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)

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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.

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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