTRG ðd; h  1Þ As before, there is another product of variables that must be linearized. On the other hand, it was considered that there is no heat stored in the TES at the initial moment and the heat stored at each moment must be lower than the storage capacity of the installed tank QTES which is, in turn, a variable that is related to the storage volume VTES, and depends on the temperature difference considered, which in this case is 13 C.

Design and optimization of the envelope and thermal installations of buildings

945

In the same way, other similar equality and inequality constraints can be written for the other configurations, as well as for the boiler. Furthermore, with regard to the thermal energy supply, the total demand (sum of the heating and DHW) has to come either from the engine, from the TES or from the boiler. As for electricity, it is considered that all production is consumed by the building and the rest is imported from the grid, so that, EDEM ðd; hÞ ¼ EICE ðd; hÞ þ EGRD ðd; hÞ with EGRD(d,h)0. In addition to these technical restrictions, there are other legal restrictions. In regulation DB HE-4 2013 [E.10] a minimum percentage of DHW is established that must be covered by cogeneration or other renewable sources. In the case of Bilbao, this minimum percentage is 30%, so the cogeneration useful heat must be higher than this value, which is QICE;U  0:30

XX d

h

QDHW ðd; hÞ

In addition, in accordance with RD 661/2007 [E.15], the equivalent electrical efficiency of the installation must be higher than 49.5%, which implies that the following inequality constraint must be met XX d

h

EICE ðd; hÞ  0:459

" XX d

h

FICE ðd; hÞ 

XX QICE ðd; hÞ d

h

#

RefHh

Finally, for the micro-CHP to be considered highly efficient, there must be primary energy saving (PES), so that the following restriction must be met. hQ hEl þ 10 RefHh Ref Elh Results For solving the problem, a methodology for optimizing the design of systems based on MILP was applied, for which algorithms were developed in the MATLAB environment. In Table E.12.2 we see the results obtained regarding the dimensioning of the condensing boiler and the storage system, the hours of operation, the number of starts, the electric and thermal engine generation, the fuel consumed by the generation equipment, the cogeneration contribution to the DHW supply, the investment and operating costs, the EEE, the emissions generated and the primary energy saving (PES) in each of the four configurations. It can be seen that configurations 1 and 3 have the best thermodynamic, economic and environmental results. The storage volume in these configurations is much lower than that obtained for configuration 2, where charging and discharging occurs separately. This, in turn, makes the number of starts and stops increase considerably for

946

Exergy Analysis and Thermoeconomics of Buildings

Table E.12.2 Optimization results for the four configurations. Configuration 0

Configuration 1

Configuration 2

Configuration 3

Generated electricity (MWh)

18.6

28.1

23.9

28.3

Useful heat (MWh)

42.7

64.3

52.7

64.6

Fuel consumed by the ICE (MWh)

71.4

107.1

92.1

107.7

Boiler rated power (kW)

95.5

85.3

70.5

85.7

Fuel consumed by the boiler (MWh)

82

60

71.7

59.7

Stored energy in the TES (kWh)

0

10.3

73.2

9.9

TES volumen(liters)

0

683

4839

653

Operating hours

3482

5222

4492

5252

Number of starts

821

856

1155

763

Contribution to the DHW (%)

54.7

82.6

58.6

82.8

Global efficiency of the installation (%)

94.5

92

91.4

91.9

Operating costs (V)

22578.8

22414.7

22651.5

22410.7

Total cost (V)

25713.1

25689.3

26139.8

25679.9

Return period (years)

e

8.9

e

8.4

Net Present Value (V)

0

241.8

e3656.1

339.6

Percentage of Primary Energy Saving (%)

19.5

20

17.5

20.1

Primary Energy Saving (MWh)

17.3

26.8

19.6

27

Equivalent Electrical Efficiency EEE (%)

77.6

78.9

71.3

78.9

Avoided CO2 emissions (t CO2 equiv)

10.4

15.9

12.7

16.1

Design and optimization of the envelope and thermal installations of buildings

947

a lower number of operation hours, such as occurs when there is no storage system. We also see that the boiler power decreases with an increasing TES volume. This is why in configuration 2 the boiler rated power is lower, which does not compensate for the thermal energy losses that take place in the TES and the lower electricity generated, due to the charging and the discharging decoupling. Configurations 1 and 3 show a positive NPV, which indicates their economic interest with respect to the configuration without TES. On the other hand, configuration 2 shows a negative NPV, which shows that this configuration is not viable. Meanwhile, the energy index values such as PES and EEE and the CO2eq emissions that are avoided are greater in configurations 1 and 3, with the lowest values being recorded in the case of configuration 2. In the environmental impact analysis, only the CO2 emissions that were avoided were taken into account. The values used for CO2 emissions from the plant energy resources were 399 g of CO2eq/kWh for conventional electricity and 252 g of CO2eq/kWh for the natural gas combustion, IDAE 2014 [E.16]. Neither the emissions nor the energy consumed during the equipment manufacturing phase was taken into account. [E.6] E. Pérez Iribarren, Optimization in the operation and design of microcogeneration plants for domestic buildings (in Spanish), PhD Thesis, University of the Basque Country, Bilbao, 2015 [E.7] A. Arteconi, N. J. Hewitt, F. Polonara, State of the art of thermal storage for demand-side management, Applied Energy 93 (2012) 371e389. [E.8] FENERCOM, Basic Guide of Microcogeneration (in Spanish), Energy Agency of the Region of Madrid, 2012. [E.9] IDAE, Evaluation of the solar potential in the air conditioning in buildings (in Spanish), Institute for the Diversification and Saving of Energy, Ministry of Industry, Tourism and Commerce, Government of Spain, 2011. [E.10] CTE, Technical Building Code, Basic Document HE4: Minimum solar contribution in the production of DHW (in Spanish), Ministry of Housing, Government of Spain, 2013. [E.11] F. J. Domínguez-Mu~noz, M. Cejudo-Lopez, J. M., Carrillo-Andrés, M. Gallardo-Salazar, Selection of typical demand days for CHP optimization, Energy and Buildings 43 (2012) 3036e3043. [E.12] Senertec Dachs Commercial Catalogue. http://www.senertec.es/es/derdachs.html [E.13] I. Beausoleil-Morrison, Experimental Investigation of Residential Cogeneration Devices and Calibration of Annex 42 Models, Annex 42, International Energy Agency Energy Conservation in Buildings and Community Systems Programme, 2007. [E.14] W. L. Winston, J. B. Goldberg, Operations research: applications and algorithms, Duxbury Press, Boston, 2004. [E.15] ROYAL DECREE 661/2007 of 25 May, by which the activity of production of electrical energy in special regime is regulated, Ministry of Industry, Tourism and Commerce, (in Spanish) BOE no. 126, 26 May 2007. [E.16] IDAE, Factors of CO2 emission and coefficients of passage to primary energy of different final energy sources consumed in the building sector in Spain (in Spanish) V03/03/2014. (Proposed document), Ministry of Industry, Tourism and Commerce, 2014

948

Exergy Analysis and Thermoeconomics of Buildings

Example E.12.5.

Trigeneration installation design in a hospital The objective of this Example is to show a procedure for the optimal design of a hospital thermal installation. In the first stage of the Example, the synthesis problem is solved using MILP techniques, resulting in which technologies will be installed and with what capacity. In this stage, the equipment technical characteristics are described with average values for a range of commercial models. In the second stage, it is decided what specific commercial equipment will be installed for each technology, as well as their number. The Example is selected from the publications of Ramos 2012 [E.18], in which, once the technical details of the selected equipment are known, the optimum operating conditions are determined in a third stage by means of an MINLP model. Solution. Thermal and electrical demands Due to the variations in demand between the different week-days and because an electricity tariff is contracted that distinguishes between working days, weekends and holidays, the annual energy demand was represented by 24 typical days (12 working days and 12 Saturday/Sunday/holiday days), where each month corresponds to 2 typical days (one working and one Saturday/Sunday/holidays). In turn, each typical day was divided into 24 periods of 1 h duration. Fig. E.12.9 shows the heating demand profile in January, April and July for working days and Fig. E.12.10 the cooling demand profile. Superstructure definition For the installation synthesis, the superstructure shown in the schema of Fig. E.12.11 was considered. Alternative internal combustion engines were the only equipment considered for the electricity generation, as it is the type of engine that is present in most of the installations in hospitals.

Figure E.12.9 Heating demand profile on weekdays.

Design and optimization of the envelope and thermal installations of buildings

949

Figure E.12.10 Cooling demand profile on weekdays.

Figure E.12.11 Superstructure proposed for hospital.

The exhaust gases enthalpy QG serves to produce the heat QHG in the form of hot water at 110e120 C, of which a fraction QG,HþDHW is used to meet the joint demand of DHW and heating QHþDHW and the rest QG,ABS is used to drive the single-effect absorption chillers. The heat recovered from the cylinders cooling water circuit and the intercooler first stage QM, in the form of hot water at 80e90  C, is exclusively used to meet the demand QHþDHW. The part of QM that is not used for the demand due to excess production can be released as waste heat QM,L through the cooling tower. Due to its low thermal level (50e60 C), the heat of the oil cooling circuit and the

950

Exergy Analysis and Thermoeconomics of Buildings

interccoler second stage are not considered useable, and so all this is released as waste heat QI,L through the cooling tower. Hot water natural gas boilers that consume fuel FB to produce QB were considered as auxiliary equipment in the superstructure. It also was taken into account the possibility of incorporating electric boilers, which consume EEB to produce QEB. For air conditioning, the possible installation of absorption chillers that consume the cogenerated heat QG,ABS during the summer for the cold production QC,ABS was proposed and also mechanical chillers, whose production QC,M will help the absorption machines to meet the cooling demand QC. Technical and economic data For carrying out the optimization, it is necessary to supply the model with the equipment technical and economic data. As representative values, the internal combustion engine electric efficiency is 37.60%, the combustion gases enthalpy to work ratio is 46.0%, the hot water enthalpy to work ratio is 70.6%, and the oil enthalpy to work ratio is 25.0%. The natural gas boilers efficiency was assumed to be 92.1%, while for the absorption chillers a COP of 0.70 was reckoned and for the mechanical chillers a COP of 4.27. The economic evaluation was carried out with values of equipment investment and energy prices for the year in which the Example was carried out. The equipment investment was expressed through linear functions dependent on the rated power. Thus, for the cogeneration modules the investment cost in V is 160,000 þ 255EM, for the absorption chillers 30,000 þ 48QC,ABS, for the natural gas boilers 15QB and for the mechanical chillers 20,000 þ 32QC.MCH, with the investment cost for the electric boilers being 10QEB. The legal regulation for cogeneration of that year indicated that the minimum equivalent electrical efficiency EEE of this type of plant should be 55% and that, in addition, in the hospital itself, at least 30% of the cogenerated electrical energy should be consumed. To take advantage of the electricity price difference between peak hours (08:00 to 24:00) and off-peak hours (24:00 to 08:00), the gas internal combustion engines in the model were run at full capacity during peak hours (in this time period the cogenerated heat is used to meet the hot water, heating and cooling demand) and were stopped in the off-peak hours. At night, the possibility of producing heat QEB with electric boilers was considered, as support equipment that takes advantage of the low electricity night price, replacing the boilers production that operate with natural gas. In order to model the energy efficiency of the equipment/technologies present in the energy superstructure, it was assumed that, at any time and independently of the equipment/technology operating load, their technical production coefficients were constant and independent of the production level P, with only P  PINS having to be satisfied, where PINS is the installed power. Objective function As we have seen, for the investment cost CINV of the equipment/technologies, linear functions were used with the size of the rated power PINS, that is, functions of the type

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CINV]K þ kPINS where K [V] is a fixed cost and k [V/kW] is the proportional coefficient that relates the variable cost with the rated power PINS[kW]. In the same way, as in the previous Example, binary variables BI(0/1) were used to indicate the absence/presence of technology i in the energy supply system. Therefore, the investment cost of equipment j can be expressed as   CINV;j ¼ Kj þ kj PINS;j BIj Likewise, it was considered that the operating costs (excluding energy) and maintenance costs COM[V/h] are proportional to the production P; that is, for the operation during the typical day d and the hour h, we have COM,j(d,h) ¼ cOM,jPj(d,h), where cOM,j[V/kWh] is the proportionality constant corresponding to technology j. The installation total annual cost is CTOT ¼ CINV þ CEN þ COM where CINV ¼

X   aBIj Kj þ kj PINS;j j

is the annualized investment cost, the result of adding the investment of each component j present (BIj ¼ 1) in the optimal structure of the energy system and multiplying the sum by the capital recovery factor a, see equation (7.55) in Chapter 7. The energy cost is CEN ¼

" XX X d

h

j

 cFj hj Pj ðd; hÞBIj þ cE ðd; hÞ EDEM ðd; hÞ

X  EENj ðd; hÞBIj  cwj ðd; hÞLj ðd; hÞ

#

j

where cFj is the fuel unitary price used in the equipment j, hj is the efficiency of the equipment j, EDEM is the electricity demand in the hour h of the typical day d, EENj is the electricity generated by the engine j, cwj(d,h) is the unit cost of utility j loss in the period and Lj(d,h) is the utility j loss in the period, that is, in the hour h of the typical day d. For its part, the operation and maintenance cost throughout the year is COM ¼

XX d

h

cOM;j Pj ðd; hÞBIj

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Exergy Analysis and Thermoeconomics of Buildings

The problem of synthesis is to minimize the objective function, that is minCTOT Technical and legal constraints For each component j, with Pmin and Pmax being the minimum and maximum proj j duction, the following inequality relationships must be met max Pmin j BIj  PINS;j ðd; hÞ  Pj BIj

In addition, for every hour h of typical day d, the equipment j production must be less than the rated power, that is Pj ðd; hÞ  PINS;j On the other hand, for each utility (heating, electricity, DHW, refrigeration) a balance equation must be satisfied. So for the u utility, where PURu(d,h) is the utility purchased in the period (d,h), Pju(d,h) is the utility production by equipment j in that period, Du(d,h) is the demand for this utility in that period, Lu(d,h) is the utility loss in the period and Su(d,h) the sale, then the equation PURu ðd; hÞ þ

X j

Pju ðd; hÞ  Du ðd; hÞ  Lu ðd; hÞ  Su ðd; hÞ ¼ 0

has to be satisfied. If hju is the technical coefficient that reflects the equipment j efficiency in the utility production u, then the following relation for each time period (d,h) must also be satisfied Pju ¼ hju Fju In addition to these constraints are those imposed by compliance with legal conditions. On the one hand, the EEE restriction imposes a condition, similar to the one we already saw in the previous Example, which, in this case, is XXX d

h

j

2 EENj ðd; hÞBIj  0:554

XXX d

h

j

3  QENj ðd; hÞ FENj ðd; hÞ  BIj 5 RefHh

For its part, the minimum electrical consumption condition within the building imposes the constraint XXX d

h

j

EENj ðd; hÞBIj  0:30

XX EDEM ðd; hÞ d

h

For solving the problem, a MILP-based design optimization methodology is applied. In this case, the optimization tool used was LINGO 2011 programme [E.19].

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Figure E.12.12 Effect of the engines rated power on the total annual cost.

Results Optimization tests were performed by imposing values on the engines installed power in the range of 0 to 1500 kWe, in all cases, counting on a capital recovery factor of 0.25/year, Fig. E.12.12. From the results obtained, it was concluded that it is beneficial to install cogeneration systems with gas engines of a power greater than 550 kW. From 1000 kW on, absorption chillers incorporation supposes a greater consumption of cogenerated heat, and consequently, the gas engines rated power can increase up to 1400 kW. If the financial conditions required a capital recovery factor of 0.40 (conservative design criterion) instead of 0.25 (the case just discussed), the optimization programme results pointed to a conventional installation (with gas boilers and mechanical chillers) as the most appropriate. Conversely, by decreasing the capital recovery factor to 0.15, the optimization results justify the use of higher installed capacity in the gas engines and absorption chillers. For a recovery factor of 0.15 in Table E.12.3 the optimal rated powers are shown for each of the technologies involved in the optimal installation definition. Table E.12.3 Optimal powers of the different technologies (a¼0.15). Cogeneration modules

Boilers

Absorption chillers

Mechanical chillers

1,370 kW

2,021 kW

441 kW

1,340 kW

Once the optimal powers are defined, we pass on to the second stage, in which it is decided which specific components will be installed for each technology and how many are needed from the search among commercially available equipment. In Fig. E.12.13 the equipment selected for the design of the hospital’s energy system is shown.

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.13 Equipment selected for the hospital. [E.18] J. C. Ramos, Optimization of the Design and Operation of Cogeneration Systems for the Residential-Commercial Sector (in Spanish), PhD Thesis, University of Zaragoza, 2012. [E.19] LINGO, Optimization Modelling Software, LINDO Systems Inc, 2011, httpw: ww. lindo.com [retrieved: 21.06.2015] Example E.12.6.

Optimum operation of a cogeneration installation in a residential

building Let us consider a building block with 171 social dwellings, a health service area, three commercial premises, annexes and linked urbanization, see Fig. E.12.14. The premises destined for health care use is located on the first floor with access from the ground floor, while the three commercial premises are located on the ground floor. The boiler room, cogeneration and hot water accumulators, and the substation are also on the ground floor.

Figure E.12.14 Social housing building.

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The objective of this Example E.12.6 is to define the operation mode of the thermal installation that minimizes the operating costs, taking into account different constraints. The detailed Example development is found in Pérez Iribarren [E.6]. Solution. Thermal and electrical demands The calculation of heating demand was carried out by the building modelling and simulation in the dynamic simulation software TRNSYS v 17. In addition to using the TMY of the locality, in this case, Vitoria-Gasteiz (Basque Country), it was necessary to define the building occupational conditions, set-point temperatures, ventilation rate, air currents, etc. According to the results of the hourly simulation, the annual heating demand turned out to be 704.9 MWh, of which 600.5 MWh correspond to the demand in housing and the remaining part to the commercial premises. The peak demand for heating is 538.8 kW, being the day of maximum demand, which is a representative day in itself in the optimization carried out, and which is February 15. The monthly heating demand profile, in MWh, is shown in Fig. E.12.15.

Figure E.12.15 Monthly heating demand profile.

In order to reduce the simulation time, in the same way as in Example E.12.4, 13 typical days were used. The monotonic demand curve was drawn from the demand for hourly heating obtained by simulation in TRNSYS using the typical days. In Fig. E.12.16 it can be seen that the monotonic heating demand curve obtained from the simulation with the actual hourly data fits very well to that obtained from the selected typical days. The DHW demand calculation was made based on the daily and monthly multiplying factors and the daily DHW consumption, set by the CTE at 28 L/person for multifamily dwellings. The number of people per dwelling was obtained according to the minimum occupation values defined in the CTE, so that single bedroom dwellings were occupied by 1.5 people and those of two and three bedrooms by 3 and 4 people, respectively.

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.16 Comparison between the monotonic heating demand curve and that obtained by using typical days.

Taking into account an accumulation temperature of 60 C that guarantees the Legionella prevention (as determined by RD 865/2003) and a monthly average network temperature established in the CTE according to the city where the plant is located, we calculate the DHW demand. This demand amounts to 289.6 MWh, which was distributed over the months, as shown in Fig. E.12.17. The monthly electricity demand, shown in Fig. E.12.18, was obtained from defined daily profiles and assuming an average annual demand for electricity in  Alava (Basque Country) of 3,100 kWh per dwelling. Description of the installation The thermal (heating and DHW) and electrical energy production is based on the integration of high-efficiency and renewable energy systems. In this case, there is an installation consisting of two high-performance natural gas boilers working in cascade, each with an adjustable power between 320 and 500 kW and two alternative

Figure E.12.17 DHW monthly demand and monthly water temperatures in the network.

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Figure E.12.18 Electricity monthly demand per dwelling (kWh).

internal combustion cogeneration engines, using natural gas and each of 5.5 kWe and 15 kW thermal. The engines work against a 3000 L storage tank through a plate heat exchanger with an efficiency of 90%. The TES integration allows it to be charged and discharged simultaneously. The flows from the TES and the boilers are directed to a discharge manifold, from which the hot water is distributed to the heating and DHW circuits. The DHW circuit passes through a 90% efficiency plate heat exchanger, whose secondary connects it to the accumulation tank, also of 3000 L. Likewise, the building has a system of 256 photovoltaic panels placed on the facades facing south, reaching a peak power of 58.69 kWp. For transforming the direct current generated by the panels to alternating current, 12 inverters of 5 kW each were installed. The installation hydraulic schema is shown in Fig. E.12.19.

Figure E.12.19 Installation hydraulic schema.

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Exergy Analysis and Thermoeconomics of Buildings

Economic data The natural gas price was 5.73 cV/kWh and the electricity purchase price was considered as the rate with time discrimination of three periods that contemplated peak, off-peak and super off-peak periods with these values: 15.08 cV/kWh (13:00e23:00), 7.19 cV/kWh (00:00e01:00, 07:00e13:00, 23:00e00:00) and 4.41 cV/kWh (01:00e07:00), respectively. The maintenance cost corresponds to that of the engines, which, as we have seen, is a function of the electricity generated, the value of which was taken as 2.5 cV/kWh. The mathematical model solution for the economic optimization of the plant operation allows the characterization of all the energy and economic flows for the operational period of 1 year. The corresponding model is described below. Objective function The optimization objective is to minimize the energy variable costs and the other operation and maintenance costs throughout the year. With FLTBj being the fuel consumption in the boiler j, FENjconsumption in the internal combustion engine j, cF the fuel unit cost, EDEM the electricity demand and QENjand EENj the thermal energy and electricity produced in the engine j, the energy cost in the hour h of the typical day d is 2 CENE ðd; hÞ ¼ cF 4 2

2 X j¼1

FLTBj ðd; hÞBIj þ

þ cE ðd; hÞ4EDEM ðd; hÞ 

2 X j¼1

2 X j¼1

3 FENj ðd; hÞBIj 5 3

EENj ðd; hÞBIj 5

while the other OM costs, taking into account that only the maintenance cost of the engines was considered, is COM ðd; hÞ ¼ 0:025

2 X j¼1

EENj ðd; hÞBICj

Therefore, energy costs plus other operation and maintenance costs throughout the year are CE&OM ¼

XX ½CENE ðd; hÞ þ COM ðd; hÞntdðdÞ d

h

where ntd(d) is the column vector that indicates the number of days that each representative day repeats throughout the year. With the objective function defined in this way, the optimization problem tries to find the minimum of that function, that is min CE&OM

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Technical, economic and legal constraints Constraints to which the operation is subject include energy balances, equipment capacity and production limits and compliance with regulations. Below are the restrictions for each installed technology. Alternative internal combustion engines The installed engines do not have the capacity to modulate, so the total fuel consumed by the engines is calculated as the product of the rated consumption and the number of engines that are operating at that moment, which will be an integer variable less than or equal to the number of installed engines. In this case, in which the installation configuration is known and only the plant operation is optimized, that number is equal to 2. Therefore, if BIC(d,h)˛(0.1) and making BIC1(d,h)þBIC2(d,h) ¼ NI(d,h), we have FEN ðd; hÞ ¼ FEN;NOM $NIðd; hÞ BIC1 ðd; hÞ þ BIC2 ðd; hÞ  2 In the complete model developed in the thesis [E.6], the consequences of starting the engines is taken into account. As there are two engines, the start-up penalty is applied when one or both engines have started in the time interval under consideration. If the difference NE(d,h)NE(d,h1) is equal to 1, the penalty is applied to the starting of an engine, while if its value is 2, both engines start at the same time and the penalty applies to both engines. During start-up, the electrical power generation in the engine is reduced by 5%, while the thermal power decreases by 8%. Low-temperature boilers The thermal energy generated by the two low-temperature boilers must be less than the installed rated thermal power, which is 500 kW per boiler. A constant efficiency value equal to 92.0% was considered, without taking into account the small variations that occur with load. This simplification was taken into account because the low temperature boilers that operate at high temperature do not suffer hardly any alterations in efficiency when varying the load. QLTB;j ðd; hÞ  QLTB;NOM QLTB ðd; hÞ ¼

FLTB;j ¼

2 X j¼1

QLTB;j

QLTB;j BIj hLTB;j

The boilers operate in cascade, so we call the boiler that begins to operate first LTB1 and the boiler that operates when LTB1 is not capable of supplying all the demand LTB2. To model this behaviour, we used a binary variable BLTB that takes value 1 when LTB1 operates at maximum load (QLTB,1 ¼ QLTB,NOM) and 0 when

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Exergy Analysis and Thermoeconomics of Buildings

LTB1 operates below the rated load and the second boiler support is not required (QLTB,1 0 RefHh RefElh where hQ ¼

XX X QENj BICj FENj d h j¼1;2

hEl ¼

XX X EENj BICj FENj d h j¼1;2

Results The optimum operation that resulted was such that the engines operate at peak hours when there is thermal demand and turn off at the off-peak and super off-peak

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Exergy Analysis and Thermoeconomics of Buildings

Figure E.12.20 Thermal balance on the day of maximum thermal demand.

hours, as shown in Fig. E.12.20 which corresponds to the day of maximum thermal demand. When the thermal demand is lower than the engines thermal generation, only a single engine operates or none, regardless of the electricity cost. From the results obtained, it can be concluded that the optimal operation responds to a tracking of the thermal demand or the electricity market price, depending on the relationship between the electricity cost and the natural gas cost, a ratio that it is obtained by equalizing the products obtained in the cogeneration equipment with those that would be obtained in separate production. In the thesis already referenced [E.6], the optimum operation mode according to environmental criteria was also recorded, specifically, the minimization of CO2eq emissions. It can be concluded that the optimal operation that minimizes the CO2eq emissions corresponds to the thermal demand tracking by the engines. [E.20] W. L. Winston, J. B. Goldberg, 2004, Operations research: applications and algorithms, Duxbury Press, Boston.

12.8

Application of Thermoeconomics to the design of thermal systems in buildings

In recent years, Thermoeconomics has gained great popularity in thermal systems design, as it is effectively a powerful tool for the design of thermal installations and power conversion plants. As we know, through it, monetary values can be assigned to all the energy and mass flows of an installation, as well as to the exergy destruction that occurs in each component. Thus, Thermoeconomics provides the designer with information about the cost formation process, as well as the interactions between the different components of the installation. The foundation lies in the idea that exergy is a rational basis for assigning monetary values to the interactions of a system with its surroundings and to inefficiencies in

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the system. As we saw in Chapter 7, by means of the cost balance equations and the auxiliary equations provided by ECT or other similar theories, installation flow costs are calculated. This is the first step in knowing the process of formation and origin of these costs, which will allow us to make decisions for a new design or to effectively improve an existing design. Naturally, the flow costs are not exclusively associated with exergy, since there may be other costs not associated with the exergy that contribute and must be taken into account. This is the case of demineralized water that needs to be provided in an installation to generate steam, or the water cost from the network in the DHWproduction, etc. Thermodynamic optimization involves minimizing the system thermodynamic inefficiencies , that is, exergy destruction and exergy losses. However, thermoeconomic optimization involves minimizing monetary costs, including those due to inefficiencies. As indicated in Bejan, Tsatsaronis and Moran 1996 [35], the cost per product unit exergy is the parameter to be optimized; it is the objective function. The effect of the interaction between the different components and the installation is reflected through the unit costs of exergy flows and exergy losses. The optimized design of a system implies the selection of the structure and the design parameters (decision variables) that minimize the products total costs throughout their useful life and under the restrictions imposed by the availability of materials, financial resources, laws and environmental regulations, as well as safety, reliability, maintainability and availability. In an optimized design, the inefficiency of each component is justified by considerations regarding investment and operating costs. In fact, the different optimization methods based on Thermoeconomics are founded on the idea that, if the unit cost of a component local irreversibility is known, we can establish the relationship between an investment aimed at increasing its efficiency and the economic saving that is presumed in the resources consumption due to that reduction of irreversibility. According to El-Sayed and Evans 1970 [36], and Gaggioli 1983 [37] there are basically two groups of methods that use Thermoeconomics for optimization: •

Calculus methods. These are based on mathematical optimization techniques to minimize the product costs. The flow costs are obtained in conjunction with optimization procedures based on the Lagrange multipliers method and determine the marginal costs.

The design of real thermal systems leads to large-scale problems due to their non-linear characteristics. However, by means of an appropriate thermoeconomic analysis and if certain conditions are met, some decomposition methods can be applied, which allows for the optimization breakdown of the installation as a whole into a series of optimization problems of components or subsystems, which are of smaller dimensions, that is, they have a smaller number of independent variables, and this greatly facilitates the solution finding. Within these thermoeconomic methods, there are basically two groups: the structural methods that use the local unit costs of the irreversibilities and the autonomous method of Evans and El-Sayed, which is, in turn, the foundation of others.

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Exergy Analysis and Thermoeconomics of Buildings

Algebraic methods. These use thermoeconomic variables to understand the interactions between Thermodynamics and Economics and they apply these variables in an iterative process to progressively reduce the installation products costs. This is not properly an optimization problem, since it is not about calculating the optimum of an objective function as in the previous methods, but rather it is about finding a better solution of the global system. It is based on the commonly accepted idea that, for a given power or size of a component or a system as a whole, a higher investment cost implies a more efficient component or system and vice versa.

12.8.1

Thermoeconomic optimization through calculus

The main objective of thermoeconomic optimization is to find a balance between capital costs and exergy costs that minimizes the product costs. Thus, using the notation of Symbolic Thermoeconomics in Chapter 8 and considering the total cost of the products throughout the system useful life (the sum of the external resource costs and capital and maintenance costs) as an objective function, it is minx CðxÞ¼t ke ðxÞPðxÞþt uZðxÞ

(12.27)

subject to the structural constraints PðxÞ ¼ Ps þ < KP > PðxÞ

(12.28)

The minimum condition, taking into account the constraints, leads us to the system of equations 0 1 n n X X vk vZ ji i @ þ cP;j Pi A ¼ 0 vxl j¼0 vxl i¼1

fl ¼ 1; 2; .; rg

(12.29)

which allows us to determine the value of the design variables (xl l ¼ 1,2,.r) that minimizes the system total cost. In the particular case of an installation in which the only external resource is a fuel and which consists of n components, the objective function to be minimized in Eq. (12.27) is simplified into (

"

minX CðxÞ ¼ minX s:H Cf ðxÞ þ

n X i¼1

#) Zi ðxÞ

(12.30)

where H is the number of operation equivalent hours throughout the year and s ¼ 3600 s/h. As we have seen in Section 12.7.4, different authors have proposed different cost models for equipment and installations. The resources cost generally varies in the opposite direction to the equipment cost with respect to the design variables. As we have said before, an improvement in the

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system structure or in the efficiency of its components implies a reduction in the resources consumption, but an increase in investment. Obviously, optimization methods based on Thermoeconomics can use multi-criteria optimization, so in the objective function, for example, environmental considerations may be included.

12.8.2 Local optimization based on the Thermoeconomic Isolation Principle The interest in using Thermoeconomics in design is that, by incorporating the complexity of structural interactions in the costs determination, it allows us to use adequate procedures for the global system optimization based on the local components optimization that go into making it up. If we look at, in particular, the thermal building installations, we can say that generally they have complex structures, due to the numerous processes and the interdependence between them, which makes their optimization difficult. However, knowing the internal costs through Thermoeconomics, allows, under certain conditions, the transformation of that complex problem into a series of simpler problems to be resolved. Under certain conditions, it is possible to break down the global optimization problem into a series of subproblems, as we have mentioned in Section 12.6.1. The cost function of an individual component of the system is Ci ðxÞ ¼ cF;i Fi ðxÞ þ Zi ðxÞ

(12.31)

If the output of component i is fixed, the above equation can be written according to the marginal exergy consumption in the form Ci ðxÞ ¼

n X j¼0

cP;j kji ðxÞPi þ Zi ðxÞ

(12.32)

We see that the minimum condition of the total system with respect to the variable xl, Eq. (12.29) coincides with the minimum condition of component i, when that variable affects only component i. Thus, if the production coefficients kji of a component depend only on a subset of the total set of independent variables, that is, vkji ¼ 0 xl ;xi vxl

(12.33)

then the optimization problem can be broken down into several subproblems. In order to know if a design variable is local or not and which components it affects, the cost change in component i is evaluated due to the change of that variable DCix ¼

n X j¼0

cP;j Dkji Pi þ DZi

(12.34)

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Exergy Analysis and Thermoeconomics of Buildings

and it is compared to the change in the total cost DCix DCTx

(12.35)

If this quotient is one or close to unity, the design variable x is local to the subsystem i, while if it is zero or close to zero, the subsystem i does not depend on the variable x. For other values, the variable x affects the subsystem i and other subsystems. This possibility of optimizing a system through decomposition into a series of subsystems was studied at the time by El-Sayed and Evans 1970 [38] and El-Sayed and Tribus1983 [39]. In their work, they established the conditions of what is called theThermoeconomic Isolation Principle, so that, as we will check in Example E.12.7, they demonstrated that in order to optimize the total system by optimizing each of the components, it is necessary for the product and the product unit cost of each component to be constant and known. In most systems Pi and cP,i of component i are modified when the design variables of the other components change, due to the existing interrelation. The more constant Pi and cP,i are, the closer the system will be to Thermoeconomic Isolation conditions and, therefore, the fewer iterations will be needed to reach the optimal solution. These ideas can be used for a global optimization problem solving strategy, according to the following steps: (1) Determine which variables are local and which are global. (2) Take an initial value for the design variables and calculate the unit exergy consumption and the product unit costs. (3) Proceed to local optimization using the appropriate algorithm and find the optimal values for local variables. (4) Find the optimal values for the system global variables. (5) Iterate from (4) until the design variables or costs do not change in the next iteration.

Local optimization is a very powerful tool for the installations design and in general for complex systems. In the most usual operating conditions, the optimal design of each component can be obtained through local optimization. The designers can concentrate their efforts on the design of the individual components, knowing that if they are close to the Thermoeconomic Isolation conditions, an optimal design will be reached, or at least an improvement of the system as a whole, Lozano 2000 [40]. As we have seen, it is essential to know the investment costs of the components as a function of their rated power and efficiency.

12.8.3

Heuristic method by successive approximations

We are going to describe an alternative to thermoeconomic optimization, that is not analytical but rather a heuristic methodology since, by means of successive approximations, it arrives at an improved design. As we say, it is an iterative method that uses the variables and results obtained from the thermoeconomic analysis, in order to iteratively propose modifications to the system. Therefore, from an existing system,

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the information obtained from thermoeconomic analysis is used to define a better one, so that rather than an optimization method, this is an improvement method. Thus, it is not a classic optimization method, but a heuristic methodology that tries to improve, step by step, the system behaviour (for example, reducing the product economic costs ), to finally obtain a best solution. Therefore, this method does not guarantee a global optimum, but in the end what we find is a better solution with respect to the starting point. The information we have after the initial system thermoeconomic analysis is: • • • • • • •

Exergy efficiency of the components. Exergy destroyed in each component. Unit exergy cost of each flow. Relative increase of the product cost with respect to the fuel in each component. Unit thermoeconomic cost of each flow. Increase in the product thermoeconomic cost with respect to the fuel in each component. Exergoeconomic factor.

The most interesting information here is given by the thermoeconomic costs, since the objective is not to thermodynamically improve the system, even at the expense of a large investment cost, but to find the improvement in which the unit costs of the final products are the lowest. In this regard, the cost increase between the product and fuel in a component gives us very valuable information, since where there is a large increase, it will be due either to a high investment cost or a low efficiency. The way to discriminate what the origin of this increase in cost is, is through the exergoeconomic factor f. Indeed, we saw in Chapter 7 that the exergoeconomic factor expresses two concepts. On the one hand, it is the relation between the cost of recovering the capital Zi(that is, the investment cost in technology) and the cost of each exergy unit destroyed in the equipment. It also reflects the contribution of capital recovery cost in the increase of the unit exergoeoconomic cost of the flows that pass through the equipment. Through the value of the exergoeconomic factor, the analyst can decide between increasing the component exergy efficiency, generally through an increase in the investment cost, or decreasing the investment cost, typically accompanied by a consequent decrease in efficiency. In the bibliography, typical values for the factor f of the different components of industrial installations and buildings are found, Querol et al. 2013 [41]. So for heat exchangers fi70%, etc. If a component presents values outside these indicated limits, it is a sign that it would probably be better to change it for a new one or perform some maintenance operation. The method of successive approximations consists of the stages that we will describe below. First of all, a thermoeconomic analysis of the initial system at its rated operation point is carried out, and the thermoeconomic variables that we have previously mentioned are evaluated. Taking into account these variable values, the components that must be modified first are selected, meaning those that have the highest values of the product cost. However, these costs alone are not enough to make this selection, since it may happen that the fuel cost is high and, then, the

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problem is not in that component. Thus, among the components with the highest product costs, those that show a greater variability of unit cost related to the fuel are selected. With respect to the value of the exergoeconomic factor, if the factor value of a component is close to one, it means that it may be of interest to reduce its investment cost and consequently, its efficiency also. If the factor is close to zero, it may be of interest to increase its efficiency and, consequently, the investment cost. Once a component with the above criteria has been chosen and the relevant modification made, a check of the system behaviour is carried out, that is, the objective function is evaluated, for example, the unit cost of the final products. If the result is positive, that is, if a reduction in those unit costs has been achieved, the modification is accepted, whereas, it is otherwise rejected. Then, in view of the thermoeconomic variable values of the modified system in that first stage, another modification is proposed on the same component, or another component is selected in order to undergo some modification. We continue in this way in an iterative stepwise process, until finally no improvement is found. We present below a series of examples on optimization by applying Thermoeconomics, referring to thermal installations in buildings. At the end of the chapter we will develop an example involving a building renovation, in which thermoeconomic optimization applies both to the installations and to the building envelope.

12.8.4

Examples

Example E.12.7.

Consider an installation consisting of a sequential system made up of three components, such that the fuel of each component is the product of the previous one, with the total product being fixed. Each component has only one independent design variable, which is the exergy efficiency and the capital cost of each component varies linearly with the amount of product. Develop equations to find the design variables that minimize the total cost and verify that the installation satisfies the Thermoeconomic Isolation Principle. Solution. We will use the subscripts 1, 2 and 3 to refer to the first, second and third component respectively. The installation total fuel is the fuel of equipment 1 which we will call F; its product is P1which coincides with the fuel of equipment 2, F2; the product of equipment 2, P2, is the fuel of equipment 3, F3, whose product is the installation total product, which we will call P. The investment, operation and maintenance cost of each component is related to its product and the independent design variable, resulting in the following three equality constraints: Z1 ¼ Z1 ðP1 ; x1 Þ

Z2 ¼ Z2 ðP2 ; x2 Þ Z3 ¼ Z3 ðP; x3 Þ

On the other hand, there will be a physical model for each component, that is, a functional relationship, which relates the fuel consumed with the product obtained, so that

Design and optimization of the envelope and thermal installations of buildings

F ¼ F1 ðP1 ; x1 Þ F2 ¼ F2 ðP2 ; x2 Þ ¼ P1

969

F3 ¼ F3 ðP; x3 Þ ¼ P2

Since the installation total product P is fixed, the objective function to be optimized will be the total cost, so that with cF being the unit cost of the fuel used by the installation, we have CT ¼ cF F þ Z1 þ Z2 þ Z3 Since it is an optimization problem subject to equality constraints, we will use the Lagrange multiplier method. The resulting Lagrangian function is L ¼ cF F þ Z1 ðP1 ; x1 Þ þ Z2 ðP2 ; x2 Þ þ Z3 ðP; x3 Þ þ l1 ½F1 ðP1 ; x1 Þ  F þ l2 ½F2 ðP2 ; x2 Þ  P1  þ l3 ½F3 ðP; x3 Þ  P2  The minimum total cost condition is determined by the following equality relationships vL v ¼ ½Z1 þ l1 F1  ¼ 0 vx1 vx1 vL v ¼ ½Z2 þ l2 F2  ¼ 0 vx2 vx2 vL v ¼ ½Z3 þ l3 F3  ¼ 0 vx3 vx3 vL v ¼ ½cF F  l1 F ¼ 00l1 ¼ cF vF vF vL v v ¼ ½Z1 þ l1 F1  l2 P1  ¼ 0 0l2 ¼ ½Z1 þ l1 F1  vP1 vP1 vP1 vL v v ¼ ½Z2 þ l2 F2  l3 P2  ¼ 0 0l3 ¼ ½Z2 þ l2 F2  vP1 vP2 vP2 The resolution of this system of six equations allows us to calculate the value of the variables for the installation optimal design. We see that in this general case, the Lagrange multipliers coincide in the optimum with the marginal exergoeconomic costs of the components. On the other hand, the first three equations represent the competition between the fuel and investment costs in the local objective functions of each component. According to the opening statement of this Example, we have the particular case in which

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Exergy Analysis and Thermoeconomics of Buildings

F1 ¼

P1 41

F2 ¼

P2 42

F3 ¼

P3 43

and also that Z1 ¼ P1 f1 ð41 Þ Z2 ¼ P2 f2 ð42 Þ

Z3 ¼ P3 f3 ð43 Þ

When these conditions are met, it is easy to verify that there is a total correspondence between the Lagrange multipliers and the unit exergoeconomic costs. Indeed, we have already seen that for equipment 1, l1 ¼ cF. Since f1(41) ¼ Z1/P1, it will be true that l2 ¼

Z1 cF þ /l2 P1 ¼ Z1 þ cF F P1 41

If we compare this last equation with the economic balance in the equipment cP,1P1 ¼ Z1þcFF we can effectively conclude that l2 ¼ cP;1 ¼ cF;2 and similarly we can verify that l3 ¼ cP;2 ¼ cF;3 Therefore, we can conclude that when the requirements of this Example are met, the system optimized design is achieved by optimizing the design of each component on a local scale, with the marginal cost of the fuel consumed (Lagrange operator) being the unit exergoeconomic cost. This is what is known as the Thermoeconomic Isolation Principle. Example E.12.8.

Optimum diameter and thickness in a steam pipe Consider a steam pipe from vapor turbine extraction. The steam mass flow rate is 3.75 kg/s, at a pressure of p¼ 9.8 bar and temperature T ¼ 543 K, where p0 ¼ 0.99 bar and T0 ¼ 298 K. The relative pipe roughness is d ¼ 45.7 mm, and the total length is 15.1 m. The emissivity of the insulation outer surface is ε ¼ 0.92 and its thermal conductivity l ¼ 0.06 W/m K. Considering an interest rate of i ¼ 0.20 and a useful life of n ¼ 20 years and knowing that the exergoeconomic cost of the steam that reaches the pipe is 17.33V/ 106kJ, calculate the pipe optimal diameter and thickness. Note: This Example was one of the first problems solved by application of Thermoeconomics, Wepfer 1979 [E.21]. Solution. In a steam pipe, the direct operating costs are the result of head losses due to friction in the steam flow and heat losses to the environment. Consequently, the pipe diameter and the insulation thickness must be sufficiently large, but how large? The answer is simple, investment in the pipeline and insulation must be made such that the total costs, sum of the operation and investment costs, are minimal.

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The objective function to be minimized is the total cost in the pipeline, which is the sum of the investment costs made in the pipe and insulation plus the operating costs, which are linked to the exergy destruction that takes place. Therefore, the objective function is CT ðD; eÞ ¼ Zpipe ðDÞ þ Zinsl ðD; eÞ þ Cf ðDÞ þ CQ ðD; eÞ where CT is the total annual cost, Zpipeis the pipe investment cost, Zinsl is the insulation investment cost, Cf is the cost of the exergy destroyed by friction and which is, therefore, linked to the steam viscosity and CQ is the cost of exergy destroyed by heat transfer. The optimization objective is to obtain the values of the pipe diameter and the insulation thickness, (D,e), which are the independent variables, and which minimize the total annual cost. As we saw in Chapter 7 the pipe capital cost is the product of the investment and the capital recovery factor. From the manufacturer’s information and cost estimation manuals, we obtain the formula that relates the pipe costs with the nominal diameter. The expression obtained at the time was n o Ipipe ðDÞ ¼ L:exp 0:72ðln DÞ2  2:52 lnðDÞ þ 7:92 r where L is the pipe length and r is the ratio of average costs for this type of system between the current year and 1978, which was the year for which this correlation was established. With this expression, to calculate Zpipe, we use Equation (7.57) of Chapter 7. Similarly, the insulation investment cost is the product of the investment and the capital recovery factor. In the case of insulation, the following adjustment equation was established Iinsl ðD; eÞ ¼ Lfð0:04933D þ 0:20875Þ:expð0:9472:lne þ 1:4804Þ þ 8gr The annual cost associated with the irreversibilities due to the friction in the steam flow process in the pipe is the product of the unitary exergoeconomic cost of the steam at the pipe inlet and the destroyed exergy due to friction, that is Cf ðDÞ ¼ cstm Df According to Equation (2.110) of Chapter 2, the exergy destruction due to friction in the flow, considering a constant temperature in the flow T, is _ 2 T0 T0 mv D_ f ¼ W_ f ¼ T T 2g

L X þ Ki D i

!

where m_ is the steam mass flow rate, v is the velocity, f the friction factor and Ki the head loss coefficient in accessory i. The friction factor depends on the Reynolds

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Exergy Analysis and Thermoeconomics of Buildings

number, as well as on the roughness of the pipe inner surface, which can be obtained from a Moody diagram or by using existing empirical correlations. The annual cost associated with the external irreversibilities due to the heat transfer from the steam temperature to that of the environment is the product of the unitary exergoeconomic cost of the steam at the pipe inlet and the destroyed exergy, which is the exergy transferred that leaves the steam through the pipe to the environment, which is   T0 CQ ðD; eÞ ¼ cstm DQ ¼ cstm 1  Q T where T is the steam temperature. We need to know the heat transfer to the environment. Calling the temperature on the insulation outer surface Ts and the temperature at the pipe outer surface Ti, the heat that is transferred through the insulation by conduction is Q¼

2plinsl LðTi  Ts Þ   De þ 2e ln De

where De is the pipe outer diameter and linsl is the insulation thermal conductivity, From a certain thickness of insulation onwards, it can be considered that the pipe outer surface temperature is equal to that of the steam that flows through its interior. The heat that is transferred between the insulation external surface and the environment is due to the combined effects of convection and radiation and is calculated by the equation 

  Q ¼ pðDe þ 2eÞL εs Ts4  T04 þ hðTs  T0 Þ where ε is the emissivity of the insulation external surface and h is the convection coefficient, which can be obtained from the relationships between the Nusselt, Grashof and Prandtl numbers. By equalizing the heat transferred by conduction through the insulation and that given to the environment, and assuming, as we have said, that Ti ¼ T, we can calculate Ts and once its value is known, the exergy of the heat transferred to the environment can be determined. This exergy is, therefore, based on the independent variables (D,e) of each of the summands that are part of the objective function. There are different mathematical methods to minimize this function, the simplest being the direct search, in which the annual cost is evaluated for different nominal pipe diameters and insulation thicknesses. The advantage of this method is that the effect of the design variables on the total cost and on the different components can be analysed later. With the data presented in this Example, the optimal diameter obtained is 00 Dopt ¼ 10 , with the cost of the pipeline being 393.0 $/m.y, the insulation thickness opt e ¼ 800 and its cost 31.5 $/m.y, the steam velocity being 18 m/s, with the cost of

Design and optimization of the envelope and thermal installations of buildings

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friction 105.6 $/m.y, the insulation surface temperature Ts ¼ 304 K and the cost of heat lost 27.5 $/m.y, for a total annual cost of 557.6 $/m.y. [E.21] W. J. Wepfer, Economic Sizing of Steam Piping and Insulation, Trans. ASME, Journal Eng. Industry, 101 (1979) 427e433. Example E.12.9.

Optimization of a biomass trigeneration plant Consider a trigeneration installation with an ORC installation, as shown in the schematic of Fig. E.12.21, the heat generator being a combustion chamber using biomass fuel and with a single effect absorption refrigerator. Using thermodynamic analysis and thermoeconomic optimization (a) Build the thermodynamic model of the ORC, the absorption refrigerator and the combustion chamber. (b) Establish expressions for the electrical power, cold/electricity and heat/electricity ratios, as well as the electrical, global and exergy efficiencies of the installation. (c) Build the thermoeconomic model of the installation. (d) Determine the biomass humidity that minimizes the operating costs.

Solution. (a) Fig. E.12.21 shows the schematic of the trigeneration installation, in which the states of the flows at the inputs and outputs of the main equipment are indicated with numbers. The fluid selected for the ORC is the n-octane whose thermodynamic properties have been obtained from [E.22]. The operation mode of an ORC has been given in Chapter 6. Let us now develop a thermodynamic model of the cycle.

Figure E.12.21 Schematic of the trigeneration installation.

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Exergy Analysis and Thermoeconomics of Buildings

Thermodynamic model of the ORC In accordance with the nomenclature adopted in Fig. E.12.21, for the mass balances, we have m_ 1 ¼ m_ 2 ¼ m_ 3 ¼ m_ 4 ¼ m_ 5 ¼ m_ 0 where the subscript 0 is used to indicate that it is the flow inside the ORC. The energy and exergy balances in the ORC components are presented below. A thermodynamic model of the absorption refrigerator is presented in Chapter 6, so we will refer to that. Then we will look at the thermodynamic model of the biomass boiler. Pump W_ p ¼ m_ 0 ðh2  h1 Þ W_ p þ m_ 0 ðb1  b2 Þ ¼ D_ p The pump isentropic efficiency is hp;s ¼

W_ p;s W_ p

  W_ p;s ¼ m_ 0 h2;s  h1

Evaporator   Q_ ev ¼ m_ 0 ðh3  h2 Þ ¼ H_ 19  H_ 20 B_ 19  B_ 20 þ m_ 0 ðb2  b3 Þ ¼ D_ ev Turbine W_ T ¼ m_ 0 ðh3  h4 Þ _ T þ m_ 0 ðb3  b4 Þ ¼ D_ T W The turbine isentropic efficiency is hT;s ¼

W_ T W_ T;s

  W_ T;s ¼ m_ 0 h3  h4;s

Heat exchanger   Q_ h ¼ m_ 0 ðh4  h5 Þ ¼ m_ h hh;2  hh;1   m_ 0 ðb4  b5 Þ þ m_ h bh;1  bh;2 ¼ D_ h

Design and optimization of the envelope and thermal installations of buildings

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Thermodynamic model of the absorption refrigerator In Chapter 6, Sections 6.2.3 and 6.2.4, we developed a thermodynamic model of the simple absorption refrigerator, in which we considered the following hypotheses: the refrigerant was pure water (states 6 to 9); states 7, 10 and 13 were saturated liquid; state 9 was saturated steam; the pressures in the condenser and generator were the same; the pressures in the evaporator and absorber were equal. We will make reference to the mass, energy and exergy balances in each component that were presented in the said Sections of Chapter 6. Thermodynamic model of the biomass combustion chamber Hot gases are generated in the combustion chamber and used as a heat source in the ORC evaporator. Prior to this, they are made to go through a cyclone to separate out the ashes that are being carried by the generated gases. The biomass used as fuel is pine sawdust, a residue obtained in the processing of pine wood. After carrying out the fuel elemental analysis it is found that the humidity is 10% and that the fuel formula is CCHHOOwhere C ¼ 50.54%, H ¼ 7.08% and O ¼ 41.68%, with some traces of sulphur that are not taken into account. Mass balance The equation of the combustion chemical reaction, assuming it undergoes a complete process, is   79 CC HH OO þ uðH2 OÞ16 þ g O2 þ N2 / a1 ðCO2 Þ18 þ a2 ðH2 OÞ18 21 17 þ a3 ðN2 Þ18 where u is the fuel moisture content and the subscripts with numbers correspond to those that have been assigned in the schema of Fig. E.12.21. The coefficients of the combustion equation are found by undertaking the elementary mass balances, and are a1 ¼ C ; a2 ¼

H þ 2u ; 2

a3 ¼

79 l; 21

l¼

2a1 þ a2  u  O 2

Energy balance An energy balance is carried out to find the gases temperature at the exit of the combustion chamber. Considering that the chamber is approximately adiabatic, we have   79 ðhbiom Þ16 þ uðhH2 OÞ16 þ g hO2 þ hN2 ¼ ða1 hCO2 þ a2 hH2 O þ a3 hN2 Þ18 21 17 In this equation, the gases temperature is unknown, flow 18, and this is to be determined. The fuel enthalpy can be obtained from the relationship that links it with its Higher Heating Value (HHV), where the biomass HHV is obtained using the Dulong and Petit equation [E.23] for the case in which the presence of sulphur is not taken into account.   O HHVbiom ¼ 338:3 C þ 1443 H  8

976

Exergy Analysis and Thermoeconomics of Buildings

Exergy balance Since there are chemical reactions in the combustion chamber, we must take physical and chemical exergy into account. The physical exergy of air and fuel at the combustion chamber inlet are zero since they enter at the environmental pressure and temperature. Once the composition and temperature of the gases at the outlet are known, the physical exergy is calculated, using the following expressions for the components of those gases:   ðbCO2 Þ18 ¼ ðhCO2 Þ18  hCO2 ;0  T0 ðsCO2 Þ18  R lnðxCO2 Þ18  sCO2 ;0   ðbH2 OÞ18 ¼ ðhH2 OÞ18  hH2 O;0  T0 ðsH2 OÞ18  R lnðxH2 OÞ18  sH2 ;0   ðbN2 Þ18 ¼ ðhN2 Þ18  hN2 ;0  T0 ðsN2 Þ18  R lnðxN2 Þ18  sN2 ;0 In terms of chemical exergy, the standard chemical exergy of all chemical species entering and leaving the combustion chamber, except for the fuel, is known. Using Szargut’s tables [E.24] we have bch;0 H2 O ¼ 9:5

kJ kJ ; bch;0 ; ¼ 19:87 CO 2 mol mol kJ ¼ 0:72 mol

bch;0 O2 ¼ 3:97

kJ ; mol

bch;0 N2

The fuel standard chemical exergy is calculated using the correlation given by Szargut [E.24], bch;0 fuel ¼ b LHVfuel For a solid fuel, in which (O/C < 2)we have b¼

1:044 þ 0:016ðH=CÞ  0:3494ðO=CÞð1 þ 0:0531  H=CÞ 1  0:4124  O=C

If we know the specific exergies, then we will have to multiply by the mass flow rates to obtain the rate of exergy that enter and leave the combustion chamber. So for the fuel  q B_ biom

16

¼ N_ biom b LHVbiom Mbiom

where N_ biom is the number of moles per unit of time and Mbiomis its molar mass. Once the composition and temperature of the gases at the combustion chamber outlet are known, its enthalpy at the inlet of the evaporator, per unit of time is

Design and optimization of the envelope and thermal installations of buildings

977

  H_ 19 ¼ N_ CO2 hCO2 þ N_ H2 OhH2 O þ N_ N2 hN2 19 and at the outlet   H_ 20 ¼ N_ CO2 hCO2 þ N_ H2 OhH2 O þ N_ N2 hN2 20 The physical exergy at the inlet and outlet are calculated in a similar way to how we have seen previously for flow 18. (b) The energy supplied to the trigeneration installation, per unit of time, is

E_ biom ¼ N_ biom LHVbiom Mbiom The electric power obtained is W_ p W_ p;d W_ net ¼ halt W_ T   hmot hmot where haltis the electrical efficiency of the alternator driven by the turbine, W_ p is the ORC pump power, W_ p;d is the solution pump power of the absorption refrigerator and hmot is the electric drive motor efficiency, which we assume has the same value for the two pumps. The trigeneration installation electrical efficiency is hel ¼

W_ net E_ biom

If Q_ c is the cooling capacity of the absorption refrigerator, the thermodynamic model of which we developed in Chapter 6, then the installation overall efficiency is hg ¼

W_ net þ Q_ h þ Q_ c E_ biom

with the heat/electricity ratio being the quotient Q_ h W_ net and the cold/electricity ratio Q_ c W_ net . Referring now to the exergy, the electrical exergy efficiency is 4el ¼

W_ net ch B_ biom

and the global exergy efficiency 4g ¼

    W_ net þ m_ h bh;2  bh;1 þ m_ c bc;2  bc;1 ch B_ biom

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Exergy Analysis and Thermoeconomics of Buildings

  where m_ h bh;2  bh;1 is the exergy given in the heating process and bc,1,bc,2are the specific exergies of the evaporator secondary at the inlet and outlet, respectively. (c) Thermoeconomic model of the trigeneration installation

Next, we give the installation thermoeconomic model. The equipment costs that were used in this Example are presented in Table E.12.4, having obtained the data from Means 2010 [E.25]. ORC pump Calling the electricity cost consumed by the pump C_ Wp , from the exergoeconomic cost balance we have C_ 2 ¼ C_ 1 þ C_ Wp þ Z_ p ORC turbine C_ 4 þ C_ Wnet ¼ C_ 3 þ Z_ T In addition, in accordance with Proposition 3 of Thermoeconomics that we saw in Chapter 7, we have c4 ¼ c3

ðProposition 3Þ

ORC heat exchanger The cost balance equation is C_ 5 þ C_ h;1 ¼ C_ 4 þ C_ h;1 þ Z_ exch

Table E.12.4 The main equipment investment costs of the trigeneration installation. I ($) ORC pump

25,000

ORC turbine

200,000

Heat exchanger

40,000

Evaporator

70,000

Absorption refrigerator

22,000

Biomass combustor

300,000

Electric generator

40,000

Biomass fuel

0.01 $/kWh (PCI)

Design and optimization of the envelope and thermal installations of buildings

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where it is satisfied that C_ h;1 ¼ 0 c5 ¼ c4 ðProposition 3Þ Absorption refrigerator From the cost balance, with C_ c being the cost of the cold produced, we obtain the equation C_ 1 þ C_ c ¼ C_ 5 þ Z_ ar and also c1 ¼ c5 ðProposition 3Þ ORC evaporator The cost balance gives us the equation C_ 3 þ C_ 20 ¼ C_ 2 þ C_ 19 þ Z_ ev where c20 ¼ c19 ðProposition 3Þ Biomass combustion chamber C_ 18 ¼ C_ 16 þ C_ 17 þ Z_ cc where C_ 16 is the acquisition cost of the biomass and C_ 17 ¼ 0, since it is atmospheric air. So far, we have 12 equations and we have 13 unknowns, so we need one more auxiliary equation. This equation can be obtained by applying Proposition 4 to the electric generator product, since the electricity consumed by the ORC pump and the net electricity has the same origin and, therefore, C_ Wp C_ net ¼ W_ p W_ net (d) Once the thermodynamic and thermoeconomic models are available, we are able to solve the optimization problem. The objective is to find the value of the independent variables that make the cost per product exergy unit of the trigeneration plant minimal, therefore, the objective function is min½ctri  ¼ min½cnet þ ch þ cc 

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Exergy Analysis and Thermoeconomics of Buildings

where cnet ¼

C_ net ; W_ net

cc ¼

C_ c ; _ BQ;ev

ch ¼

C_ h _ BQ;h

In this case, the independent variable is the humidity that the biomass must contain to ensure that the sum of the exergy unit costs of the three products is minimum. With u being the moisture content, referred to per unit fuel mass, while per mole of moist fuel it is. u ¼ u ðMfuel þ uMH2 OÞ The mathematical procedure followed to achieve the optimization was Powell’s method. It is an extension of direct search methods and its description can be found in any number of books which deal with this optimization topic, Ravindrah et al. 2006 [E.26]. As said before, the independent variable to be optimized is, therefore u, which is constrained in the interval 0:05  u  0:4, and there is additionally the condition that the system must generate a net electrical power of 500 kW. When the problem is solved, it is found that the value taken by the independent variable in the optimum is u ¼ 10:1 %. Readers wishing for more information can consult the doctoral thesis of Al-Sulaiman 2010 [E.27]. [E.22] S. Vijayaraghavan, D. Y. Goswami. Organic working fluids for a combined power and cooling cycle, Journal of Energy Resources Technology, Transactions of the ASME, 127(2) (2005) 125e130. [E.23] P. Basu, Combustion and Gasification in Fluidized Beds, CRC Press, 2006. [E.24] J. Szargut, Exergy Method: Technical and Ecological Applications, WIT Press, 2005. [E.25] R. S. Means (ed.), RS Means Mechanical Cost Data, RS Means Company, 33rd edition, 2010. [E.26] A. Ravindran, K. Ragsdell, G. Reklaitis, Powells Conjugate Direction Method en Engineering Optimization: Methods and Applications, J. Wiley and Sons, 2006. [E.27] F. A. Al-Sulaiman, Thermodynamic Modelling and Thermoeconomic Optimization of Integrated Trigeneration Plants Using Organic Rankine Cycles, PhD Thesis, University of Ontario, Canada, 2010.

12.9

Energy renovation of buildings

What is energy renovation of a building? We answer this question by saying that basically, it covers three different aspects, with the following objectives: • • •

Reduce the building’s energy demand by acting on its thermal envelope (glass, carpentry, facades, roofs, etc.) Improve the energy efficiency of its energy consuming installations (heating, cooling, lighting, etc.) Use energies that are less polluting and renewable (solar, geothermal, biomass, etc.)

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Thus, the first measure is the enevelope rehabilitation, with the aim of reducing the demand for heating and cooling, through the application of energy efficiency criteria. In the following Section, we present a summary of the different strategies for the envelope rehabilitation.

12.9.1 Envelope renovation There are several possibilities when rehabilitating a building envelope. The main difference between them lies in the relative position of the insulating material within the constructed solution. The choice of one or the other will depend on the economic costs, the architectural possibilities offered by the building and the regulations applicable in each case. An ETIS (Exterior Thermal Insulation System) consists of applying an insulating coating protected by mortar to the facade, fixing it to the support mechanically and/ or with adhesives. This system is supplied as a set and can be used both in new construction and in existing buildings, see Fig. 12. 7. Among its advantages, we can point out the following: • • • • • • • • •

Thermal bridges are eliminated, adapting to the facade geometric shape. The facade aesthetics are improved, rejuvenating its appearance. Minimum maintenance. Avoids work inside. It can be installed in occupied buildings with little inconvenience for users. It does not reduce useful space. Improves acoustic insulation. Direct solar radiation is reduced. It forms a structural protection against the external elements (rain, pollution, etc.). Thermal inertia is conserved.

Figure 12.7 Appearance of an ETIS system.

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Exergy Analysis and Thermoeconomics of Buildings

The most important disadvantage is its cost. Unlike ETIS, a system with a ventilated facade (referred to in Chapter 1) consists of a rigid or semi-rigid insulation, generally made of mineral wool, fixed to the existing façade, and a protection sheet (formed by glass, plates, composite, etc.) separated from the insulation, forming a chamber through which air circulates by simple convection. The protection sheet is fixed to the wall support by means of substructures designed for this purpose, see Fig. 12. 8. The following are the most important advantages: • • • • • • • • • • • •

Thermal bridges are eliminated, adapting to the facade geometric shape. The facade aesthetics are improved, rejuvenating its appearance. Minimum maintenance. Avoids work inside. Therefore, it can be installed in occupied buildings with little inconvenience for users. It does not reduce useful space. Improves acoustic insulation. Direct solar radiation is reduced. It forms a structural protection against the external elements (rain, pollution, etc.). Thermal inertia is conserved. Depending on ventilation conditions, it contributes to the elimination of interior health problems, such as humidity and condensation. It does not require previous preparations of the wall surface. It optionally allows for the housing of facilities between the chamber and the insulator.

The main drawbacks are: • •

High cost. Significant increase in the facade thickness.

Unlike the two previous solutions, a system using thermal insulation on the interior consists of applying the thermal insulation inside the building and coating it with a suitable material. It is a system to be used in cases of internal rehabilitation, or when the building external appearance should not be modified (as in the case of

Figure 12.8 Appearance of a ventilated facade under construction.

Design and optimization of the envelope and thermal installations of buildings

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Figure 12.9 Thermal insulation on the interior.

historic buildings), see Fig. 12.9. The materials commonly used are expanded polystyrene or mineral wool, with coatings based on plasterboard, brick, etc. The main advantages of this system are: • • •

Minimum maintenance. Scaffolding systems that invade public spaces are not needed. It is the only system suitable for buildings with a level of protection due to their historical worth.

Drawbacks that may be noted include: • • • •

Medium-high cost. Loss of useful surface. It does not resolve thermal bridges. Its installation is annoying for the building users if it is occupied.

If it is impossible to gain access from the exterior, the solution of injecting thermal insulation into an air chamber can also be implemented, provided that such a chamber exists and it is accessible. Generally, the thermal insulation is cellulose, polyurethane foam or inflated mineral wool, see Fig. 12.10. The advantages of this system are: • • • • • • •

Solution for when there is no possibility to use a system from the outside. Provides rigidity to the facade. Minimum maintenance. Avoids work inside so that it can be installed in occupied buildings with little inconvenience for users. It does not reduce useful space. Thermal inertia is conserved. Economical.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 12.10 Insulation injected into an air chamber.

Drawbacks that may be noted include: • • •

Total coverage of the chamber cannot be guaranteed since the application is not visible. It does not protect against external elements. The facade aesthetic aspect is not modified.

Finally, note that when demolishing an adjacent building, dividing facades appear, with significant deficiencies in their finish, such as cavities, lack of seals and impermeability, and of course, absence of thermal insulation. Therefore, in these facades, it is necessary to incorporate insulation, see Fig. 12.11. One of the techniques used is

Figure 12.11 Sprayed polyurethane system for exposed dividing walls.

Design and optimization of the envelope and thermal installations of buildings

985

sprayed polyurethane foam, which also provides sealing and consistency. For a detailed study of the alternatives in energy rehabilitation, see Granados 2014 [42].

12.9.2 Legislation relating to the buildings energy renovation 12.9.2.1 European Union Directives Both in the residential sector buildings and in the tertiary sector there is a great potential to make economically attractive investments in renovation, although there is significant inertia for undertaking this work since only about 1% of the existing surface is renewed annually. Faced with this reality, the EU has tried to increase energy efficiency measures in existing buildings through a series of Directives. As we saw in Chapter 1, it was in 2002, when Directive 2002/91/EC (Energy Performance of Buildings Directive) was enacted. Its update in Directive 2010/31/UE, in article 7, establishes that the renovated buildings when they undergo a major reform (reform with a budget exceeding 25% of the building value, without counting the value of the land on which it is built, or renovation in which more than 25% of the building envelope is renewed) must meet the same requirements that are asked of new buildings. However, these circumstances materialize on a few occasions, so in most cases, there is no obligation for owners to implement measures to improve energy efficiency. Recognizing that the established objectives were not being met, the EU introduced new legislation, the Energy Efficiency Directive EED2012/27/EU. This Directive modifies and replaces the Cogeneration Directive 2004/8/EC and the Energy Services Directive 2006/32/EC. Article 4 of this Directive says that MS should establish a longterm strategy to invest in the rehabilitation of residential and tertiary buildings, both public and private. This strategy is defined for Spain in the National Energy Efficiency Action Plans, updated every 3 years. In addition, the EED 2012/27/EU establishes the exemplariness of public buildings so that, as of 1 January 2014, 3% of the heated and/or refrigerated surface of occupied public buildings must be renewed every year, so that the rehabilitated buildings meet at least the minimum efficiency required by each MS, in application of Article 4 of Directive 2010/31/EU. Furthermore, the Renewable Energy Directive 2009/28/EC requires MS to introduce measures to increase the share of renewable energies in buildings, both old and new, that undergo major rehabilitation.

12.9.2.2 Spanish legislation In Spain, the model that emerged in the years prior to 2008, fundamentally focused on new homes construction, which unbalanced the necessary equilibrium that should exist between construction activities and activities aimed at conserving in appropriate conditions the area already built. In addition, we must take into account the great distance that separates the built-up area in Spain from European requirements related to the buildings energy efficiency. In fact, close to 60% of Spanish homes were built without any minimum energy efficiency standards (the first is from 1979), which places Spain in a difficult position in terms of compliance with commitments to Europe,

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Exergy Analysis and Thermoeconomics of Buildings

European Commission 2013 [43]. In addition, of the 10.7 million homes in buildings with four or more floors, four million still do not have an elevator, and a very high percentage of homes are in a poor state of preservation. The Law on Urban Rehabilitation, Regeneration and Renewal [44] aims to meet the European 2020 Strategy in Spain. The objectives pursued by this Law are focused on promoting rehabilitation, regeneration, rental of housing and urban renewal, offering a suitable regulatory framework for the reconversion and reactivation of the construction sector and also promoting quality, sustainability and competitiveness, especially in relation to the objectives of efficiency and energy saving, thus bringing the Spanish regulatory framework closer to the European. Among the novelties of this Law, it regulates the Building Assessment Report, which tries to overcome shortcomings in the Technical Inspection of Buildings. In addition to assessing the state of conservation, this report provides information on the degree of compliance with current regulations on accessibility and includes the Energy Efficiency Certification. The report is only required for residential buildings of collective housing that are more than 50 years old and provided that they have not passed the Technical Inspection of Buildings in accordance with its own regulation. It also establishes a series of mechanisms that allow for external financing to make rehabilitation more accessible. In a special way, the Economic Viability Report that accompanies each action is introduced and which could justify the application of exceptional rules to link increases in buildability, as well as changes to the different operations of rehabilitation, regeneration and/or urban renewal. The Energy Saving and Efficiency Plan PAEE 2011e20 [45] is the second National Energy Saving and Efficiency Plan, designed as a central tool for the energy policy of the Spanish State. The second part of the Plan refers to sectoral analysis and, in Chapter 6, it refers to building and equipment. Each sector includes a description of the current situation and of the measures put in place and those that have been planned to enable the achievement of the intermediate (until 2016) and general (until 2020) objectives. The measures in PAEE 2011e20, aimed at the reform and renovation of existing buildings, take into account the following aspects: • • • • • • •

Energy renovation of existing buildings thermal envelope. Improvement of the energy efficiency of existing buildings thermal installations. Improvement of the energy efficiency of existing buildings interior lighting installations. Comprehensive renovation of existing buildings with high energy ratings. Building renovations with almost zero energy consumption. Improvement of the energy efficiency of commercial cold installations. Improvement of the energy efficiency in the area of appliances.

Among all the measures proposed in PAEE 2011e20, the first two concerning to buildings, which have been detailed above, are among the three of the highest priority. These two measures represent more than 16% of the final energy saving foreseen by the set of priority measures in PAEE, which gives us an idea of the importance of rehabilitation in the energy saving objectives set at the national level.

Design and optimization of the envelope and thermal installations of buildings

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12.9.3 Simulation and optimization tools for renovation The use of simulation and optimization tools for renovation measures is a quick and economical method to estimate the foreseeable savings and costs implied by the implementation of these measures. Although the numerous existing simulation software is not geared towards rehabilitation, there are some specific programmes that have been developed in recent years. Lee et al. 2015 [46] have reviewed different software and classified them into three groups, depending on whether they are based on (a) empirical data, (b) normative calculations and (c) physical modelling. These last types of models are the most complex and also the most reliable, using DOE 2.2, EnergyPlus, etc. as calculation module in most cases. Fig. 12.12 shows the percentage of use of simulation software in the search for optimized solutions in buildings, Nguyen et al. 2014 [47]. In practice, the way to evaluate the different renovation alternatives is to consider them one after another, analysing each solution based on experience. The limitation of this method is that a few scenarios are analysed, so the solution adopted may be far from optimal. In recent years, parametric or factorial tools have been developed, which allow a large number of simulations to be carried out, which can provide data to train neural networks, Asadi et al. 2014 [49]. The limitation of these methods is that they are computationally demanding and time-consuming. Another method that is also used is the multicriteria method, in which a series of predefined alternatives are compared with each other. There is no certainty in finding the optimal solution since the options considered are restricted by the user. One approach that has demonstrated the ability to explore numerous possibilities efficiently is multi-objective optimization. Three types of algorithms have been used in optimization problems applied to buildings: enumerative, deterministic and stochastic, Attia et al. 2013 [50]. As indicated by Nguyen et al. 2014 [47] stochastic methods are the most widely used, with genetic algorithms being the most popular.

Figure 12.12 Use of simulation software in building optimization.

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Exergy Analysis and Thermoeconomics of Buildings

Several studies have demonstrated the validity of multi-objective optimization in rehabilitation projects, Malatji et al. 2012 [48]. Numerous problems of envelope improvement, of thermal installations, of renewables incorporation, etc. have been investigated with different objectives such as energy saving, comfort of the occupants, total investment, cost during the lifetime, etc. Modelling tools and optimization procedures are generally based on the First Law. However, as has been discussed throughout this book, energy analysis results in similar efficiencies between very different system configurations, so it has great limitations when it comes to evaluating the characteristics of energy conversion systems. In addition, it has difficulties in finding the exact location of the place where inefficiencies occur along the energy chain. However, recent research has shown how the primary energy consumption in buildings can be reduced by applying different principles based on exergy, Terés et al. 2013 [51].

12.9.4

Renovation optimization searching for the nZEB building

In comprehensive buildings renovation, it is necessary to proceed with the joint (and simultaneous) installations and envelope optimization. We will present a model, Iturriaga et al. 2017 [52], which allows for the choice of the best rehabilitation alternative, between the different installation technologies and the different types of envelopes. Thus the optimization resolves as to what extent it is more advantageous to improve the efficiency of the facilities and to what extent the envelope. This is a mathematical model of simple and flexible optimization that allows for the best design selection from a set of quasi-infinite solutions. Regarding facilities, the model includes binary variables to represent the operating status of those technologies that have restrictions on load regulation by including the switching on and off of equipment. This aspect, although it significantly increases the computational cost, allows for the inclusion of real behaviour, which has great importance in the optimal results obtained. With regard to energy facilities, the model is based on the definition of a general superstructure that represents all the possible technologies, integration modes and operation strategies for the building energy supply. The mathematical model divides the energy supply system into different modules (sub-systems), which in an interrelated way, result in the general superstructure. This is intended to include all technologies available on the market, present and future, allowing interactions of energy flows between these modules and the building environment (for example, electrical grids, heating or district cooling). The time horizon has been discretized into a set of reference days, which allows for the optimization by means of the latest generation solvers with acceptable computing times. The model as a whole integrates an energy model, an economic model and the optimization problem itself. Readers wishing to know more can consult the doctoral thesis of Iturriaga 2017 [53]. The model is basically thought of from the installations point of view. Therefore, the theoretical basis for implementing any envelope solution is to propose a virtual technology for the thermal energy generation equivalent to that saved. Specifically, the said virtual technology would produce in each time interval, without any fuel

Design and optimization of the envelope and thermal installations of buildings

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consumption, the same amount of thermal energy that the implementation of the said solution would save. By taking this into consideration, the introduction of the said virtual technology must be carried out at the same thermal level in which the thermal heating demand occurs. It must be taken into account that the rehabilitation actions are not additive, that is, when a certain solution is selected for the envelope, any other solution is automatically discarded. This fact differentiates envelopes as heat generating technologies, with respect to the rest of the technologies considered. Any energy supply system can be understood as the sum of different integrated energy modules to meet the demands (heating, DHW, cooling and electricity). For this reason, the following modules are identified in the model: high temperature (HT) heating module that works in a range of 110e130 C, medium temperature (MT) heating module that operates in the range of 60e80 C, low temperature (LT) heating module in the range of 40e55 C, cooling module and electricity module. These modules are integrated in different ways depending on the different technologies under consideration. The different building demands are outputs from the different modules. Thus, the cooling and electricity demands are outputs from the cooling and electricity modules, the demand for DHW is an output from the MT heating module, and the heating demand is an output from the LT heating module, which is a common trend nowadays considering the promotion of LT heating systems In any case, the superstructure could be adapted to existing old buildings by placing the demand for heating at the output of the MT or HT modules. The fuels have been considered divided into two types: manageable and non-manageable. Renewable sources such as solar or wind belong to the second group since their operation cannot be optimized. All modules have a bidirectional connection with the building environment. This allows for the purchase (or sale) of part of the production to other users, or the connection to a district heating or cooling network, or to any other source or energy sink. In the case of the electricity module, this connection represents the interconnection with the electrical grid. The representation of the proposed superstructure tries to include all possible configurations of energy supply systems, for each of the modules, based on existing technologies. The model includes binary variables to represent the operating state of those technologies that present restrictions to load regulation, by including the switching on and off of the equipment. The technologies considered for optimization are shown in Table 12.1, grouped into the different modules. Only sufficiently mature technologies which are implemented in the market have been considered. The investment costs and efficiencies considered in the model for each technology are constructed from data published by different equipment manufacturers. The curves that characterize the operation of these technologies are non-linear and considering them as such within the model would imply introducing great mathematical complexity when solving the problem and the need for a considerable calculation power. In order to avoid introducing these non-linearities, the continuous trend curve of each technology has been discretized to a finite number of rated powers. In short, a general model based on integer and mixed MILP linear programming has been developed, both for the optimization of the envelope and the energy supply systems in the

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Exergy Analysis and Thermoeconomics of Buildings

Table 12.1 Types of technologies considered in the model. High temperature heating module (HT)

Medium temperature heating module (MT)

Low temperature heating module (LT)

Electricity module

Solar collector

Solar collector

Solar collector

Photovoltaic panel

Rankine Organic Cycle (ORC)

Internal combustion engine

Natural gas condensing boiler

Thermal energy storage (TES)

Gas turbine

Air-to-water heat pump Thermal energy storage (TES)

building and within the working framework of the nearly zero energy building (nZEB) standard, The economic model has been developed taking into account that the economic impact of energy supply systems implementation is the result of considering fixed costs and variable costs. This model has considered the methodology proposed by BPIE [54] [E.31], which is based on the Net Present Value method defined in EN15459 [55] [E.32]. The objective function is the annual cost of satisfying the different module demands. Therefore, the optimization problem integrates the energy model and the economic model in a holistic way. The optimization consists of finding the variables that minimize the annual cost min C annual subject to: (a) energy balance constrants at the technology level; (b) constraints of energy supply systems; (c) building-level constraints; (d) limits of the variables. MatLab R2014a [56] and CPLEX v12.6.2 [57] are used as latest generation solver MILP for the optimization. Matlab is a very powerful environment as an integrator; it has many calculation libraries, specific packages for engineering and is easily linked to other software such as Excel and CPLEX, for example. Its use is widespread in R&D departments of engineering companies and technology centres, although it has the disadvantage that it is a paid-for programme. A free alternative would be the R programme [58] that is being developed powerfully and which may soon become an alternative comparable to Matlab in terms of efficiency. For its part, CPLEX is a state-of-the-art optimization library developed by IBM, which has the advantage of being cross-platform and multilanguage (C, Python, Matlab, Excel).

12.9.5

Renovation optimization based on Thermoeconomics

In the past decade, simulation building models have been developed that contemplate exergy analysis, but for the evaluation of rehabilitation measures the incorporation of

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economic aspects and, therefore, of Thermoeconomics is required. It is clear that these models cannot replace the experience and knowledge of the technicians, but they can be a complementary tool of great help. Some exergoeconomic-based software tools that seek multi-objective optimization in renovation projects have also been developed. Of note is EXRET_Opt prepared by Garcia-Kerdan et al. 2017 [59], a tool for the evaluation and optimization of renovation designs, which considers three objectives: energy consumption, thermal comfort of the occupants and exergy destruction. The software covers the different energy systems of the building using tools developed in the ECB Annex 49 [60] and calculates the electricity flows based on the work of Rosen and Bulucea 2009 [61]. Once the different building components have been identified, ranging from the envelope, indoor air, emission terminal systems, distribution systems, generation and storage to the transformation of primary energy, the corresponding energy and exergy balances are carried out, obtaining flow exergies and exergy destructions. Thus, the total exergy demand of the building is Bdem ¼

X Bdem;i

(12.36)

i

where the subscript i refers to each of the final demand types (heating, DHW, cooling, electricity). The exergy associated with the primary energy needed to satisfy this demand for exergy at the instant tk is Bprim ðtk Þ ¼

X Egen;i ðtk Þ i

hgen;i ðtk Þ

Ff ;i Fp;i þ Edem ðtk ÞFp;el

(12.37)

where Egen,iis the energy consumed by the thermal installation i, hgen,iis the energy efficiency of that installation, Ff,i is the fuel quality factor used and Fp,iis the factor for passing to primary exergy, Edem is the electricity demand and Fp,el is the primary exergy factor for electricity. Therefore, the total exergy destroyed in the building is D¼

X X Bprim ðtk Þ  Bdem ðtk Þ k

(12.38)

k

Then, in each element of the system under consideration, the fuels and products are defined, and the corresponding costs of the flows and destructions are calculated, by means of the corresponding cost balance equations. A new exergoeconomic index is defined, which is the exergoeconomic cost-benefit indicator, calculated according to the equation ICB ¼ C_ D þ Z_  G_

(12.39)

_ the capital cost rate of the rehawhere C_ D is the rate of exergy destruction cost, Zis _ bilitation measures adopted and G is the benefit (cost reduction) obtained with the

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Exergy Analysis and Thermoeconomics of Buildings

renovation measures. This parameter is calculated considering a lifetime for the building of 50 years, assuming a certain interest on the money and is expressed in V/h. In order to evaluate the advisability or not of a rehabilitation alternative, a base case is considered first, without rehabilitation, in which only the term C_ D is non-zero. If, once a renovation solution has been proposed, and the renovated building has an index lower than that base value, then the proposed solution is effective, that is, if ICB,i < CB, basethe solution is effective from the exergy and economic point of view, and if ICB,i > CB, basethen the proposal is inefficient. In the ExRET-Opt software, three objective functions are defined. One of them is the annual exergy destruction in the building (kWh/m2year), which is O1 ðXÞ ¼ D

(12.40)

Another objective function is the discomfort hours that the building users may suffer. O2 ðXÞ ¼ ðPMVji0:5Þ

(12.41)

where PMV is Fanger’s Predicted Mean Vote [62]. The third objective function is the Net Updated Value of the investment required in the rehabilitation, which is O3 ðXÞ ¼ NUV ¼ I þ

N X n¼1

G RV þ ð1 þ iÞn ð1 þ iÞN

(12.42)

where RV is the residual value of the investment after its useful life. The investment in the envelope is usually considered to have a useful life of 50 years, while the investment in the installations has a useful life that can be considered to be 25 years. The software takes into account three types of constraints. One of them refers to the limitation of available capital to undertake the rehabilitation. The second is based on the fact that the updated return time must be less than a certain number of years. Finally, the third constraint is based on fixing the maximum number of hours per year in which conditions of discomfort are allowed. The independent variables Xi to be optimized are the set of variables that refer to the modifications that will be introduced in the renovation, so they refer to the heating installations, the envelope, the windows and the incorporation of renewable energies. In total, the vector X is a 10-dimensional vector, that is.

 X ¼ X HVAC ; X fac ; X roof ; X ilum ; .; X PV

(12.43)

The optimization is carried out by means of a genetic multi-objective algorithm AG. This is a stochastic method that mimics the evolution of species described by Charles Darwin. The software is made up of five modules:

Design and optimization of the envelope and thermal installations of buildings

• • • • •

Module Module Module Module Module

993

1. Data entry and base building modelling. 2. Building model calibration. 3. Exergy and exergoeconomic analysis. 4. Rehabilitation scenarios. 5. Optimization through AG.

In addition, ExRET-Opt can operate in three different modes. For the evaluation of the base building, uses Modules 1 to 3. For the renovation parametric evaluation uses Modules 1 to 4, while in the optimization, all five Modules are used. This type of tool can also be used for the evaluation of future decarbonization scenarios in the buildings sector, Garcia Kerdan et al. 2017 [63].

12.9.6 Examples Example E.12.10.

Comprehensive renovation of a residential building in Bilbao Let us look at a residential building in Bilbao (Basque Country), built in the 50s of the last century on which a comprehensive rehabilitation is to be performed, and which is located in a neighborhood with many other buildings of similar characteristics, see Fig. E.12.22. The building rehabilitation software described in Section 12.9.4 will be used, seeking optimization in the joint rehabilitation of the installations and the envelope. Demand for heating, DHW and electricity has been considered, but there is no demand for cooling.

Figure E.12.22 Building to be rehabilitated and its urban area.

The building consists of six floors with 36 homes in total, distributed over three portals (that is two homes per floor in each portal). The average useable area per dwelling is 55 m2, which gives a total area of 1980 m2. The total roof area of the building is 418 m2; however, only 40% of it, which is 167 m2, is considered to be suitable for installations. This limitation on the roof useable surface area has the

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Exergy Analysis and Thermoeconomics of Buildings

purpose of guaranteeing a minimum distance between solar thermal collectors and/or photovoltaic panels and thus avoiding the shadow effects. The building is connected to the electricity grid, but it is not connected to any district heating that allows the purchase or sale of thermal energy. The total surfaces of the different envelope components under consideration are shown in Table E.12.5. Table E.12.5 Surfaces of the envelope components. Envelope

Surface (m2 )

Facade

1714.2

Roof

417.6

Windows

398.3

Table E.12.6 shows the costs considered in the model for the implementation of the different solutions [E.28]. In these unit costs, the scaffolding cost is not included, although it could be done without any need to modify the model. However, due to the significant cost of the scaffolding, it seems logical to think that energy rehabilitation work on the building is carried out when the building needs work done on its facades, either for cleaning or for repair. Table E.12.6 Transmittances and costs of the different envelope solutions. Envelope

Insulation (cm)

U (W/m2K)

Investment (V/m2)

Facade

2

0.74

0

6

0.43

6.46

8

0.36

8.42

14

0.24

14.94

10

0

0

6

0.53

10.05

14

0.28

20.81

20

0.19

Roof

29.11 2

Envelope

Glass

U (W/m K)

Investment (V/m2)

Windows

4 / 6 / 4.

4.12

0

6 / 12 / 6.

2.76

133.28

3 /12 /3 low emissive

1.89

176.08

4 / 16 / 4 / 16 / 4.

1.15

212.4

The useful life that has been considered for new envelopes is 50 years (compared to 20 years of useful life for the installations). No maintenance costs have been taken into account for the envelopes. The electricity and fuel costs used are those shown in Table E.12.7.

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Table E.12.7 Electricity and fuels prices. Fuel

Unit cost (V/kWh)

Natural Gas - CNG

0.054

Biomass (pellet) - CBIO

0.041

Electricity (purchase) - CELE

0.223

Heat (sale)-CHT , CMT , CLT

0

Electricity (sale) - C ELE 

0.0496

Solution. In comprehensive rehabilitation of buildings, it is necessary to proceed with the joint (and simultaneous) optimization of installations and envelope. The model described, Iturriaga et al. 2017 [52] not only allows the choice of the best solution among certain generation technologies but also, simultaneously, chooses the best solution among certain alternatives for the envelope. Thus the optimization resolves as to what extent it is more advantageous to improve the efficiency of the facilities and to what extent the envelope optimization. Different energy saving measures were studied for the envelope, acting on roofs, facades and windows and 64 possible combinations were considered. These consisted of four different types of facades using insulation of 2 cm (existing solution), 6, 8 and 14 cm; four types of roofs, one without insulation (existing solution) and the rest using insulation of 6, 14 and 20 cm and four types of windows, with 4/6/4 glass (existing solution), 6/12/6, 3/12/3 low emissive and 4/16/4/16/4. Each of the 64 alternatives includes a combined renovation solution on the facade, on the roof and the windows. Therefore, for a certain renovation, all the facades have the same constructed solution, just as the entire roof has the same constructed solution and all the windows are equal. Therefore, an optimization was not contemplated in which it was possible that different building facades have different renovations. The alternatives were considered in two large blocks: maintaining the existing windows and replacing them. This was done because window replacement implies a significant financial outlay that is not always justifiable under strictly energy criteria. Nowadays, other factors, such as noise or safety, are involved in the decision to change windows, and these are often more decisive criteria in decision making than the energy saving obtained. Heating, DHW and electric demands If known, the thermal and electric demand curve data can be imported into the model. If they are not known, a method is included in the software to obtain approximate curves, based on some easily accessible climatic data, as was the case in this Example. In relation to the heating demand, for each typical day of the month with the maximum and minimum monthly average temperatures, Erbs’ expression [E.29] was used to obtain the scheduled temperature of the typical day of each month. For this temperature distribution, the annual degrees-days and the degree-days corresponding to each time interval were calculated.

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Exergy Analysis and Thermoeconomics of Buildings

The annual DHW and electricity demands for the building in the Example are 33.62 kWh/m2year and 35 kWh/m2year respectively, regardless of the selected alternative envelope, since it is not affected by these demands. However, the annual heating demand varies depending on the envelope. The heating demands for a total of eight rehabilitation alternatives of the envelope were calculated with TRNSYS, in order to check the validity of the results obtained with the simplified method used in the model, and showing a good degree of approximation. In the case that concerns us, since there were validated simulations of the building, the base temperature was obtained directly by statistical analysis. The building was simulated using TRNSYS for each of the eight proposed envelopes and the room temperature, and heating demand for each hour of the year was obtained for each one. Having this data meant knowing at what times of the year it was necessary to turn the heating on and off, and also to know what the ambient temperature was at those times. The average of these temperatures throughout the year is the base temperature that was used for each envelope. However, in many cases simulations are not available to obtain a value for the base temperature. In these situations, it would be necessary to obtain it through a more theoretical procedure, such as the one proposed by Kusuda [E.30], according to which, the base temperature can be calculated as the temperature set inside the dwelling minus the quotient between internal solar gains and the sum of each envelope transmittance through its respective surface, for the entire building. Results The proposed method of joint optimization of facilities and envelope was applied to the selected building, considering three different cases: (a) Optimal cost solution (b) Non-renewable zero-energy building (ZEB), without considering domestic electricity consumption in the limit condition of non-renewable primary energy consumption equal to zero (NRPE ¼ 0) and (c) Zero energy building (ZEB’) including domestic electricity consumption in the limit condition of non-renewable primary energy consumption equal to zero (NRPE’ ¼ 0). In Table E.12.8 the results obtained are shown in relation to the configuration of the power supply system and to the envelope selected in each case. Table E.12.8 Optimum installation and envelope in the three cases considered. Technology

ZEB’ (NRPE’[0)

ZEB (NRPE[0)

Optimal cost

Parabolic collector

e

e

e

Organic Rankine cycle CHP

e

e

e

High temperatura thermal storage

e

e

e

Vacuum tube collector

e

20 kWe

20 kWe

Internal combustion engine

e

e

e

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997

Table E.12.8 Optimum installation and envelope in the three cases considered.dcont’d Technology

ZEB’ (NRPE’[0)

ZEB (NRPE[0)

Optimal cost

Gas turbine

e

e

e

Biomass boiler

50 kW

e

e

Conventional natural gas boiler

175 kW

175 kW

175 kW

Medium- temperature thermal storage

e

1000 l

1000 l

Flat collector

e

e

e

Natural gas condensing boiler

e

e

e

Air-to-water heat pump

e

e

e

Low- temperature thermal storage

e

e

e

Mono and polycristallyne PV modules

390 (383%)

84 (82.5%)

-

Envelop

ZEB’ (NRPE’[0)

ZEB (NRPE[0)

Optimal cost

Insulation in facade

8 cm (U¼0.36 W/ m2K)

8 cm (U¼0.36 W/ m2K)

6 cm (U¼0.36 W/ m2K)

Insulation in roof

14 cm (U¼0.26 W/ m2K)

14 cm (U¼0.26 W/ m2K)

6 cm (U¼0.26 W/ m2K)

Windows

4 / 6 / 4. cm (U¼4.12 W/ m2K)

4 / 6 / 4. cm (U¼4.12 W/ m2K)

4 / 6 / 4. cm (U¼4.12 W/ m2K)

It can be seen that as the limit consumption requirement of non-renewable primary energy becomes more restrictive, a greater number of photovoltaic panels appear in the solution: thus, while the optimal cost case does not include any panels, in the other two cases, it does. The case of ZEB0 would involve the installation of panels outside the building itself, since its number exceeds the space availability on the roof. The optimization provides the operation data of the different technologies that are included in Table E.12.9. The presence of two different envelope solutions in the three cases of study, means that the thermal demand is not the same in all cases, being higher in the case of optimal cost, since for that case a lower envelope insulation was selected. In the cases of optimal cost and ZEB, thermal demand is mainly covered by the cogeneration engine, with the conventional boiler entering to cover peak

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Exergy Analysis and Thermoeconomics of Buildings

Table E.12.9 Operation results for the three cases analyzed.

NRPE

ZEB’ (NRPE’[0)

ZEB (NRPE[0)

Optimal cost

91.1

0

26.1

NRPE’ (kWh/m y)

0

91.1

117.2

Thermal energy demand (kWh/y)

134,829

134,829

140,115

Internal combustion engine (kWh/y)

0

137,823

161,536

Conventional boiler (kWh/y)

0

14

2,705

Biomass boiler (kWh/y)

134,829

0

0

Stored energy (kWh/y)

0

50,417

50,388

Wasted heat (kWh/y)

0

3,008

24,126

Electricity demand (kWh/y)

69,299

69,299

69,299

Generated electricity (kWh/y)

74,156

77,138

71,690

Internal combustion engine (kWh/y)

0

61,166

71,690

Cogeneration PES (%)

e

25.43

19.52

Photovoltaic panels (kWh/y)

74,156

15,972

0

Sold electricity (kWh/y)

43,812

26,342

21,182

Self-consumed electricity (kWh/y)

30,344

50,796

50,508

Purchased electricity (kWh/y)

38,955

18,504

18,791

NRPE (kWh/ m2 y) 2

Thermal energy

Electricity

demands. In both cases, the units installed are the same; however, the engine is started for more hours in the case of optimal cost, which increases the amount of heat dissipated and this, in turn, reduces the cogeneration PES, although it generates a greater amount of electricity. In the case of ZEB0 the thermal demand is covered exclusively with the biomass boiler. The electrical demand is the same in the three cases under study and is covered with different strategies depending on each case. In the case of optimum cost, the demand is covered by the cogeneration engine and the imported energy, since the solution in this case does not involve photovoltaic panels installation. In the ZEB case, it is covered by cogeneration, photovoltaic panels and grid electricity. In this case, the requirement of limit consumption of non-renewable primary energy is higher than the previous one, which implies a lower number of operation hours of the cogeneration engine. To cover this deficit in the electricity generation, photovoltaic production increases. Finally, in the case of ZEB0 the electrical demand is

Design and optimization of the envelope and thermal installations of buildings

999

covered by photovoltaic panels (in a much greater proportion than in the two previous cases) and by electrical energy imported from the grid. The surplus electricity is exported to the electricity grid, the ZEB0 being the case in which the greatest amount of energy produced is exported. However, it is also this case that uses the largest amount of electricity from the grid. This is because the electricity generation is exclusively through photovoltaic panels, whose operation cannot be managed, generating electricity when it receives radiation regardless of the building electrical demand. It can be seen that in the case of optimal cost the electric consumption exceeds 70% of the electricity generated, while in the case of ZEB it is less than 66% and in the case of ZEB0 it is only 41%. Next, the economic analysis results are given. The investment required for each of the three case studies is given in Fig. E.12.23, in which the contribution to the total investment of each technology and the envelope can be seen. The photovoltaic generation plant represents the greatest impact on the total investment, while the investment attributed to the envelope is relatively small. This is due in large part to the fact that the investment in technologies is for a useful life considered to be 20 years, while that of the envelope is for a useful life of 50 years. For this reason and to homogenize the data, an investment proportional to 20 years was considered. The economic analysis was carried out by comparing the investment with respect to economic savings, calculating the immediate simple payback period, with the results in Table E.12.10. The variable cost corresponds to the fuels and electricity costs needed to operate the plant plus the maintenance costs. The annual cost includes the variable cost, plus the annual capital cost, both of technologies and envelope. The annual saving was calculated with reference to a base case, which consists of covering the thermal demand of the current building (without improvements to the insulation) with the installation of a 200 kW natural gas boiler, the electricity demand being covered by purchased electricity from the grid. Solving the optimization problem for different cases of NRPE (or NRPE0 ), we obtained the optimal cost curve that is shown in Fig. E.12.24. The cases of ZEB 350

Investment (×103 €)

300 250 200 150 100 50 0 NRPE′ IC engine CHP Conv. boiler

NRPE Biom. boiler TES

OPTIMAL COST PV system Envelop

Figure E.12.23 Investment in envelope and installations for the three cases considered.

1000

Exergy Analysis and Thermoeconomics of Buildings

Table E.12.10 Economic results for the three cases analyzed. ZEB’ (NRPE’[0)

ZEB (NRPE[0)

Optimal cost

Investment (V)

313,466

143,444

85,448

Variable cost (V/y)

15,749

13,218

13,961

Annual cost (V/y)

31,422

20,390

18,266

Annual saving (V/y)

3,758

6,289

5,546

Payback period (y)

76.6

18.7

10.8

and ZEB0 have been highlighted in the Figure and the region of viable solutions is shaded in grey. It can be appreciated that when the limit consumption requirement of nonrenewable primary energy is less than 4 kWh/m2, without considering the domestic electrical consumption (NRPE) or less than 87.1 kWh/m2, including it (NRPE0 ), the solutions are not economically viable as they show payback periods greater than the life expectancy of the plant (20 years). Therefore, the ZEB case (without considering domestic electrical consumption) is achievable, but not the ZEB0 case. The solution for which the available area limit on the roof for the location of installations is reached is for an NRPE consumption of less than 0 (18.6 kWh/m2y or NRPE’ ¼ 72.5 kWh/m2y). Optimal energy supply solutions below this value of NRPE involve the location of the photovoltaic generation plant outside the building, due to not having enough space on the roof. [E.28] http//www.ventanka.es/precios-online, retrieved May 2017.

Payback period (years)

NRPE′ (kWh/m2y) -8,9 0 60 55 50 ZEB′ 45 40 35 30 25 20 15 10 5 0 -100

-16,1

41,1

66,1

91,1

116,1

141,1

Viability limit ZEB

Upper limit

-75

-50

-25

Optimum

0

25

NRPE (kWh/m2y)

Figure E.12.24 Minimum annual cost for different NRPE values.

50

Design and optimization of the envelope and thermal installations of buildings

1001

[E.29] D. G. Erbs, Models and applications for weather statistics related to building heating and cooling load, Ph. D. Thesis, Mechanical Engineering Department, University of Wisconsin Madison, USA, 1983. [E.30] T. Kusuda, Comparison of the TC 4.7 simplified energy calculation procedure and seven comprehensive computer simulation energy procedures, ASHRAE Journal, August 1981.

Subscripts 0 dem, prim F, P gen, el OPT

Initial values Demand, primary energy Fuel, product Generation, electricity Optimum values

Superscripts *

Local minimum

Nomenclature G_ Z_ C_ D {o} {w} {z} Dtn, N a c Cf(x) E,B,D f f(x) f, HHVf F, P fu g(x) H h(x) HT, MT, LT I ICB

Cost reduction Capital cost rate of the renovation measures Rate of exergy destruction cost Set of independent variables for operation optimization Set of independent variables for design optimization Set of independent variables associated with the synthesis Duration of intervals and number of intervals Capital recovery factor Unit cost Cost of external resources Energy, exergy, exergy destruction Exergoeconomic factor Objective function Consumption and higher heating value of fuel f Fuel vector, product vector Annual utilization factor Inequality constraint Number of operation equivalent hours per year Equality constraint High, medium and low temperature Investment required Exergoeconomic cost-benefit indicator

1002

Ii(x) IN, OUT k

L LLi, ULi Pn x Zi(x) h,4 l, m s f U

Exergy Analysis and Thermoeconomics of Buildings

Investment cost of component i Inputs, outputs Unit consumption Matrix of marginal consumption distribution Lagrangian function Lower and upper limit of the variable xi Rated power Independent variables vector Capital and maintenance cost of component i Energy and exergy efficiency Multipliers for each equality and inequality constraint Number of seconds in an hour Maintenance factor Transfer function

References [1] W. Stoecker, Design of Thermal Systems, McGraw-Hill, New York, 1971. [2] R. Boehm, Design Analysis of Thermal Systems, John Wiley & Sons, New York, 1987. [3] W. Janna, Design of Fluid Thermal Systems, PWS-KENT Publishing Co., New York, 1993. [4] A. Bejan, Entropy Generation Minimization, CRC Press, Boca Raton, Florida, 1996. [5] B. Linnhoff, Pinch analysis. A state-of-the-art overview, Transactions of the Institute of Chemical Engineers 71 A (1993) 503e522. [6] M. Moran, Availability Analysis: A Guide to Efficient Energy Use, Prentice Hall, New Jersey, 1982. [7] E. Sciubba, in: C.A. Frangopoulos (Ed.), Modeling and Simulation Methods, vol. II, EOLSS Publisher, Oxford, U.K., 2009. [8] A.W. Westerberg, G. Stephenopoulous, Studies in chemical process synthesis. I: branch and bound strategy with list techniques for the synthesis of separation schemes, Chemical Engineering Science 30 (1975) 963. [9] M.A. Lozano, J. Ramos, Optimal cogeneration technology selection for residential and commercial buildings, Cogeneration and Distributed Generation Journal 25 (4) (2010) 8e19. [10] C.A. Frangopoulos, Optimization methods for energy systems, in: C.A. Frangopoulos (Ed.), Exergy, Energy System Analysis and Optimization, vol. II, EOLSS Publisher, Oxford, U.K., 2009. [11] Y. Collette, P. Siarry, Multiobjective Optimization. Principles and Case Studies, SpringerVerlag, Berlin, 2004. [12] U. Diwekar, Introduction to Applied Optimization, Kluwer, 2003. [13] W.I. Winston, Operations Research, Thomson, 2005 (in Spanish). [14] C.A. Frangopoulos, Optimization methods for energy systems, in: C.A. Frangopoulos (Ed.), Exergy, Energy System Analysis and Optimization, EOLSS, UK, 2009. [15] I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, Adaptative Computation and Machine Learning Series, The MIT Press, 2016.

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[16] B. Paoletti, E. Sciubba, Artificial intelligence applications in the design of thermal systems, in: R. Boehm (Ed.), Developments in the Design of Thermal Systems, Cambridge University Press, 1997. [17] C.A. Frangopoulos, Intelligent functional approach: a method for optimal synthesisdesign-operation of complex systems, in: S.S. Stecco, J.M. Moran (Eds.), A Future for Energy, World Energy Research Symposium, Florence, 1990. [18] C.A. Frangopoulos, M.R. von Spakovsky, E. Sciubba, Design and synthesis optimization of energy systems, in: C.A. Frangopoulos (Ed.), Exergy, Energy System Analysis and Optimization, EOLSS, UK, 2009. [19] J.R. Mu~noz, M.R. von Sapkovsky, A decomposition approach for the large-scale synthesis/ design optimization of highly coupled, highly dynamic energy systems, International Journal of Applied Thermodynamics 4 (1) (2001) 19e33. [20] H.M. Newman, BACnet. The Global Standard for Building Automotion and Control Networks, Momentum Press, New York, 2013. [21] A. Bischi, L. Taccari, E. Martelli, E. Amaldi, G. Manzolini, P. Silva, S. Campanari, E. Macchi, A detailed MILP optimization model for combined cooling, heat and power system operation planning, Energy 74 (2014) 12e26. [22] A. Frangioni, C. Gentile, F. Lacalandra, Tighter approximated MILP formulations for unit commitment problems, power Systems, IEEE Transactions 24 (2009) 105e113. [23] T. Li, M. Shahidehpour, Price-based unit commitment: a case of Lagrangian relaxation versus mixed integer programming, power Systems, IEEE Transactions 20 (2005) 2015e2025. [24] M.A. Lozano, J.C. Ramos, L.M. Serra, Cost optimization of the design of CHCP (combined heat, cooling and power) systems under legal constraints, Energy 35 (2010) 794e805. [25] A. Costa, A. Fichera, A mixed-integer linear programming (MILP) model for the evaluation of CHP system in the context of hospital structures, Applied Thermal Engineering 71 (2014) 921e929. [26] K.C. Kavvadias, Z.B. Maroulis, Multi-objective optimization of a trigeneration plant, Energy Policy 38 (2010) 945e954. [27] S. Fazlollahi, P. Mandel, G. Becker, F. Maréchal, Methods for multi-objective investment and operating optimization of complex energy systems, Energy 45 (2012) 12e22. [28] J. Szargut, K. Maczek, Exergy balance of the absorption refrigeration process, Nesz. Nauk. Politech. Slask. 104 (1964) 35e51. [29] G. Tsatsaronis, Thermoeconomic Analysis of Energy Conversion Processes, PhD Thesis, RWTH Aachen University, 1982. [30] P. Levi, Second Law Analysis of Cogeneration Plants, PhD Thesis, The Catholic University of America, 1984. [31] R. Turton, R.C. Bailie, W.B. Whiting, J.A. Shaeiwitz, Analysis, Synthesis and Design of Chemical Processes, third ed., Prentice Hall, 2009. [32] A. Lew, H. Mauch, Dynamic Programming. A Computational Tool, Springer-Verlag, Berlin Heidelberg, 2007. [33] Optimization Toolbox, MATLAB, The MathWorks, Inc. [34] G. Brassard, P. Bratley, Fundamentals of Algorithmics, first ed., Pearson, 1995. [35] A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design and Optimization, John Wiley and Sons, 1996. [36] Y. El-Sayed, R. Evans, Thermoeconomics and the design of heat systems, Journal of Engineering for Power (January 1970) 27e35. [37] Efficiency and costing, in: R. Gaggioli (Ed.), ACS Symposium Series 235 (1983).

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[38] Y.M. El-Sayed, R.B. Evans, Thermodynamics and the design of heat systems, Transactions ASME Journal Engineering Power 92 (1970) 27e34. [39] Y.M. El-Sayed, M. Tribus, Strategic use of thermoeconomics for systems improvement, ACS Symposium Series 235 (1983) 215e238. [40] M.A. Lozano, Notes on Energy Optimization, University of Zaragoza, 2000 (in Spanish). [41] E. Querol, B. Gonzalez-Regueral, J.L. Pérez-Benedito, Practical Approach to Exergy and Thermoeconomic Analysis of Industrial Processes, Springer, 2013. [42] H. Granados, Energy Rehabilitation of Buildings, Construction Labour Foundation, 2014 (in Spanish). [43] European Commission, Europa 2020: The European Strategy of Growing, DirectorateGeneral for Communication, Publications Office of the European Union, Luxembourg, 2013. [44] Head of State, Law 8/2013 on urban rehabilitation, regeneration and renovation (in Spanish), BOE, June 27 , 2013. [45] IDAE, Energy Saving And Efficiency Plan, Secretary of State for Energy, Madrid, 2011 (in Spanish). [46] S.H. Lee, T. Hong, M.A. Piette, S.C. Taylor-Lange, Energy retrofit analysis toolkits for commercial buildings: a review, Energy 89 (2015) 1087e2000. [47] A.T. Nguyen, S. Reiter, P. Rigan, A review on simulation-based optimization methods applied to building performance analysis, Applied Energy 13 (0) (2014) 1043e1058. [48] E.M. Malatji, J. Zhang, X. Xia, A multiple objective optimization model for building energy efficiency investment decision, Energy and Buildings 44 (0) (2012) 81e87. [49] E. Asadi, M.C. Gameiro da Silva, C.H. Antunes, L. Dias, L. Glicksman, Multi-objective optimization for building retrofit: a model using genetic algorithm and artificial neural network and an application, Energy and Buildings 81 (0) (2014) 444e456.  [50] S. Attia, M. Hamdy, W. OBrien, S. Carlucci, Assessing gaps and needs for integrating building performance optimization tools in net zero energy buildings design, Energy and Buildings 60 (0) (2013) 110e124. [51] J. Terés-Zubiaga, S.C. Jansen, P.G. Luscuere, J.M. Sala, Dynamic exergy analysis of energy systems for a social dwelling and exergy based system improvement, Energy and Buildings 64 (0) (2013) 359e371. [52] E. Iturriaga, U. Aldasoro, A. Campos-Celador, J.M. Sala, A general model for the optimization of energy supply systems of buildings, Energy 138 (2017) 954e966. [53] E. Iturriaga, Development of a Simple Method for the Optimization of the Installations and Envelop of Residential Buildings in the Basque Country, PhD Thesis, University of the Basque Country, 2017 (in Spanish). [54] BPIE, Cost optimality, Discussing Methodology Challenges within the Recast of Energy Performance of Buildings Directive, Building Performance Institute Europe (BPIE), 2010. [55] EN 15459:2007, Energy Performance of Buildings - Economic Evaluation Procedure for Energy Systems in Buildings, 2007. [56] MATLAB Version R2014a, The MathWorks Inc., Natick, Massachusetts, 2014. [57] IBM ILOG CPLEX optimizer, December 2015. http://www01.ibm.com/software/ commerce/optimization/cplex optimizer. [58] https://www.r-project.org/, May 2017. [59] I. Garcia Kerdan, R. Rasian, P. Ruyssevelt, D. Morillon Galvez, ExRET-Opt: an automated exergy/exergoeconomic simulation tool for building energy retrofit analysis and design optimization, Applied Energy 192 (2017) 33e58. [60] ECB-Annex 49, in: H. Torio, D. Schmidt (Eds.), Detailed Exergy Assessment Guidebook For the Built Environment, IEA ECBS, Fraunhofer IBP, 2011.

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[61] M. Rosen, C.A. Bulucea, Using exergy to understand and improve the electrical power technologies, Entropy 11 (4) (2009) 820e835. [62] P.O. Fanger, Thermal Comfort, Danish Technical Press, McGraw-Hill, New York, 1970, 1973. [63] I. Garcia Kerdan, R. Rasian, P. Ruyssevelt, D. Morill on Galvez, The role of an exergybased building stock model for exploration of future decarbonisation scenarios and policy making, Energy Policy 105 (2017) 467e483.

Section F Exergy in the thermodynamics of continuous media

Exergy in continuous media. Application to equipment design

13.1

13

Summary

The different chapters of this book are based on Classical Thermodynamics, so that the systems analysed are in a state of equilibrium and if they evolve, the type of process they experience is quasi-static. To overcome the difficulties that these simplifications introduce, in this chapter, we will use the Thermodynamics of Continuous Media. Although the aim, in this chapter, is to write the equations of the exergy locally, we will first present a brief review of a series of notions in Thermodynamics of Continuous Media and will refer to the Law of Mass Conservation, which we will write locally and for a CV. We will then write the Law of Energy Conservation and afterwards use the Second Law, thereby undertaking the entropy balance locally and for a CV. In this way, we will be ready to deal with exergy balances, locally and for a CV. Once these ideas are set out, the exergy concept can be applied to continuous media, thus defining the scalar field of exergy. For each point and at each instant the

Exergy Analysis and Thermoeconomics of Buildings. https://doi.org/10.1016/B978-0-12-817611-5.00013-8 Copyright © 2020 Elsevier Inc. All rights reserved.

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Exergy Analysis and Thermoeconomics of Buildings

relationship that links the entropy generation with exergy destruction is described. The equation of the local exergy balance is then written, analysing in detail the exergy destruction due to irreversibilities in heat transfer and fluid flows. These ideas are subsequently applied to some examples of interest. We will finish the chapter by extending the Exergy Cost Theory to continuous media. Many engineering and architecture professionals now work with CFD software packages, for example, to analyse the air motion in buildings and optimize ventilation systems, for the analysis and design of ventilated facades, to improve the design of equipment such as biomass boilers, etc. The aim in this chapter is to present exergy balances so that they can be implemented in these CFD software packages, in order to obtain additional information that can only be found through the use of the exergy methodology.

13.2

Introduction

Classical Thermodynamics is based on the concept of the equilibrium state, such that only that type of state can be studied. In effect, the fundamental problem of Classical Thermodynamics refers to uniform systems with internal bonds and consists of determining the final equilibrium state that is reached, once some of those bonds have been eliminated. This state is described by means of a certain number of independent parameters (thermodynamic properties); the other properties are determined with the help of the system’s state equations. Thus, Classical Thermodynamics (or Thermostatics) cannot describe the evolution of systems while they are experiencing some process since they are then out of equilibrium. For studying the processes, it uses a quasi-static process model, in which the thermodynamic properties are modified infinitely slowly so that the system follows a succession of equilibrium states, Pippard 1974 [1]. It is evident that these processes are unreal since they do not involve time, or velocity, etc., given that they are an orderly succession of equilibrium states. It so happens that many real processes can be modelled as quasi-static since the rate of change of the properties that determine the system state is much slower than the average rate of change of those variables in the relaxation process between the same initial and final states. That being said, we are often forced to work with systems both in the Natural Sciences and in Engineering that could hardly be described as uniform, with their evolution being very far from that model of the quasi-static process. For overcoming these difficulties, Field Theory is extended to the discipline of Thermodynamics, that is, thermodynamic systems are considered as continuous media so that we can suppose them to be made up of an infinite number of infinitesimal subsystems. These types of systems and the processes they undergo are part of what is called Thermodynamics of Irreversible Processes, or as we will describe it in this chapter Thermodynamics of Continuous Media or Fluid Thermodynamics.

Exergy in continuous media. Application to equipment design

1011

In this chapter, we will first give a brief introduction to Fluid Thermodynamics. The mathematical equations that constitute the basic structure of this discipline are the Law of Mass Conservation, the Laws of Linear Momentum and Angular Momentum, the Law of Energy Conservation and the Second Law or Law of Entropy Generation. Readers interested in the general formulation of these Laws can consult any of the numerous existing works, for example, Silhavy 1997 [2]. The systematics that we will follow in the presentation of these Laws will in all cases be the same: it begins considering a certain portion of the fluid, a Control Mass (CM), for which the corresponding Law is formulated. The application of the Transport Theorem allows this Law to be expressed locally, that is, in each of the points of the continuous medium. Finally, through the Generalized Transport Theorem, the corresponding balance is written for any CV. The CV technique has been widely used throughout this book since the balances of the different magnitudes are expressed by algebraic equations (or differentials in a nonstationary regime) that are relatively simple. However, this methodology is used when a detailed description of the fluid evolution within the CV is not required; in other words, when knowledge of its global behaviour is enough. When we apply exergy analysis to the systems and their components, for example, to the thermal equipment and energy supply installations, as we have seen throughout various chapters, we are considering each system as a black box, with fluid flows that come in and go out. However, from a phenomenological point of view, this treatment involves a significant loss of information. When, in Chapter 5, Section 5.8, a boiler is analysed, for example, it can be seen that exergy destruction is very important. This destruction is caused by the processes that take place, such as the diffusion of fuel and oxidant, the combustion chemical reactions, the heat transfer with significant temperature differences between hot gases and water, and the existence of friction in the water, air and gas flows. In order to analyse these processes in detail, we need a theory that describes the flows depending on the time and the local coordinates, which will allow us not only to detect but also quantify irreversibilities and study their causes. In recent years, local exergy analysis, that is, the application of the differential exergy equation has begun to be accepted in the world of engineering, with the aim of improving the energy efficiency of systems and energy processes. Of note are publications such as those by Chen et al. 2003 [3,4] in which exergy destruction associated with fluctuations in a turbulent regime is analysed, and a criterion is established to reduce the rate of exergy destruction in transport processes. The work of Lior et al. 2004 [5] also deserves to be mentioned. The Laws to which we refer are general and, therefore, applicable to all substances, whatever their nature. So, if specific problems need to be solved, it is clear that something more than these general Laws is required, as the different substances in effect behave very differently in the same situation. Therefore, additional information in the form of equations or inequalities is required which describes the response of the substance in question. These are the so-called constitutive relations.

1012

13.3

Exergy Analysis and Thermoeconomics of Buildings

Brief review of some notions of fluid mechanics

Basically, there are two methods to obtain the equations that govern the movement of a fluid. One way is to consider the fluid as a set of molecules whose motion is governed by the laws of Dynamics. This theory tries to predict the macroscopic behaviour of fluids based on the laws of Mechanics and Statistics, LeVeque 1992 [6]. It is a theory that is not fully developed for polyatomic gases or for liquids and is not, of course, a theory that we will follow in this chapter. An alternative method for obtaining the equations that govern the motion of fluids is based on the notion of the continuum. The idea of the continuum completely ignores the fine details of atomic or molecular structure and considers that matter is continuously distributed in space, with the exception of discontinuity surfaces that represent interfaces or shock waves. This idea of the continuum implies that any portion of it that is considered, no matter how small, manifests the same properties as those of the system considered as a whole. We describe the state of the continuous medium through a certain number of continuous functions of the position, that is, through a certain number of fields, such as the fields of pressure, velocity, density, enthalpy, entropy, etc. A process experienced by the continuous medium is being described when time appears as a variable. Experience confirms that the local and instantaneous relations between thermodynamic properties of a continuous medium are the same as for the uniform system in equilibrium; therefore, they are independent of the local gradient values. In other words, every equation of state of a uniform system in equilibrium is applied at each instant and each point of the continuous medium. Such a claim is known as the Principle of Local Equilibrium, Sears and Salinger 1978 [7]. The Principle of Local Equilibrium is, of course, valid when the gradients are not very important. How large these gradients should be so that the Principle is not valid can only be answered with reference to the experimental path. The problem can also be approached theoretically with the help of Statistical Mechanics, but in this case, there is no unequivocal answer either.

13.3.1

Material and spatial description of the motion

The mathematical description of the motion of a continuous medium (whether solid, liquid or gas) requires the introduction of reference axes, whose origin and orientation are chosen for convenience and which are fixed in space. In practice, a laboratory system is chosen, fixed with respect to the Earth. We distinguish between spatial points, fixed with respect to the reference system and material points or particles, considered as elements of the continuum and, therefore, forming part of its motion. We also distinguish between material and spatial curves, material and spatial surfaces, etc. At a given moment, a portion of the continuous medium occupies a certain region of space. As a result of it being in motion and deforming, it will occupy different regions over time. Each of these regions constitutes what is called a configuration of the fluid portion.

Exergy in continuous media. Application to equipment design

1013

At a given instant, a configuration comprises a set of points Xi (X in symbolic notation). There is a bijective correspondence particle $ X so that each particle is characterized by the vector X: At a later time, the configuration will be different, so that the coordinate particle xi (x in symbolic notation) will have moved to a new position. A possible description of the
motion of that continuous medium portion is given by  the vector equation x ¼ x X; t and is expressed in its components xi¼(Xj, t) which are three equations with the parameter t. These equations define the material description of the continuum motion, which is also called the Lagrange description. The velocity and acceleration in this material description are obtained by the first partial derivative and second derivative, respectively, with regards to time. On many occasions, it is more convenient to express the velocity and acceleration as a function of x instead of X. Since the transformation x/X is bijective, we can obtain X as a function of x and t, that is X ¼ Xðx; tÞ. So, we can express the velocity vector as a function of the current position of the particle, that is to say
 vðx; tÞ ¼ v Xðx; tÞ; t

(13.1)

This vector specifies the velocity of all the material points, as a continuous and differentiable function. This description is known as the Euler description, and it is sometimes said that this velocity field is the spatial velocity field. Both the material description and the spatial description are used in the Mechanics of Continuous Media. The material description contains more information, since knowledge of X means that the initial position of the particle is defined. It is the description which is generally needed for Solid Mechanics, in which one of the quantities of interest is the deformation, that is, the displacement of points from their initial positions. On the other hand, in Fluid Mechanics, most of the problems are formulated using the spatial description, since the displacements of the particles are not of direct interest.

13.3.2 Meaning of the material derivative Consider a continuous medium whose state of motion is described by the velocity field vi(xj,t) and that there is a material particle of the medium located at a given instant at P, any point of that medium with coordinates xj. In addition to the reference system, we now introduce the system that accompanies P during its motion, which we call the accompanying system, defined in such a way that its origin is always at point P and such that, its axes are parallel to the axes of the reference system. Let J be a field, generally, of tensorial order n, a function of position and time. For an observer moving dxj in the time dt, since dxj ¼ vjdt, the change experienced by the tensor is dJ ¼

vJ vJ þ vj dt vt vxj

(13.2)

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Exergy Analysis and Thermoeconomics of Buildings

The first term on the right of equality (vJ/vt dt) is the local change, that is, the   tensor change at the point P and during the interval dt. The second, vJ vxj vj dt , is due to the displacement of the observer with the particle and constitutes what is called the convective change. Dividing the previous expression by dt then gives the material derivative of the tensor, which is DJ vJ vJ ¼ þ vj Dt vt vxj

(13.3)

using the symbol D/Dt to represent the material derivative, which as we see is composed of a local derivative and a convective derivative, Ziegler 1983 [8]. So for the scalar density field r the material derivative is Dr vr vr ¼ þ vj Dt vt vxj

(13.4)

and in symbolic notation  Dr vr
¼ þ v$V r Dt vt

(13.5)

Therefore, the acceleration in symbolic notation will be a¼

13.3.3

 vv
þ v$V v vt

(13.6)

Transport theorem

In this chapter, we will find different quantities defined as volume integrals, extending over a certain region V of the continuum. The simplest example is mass Z (13.7) m ¼ rðxi ; tÞds V

In general for the tensor per unit mass j, its value J in volume V is Z J ¼ rðxi ; tÞjðxi ; tÞds

(13.8)

V

We will find an expression that reflects the rate of change of J, and for this, we will follow the evolution of a CM that at time t occupies the volume V, this volume being limited by a surface A. It is easy to verify that Z Z Z d vðrjÞ ds þ rjv$ndA rjds ¼ (13.9) dt vt V

V

A

Exergy in continuous media. Application to equipment design

1015

This equation is known as the Reynolds transport theorem, Fl€ugge 1972 [9]. It tells us that the rate of change of a quantity (in general, a tensor) of a certain fluid portion is the sum of two components: one is the local change, and the other is associated with the fluid motion itself. Keeping in mind Gauss’s divergence theorem, the previous expression becomes d dt

Z 

Z rjds ¼ V

V

 vðrjÞ þ Vðv$rjÞ ds vt

(13.10)

which is another way of writing the transport equation. Likewise, using Eq. (13.3) that defines the material derivative, we have d dt

Z 

Z rjds ¼ V

V

 DðrjÞ þ rjV$v ds Dt

(13.11)

which is a third way of writing the transport equation. In the particular case in which the magnitude j satisfies the conservation condition, the term on the left of the  R  previous equations is cancelled, dtd rjds ¼ 0 . This means that the magnitude V

remains constant for an observer that moves with the volume V. Equating the terms on the right to zero and given that this equality is fulfilled for any volume V, from the last two equations, we can write vð9jÞ þ V$ðv$rjÞ ¼ 0 vt

(13.12)

DðrjÞ þ rjV$v ¼ 0 Dt

(13.13)

which represent the conservation condition locally. We will use these equations later when we write the mass or energy balance equations locally. As a very simple example of application, consider that rj ¼ 1. We then have dV ¼ dt

Z v$ndA

(13.14)

A

and applying Gauss’s divergence theorem gives dV ¼ dt

Z V$vds V

(13.15)

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Exergy Analysis and Thermoeconomics of Buildings

In the limit when V/0, we get limV/0

1 dV ¼ V$v V dt

(13.16)

This formula, which is originally due to Euler, tells us that the velocity divergence (V$v) represents the relative velocity change of the volume of an infinitesimal fluid particle. Thus, in an incompressible fluid, V $v ¼ 0 is satisfied. The transport theorem, as we have written it, refers to a certain portion of the fluid, that is, to a control mass (CM). However, on most occasions, knowing the derivative with respect to the time of a magnitude in an open system is more significant, that is to say in the language of Thermodynamics, in what we call a CV. To determine the rate of change of any magnitude of the CV we can replace it with a fictitious material system, that is, a CM associated with the CV. The only restriction that must be imposed on this CM is that the normal component of the velocity at the limits of the system coincides with the normal component of the velocity at the bounding surface of the CV. Thus, Eq. (13.10) will be equally valid, replacing velocity v with velocity vs which is the velocity of the CV bounding surface and, therefore, d dt

Z

Z rjds ¼ V

V

vðrjÞ ds þ vt

Z rjvs $ndA

(13.17)

A

where V and A are the volume and the bounding surface of the CV and vs is, as we have said, the velocity of said surface, which, in general, varies from one point to another of the surface and is a function of time. This equation is called the generalized Reynolds transport theorem, White 2003 [10]. The generalization of these equations for the case of a multiphase system, with interfaces in which discontinuities occur, can be found, for example, in Slattery 1972 [11]. Finally, there is a relationship that we will use later and which we are now going to deduce. According to the transport theorem, Eq. (13.11), we have that d dt

Z 

Z rjds ¼ V

V

  Z  DðrjÞ D9 Dj þ rjV$v ds ¼ þ rV$v j þ r ds Dt Dt Dt V

(13.18) and using the continuity equation Eq. (13.32), which we will deduce later, gives d dt

Z

Z rjds ¼

V

r V

Dj Dt

(13.19)

Exergy in continuous media. Application to equipment design

1017

13.3.4 Stress tensor Let there be a fluid in motion, and let us suppose a portion of it limited by an imaginary bounding surface. Let us consider a point P of the surface that limits the chosen mass and let DA be an area element around the point, where n is the normal unit vector, whose positive sense is considered as outward. According to Mechanics, the action of the external medium on the surface element DA ¼ DAn is equivalent to a resultant force DF and a torque DM. The quotient T¼

DF DA

(13.20)

is the force per unit area around P, that is, it is the average stress at point P. The limit, limDA/0

DF dF ¼ ¼T DA dA

(13.21)

represents the stress vector at point P. Such stress, T ¼ T ðnÞ ðx; tÞ, depends not only on position and time but also as is studied in the Mechanics of Continuous Media, on the direction of the unit vector n. On the other hand, using the same limit for the torque, and in accordance with the Euler-Cauchy principle, gives, limDA/0

DM ¼0 DA

(13.22)

The stress vector can always be broken down into a component parallel to the n direction and another perpendicular to it, which is called the shear component. If we consider the particular case in which the unit vector n is parallel to any one of the Cartesian axes (n ¼ ei ), the stress T ðei Þ, which is not generally parallel to ei , can be broken down into three Cartesian components. If we use sij for component j, we can write T ðei Þ ¼ sij ej

(13.23)

The first subscript of sij refers to the direction of the component, while the second subscript defines the normal direction of the surface under consideration. Fig. 13.1 shows a fluid particle of a cubic form, with its sides parallel to the coordinate planes and with components of stress indicated on the different faces. The set of the nine quantities sij makes up the so-called stress tensor. Its physical meaning is very important since we can represent T ðnÞ ðx; tÞ, whatever n and the point under consideration may be, as a function of that tensor. For a fluid at rest or moving as a rigid solid, the stress is expected to be reduced to the hydrostatic pressure, which gives rise to the breakdown of the stress tensor into two parts s ¼  pd þ s

(13.24)

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Exergy Analysis and Thermoeconomics of Buildings

Figure 13.1 Stress tensor.

where d is the Kronecker delta tensor. The first summand on the right is called the pressure tensor, while the second is the viscous stress, which will be zero for a fluid at rest or moving as a rigid solid. Expressing the previous relationship as a function of the components, we have sij ¼  pdij þ sij

(13.25)

In the hydrostatic case sij ¼ 0 and therefore, sij ¼ pdij, so that T iðnÞ ¼ sij nj ¼ pdij nj ¼ pni

(13.26)

that is to say, T ðnÞ ¼ pn. So, the surface force is a compression force that acts perpendicularly on the surface, which is consistent with our idea of pressure. In the general case, where there is motion, the hydrostatic stress does not have a precise meaning. However, in order to move forward in this chapter, it is important to establish the relationship between the thermodynamic pressure and the components of the stress tensor. Since the thermodynamic pressure, defined by the thermal state equation p ¼ p(r,T), refers to a state of equilibrium in the absence of movement, under these conditions we have seen that the components sij cancel out and, therefore, the normal components of the stress are equal and match the thermodynamic pressure with a changed sign. The second component of the stress tensor, the viscous stress sij depends on the local motion of the fluid through the deformation tensor, Sala 1987 [12]. Arguments based on the tensor symmetry and the fluid isotropy, allow the following expression for the stress tensor to be obtained   t   2
s ¼  pd þ s ¼ pd þ m Vv þ Vv  V$v d 3

(13.27)

Exergy in continuous media. Application to equipment design

where Vv is the second-order tensor gradient of the vector field v and

1019 t

 Vv is the

transpose of that second-order tensor Vv, with m being the viscosity. This expression of the stress tensor is the constitutive equation for the stress of a linear fluid or newtonian fluid. Most fluids, such as water, air, etc., satisfy this model. There are, however, other fluids, such as polymers, some lubricants, etc., for which the above linear constitutive equation is not applicable; they are the so-called non-newtonian fluids, Truesdell 1968 [13].

13.3.5 The notion of continuum in multicomponent systems On numerous occasions, we can find fluid flows made up of several chemical substances that may experience an arbitrary number of homogeneous or heterogeneous chemical reactions. So we need to define a continuous medium model for a system consisting of N different chemical species. This model must be such that it allows the evolution of each chemical species to be individually followed, as the mixture of these N substances undergoes some process, such as some deformation, chemical reactions, etc. The model that we will adopt to describe the multicomponent system will be a superposition of the N models of continuous media of each of the substances. Therefore, according to this model, at each point in space occupied by the multicomponent system, there are N particles of different substances. Although the terms component or constituent are sometimes used interchangeably, in the language of Thermodynamics, they have distinct meanings. The constituent is understood to be each of the different chemical species that occur in the system, while the number of components is constituents minus the independent chemical reactions between the substances. Thus, a system in equilibrium consisting of C, CO, CO2, O2 and N2 has five constituents, but only three components, since there are two independent chemical reactions Cþ1/2O2 5 CO and C þ O2 5 CO2. The other chemical reactions are not independent, insofar as they can be expressed by a combination of these two. In a multicomponent system, the composition can be expressed in various ways, the most frequent being those indicated below. The mass concentration rg is the mass of the component g per unit volume. The molar concentration cg ¼ rg/Mg is the number of moles of the chemical species g per unit volume, where Mg is the molar mass of g. The mass fraction yg ¼ rg/r is the ratio between the density of the chemical species N P g and the total density, since r ¼ rg . The molar fraction xg ¼ cg/c is the ratio g¼1

between the number of moles of the chemical species g and the total number of moles, N P since c ¼ cg . g¼1

The velocities of the different chemical species are different, and there are different ways of expressing the average values of these velocities, to finally obtain the velocity

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Exergy Analysis and Thermoeconomics of Buildings

of the multicomponent system. Let vg be the velocity of the component g with respect to the stationary axes. The average mass velocity of the multicomponent system is PN

g¼1 r

v ¼ PN

g vg

g¼1 r

(13.28)

g

The product rv represents the mass that passes per unit of time through a unit area placed perpendicular to the vector v; therefore, v is the local velocity that would be measured with a pitot tube. Similarly, the average molar velocity can be defined as 

PN

g¼1 c

v ¼ PN

g vg

g¼1 c

(13.29)

g

In the same way, the product cv is the number of moles that pass per unit of time through a unit area placed perpendicular to the velocity v . Likewise, other average velocities can be defined, but they are of less interest. Of most interest in applications is knowing the particle velocities with respect to the average velocities, rather than with respect to the stationary axes. The diffusion velocities vg  v, or vg  v , which reflect the velocity of the component g with respect to the local velocity of the fluid stream, are thus defined. Once the average velocities are defined, and the different ways of indicating the composition are shown, the mass flows are ready to be expressed. The mass flow (or molar flow) of the chemical species g is a vector representing the mass (or moles) rate of the chemical species g that passes through the unit area. The flow can be referred to with respect to the stationary coordinate system or with respect to the velocities v or v . With respect to the stationary reference system, we define the mass g flow rate vector as ng ¼ rg vg ; or the molar flow rate vector as N ¼ cg vg . On the other hand, with respect to the average mass velocity, we also define the mass flow g rate vector as j ¼ rg ðvg  vÞ and the molar flow rate vector as J g ¼ cg ðvg  vÞ. Likewise, with respect to the average molar velocity, we also have the mass flow rate g g vector as j ¼ rg ðvg  v Þ and the molar flow rate vector as J ¼ cg ðvg  v Þ All the previously defined flows are related to each other. Thus N P g g g J ¼ cg ðvg  v Þ ¼ N  xg N , etc. On the other hand, we have that g¼1 N P

J

g

¼ 0, which means that the sum of the diffusion molar flow rates with respect

g¼1

to the average molar velocity is zero, for any multicomponent system. The use of one or the other flow depends on the type of problem that arises, Sinaiski and Lapiga 2007 g [14]. Thus, the mass flow rates N and ng are used mainly in engineering since in the process calculations, it is preferable to refer the mass flow rates to a fixed in the equipment coordinate system.

Exergy in continuous media. Application to equipment design

1021

13.3.6 Considerations concerning turbulence Turbulent motion is very common, both in nature (atmospheric air, river flows, etc.) and in installations (flows in boilers, in heat exchange equipment, air flows in ventilated facades, etc.) so that most flows of interest to us are turbulent. Since turbulence significantly modifies aspects such as friction, heat transfer rate, mixing speed, etc., knowledge of its action is important. There is no complete theory of turbulence, although different flow visualization methods, adequate instrumentation and various numerical methods for its simulation have been developed so that their combined use allows a characterization of the turbulent motion. Turbulent flow is characterized by its irregularity, that is, the appearance of fluctuations in the variables of fluid dynamics, such as velocity, temperature, etc., with very different magnitudes and times. The phenomena of mass transfer, energy and momentum transfer are significantly amplified by the effect of turbulence. They occur at high Reynolds numbers and are dissipative flows, that is, there is a continuous energy transfer to maintain turbulence; otherwise it decays rapidly. In Fig. 13.2 the turbulence generated in the air on a building leeward side is shown. In the development of turbulence, whirls or larger vortices draw energy from the main flow. The size or scale of these vortices is similar to the scale of the flow, but as they are unstable, the interaction effect between them tends to divide them into smaller vortices, which in turn tend to divide again and so on. The process occurs in a cascade, so in turbulent motion, a great variety of scales coexist. The division process continues until the scale of the vortices is so small that the Reynolds number is not large enough for the instability to persist and the kinetic energy in these smaller vortices is transformed into thermal energy by viscous dissipation. This variety of different scale whirls is usually grouped into three levels: macro scales, intermediate

Figure 13.2 Turbulence on the leeward side of a building.

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Exergy Analysis and Thermoeconomics of Buildings

scales and micro-vortices. For a study of turbulence, consult the works of Pope 2000 [15], or Nieuwstadt et al. 2016 [16]. Even the micro-scale is several orders of magnitude above the molecular scales, so that the Thermodynamics of Continuous Media equations can be applied. Currently, the exact resolution of these equations describing the turbulent flow is not possible. However, in recent years, due to the development of specific algorithms and the power of computers, there has been a breakthrough in numerical resolution, giving rise to what is called Computational Fluid Dynamics (CFD). The direct resolution of the NaviereStokes equations or DNS (Direct Numerical Simulation) is the most obvious and precise way to solve the turbulent flow. For this, all spatial and temporal scales have to be solved without averaging, so that the only errors come from numerical discretizations. However, the high computational cost makes it unfeasible, except for very simple situations. Since large scales are the most efficient in the transport of properties, it is possible to try to simulate more accurately the larger scales, giving rise to the large vortices simulation or LES (Large Eddy Simulation). Even so, this type of simulation is demanding in terms of computer capacity and calculation time. However, the types of models that are most used in engineering to predict turbulent flows are those based on statistical methods, that is, on the averaging of the Naviere Stokes equations or RANS (ReynoldseAveraged NaviereStokes equations) models. When averaging the equations, there are six additional stresse components appear, called Reynolds stresses, so some turbulence model is needed to close the equations. The best known are the 0 - equations model or mixing - length model, the 1- equation model or kε model, the Reynolds stress model (RSM) and the algebraic stress model (ASM), Chassaing 2000 [17].

13.4

Conservation of mass

The mass of a closed system is independent of time so that, if we follow the evolution over time of a CM, after the various translations, rotations and deformations experienced by it, the mass does not vary and, therefore, d dt

Z rðxi ; tÞds ¼ 0

(13.30)

V

Once this Law is shown, the next step is to obtain an equation that expresses the idea of the mass conservation at each point of the continuous medium under consideration. For this we will use the Reynolds transport theorem in its particular form, that is, referring to a conservative magnitude. Fig. 13.3 shows an image of Lavoisier to whom the Law of Mass Conservation is attributed among others (Proust, Dalton and Lomonosov).

Exergy in continuous media. Application to equipment design

1023

Figure 13.3 Image of Lavoisier (1743e94).

13.4.1 Continuity equation From Eq. (13.12) substituting the generic tensor for the unity, we have vr þ V$ðrvÞ ¼ 0 vt

(13.31)

or also from Eq. (13.13) Dr þ rV$v ¼ 0 Dt

(13.32)

The above Eqs. (13.31) and (13.32) are two ways to write the continuity equation. Both express the condition that the mass must be conserved at each point of the continuous medium. If the density of the fluid particle does not change with time, Eq. (13.31) becomes V$v ¼ 0

(13.33)

and the movement is said to be isochoric. If the density is independent of time and position, it is then said that the fluid is incompressible. Therefore, a sufficient but not necessary condition for isochoric motion is that the fluid is incompressible. If we want to express the equation referring to the turbulent regime, we must use the temporal averages of the variables. Thus, by temporally averaging Eq. (13.31), using

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Exergy Analysis and Thermoeconomics of Buildings

the Leibnitz rule for the differentiation of an integral and taking into account that the divergence operation commutes with that of the temporal average, we get vhri þ V$hrvi ¼ 0 vt

(13.34)

It is important to note that in general, hrvi s hrihvi, since the average value of a product is not equal to the product of the average values.

13.4.2

Continuity equation in multicomponent systems

We shall now look at a CM made up of several different chemical species. The possibility of chemical reactions does not prevent the Law of Mass Conservation from being fulfilled for the total of the chemical species, so that Eq. (13.30) is still valid, and now N P r ¼ rg . Referring to one of the chemical species g, the equation of mass conserg¼1

vation takes the following form Z Z d rg ds ¼ K g ds dt V

(13.35)

V

where Kg ¼ Kg(xj,t) is the production rate of component g, due to the homogeneous chemical reactions that take place. Thus, where Mg is the molar mass of g and xq the advance degree of the chemical reaction q,(q ¼ 1,2,.,R) as defined by De Donder 1928 [18], the rate of g production is Kg ¼ Mg

R X q¼1

ngq

R X dxq ¼ Mg ngq vq dt q¼1

(13.36)

where ngq is the stoichiometric coefficient of g in the chemical reaction q, vq is its reaction rate and R is the number of simultaneous chemical reactions. As we have said before, the limits of the volume integrals that appear in Eq. (13.35) are a function of time. The quantity Kg is furthermore considered to be continuous and differentiable as many times as desired. This means that the continuity equation for the generic component g is vrg þ V$ðrg vg Þ ¼ K g vt

(13.37)

and using the material derivative Dg/Dt, that is, from the point of view of an observer moving within the fluid at velocity vg , one can write Dg rg vrg
g  g ¼ þ v $V r Dt vt

(13.38)

Exergy in continuous media. Application to equipment design

1025

Sometimes it is more convenient to express the continuity equation as a function of the concentration cg. Keeping in mind that cg ¼ rg/Mg we have vcg Kg þ V$ðcg vg Þ ¼ g vt M

(13.39)

Numerous other similar expressions can be found for the continuity equation, depending on (a) whether the material derivative or the local derivative is used, (b) according to the reference system chosen and (c) depending on whether mass or molar units are used. So, for example, using the mass flow rate with respect to the average speed, we have vrg g þ V$ðrg vÞ þ V$j ¼ K g vt

(13.40)

If we look now to the set of components that constitute the multicomponent system, N P Kg ¼ 0 we again obtain Eq. (13.31). We thus arrive at the expected conclusion g¼1

It is important to note that, since heterogeneous chemical reactions take place at interfaces (for example, on a catalyst surface), the production rate of a chemical species by a heterogeneous reaction does not appear as a term in the mass balance differential equation, but as a boundary condition on the surface where that reaction occurs, Moelwyn-Hughes 1957 [19]. Thus, homogeneous and heterogeneous chemical reactions not only differ in their physical characteristics but also in the way in which they are described. As we know, the branch of Physical Chemistry that describes the mechanisms of chemical reactions and the rates at which they take place is Chemical Kinetics, Espenson 1981 [20].

13.4.3 Control volume mass balance Let us look at the CV of Fig. 13.4, in which the dotted line indicates the bounding surface of the system under consideration. This is obviously an open system, with several input and output sections. According to the generalized transport theorem, Eq. (13.17) and by substituting the tensor field for the scalar unity, we get d dt

Z

Z rds ¼

V

V

vr ds þ vt

Z rvs $ndA

(13.41)

A

where, as we have said before, V and A are the volume and the bounding surface of the CV, in general as a function of time and vs is the surface velocity, which is a function of position and time. This equation, although obviously true, is certainly not very useful  R vr in its current form, since the first term on the right vt ds is almost impossible V

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Exergy Analysis and Thermoeconomics of Buildings

Figure 13.4 Control volume with several input and output sections.

to evaluate, given that, generally, we will not have information on how v9/vt varies inside the CV. In order to eliminate that term and replace it with another equivalent, we use the continuity Eq. (13.31). If we integrate this equation over the CV to which we are referring, after applying Gauss’s theorem, we get Z V

vr ds ¼  vt

Z rðv$nÞdA

(13.42)

A

Carrying this result over to Eq. (13.41) we have d dt

Z

Z rds ¼

V

rðv  vs Þ$ðnÞdA

(13.43)

A

The term on the left represents the rate of change of the mass contained within the CV under consideration. Since v  vs is the fluid relative velocity with respect to the bounding surface of the system, the term on the right is the rate of the mass transport through its limits. Given that v  vs is different from zero only in the surface permeable part, that is, in the input and output sections, the above equation can equally be written as d dt

Z

Z rds ¼

V

rðv  vs Þ$ðnÞdA

(13.44)

Aðin;outÞ

which is the mass balance equation for the CV. In short, the term on the left of the equality represents the rate of change of the mass contained in the CV, while the term

Exergy in continuous media. Application to equipment design

1027

on the right corresponds to the mass transport rate across its bounding surface. In the input sections, the scalar product of the relative velocity v  vs , and the unit vector, n, is negative, since the sense assigned to n is out of the surface, whereas in the output sections that scalar product is positive. Hence, the negative sign that appears before n in the balance equation. In most CVs of technical interest, vs ¼ 0, that is, the bounding surface remains at rest. In effect, we usually refer to fixed CVs and rigid surfaces, so that, in that case, the above equation is simplified to Z Z d rds ¼ rv$ðnÞdA (13.45) dt V

Aðin;outÞ

In technical applications, no appreciable errors are included if it is understood that, in the input and output sections, the flow is one-dimensional. This means that, throughout the cross-section to the flow, all the thermodynamic and flow properties are constant and vary only in the flow direction. Therefore, given this hypothesis, for each input or output section, both v and r are constants, with v being codirectional with n. In this case, the mass balance equation can be written more compactly in the way in which it appears in classical thermodynamics texts, which is in out X dmVC X ¼ ðrvAÞj  ðrvAÞj dt j j

(13.46)

In the case of a turbulent regime, we use the temporal averages and the mass balance equation for the CV is d dt

Z

Z hrids ¼

V

ðhrvi  hrvs iÞ$ðnÞdA

(13.47)

Aðin;outÞ

This equation is not valid for systems that contain or are limited by fluid-fluid interfaces since the positions of these interfaces are random functions of time, and there are important interface effects that are directly attributable to the turbulence. For an indepth analysis of situations of this type see Slattery 1972 [11]. Finally, the mass balance for a generic component g of a multicomponent system allows us to write the following equation d dt

Z

Z rg ds ¼

V

Aðin;outÞ


 rg vg  vgs $ðnÞdA þ

Z K g ds

(13.48)

V

In this equation, A(in,out) must be interpreted in the broadest sense, so that it includes both surfaces that allow the flow of g by convection, as well as liquid-liquid, liquidsolid, etc. interfaces through which the chemical species g is transported primarily by

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Exergy Analysis and Thermoeconomics of Buildings

diffusion. To show these diffusion effects, we will express the previous equation by entering the average mass velocity, which then gives d dt

Z

Z

Z

r ds ¼

r ðv  vs Þ$ðnÞdA þ

g

V

Aðin;outÞ

g

Z

j $ðnÞdA þ

g

Aðin;outÞ

K g ds V

(13.49) Said in words, this equation expresses that the rate of mass change of the chemical species g contained in the CV is equal to the rate with which it is transported by convection to the CV plus the rate with which it is exchanged with the outside by diffusion (with respect to the average mass velocity), plus the rate with which it is produced by chemical reactions that take place in the CV. In the case of a turbulent regime in multicomponent systems, the average values would be considered; for more details see Slattery 1972 [11].

13.5

Energy balance

Consider a portion of a fluid, a CM, which at a certain moment occupies the volume V, and where A is its bounding surface. The internal energy of this system is Z U¼

rðxi ; tÞuðxi ; tÞds

(13.50)

V

When formulating the First Law in the language of Field Theory, it is necessary to keep in mind that the continuum is in motion. Taking into account the transport theorem, Eq. (13.11), we have that the rate of change of the internal energy plus the kinetic energy of that CM is  1 2    Z Z D uþ v  d 1 2 Dr 1 2 2 þ rV$v u þ v þ r r u þ v ds ¼ ds dt 2 Dt 2 Dt V

V

(13.51) and applying the continuity equation, Eq. (13.32), we finally have that d ðU þ Ek Þ ¼ dt

Z r V

 D 1 u þ v2 ds Dt 2

R R where U ¼ 9uds and Ek ¼ 9 12v2 ds. V

V

(13.52)

Exergy in continuous media. Application to equipment design

1029

According to the First Law, this rate of change of the internal plus kinetic energy is equal to the sum of the rate of work due to the forces acting on the system plus the energy transmitted to the system by other mechanisms, Potter and Foss 1983 [21]. The rate of work due to the forces acting on the system can be broken down into the sum of two terms. One of these is the rate of work due to the contact forces that the external environment exerts on the bounding surface. The other term is the rate of work due to external forces f , such as gravitational forces, electromagnetic fields, etc. Therefore, we have that the rate of work is Z   Z v$ðs$nÞdA þ r v$f ds (13.53) V

A

The energy transmitted to the system through its boundary surface is, on the one hand, the contact energy due to the external environment. Leaving aside that in a multicomponent system there is also energy transmitted as a consequence of diffusion, the energy which concerns us is associated with the heat flow vector, which is Z q $ðnÞdA (13.54) A

There is also another term for transmitted energy that is external to the system, such as solar radiation, or induction heating when energy is transferred to polar molecules in the system by means of variable magnetic fields. There can also be a mutual energy exchange; for example, if the system is hot gas, the CM under consideration will exchange radiation with the rest of the system. If we call the scalar field that represents the external energy transmission rate Qr (considering that only radiation exists), this term in the balance equation will be Z rQr ds (13.55) V

In short, the energy balance equation becomes Z  Z   Z Z Z d 1 r u þ v2 ds ¼ v$ðs$nÞdA þ r v$f ds þ q$ðnÞdA þ rQr ds dt 2 V

V

A

V

A

(13.56) In the case that the field of external forces is conservative, then f derives from a potential function, that is, f ¼ Vf. If in addition f is independent of time, that is, vf/vt ¼ 0, applying the transport theorem, we have Z  Z Z Z d 1 2 r u þ v þ f ds ¼ v$ðs$nÞdA þ q$ðnÞdA þ rQr ds (13.57) dt 2 V

A

A

V

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Exergy Analysis and Thermoeconomics of Buildings

The most frequent situation is that this force field is gravitational, in which case f ¼ g and in general f ¼ g:r. If g ¼ ð0; 0; gÞ then f ¼ gz. By breaking down the stress tensor according to Eq. (13.24), the above equation gives d dt

Z Z Z Z Z  1 2 r u þ v þ gz ds ¼ pv$ðnÞdA þ v$ðs$nÞdA þ q$ðnÞdA þ rQr ds 2 V

A

A

V

A

(13.58) and if we stop using symbolic notation and express this equation according to the components, we can write it as d dt

Z  Z Z Z Z 1 r u þ v2 þ gz ds ¼  pvi ni dA þ vi sij nj dA  qi ni dA þ rQr ds 2 V

A

A

V

A

(13.59) If it is a multicomponent system, where yg is the mass fraction of component g and vg its velocity, Eq. (13.56) has the following form d dt

Z

N X 1 g g2 y v r uþ 2 k¼1 V Z þ rQr ds

!

Z v$ðs$nÞdA þ

¼ A

Z X N V

g¼1

  Z g g r v $f þ q$ðnÞdA g

A

V

(13.60) In the case that the regime is turbulent, the variables should be averaged, as we have indicated before for the mass balance. The reader may wish to consult the work of Baehr and Stephan 1998 [22].

13.5.1

Energy local balance

From the transport theorem, Eq. (13.11) and the continuity Eq. (13.32) we can write  Z  Z d 1 2 D 1 2 r u þ v ds ¼ r u þ v ds (13.61) dt 2 Dt 2 V

On the other hand, the first term on the right of Eq. (13.56) can be transformed into a volume integral by Greens transformation, which is Z

Z v$ðs$nÞdA ¼

A

V$ðs$vÞds V

(13.62)

Exergy in continuous media. Application to equipment design

1031

Also, we have Z

Z q$ðnÞdA ¼

A

V$qds

(13.63)

V

Taking into account these equalities and since the volume is arbitrary, we obtain the following equation, which must be satisfied at each point of the system under consideration    D 1 2 r u þ v ¼ V$ðs$vÞ þ r v$f  V$q þ rQr Dt 2

(13.64)

This differential equation expresses the condition of the energy balance, which is satisfied at each point of the medium. It is a way of expressing the Principle of Energy Conservation, which is known as the equation of local energy balance or differential energy balance. From this equation, to obtain the internal energy balance we will get the local equation of the linear moment, also known as the first Cauchy equation, see Sinaiski and Lapiga 2007 [14], and which has the following form r

Dv ¼ V$s þ rf Dt

(13.65)

Scalarly multiplying this equation by the velocity vector gives    D 1 2 v ¼ V$ðs$vÞ  s: Vv þ r v$f r Dt 2

(13.66)

and subtracting this equation from Eq. (13.64), we finally have r

Du ¼ s: Vv  V$q þ rQr Dt

(13.67)

which is called the local thermal energy equation. Breaking the stress tensor down into its components of pressure and viscosity tensor according to Eq. (13.24), we can write r

Du ¼  pV$v þ s: Vv  V$q þ rQr Dt

(13.68)

and developing the above equation into its cartesian components r

Du ¼  pvi;i þ sij vi;j  qi;i þ rQr Dt

(13.69)

It is interesting to compare this equation with the local mechanical energy balance. There are two terms (pV$v) and ( s : Vv) that can be seen that are common to both and

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Exergy Analysis and Thermoeconomics of Buildings

that furthermore appear with opposite signs. This means that those terms describe the conversion of mechanical energy into thermal energy. The term (pV$v) can be positive or negative, depending on whether the fluid expands or contracts; it is thus a reversible mode of energy transformation. On the other hand, the term ( s : Vv) is intrinsically positive; it represents the degradation of mechanical energy into thermal energy. Returning again to Eq. (13.64) if the external force field f is conservative, as we have said before, it means that it can be obtained from a scalar potential f, so that f ¼ Vf. If it is also independent of time, it is then verified that rv $ f ¼ r

Df Dt

(13.70)

so that if we consider that it is the gravitational field, we have r

 D 1 u þ v2 þ gz ¼  V$ðpvÞ þ V$ðs: vÞ  V$q þ rQr Dt 2

(13.71)

This equation is known as the local balance of total energy, with the total energy being e ¼ u þ 12v2 þ gz.

13.5.2

Energy local balance in multicomponent systems

From Eq. (13.64) and referring now to a multicomponent system we can write the equation ! N X D 1 g g2 1 2 y w þ v ¼  V$ðpvÞ þ V$ðs: vÞ r uþ Dt 2 2 g¼1  V$q þ rQr þ

N X

(13.72)

  g 9g vg $f

g¼1

where wg represents the velocity of the chemical species g relative to the average mass velocity v, that is, wg ¼ vg  v . Subtracting the mechanical energy from the previous equation, Truesdell 1968 [13], gives r

N N X Du D X 1 g g2 g g ¼  V$ðpvÞ þ V$ðs: vÞ  V$q þ rQr þ y u f $j  r Dt Dt 2 g¼1 g¼1

(13.73) Truesdell, in the cited work [13], defines internal energy as P

¼ u þ 1 2yg wg2 ), thus grouping the term on the left with the last on the right g P

of the previous equality. However, in most situations of interest, this sum 1 2yg wg (u

g

is small and is not usually taken into account. When the external force field is only

Exergy in continuous media. Application to equipment design

1033

gravitational, it is usually of more interest to write the First Law in a way that expresses the total energy balance, the sum of the internal, kinetic and potential energy. In Ref. [11] the corresponding equations are deduced, both for an observer at rest and while following the motion.

13.5.3 Some particular cases of interest Generally, we are more interested in changes in temperature than changes in internal energy. Taking into account the differential equation that relates the internal energy and entropy, and using one of Maxwell’s relations, Callen 1960 [23], we can write    Du DT vp Dv ¼ rcv þ T (13.74) r p r Dt Dt vT v Dt From this relationship and the continuity equation, we get rcv

 DT vp ¼ T V$v þ s: Vv  V$q þ rQr Dt vT v

(13.75)

thus obtaining a differential equation in the scalar field of temperatures. We are now going to refer to a series of simplified forms of this equation, which in fact are the ones that have the greatest application. We will suppose in the first place that the constitutive equation which is called the Fourier law is valid, so that q ¼ lVT, where l is the thermal conductivity. We will also assume that this is independent of temperature and therefore of position, that is, it is a constant. Consider on the other hand that Qr is zero, that is, there are no radiation or other external actions, and also that the dissipation term is zero. If the medium is a solid or incompressible fluid, we have that V $v ¼ 0 and also cp ¼ cv, so that rcp

DT ¼ lV2 T Dt

(13.76)

If the temperature distribution is stationary, then the Laplace equation is satisfied V2 T ¼ 0

(13.77)

13.5.4 Control volume energy balance If in the generalized transport theorem Eq. (13.17), we particularize the generic tensor  in the scalar

u þ 12v2 , we have the equation

  1 Z  Z  Z v r u þ v2 d 1 2 1 2 2 ds þ r u þ v vs $ndA r u þ v ds ¼ dt 2 2 vt V

V

A

(13.78)

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Exergy Analysis and Thermoeconomics of Buildings

Similarly to the mass balance, to assess the term on the right of (13.78) the local energy change in each of the points inside the CV needs to be known. But, precisely, this control volume technique tries to establish the energy balance or of any other magnitude, based on quantities that refer to the limits of the system, so that it is considered as a black box. To overcome this difficulty, consider a CM such that at the time under consideration it occupies a certain volume V(CM) and is limited by the surface A(CM). According to the Reynolds theorem Eq. (13.9), if the tensor field is particularized in the scalar (uþ1/2v2) we get   1 2   Z Z Z v r uþ v d 1 1 2 ds þ r u þ v2 ds ¼ r u þ v2 v$ndA dt 2 2 vt VðCMÞ

VðCMÞ

AðCMÞ

(13.79) where v is the fluid velocity field. The above equation represents the energy balance in a certain CM. Then, by finding the first term on the right of the equality and using the energy balance equation in a closed system Eq. (13.56), we have   1 Z v r u þ v2 Z Z 2 ds ¼ v$ðs$nÞdA þ rv$f ds vt VðCMÞ

Z

Z

AðCMÞ

q$ðnÞdA þ

þ AðCMÞ

Z

rQr ds  VðCMÞ

AðCMÞ



VðCMÞ

1 2 r u þ v v$ndA 2

(13.80)

If we choose the CM so that at the instant under consideration it coincides with the CV, we will have V(CM) h V and A(CM) h A. In that case, the term on the left of (13.80) coincides with the first one on the right of (13.78), and is the one we want to eliminate. Substituting, gives Z  Z 1 2 r u þ v ðv  vs Þ$ðnÞdA  v$½s$ðnÞdA Z  2 d 1 r u þ v2 ds ¼ A A dt 2 V ð2Þ ð1Þ Z Z   Z  r v$f ds þ q$ðnÞdA þ rQr ds V

V

A

ð3Þ

ð4Þ

ð5Þ (13.81)

Exergy in continuous media. Application to equipment design

1035

This is the energy balance general equation in the CV under consideration. The term on the left of the equality represents the rate of change of the internal energy plus the kinetic energy contained in the CV. Since the energy is conserved, this change is due to the energy transmitted from the external environment, as a consequence of the heat and work exchanged and due to the energy associated with the mass transport through the CV bounding surface. In fact, • • • • •

Term (1) corresponds to the rate of energy transported across the boundary surface. Term (2) represents the rate of work exchanged between the system and the external environment due to contact forces. Term (3) corresponds to the rate of work done by external forces. Term (4) is the rate of contact energy exchanged across the boundaries (heat). Term (5) is the rate of external energy transmitted to the system, usually exchanged radiation.

By taking into account the identity v $½s$ðnÞ h ðv  vs Þ$½s$ðnÞ þ vs $ ½s$ðnÞ, the above equation can be written as d dt

Z  Z   1 1 r u þ v2 ds ¼ r u þ v2 ðv  vs Þ$ðnÞ  ðv  vs Þ$½s$ðnÞ dA 2 2 V A Z Z   Z Z  vs $½s$ðnÞdA  r v$f ds þ q$ðnÞdA þ rQr ds V

A

A

V

(13.82) Breaking down the stress tensor according to Eq. (13.24) and using the terminology adopted by Gaggioli 1961 [24], we introduce the term ef which we call flow energy (or transfer energy), and which represents the energy exchanged by the system per unit mass, so that 1 ðv  vs Þ$½s$ðnÞ ef ¼ h þ v2  2 rðv  vs Þ$ðnÞ

(13.83)

In most cases, the term associated with shear stress is usually considered negligible so that ef ¼ hþ1/2v2. The second integral on the right in Eq. (13.81) is, as we have seen, the rate of work done by the surface stress in the mobile bounding surface of the system, that is, it is the rate of shaft work, W_ t . Term (3) is the rate of work exchanged due to external forces so that when the only force field is gravitational, which is conservative, we can write Z Z   Z Df d ds ¼  r v$f ds ¼  r rgds Dt dt V

V

(13.84)

V

which, as we see, represents the rate of change of the gravitational potential energy.

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Exergy Analysis and Thermoeconomics of Buildings

R R R We now designate Q_ ¼ q$ðnÞdA, and Ek ¼ r 12v2 ds, Ep ¼ rgds and V V A R U ¼ ruds. The effect of the viscous component has also been considered to be V negligible in the input and output sections, and these are assumed to have a onedimensional flow. So, we are left with the equation in out X X d ðU þ Ek þ Ep Þ ¼ m_ j ðh þ ek þ ep Þj  m_ j ðh þ ek þ ep Þj þ Q_  W_ t dt j j

(13.85) which brings us back to the energy balance equation, as we have seen in Chapter 2. Different forms of the energy balance equation in a CV for a turbulent regime and multicomponent systems can be found in Slattery 1972 [11].

13.6

Entropy balance

Consider a fluid portion, a CM (for now a pure substance), which at a certain moment occupies the volume being A its close bounding surface. If sðx; tÞ is the scalar entropy field at the point of coordinates x and at time t, the CM entropy at that moment is Z S¼

rðxi ; tÞsðxi ; tÞds

(13.86)

V

From the transport theorem and the continuity equation, we have dS ¼ dt

Z r V

Ds ds Dt

(13.87)

On the other hand, when there is no diffusion, the contact energy is the heat exchanged. In this way, remembering what was said in Chapter 2, the rate of entropy change due to heat transfer is Z A

q $ðnÞdA ¼ T

Z fS $ðnÞdA

(13.88)

A

where fS ¼ q T can be interpreted as the entropy flux vector, that is, the rate of entropy transferred per unit area associated with the heat exchanged. Therefore, according to what we have seen in Chapter 2, the Second Law allows us to write d dt

Z

Z rsds 

V

fS $ðnÞdA A

(13.89)

Exergy in continuous media. Application to equipment design

1037

and therefore, the rate of entropy change in the volume under consideration is always greater than the entropy flux exchanged by the system in that unit of time. The latter is due to the transmission of contact energy, which in this case is due to the heat exchanged through the bounding surface. If the previous relationship is satisfied with the equality sign, the process is said to be reversible and, if not, irreversible. For thermodynamically homogeneous materials and those in which the internal energy does not depend on the deformation, the fundamental equation is of the form u ¼ u(s,v), as is the case of pure substances that we are currently considering, Sala 2016 [25]. Therefore, we have r

Du Ds Dv Ds ¼ rT  pr ¼ rT  pV$v Dt Dt Dt Dt

(13.90)

Carrying this relation over to the equation of thermal energy local balance Eq. (13.68), we have r

 1 Ds 1 1 ¼ s: Vv  V$q þ rQr Dt T T T

(13.91)

which can be transformed into   Ds 1 1 1 1 q  2 q$VT þ rQr r ¼ s: Vv  V$ Dt T T T T

(13.92)

Integrating this equation for volume V, taking into account (13.87) and applying Gauss’s theorem, gives d dt

Z

Z rsds ¼

V

A

1 q$ðnÞdA þ T

 Z   rQr 1 1
 2 q$VT þ s: Vv þ ds T T T

(13.93)

V

This equation represents the Second Law formulation for continuous media, having succeeded in replacing the inequality (13.89) with an equality. In effect, the entropy balance in a CM has been expressed by an equation that reflects the following equality: 9 9 8 8 Entropy flux > > Rate of entropy > > > > > = < = > < generation ¼ associated with þ of entropy > > > > > > > > > > ; : ; > : ; > : in the CM heat exchanged contained in the CM 8 > >
> =

(13.94)

Note that this equation has been deduced for a continuous medium and, therefore, is not valid in a medium that contains discontinuity surfaces, such as those due to interfaces or shock waves. Readers wishing to know more in these aspects can consult the work of Glansdorff and Prigogine 1971 [26]. Fig. 13.5 is a photograph of the monolith in memory of L. Boltzmann, who was able to give a microscopic interpretation of

1038

Exergy Analysis and Thermoeconomics of Buildings

Figure 13.5 In memory of L. Boltzmann (1844e1906).

entropy and thus established the connection between the micro-world and the macroworld.

As we have seen earlier, fS ¼ q T is the entropy flux vector, with the surface integral of the term on the right of Eq. (13.93) being the entropy exchanged by the system due to heat flux. As this flux can be towards the system or coming out of it, the entropy can increase or decrease depending on the direction of heat flux. The volume integral of the second term is, however, intrinsically positive, according to inequality (13.89). Represents the entropy generation rate, due to the irreversibilities that have taken place in the volume under consideration. Per unit of volume that term is sg ¼ 

 1 1 1 q$VT þ s: Vv þ rQr 2 T T T

(13.95)

The first term on the right of the equality represents the entropy generated due to thermal dissipation. Experience indicates that heat transfer always takes place in the opposite direction to that of the temperature gradient (in the physics basic texts, it is said that ‘heat is transferred from higher to lower temperature’). This means that 

1 q$VT > 0 T2

(13.96)

The second term represents the change in entropy due to friction work. Whenever there is work due to viscous forces, such as the deformation of a wire or rotation in greased bearings, we observe that an increase in temperature occurs. At each point

Exergy in continuous media. Application to equipment design

1039

of the metal that is deformed, at each point of the grease on the bearings there is a transformation of mechanical energy to thermal energy. Therefore, our daily experience tells us that the term for viscous dissipation is always positive. For newtonian fluids, it is easy to demonstrate, Sala 1987 [12], that this term turns out to be the square of a certain quantity and, therefore, is intrinsically positive, that is to say s: Vv > 0

(13.97)

13.6.1 Some consequences of the entropy local balance Previously we deduced Eq. (13.92), which represents the entropy balance at each point of the continuous medium. According to the comments made earlier on the signs of the terms of entropy generation, at each point of the continuous medium, the following must be satisfied  Ds 1 1 1 1 r þ V$ q  rQr ¼  2 q$VT þ s: Vv  0 (13.98) Dt T T T T which is known as the Clausius-Duhem inequality. While Cauchy’s second law states that the stress tensor must be symmetric, this inequality establishes constraints on the heat flux vector and stress tensor. Thus, for a newtonian fluid and considering that Fourier’s law is satisfied, it is shown that both the thermal conductivity and the viscosity must be intrinsically positive, Truesdell and Toupin 1960 [27].

13.6.2 Entropy local balance in multicomponent systems For a multicomponent system the equation of local entropy balance, Sala 1987 [12], is ( ! N X  Ds 1 1 gg 1 1
m j þ r ¼  V$ q  q$VT þ rQr þ s: Vv Dt T T T T c¼1 (13.99) )   g  X N N X m g g  j $ TV K g mg f  T g¼1 g¼1 g

where mg is the chemical potential of the component g, j is the mass flow rate of the g component g with respect to the average mass velocity, f is the external force on the component g and Kg is its production rate per unit of volume, due to the homogeneous reactions that take place. In the same way, as for a pure substance, two terms with a different meaning appear. One is the entropy flux vector, the first term on the right of the previous equality, which now has the following form fS ¼

N q X mg g  j T g¼1 T

(13.100)

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Exergy Analysis and Thermoeconomics of Buildings

Taking into account that the chemical potential of a component is the partial Gibbs g g g function of said component, that is, mg ¼ b g ¼b h  Tbs we have ! N N X X 1 g g g bs j fS ¼ q hg j þ (13.101) T g¼1 g¼1 Not to be confused with the vector magnitudes, we represent the partial properties g by means of the symbol by instead of yg (for the generic variable y), as is usual in thermodynamics texts. We now define the thermal energy flux vector ε, such that ε¼q 

N X

g g b h j

(13.102)

g¼1

which, as we see, includes the heat flux and the enthalpy transported by diffusion of the different components that make up the system. The symbol q represents the heat flux vector, that is, the energy transmitted by contact as a consequence of the movement of the molecules with respect to the average mass velocity. The vector ε is the energy flux vector due to the molecular movement with respect to the velocity of the different chemical species that make up the multicomponent system. As a result, the entropy flux vector is fS ¼

N ε X g g bs j þ T g¼1

(13.103)

so as to say that it is the entropy flux transported by the thermal energy and diffusion. The second term on the right of Eq. (13.99) represents the entropy generation. By introducing the thermal energy flux vector, the entropy generation term can be written as  N  1 X 1 1 1 g g g g sg ¼  2 ε$VT þ rQr þ s: Vv  j $ Vm þ bs VT  f T T T T g¼1 

N 1 X K g mg T g¼1

(13.104) Finally, it is of interest to express the rate of entropy production by introducing the chemical affinity. For a chemical reaction q, where xq is the reaction degree of progress, the chemical affinity Yq is defined according to the following expression, Sala 2016 [25].  Yq ¼ 

vG vxq

T;p

¼

N X g¼1

 M g ygq

vG vmg

T;p;mi ;ði s cÞ

¼

N X g¼1

M g ngq mg

(13.105)

Exergy in continuous media. Application to equipment design

1041

Combining this relationship with Eq. (13.36) gives N X

K g mg ¼

g¼1

N X

mg

g¼1

R X

M g ngq vq ¼ 

q¼1

R X

Yq vq

(13.106)

q¼1

finally obtaining the following expression for the rate of entropy generation at each point of the continuous medium 1 sg ¼ T

N R X X 1 g g j $L þ Yq vq  ε$VT þ s: Vv  T g¼1 q¼1

g

! (13.107)

g

g

where L ¼ Vmg þ bs VT  f and the term associated with radiation has not been taken into account. The term that appears in parentheses is known as friction, so friction in Thermodynamics is the product of temperature and the rate of entropy generation. In Mechanics, friction is understood as the dissipative effect due to tangential forces, while in Thermodynamics the meaning of friction is wider, as we shall see below. For this we return to Eq. (13.107) and rearranging the summands inside the parentheses and writing the resulting expression as its cartesian components, we have R X

Tsg ¼

Yq vq þ

q¼1

ð1Þ

N X

jgi mg;i þsij vi;j þ

g¼1

ð2Þ

ð3Þ

N X g¼1

N εi X g jgi fig  T;i  bs ji T;i T

ð4Þ

g¼1

ð5Þ

(13.108)

ð6Þ

Interpreting the terms on the right of this equality, we see that friction is the result of the following processes: (1) (2) (3) (4) (5) (6)

Chemical reactions with affinities other than zero. Diffusion with chemical potential gradients. Irreversible deformation. Diffusion through an external force field, different for each chemical species. Flux of thermal energy through a temperature gradient. Entropy flux diffusion through a temperature gradient.

Thus, terms (1) and (2), which correspond to chemical friction, represent the irreversible conversion of chemical energy into thermal energy; terms (3) and (4) are the irreversible conversion of mechanical energy into thermal energy, they correspond to mechanical friction; and finally, terms (5) and (6) represent thermal friction, which is associated with the thermal energy transport through temperature gradients. Therefore, friction represents the conversion of mechanical and chemical energy into a form of lower quality energy, which is thermal energy, as well as the transport of thermal energy from higher temperature to lower temperature.

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Exergy Analysis and Thermoeconomics of Buildings

Although both friction and entropy generation are valid measures of irreversibility, exergy destruction, which is directly linked to them, is a method of assessing irreversibilities that has decided advantages, as we have seen throughout this book and as we will insist at the end of this chapter.

13.6.3

Control volume entropy balance

Consider the CV represented in Fig. 13.4, with several input and output sections and whose boundary surface can change shape and size, with vs ðxi ; tÞ being its velocity field. If in Eq. (13.17), which represents the generalized transport theorem, we replace the tensor field j by the scalar s, we have d dt

Z

Z rsds ¼ V

V

vðrsÞ ds þ vt

Z rsvs $ndA

(13.109)

A

Similar to what we discussed when studying the mass and energy balances, to assess the term on the right of the previous equality, the local entropy change at each of the points inside the CV needs to be known. To overcome this difficulty, consider a CM such that at the time under consideration it occupies a certain volume V(CM) and its close bounding surface is A(CM). According to the Reynolds theorem Eq. (13.9), if the tensor field is particularized into the scalar s, we get d dt

Z

Z rsds ¼

VðCMÞ

Z

vðrsÞ ds þ vt

VðCMÞ

rsv$ndA

(13.110)

AðCMÞ

where v reprrsents the fluid velocity field. The above equation represents the entropy balance in the CM, so that by finding the first term on the right of the equality and using the entropy balance equation in a closed system, Eq. (13.93), we have Z VðCMÞ

vðrsÞ ds ¼ vt

Z

Z

Z

fS $ð nÞdA þ AðCMÞ

sg ds  VðCMÞ

rsv$ndA

(13.111)

A

We now choose the CM so that at the moment under consideration it coincides with the CV, that is to say, V(CM) h V and A(CM) h A. In that case, the term on the left of the previous equality matches the first term on the right of (13.109), which was the one we wanted to eliminate. Substituting, gives d dt

fS $ð nÞdA þ

¼ rsds

V

Z

Z

Z

AðCMÞ

Z rsðv  vs Þ$ðnÞdA þ sg ds

VðCMÞ

ð1Þ

A

ð2Þ

ð3Þ

(13.112)

Exergy in continuous media. Application to equipment design

1043

Let us interpret the meaning of each of the terms in this equation. The term on the left represents the rate of change of the entropy contained in the CV. Term (1) on the right is the entropy flux as a consequence of the heat exchanged. Term (2) represents the rate of entropy exchanged with the outside, due to the mass transport through the permeable part of the boundary surface. Term (3) is the entropy generated within the CV due to internal irreversibilities. Let us consider a series of simplifications. If the one-dimensional flow model is valid in the input and output sections, Eq. (13.112) can be written as d dt

Z

Z rsds ¼

V

fs $ðnÞdA þ A

in X i

m_ i si 

out X i

Z m_ i si þ

sg ds

(13.113)

V

In the case of steady-state, the term on the left of the equality is cancelled, and so everything becomes independent of time. If, in addition, the fluid is a pure substance, the entropy flux is due exclusively to the heat exchanged, so we have the equation out X i

m_ i si 

in X j

Z m_ j sj ¼ A

1 q$ðnÞdA þ T

Z sg ds

(13.114)

V

If there is only one input section (in) and one output section (out) and the system is adiabatic, there is no entropy flux so we can conclude sout > sin

(13.115)

that is to say, the entropy of the fluid in the output section is higher than that in the input section. In the particular case if there is no entropy production, that is to say, if in addition to being an adiabatic process it is also reversible, then sout ¼ sin

13.7

(13.116)

Introduction to Onsager theory

When, in the equations of mass, momentum or energy balance, we want concentration, velocity or temperature profiles to appear, the flows are replaced according to the transport properties and those concentration, velocity or temperature gradients respectively. For this, a series of phenomenological laws are used that describe the irreversible processes in the form of proportionalities, such as Fourier’s law, regarding the heat flux and the temperature gradient, Fick’s law, regarding the matter flow rate in a component in a multicomponent system and its concentration gradient, and Newton’s law, regarding the deforming force and the velocity gradient. Other similar phenomenological laws are Ohm’s law, regarding the current and the electric potential gradient and the chemical reactions laws, between the reaction rate and chemical potentials.

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Exergy Analysis and Thermoeconomics of Buildings

However, the reality is not so simple. It happens that, when two or more of the above-mentioned phenomena occur simultaneously, they interfere and give rise to new effects. Thus, although the most important contribution to the mass flow rate is due to the concentration gradient, others such as the pressure gradient or temperature or the external force field, acting unequally between the different components, also produce the diffusion movement of the species in the fluid, de Groot 1952 [28]. A well-known example of interference is the coupling of diffusion and heat conduction that gives rise to the thermal diffusion effect or Soret effect, consisting of a concentration gradient appearing as a result of a temperature gradient. There is also its inverse phenomenon, the Dufour effect, which is the temperature gradient that appears as a consequence of a concentration gradient, Prigogine 1955 [29]. Considering other interfering phenomena we can mention the two reciprocals of thermoelectricity as being well known, and which arise from the interference between heat conduction and electrical conduction. The Peltier effect is the heat transfer in the welds of different nature metals as a result of an electric current, whereas the Seebeck effect is the electromotive force that is generated if the welds of these metals are maintained at different temperatures. Likewise, the diffusion potential is an example of interference between diffusion and electrical conduction, and there are numerous other interfering phenomena that are of considerable interest, Eu 1992 [30]. A systematic and general theory of Irreversible Process Thermodynamics (IPT), which explores the connection between Thermodynamics and Transport Processes is based on the works published by Onsager, Hemmer et al. 2013 [31] and later completed by Casimir. In Onsager theory, the causes that produce irreversible phenomena, such as the temperature gradient, concentration gradient, electric potential gradient, chemical affinity, etc., are called generalized forces and are usually represented by the symbol Xi(i ¼ 1,2,.,n). These forces cause irreversible phenomena, such as heat flux, matter diffusion, electric current, chemical reaction rate, etc. These phenomena are called flows or currents and are usually designated by the symbol Ji(i ¼ 1,2,.,n). Interfering effects are described mathematically by the addition of new terms to classical phenomenological laws. Thus, any flow can be produced by any force (although there are limitations imposed by Curie’s Symmetry Principle), so that irreversible phenomena can be expressed by phenomenological relationships of the type Ji ¼

X Lik Xk

(13.117)

k

where Lik is the phenomenological coefficient that relates the flow Ji with the force Xk. The coefficients Lii are, for example, the thermal conductivity, the electrical conductivity, the ordinary diffusion coefficient, etc., while the coefficients Lik for i s k refer to the type of interfering phenomena; thus, the thermal diffusion coefficient, the Dufour coefficient, etc. Onsager theory is based on a fundamental theorem that establishes that, whenever an appropriate choice is made for the flows and the forces, the phenomenological coefficients matrix is symmetric, that is, Lik ¼ Lki. These identities, known as Onsager

Exergy in continuous media. Application to equipment design

1045

reciprocal relations, express a connection between two reciprocal phenomena, which arise from the mutual interference of irreversible phenomena that takes place simultaneously. The proper choice of flows and forces means that the entropy generation can be expressed as follows sg ¼

1X Jk Xk T k

(13.118)

The validity of IPT is restricted to the validity domain of linear phenomenological laws, such as Fourier’s law. In the case of chemical reactions, the reaction rate must be slow enough not to significantly disturb the maxwellian equilibrium distribution of the velocities of each component, which only excludes chemical reactions with abnormally low activation energies. This Linear Thermodynamics, characterized by the use of linear phenomenological laws and constant transport coefficients, is already considered as being classical. Despite the usefulness of the results obtained, the intrinsic limitation of being close to equilibrium cannot be ignored. Thus, in transport phenomena, it may be necessary to take into account the variation of phenomenological coefficients, for example, the thermal conductivity change with temperature. These effects destroy the linearity of phenomenological equations, so in recent years Thermodynamics has been extended to study non-linear situations in-depth.

13.8

Exergy in continuous media

In the previous chapters, we worked with the physical and chemical exergy for uniform systems, as presented in the study of Classical Thermodynamics (Thermostatics). Let us now refer to exergy in the Thermodynamics of Continuous Media. We will replace the property a with the scalar field a(xi,t) so that for a closed system aðxi ; tÞ ¼ uðxi ; tÞ  T0 ðtÞsðxi ; tÞ þ p0 ðtÞvðxi ; tÞ  ½u0 ðtÞ  T0 ðtÞs0 ðtÞ þ p0 ðtÞv0 ðtÞ (13.119) Similarly, when we refer to a CV, the physical flow exergy is now replaced by the scalar field b(xi,t), such that bðxi ; tÞ ¼ hðxi ; tÞ  T0 ðtÞsðxi ; tÞ  ½h0 ðtÞ  T0 ðtÞs0 ðtÞ

(13.120)

In these expressions, there appears the dependence on time of the system thermodynamic properties in the dead state. This is because, in general, the system composition varies with time and, consequently, its corresponding dead state as well. In addition, it also happens that the environmental conditions of temperature and pressure are variable with time.

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Exergy Analysis and Thermoeconomics of Buildings

In the previous Sections, we referred to the mass balance, energy and entropy balance in continuous media. The systematics that we followed were always the same. We considered first a closed system, a CM, and then we applied the corresponding conservation law or production in the case of entropy. Next, and by application of the transport theorem, we wrote the corresponding equation locally and then we obtained the balance equation for any CV. Now we will proceed in a similar way; by combining the energy and entropy balances in a CM, we will obtain the corresponding exergy balance. We will later find the expressions to reflect the exergy balance locally, breaking down the exergy into its physical and chemical components. Finally, by application of the generalized transport theorem, we will obtain the expression for exergy balance in a CV.

13.8.1

Control mass exergy balance

Consider again a fluid portion, a CM, which at a certain moment occupies a volume V. We will first look at the case of a pure substance and assume that there is no energy transmission by radiation. Later, we will consider multicomponent systems and the energy transmission through radiation. In a certain moment, the rate of exergy change (sum of the physical and chemical exergy plus the kinetic energy) is d d dS dV d ðA þ Ek Þ ¼ ðU þ Ek Þ  T0 þ p0  ðU0  T0 S0 þ p0 V0 Þ dt dt dt dt dt

(13.121)

The first term on the right of the equality is obtained from Eq. (13.56), while the second from Eq (13.93). We consider that the RE is in a steady-state and the system composition does not vary, then U0, S0, T0, p0 are constants. Therefore, taking into account Eq. (13.14), from the above equation we have d ðA þ Ek Þ ¼ dt

Z

Z

Z   p0 v$ndA þ r v$f ds

A

V

v$ðs$nÞdA þ A

Z Z  T0 q$ðnÞdA  T0 sg ds þ 1 T

(13.122)

V

A

If in this equation, we break down the stress tensor into its components and consider that the external force field is gravitational, the previous equation becomes d ðA þ Ek þ Ep Þ ¼ dt

Z

Z v$ðs$nÞdA þ

A

ðp  p0 Þv$ðnÞdA A

Z  Z T0 q$ðnÞdA  T0 sg ds þ 1 T A

V

(13.123)

Exergy in continuous media. Application to equipment design

1047

This equation shows us that the rate of change of the capacity to produce useful work (sum of the rate of change of exergy plus kinetic and potential energy) is the rate of useful work exchanged by the contact forces, tangential and normal components, plus the rate of exergy transferred with the heat flux exchanged and minus the rate of exergy destruction that occurs inside the system under consideration. Indeed, the last term on the right of the equality is the product of the environmental temperature with the entropy generated in the system. Thus, according to the GouyStodola equation that we have seen in Chapter 2, this term represents the rate of exergy destruction in the CM.

13.8.2 Physical exergy local balance The local exergy balance, or differential equation of exergy balance, is easily deduced from the macroscopic equation previously obtained. Applying the transport theorem Eq. (13.11) and taking into account the continuity equation Eq. (13.32), we have  1 Z Z rD a þ v2 d 2 ds (13.124) rða þ ek Þ ¼ dt Dt V

V

Using Gauss’s theorem to transform the surface integrals that appear in the term on the right of Eq. (13.123) and since the resulting equation is satisfied for any volume considered, we have  1 2  rD a þ v þ gz T0 2 ¼  V$ðp  p0 Þn þ V$ðs$nÞ þ V$ 1  q  T 0 sg Dt T (13.125) This equation has been written for an observer who moves with the fluid velocity. Using the relationship in Eq. (13.3) we can also write for an observer at rest. In this case, the equation takes the form     v 1 2 T0 q r a þ v þ gz ¼ V$ðs: vÞ þ p0 V$v  V$ 1  vt 2 T    1 2 þ V$ r a þ v þ gz v  T0 sg 2

(13.126)

For the particular case of a fluid at rest, and considering that there is no energy transport by radiation, theexergy balance equation is r

 Da T0 ¼  V$ 1  q  d_ Dt T

(13.127)

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Exergy Analysis and Thermoeconomics of Buildings

Returning to Eq. (13.126) and generalizing for a multicomponent system, the local exergy balance equation for a resting observer takes the following form  X v T0 g ½rða þ ek Þ ¼ V$ 1  ε þ V$ðs: vÞ þ p0 V$v þ rg vg $f vt T g  X  g g g V$½rða þ ek Þv  V$ b b b b 0 j  d_

(13.128)

g

where ε is linked to the thermal energy flux, that is, it is the energy flux due to molecular movement with respect to the velocity of the different chemical species. Thus, g the vector ð1  T0 =TÞε is the exergy of the thermal energy flux. In addition, we use b b g for the partial exergy associated with the component g and j for the diffusion flow of that component. In the case of a system constituted by a component, we have that ε ¼ q and so we come back to the expression for the exergy transferred by the heat flux. Readers interested in deducing Eq. (13.128) can consult Sala 1987 [12].

13.8.3

Chemical exergy local balance

As we have seen in Chapter 2, the total exergy of a system can be broken down into two terms. One of these is what we call physical or thermomechanical exergy (which in turn can be broken down into a thermal and mechanical component). The other is the chemical exergy, which represents the maximum useful work that can be obtained from a system that is in the ambient state (restricted equilibrium with the environment) until it is taken to the dead state, that is, to the state of complete equilibrium with the RE. Let us obtain the equation that reflects the local balance of the
standard chemical  exergy of a system. If (y1,y2,.) is the system composition and y10 ; y20 ; . that of the corresponding dead state of total equilibrium with the standard RE, the specific chemical exergy is

 bch ¼ g0 T0 ; p0 ; y1 ; y2  g00 T0 ; p0 ; y10 ; y20 ; . (13.129) where g0 is the Gibbs function in the ambient state and g00 the Gibbs function in the dead state. According to the definition of chemical potential, we have g0 ¼

X


yg m0;g T0 ; p0 ; y1 ; y2 ; .

(13.130)

g

On the other hand r

X X Dm0;g Dg0 Dyg ¼ r m0;g þ r yg Dt Dt Dt g g

(13.131)

Exergy in continuous media. Application to equipment design

Bearing in mind the GibbseDuhem equation, we have therefore, r

X Dg0 Dyg ¼ r m0;g Dt Dt g

1049

P g

yg dm0;g ¼ 0 and,

(13.132)

The term on the right of this equality can be written in a different way. For this, we will take into account the continuity equation of the chemical species g, according to which vrg g ¼  V$rg vg þ K g ¼ v$Vrg  rg V$v  V$j þ K g vt

(13.133)

so that Drg Dyg Dr g ¼ yg rV$v  V$j þ K g ¼r þ yg (13.134) Dt Dt Dt

Keeping in mind the continuity equation

Dr Dt þ rV$v ¼ 0 for the set of chemical species that make up the system Dr Dt þ rV$v ¼ 0, we finally get r

Dyg g ¼  V$j þ K g Dt

(13.135)

and, therefore, r

X X Dg0 g ¼ m0;g V$j þ K g mg0 Dt g g

(13.136)

Similarly, we get that r

X Dg00 X 0;g g ¼ m0 V$j þ K g m0;g 0 Dt g g

(13.137)

Now, the dead state is a complete thermodynamic with the RE, so that P equilibrium P according to the condition of chemical equilibrium yg m0;g ¼ 0, K g m0;g 0 0 must also g be zero. Therefore, combining the previously obtained results, wegfinally have that r

 X g X Dbch g ¼ V$j þ K g m0;g m0  m0;g 0 0 Dt g g

(13.138)

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Exergy Analysis and Thermoeconomics of Buildings

In order to give an accurate interpretation of each of the terms that appear in the equation of chemical exergy local balance, the above equation can be reformulated, transforming it into the following r

Dbch ¼ Dt

X

K g mg þ

g

X

Xg

 Xg  K g m0;g  mg þ j $Vmg þ j $V m0;g  mg

g

g

ð2Þ

ð1Þ 

X

V$

h

g

ð3Þ

ð4Þ

 i g m0;g  m0;g j 0

g

ð5Þ (13.139)

P Bearing in mind that 1 T K g mg is the rate of entropy generation per unit g

volume, we can interpret each of the terms of the previous equation. The rate of chemical exergy change is the result of the following terms: • •

• • •

Term (1) is always negative and represents the irreversible chemical exergy decrease, as a consequence of chemical reactions. Term (2) represents the reversible chemical exergy change with reversible chemical reactions. This term takes positive or negative values depending on whether these are carried out in one sense or the other. This change is the transformation to thermal energy in a way that, more specifically, represents the reversible exchange of internal chemical energy to thermal energy through chemical reactions. Term (3) corresponds to the irreversible chemical exergy decrease due to diffusion. Term (4) corresponds to the reversible change associated with diffusion. The last, term (5), represents the chemical exergy transport with the flow of diffusion energy.

13.8.4

Control volume exergy balance

Consider a CV like the one in Fig. 13.6 whose boundary surface is subject to the velocity field vs ðxi ; tÞ. We will first look at the case of a pure substance, and later we will examine multicomponent systems. Applying the generalized transport theorem Eq. (13.19) for the scalar (aþ1/2v2) we have   1 2  Z Z  Z v r aþ v d 1 2 1 2 2 ds þ r a þ v vs $ndA r a þ v ds ¼ dt 2 2 vt V

V

A

(13.140)

Exergy in continuous media. Application to equipment design

1051

Similarly, as we have seen for the other magnitudes, to overcome the difficulty of assessing the first term on the right of the previous equality, a CM is contemplated such that at the moment under consideration the volume it occupies and its close bounding surface coincide with those of the CV. Carrying out the exergy balance on the CM Eq. (13.123) and returning to the previous equation, gives d dt

Z

Z rða þ ek Þ ¼

V

Z rðb þ ek Þðv  vs Þ $ndA þ

A

Z

Z

v$ðs$nÞdA þ

þ

rv$f ds þ V

A

ðp  p0 Þv$ðnÞdA A

Z Z  T0 q$ðnÞdA  T0 sg ds 1 Ts

(13.141)

A

If we consider that the external force field f is the gravitational field, we can write the previous equation as Z d dt

Z rðb þ ek þ ep Þðv  vs Þ$n dA þ

Z rða þ ek þ ep Þ ¼

A

ðp  p0 Þv$ðnÞdA A

V

ð1Þ  Z Z Z T0 þ q$ðnÞdA T 1 þ v$ðs$nÞdA sg ds 0 Ts

ð2Þ

A

A

ð3Þ

ð4Þ

ð5Þ (13.142)

According to this equation, the rate of exergy plus kinetic and potential energy variation of the CV is the sum of the following terms: • • • • •

Term (1) represents the rate of flow exergy plus the kinetic and potential energy exchanged by the CV through the permeable part of its boundary surface, that is, through the input and output sections. Term (2) is the rate of useful work exchanged by the normal component of the contact forces acting on the CV bounding surface. Term (3) is the rate of work due to the tangential components. Term (4) corresponds to the exergy transferred with the heat flux exchanged. The last, term (5), corresponds to the rate of exergy destruction in the CV due to the irreversibilities associated with the processes that take place in it.

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Exergy Analysis and Thermoeconomics of Buildings

Figure 13.6 Hot water boiler as an example of a CV.

If we assume that the effect of viscosity is negligible in the input and output sections and that in those sections the flow is one-dimensional, the exergy balance equation that we finally have left is e s X X d ðA þ Ek þ Ep Þ ¼ B_ Q  W_ þ m_ i ðb þ ek þ ep Þi  m_ j ðb þ ek þ ep Þj  D_ dt i j

(13.143) which corresponds to Equation (2.53) that we deduced in Chapter 2. If we consider a stationary-state and a single input section and another single output section, the above equation is simplified into Equation (2.56) in Chapter 2. Fig. 13.6 shows a water boiler as a CV example, in which the broken line represents the system boundary surface.

13.8.5

Exergy balance in multicomponent systems

We will now develop the exergy balance in a CV for multicomponent systems. We must bear in mind that the system composition is variable with time, due for example to possible chemical reactions between its components. As a result, the dead state will also have a variable composition. In a certain moment, the rate of the exergy plus the kinetic energy change is d d dS dV d ðA þ Ek Þ ¼ ðU þ Ek Þ  T0 þ p0  ðU0  T0 S0 þ p0 V0 Þ dt dt dt dt dt

(13.144)

Exergy in continuous media. Application to equipment design

1053

We are going to develop each of the terms on the right of the equality. For a multicomponent system, the energy balance in a CV has the equation Z Z X Z g g d b ðU þ Ek Þ ¼ ε$ðnÞdA þ h j $ðnÞdA þ ret ðv  vs Þ$ðnÞdA dt g A

A

Z



s$vs $ðnÞdA þ

Z X

g

rg vg $f ds

g

V

S

A

(13.145) where as we have seen, ε represents the thermal energy flux vector. From the entropy balance, Eq. (13.99) gives Z Z X dS ε g g bs j $ðnÞdA $ðnÞdA  T0 To ¼ T0 dt T g A

A

Z

 To

Z

rsðv  vs Þ$ðnÞdA  T0

(13.146) sg ds

V

A

The third term (podV/dt) on the right of Eq. (13.144) can be written as follows Z dV ¼ p0 vs $ndA p0 (13.147) dt A

For its part, the fourth term can be transformed, taking into account that Z dU0 X vU0 dmg X g dmg X g b b ¼ ¼ uo ¼ (13.148) u 0 rg ðv  vs Þ$ðnÞdA g dt dt dt g vm g A

and similarly p0

X g dV0 b ¼ p0 u0 dt g

Z rg ðv  vs Þ$ðnÞdA

(13.149)

A

Taking into account P thegEuler relation, according to which, for a generic variable x we have that rx ¼ rg bx , then this fourth term can be expressed as follows g Z d  ðU0  T0 S0 þ p0 V0 Þ ¼  rðh0  T0 s0 Þðv  vs Þ$ðnÞdA dt A

þ

XZ  g

A

g g b h 0  T0bs 0 j $ndA

(13.150)

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Exergy Analysis and Thermoeconomics of Buildings

Substituting these expressions for the terms in Eq. (13.144), Sala 1992 [8], we finally get Z  Z Z X T0  


g ε$ðnÞdA þ 1 s þ p0 d $vs $ðnÞdA  rg vg $f ds T dðA þ Ek Þ g V A ¼ A dt ð3Þ

ð2Þ

ð1Þ

 Z  Z X" p ðv  vs Þ$½s$ðnÞ p0 g g þ r a þ ek þ   ðv  vs Þ$ðnÞdA þ b h  T0bs r rðv  vs Þ$ðnÞ r A

A

ð5Þ

ð4Þ 

g b h0

g

!3 Z g 5g  T0bs 0 j $ðnÞdA  T0 sg ds V

ð6Þ (13.151) Each term of the previous balance equation can be linked to each of the energy transport processes so that the exergy content of the different forms of energy appears naturally and immediately. In effect •

• •

•

The exergy transport associated with term (1) is linked to the thermal energy flux, that is to say, it is the exergy flux due to the molecular movement with respect to the velocity of the different chemical species. Thus, the vector bε ¼ ð1  T0 =TÞε is the exergy of the thermal energy flux vector. In the case of a system consisting of one component, we have that ε ¼ q and we come back to the expression corresponding to the exergy transferred by the heat flux. Term (2) represents the rate of exergy exchanged due to the useful work done per unit of time by the stress tensor on the boundary surface of the system. Term (3) is the rate of work due to the external force field. When only the gravitational field is present, that work corresponds to the potential energy change, and usually, this term is passed to the left end of the equality, so that for the rate of exchanged work we have the   R
expression W_ ¼ s þ p0 d $vs $ðnÞdA. A

Term (4) is a consequence of the fluid movement through the limits of the system with the average mass velocity, which is why we call it the exergy of the energy flow. Taking into account the relationship between the variables exergy a and flow exergy b, its local value, per unit mass transported across the boundary surface it is

b þ ek 

ðv  vs Þ$½s$ðnÞ rðv  vs Þ$ðnÞ

(13.152)

Exergy in continuous media. Application to equipment design

1055

•

Term (5) is due to diffusion in the limits of the system, so it corresponds to the exergy of g transport energy by diffusion. Recalling the nomenclature, we use b b for the partial property RP g g b b j $ðnÞdA. of the exergy associated with component g, so that term is

•

Finally, Rterm (6) represents the rate of exergy destruction at that instant inside the CV, that is D_ ¼ T0 sg ds.

A g

V

13.8.6 Examples In previous Sections, we have shown that all irreversible transport mechanisms produce exergy destruction. Among these mechanisms, we will look at the heat transfer and flow with friction, two phenomena of great importance in engineering and that together with mixing are responsible for most of the exergy destroyed in processes, Kays and Perkins 1971 [32]. We will carry out an application of the exergy local balance, looking at the case of single- component fluids and, therefore, not considering diffusion or the possibility of chemical reactions. We will look at two different situations. In the first case, we will study a fluid flow through a pipe with heat transfer through its walls and determine the diameter that minimizes the rate of exergy destruction. In the second case, we will analyse the irreversibility of various techniques used to increase the rate of heat transfer. Local exergy destruction in a fluid flow through an adiabatic pipe. Find expressions for the rate of exergy destruction of laminar flow in an adiabatic pipe, in the following two cases:

Example E.13.1.

(a) Couette flow (b) Poiseuille flow

Solution (a) We are going to first look at a fluid flow through an adiabatic pipe in a laminar regime. Even in this case, the determination of the flow velocity involves solving a system of differential equations in partial derivatives. The mathematical problem is not easy, including in the case of incompressible newtonian fluids, as there is no single solution to the NaviereStokes equation that is consistent with continuity.

In general, the flow velocity can be determined by analytical or numerical methods, solving the NaviereStokes equations (newtonian fluids), under the appropriate set of initial and boundary conditions. Once this problem is solved, the rate of exergy destruction at each point of the flow is determined by the expression  T0 T0 D_ ¼ s: Vv ¼ mf T T where f is known as the dissipation function, that is  2 1 XX 2 f¼ vi;j þ vj;i  vk;k dij 2 i j 3

1056

Exergy Analysis and Thermoeconomics of Buildings

Knowledge of the dissipation function can be of great interest, for example, in lubrication problems with viscous fluids. The evaluation of dissipation allows us to understand the heat source that appears in the energy balance equation, an equation that needs to be solved in order to calculate the temperature field in the lubricant medium. Consider first a very simple laminar flow, Couette flow, Yuang 1967 [E.1], which is a one-dimensional flow characterized by the following distribution of velocities vx ¼

z U D

where z is the height and U is the maximum velocity, in the coordinate z ¼ D. The rate of exergy destruction gives  2  2 T0 vvx T0 U D_ ¼ m ¼ m D T vz T (b) As a second example, we shall look at the Poiseuille flow [E.1], for which the velocity field is

3 vx ¼ < vx > 2



z 1 D=2

2

where D is the pipe diameter. The rate of exergy destruction is !2  2 2  T vv T < v > z x x 0 0 D_ ¼ m ¼ 36m D D2 T vz T =

These two simple examples show that, in a laminar regime, the rate of exergy destruction due to the degradation of mechanical energy as a consequence of viscosity, takes place in the mass of the fluid, that is, throughout the length and width of the flow field. In the particular case of Poiseuille flow, the destruction is strictly zero along the axis, that is for z ¼ 0. Thus, in a laminar regime, the entire flow field participates in the exergy destruction. In a turbulent regime, viscous dissipation occurs mainly in the vicinity of the pipe wall. It is concentrated in a thin sheet around the walls so that the layers inside the stream hardly contribute to the exergy destruction. The experimental determination of the viscous dissipation terms is extremely complex, Hinze 1975 [E.2]. [E.1] S.W. Yuan, Foundations to Fluid Mechanics, Prentice-Hall, 1967 [E.2] J.O. Hinze, Turbulence, McGraw-Hill, 1975. Example E.13.2.

Optimum diameter of a pipe Consider a fluid flow inside a conduit of arbitrary geometry and with heat transfer through its walls. Find

Exergy in continuous media. Application to equipment design

1057

(a) An expression to calculate the rate of exergy destruction along the pipe based on the friction factor f and the Stanton number, St (b) The particularized expression for the case of a circular pipe of diameter D.

Solution (a) In most situations of interest in engineering, it is not possible to find the field of velocities and temperatures. This is the case that occurs when the regime is turbulent, or when the geometry is so complicated that an analytical solution, or even a numerical solution, cannot be found, describing the velocity and temperature at each point of the fluid.

However, in a large number of these problems, heat transfer and friction data is available, data that has been obtained along the solid surface that bounds the flow. Thus, the heat transfer in a pipe in turbulent flow regime can be found by correlations of the friction factor and the Stanton number, obtained from a large number of experiments, Kays and London 1964 [E.3]. In the Example that we are considering, since it will not be possible to determine the irreversibility at each point of the flow, we will use the information contained in the usual correlations of the friction factor and the average transfer coefficient, to calculate the rate of exergy destruction per unit length along the stream, in which case we will assume that the flow is one-dimensional.

Figure E.13.1 Elementary control volume of the stream under consideration.

Consider an elementary length dz along the stream. The rate of entropy generation in the differential volume under consideration, see Fig. E.13.1, is _  dSg ¼ mds

q_ dz T þ DT

where m_ is the mass flow rate, TþDT the wall temperature in contact with the fluid, T the fluid temperature and q_ the rate of heat transferred through the wall, per unit length. Applying the energy balance in that elementary volume, we have _ ¼ qdz _ mdh

1058

Exergy Analysis and Thermoeconomics of Buildings

verifying the relationship dh ds 1 dp ¼T þ dz dz r dz From the entropy balance in this differential CV, we have _ ¼ qdz _ ðT þ DTÞ þ dsg and the energy balance is mdh _ _ mds ¼ qdz. Substituting in the previous equality and applying the Gouy-Stodola equation, gives that the rate of exergy destruction per unit length of the conduit is  dD_ qDT dp m_ ¼ T0 2 þ T0  dz T ð1 þ DT=TÞ dz rT

(E.1)

In this equation, the first term on the right represents the rate of exergy destruction by heat transfer with a temperature difference DT, while the second corresponds to friction. On many occasions, DT/T is much smaller than 1 and so, we can write approximately as  dD_ DT dp m_ ¼ T0 2 q_ þ T0  dz T dz rT Once this expression is obtained, the next step is to relate it to the data that is usually available for most of the different conduit and pipe geometries. Note that the contribution to exergy destruction of DT and Dp, although they appear separate, are nevertheless intimately related through the geometry and the flow parameters. The relationship between the rate of heat transfer q_ and the temperature difference between the conduit inner surface and the fluid, DT, are expressed in the correlations using the Stanton number, St, which is St ¼

q_ ðpe DTÞ h ¼ cp G cp G

_ where G ¼ m=A is the mass flow rate per unit cross-section and h is the average convection coefficient. In most geometries, this Stanton number depends on the Reynolds number, Re ¼ DG/m, where D is the hydraulic diameter defined according to D ¼ 4A/pe as well as another series of parameters that describe the fluid and geometry specific. On the other hand, the second term of Eq. (E.1), which refers to friction, is usually expressed by the correlations of the friction factor f, which is  rD dp f ¼  2G2 dz

Exergy in continuous media. Application to equipment design

1059

This friction factor depends on the Reynolds number Re and the roughness, as well as other geometrical parameters of the conduit and its surface. In the event that both the heat transfer rate and the mass flow rate are specified, taking into account the above, gives dD_ D 2m_ 3 f q_2 ¼ T0 2 þ T0 2 _ p St dz 4T mc r T D2 Under these assumptions, the pipe configuration has two degrees of freedom: the wet perimeter pe and the area A, or, any other pair of independent parameters, such as (Re,D), or (G,D). The above expression clearly indicates that a large Stanton number St reduces the contribution of heat transfer to exergy destruction, while a large friction factor f increases that due to viscous effects. (b) In the

particular case of a cylindrical pipe of diameter D, since Nu ¼ StReDPr, where Re;D ¼ 4m_ pmD, then Eq. (E.1) takes the following form


dD_ 32m_ 3 f Re;D q_2 þ 2 2 ¼ T0 2
dz p r T D5 kT Nu Re;D ; Pr

Thus in the case of a cylindrical pipe, the rate of exergy destruction depends on a single parameter, either the diameter D or Re,D. As D increases Re,D decreases and the resulting effect is a decrease in the rate of exergy destruction by friction, but an increase by heat transfer. Consequently, parameter D causes opposite effects in the two terms that constitute the rate of exergy destruction. This result allows us to come to the conclusion that there is an optimal diameter, for which the rate of exergy destruction becomes minimal. As an example, consider a flow with fully developed turbulence. The Nusselt number is obtained from the correlation 0:4 Nu ¼ 0:023R0:8 e;D Pr

and the friction factor is obtained from the KarmaneNikuradse relation, according to  pffiffiffiffiffi  1 pffiffiffiffiffi ¼  0:8 þ 1:87ln Re;D 4f 4f Using these expressions in Eq. (E.1) and making vD/vRe,D ¼ 0, Bejan 1979 [E.4] obtained the expression for the Reynolds number that minimizes the rate of exergy destruction ¼

2:023P0:071 r

!0:358

rm_ q_ 5

=

Ropt e;D

1

m 2 ðkTÞ2

1060

Exergy Analysis and Thermoeconomics of Buildings

[E.3] W.M. Kays, A.L. London, Compact Heat Exchangers, McGraw-Hill, London, 1964. [E.4] A. Bejan, A study of entropy generation in fundamental convective heat transfer, Journal of Heat Transfer 101 (4) (1979) 718e725. Example E.13.3.

Irreversibility in the techniques for increasing the rate of heat transfer For the various existing techniques for increasing the rate of heat transfer:

(a) Define a dimensionless number of exergy destruction to evaluate the effectiveness of the technique used. (b) Obtain an expression to calculate the rate of exergy destruction in a fin.

Solution The objective of these techniques is to increase the heat transfer coefficient with respect to the base situation and at the same time, achieve that objective without having to excessively increase the pumping power needed to achieve the desired heat exchange. There is, therefore, a conflict in the application of these techniques, and we need to know which is the most appropriate for achieving that acceleration in the rate of heat transfer. There is a great diversity of techniques, and there is no universally accepted evaluation criterion, Zimparov and Vulchanov 1994 [E.5], so that the exergy method gives a solid thermodynamic basis for evaluating them. (a) Consider a differential element of the heat exchanger, length dz. Let m_ be the mass flow rate of one of the fluids and q_ the heat flux exchanged per unit length of the heat exchanger, flux that is perpendicular to the separation surface between both fluids. We have seen in Example E.13.2 that the rate of exergy destruction per unit length is given by Eq. (E.1). If
we call the _ rate of exergy destruction due to heat transfer between
the

fluid  and the wall d D dz DT , and the rate of exergy destruction caused by friction d D_ dz Dp , we have

   dD_ d D_ d D_ dD_ ¼ þ ¼ ð1 þ fÞ dz dz DT dz Dp dz DT

where f is the relationship between irreversibility caused by heat transfer and friction. The effect on the irreversibility of an enhancement heat transfer technique can be assessed by

is

directly comparing the rate of exergy destruction when that technique used, dD_ dz; with the rate of exergy destruction in the original situation dD_ 0 dz. A dimensionless number for exergy destruction is thus defined

dD_ dz

Ni ¼ dD_ 0 dz One of the most often used techniques is to increase the wall roughness where heat transfer takes place, Dipprey and Sabersky 1963 [E.6]. Since the wall roughness has a negligible effect on the flow cross-section and on the hydraulic diameter, the irreversibility number Ni takes the following form, Bejan and Pfister 1980 [E.7]  ðSt Þ0 ðSt Þ0 f0 f þ  Ni ¼ St 1 þ f 0 f0 St

Exergy in continuous media. Application to equipment design

1061

Bejan compared the roughness due to grains of sand with that caused by small ribs of height h and separated by the distance L. The conclusion of his investigation was that the roughness of the ribs of relative height h/D is equivalent to that of sand grains of relatively greater height and that the spacing has a much lower effect on Ni than the  that Ni decreases progressively as L increases. In addition, for a given pipe
height, such ðRe Þ0; f0 he determined the ribs optimal geometry (h,L). Another technique to enhance the rate of heat transfer is to cause turbulent movement of the fluid. Oulette and Bejan 1979 [E.8] studied the exergy destruction originated by these whirls. (b) Finally, we are going to refer to the fins technique. By increasing the wall surface in contact with the fluid, the drag force is also increased and consequently the irreversibility due to friction. Thus, in general, for a certain type of fin, there will be an optimum size for which the balance between the exergy destruction due to heat exchanged and friction causes minimum exergy destruction.

For a fluid flow that exchanges heat with a solid immersed in it, that is, it is an external flow, it can be deduced, see Sala 1987 [12], that the rate of exergy destruction in heat transfer between the fluid and the solid is
 D_

¼ ext

T0 2 TN

Z _ þ ðTs  TN ÞqdA A

T0 FD vN TN

where TN, vN are the temperature and the velocity of the flow in the zones not disturbed by the solid, Ts is the surface temperature of the solid, A is its area and FD is the thrust that it experiences, that is, the cross-section multiplied by the pressure difference. But furthermore, since the fin is not isothermal, there is also exergy destruction in its interior, see Fig. E.13.2.

Figure E.13.2 Fin profile, temperatures and heat fluxes.

1062

Exergy Analysis and Thermoeconomics of Buildings

The rate of exergy destruction in the fin is
 D_

Z int

¼ T0 A

Q_ q_ dA  T0 B T TB

where TB is the temperature at the base of the fin, Q_ B the rate of heat exchanged by the base and T the fin surface temperature. Adding both expressions gives the rate of total exergy destruction Q_ ðTB  TN Þ FD vN D_ ¼ T0 B þ T0 2 TN TN where it has been assumed that TBTNTN. The optimal fin size is obtained by calculating the minimum of the previous expression, subject to a series of constraints that may come from the type of fluid, the shape and material of the fin, the heat transfer through the base, etc. This optimization study was carried out by Poulikakos [E.9] for fins of different geometries. [E.5] V.D. Zimparov, N.L. Vulchanov, Performance evaluation criteria for enhanced heat transfer surfaces, International Journal of Heat Transfer 37 (12) (1994) 1807e16. [E.6] D.F. Dipprey, R.H. Sabersky, Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers, International Journal of Heat and Mass Transfer 6 (5) (1963) 329e332. [E.7] A. Bejan, P.A. Pfister, Evaluating heat transfer augmentation techniques based on their impact on entropy generation, Letters Heat and Mass Transfer 7 (1980) 97e106. [E.8] W.R. Oulette, A. Bejan, Conservation of available work (exergy) by using promoters of swirl flow in forced convection heat transfer, Energy International Journal 5 (1979) 587e596. [E.9] D. Poulikakos, Fin geometry for minimum entropy generation, M.Sc. Thesis, Department of Mechanical Engineering, University of Colorado, Boulder, USA, 1980.

13.9

Exergy cost in continuous media

Local exergy analysis, based on local exergy balances, is beginning to have some acceptance in engineering practice, Lior et al. 2004 [5]. However, local exergy analysis is not enough to understand the cost formation process, since the differential equation of the exergy cost needs to be solved, thereby allowing this formation process to be understood. As we have seen in Chapter 7, Thermoeconomics in its different formulations considers the system which is the object of study as a set of components, which are interrelated through mass and energy flows. Each of the components is considered as a black box so that this approach does not analyse the phenomena that occur inside, which inevitably leads to a significant information loss. Thus, when analysing a

Exergy in continuous media. Application to equipment design

1063

heating installation, the component where exergy destruction is most important is usually the boiler. Through Thermoeconomics we know how to locate and quantify this destruction cost. However, this destruction is due to various phenomena that take place in the boiler, such as combustion, heat transfer by conduction, convection and radiation, reactants diffusion, water flow with friction and combustion gases flow with friction, etc. It would be of great value to have a local and time-dependent exergy cost theory that would allow us to break down the effect on the resources consumption of each of these irreversible phenomena, in order to minimize their impact. Several authors have contributed to the development of local theories. Of particular importance is the work of Bejan 1996 [33], who delved into the phenomena that take place inside those black boxes, using the Laws of Thermodynamics, Fluid Mechanics and Theory of Heat Transfer, with the aim of minimizing the entropy generation. There are also other authors who have published works concerning local entropy generation, such as Natalini and Sciubba 1999 [34], Baytas 2000 [35], Magherbi et al. 2003 [36], etc. However, in these works, the economic costs of the irreversibilities are not quantified. In the local formulation of exergy balances is to be highlighted the aforementioned work of Sala 1987 [7]. The first important contribution to a Local Exergy Cost Theory was due to Chen et al. 2002 [37], who even considered exergoeconomic costs, which can be a contradiction since these costs are defined at the component level. In this brief bibliographical review, we also highlight Rangel et al. 2004 [38].

13.9.1 Local exergy cost balance Taking into account the meaning of exergy cost that we have seen in Chapter 7 and following the same approach as for the rest of the magnitudes that we have considered in the previous Sections, with k* being the exergy cost, we can write the local exergy cost balance according to the following equation r

   Dk  vk ¼r þ v$Vk ¼ V$J k Dt vt

(13.153)

where Jk represents the diffusion of the exergy cost per unit volume, which we will now deduce. The exergy cost k* is a function of the coordinates and time, that is to say, k* ¼ k*(xi,t). Let us first consider the case of a one-component system. In the local exergy cost balance equation, the phenomena that have an effect on the exergy cost are work due to the pressure, viscous stresses and heat flux. Therefore, the term on the right of Eq. (13.153) is 

V $ J k ¼ k   V $ ðpvÞ þ V$ðs: vÞ  V$ð1  T0 =TÞ q

(13.154)

1064

Exergy Analysis and Thermoeconomics of Buildings

Introducing into Eq. (13.153) the previous expression and the unit exergy cost, gives       Dðk Þ vðk Þ T0   ¼r þ v$Vðk Þ ¼ k  V$ðpvÞ þ V$ðs: vÞ  V$ 1  q r Dt vt T (13.155) which can also be written in a more compact way       
Dðk Þ vðk Þ T0    ¼r þ v$Vðk Þ ¼ V$ k s þ p0 d : v þ k lVT 1  r Dt vt T (13.156) The first term on the right represents the increase in the exergy cost due to the work done on the system by the pressure and the viscous component of the stress tensor, while the last term corresponds to the increase of the exergy cost associated with heat transfer. Rangel [39] develops two examples of application of the Local Exergy Cost Theory in his doctoral thesis. In one case, he refers to a two-dimensional flow of an incompressible fluid, in a laminar regime and in which the flow exchanges heat from the outside. In the other case, he refers to a flow of another incompressible fluid between two parallel plates, which transfers heat to the environment. In both situations, he calculates the rate of exergy destructions associated with the irreversibilities and the consequent increase in the exergy cost.

Superscripts 0 g

Initial values g component

Subscripts 0 s q i; o

Dead state Surface Chemical reaction Input, output

Nomenclature U; W S; D

Internal energy, work Entropy, exergy destruction

Exergy in continuous media. Application to equipment design

b; bch r; m; T; p A; V t x X v a J n ei F M f sij s d s 3 P ui vi [ ui vi i[1 vi;j v:w Vb T t T VT V:v Vv V:T T : Vv Mg rg cg y; x v v g ng , N g

j ;J g

g

j ;J

g

D =Dt Kg ygq

1065

Specific flow exergy, specific chemical exergy Density, mass, temperature, pressure Area, volume Time Particle position vector (Euler description) Particle position vector (Lagrange description) Velocity vector Acceleration vector n-th order tensor Normal unitary vector Cartesian unitary vectors Force Torque External force vector i-th component of the stress vector acting upon the positive side of the plane ej ¼ constant Second- order stress tensor Kronecker second-order tensor Second-order shear stress tensor Summation convention

Convention to represent partial derivatives vi;j ¼ vvi vxj Inner product of two vectors ( v:w ¼ vi wi Þ Gradient of the b scalar field Second-order tensor Transpose of the second-order tensor


 Gradient of the second-order tensor field
T VT ¼ vTij vxk ei ej ek Divergence of the spatial vector field v V:v ¼ vvi vxi )

tensor  gradient of the spatial vector field v
Second-order Vv ¼ vvi vxj ei ej


Divergence of the second-order tensor field T V:T ¼ vTij vxj ek Scalar contract product of two second-order tensors T : Vv ¼ Tij vi;j Molar mass of g component Mass of g component per unit volume Number of moles of g component per unit volume Mass fraction, molar fraction Average mass velocity Average molar velocity Mass flow rate vector, molar flow rate vector of g component respect to a stationary reference system Mass flow rate vector, molar flow rate vector of g component respect to the average mass velocity Mass flow rate vector, molar flow rate vector of g component respect to the average molar velocity Material derivative Production rate of g component due to chemical reactions Stoichiometric coefficient for the g chemical species in the q chemical reaction

1066

xq R Yq Ek q Qr f l g mg g g g b g h ; bs ; b 4S ε s_g Xi Ji Lik k

Exergy Analysis and Thermoeconomics of Buildings

degree of progress of the q chemical reaction Number of simultaneous chemical reactions Chemical affinity of the q chemical reaction Kinetic energy Heat flux vector External energy transmission rate Escalar potential Thermal conductivity Specific Gibbs function chemical potential of g component Partial enthalpy, partial entropy, partial Gibbs function of g component Entropy flux vector Thermal energy flow vector Rate of entropy generation Generalized force Flow (current) Phenomenological coefficient that relates flow Ji with force Xk Unit exergy cost

References [1] A.B. Pippard, The Elements of Classical Thermodynamics, Cambridge University Press, 1974. [2] M. Silhavy, The Mechanics and Thermodynamics of Continuous Media, Springer-Verlag Berlin Heidelberg, 1997. [3] Q.L. Chen, S.P. Wang, Q.H. Yin, B. Hua, Exergy destruction due to mean flow and fluctuating motion in incompressible turbulent flows through a tube, Energy 28 (2003) 809e823. [4] Q. Chen, Q. Yin, G. Han, B. Hua, S. Wang, A criterion for accelerating exergy transfer processes and decreasing exergy destruction, in: T.U. of Denmark (Ed.), Proceedings of the 16th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems, vol. 2, 2003, pp. 989e997. Denmark. [5] N. Lior, W. Sarmiento-Darkin, H.S. Al-Sharqawi, The exergy fields in transport processes: their calculation and use, in: Proceedings of the ASME-ZSIS International Thermal Science Seminar, Bled, Slovenia, vols. 155e169, 2004. [6] R.J. LeVeque, Numerical Methods for Conservation Laws, Birkh€auser, 1992. [7] F.W. Sears, G.L. Salinger, Thermodynamics, Kinetic Theory and Statistical Thermodynamics (in Spanish), Reverté, 1978. [8] H. Ziegler, An Introduction to Thermomechanics, North-Holland, 1983. [9] W. Fl€ugge, Tensor Analysis and Continuum Mechanics, Springer Verlag, 1972. [10] F.M. White, Fluid Mechanics, McGraw-Hill Education, 2003. [11] J.C. Slattery, Momentum, Energy and Mass Transfer in Continua, McGraw-Hill, 1972. [12] J.M. Sala, Thermodynamics of Fluids and the Method of Exergy Analysis (in Spanish), University of the Basque Country (UPV/EHU), 1987. [13] C. Truesdell, Essays in the History of Mechanics, Springer-Verlag, 1968. [14] E.G. Sinaiski, E.J. Lapiga, Separation of Multiphase Multicomponent Systems, Wiley-VCH, 2007.

Exergy in continuous media. Application to equipment design

1067

[15] S.B. Pope, Turbulent Flow, Cambridge University Press, 2000. [16] F. Nieuwstadt, J. Westerweel, B. Boersma, Turbulence. Introduction to Theory and Applications of Turbulent Flows, Springer, 2016.  [17] P. Chassaing, Turbulence en Mechanique de Fluides, Cépadués-Editions, 2000. [18] T. de Donder, Affinity (in French), Gauthiers-Villars, 1928. [19] E.A. Moelwyn-Hughes, Physical Chemistry, Wiley-VCH Verlag, Weinheim, 1957. [20] J.H. Espenson, Chemical Kinetics and Reaction Mechanisms, Wiley, 1981. [21] M.C. Potter, J.F. Foss, Fluid Mechanics, second ed., Great Lakes Press Inc., Michigan, 1983. [22] H.D. Baehr, K. Stephan, Heat and Mass Transfer, Springer, 1998. [23] H.B. Callen, Thermodynamics, J Wiley & Sons, 1960. [24] R.A. Gaggioli, Thermodynamics and the Non-equilibrium System, PhD Thesis, University of Wisconsin, 1961. [25] J.M. Sala, Thermodynamics of Multicomponent Systems (in Spanish), University of the Basque Country (UPV/EHU), 2016. [26] P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, John Wiley, 1971. [27] C. Truesdell, R.A. Toupin, in: Fl€ugge (Ed.), Principles of Classical Mechanics and Field Theory, Handbuch der Physik, vol. 3, Springer-Verlag, 1960. [28] S.R. de Groot, Thermodynamics of Irreversible Processes, North-Holland Publ., Amsterdam, 1952. [29] I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Charles C Thomas Publisher, 1955. [30] B.C. Eu, Kinetic Theory and Irreversible Thermodynamics, John Wiley & Sons, 1992. [31] P.C. Hemmer, H. Holden, S.K. Ratkje (Eds.), The Collected Works of Lars Onsager, World Scientific Series in 20th Century Physics, 2013. [32] W.M. Kays, H.C. Perkins, in: W.M. Rohsenow, J.P. Hartnett (Eds.), Forced Convection, Internal Flow in Ducts, Handbook of Heat Transfer, McGraw-Hill, 1973. [33] A. Bejan, Entropy Generation Minimization, CRC Press, Boca Raton, 1996. [34] G. Natalini, E. Sciubba, Minimization of the local rates of entropy production in the design of air-cooled gas turbine blades, Journal of Engineering for Gas Turbines and Power 121 (3) (1999) 466e475. [35] A.C. Baytas, Entropy generation for natural convection in an inclined porous cavity, International Journal of Heat and Mass Transfer 43 (2000) 2089e2099. [36] M. Magherbi, H. Abbassi, A. Ben Brahim, Entropy generation at the onset of natural convection, International Journal of Heat and Mass Transfer 46 (2003) 3441e3450. [37] Q.L. Chen, S.P. Wang, Q.H. Yin, B. Hua, Theoretical research on the transfer equation of exergy cost, in: C. F. B. T., G. Tsatsaronis, M.J. Moran (Eds.), ECOS 2002: Proceedings of the 15th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems, vol. 1, Institute for Energy Engineering, Technische Universit€at Berlin, Germany, 2002, pp. 207e214. [38] V.H. Rangel, S. Uson, A. Valero, C. Cortes, Basics of a microscopic representation of the exergy cost theory, in: R. Rivero, L. Monroy, R. Pulido, G. Tsatsaronis (Eds.), EnergyEfficient, Cost-Effective and Environmentally-Sustainable Systems and Processes, vol. 2, Mexican Petroleum Institute, Guanajuato, Mexico, 2004, pp. 551e560. [39] V.H. Rangel, Thermoeconomic Diagnosis of Large Industrial Boilers: Microscopic Representation of the Exergy Cost Theory, Doctoral Thesis, Superior Polytechnique Center, University of Zaragoza, 2005.

Index Note: ‘Page numbers followed by “f ” indicate figures and “t” indicate tables’. A ABS. See Absorber (ABS) Absolute entropy, 216 Absolute humidity, 189 Absorber (ABS), 457, 462e463, 463f, 469 Absorber Heat eXchange (AHX), 460 Absorption cycles, 456 engines, 457 Absorption refrigerators, 46, 979 energy analysis of components, 461e468 examples, 471e475 exergy analysis of components, 468e471 absorber, 469 condenser, 469e470 evaporator, 470 expansion valve, 470 generator, 468 heat recuperator, 469 regulation valve, 469 solution pump, 469 total cycle, 470e471 simple absorption cycle, 457e460 thermodynamic model of, 975 types and characteristics, 456e457 Absorptivity, 152e153 Academic context, 914e915 Accumulated exergy cost, 616e617 Active components, 915e916 Active glass, 28 Active glazing, 36e37, 37f Adaptive comfort, 320 ADHAC. See Association of Heating and Cooling Networks (ADHAC) Adiabatic mixture of two flows, 495e496, 495f Adiabatic system, 1043 Administrations, exergy and, 57e58 Adsorption

adsorption/desorption principle, 476 energy and exergy analysis of adsorption engine, 479 process, 485 Adsorption cooling systems, 46, 475e488 AHU with rotary desiccant dryer energy analysis, 481e483 exergy analysis, 483e485 energy and exergy analysis of adsorption engine, 479 examples, 485e488 operation of single-effect adsorption machine, 476e478 principle of adsorption/desorption, 476 rotary desiccant dryers, 480e481 Advanced configurations, 46 Advanced exergy theory, 770e784 applications, 775e777 destruction of endogenous and exogenous exergy, 773e775 examples, 777e784 exergy destruction and avoidable and unavoidable costs, 771e773 Advanced integrated façades, 30e31 Aerogels, 28 Aerothermal heat pumps, 391 AExA. See Exergoenvironmental analysis (AExA) Ahrendts model, 206e207 AHU. See Air handling units (AHU) AHX. See Absorber Heat eXchange (AHX) AI. See Artificial Intelligence (AI) Air air/water heat pumps, 43 systems, 350 inside building, 347e349 conditioning adiabatic mixture of two flows, 495e496

1070

Air (Continued) combination of basic processes for, 496e498, 497f dehumidification by cooling, 490e492 examples, 498e516 exergy analysis of, 488e516 humidifying or dehumidifying by mixing with water, 493e494 processes, 354 sensitive heating or cooling, 489e490 system, 37 mass flow rate, 516 quality and regulatory development of ventilation in Spain, 517e518 Air handling units (AHU), 480 energy analysis with rotary desiccant dryer, 481e483, 481fe482f exergy analysis with rotary desiccant dryer, 483e485 Algebraic methods, 964 Algebraic stress model (ASM), 1022 All-air systems, 348e350, 349f All-water systems, 350 Allocating costs method, 651e656 SPECO method, 655e656 TFA, 652e655 Allocation of loads, 826 Alternative internal combustion engines, 427e428, 959 micro engines, 45 Ambient air, 208e209 Ambient state, 113 Amortization, 932e933 Annuity, 601 Artificial Intelligence (AI), 926 ASM. See Algebraic stress model (ASM) Association of Heating and Cooling Networks (ADHAC), 423 Atmospheric/atmosphere, 207, 401 air, 510 airflow, 403 boilers, 374 Automatic boilers, 374 Autonomous method, 963e964 Average mass velocity of multicomponent system, 1019e1020 Average molar velocity, 1020 Average seasonal effectiveness, 520 Average seasonal efficiency, 521

Index

Average seasonal exergy efficiency, 521 Avoidable costs, exergy destruction and, 771e773, 781f B Balance sheet, 21 Balanced hearth boilers, 374 Basic Document DB-HE, 23 Beta-type Stirling engine, 415 Bifurcation(s), 606 equation, 629t parameters, 625, 665 BIM. See Building Information Modelling (BIM) Binary variables, 924, 951 Binding materials, 234 Biomass, 6 boilers, 43, 377 thermodynamic model of biomass combustion chamber, 975 Biosphere, 800 BiPV system, 31 Black box, 423 Blackbody emission power, 150e151 radiation, 149e151 exergy of, 156e159 isentropic expansion of, 157f thermodynamics of, 155e156 Boiler building and thermal facility, 881e885 CB, 753 components and flows, 885t energy analysis, 888 exergoeconomic costs, 891e893 exergy analysis, 888 exergy costs, 888e891 functional analysis, 886 heating and DHW demands, 885 impact on CO2 emissions, 893e894 numbering and symbols, 884f technology, 931 Boundaries of building, 20 BPIE. See Building Performance Institute Europe (BPIE) Branch and bound method, 934 Breakdown method, 775 Brine motor pump, 406e407 Building Assessment Report, 986

Index

Building Information Modelling (BIM), 50 Building Performance Institute Europe (BPIE), 22 Building Regulation Act, 518 Building(s), 50 arguments for incorporating exergy in, 52e58 chemical exergy of substances in, 234e256 current regulatory environment regarding energy in, 19e25 energy and, 15e18, 15f consumption data, 18 demand, 15e16 sources, 16e18, 17f system components, 16 energy and exergy demand of, 325e338 heat exchanges in, 264e266 new materials in, 26e29 new types of building skins, 29e41 active glazing, 36e37, 37f advanced integrated façades, 30e31 different types of inertial systems, 33e34 dynamic insulation, 39e41, 40f envelopes with PCM, 37e39 green roofs and green façades, 32e33 thermo-active foundations, 35e36, 36f thermo-active slabs, 34e35 RE in, 208e209 sustainability in, 798e802 C Calculus methods, 925, 963 of variations, 926 Caloric theory, 100 Canonical variables, 716 Capital recovery factor, 602, 640 Carathéodory’s Axiomatic Formulation of Thermodynamics, 71 Carbon dioxide emissions (CO2 emissions), 9 impact on boiler and CHP, 893e894 geothermal heat pump, 881 natural gas boilers, 866 trigeneration facility of hospital, 905 of resources, 847, 848t Carbon footprint, 803 Carnot cycle, 398

1071

Carnot engine, 167, 398 Carnot factor, 418 Carnot’s performance, 109 Carnot’s theory, 100 CC. See Characteristic curves (CC) CDC. See Chronological demand curve (CDC) CDP. See Cumulative degree of perfection (CDP) CEPC. See Chemical Engineering Plant Index (CEPC) CExC. See Cumulative Exergy Content (CExC) CF. See Correction factor (CF) CFD. See Computational Fluid Dynamics (CFD) Change(s) of chemical exergy per unit of time, 1050 of energy, 77 Characteristic curves (CC), 758 Characterization, 807 Chebyshev’s theorem, 940 Chemical affinity, 1040 Chemical Engineering Plant Index (CEPC), 933 Chemical exergy, 1048. See also Physical exergy of combustion gases in boiler, 236 of concentration, 219 of construction materials, 234 of fuels, 240e243, 242t of humid air, 237e239 of mixture of real gases, 239e240 of substances, 234e256 of water, 235e236 Chemical friction, 1041 Chemical internal energy, 78e79 Chemical irreversibilities chemical reactions, 177e179 exergy destruction due to, 175e179 mixture of different substances, 176e177 same substance at different temperatures, 175e176 Chemical potential, 211e212, 1048 Chemically reactive materials, 821 CHP. See Combined heat and power (CHP) Chronological demand curve (CDC), 429 CKP. See Clausius-Kelvin-Planck formulation (CKP)

1072

Classical energy analysis, 377e379 flow of energy in heating boiler, 377f typical values of losses in conventional boiler, 380f Classical or academic situation, 913 Classical thermodynamics, 69, 72e73, 1010 Classification, 807 Clausius-Duhem inequality, 1039 Clausius-Kelvin-Planck formulation (CKP), 70e71 Climate change, 12, 793 Closed systems available work in, 119e121 balance of exergy in, 124e134 energy balance in, 77e79 physical exergy of, 119, 121e123 CM. See Control mass (CM) Co-products, 573 Coal revolution, 10 CobbeDouglas production function, 932e933 C odigo Técnico de la Edificacion (CTE). See Technical Building Code (TBC) Coefficient of efficiency, 393 Coefficient of performance (COP), 393, 467 Cogeneration, 45e46, 409 in buildings, 410 cogeneration with ORC, 419e420 comments on, 409e410, 436e438 and demand for energy in buildings, 410e411 energy parameters of cogeneration, 423e426 examples, 431e436 exergy parameters of cogeneration, 426e428 feasibility of cogeneration in buildings, 428e431 heating and cooling networks, 420e423 micro-cogeneration technologies, 411e418 plant, 583 Cold water mass flow, 491e492 Combined heat and power (CHP), 409 building and thermal facility, 881e885 components and flows, 885t energy analysis, 888 exergoeconomic costs, 891e893 exergy analysis, 888

Index

exergy costs, 888e891 functional analysis, 886 heating and DHW demands, 885 impact on CO2 emissions, 893e894 numbering and symbols, 884f Combustion air, 378 gases, 381 systems, 379 Commercial optimization programmes, 934 Complete AHU system, 485 Components, 1019 Composition of gases after condensing, 388t of gases at outlet of combustion chamber, 388t of reactants and products, 385t Compression process, 399e400 Compressor, 399, 651 Computational Fluid Dynamics (CFD), 1022 Concentration collectors, 534 Condensation system, 456 temperature, 419 Condenser function, 702 Condensers, 366, 400, 402, 458, 464e465, 465f, 469e470 Condensing boilers, 42e43, 42f, 375 Conditioned space, 846 Conditioning system, 846 Constituents, 1019 Constitutive relations, 1011 Constraints, 921 Construction materials, exergy of, 234 Contact forces, 1029 Continuity equation, 1023e1024 in multicomponent system, 1024e1025 Continuous programming, 926 Continuum, 1012 in multicomponent systems, 1019e1020 Contrast, 916 Control mass (CM), 85, 1011, 1016 exergy balance in, 1046e1047 Control system, filtering malfunctions to, 742e743 Control volume (CV), 85e87, 86fe87f, 1011 energy balance in, 87e89, 1033e1036

Index

entropy balance in, 1042e1043 exergy balance in, 138e148, 1050e1052 examples, 140e148 mass balance in, 1025e1028 Convection change, 1014 coefficient on façade exterior surface, 293 energy balance, 277e278 exergy transport by, 277e281 Conventional boilers, 374 Conventional energy analysis, 167, 367e368, 440e442 Conventional insulation, 27 Conventional methodologies for analysis of sustainability, 802e816 analysis of environmental risks, 802e803 carbon footprint, 803 cumulative energy content, 804e805 EIA, 803 environmental audit, 804 EPD, 803e804 examples, 810e816 LCA, 805e809 COP. See Coefficient of performance (COP) Correction factor (CF), 395 Cost accounting engineering economy, 600e602 example of sequential system, 602e604 and exergy, 598e604 exergy cost and exergoeconomic cost, 599e600 theory, 665 balance equation, 772 Counter-current, 366 Coupling absorption chillers, 410e411 CPLEX v12.6.2, 990 Cross-flow, 366, 520 Cumulative consumption of exergy, 599 Cumulative degree of perfection (CDP), 823 Cumulative Ecological Consumption of Exergy (ExCCC), 823e824 Cumulative Exergy Content (CExC), 804e805, 822e824 Currents, 1044 CV. See Control volume (CV)

1073

D Dead state, 113 Decision variables, 934 Decomposition, 963 methods in complex problems, 926e927 programming, 926 in time, 927 Degradation of energy, 99 Dehumidification by cooling, 490e492, 491f by mixing with water, 493e494 Demand demand-driven model, 680e697 for energy, 15e16 Depletion of energy resources, 798 quantification of, 797 Design of thermal system, 917, 919f variables, 920e921 Desorption process, 485 Detailed dynamic method, 309e310 Detection of intrinsic malfunctions, 745 Deterministic programming, 926 Development, 797 DF. See Dysfunctions (DF) DH. See District heating (DH) DHC networks. See District heating and cooling networks (DHC networks) DHW. See Domestic hot water (DHW) DI. See Dynamic insulation (DI) Diagnostic vector, 565 Diffuse/diffusion potential, 1044 radiation, 162 sectors, 15, 798 solar radiation, 162 surface, 151 velocities, 1020 Direct costs, 600 Direct energy, 15, 799 Direct incorporation, 37e38 Direct method, 35, 378e379, 925 Direct Numerical Simulation (DNS), 1022 Direct problem, 726 Direct solar-driven systems, 539 Direct systems, 421e422 Direct-expansion system, 350 Discharging period, 441, 444

1074

Dispersed particles, 28 Dispersion, 818 Dissipation components, 697 equipment, 511, 579e580 function, 1055 Distribution matrix, 633 pipes, 422f system, 357e363 examples, 359e363 heat losses in distribution pipe, 358f Distributors, 363 District heating (DH), 47, 48f District heating and cooling networks (DHC networks), 47e49, 420e421 DNS. See Direct Numerical Simulation (DNS) Domestic hot water (DHW), 15e16, 21, 47, 346, 995 boilers, 373e390 classical energy analysis, 377e379 examples, 383e390 exergy analysis, 381e383 installations, 363 instant and seasonal efficiency, 380e381 types and characteristics, 373e377 radiant floor installation, 376f traditional system in Madrid, 376f Double-flow systems, 45 Dry fluids, 419 Dufour effect, 1044 Dulong and Petit equation, 975 Dynamic exergy transmittance, 311, 315 Dynamic insulation (DI), 39e41, 40f Dynamic methods, 327 Dynamic programming, 926 Dynamic transmittance, 40, 315 Dysfunctions (DF), 732e759 matrix, 753t theory, 726 E Earth/water heat pumps, 43 Eco-Indicator 95 method, 809, 832e834 Eco-Indicator 99 method, 809 Ecodesign Directive (ErP), 375 Ecological cost, 616e617 Economic aspects, exergy and, 55e56

Index

Economic model, 990 ECT. See Exergy cost theory (ECT) EEA. See Exergoeconomic analysis (EEA); Exergy Economics Approach (EEA); Extended exergy accounting (EEA) EEE. See Equivalent electrical efficiency (EEE) EER. See Energy efficiency ratio (EER) EExA. See Extended exergy analysis (EExA) EExE. See Equivalent Electric Exergy Efficiency (EExE) EFA. See Engineering Functional Analysis (EFA) Effective Temperature, Discomfort model (ET-DISC model), 320 Effectiveness-Number of Transfer Units (e NTU), 763 Efficiency, 170 factor, 493, 535 EIA. See Environmental Impact Assessment (EIA) ELCA. See Exergy Life Cycle Assessment (ELCA) Electric(al) boilers, 373 demands, 939, 948, 955, 995 efficiency, 537 energy, 398 exergy efficiency, 977 heat pumps, 391 power, 406 supply, 961 system, 395e396 Electricity consumption, 398 production, 410 Electrochemical processes, 416 Electrochromic glass, 28 Electrolyte, 416 EmA. See Emergy analysis (EmA) Emergy analysis (EmA), 824 Emissions, exergy as method of characterization of, 821e822 Emissivity of grey surface, 151 Emitting elements, 347e348 Endogenous exergy, destruction of, 773e775, 782f

Index

Endothermic reaction, 215 Energy, 4 analysis absorber, 462e463 of adsorption engine, 479 of AHU with rotary desiccant dryer, 481e483, 482f boiler and CHP, 888 of components, 461e468 condenser, 464e465 evaporator, 466 expansion valve, 465 generator, 461e462 geothermal heat pump, 873 heat recuperator, 463e464 natural gas boilers, 857e858 regulation valve, 464 of solar photovoltaic array, 531e532 of solar thermal collector, 535 solution pump, 464 total cycle, 467e468 trigeneration facility of hospital, 901e902 of ventilation system with heat recovery, 521e523 audits, 560 calculation, 325e333 detailed method, 331e333 examples, 333e338 gains (losses) of heat, 325e326 indirect method for calculating energy demand, 328e330 preliminary comments, 330 simplified method, 330e331 thermal loads and energy demand, 326e327 chains, 9e10, 10f cogeneration and demand for energy in buildings, 410e411 concept and laws of, 4e6 quality of energy, 5f consumption data in buildings, 18 content, 804 crisis, 76 current regulatory environment regarding energy in buildings, 19e25 European Union Directives, 19e22 transposition to Spanish legislation, 22e25

1075

demand of building, 325e338 diagnosis, 722e725 sensors in heating and DHW installation, 723f efficiency states, 423 energy and building sector, 15e18 integrated design process, 50e52 new materials in buildings, 26e29 glass, 28 thermal insulation, 26e28 new thermal installations, 41e49 new types of building skins, 29e41 parameters of cogeneration, 423e426 minimum values for EEE, 426t quality, 409 rehabilitation of buildings, 980e1001 examples, 993e1001 heating, DHW and electric demands, 995 legislation relating to, 985e986 optimization of rehabilitation based on thermoeconomics, 990e993 rehabilitation of envelope, 981e985 rehabilitation optimization searching for NZEB building, 988e990 results, 996 simulation and optimization tools for rehabilitation, 987e988 resources, 818 sources, 4e6 oil extraction, 7f parabolic trough collectors of solar power plant, 8f wind-power generator, 7f storage, 47, 410 and sustainability, 10e14 systems, 913 thermodynamics and, 75e76 vectors, 9 Energy balance, 266e267, 359, 564e572, 975, 1028e1036 in closed systems, 77e79 in control volume, 1033e1036 in CV, 87e89 equation, 367, 515 on exterior surface of façade, 291e296 convection coefficient, 293

1076

Energy balance (Continued) equivalent temperature and sun-air temperature, 295e296 radiation exchange with heavens and surroundings, 293e294 on interior surface of façade, 287e288 local, 1030e1032 transport exergy by convection, 277e278 Energy efficiency ratio (EER), 393, 467 Energy Roadmap 2050, 20 Energy Savings and Efficiency Action Plan (2010e20), 18, 23 Energy-Related Products Directive (ErP), 42 Energy-using products (EuP), 19 EnergyPlus software, 327 Engine cooling heat, 397 Engineering economy, 600e602 Engineering Functional Analysis (EFA), 651 Enthalpy, 229, 378, 612 of formation, 213e214 of reaction, 214e216 Entropy, 71, 101e108 balance, 1036e1043 in control volume, 1042e1043 local, 1039 Onsager theory, 1043e1045 change of entropy of universe, 103e108 examples, 105e108 flow vector, 1036e1037 production, 102e103, 1038 of reaction, 214e216 transfer, 101 Environment(al), 111e112 analysis of environmental risks, 802e803 audit, 804 energy, 399 exergy and, 56e57 externalities, 794e796 model, 113 reference, 112e114 thermoeconomy, 59e60 Environmental Impact Assessment (EIA), 803 Environmental product declaration (EPD), 803e804 EPD. See Environmental product declaration (EPD) Equality constraints, 921e922, 922f

Index

Equipment cost functions, 931e933 Equivalent Electric Exergy Efficiency (EExE), 428 Equivalent electrical efficiency (EEE), 425, 940e941, 950, 952 Equivalent temperature, 295e296 Erbs’ expression, 995 ErP. See Energy-Related Products Directive (ErP) ET-DISC model. See Effective Temperature, Discomfort model (ET-DISC model) ETIS. See Exterior Thermal Insulation System (ETIS) Euler description, 1013 Euler’s theorem, 210e211 EuP. See Energy-using products (EuP) European Union Directives, 19e22, 985 Evaporation rate, 499 Evaporators, 366, 402, 466, 466f, 470, 974 ExCCC. See Cumulative Ecological Consumption of Exergy (ExCCC) Exergetic behaviour indicator of wall, 311e316 Exergetic methodology, 54e55 Exergies of flows, 680e682 Exergoeconomic analysis (EEA), 562 Exergoeconomic costs, 599e600, 604, 617e619, 704e708, 1063 boiler and CHP, 891e893 exergoeconomic cost-benefit indicator, 991e992 of flows, 667e668 of fuel and product, 672e674, 685e688 of fuel and products of components, 619e620 fuel expressed in, 743e745 geothermal heat pump, 878e881 trigeneration facility of hospital, 904e905 Exergoeconomics, 56, 57f, 559 Exergoenvironmental cost, 827, 835 factor, 830 Exergoenvironmental analysis (AExA), 826e830, 835 Exergoenvironmics, 57 Exergy, 3e4, 53, 105, 111 AExA, 826e830 of air in buildings, 239 for analysis of sustainability, 822e840

Index

balance, 267e268, 279e281 in closed system, 124e134 examples, 125e134 examples, 288 on exterior surface of façade, 296e298 on interior surface of façade, 286e291 benefits of exergy analysis method, 167e171 exergy efficiency, 168e171 of blackbody radiation, 156e159 in buildings, 52e60 CExC, 822e824 characteristics, 54 of combustion gases in boiler, 236 of construction materials, 234 in continuous media, 1045e1062 cost, 1062e1064 energy balance, 1028e1036 entropy balance, 1036e1043 examples, 1055e1062 exergy balance in CM, 1046e1047 exergy balance in control volume, 1050e1052 fluid mechanics, 1012e1022 law of conservation of mass, 1022e1028 local chemical exergy balance, 1048e1050 local exergy balance, 1047e1048 costs, 599e600, 667e668, 704e708, 726 boiler and CHP, 888e891 of fuel and product, 672e674, 685e688 geothermal heat pump, 877e878 natural gas boilers, 862e863 trigeneration facility of hospital, 903e904 demand of building, 325e338 destruction, 351, 359, 1042 due to chemical irreversibilities, 175e179 in fin, 1062 index, 596 in irreversible processes, 123e124 due to mechanical irreversibilities, 171e173 due to thermal irreversibilities, 173e175 and economic aspects, 55e56 EEA, 825e826 efficiency, 168e171, 381, 382f, 471, 577, 585, 847

1077

ELCA, 824e825 electric efficiency, 426 EmA, 824 and environment, 56e57 examples, 830e840 exergoenvironmental analysis, 835 LCA of installation, 831 exchanged by building through opaque envelope, 303e310 detailed dynamic method, 309e310 quasi-steady method, 304e308 simplified dynamic method, 309 steady-state method, 303e304 exergy and administrations, 57e58 flow associated with heat, 115e118 examples, 117e118 of flows, 666e667 indicators, 728e732 and inertia of walls, 271e277 inertia and exergy, 273e277 thermal inertia, 272e273 limitations of exergy analysis, 58 marginal consumption, 684 method, 52 as method of characterization of emissions, 821e822 as method of characterization of resources, 817e820 methodologies, 558 need for exergetic methodology, 54e55 notions, 52e53 parameters of cogeneration, 426e428, 427f performance, 577e579 physical flow, 134e137 and sustainability, 817e822 sustainable building, 60e61 and thermal comfort, 316e325 of thermal radiation, 148e167 transport by convection, 277e281 units, 731 of water, 235e236 Exergy analysis, 368e369, 442e445 air inside building, 347e349 boiler and CHP, 888 chain of energy supply in building, 347f cogeneration in buildings, 409e438 distribution system, 357e363 end elements, 349e357 examples, 352e357

1078

Exergy analysis (Continued) exergy analysis of radiator, 350e351 geothermal heat pump, 873e877 heat exchangers, 365e373 pumps, 390e409 heating and DHW boilers, 373e390 methods, 111 natural gas boilers, 858e862 of systems, 595e598 indexes, 596e597 methodology, 597e598 TES, 438e450 of thermal equipment in buildings (II) absorption refrigerators, 456e475 adsorption cooling systems, 475e488 of basic air conditioning processes, 488e516 use of solar energy, 529e548 ventilation systems, 516e529 three-way valves, 363e365 trigeneration facility of hospital, 902e903 Exergy balance, 397, 564e572, 976 in CM, 1046e1047 in components of heat pump, 399e401 real cycle of vapour compression heat pump, 400f in CV, 138e148, 1050e1052 multicomponent systems, 1052e1055 in human body, 323e325 new form of, 576e577, 576f Exergy cost theory (ECT), 562e563, 605e651, 664, 835 accumulated exergy cost, 616e617 closure of system of equations, 613e615 exergoeconomic costs, 617e619 of fuel and products of components, 619e620 exergy cost of fuel and products of components, 615e616 propositions, 605e613 equipment and waste treatment equipment, 595f equipment with two output flows, 609f generic equipment with several output flows, 609f Exergy Economics Approach (EEA), 651 Exergy Life Cycle Assessment (ELCA), 824e825

Index

Exogenous exergy, destruction of, 773e775, 782fe783f Exogenous irreversibilities, 733 Exothermic process, 476 reaction, 215 Expansion valve, 401, 457e458, 465, 466f, 470 Extended exergy accounting (EEA), 825e826 Extended exergy analysis (EExA), 823e824 Extended Thermodynamics, 73e74 Exterior solicitations, 264 Exterior Thermal Insulation System (ETIS), 981, 981f External bifurcations, 611, 611f External costs, 13, 794 External forces, 1029 External malfunction, 740 Externalities, 12e14, 13f ExternE Project, 13e14, 794e795 F Façade exterior surface, 291e303 energy balance, 291e296 examples, 298e303 exergy balance, 296e298 interior surface, 286e291 energy balance on, 287e288 examples, 289e291 exergy balance on, 288 Factorial tools, 987 FEA. See First Exergoeoconomic Approach (FEA) Feasibility of cogeneration in buildings, 428e431 study, 428 FESR. See Fuel Energy Saving Ratio (FESR) FF. See Fill factor (FF) Fick’s law, 1043 Fifth Environmental Action ProgramF, 13e14 Fifth Environmental Action Programme, 794e795 Fill factor (FF), 531 Filtering malfunctions to control system, 742e743

Index

Final energies, 9 Fire-tube boilers, 373, 373f First Exergoeoconomic Approach (FEA), 651 First law in language of field theory, 1028 of thermodynamics, 4, 52, 61, 69, 77e98, 318 energy balance in closed systems, 77e79 energy balance in control volume, 87e89 examples, 79e85, 89e98 meaning of control volume, 85e87 First-order necessary conditions, 923 Fixed cost, 600 Flat collectors, 44, 533, 534f Flow(s), 847, 1044 energy, 1035 of gases, 643 process, 358e359 waste, 575 work, 68 Fluid mechanics, 1012e1022 continuum in multicomponent systems, 1019e1020 material derivative, 1013e1014 and spatial description of motion, 1012e1013 stress tensor, 1017e1019, 1018f transport theorem, 1014e1016 turbulence, 1021e1022 Fluid streams, 366 Formation reaction, 213e214 Fossil energy, 346 Fossil fuels, 6e9, 346, 797 Fourier law, 1033, 1043 FP representation, 665e680 examples, 674e680 exergy costs and exergoeconomic costs of flows, 667e668 of fuel and product, 672e674 exergy of flows, 666e667 FP(R) formulation, 704e706 exergy costs and exergoeconomic costs, 704e706 fuel and product of components, 668e671 global efficiency installation, 671e672 relationship between FP and PF representations, 688e689

1079

with residues, 697e716 Free condition, 748 Friction, 172, 1041, 1058 work, 172 FTA. See Functional thermoeconomic analysis (FTA) Fuel, 573e576 cells, 45e46, 416e418, 417f, 417t, 418f chemical exergy, 240e243 energy, 378e379 expressing in exergoeconomic costs, 743e745 formula impact, 726 fuel/product diagram, 575, 873, 874f impact on, 728e732 Fuel and product of components, 615e616, 668e671, 670t, 682e684 exergoeconomic costs, 619e620 exergy cost, 615e616 exergy costs and exergoeconomic costs of, 672e674, 685e688 Fuel Energy Saving Ratio (FESR), 424 Functional analysis boiler and CHP, 886 geothermal heat pump, 871e873 natural gas boilers, 854e857 trigeneration facility of hospital, 897e901 Functional diagram, 575 Functional thermoeconomic analysis (FTA), 652 Functional unit (UF), 806 Fusion, 8, 390e391 G Gas heat pumps, 391 Gas microturbine, 45, 45f, 413e415, 415f, 433, 437 Gas utilization efficiency (GUE), 394 Gas-driven heat pump, 399 Gases, 373 GateCycle, 915 GAX. See Generator Absorber eXchange (GAX) Gebhart method, 284 General Theory of Systems, 563 Generalized forces, 1044 Generalized Gradient method, 925e926 Generalized inverse matrix, 669

1080

Generalized residual diagrams, 239e240 Generalized Reynolds transport theorem, 1016 Generator, 461e462, 461f, 468 Generator (G), 457e458 Generator Absorber eXchange (GAX), 460 Geometric programming method, 926 Geothermal energy, 8 Geothermal heat pumps, 391e392 building and thermal facility, 866e869, 868fe869f components and flows, 871t energy analysis, 873 exergoeconomic costs, 878e881 exergy analysis, 873e877 costs, 877e878 functional analysis, 871e873 heating and DHW demands, 871, 871f impact on CO2 emissions, 881 numbered flows, 870f numbering, symbols and brief descriptions, 870t reorganization of schema and symbols, 869f GHG. See Greenhouse gases (GHG) Gibbs method, 74e75 Gibbs potential of formation, 216e217 maximum work and change of, 217e218 of reaction, 216e217 Gibbs theory, 71 Gibbs thermodynamics, 71 GibbseDuhem equation, 1049 Glass, 28, 234 Global efficiency installation, 671e672, 685 Global energy balance, 393e394 electrically driven heat pump, 394f gas-driven heat pump, 395f Global exergy balance, 397e399, 470 Global minimum, 922e923, 923f Global resources, 724 Global Warming Potential (GWP), 803 Gouy Stodola equation, 123, 268, 1058 Graph Theory, 558 Grassmann diagram, 142f, 145f, 168 Gravitational force, 1030 Gravitational potential energy, 4 Green façades, 32e33

Index

Green roofs, 32e33 Green transform, 1030 Greenhouse effect, 154, 808 Greenhouse gases (GHG), 794 Grey surface, 151 Growth, 797 GUE. See Gas utilization efficiency (GUE) GWP. See Global Warming Potential (GWP) H Heat collector (HC), 861 Heat conduction in wall energy balance, 266e267 examples, 269e271 exergy balance, 267e268 Heat exchanger, 366fe367f, 477, 583, 678, 974 analysis of mechanisms of irreversibilities, 369e370 in building, 264e266, 265f conventional energy analysis, 367e368 examples, 370e373 exergy analysis, 368e369 destruction in, 160e161 types and characteristics, 365e367 Heat flux, 351, 362 Heat gains, 325e326 Heat generating technologies, 988e989 Heat lost plus exergy destructions, 487 Heat production (HP), 861 Heat pumps, 391f, 393f. See also Geothermal heat pumps examples, 402e409 exergy balance in components, 399e401 global energy balance, 393e394 global exergy balance, 397e399 seasonal average efficiency, 395e397 types and characteristics, 390e392, 392f Heat quality factor, 115e116 Heat recovery, energy and exergy analysis of ventilation system with, 521e523, 521f Heat recuperator, 463e464, 463f, 469, 519e521, 519f Heat Theorem of Nernst Statement, 215 Heat transfer, 488e489 fluid, 421

Index

Heat traps, 154e155 Heating, 995 and cooling networks, 420e423, 421f and DHW demands boiler and CHP, 885 geothermal heat pump, 871, 871f natural gas boilers, 852e854 process, 399, 489 radiator, 350 Heating, ventilation and air conditioning (HVAC), 15, 188 system, 846 Heating boilers classical energy analysis, 377e379 examples, 383e390 exergy analysis, 381e383 instant and seasonal efficiency, 380e381 types and characteristics, 373e377 radiant floor installation, 376f traditional system in Madrid, 376f Heliothermic energy, 8 Heuristic methods, 919 for successive approximations, 966e968 HHV. See Higher heating value (HHV) High coverage rate, 430 High temperature (HT), 533, 989 High-quality energy, 346 Higher heating value (HHV), 975 Hot ventilation and air conditioning (HVAC). See Heating, ventilation and air conditioning (HVAC) HP. See Heat production (HP) HT. See High temperature (HT) Humid air exergy, 237e239 Humidifying by mixing with water, 493e494 HVAC. See Heating, ventilation and air conditioning (HVAC) Hybrid, 47 PVT modules, 537e539 solar panels, 44 Hybridization, 47 Hydraulics, 6 compensator, 692e693 Hydrosphere, 207 Hydrothermal heat pumps, 391

1081

I ICT, 49 IDAE. See Institute for Diversification and Saving of Energy (IDAE) Ideal gas, physical exergy of, 185e186, 187f IEAeECBCS program. See International Energy Agency’s Energy and Buildings Communities Program (IEAeECBCS program) ILGO. See Iterative local-global optimization (ILGO) ILP. See Integer linear programming (ILP) Immersion, 37e38 Impact assessment, 807e808 Implicit method, 305 Incidence matrix, 571, 572t Incidence matrix A, 563 Inclusion of residues in diagnosis, 738e741 Incompressible fluid, 1023 Independent variables, 920e921, 980 Index(es), 596e597 of exergy loss, 596 Indirect costs. See Fixed cost Indirect energy, 15, 799 Indirect method, 35, 378e379, 925 Indirect solar-driven systems, 539 Indirect systems, 421e422 Induced anomaly, 727e728 Induced malfunctions, 741e742 Industrial Revolution, 10 Inequality constraints, 921e922, 922f Inertia, 33 and exergy, 273e277 Inertial systems, 33e34 Information, 105 Infrared region of spectrum, 148e149 Instant and seasonal efficiency, 380e381 Instantaneous COP, 393 Instantaneous exergy efficiency, 397e398, 407 Institute for Diversification and Saving of Energy (IDAE), 852e854 Integer linear programming (ILP), 431 Integer programming, 926 Integrated design process, 50e52 agents participating in BIM project, 51f control for optimized operation, 52

1082

Integrated design process (Continued) design of building and preliminary evaluation, 51 location for building, 50e51 preliminary design, 51 Intelligent control, 49 Intelligent self-adaptive regulation, 49 Inter-seasonal storage, 47 Interfering effects, 1044 Interior solicitations, 265 Internal combustion micromotors, 411e413, 412fe413f, 437 Internal efficiency, 170 Internal energy, 4 Internal equilibrium, RE in, 205e207 Internal exchanger, 407 Internal exergy destruction, 358, 361e362 Internal irreversibilities, 124 Internal malfunction, 739 Internal rate of return (IRR), 431 International Energy Agency’s Energy and Buildings Communities Program (IEAeECBCS program), 943 International Union of Pure and Applied Chemistry (IUPAC), 213 Intrinsic anomaly, 727e728 Intrinsic malfunctions, 741e742, 758 detection, 745 separation from induced malfunctions, 759e762 Inverse problem, 726 Investment cost, 931e932, 935e936 IPT. See Irreversible Process Thermodynamics (IPT) IRR. See Internal rate of return (IRR) Irradiation, 152 Irreversibilities mechanisms, 171e179, 369e370 differential control volume in heat exchanger, 370f exergy destruction to chemical irreversibilities, 175e179 to mechanical irreversibilities, 171e173 to thermal irreversibilities, 173e175 Irreversibility, 559e560 matrix operator, 734, 740 Irreversible process, 400 exergy destruction in, 123e124

Index

Irreversible Process Thermodynamics (IPT), 1044 Isenthalpic process, 401 Isentropic efficiency, 170 fluids, 419 Isochoric movement, 1023 transformations, 415 Isoenthalpic process, 458 Isolated method, 35 Iterative local-global optimization (ILGO), 927 IUPAC. See International Union of Pure and Applied Chemistry (IUPAC) K KarmaneNikuradse relation, 1059 Kelvin degree (K), 69 Kinetic energy, 4 Kirchhoff’s law, 153e154 Kubik intelligent building of Tecnalia in Bilbao, 915, 915f Kuhn-Tucker conditions, 925e926 L Laboratory of Quality Control for Buildings (LCCE), 746 Lagrange multipliers theory, 925e926 Lagrangian function, 924 Land, 392 Large Eddy Simulation (LES), 1022 Last-In First-Out method (LIFO method), 562 Last-In-First-Out Approach (LIFOA), 651 Latent thermal energy, 438 Law of conservation of energy, 4 Law of conservation of mass, 1022e1028 continuity equation, 1023e1024 in multicomponent system, 1024e1025 mass balance in control volume, 1025e1028 Law of mechanical energy conservation, 75 Law of Stable Equilibrium, 72 Law on Urban Rehabilitation, Regeneration and Renewal, 986 LCA. See Life cycle assessment (LCA) LCCE. See Laboratory of Quality Control for Buildings (LCCE)

Index

LCI. See Life cycle inventory (LCI) LED. See Light-emitting diode (LED) Leibnitz rule, 1023e1024 LES. See Large Eddy Simulation (LES) LGO. See Local-global optimization (LGO) Life cycle, 793e794 of product, 11e12, 11f Life cycle assessment (LCA), 793e794, 805e809, 831 construction products, 810t definition of objectives and scope, 806 evaluation and interpretation of results, 809 impact assessment, 807e808 LCI, 806e807, 807f phases, 806f stages, 805e809 Life cycle inventory (LCI), 806e807, 807f LIFO method. See Last-In First-Out method (LIFO method) LIFOA. See Last-In-First-Out Approach (LIFOA) Light source, 148e149 Light-emitting diode (LED), 28 Limits of variables, 922 Linear functions, 950e951 Linear programming method, 926 Liquid crystals, 28 liquid fuels, 373 liquid-vapour mixture, 192 Lithium bromide absorbing water, 456 Lithosphere, 207 Loading period, 440e441 process, 443 Local change, 1014 Local chemical exergy balance, 1048e1050 Local energy balance, 1030e1032 cases, 1033 multicomponent systems, 1032e1033 Local entropy balance, 1039 multicomponent systems, 1039e1042 Local exergy analysis, 1011 balance, 1047e1048 cost balance, 1063e1064 Local minimum, 922e923, 923f Local optimization, 965e966 Local theories, 1063

1083

Local thermal energy equation, 1031 Local thermodynamics equilibrium principle, 86 Local velocity divergence, 1016 Local-global optimization (LGO), 927 Long-wave radiation, 149, 348 Loss flows, 558e559 Low temperature (LT), 533, 989 boilers, 375, 959 Low-energy buildings, 271 Low-ex buildings, 25 LT. See Low temperature (LT) M Maastricht Treaty (1993), 13e14, 794e795 Macro-encapsulation, 37e38 Macroscopic Thermodynamics of Equilibrium (MTE), 71 Maintenance costs, 932e933 Malfunctions (MF), 758e759 diagnosis through, 732e758 cost, 736e738 examples, 746e758 filtering malfunctions to control system, 742e743 free condition, 748 impact on fuel expressed in exergoeconomic costs, 743e745 inclusion of residues in diagnosis, 738e741 intrinsic and induced, 741e742 problem of detection of intrinsic, 745 matrix, 735 theory, 726 Marginal exergy consumption, 729 Marshall and Swift Equipment Cost Index (MSEC), 933 Mass concentration, 1019 flows, 364, 368, 1020 fraction, 389, 1019 transfer, 488e489 Mass balance, 564e572, 975 in control volume, 1025e1028 examples, 565e572 Material derivative, 1013e1014 Material description of motion, 1012e1013 Material points or particles, 1012

1084

Mathematical optimization methods, 924e927 decomposition methods in complex problems, 926e927 MatLab R2014a, 990 Matrix Algebra, 558 of dysfunctions, 735 Maximum exergy efficiency, 398 MaxwelleBoltzman equation, 74 MCFC. See Molten carbonate fuel cells (MCFC) MDC. See Monotonic demand curve (MDC) Mechanical component of physical exergy, 137 Mechanical drive systems and mechanical extraction, 518e519 and natural extraction, 518 Mechanical energy, 4 Mechanical equivalent of heat, 100 Mechanical friction, 401, 1041 Mechanical irreversibilities, exergy destruction to, 171e173 Medium temperature (MT), 989 Merkel diagram, 461 Methane, 389 Methyl chloroform, 792e793 Mexogenous exergy destruction, 783e784 MF. See Malfunctions (MF) Micro-CHP unit, 940 Micro-cogeneration, 410 facilities, 411 installation, 413 technologies, 411e418 fuel cells, 416e418 gas microturbines, 413e415 internal combustion micromotors, 411e413 stirling engines, 415e416 unit, 434 Microencapsulation, 37e38 Micromotors, 411 Microturbines, 413, 414f MILP. See Mixed Integer Linear Programming (MILP) Minerals, 797 MINLP. See Mixed Integer Non-Linear Programming (MINLP)

Index

Mixed Integer Linear Programming (MILP), 929 algorithms, 940e941 Mixed Integer Non-Linear Programming (MINLP), 929 Mixers, 363 Mixing box, 495 in installation, 495f Modified exergy performance, 771 Molar concentration, 1019 Molar fraction, 388, 1019 Molten carbonate fuel cells (MCFC), 418 Molten carbonates, 416e417 Monetary costs, natural gas boilers, 863e865 Monetization, 13, 794, 795f Mono-Si. See Monocrystalline silicon (Mono-Si) Monochromatic emission power, 149e150 Monocrystalline silicon (Mono-Si), 530e531 Monotonic demand curve (MDC), 429 Motor-compressor group, 408 MSEC. See Marshall and Swift Equipment Cost Index (MSEC) MT. See Medium temperature (MT) MTE. See Macroscopic Thermodynamics of Equilibrium (MTE) Multi-objective optimization, 987 methods, 920 model, 929 Multi-objective programming, 926 Multi-stage cycles, 478 Multicomponent systems continuity equation in, 1024e1025 exergy balance in control volume, 1052e1055 local energy balance, 1032e1033 local entropy balance, 1039e1042 Multicriteria method, 987 N Nanotechnology, 29 Natural gas, 42 consumption, 669 sealed boiler, 374, 374f Natural gas boilers, 346, 849e866 annual energy efficiency, 858t blocks of dwellings, 850f

Index

components and flows, 853t description, 849e852 energy analysis, 857e858 chain of facility, 853f exergy analysis, 858e862 costs, 862e863 functional analysis, 854e857 heating and DHW demands, 852e854 impact on CO2 emissions, 866 monetary costs, 863e865 numbering of flows, 853f and symbols, 852t schema of facility, 850f seasonal energy efficiency of components, 857te858t simplification of schema and symbols, 851f Natural intake and mechanical extraction systems, 518 Natural resources, 14, 111e112, 818 NaviereStokes equations, 1022 NBE. See Normas Basica de la Edificacion (NBE) Nearly zero energy buildings (nZEB), 20, 21f, 24e25, 41 rehabilitation optimization searching for, 988e990 Negentropy flows, 653, 654f method, 701e704 FP(R) and PF(R) symbolic representations, 708f T-s diagram of Rankine Cycle, 702f Net active seasonal average efficiency (SCOPnet), 395 Net present value (NPV), 431 Net seasonal primary power-active ratio (SPERnet), 395 New materials in buildings, 26e29 New thermal installations, 41e49 biomass boilers, 43 cogeneration, 45e46 condensing boilers, 42e43 district heating and cooling systems, 47e49 energy storage, 47 heat pumps, 43 hybrid installations, 47

1085

intelligent control, 49 solar collectors, 44 trigeneration, 46 ventilation systems, 45 Newton’s law, 1043 of cooling, 277 Newtonian fluid, 1018e1019 Non-linear programming method, 926 Non-renewable consumption, 396 energy, 6 zero-energy building, 996 Non-slipping condition, 277 Normalization, 807e808 Normalized environmental profile, 808 Normas Basica de la Edificaci on (NBE), 517 NPV. See Net present value (NPV) NTU. See Number of transfer units (NTU) Nuclear energy, 8e9 Nuclear fission, 8 Nuclear internal energy, 78e79 Nuclear revolution, 10 Number of transfer units (NTU), 641e642 NTU-effectiveness method, 368 nZEB. See Nearly zero energy buildings (nZEB) O Objective function, 920e922, 934, 990, 950, 958 Ohm’s law, 1043 Oil revolution, 10 On-demand ventilation systems, 519 One-dimensional flow model, 138 Onsager reciprocal relations, 1044e1045 Onsager theory, 73, 1043e1045 Opaque envelope, exergy exchanged by building through, 303e310 Open systems CV as, 85e86 exergy balance in, 68 Open-cycle desiccant refrigeration systems, 480 Operating temperature, 322, 331 Operation of thermal system, 918 Operational diagnosis of thermal installations in buildings advanced exergy theory, 770e784

1086

Operational diagnosis of thermal installations in buildings (Continued) diagnosis through malfunctions and dysfunctions, 732e758 energy diagnosis, 722e725 exergy indicators, 728e732 method of characteristic equations, 758e770 examples, 762e770 intrinsic malfunctions separation, 759e762 thermoeconomic diagnosis, 725e728 Optimal cost solution, 996 Optimal diameter, 1059 Optimal powers, 953e955 Optimal system, 913 Optimization, 913 in design of thermal installations in buildings, 928e962 alternative internal combustion engines, 959 description of installation, 956 economic and environmental data, 942 economic constraints, 959 electrical supply, 961 equipment cost functions, 931e933 equipment selection with optimal performance, 930 examples, 935e962 installation, 940 legal constraints, 961 low temperature boilers, 959 objective function, 950, 958 operation mode, 933e934 photovoltaic installation, 960 results, 946t, 945, 953, 961 selection of optimal generation equipment, 931 simple optimization problems, 929 solution of optimization problem, 934e935 storage tank, 960 superstructure, 948 technical and economic data, 950, 958 technical and legal constraints, 943, 952, 959 thermal and electrical demands, 939, 948, 955

Index

thermal energy supply, 960 TES integration, 941 mathematical aspects, 923e924 mathematical formulation of, 920e924 of rehabilitation based on thermoeconomics, 990e993 ORC. See Organic Rankine cycle (ORC) Organic Rankine cycle (ORC), 419e420, 420f cycle pump, 978 heat exchanger, 978 thermodynamic model of, 974 evaporator, 974 heat exchanger, 974 pump, 974 turbine, 974 turbine, 978 Overall exergy efficiency, 427 Overconsumption, 726 P PAFC. See Phosphoric acid fuel cells (PAFC) Palladium, 416e417 Parallel flow, 460, 460f, 520 Parametric tools, 987 Partial molar variables, 210e211 Partial variables, 211 PASLINK trial, 314 Passive components, 915e916 Passive glass, 28 Passive systems, 846 Payback period (PB), 431 PCM. See Phase change materials (PCM) PCR. See Product category rules (PCR) PE. See Primary energy (PE) Peltier effect, 1044 Percentage of Energy Saving (PES), 425, 522e523, 945 PES. See Percentage of Energy Saving (PES) PF representation, 680e697 examples, 689e697 exergies of flows, 680e682 exergoeconomic costs of fuel and product, 685e688 exergy costs of fuel and product, 685e688 fuel and product of components, 682e684 global efficiency installation, 685

Index

PF(R) formulation, 706e708 exergy costs and exergoeconomic costs, 707e708 relationship between FP and PF representations, 688e689 with residues, 697e716 Phase change materials (PCM), 37, 438 envelopes with, 37e39 Phosphoric acid, 416e417 Phosphoric acid fuel cells (PAFC), 418 Photochromic glass, 28 Photon-electron interactions, 530 Photons, 149 Photovoltaic (PV), 529e548 arrays, 530 cells, 529 conversion, 529 energy, 8 façade, 31 installation, 960 solar installation, 530, 530f systems, 414 technology, 31 Physical decomposition, 927 Physical exergy, 1048. See also Chemical exergy calculation, 184e203 through residual variables, 192e193 of closed system, 119e123 examples, 193e203 of humid air, 188e191 of ideal gas, 185e186, 187f of incompressible solids and fluids, 191 of liquid-vapour mixture, 192 of mixture of ideal gases, 186e188 Physical flow exergy, 134e137 thermal and mechanical components, 136e137 Physical structure of installations, 563e564 Piezoelectric transducer immersed in water, 493 Plates, 366 Platinum, 416e417 PMV index. See Predicted Mean Vote index (PMV index) Poiseuille flow, 1056 Polymeric electrolyte cells, 45, 416e417 Polymeric proton-conducting membrane, 416e417

1087

PPD index. See Predicte Dissatisfied index (PPD index) Predicte Dissatisfied index (PPD index), 320 Predicted Mean Vote index (PMV index), 320 Predictive model, 724 Prefabricated energy exchanger piles, 35 Pressure tensor, 1017e1018 Pressurized hearth boilers, 374 Primary energy (PE), 9, 861 Primary energy savings (PES). See Percentage of Energy Saving (PES) Primary Exergy Savings Index, 428 Principle of Local Equilibrium, 1012 Principle of Thermoeconomic Isolation, 966 Process evaporative cooler, 484 Product category rules (PCR), 804 Productive structure, 558e559 Productive structure of installations, 572e595 dissipative equipment, 579e580 examples, 580e595 exergy performance and unit exergy consumption, 577e579 fuel, product and losses, 573e576 new form of exergy balance, 576e577 Products, 558e559 and losses, 573e576 Profitability analysis, 431 Proton-exchange membrane cells. See Polymeric electrolyte cells Protons, 416 Psychrometric processes, 489 Pump, 457, 974 PV. See Photovoltaic (PV) PVT. See Thermal/photovoltaic modules (PVT) Q Quadratic programming method, 926 Quality of energy, 4, 52, 108e111, 110f degradation of, 124 Quasi-static process model, 1010 Quasi-steady method, 304e308, 327 R Radiant barriers, 26 Radiation, 148

1088

Radiation (Continued) exchange with heavens and surroundings, 293e294 exergy exchange, 285e286 between interior surfaces of room, 284e286 between surfaces, 281e286 between two grey surfaces, 282e283 Radiative energy exchange, 284e285 Radiator, exergy analysis of, 350e351 Radiator system (RS), 747 Radiosity, 153 Rankine cycle, 419 RANS equations. See ReynoldseAveraged NaviereStokes equations (RANS equations) Rayleigh scattering, 162 RE. See Reference environment (RE) Recuperator (R), 457 Reference environment (RE), 112e114 in buildings, 208e209 in internal equilibrium, 205e207 modelling, 203e209 RE associated with process, 204e205 RE based on stability, 207e208 substances present in, 219e220 Reference state, 723e725 Reference substances, 207 Reflectivity, 152e153 Refrigerant system, 350 Refrigerant-absorbent pair, 46 Refrigeration, 476, 481 heat battery, 484 installation, 648 Regenerative cycle, 419, 420f Regenerative heat exchange, 459 exchanger, 484 Regenerator, 415 Reglamento de Instalaciones Térmicas de los Edificios (RITE), 518 Regulating valve, 459 Regulation of Thermal Installations in Buildings (RTIB), 22, 41 Regulation valve, 464, 464f, 469 Rehabilitation of envelope, 981e985 optimization searching for NZEB building, 988e990

Index

Renewable energies, 6e9, 12, 51, 346 Renewable energy sources (RES), 20 Reserves, 797 Residues cost formation process, 675f, 698e701, 698f FP and PF representations with, 697e716 examples, 708e716 FP(R) formulation, 704e706 negentropy method, 701e704 residues process cost formation, 698e701 inclusion in diagnosis, 738e741 Resources exergy as method of characterization, 817e820 limitation of, 797e798 Restricted equilibrium, 113 Reverse Carnot cycle, 404 Reversible energy, 5 Reversible heat pumps, 391 Reynolds number, 1059e1060 Reynolds stress model (RSM), 1022 Reynolds stresses, 1022 Reynolds transport theorem, 1015 ReynoldseAveraged NaviereStokes equations (RANS equations), 1022 RITE. See Reglamento de Instalaciones Térmicas de los Edificios (RITE) Rotary desiccant dryers, 480e481, 484 energy analysis of AHU with, 481e483 exergy analysis of AHU with, 483e485 complete AHU system, 485 process evaporative cooler, 484 regeneration evaporative cooler, 484 regeneration heat battery, 484 regenerative heat exchanger, 484 systems, 480 Rotary flow recuperators, 520 RS. See Radiator system (RS) RSM. See Reynolds stress model (RSM) RTIB. See Regulation of Thermal Installations in Buildings (RTIB) S Sankey diagram, 142f, 168 SATE system, 313e314, 316 Saturated liquid-vapour mixture, 366

Index

SCOPnet. See Net active seasonal average efficiency (SCOPnet) Sealed boilers, 374 Search method, 925 Seasonal average efficiency, 380, 395e397 Seasonal efficiency, 380e381 Seasonal energy efficiency factor (SEER), 395 Seasonal exergy efficiency, 382 Seasonal exergy efficiency factor (SPxF), 399 Seasonal performance factor (SPF), 395 Sech-Spahousec project, 18 Second law of thermodynamics, 5, 61, 69, 98e101 Secondary energies, 9 Seebeck effect, 1044 SEER. See Seasonal energy efficiency factor (SEER) Semi-automatic boilers, 374 Sensitive cooling, 489e490 Sensitive energy TES, 438 Sensitive heat factor (SHF), 492 Sensitive heating, 489e490 Sensitivity analysis, 431, 935 Sequential method, 822e823, 913 Sequential Quadratic Programming method, 925e926 Sequential system, 602e604, 603f Series flow, 460 SET. See Standard effective temperature (SET) SETAC. See Society of Environmental Toxicology and Chemistry (SETAC) Shear component, 1017 SHF. See Sensitive heat factor (SHF) Short-wave radiation, 149 Silica-based aerogels, 28 SimaPro software, 832e834 Simple absorption cycle, 457e460 Simple flow systems, 519 Simplified dynamic method, 309 Simulation, 914e916 Simulator, 916 Simulink, 915 Simultaneous method, 823, 913 Single-effect adsorption machine operation, 476e478, 477f adsorption engine with two chambers, 477f

1089

Single-effect cycle, 476e477 Small and medium businesses (SMBs), 22 Small-power cogeneration, 410 SMBs. See Small and medium businesses (SMBs) Social externalities, 796e797 Society of Environmental Toxicology and Chemistry (SETAC), 805 SOFC. See Solid oxide fuel cells (SOFC) Solar collectors, 44, 529 Solar cooling, 456 Solar energy, 421, 529e548 energy analysis of solar PV array, 531e532 of solar thermal collector, 535 examples, 540e548 exergy analysis of solar PV array, 532e533 of solar thermal collector, 535e537 hybrid PVT modules, 537e539 reference frame for exergy analysis, 539e540 types and characteristics of solar photovoltaic cells, 530e531 of solar thermal collectors, 533e534 Solar radiation, 6, 8, 149 exergy of, 161e163 Solar systems, frame of reference for exergy analysis of, 539e540 Solar thermal collectors, 533e534 energy analysis, 535 exergy analysis, 535e537 heating and subsequent humidification, 497 Solar walls, 39 Solid fuel boilers, 373 Solid oxide cells, 45, 416e417 Solid oxide fuel cells (SOFC), 418 Solid-liquid phase changes, 438 Solution pump, 464, 465f, 469 Soret effect, 1044 Sorption, 476 Spain, ventilation systems in, 517e518 Spanish legislation, 985e986 transposition to, 22e25 Spatial description of motion, 1012e1013 Spatial points, 1012 Specific constant heat, 362 Specific Exergy Costing (SPECO), 651, 655e656

1090

Speed of light, 148 SPERnet. See Net seasonal primary poweractive ratio (SPERnet) SPF. See Seasonal performance factor (SPF) Sprayed polyurethane foam, 984e985 SPxF. See Seasonal exergy efficiency factor (SPxF) ST. See Symbolic thermoeconomics (ST) Stable thermal source, 392 Standard boilers, 374 Standard chemical exergy, 208 calculation, 218e234 alternative method, 223e225 examples, 226e234 by general method, 221e223 substances present in RE, 219e220 Standard conditions (STC), 532 Standard effective temperature (SET), 320 Standard entropy of reaction, 215 Standard states, 212e213 Standing boilers, 374 Stanton number (St number), 1058 Statistical thermodynamics, 74e75, 74f, 78 STC. See Standard conditions (STC) Steady-state method, 303e304 Steam boiler, 584, 584f Stirling engines, 45, 415e416, 416f Stochastic programming, 926 Stone materials, 234 Storage period, 441, 443 Storage tank, 960 Stress tensor, 1017e1019, 1018f vector, 1017 Structural methods, 963e964 Sub-product flows, 611 Sublimation, 390e391 Substances present in RE, 219e220 Substation of district heating system, 422, 422f Sun-air temperature, 295e296 Superstructure, 948 methods based on, 920 Supply-driven model, 665e680 Surface force, 1018 Sustainability, 792e798 in buildings, 798e802 conventional methodologies for analysis, 802e816

Index

energy and, 10e14 externalities, 12e14, 13f life cycle, 11e12, 11f limited nature of natural resources, 14 environmental externalities, 794e796 exergy and, 817e822 methodologies for analysis, 822e840 life cycle, 793e794 limitation of resources, 797e798 social externalities, 796e797 sustainable construction, 799e802 Sustainable building, 60e61, 799 Sustainable construction, 61 Symbolic computation, 666 Symbolic exergoeconomics, 664 Symbolic thermoeconomics (ST), 629, 664 FP and PF representations with residues, 697e716 FP representation or supply-driven model, 665e680 representation PF or demand-driven model, 680e697 in thermal installations analysis, 716e717 Synthesis problem, 919e920 of thermal system design, 917 Systems of simple continuous flow, 45 T TABS. See Thermo-Active Building Systems (TABS) Technical Building Code (TBC), 22e23, 518 Technical savings, 725 Technology, 5e6 TES. See Thermal energy storage systems (TES) TFA. See Thermoeconomic Functional Analysis (TFA) Thermal comfort, exergy and, 316e325 standards, 318e321 thermal model of human body and energy balance, 321e323 Thermal component of physical flow exergy, 136e137 Thermal compressor, 457 Thermal conductivity, 415 Thermal conversion, 529 Thermal demands, 939, 948, 955

Index

Thermal energy, 421e422. See also Solar energy efficiency, 537 flow vector, 1040 management system, 417e418 supply, 960 Thermal energy storage systems (TES), 421, 438, 439fe440f, 938 conventional energy analysis, 440e442 examples, 445e450 exergy analysis, 442e445 integration, 941 preliminary considerations, 438e440 Thermal friction, 1041 Thermal inertia, 34, 272e273 Thermal installation in building, 558, 722 optimization design of, 928e962 ST in analysis, 716e717 Thermal insulation, 26e28 into air chamber, 983 on interior, 982e983 Thermal irreversibilities, exergy destruction due to, 173e175 Thermal loads and energy demand, 326e327 Thermal mass, 272 Thermal model of human body, 321e323 Thermal modules, 529e548 Thermal oil, 419 Thermal radiation, exergy of, 148e167 examples, 163e167 exergy of blackbody radiation, 156e159 destruction in heat exchange, 160e161 of solar radiation, 161e163 review of preliminary concepts, 148e155 absorptivity, reflectivity and transmissivity, 152e153 blackbody radiation, 149e151 grey and diffuse surfaces, 151 heat traps, 154e155 Kirchhoff’s law, 153e154 thermodynamics of blackbody radiation, 155e156

1091

Thermal storage, 47 Thermal system design, 912 distribution system of experimental installation, 916f energy rehabilitation of buildings, 980e1001 mathematical formulation of optimization, 920e924 mathematical optimization methods, 924e927 modelling and simulation, 914e916 optimization in thermal installations design, 928e962 problem of synthesis, 919e920 stages in, 917e920 thermoeconomics application to thermal systems design, 962e980 methodology for analysis, 848, 848t Thermal/photovoltaic modules (PVT), 537 Thermo-Active Building Systems (TABS), 34e35 Thermo-active foundations, 35e36, 36f Thermo-active slabs, 34e35 Thermochemical storage, 39, 439 Thermochromic glass, 28 Thermodynamic(s), 5e6, 61, 68e76, 717 analysis, 559 of blackbody radiation, 155e156 cycle, 390 efficiency, 577 and energy, 75e76 first law of, 77e98 formulations, 70e73 method, 775 model of absorption refrigerator, 975 of biomass combustion chamber, 975 of ORC cycle, 974 notions of multicomponent systems, 210e218 chemical potential, 211e212 enthalpy of formation, 213e214 enthalpy of reaction and entropy of reaction, 214e216 Gibbs potential of formation and Gibbs potential of reaction, 216e217

1092

Thermodynamic(s) (Continued) maximum work and change of Gibbs potential, 217e218 standard states, 212e213 pressure, 1018 properties, 724 second law of, 98e101 state approaches, 362 statistical, 74e75 study, 897 system, 68 temperature, 370, 538 scale, 69 TIP, 73e74 variables, 69, 1010 Thermodynamics of Continuous Media, 73e74, 1009e1010, 1022, 1045 Thermodynamics of Equilibrium, 72e73 Thermodynamics of Irreversible Processes (TIP), 73e74 Thermoeconomic Functional Analysis (TFA), 651e655, 652f Thermoeconomics, 56, 168, 558e563, 724, 771 diagnosis, 560, 725e728, 743f intrinsic anomalies and induced anomalies, 727e728 maintenance operations in air conditioning installation, 727f exergy analysis of systems, 595e598 cost accounting and, 598e604 cost theory, 605e651 isolation principle, 927 mass, energy and exergy balances, 564e572 methods of allocating costs, 651e656 optimization of rehabilitation based on, 990e993 physical structure of installations, 563e564 productive structure of installations, 572e595 thermal installations of buildings, 558 Thermoeconomics application to thermal systems design, 962e980 absorption refrigerator, 979 energy balance, 975 examples, 968e980 exergy balance, 976

Index

heuristic method for successive approximations, 966e968 local optimization, 965e966 mass balance, 975 optimization through calculus, 964e965 ORC cycle pump, 978 evaporator, 979 heat exchanger, 978 turbine, 978 thermodynamic model of absorption refrigerator, 975 of biomass combustion chamber, 975 of ORC cycle, 974 Thermomechanical exergy, 1048 Thermomechanical flow exergy, 136e137 Thin-film panels, 530e531 Three-way valves, 363e365 exergy destruction in flows mixture, 365f mixing valve in heating system, 364f operation of mixing valve, 363f Throttle valve, 579, 579f Tidal energy, 8 TIP. See Thermodynamics of Irreversible Processes (TIP) TMY. See Typical meteorological year (TMY) Transfer function, 914 Transfer heat, 390 Translucent metallic screens, 31 Transmissivity, 152e153 Transport theorem, 1014e1016 Tri-Thermic system of cold production, 478 Trigeneration, 46, 46f, 456 Trigeneration facility of hospital, 894e905 building and thermal facility, 894e897, 896f components and flows, 897t energy analysis, 901e902 exergoeconomic costs, 904e905 exergy analysis, 902e903 costs, 903e904 functional analysis, 897e901 impact on CO2 emissions, 905 numbering, symbols and brief descriptions, 897t

Index

TRNSYS software, 293e294, 308, 327, 359, 777 TRNSYS v 17, 767, 884e885 Tubular exchangers, 367 Turbine, 974 Turbulence, 1021e1022 Turbulent flow, 1021 Turbulent motion, 1021 Typical meteorological year (TMY), 939 U UF. See Functional unit (UF) Ultrasonic humidification, 493 Unavoidable costs, exergy destruction and, 771e773, 781f Uni-objective programming, 926, 929 Unit consumption of exergy, 742 Unit exergoeconomic costs, 618 Unit exergy consumption, 577e579 cost, 599, 608, 695 Unit prices, 847, 848t Unit product exergy costs, 713 Unity, 427 Upstream installation, 733e734 Utilization factor, 430 V Vacuum insulation panels (VIP), 27, 27f Vacuum tubes, 44, 534 van’t Hoff box, 217 Vapour quality, 192 Vapourization, 390e391 Variable costs, 600 Variation of irreversibility, 728 Vegetable roofs, 32 Ventilated façades, 30, 30f, 917, 982 Ventilation installations, 518e519 systems, 45, 516e529 air quality and regulatory development of ventilation in Spain, 517e518 energy and exergy analysis of ventilation system, 521e523

1093

examples, 524e529 heat recuperators, 519e521 types of ventilation installations, 518e519 VIP. See Vacuum insulation panels (VIP) Viscous dissipation, 1056 Viscous stress, 1017e1018 Volatile Organic Compounds (VOC), 517 Volumetric phenomenon, 149 W Wall boilers, 374 Waste, 558e559 Water exergy, 235e236 humidifying or dehumidifying by mixing with, 493e494 air humidification, 494f humidification by means of sprayers, 493f vapour, 388 water-tube boilers, 373 Water/glycol receives heat, 449 Water/sulfuric acid, 456 Water/water heat pumps, 43 Watts steam engine, 76, 76f Wave energy, 6 Weighting factor (WF), 395 Weighting system, 20 Wet fluids, 419 WF. See Weighting factor (WF) Wien’s displacement law, 149e150 Wind energy, 6 Wood boilers, 43 Wood fibre, 26 Z Z transform method, 328 Zero-ELCA, 825 Zero-energy building (ZEB), 996 Zeroth law of thermodynamics, 69