Strategic planning for the sustainable production of biofuels 9780128181782, 0128181788

Table of contents :
Content: 1. Introduction 2. Involving environmental aspect in the strategic planning of a biomass conversion system 3. Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives 4. Distributed biorefining networks for the valued-added processing of water hyacinth 5. Optimization of the supply chain associated to the production of bioethanol from residues of the agave from the tequila process in Mexico 6. Financial risk assessment and optimal planning of biofuels supply chains under uncertainty 7. Stochastic design of biorefinery supply chains considering economic and environmental objectives 8. Mixed-integer dynamic optimization or planning distributed biorefineries Appendix A. GAMS code for the model of Chapter 2 B. GAMS code for the model of Chapter 3 C. GAMS code for the model of Chapter 4 D. GAMS code for the model of Chapter 6 E. GAMS code for the model of Chapter 7 F. GAMS code for the model of Chapter 8

Citation preview

Strategic Planning for the Sustainable Production of Biofuels

Strategic Planning for the Sustainable Production of Biofuels Jose´ Marı´a Ponce-Ortega Universidad Michoacana de San Nicola´s de Hidalgo, Morelia, Mexico

˜ez-Aguilar Jose´ Ezequiel Santiban Tecnologico de Monterrey, Monterrey, Mexico

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright r 2019 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. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-12-818178-2 For Information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

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Preface Biorefinery systems are a well-suited solution for replacing fossil fuels. Several aspects need to be taken into consideration when implementing such a system, including the selection of feedstocks, processing routes, products, sites for harvesting, processing and markets, in addition to different sustainability criteria. Optimal planning of biorefinery systems is an important task. But it is a complicated task that involves making decisions about the aforementioned aspects. To this end, this book presents general optimization models that can be used by researchers, students and decision makers for the design and planning of sustainable biorefinery supply chains. The mathematical formulations provided here take into account relevant issues such as biomass feedstocks available in multiple harvesting sites, availability and seasonality of biomass resources, different geographical locations for processing plants that produce multiple products using diverse production technologies, economies of scale for the production technologies, demands and prices of multiple products in different markets, locations of storage facilities and a number of transportation modes between the supply chain components. Sustainability is incorporated into the proposed models by including simultaneous economic, environmental and social performance in the evaluation of the supply chain designs. This text uses GAMS and MATLAB software to code and solve the different supply chain planning problems, something not found in similar books. GAMS makes it easy to implement optimization formulations, and MATLAB helps with the subroutines. Several case studies for the strategic planning of biorefinery systems are also presented in this book, and the corresponding data are incorporated in the optimization code given. It is thus easy to modify the GAMS code for different case studies by incorporating the proper data. The content of this book is described as follows. Chapter 1, Introduction, offers an introduction to supply chain management in biorefining systems and introduces the basic concepts used in the strategic planning of such along with a literature review. Chapter 2, Environmental Aspects in the Strategic Planning of a Biomass Conversion System, presents a multiobjective optimization model based on a mathematical

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programming formulation for the optimal planning of a biorefinery, considering the optimal selection of feedstock, processing technology and multiple products. The multiobjective optimization problem simultaneously considers profit maximization and environmental impact minimization. The economic objective function takes into account the availability of bioresources, processing limits and demand of products, as well as the costs of feedstocks, products and processing routes, while the environmental assessment includes the overall environmental impact measured through the ecoindicator-99 based on lifecycle analysis methodology. Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives, presents a multiobjective, multiperiod mixed-integer linear program that seeks to maximize the profit of the supply chain, to minimize its environmental impact and to maximize the number of jobs generated by its implementation. The environmental impact is measured by the ecoindicator-99 according to the lifecycle assessment technique, and the social objective is quantified by the number of jobs generated. The Pareto-optimal solutions are obtained using the ε-constraint method. To illustrate the capabilities of the proposed multisite system model, a case study addressing the optimal design and planning of a biorefinery supply chain to fulfill the expected ethanol and biodiesel demands in Mexico is presented. Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, presents a general superstructure and a mathematical programming model for the sustainable elimination of water hyacinth through a distributed biorefining network. The proposed model optimizes the selection of the products, the siting and sizing for the processing facilities and the selection of the markets while accounting for technical and economic constraints. A case study for the central part of Mexico, where water hyacinth is a serious problem, is used to show the applicability of the proposed holistic approach. The results show that an optimally synthesized distributed biorefining network is capable of the sustainable and economic elimination of water hyacinth from contaminated water bodies while generating value. Additionally, the results shown through Pareto curves allow the identification of a set of optimal solutions featuring tradeoffs between the economic and the environmental objectives. Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol From Residues of Agave from the Tequila Process in Mexico, presents an optimization framework for designing a supply chain for the bioethanol production from residues of agave bagasse obtained in the tequila processing in Mexico, where central and distributed bioethanol processing plants are considered. The bioethanol production process in the central and distributed plants is modeled according to conversion factors for the different processing steps obtained from experimental data. The proposed optimization formulation also considers the total available agave and the bioethanol demand in Mexico. Several

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scenarios are analyzed for the bioethanol production from agave bagasse in Mexico, where positive results are obtained from the reuse of residues of agave bagasse for the bioethanol production with considerable profits and satisfying a significant demand of the gasoline required in the zone. Chapter 6, Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains Under Uncertainty, presents a mathematical programming model for the optimal planning of a distributed system of biorefineries that considers explicitly the uncertainty associated with the supply chain operation as well as the associated risk. The capabilities of the approach proposed are demonstrated through its application to the production of biofuels in Mexico considering multiple raw materials and products. Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, presents an approach to optimal planning with an uncertain price of feedstock for a biomass conversion system involving both economic and environmental issues. The environmental impact is measured using ecoindicator-99 and the economic aspect is considered through the net annual profit. On the other hand, the uncertain raw material price was considered by the stochastic generation of scenarios using the Latin Hypercube method followed by the implementation of the Monte-Carlo method, where a deterministic optimization problem was solved for each of the scenarios to select the structure of the more robust supply chain relying on statistical data. The proposed approach was applied to a case study of a distributed biorefinery system in Mexico. Chapter 8, Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries, presents a dynamic optimization model for the optimal planning of a distributed biorefinery system taking into account the time dependence of the involved variables and parameters. In addition, this chapter incorporates a model predictive control methodology to obtain the behavior of the storages and orders of the supply chain, where the objective function is the difference between the required and satisfied demands in the markets. Thus, this study considers relevant issues including multiple available biomass feedstocks at various harvesting sites, the availability and seasonality of biomass resources, potential geographical locations for processing plants that produce multiple products using diverse production technologies, economies of scale for the production technologies, demands and prices of multiple products in each consumer, locations of storage facilities and a number of transportation modes between the supply chain components. The model was applied to a case study for a distributed biorefinery system in Mexico. Finally, the authors wish to acknowledge the Universidad Michoacana de San Nicola´s de Hidalgo and the Tecnologico de Monterrey for giving them the opportunity to work on this important project as well as the needed support to finish it.

CHAPTER 1

Introduction 1.1 Importance of Biofuels and Biorefineries Currently, the increasing demand for energy around the world has led to several challenges associated with the use of fossil fuels. In addition to the continuous depletion of fossil fuel reserves, there are substantial problems related to the climate change caused by greenhouse gas emissions (GHGE) from burning fossil fuels. These challenges have spurred research to develop new sources of energy and modern low-carbon technologies that can reduce the negative environmental impact by fossil fuels and improve the economic and social aspects of sustainability. In this context, biomass has gained considerable attention as a feedstock for energy production because of its attractive characteristics, including its availability as a renewable resource, reduction in the GHGE life cycle, creation of new infrastructure, and associated jobs and flexibility to produce a wide variety of products. The inherent flexibility of biomass feedstocks to produce several products (biofuels, polymers, specialty chemicals, etc.) has encouraged an increasing body of research to investigate the synthesis of processing pathways or technologies for designing better biorefineries. Recently, Bao, Ng, Tay, Jime´nez-Gutie´rrez, and El-Halwagi (2011) developed a shortcut method to synthesize and screen integrated biorefineries. In this approach, a structural representation is used to track individual chemicals while allowing the processing of multiple chemicals in production technologies. Ng (2010) presented an optimization-based automated targeting procedure to determine the maximum biofuel production and revenue levels in an integrated biorefinery. A novel and systematic two-stage approach to synthesize and optimize a biorefinery configuration given available feedstocks and desired products was proposed by Pham and El-Halwagi (2012). In addition, Ponce-Ortega, Pham, ElHalwagi, and El-Baz (2012) proposed a new general systematic approach to selecting optimal pathways for a biorefinery design. Furthermore, Aksoy, Cullinan, Sammons, and Eden (2008) proposed a method to design integrated biorefineries. However, previous approaches have not considered optimizing the supply chain (SC) for biorefineries.

1.2 Strategic Planning With respect to the SC optimization of biorefineries, Sammons, Eden, Yuan, Cullinan, and Aksoy (2007) proposed a systematic framework to optimize the product portfolio and Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00001-8 © 2019 Elsevier Inc. All rights reserved.

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process configuration in integrated biorefineries. Subsequently, Sammons et al. (2008) developed a methodology to assist the bioprocessing industry in evaluating the profitability of different possible production routes and product portfolios while maximizing stakeholder value through the mixed-integer linear programming (MILP) model presented by Van Dyken, Bakken, and Skjelbred (2010). This model was developed to design biomass-based SCs. Elms and El-Halwagi (2009) presented a procedure to schedule and operate biodiesel plants considering various feedstock options. Bowling, Ponce-Ortega, and El-Halwagi (2011) included the effect of economies of scale on the selection, sizing, location, and planning of a multisite biorefinery system. Akgul, Zamboni, Bezzo, Shah, and Papageorgiou (2011) presented MILP models to optimally design the bioethanol SC. Aksoy et al. (2011) studied four biorefinery technologies for feedstock allocation, optimum facility location, economic feasibility, and their economic impacts on Alabama. A mixed-integer nonlinear programming optimization model for a sustainable design and behavior analysis of the sugar and ethanol SC was proposed by Corsano, Vecchietti, and Montagna (2011). Furthermore, Kim, Realff, Lee, Whittaker, and Furtner (2011) presented a general optimization model that enables the selection of fuel-conversion technologies, capacities, biomass locations, and the logistics of transportation from forestry resource locations to the conversion sites and final markets. Mansoornejad, Chambost, and Stuart (2010) presented a methodology that links product/process portfolio design for making optimal long-term decisions for forest biorefineries. It is worth noting that previous approaches have only included different economic objectives for optimizing biorefinery SCs. To assess the environmental impact, Cherubini et al. (2009) evaluated different technologies for biofuel production based on the energetic efficiency while considering the environmental impact using a single optimization approach. This approach does not include trade-offs between economic and environmental objectives. Herva, Franco, Carrasco, and Roca (2011) classified a series of environmental indicators that can be applied to evaluate production processes and products. Hugo and Pistikopoulos (2005) presented a multiobjective optimization approach to consider economic and environmental objectives in the SC optimization problem. Zamboni, Shah, and Bezzo (2009) proposed a general modeling framework to drive the decision-making process to strategically design biofuel SC networks, where the design task was formulated as an MILP problem that considers the simultaneous minimization of the SC operating costs and the environmental impact (measured in terms of GHGE). An MILP optimization approach to designing sugar-based SC biorefineries that involves economic and environmental concerns was reported by Mele, Guille´n-Gosa´lbez, and Jime´nez (2009). You and Wang (2011) presented an optimization model to design and plan biomass and liquid SCs based on economic and environmental criteria; this approach was illustrated through a case study for the state of Iowa. Elia, Baliban, Xiao, and Floudas (2011) developed an MILP formulation to analyze the US energy SC network for hybrid coal, biomass, and natural gas-to-liquids facilities.

Introduction 3 A multiobjective optimization model to optimize a biorefinery was reported by Santiban˜ezAguilar, Gonza´lez-Campos, Ponce-Ortega, Serna-Gonza´lez, and El-Halwagi (2011), an approach that simultaneously maximized profit while minimizing environmental impact. Recently, You, Tao, Graciano, and Snyder (2012) proposed a new approach to optimally plan biofuel SCs considering economic, environmental, and social objectives. However, these previously reported methodologies to optimize biorefinery SCs have not simultaneously considered the sustainability criteria.

1.3 Optimization Optimization refers to finding the best solution of a given problem, accounting for specific limitations. Mathematically, optimization is used to maximize or minimize a given objective function subject to a set of equality and/or inequality constraints, where there are a set of degrees of freedom involved. Optimization problems can be classified as linear and nonlinear and continuous or discrete. Furthermore, when more than one objective is considered, the optimization problems are classified as mono- or multiobjective depending on the number of objective functions. It should be noted that software such as GAMS (Brooke, Kendrick, Meeruas, & Raman, 2011) can be used to solve all these problems, and in this book such software was used to implement the presented optimization model.

1.4 Sustainability During the last three decades, several authors have developed diverse assessment frameworks that integrate a number of dimensions required for sustainable development, which is defined as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (WCED, 1987). In this context, Jansen (2003) identified three relevant dimensions for sustainable development: the interactions between culture, structure, and technology; the optimization/improvement/ renewal approaches; and the parts involved. Vachon and Mao (2008) assessed the linkage between SC characteristics and three suggested dimensions of sustainability, namely, environmental performance, corporate environmental practices, and social sustainability. An overview of the environmental, social, and economic footprints indicators that can be used to measure sustainability was presented by Cucek, Klemes, and Kravanja (2012). Recently, Lozano (2008) proposed the concept of two-tiered sustainability equilibria for depicting sustainability. This concept centers on the interaction between economic, environmental, and social, as well as other aspects over time. After analyzing sustainability reports from three companies using a holistic perspective, Lozano and Huisingh (2011) identified the connections between the economic, ecological, and social dimensions and, in certain cases, were able to relate these connections to time. These authors proposed a new category, “interlinked issues and dimensions,” as the final stage in sustainability reporting analysis.

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The interlinked category could help companies address the short- and long-term ecological/ societal horizons along with their economic scope. In an additional study, Lozano (2012) provided an analysis of 16 of the most widely used initiatives that have been developed to contribute to sustainability factors (economic, environmental, social, and time). This researcher proposed the “Corporate Integration of Voluntary Initiatives for Sustainability” framework to understand and apply the corporate sustainability initiatives better.

1.5 Description of the Book This book presents several optimization strategies for the optimal planning of biorefining systems. For all the presented optimization strategies, the corresponding GAMS code has been included Chapter 2, Involving Environmental Aspect in the Strategic Planning of a Biomass Conversion System, presents an optimization formulation for the optimal planning of distributed biorefining systems that consider economic and environmental aspects. In Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives, the social dimension of sustainability is included as a third objective function. In Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, an optimization formulation for the optimal planning of distributed biorefining systems for the proper use of water hyacinth is given, whereas Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol From Residues of Agave From the Tequila Process in Mexico, considers agave residues. Chapter 6, Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains Under Uncertainty, looks at the financial risk involved in the planning of a biorefining system, and Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, considers the stochastic optimization of distributed biorefining systems. Finally, Chapter 8, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, presents a dynamic optimization approach for the optimal planning of biorefining systems.

References Akgul, O., Zamboni, A., Bezzo, F., Shah, N., & Papageorgiou, L. G. (2011). Optimization-based approaches for bioethanol supply chains. Industrial and Engineering Chemistry Research, 50(9), 4927 4938. Aksoy, B., Cullinan, H. T., Webster, D., Gue, K., Sukumaran, S., Sammons, N. E., Jr., . . . Eden, M. R. (2011). Woody biomass and mill waste utilization opportunities in Alabama: Transportation cost minimization, optimum facility location, economic feasibility, and impact. Environmental Progress and Sustainable Energy, 30(4), 720 732. Aksoy, B., Cullinan, H. T., Sammons, N. E., Jr., & Eden, M. R. (2008). Identification of optimal poultry litter biorefinery location in Alabama through minimization of feedstock transportation cost. Journal of Environmental Progress, 27(4), 515 523. Bao, B., Ng, D. K. S., Tay, D. H. S., Jime´nez-Gutie´rrez, A., & El-Halwagi, M. M. (2011). A shortcut method for the preliminary synthesis of process-technology pathways: An optimization approach and application

Introduction 5 for the conceptual design of integrated biorefineries. Computers and Chemical Engineering, 35(8), 1374 1383. Bowling, I. M., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2011). Facility location and supply chain optimization for a biorefinery. Industrial and Engineering Chemistry Research, 50(10), 6276 6286. Brooke, A., Kendrick, D., Meeruas, A., & Raman, R. (2011). GAMS-language guide. Washington, DC: GAMS Development Corp. Cherubini, F., Bird, N. D., Cowie, A., Jungmeier, G., Schlamadinger, B., & Woess-Gallasch, S. (2009). Energy and greenhouse gas-based LCA of biofuel and bioenergy systems: Key issues, ranges and recommendations. Resources Conservation and Recycling, 53(8), 434 447. Corsano, G., Vecchietti, A. R., & Montagna, J. M. (2011). Optimal design for sustainable bioethanol supply chain considering detailed plant performance model. Computers and Chemical Engineering, 35(8), 1384 1398. Cucek, L., Klemes, J. J., & Kravanja, Z. (2012). A review of footprint analysis tools for monitoring impacts on sustainability. Journal of Cleaner Production, 34, 9 20. Elia, J. A., Baliban, R. C., Xiao, X., & Floudas, C. A. (2011). Optimal energy supply network determination and life cycle analysis for hybrid coal, biomass and natural gas to liquid (CBGTL) plants using carbon-based hydrogen production. Computers and Chemical Engineering, 35(8), 1399 1430. Elms, R. D., & El-Halwagi, M. M. (2009). Optimal scheduling and operation of biodiesel plants with multiple feedstocks. International Journal of Process Systems Engineering, 1(1), 1 28. Herva, M., Franco, A., Carrasco, E. F., & Roca, E. (2011). Review of corporate environmental indicators. Journal of Cleaner Production, 19, 1687 1699. Hugo, A., & Pistikopoulos, E. N. (2005). Environmentally conscious long-range planning and design of supply chain networks. Journal of Cleaner Production, 13(15), 1471 1491. Jansen, L. (2003). The challenge of sustainable development. Journal of Cleaner Production, 11(3), 231 245. Kim, J., Realff, M. J., Lee, J. H., Whittaker, C., & Furtner, L. (2011). Design of biomass processing network for biofuel production using an MILP model. Biomass and Bioenergy, 35(2), 853 871. Lozano, R. (2008). Envisioning sustainability three-dimensionally. Journal of Cleaner Production, 16(17), 1838 1846. Lozano, R. (2012). Towards better embedding sustainability into companies’ systems: An analysis of voluntary corporate initiatives. Journal of Cleaner Production, 25, 14 26. Lozano, R., & Huisingh, D. (2011). Inter-linking issues and dimensions in sustainability reporting. Journal of Cleaner Production, 19(2 3), 99 107. Mansoornejad, B., Chambost, V., & Stuart, P. (2010). Integrating product portfolio design and supply chain design for the forest biorefinery. Computers and Chemical Engineering, 34(9), 1497 1506. Mele, F. D., Guille´n-Gosa´lbez, G., & Jime´nez, L. (2009). Optimal planning of supply chains for bioethanol and sugar production with economic and environmental concerns. Computer Aided Chemical Engineering, 26, 997 1002. Ng D.K.S. (2010). Automated targeting for the synthesis of an integrated biorefinery. Chemical Engineering Journal, 162(1), 67 74. Pham, V., & El-Halwagi, M. M. (2012). Process synthesis and optimization of biorefinery configurations. AIChE Journal, 58(4), 1212 1221. Ponce-Ortega, J. M., Pham, V., El-Halwagi, M. M., & El-Baz, A. (2012). A disjunctive programming formulation for the optimal design of biorefinery configurations. Industrial and Engineering Chemistry Research, 51(8), 3381 3400. Sammons, N., Jr, Eden, R. M., Yuan, W., Cullinan, H., & Aksoy, B. (2007). A flexible framework for optimal biorefinery product allocation. Environmental Progress and Sustainable Energy, 26(4), 349 354. Santiban˜ez-Aguilar, J. E., Gonza´lez-Campos, J. B., Ponce-Ortega, J. M., Serna-Gonza´lez, M., & El-Halwagi, M. M. (2011). Optimal planning of a biomass conversion system considering economic and environmental aspects. Industrial and Engineering Chemistry Research, 50(14), 8558 8570.

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Vachon, S., & Mao, Z. (2008). Linking supply chain strength to sustainable development: A country-level analysis. Journal of Cleaner Production, 16(15), 1552 1560. Van Dyken, S., Bakken, B. H., & Skjelbred, H. I. (2010). Linear mixed-integer models for biomass supply chains with transport, storage and processing. Energy, 35(3), 1338 1350. WCED (World Commission on Environment and Sustainable Development). (1987). Our common future (The Brundtland Report). Oxford, Bungay, Suffolk, UK: Oxford University Press. You, F., & Wang, B. (2011). Life cycle optimization of biomass-to-liquids supply chains with distributedcentralized processing networks. Industrial and Engineering Chemistry Research, 50(17), 10102 10127. You, F., Tao, L., Graciano, D. J., & Snyder, S. W. (2012). Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with life cycle assessment and input output analysis. AIChE Journal, 58(4), 1157 1180. Zamboni, A., Shah, N., & Bezzo, F. (2009). Spatially explicit static model for the strategic design of future bioethanol production systems. 2. Multi-objective environmental optimization. Energy and Fuels, 23(10), 5134 5143.

Further Reading Castro, P. M., & Grossmann, I. E. (2006). An efficient MILP model for the short-term scheduling of single stage batch plants. Computers and Chemical Engineering, 30(6 7), 1003 1018. Chouinard-Dussault, P., Bradt, L., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2011). Incorporation of process integration into life cycle analysis for the production of biofuels. Clean Technologies and Environmental Policy, 13(5), 673 685. Diwekar, U. M. (2003). Introduction to applied optimization. Norwell, MA: Kluwer Academic Press. Dutta, A., Dowe, N., Ibsen, K. N., Schell, D. J., & Aden, A. (2010). An economic comparison of different fermentation configurations to convert corn stover to ethanol using Z, mobilis and saccharomyces. Biotechnology Progress, 26(1), 64 72. Geodkoop, M., Spriensma, R. (2001). The eco-indicator 99, a damage oriented for life cycle impact assessment: Methodology report and manual for designers. Technical report. Amersfoort, The Netherlands: PRe Consultants. Guinee, J. B., Gorree, M., Heijungs, R., Huppes, G., Kleijn, R., Van Duin, R., . . . Huijbregts, M. A. J. (2002). Handbook on life cycle assessment: Operational guide to the ISO standards. Dordrecht, The Netherlands: Kluwer Academic Publishers. Holladay, J. E., Bozell, J. J., White, J. F., Johnson, D. (2007). Top value-added chemicals from biomass. Volume II: Results of screening for potential candidates from biorefinery lignin. Report No. PNNL-16983, Washington, DC: Pacific Northwest National Laboratory. Huber, G. W., Iborra, S., & Corma, A. (2006). Synthesis of transportation fuels from biomass: Chemistry, catalysts, and engineering. Chemical Reviews, 106(9), 4044 4098. Kazi, F., Fortman, J., Anex, R., Kothandaraman, G., Hsu, D., Aden, A., & Dutta, A. (2010). Techno-economic analysis of biochemical scenarios for production of cellulosic ethanol. Golden, CO: National Renewable Energy Laboratory, NREL/TP-6A2-46588, Denver, USA. Maravelias, C. T., & Grossmann, I. E. (2003). New general continuous-time state-task network formulation for short-term scheduling of multipurpose batch plants. Industrial and Engineering Chemistry Research, 42 (19), 3056 3074. Pokoo-Aikins, G., Nadim, A., Mahalec, V., & El-Halwagi, M. M. (2010). Design and analysis of biodiesel production from algae grown through carbon sequestration. Clean Technologies and Environmental Policy, 12(3), 239 254. Ponce-Ortega, J. M., Jimene´z-Gutie´rrez, A., & Grossmann, I. E. (2008). Optimal synthesis of heat exchanger networks involved isothermal process streams. Computers and Chemical Engineering, 32(8), 1918 1942.

Introduction 7 Sammons, N. E., Jr, Yuan, W., Eden, M. R., Aksoy, B., & Cullinan, H. T. (2008). Optimal biorefinery product allocation by combining process and economic modeling. Chemical Engineering Research and Design, 86 (7), 800 808. Saxena, R. C., Adhikari, D. K., & Goyal, H. B. (2009). Biomass-based energy fuel through biochemical routes: A review. Renewable and Sustainable Energy Reviews, 13(1), 167 178. Saxena, R. C., Seal, D., Kumar, S., & Goyal, H. B. (2008). Thermo-chemical routes for hydrogen rich gas from biomass: A review. Renewable and Sustainable Energy Reviews, 12(3), 1909 1927. Werpy, T., Petersen, G., Aden, A., Bozell, J., Holladay, J. (2004). Top value added chemicals from biomass. Volume I: Results of screening for potential candidates from sugars and synthesis gas. Washington, DC: Pacific Northwest National Laboratory (PNNL) and National Renewable Energy Laboratory (NREL). Zhu, Y., & Jones, S. (2009). Techno-economic analysis for the thermochemical conversion of lignocellulosic biomass to ethanol via acetic acid synthesis. Washington, DC: Pacific Northwest National Laboratory, PNNL-18483, Richland, WA, USA.

CHAPTER 2

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 2.1 Introduction This chapter presents a multiobjective optimization model based on a mathematical programming formulation for the optimal planning of a biorefinery, considering the optimal selection of feedstock, processing technology and a set of products. The multiobjective optimization model simultaneously considers the profit maximization and the environmental impact minimization. The economic objective function accounts for the availability of bioresources, processing limits and demand of products, as well as the costs of feedstocks, products and processing routes, while the environmental assessment includes the overall environmental impact measured through the ecoindicator-99 based on the lifecycle analysis methodology. Even though the economic and environmental objectives contradict each other, with the proposed methodology it is possible to obtain the Pareto curve that identifies the set of optimal solutions for both objectives. The proposed methodology is applied to a case study for planning of a biorefinery in Mexico.

2.2 Outline of the Optimization Model The problem addressed in this chapter can be described as follows: given a set of M available feedstocks, which can be converted into K different products and several byproducts B through different processing routes R; t is not easy to obtain the optimal products, processing routes and distribution, where there is not necessarily a single option to obtain the required products. Each processing route is associated with an efficiency of feedstocks to products and an efficiency for feedstocks to byproducts, which are identified as conversion factors ðαÞ. The optimal solution is the best combination of these sets of variables with the highest benefits from an economic and environmental perspective. The superstructure for the general problem addressed in this chapter is presented in Fig. 2.1. It should be noticed that a superstructure is a general representation of all the possible configurations where the optimal solution can be found. Note that this superstructure represents different options to select from. Of course, the decision is more complicated when the number of possible options increases, as is the case for the biorefinery production problem addressed in this chapter. Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00002-X © 2019 Elsevier Inc. All rights reserved.

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A conversion factor β (k,r,m,b) is used for by-products

A conversion factor α (k,r,m) is used for products

Bioresource 1

By-product 1

Product 1 Processing route 1 By-product 2

Bioresource 2

Processing route 2

Product 2

Processing route 3 Bioresource 3

Product 3

By-product 3

Processing route 4

Bioresource 4

Processing route 5

Product 4 By-product 4

Processing route r Bioresource m

Product k

By-product b

Figure 2.1 Proposed superstructure for the optimal planning of a biorefinery production system. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

2.3 Mathematical Model The indexes used are defined prior to presenting the model formulation. m represents the type of feedstock, r represents the processing route used for products yielded from bioresources, k is associated with the type of product and b corresponds to byproducts. The model formulation is described as follows.

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 11

2.3.1 Mass Balances Most of the formulations that involve the processing of feedstocks to products present nonlinearities, giving rise to nonconvex problems. By considering the conversion of feedstocks to products as a blackbox, the mass balance can be associated with an efficiency (conversion) factor for each processing technology, and then it is possible to linearize the mass balance. The number of equations for these balances depends on the number of possible feedstocks, processing routes, products and byproducts. For the main product k produced from the raw material m through the route r, the material balance can be stated as follows: Pkmr 5 αkmr Fkmr ;

kAP; mAM; rAR

(2.1)

where αkmr is the conversion factor for the product k from the bioresource m through the route r. Pkmr and Fkmr are the flow rates of products and raw materials, respectively. For the byproduct b yielded when the product k is produced from the raw material m through the route r, the following material balance is required: Bkmrb 5 β kmrb Fkmr ;

kAP; mAM; rAR

(2.2)

In the previous equation, β kmrb is the conversion factor for the amount of byproduct b produced when the bioresource m is processed through the route r to produce the main product k. Bkmrb is the flow rate of the byproduct b generated.

2.3.2 Maximum Availability for Feedstocks Besides the mass balances, a set of constraints are considered for the availability of feedstocks in a given region, since it is not possible to use more than the existing amount for its processing to the corresponding final products. The availability is restricted by the data for the specific region where the model is applied, and it is different for each feedstock. The maximum availability constraints can be stated as the sum of the quantities of the feedstock used in the manufacture of each product through each processing route, and it must be lower than the total amount of the feedstock available. These constraints are stated as follows: XX Fkmr # Fmmax ; mAM (2.3) k

r

In previous constraints, Fmmax is the maximum amount available for the bioresource m, and it is a parameter known prior to the optimization process.

2.3.3 Maximum Products Demand Another constraint considers the product demand to prevent higher production rates than necessary to avoid waste of sources and to guarantee its consumption.

12

Chapter 2 XX m

Pkmr # Pmax k ;

kAP

(2.4)

r

is a parameter that represents the maximum demand from product k. where Pmax k

2.3.4 Maximum Processing Limits Some constraints are also needed to consider the capacity of the involved technologies, which are stated as follows: Pkmr # Pmax kmr ;

kAP; mAM; rAR

(2.5)

where Pmax kmr is the maximum amount of the product k that can be produced from the bioresource m through the technology r.

2.3.5 Objective Functions The objective function considers simultaneously the maximization of the total profit and the minimization of the overall environmental impact as follows: Objective function 5 ½maxfProfitg; minEI

(2.6)

Profit is the total net revenue obtained for the sales of products and byproducts minus the costs for the raw materials and processing, whereas EI is the total environmental impact with respect to the use of bioresources, use of products and processing. The overall environmental impact is calculated through the processing route because this considers the use of resources and the generated wastes. It should be noted that both objectives contradict each other; that is, the maximum gain corresponds to the highest environmental impact (point C of Fig. 2.2), whereas the solution corresponding to the minimum environmental impact represents the minimum gain (point A of Fig. 2.2). Between these two extreme solutions, there is a set of optimal solutions (set of Pareto optimal solutions) that meet both objectives, and can help decision makers choose the solution that best fits the requirements of the project. Before we present the optimization procedure, the economic and environmental objectives are described.

2.3.6 Economic Objective The economic objective function is formulated in terms of the total annual profit. This function takes into account the costs of feedstocks, products, byproducts and the processing routes, and is stated as follows: XXX XXXX Profit 5 Pkmr Ckvalue 1 Bkmrb Cbvalue m r k b X Xk Xm r XXX (2.7) processing 2 Fkmr Cmcost 2 Pkmr Ckmr k

m

r

k

m

r

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 13

Figure 2.2 Pareto solution for the case studied. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

where Ckvalue is the net price for the product k including transportation, Cbvalue is the net price for the byproduct b, Cmcost is the cost for the bioresource m including the transportation from the processing is the processing cost for the route r from m to k. cropland to the processing facility and Ckmr However, Eq. (2.7) requires significant CPU time to determine the solution. Using Eq. (2.2) in Eq. (2.7) yields the following equation: XXX XXXX Profit 5 Pkmr Ckvalue 1 β kmrb Fkmr Cbvalue m r k b X Xk Xm r XXX (2.8) processing cost 2 Fkmr Cm 2 Pkmr Ckmr k

m

r

k

m

r

Eq. (2.8) decreases the number of variables by k 3 m 3 r 3 b, which helps to reduce significantly the CPU time needed to solve this problem.

2.3.7 Environmental Objective The environmental assessment includes the overall environmental impact measured through the ecoindicator-99 based on the lifecycle analysis methodology. Even though this

14

Chapter 2

methodology has regional and term limitations, it is an objective measure of the environmental impact caused by a specific substance, process or activity, since it is standardized, updated and accepted by the scientific community. The ecoindicator-99 is based on the lifecycle analysis methodology and takes into account 11 impact categories, which are classified into three main damage categories. These categories and subcategories are the following: 1. Damage to the human health. a. Carcinogenic effects on humans. b. Respiratory effects on humans caused by organic substances. c. Respiratory effects on human caused by inorganic substances. d. Human health effects caused by ionizing radiation. e. Human health effects caused by ozone layer depletion. f. Damages to human health caused by climate change. 2. Damage to the ecosystem quality. a. Damage to the ecosystem quality caused by ecotoxic emissions. b. Damage to the ecosystem quality caused by the combined effects of acidification and eutrophication. c. Damage to the ecosystem quality caused by land occupation and land conversion. 3. Damage to the resources. a. Damage to the resources caused by extraction of minerals. b. Damage to the resources caused by extraction of fossil fuels. The method to determine the ecoindicator-99 involves weights for the different impact categories to consider the involved trade-offs. This weighting is based on the ISO14042 and ISO14000 standards. There are three different perspectives to determine the ecoindicator-99 (i.e., hierarchical, egalitarian and individualist) and each has a weight for each damage category. From a hierarchical perspective, the considered time is large, and the substances are included in the damages only if there is a consensus with respect to their effect. In the hierarchical perspective, it is assumed that the damages can be avoided. With respect to fossil fuels, there is an assumption that they cannot be replaced easily. From the egalitarian perspective the time elected is large. The substances are included if there is no indication of their effect. In the egalitarian perspective, the damages cannot be avoided and catastrophic effects can be produced. Concerning fossil fuels, the assumption that the fossil fuels cannot be substituted is considered. From the individualist perspective, the elected time is short (100 years or less), and the substances are included if they have possible effects. In the individualist perspective, it is

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 15 assumed that the damages are subject to changes due to technological improvements. In the case of fossil fuels, it is assumed that the fossil fuels cannot be exhausted. In this chapter, the environmental objective function considers the global environmental impact, and the lifecycle is involved when the ecoindicators for resource extraction, product disposal and feedstock processing are considered. XXX EI 5 Fkmr Ecoindicatorresource m X kXmX r XXX (2.9) 1 Pkmr Ecoindicatordisposal 1 Pkmr Ecoindicatorprocessing k kmr k

m

r

k

m

r

, Ecoindicatordisposal where EI is the overall environmental impact, and Ecoindicatorresource m k and Ecoindicatorprocessing are the ecoindicators-99 for the resources, products and processing, kmr respectively. To determine these ecoindicators and to set them as parameters, lifecycle analysis for the bioresources, products and processing is needed prior to the optimization process. The methodology described by Geodkoop and Spriensma (2001) is used here to determine the overall ecoindicators applied. Ecoindicatorresource accounts for the overall m environmental impact for the feedstock production m as well as the transportation from the cropland to the processing facility; Ecoindicatordisposal considers the overall environmental k impact for the transportation, use and final disposal of the product k; and Ecoindicatorprocessing accounts for the overall environmental impact for the processing route. kmr

2.4 Solution Strategy The constraint method is implemented here (see Diwekar, 2003) to determine the set of optimal solutions that meet both objectives and that are used to build the Pareto curve. The addressed problem can be stated as follows: Objective function 5 ½max Profit; minEI s:t: Eqs: ð2:1Þ 2 ð2:5Þ

(2.10)

where Profit and EI are defined in Eqs. (2.8) and (2.9), respectively. First, to determine the point C of Fig. 2.2, the maximization of the Profit is carried out without considering the EI as follows: maxfProfitg s:t: Eqs: ð2:1Þ 2 ð2:5Þ

(2.11)

It is worth noting that usually the solution of previous model yields the solution with the maximum EI in the Pareto curve.

16

Chapter 2

Then, to determine the point A of Fig. 2.2, the minimization of EI without taking into account the Profit is solved as follows: minEI s:t: Eqs: ð2:1Þ 2 ð2:5Þ

(2.12)

The solution of the problem given by Eq. (2.12) usually produces the minimum Profit in the Pareto curve, because this model does not consider the Profit. These two extreme solutions (solutions C and A given by Eqs. (2.11) and (2.12), respectively) then are used as limits to build the Pareto curve by solving the following problem: maxfProfitg s:t: EI # ε Eqs: ð2:1Þ 2 ð2:5Þ

(2.13)

To yield the Pareto curve, the previous problem given by Eq. (2.13) is solved for different values of ε. The limits for ε are the EI obtained from solutions C and A given by Eqs. (2.11) and (2.12) that correspond to the maximum and minimum EI. The GAMS code for the model presented in this chapter is shown in Appendix A.

2.5 Case Study To test the proposed methodology, a case study to establish a biorefinery system in the central region of Mexico is used. This case involves 21 bioresources available in the central region of Mexico that can be used as feedstocks to obtain three products and eight byproducts; furthermore, there are ten different processing routes available. Note that although this problem corresponds to a specific region of Mexico, the model formulation can be applied to any region anywhere. The conversion factors for the different processing technologies were taken from the results obtained by Horta-Nogueira (2006), Trindade (2006), Lazcano-Martı´nez (2006), Mu¨ller-Langer, Probst, Thra¨n, and Weber (2006), and from existing technologies for producing biofuels developed in Brazil, the United States, the European Union and some Latin-American and Asian countries that have developed and implemented innovative technologies in this context. The data are presented in Table 2.1. Table 2.2 shows the processing costs for different processing routes from different available raw materials to the desired products used for the example presented. Additional required data such as feedstock, product and byproduct costs, availability and demand could come from governmental institutions depending on the region where the

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 17 Table 2.1: Conversion factors for different technologies for biofuels production given as the mass ratio of the amount of produced biofuel and input feedstock Product

Raw Material

Processing Route

Ethanol Wood chips Pretreatment acid hydrolysis and fermentation Ethanol Wood chips Gasification and biosynthesis Ethanol Wood chips Gasification and chemical synthesis Ethanol Wheat straw Pretreatment acid hydrolysis and fermentation Ethanol Wheat straw Production of ethanol with hydrogen from dark fermentation Hydrogen Oil palm shell Catalytic pyrolysis La/AL2O3 Hydrogen Oil palm shell Catalytic pyrolysis gama/Al2O3 Hydrogen Rice straw Catalytic pyrolysis Cr2O3 Hydrogen Sawdust Catalytic pyrolysis Cr2O3 Hydrogen Sawdust Catalytic pyrolysis nickel Hydrogen Commercial wood Catalytic pyrolysis Cu-MCM-41 Ethanol Sugarcane Pretreatment acid hydrolysis and fermentation Ethanol Wheat Pretreatment acid hydrolysis and fermentation Ethanol Corn grain Pretreatment acid hydrolysis and fermentation Ethanol Sorghum grain Pretreatment acid hydrolysis and fermentation Ethanol Cassava root Pretreatment acid hydrolysis and fermentation Ethanol Sugar beet Pretreatment acid hydrolysis and fermentation Ethanol Sweet sorghum Pretreatment acid hydrolysis and fermentation Biodiesel Soy Extraction and transesterification with methanol Biodiesel African palm oil Extraction and transesterification with methanol Biodiesel Sunflower Extraction and transesterification with methanol Biodiesel Castor Extraction and transesterification with methanol Biodiesel Cotton Extraction and transesterification with methanol Biodiesel Rapeseed Extraction and transesterification with methanol Biodiesel Jatropha Extraction and transesterification with methanol Biodiesel Sawflower Extraction and transesterification with methanol

Mass Ratio 0.1669 0.2625 0.1887 0.2723 0.1314 2.6000 2.6200 22.8700 25.7000 5.3000 0.8700 0.0592 0.2857 0.3149 0.2999 0.2999 0.0868 0.0553 0.1763 0.2064 0.2950 0.3543 0.1668 0.3595 0.3268 0.2850

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

model will be applied. In the case of Mexico, these data can come from institutions such as the Ministry of Agriculture (SAGARPA-SIAP, 2010), Ministry of Energy (SENER), Ministry of Economy (SE) and Ministry of Environment (SEMARNAT, 2006), and in the case of the United States this information could come from the Department of Energy and the Department of Agriculture. For the case study presented in this chapter, data from the SAGARPA-SIAP (2010) and SEMARNAT (2006) were used (see Table 2.3). Table 2.4 shows the cost and the availability for bioresources for the proposed scenario (based on the data for the SENER—Bioenergetics Production Program), whereas Tables 2.5 and 2.6 show the costs and demands for the products and byproducts in the proposed scenario. The impact factors were obtained by applying the lifecycle analysis methodology and considering the products, processes and associated activities (transportation, waste production, etc.) from cradle to grave. The impact factors were quantified by the ecoindicator-99 (Geodkoop & Spriensma, 2001; Guine´e et al., 2002). As mentioned above, an eco-indicator-99 was determined for each feedstock, product and processing route and

18

Chapter 2

Table 2.2: Conversion factors for different technologies for biofuel production given as the mass ratio of the amount of produced byproduct and input feedstock Product Raw Material

Processing Route

Byproduct

Mass Ratio

Hydrogen

0.0220

Ethanol

Wheat

Pretreatment acid hydrolysis and fermentation

Ethanol

Wheat

Pretreatment acid hydrolysis and fermentation

Ethanol

Corn grain

Pretreatment acid hydrolysis and fermentation

Ethanol

Corn grain

Pretreatment acid hydrolysis and fermentation

Ethanol

Sorghum grain Sorghum grain Cassava root Sugar beet Soy African palm oil Sunflower Rapeseed Jatropha Sawflower

Pretreatment acid hydrolysis and fermentation

Acetic acid Carbon dioxide Carbon dioxide Grain distillery Carbon dioxide Grain distillery Carbon dioxide Grain distillery Carbon dioxide Green foliage Dry pulp Cattle cake Oil palm

0.0315 0.1400

Sugarcane

Production of ethanol with hydrogen from dark fermentation Pretreatment acid hydrolysis and fermentation Production of ethanol with hydrogen from dark fermentation Pretreatment acid hydrolysis and fermentation

Ethanol

Wheat straw

Ethanol Ethanol

Wheat straw Wheat straw

Ethanol

Ethanol Ethanol Ethanol Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel

Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction Extraction Extraction Extraction

and and and and

transesterification transesterification transesterification transesterification

with methanol with methanol with methanol with methanol

Cattle Cattle Cattle Cattle

cake cake cake cake

0.0607 0.4300 0.2560 0.3333 0.2850 0.3333 0.2850 1.5000 0.0125 0.8000 0.0310 0.6130 0.5000 0.6510 0.7280

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

the ecoindicators for bioresources, products and processing technologies from cradle to grave are given in Tables 2.7, 2.8 and 2.9, respectively. The mathematical model for addressing the case study was coded in the software GAMS (Brooke, Kendrick, Meeruas, & Raman, 2018). The model consists of 1262 variables and 664 constraints and each one the Pareto solutions was solved using the solver CPLEX in no more than 0.016 seconds of CPU time on a computer with an i7 at 2.67 GHz processor with 9 GB of RAM. First, the solution for the minimum environmental impact (point A of Fig. 2.2) was obtained by solving the model formulation given by Eq. (2.12). This solution provided values of EI and Profit equal to zero points and zero million dollars, respectively (which means that nothing is produced and therefore the minimum environmental impact is equal to zero). Then, the problem for the maximum Profit (point C of Fig. 2.2) given by

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 19 Table 2.3: Processing costs for different raw materials, processing routes and products Product

Raw Material

Processing Route

Ethanol Ethanol Ethanol Ethanol Ethanol

Wood chips Wood chips Wood chips Wheat straw Wheat straw

Pretreatment acid hydrolysis and fermentation Gasification and biosynthesis Gasification and chemical synthesis Pretreatment acid hydrolysis and fermentation Production of ethanol with hydrogen from black fermentation Catalytic pyrolysis La/AL2O3 Catalytic pyrolysis gamma/Al2O3 Catalytic pyrolysis Cr2O3 Catalytic pyrolysis Cr2O3 Catalytic pyrolysis nickel Catalytic pyrolysis Cu-MCM-41 Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol

Hydrogen Oil palm shell Hydrogen Oil palm shell Hydrogen Rice straw Hydrogen Sawdust Hydrogen Sawdust Hydrogen Commercial wood Ethanol Sugarcane Ethanol Wheat Ethanol Corn grain Ethanol Sorghum grain Ethanol Cassava root Ethanol Sugar beet Ethanol Sweet sorghum Biodiesel Soy Biodiesel Oil palm Biodiesel Sunflower Biodiesel Castor Biodiesel Cotton Biodiesel Rapeseed Biodiesel Jatropha Biodiesel Sawflower

Cost (USD/Ton Processed)    38.29        30.40 50.68 55.86 53.20 88.20 27.50 16.10 47.02 55.05 78.67 94.50 44.50 95.87 87.16 76.01

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Eq. (2.11) was solved to obtain the values of EI and Profit equal to 2.2546 3 109 points and 1.8539 3 109 million dollars, respectively. The significant gap between the minimum and maximum EI identified in the Pareto curve should be noted. Then, the problem given by Eq. (2.13) was solved for different values of ε between the minimum EI (given by solution A) and the maximum EI (given by solution C) to determine the Pareto curve, as can be seen in Fig. 2.2. Note that the Pareto curve represents a set of optimal solutions that meets both objectives simultaneously, decision makers can use to find the solution that best fits the specific requirements. In this case, we identify the solution B (see Fig. 2.2) that corresponds to about a quarter of the maximum environmental impact and about 80% of the maximum profit. Tables 2.10 and 2.11 show the solutions for the points B and C identified in the Pareto curve of Fig. 2.2. It is noteworthy that none of the optimal solutions involve the use of food-grade feedstocks. With respect to the ethanol production, the comparison between solution B and the maximum profit shows that in the first one 50% of ethanol demand is fulfilled using 10%

Table 2.4: Availability and feedstock used cost for biofuel production in Mexico Raw Material

Cost (USD/Ton)

Availability (Ton/Year)

Wood chips Wheat straw Oil palm shell Rice straw Sawdust Commercial wood Sugarcane Wheat Corn grain Sorghum grain Cassava root Sugar beet Sweet sorghum Soy Oil palm Sunflower Castor Cotton Rapeseed Jatropha Sawflower

86.60 38.85 367.89  0.00 60.62 28.98 286.10 207.40 167.77 230.71 150.29 31.11 330.58 66.31 12.66 533.84 361.89 227.08 110.40 269.07

190,600.57 52,559.77 0.00 0.00 13,672.93 69,005.34 51,090,720.79 1,902,794.67 1,573,914.77 6,593,050.48 13,639.50 167.00 5,032,396.62 153,022.20 307,756.87 111,208.00 8.50 365,226.98 503.86 529.80 95,831.27

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Table 2.5: Cost and demand of products for the proposed scenario Product

Cost (USD/Ton)

Demand (Ton/Year)

Proposed Scenario

Ethanol Hydrogen Biodiesel

696.82 2470 841

3616.888 375,482.918 814.000

Considering 10% of ethanol in total gasoline Considering that it is 20% of demand of natural gas Considering 5% of biodiesel in diesel

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Table 2.6: Cost of byproducts produced from different feedstocks Byproducts

Raw Material

Cost of byproducts (USD/Ton)

Grain distillery Grain distillery Grain distillery Dry pulp Green foliage Oil palm African Cattle cake Cattle cake Cattle cake Cattle cake Cattle cake Hydrogen

Wheat Corn grain Sorghum grain Sugar beet Cassava root Palm oil Jatropha Soy Rapeseed Sawflower Sunflower Wood chips

140.06 140.06 140.06 112.04 9.80 634.92 72.92 201.21 93.37 40.43 60.97 2470

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 21 Table 2.7: Ecoindicator-99 for each feedstock Raw Material

Ecoindicator 99/Ton

Wood chips Wheat straw Oil palm shell Rice straw Sawdust Commercial wood Sugarcane Wheat Corn grain Sorghum grain Cassava root Sugar beet Sweet sorghum Soy Oil palm Sunflower Castor Cotton Rapeseed Jatropha Sawflower

211.12 146.09 14.61 0.00 169.32 169.32 12.14 146.09 199.78 250.56 62.47 48.33 41.84 444.06 14.61 2.04 631.69 245.08 404.00 14.61 614.38

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a PonceOrtega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Table 2.8: Ecoindicator-99 for product amount produced and used as biofuel according to the proposed scenario Product

Ecoindicator-99/Ton

Ethanol Hydrogen Biodiesel

32.12 0 10.15

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

of wood chips and 60% of sugarcane. Nonetheless, for the second case, besides wood chips and sugarcane, sorghum is needed to fulfill the 50% of ethanol demand; however, sorghum yield per hectare is lower than sugarcane. Regarding biodiesel, rapeseed appears in the optimal set of solutions, but its production is extremely low and it does not increase the biodiesel demand fulfillment. On the other hand, it can be seen that in both cases the nonfood-grade feedstock Jatropha is part of the optimal solution. In spite of the fact that there are no official records for Jatropha before 2009 in Mexico, an update of the records for this crop is expected in the future since it takes about 5 years to stabilize its seed production. Consequently, it is expected that the compliance of biodiesel demand will increase from 30% to 50%.

22

Chapter 2 Table 2.9: Ecoindicator-99 for processed feedstock amount for biofuel production

Product

Raw Material

Processing Route

Ecoindicator-99 /Ton

Ethanol Ethanol Ethanol Ethanol Ethanol

Wood chips Wood chips Wood chips Wheat straw Wheat straw

39.31 9.90 10.39 11.84 0.70

Hydrogen Hydrogen Hydrogen Hydrogen Hydrogen Hydrogen

Oil palm shell Oil palm shell Rice straw Sawdust Sawdust Commercial wood Sugarcane Wheat Corn grain Sorghum grain Cassava root Sugar beet Sweet sorghum Soy Oil palm Sunflower Castor Cotton Rapeseed Jatropha Sawflower

Pretreatment acid hydrolysis and fermentation Gasification and biosynthesis Gasification and chemical synthesis Pretreatment acid hydrolysis and fermentation Production of ethanol with hydrogen from black fermentation Catalytic pyrolysis La/AL2O3 Catalytic pyrolysis gamma/Al2O3 Catalytic pyrolysis Cr2O3 Catalytic pyrolysis Cr2O3 Catalytic pyrolysis nickel Catalytic pyrolysis Cu-MCM-41 Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Pretreatment acid hydrolysis and fermentation Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol

1.84 13.10 17.16 5.85 42.05 2.75 5.85 9.02 10.56 15.09 18.13 8.54 18.39 16.72 14.58

Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel Biodiesel

     

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Table 2.10: Solution of case B (Profit equal to 1394 million US dollars and EI equal to 51 3 107 PTS) Raw Material (Ton/Year) Wheat straw Sugarcane Sawdust Commercial wood African palm Sunflower Jatropha

52,559.77 2.97 3 1007 1.37 3 1004 6.90 3 1004 3.08 3 1005 1.11 3 1005 529.8

Product (Ton/Year) Ethanol Ethanol Hydrogen Hydrogen Biodiesel Biodiesel Biodiesel

14,312.025 1.76 3 1006 3.51 3 1005 6.00 3 1004 63,521.018 32,806.36 173.139

Processing Route P. acid hydrolysis and fermentation P. acid hydrolysis and fermentation Catalytic pyrolysis with Cr2O3 Catalytic pyrolysis with Cu-MCM-41 P. extraction and transesterification P. extraction and transesterification P. extraction and transesterification

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Focusing on hydrogen production, note that there is no change in the first part of the Pareto curve where hydrogen production is performed and its demand is not totally fulfilled according to the proposed scenario. However, a sudden increase in profit is observed with

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 23 Table 2.11: Solution case C (Profit equal to 1853 million US dollars and EI equal to 225 3 107 PTS) Raw Material (Ton/Year) Wood chips Wheat straw Sugarcane Sorghum grain Sawdust Commercial wood African palm Sunflower Rapeseed Jatropha

1.91 3 1005 52,559.77 2.66 3 1007 6.59 3 1006 1.37 3 1004 6.90 3 1004 3.08 3 1005 1.11 3 1005 503.86 529.8

Product (Ton/Year) Ethanol Ethanol Ethanol Ethanol Hydrogen Hydrogen Biodiesel Biodiesel Biodiesel Biodiesel

50,032.65 14,312.025 1,575,300 1.98 3 1006 3.51 3 1005 6.00 3 1004 63,521.018 32,806.36 181.138 173.139

Processing Route P. gasification y biosynthesis P. acid hydrolysis and fermentation P. acid hydrolysis and fermentation P. acid hydrolysis and fermentation Catalytic pyrolysis with Cr2O3 Catalytic pyrolysis with Cu-MCM-41 P. extraction and transesterification P. extraction and transesterification P. extraction and transesterification P. extraction and transesterification

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

no environmental impact change. This is a good indication that hydrogen is a cleaner biofuel than ethanol and biodiesel. Nonetheless, it does not mean there is no environmental impact, because environmental impact could be involved during feedstock extraction, processing or hydrogen combustion. Finally, Fig. 2.3 shows the diagrams for the solutions of cases B and C identified in the Pareto curve of Fig. 2.2.

2.6 Sensitivity Analysis A sensitivity analysis was done based on the availability of the sugarcane, considering a decrease from 100% to 0% of sugar availability using intervals of 20% points. For each analyzed scenario, it was observed that when the availability of sugarcane decreases the overall profit also decreases proportionally, whereas the opposite occurs for the overall environmental impact. This is due to an increase in the ethanol production, since different raw materials (i.e., sorghum, wood, etc.) must be used because the sugarcane can only be used to produce ethanol (see Table 2.12); however, the use of these different raw materials yields a decrease in the overall profit and simultaneously an increase in the overall environmental impact. Fig. 2.4 shows the results for the sensitivity analysis for the case when the availability of sugarcane decreases. The line for the 100% of sugarcane availability is the base case, whereas the other cases represent lower availability of sugarcane. Notice that when the availability of the sugarcane decreases, the Pareto curve moves down to suboptimal solutions. Table 2.12 presents the solution for the case when the availability of the sugarcane is 40% of that required for the case when EI must be lower than 145 3 107 points for the ecoindicator 99; this solution is identified as point D of Fig. 2.4 and the overall profit corresponds to $1600 3 106/year. These results show that the proposed methodology can be used to analyze different scenarios considering simultaneously the economic and environmental aspects.

24

Chapter 2

Figure 2.3 Flow diagrams for (A) solution B and (B) solution C of the Pareto curve. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011. Table 2.12: Solution case D (Profit equal to 1600 million US dollars and EI equal to 145 3 107 PTS for sugarcane availability equals to 40% of maximum allowable) Raw Material (Ton/Year) Wood chips Wheat straw Sugarcane Grain sorghum Sawdust Commercial wood African palm Sunflower Jatropha

1.91 3 1005 52,559.77 2.04 3 1007 3.95 3 1006 1.37 3 1004 6.90 3 1004 3.08 3 1005 1.11 3 1005 529.80

Product (Ton/Year) Ethanol Ethanol Ethanol Ethanol Hydrogen Hydrogen Biodiesel Biodiesel Biodiesel

31,811.14 14,312.023 1,207,680 1,184,605 3.51 3 1005 6.00 3 1004 63,521.02 32,806.36 173.14

Processing Route P. gasification and biosynthesis P. acid hydrolysis and fermentation P. acid hydrolysis and fermentation P. acid hydrolysis and fermentation Catalytic pyrolysis with Cr2O3 Catalytic pyrolysis with Cu-MCM-41 P. extraction and transesterification P. extraction and transesterification P. extraction and transesterification

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 25

Figure 2.4 Sensitive analysis for different values of the availability for sugarcane. From Jose´ Ezequiel Santiban˜ezAguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, et al, Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects, Industrial & Engineering Chemistry Research, 2011.

2.7 Concluding Remarks This chapter has presented a mathematical programming formulation for the optimal planning of a biorefinery system considering simultaneously the maximization of the total net profit and the minimization of the total environmental impact. The profit accounts for the sales of the products and byproducts minus the costs of raw materials and the costs for processing, whereas the environmental impact is measured through the ecoindicator-99, which is based on the lifecycle analysis for the raw materials, processing and products. An efficient method was presented in this chapter to consider adequately the objective function because these two objectives contradict each other. The model is a linear programming problem that can be easily solved without numerical complications. The model was applied to a case study for the planning of the production of a biorefinery in the central part of Mexico accounting for the specific bioresources available in this region. Results show that the model may help solve the problem of biofuel production from food-grade feedstocks, since it does not consider this type of crop as part of the optimal solutions. Finally, the model is general, and it can be applied to others different cases.

26

Chapter 2

2.8 Nomenclature for Chapter 2 2.8.1 Parameters αkmr β kmrb Cbvalue Ckvalue Cmcost processing Ckmr

Feedstock conversion to products through different processing routes Feedstock conversion to byproducts from different processing routes and products Sales price for byproduct b Sales price for product k Purchase price for feedstock m Processing cost for product k, from feedstock m, thorough processing route r Processing

Ecoindicatorkmr

Ecoindicatorresource m disposal Ecoindicatork max Fm Pkmax Prmax

Ecoindicator-99 for processing feedstock m, to produce product k through processing route r Ecoindicator-99 for feedstock extraction Ecoindicator-99 for use and disposal of products Maximum availability of feedstock m Maximum demand of product k Upper limit for processing for each processing route

2.8.2 Variables Bkmrb EI Fkmr Pkmr Profit

Mass rate for byproduct b from feedstock m and product k through processing route r Global environmental impact Mass rate for feedstock m to produce product k through processing route r Mass rate for product k from feedstock m and processing route r Total annual Profit

2.8.3 Indexes b k m r

Byproduct Product Feedstock Processing route

References Brooke, A., Kendrick, D., Meeruas, A., & Raman, R. (2018). GAMS-language guide. Washington, DC: GAMS Development Corporation. Diwekar, U. M. (2003). Introduction to applied optimization and modeling. The Netherlands: Kluwer Academic Press. Geodkoop, M., & Spriensma, R. (2001). The eco-indicator 99, A damage oriented for life cycle impact assessment. Methodology report and manual for designers; Technical report. Amersfoort, The Netherlands: PRe´ Consultants.

Environmental Aspects in the Strategic Planning of a Biomass Conversion System 27 Guine´e, J. B., Gorre´e, M., Heijungs, R., Huppes, G., Kleijn, R., de Koning, A.. . . (2002). Handbook on life cycle assessment. Operational guide to the ISO standards. Dordrecht, The Netherlands: Kluwer Academic Publishers. Horta-Nogueira, L.A. (2006). Task 5: Ethanol and ETBE production and end-use in Mexico. Potential and feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ. Lazcano-Martı´nez, I. (2006) Task B: Agricultural aspects and sources for biodiesel production. Potential and feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ. Mu¨ller-Langer, F., Probst, O., Thra¨n, D., & Weber, M. (2006), Task C: Biodiesel production and end-use in Mexico: Current and future (scenario building). Potential and feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ. SAGARPA-SIAP. (2010). Almanac for the sowing 2008-2009. SENER, bioenergetics production program. ,http://www.siap.gob.mx/index.php?option 5 com_wrapper&view 5 wrapper&Itemid 5 350.. Santiban˜ez-Aguilar, J.E., Gonza´lez-Campos, J.B., Ponce-Ortega, J.M., Serna-Gonza´lez, M., & El-Halwagi, M. M. (2011). Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects. Industrial and Engineering Chemistry Research, 50(14), 85588570. SEMARNAT. (2006). Forest almanac 2006. ,http://www.semarnat.gob.mx/tramites/gestionambiental/ forestalsuelos/Anuarios/Anuario%20Forestal%202006.pdf.; ,http://www2.ine.gob.mx/descargas/ cclimatico/e2008e_bioenergia.pdf.. Trindade, S.C. (2006) Task 7: Rationales, drivers and barriers for fuel ethanol and ETBE market introduction. Potential and feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ.

CHAPTER 3

Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives 3.1 Introduction Biorefineries appear to be a viable solution to replace traditional fossil fuel refineries, but their implementation requires the exploration of several aspects, including feedstock selection, processing routes, products, harvesting sites, processing and markets, as well as numerous other sustainability criteria. To determine the optimal solution to these problems is quite complicated. Therefore, this chapter presents an optimization model to design and plan sustainable biorefinery supply chains (SCs) that consider these issues. These issues include the various available biomass feedstocks at different harvesting sites, the availability and seasonality of biomass resources, potential geographical locations for processing plants that produce multiple products using diverse production technologies, economies of scale for the production technologies, demands and prices of multiple products in each market, locations of storage facilities, and a number of transportation modes between the SC components. Sustainability considerations are incorporated into the proposed model by including simultaneous economic, environmental, and social performance data in the evaluation of the SC designs. The problem was formulated as a multiobjective, multiperiod, mixed-integer linear program that seeks to maximize the profit of the SC, minimize its environmental impact, and maximize the number of jobs generated by its implementation. The environmental impact was measured by the ecoindicator-99 according to the life cycle assessment technique, and the social objective was quantified by the number of jobs generated. The Pareto optimal solutions were obtained using the ε-constraint method. To illustrate the capabilities of the proposed multisite system model, a case study is presented that addresses the optimal design and planning of a biorefinery SC to fulfill the expected ethanol and biodiesel demands in Mexico. The results indicate that cost-effective and sustainable solutions can be obtained that satisfy the Mexican demand by choosing feedstocks that are available year-round and do not significantly adversely impact

Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00003-1 © 2019 Elsevier Inc. All rights reserved.

29

30

Chapter 3

the environment. Furthermore, the number of jobs generated by implementing the biorefinery SC would have a significant social impact.

3.2 Problem Statement The problem addressed in this work concerns the long-term planning of a biomass processing SC while optimizing three objectives: the profit, environmental impact, and social impact. As shown in Fig. 3.1, the SC includes a set of harvesting sites (i.e., biomass crop fields), multiproduct processing plants, storage facilities, and final markets. The SC produces biofuels and other chemicals from one or more biomass feedstocks (raw materials) that are available from a number of widely distributed potential harvesting sites. These harvesting sites have an associated crop capacity for each raw material over each time period. The set of raw materials is purchased and transported from the set of harvesting Different periods of time

Places Harvesting sites (H) Processing plants (PH) Main processing plant Markets (MK)

Activities Transportation from homes Transportation from hubs and main plant Production of raw material Processing of raw material Storage of raw material Storage of product Selling of product

Figure 3.1 Schematic representation of the issue. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 31 sites to each processing plant, which transforms them into different products that are either sold in a set of markets or further processed. Thus, each production plant can be linked to one or more market sites. Furthermore, the biorefinery SC permits the shipment of intermediate products between plants. Thus, Fig. 3.1 shows the network superstructure with possible transportation links between its components. It should be noted that the market requires an influx of appropriate products based on customer demand. Two types of plants are considered within the superstructure to produce different products from different raw materials. These plants are classified according to their size (i.e., production capacity) and location: one is a central plant that can produce all products and features a very large production capacity, while the other one is a secondary plant that has a limited or small processing capacity for each product. The central plants are usually located in industrialized zones, while the secondary processing plants are distributed near the harvesting sites located far from industrialized zones. The unit processing cost for the secondary plants exceeds that of central plants, but they can reduce overall transportation costs. This reduction contributes to a significant decrease in the transportation requirements of the biomass feedstocks, which represents the largest volume of material to be transported in the SC. This study features only a central plant and a set of secondary plants. As shown in Fig. 3.2, each processing plant can use different production technologies to obtain multiple finished and intermediate products from several raw materials. Thus, processing plants are modeled in terms of a set of production routes that determine multiple output materials (biofuels and other chemicals) from several potential input materials (biomass feedstocks). The amount of each product generated by all available manufacturing technologies is assumed to relate to the biomass feedstock consumption through a linear mass balance equation that is expressed in terms of a constant production yield (i.e., the mass of raw materials consumed per unit mass of product manufactured for each technology).

Figure 3.2 Overview of the structure for each processing plant. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

32

Chapter 3

The biomass crop fields, secondary and central processing plants and markets included in the SC superstructure might be located at multiple sites and connected by transportation links (Fig. 3.1). In this case, the trucks used were assumed to primarily transport raw materials from the harvesting sites to the processing plants and transport intermediate products between plants, if necessary. Pipelines were also assumed to transport products from plants to markets. The goal was to determine the optimal configuration of the distributed biorefining SC and the associated planning decisions that simultaneously maximize profit and social impact, minimize the environmental impact and satisfy the demands of each market over the specified planning horizon.

3.3 Model Formulation The problem was based on a state-task network methodology that was implemented by Maravelias and Grossmann (2003) for the short-term scheduling of multipurpose batch plants. This methodology was also used by Castro and Grossmann (2006) for the short-term scheduling of single stage, multiproduct batch plants. In their study, the states were represented by materials at different locations and times; in this case, the states represented the feedstocks at harvesting sites, the feedstocks in processing facilities, the products in processing plants and the products in markets. Each one of these states is unique (i.e., each material depends on the location). Conversely, tasks are the different activities that consume a given time and divide the states (i.e., a given feedstock is transported after harvesting to produce a raw material in a processing plant). Each activity has an associated binary variable and is time dependent. In addition, each activity features different economic, environmental, and social impacts. Fig. 3.3 shows an example solution for the problem addressed in this chapter. In the model formulation, uppercase letters are used to define sets (H for harvesting sites, PH for secondary processing plants, MK for markets, M for raw materials, K for products, R for processing routes, and T for periods of time). In addition, lowercase letters are used to represent the elements of each set. In this context, Fig. 3.4 shows a general representation for the sets and their corresponding elements. The main indices are defined as follows: m corresponds to the bioresources, k is an index that represents products, r indicates different processing routes, and t is the period of time to complete an activity. Other indexes denote the geographical locations for these activities; for example, h represents possible production sites for raw materials, ph is used to indicate the secondary processing plants, and mk indicates the different markets where products could be sold. The main processing plant does not have an index since it is unique. Furthermore, superscripts can differentiate some variables, such as the flows at the entry and outlet.

Specific time of duration

Time of beginning

Sugar cane at home 1

Transportation from home 1 to hub 1

Sugar cane at hub 1

Hydrolysis and fermentation from sugar cane to ethanol

Ethanol at hub 1

Transportation from hub 1 to market 1

Ethanol at market 1

1 Economic impact 2

Environmental impact t–1

t

Social impact

Figure 3.3 Example for the production chain. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo SernaGonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

34

Chapter 3

Figure 3.4 General representation of sets used and their elements. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

3.3.1 Mass Balances for Harvesting Sites The mass balance of the raw material, m, at the harvesting site, h, at the end of time period
 harvesting sites t Mm;h;t equals the amount of raw material from m at the end of the previous time

 harvesting sites produced period Mm;h;t21 plus the amount m produced at the end of time period t Mm;h;t minus the total quantity of feedstock m transported from all the harvesting sites to 1 1 0 0 harvesting sites2

B plant secondary @Mm;h;ph;t

harvesting sites2

C B main A and main @Mm;h;t

C A plants. This relationship is

modeled by the following equation: harvesting sites harvesting sites produced Mm;h;t 5 Mm;h;t21 1 Mm;h;t

2

X

harvesting sites2 plant

Mm;h;ph;t

harvesting sites2 main

2 Mm;h;t

(3.1) ;

’mAM; hAH; tAT

ph

In Eq. (3.1), the symbol ’ is used to define indexes for which the equation is valid; whereas the symbol A is used to indicate the set that contains the considered indices.

Optimal Planning and Site Selection 35

3.3.2 Mass Balances for Processing Hubs (Secondary Plants) To account for the economies of scale, the proposed approach takes advantage of the processing hubs or secondary plants, which are processing facilities distributed around the geography involved in the SC to decrease the transportation cost for the raw materials and products (for example, see Bowling, Ponce-Ortega, & El-Halwagi, 2011). Therefore, every secondary plant, ph, exchanges mass with each harvesting site, h, each market, mk, and the main plant. All secondary plants can store raw materials and products, and their mass balances are defined as follows.

3.3.3 Raw Materials in Hubs




plant Mm;ph;t



For every raw material m, the final inventory in secondary plant ph at the end of time period t is equal to the initial inventory in the hub at the end of the previous period 0 1 harvesting sites2
 B plant C plant Mm;ph;t21 plus the input flow rate from each harvesting site @Mem;h;ph;t A minus the amount of raw material processed in the hub through processing route r to produce product k 1 0 plant2
 B main C processing Mm;k;r;ph;t and the output flow rate to the main plant @Mm;ph;t A. Thus, the mass balance for each raw material m in hub ph at any time period t can be stated as follows: plant plant Mm;ph;t 5Mm;ph;t21 1

harvesting sites2 plant2 X X processing plant main Mem;h;ph;t 2 Mm;k;r;ph;t 2Mm;ph;t ; r h k

X

’mAM;phAPH;tAT (3.2)

3.3.4 Products in Hubs Similarly, the mass balance relationship of product k produced in secondary plant ph over a time period t is given by the following equation: Pplant k;ph;t

5 Pplant k;ph;t21

1

XX m

r

Pproduced m;k;r;ph;t

plant2 main 2 Pk;ph;t

2

X

plant2 market Pk;ph;mk;t ;

’mAM;

phAPH;

tAT

mk

(3.3) where Pplant k;ph;t is the final inventory of product k in secondary plant ph at the end of time period t, Pplant k;ph;t21 is the inventory of product k in secondary plant ph at the end of the previous time period, Pproduced m;k;r;ph;t is the amount of product k produced from raw material m by

36

Chapter 3

technology r in the secondary plant ph at time period t,

plant2 main Pk;ph;t

is the amount of product k plant2 market mk Pk;ph;mk;t

P

transported from the secondary plant ph to the main plant at time period t and is the amount of product k shipped from the secondary plant ph to market mk over time period t. It should be noted that products are not transported between secondary plants.

3.3.5 Mass Balances for the Main Plant Similar to processing hubs, the central plant model consists of mass balances for raw materials and products as follows.

3.3.6 Raw Materials in the Main Plant The mass balance for each raw material m states that the final inventory of the feedstock in
 main is equal to the inventory at the end of the main plant at the end of time period t Mm;t 1 0 plant2
 B main C main the previous period Mm;t21 plus the total flow rate from all the hubs @Mem;ph;t A and 0 harvesting sites

1

harvesting sites2 B main C @Mem;h;t A

minus the amount of feedstock m converted into 0

product k through processing technology r over time period t

1

processing C B main A. @Mm;k;r;t

This

relationship can be modeled as follows: main main Mm;t 5Mm;t21 1

harvesting sites2 plant2 processing X main X X main main Mem;h;t 1 Mem;ph;t 2 Mm;k;r;t ; r h ph k

X

’mAM; tAT (3.4)

3.3.7 Products in the Main Plant The mass balance for each product k at the main plant states that the final inventory of that
 product at time t Pmain is equal to the inventory at the end of the previous time period k;t 0 1 produced2
 B main C Pmain A k;t21 plus the amount produced from raw material m by processing route r @Pm;k;r;t

Optimal Planning and Site Selection 37 0 and the input flow rate from all the secondary plants

Pmain k;t

main2 B market C @Pk;mk;t A.

5 Pmain k;t21

minus the amount delivered

1

0 to markets

1

plant2 B main C @Pek;ph;t A,

1

This relationship is modeled as follows:

XX m

producedmain Pm;k;r;t

1

r

X

plantmain Pek;ph;t

ph

2

X

mainmarket Pk;mk;t

;

’kAK;

tAT (3.5)

mk

It should be noted that the proposed model considers that the biomass processing distributed to secondary plants will occur at relatively small scales near the harvesting sites, while the main plant is large and located in an industrialized zone. This situation arises because feedstocks are obtained from multiple and widely distributed harvesting sites. These distances result in excessive transportation costs of raw materials to a single, large processing plant. Therefore, the distribution of facilities in this model takes advantage of the economies of scale (i.e., unit processing costs decrease as the plant size increases). Furthermore, this model simultaneously reduces the transportation costs of materials by decreasing the amount of materials that must be shipped between the plants of the distributed SC. In addition, the raw materials are not transported between secondary plants, and the maximum storage capacity in the main plant is larger than that of the secondary plants.

3.3.8 Mass Balances for Markets Each market, mk, requires a mass balance that only includes products. For each product k in market mk, the final inventory at the end of time period t is equal to the inventory at the end of the previous time period plus the amount of product sent to that market from

 -market and the main plant Pemain-market , minus the amount of secondary plants Peplant k;mk;t k;ph;mk;t
 product sold Psold k;mk;t : market Pmarket k;mk;t 5 Pk;mk;t21 1

X

plant-market main-market Pek;ph;mk;t 1 Pek;mk;t 2 Psold k;mk;t ;

’kAK;

mkAMK;

tAT

ph

(3.6)

3.3.9 Constraints for Total Product Sales Eq. (3.7) forces the total sales of product k in market mk at time period t to be lower than or equal to the demand target level (i.e., the maximum demand that it is necessary to fulfill). demand Psold k;mk;t # Pk;mk;t

’kAK;

mkAMK;

tAT

(3.7)

38

Chapter 3

3.3.10 Storage Constraints Storage is the first activity considered. Two disjunctions are used to model this phenomenon. The first disjunction states that the Boolean variable Ysls;l;t is true (i.e., storage is required) if the amount of stored material l in a given location s (s can be h, ph, main, mk) during time interval t is greater than 0 and limited by lower bound Smlowerl and upper s;l bound Smupperl (i.e., storage capacity). These bounds were previously determined based on s;l geographical and technical limitations. If these conditions are not satisfied, the Boolean variable, Ysls;l;t , is false (i.e., storage is not required) and the amount stored is 0. It should be noted that the lower storage bound can be 0; however, lower storage bounds are usually greater than 0 to account for the effects of economies of scale on the storage capacity of biorefinery SCs. " #   Ysls;l;t :Ysls;l;t 3 ; ’sAS; lAL; tAT Sls;l;t 5 0 Smlowerl # Sls;l;t # Smupperl s;l s;l To model previous disjunction as a set of linear relationships, the following constraints were included: ysls;l;t Smlowerl # Sls;l;t # ysls;l;t Smupperl ; s;l s;l

’sAS;

lAL;

tAT

(3.8)

Previous relationships also permit the activation of the binary variable ysls;l;t when storage is required during time interval t in a given location s for material l. The cost to store material l in a given location s depends on two contributions. The first contribution is associated with the total storage capacity (i.e., the material stored over the entire planning horizon). The second contribution is fixed by the maximum value of the storage capacities required over the entire time horizon. Therefore, additional binary variables are needed to determine the storage over any time period in any place. This is modeled by the following logical l necessary yss;l

5 1), this facility must be P l used over at least one time period of the entire horizon (i.e., t yss;l;t $ 1): relationships: If the storage facility is installed (i.e.,

X

ysls;l;t

l necessary $ yss;l ;

’sAS;

t

In addition, if at least one period requires storage (i.e., must be installed (i.e.,

l necessary yss;l

P

lAL

l t yss;l;t

(3.9)

$ 1), the storage facility

5 1):

ðMaximum number of periodsÞ

l necessary yss;l

2

X t

ysls;l;t $ 0;

’sAS;

lAL

(3.10)

Optimal Planning and Site Selection 39 In the preceding equation, maximum number of periods denotes the maximum number of time periods considered for the SC (this can be 12 months, 24 months, etc.). For example, P consider a maximum number of periods of 12 months; if t ysls;l;t 5 1, Eq. (3.10) takes the form

l necessary 12yss;l

constraint. The 12

l necessary yss;l

l necessary 2 1 $ 0; ’sAS; lAL, and yss;l must be one to satisfy this P l situation also arises when t yss;l;t 5 12; in this case, Eq. (3.10) is given

2 12 $ 0; ’sAS; lAL, and

l necessary yss;l

by

must also equal 1. Therefore, Eq. (3.10)

l necessary yss;l

when ysls;l;t is 1 during at least one period. P It should be noted that if only Eq. (3.9) is implemented when t ysls;l;t $ 1, then Eq. (3.9)

is used to activate the binary variable

l necessary yss;l .

l necessary yss;l

does not constrain the value of Therefore, can be 0 or 1. This necessitates the implementation of Eq. (3.10). However, if only Eq. (3.10) is implemented, when

l necessary yss;l

5 1, all values ofysls;l;t can be 0 or 1. As such, Eq. (3.9) is required to

ensure that at least one value of ysls;l;t equals 1. Therefore, the model requires both of these relationships. The storage capacity then depends on the maximum value of the storage capacities required for each time period of the entire planning horizon: Smls;l $ Sls;l;t ; ’sAS; lAL; tAT

(3.11)

The total storage cost for a SC is the sum of the capital and operating costs of the storage facilities. In the present work, the capital cost for each storage facility is represented by a fixed-charge function, which is expressed as the sum of a fixed cost charge (Csmfs;ll ) and a variable cost to account for the economies of scale. The fixed cost accounts for all the expenditures independent of the storage facility size, including the required piping, l necessary , yss;l

is associated with instrumentation, and electrical facilities. A binary variable, each storage facility in the superstructure that represents the existence of facility s. If a particular storage facility is selected for a given location in any period, the corresponding l necessary yss;l

equals 1, otherwise it equals 0. If a particular storage facility is not selected, associated costs should not appear in the economic objective function. To ensure that this condition is met, the fixed term in the investment cost function, Csmfs;ll , must be multiplied

40

Chapter 3 l necessary yss;l

by the binary variable of the corresponding storage facility, . This approach effectively eliminates alternatives with a significant number of storage facilities that are more expensive than solutions requiring fewer storage facilities for the same total storage capacity (i.e., a solution with two storage facilities is more expensive than a solution requiring only one storage facility for any one given storage capacity). In addition, the capital costs for the storage facilities include a variable portion that depends on the required facility size; thus, the maximum storage capacity required over all time periods (Smls;l ) is multiplied by the unit capital cost (Csmvls;l ) to determine the variable capital costs for the storage facilities. The second cost associated with the storage activity corresponds to the P operational costs ( t Csms Sls;l;t ), which include expenditures for maintaining the stored materials in good condition (electricity, pesticides, cleaning, maintenance, management, etc.). Operational costs increase or decrease in relation to the amounts of materials stored and the length of time they are stored. Therefore, the operational costs of storage facilities are calculated by summing the product of the amount of materials stored for each period (Sls;l;t ) and the unit operational cost for the storage (Csm) over all the periods in which storage is needed. The total cost for the storage facilities of the studied SC is then modeled by the following disjunction: 3 2 l

2 6 6 6 6 4

storage l

Cms;l

7 3 6 l 7 6 :Yss;lnecessary 7 6 necessary 7 7 6 storage Yss;l 7 7 6 7; 7 36 l 7 7 6 50 7 5 6 Cms;l 7 6 P l l l l 7 6 l 5 Csmfs;l 1 Csmvs;l Sms;l 1 t Csms Ss;l;t 5 4 Sms;l 5 0 l Ss;l;t 5 0; ’tAT

’sAS; lAL

Previous disjunction is reformulated to express its constraints in terms of disaggregated variables (for examples of reformulation for disjunctions, refer to Ponce-Ortega, Jimene´zGutie´rrez, & Grossmann, 2008). storage l Cms;l

l necessary l 5 Csmfs;l yss;l

1 Csmvls;l Smls;l 1

X

Csms Sls;l;t ;

’sAS;

lAL

(3.12)

t storage l Cms;l

storageMAX l l necessary # Cms;l yss;l ;

’sAS;

lAL

(3.13)

Optimal Planning and Site Selection 41

Smls;l Sls;l;t

# SmlMAX s;l

# SlMAX s;l;t

l necessary yss;l ;

l necessary yss;l ;

’sAS; ’sAS;

lAL

lAL;

tAT

(3.14)

(3.15)

In the above set of equations, the cost that depends on the maximum storage capacity is represented by Csmvls;l Smls;l . Because the actual investment cost function for a storage facility is a nonlinear cost function, storage is an activity in the SC that also allows the exploitation of economies of scale and the reduction of costs. In this work, a linear fixedcharge cost function adequately approximates the nonlinear cost function of the amount of stored material over a given valid interval. For each storage facility, this linear fixed-charge cost function has a fixed cost,

l necessary l Csmfs;l yss;l

Csmvls;l Smls;l , that depends Csmvls;l is the slope of the

term, term, amount of stored material.

, associated with the facility and a variable

on the maximum amount of materials stored. In the latter line that relates the cost for the storage facility to the

The preceding equations are used define the binary variable of storage s in any location l at time period t as either 1 if established or 0 if it is not. When the binary variable equals 1, the upper bounds for the storage cost and storage capacity are also included. It should be noted that the material can be stored in six different places, including harvesting sites, hubs, and the central plants for feedstocks, and hubs, the central facility and markets for products.

3.3.11 Transportation Constraints The model considers six transportation links between the components of the biorefinery SC. For raw materials, these links are the transportation from harvesting sites to secondary processing 0 1 0 1 harvesting sitesharvesting sitesB plant B main C C plants @Mm;h;ph;t A, to the main processing plant @Mm;h;t Aand between 0 secondary processing plants and the main processing plant

plantB main @Mm;ph;t

1 C A. For products, these

links consist of the transportation from secondary processing plants to the main processing plant

42

Chapter 3

0

1

plantB main @Pk;ph;t

0

C A, from secondary processing plants to markets 0

processing plant to markets

mainB market @Pk;mk;t

1

plantB market C @Pk;ph;mk;t Aand

from the main

1 C A. The transported amounts of materials are limited by

upper and lower limits, which are formulated by the following binary variables: harvesting sitesharvesting sitesplantplantplantmainplant main main main market market ymm;h;ph;t , ymm;h;t , ymm;ph;t , ypk;ph;t , ypk;ph;mk;t , and ypk;mk;t . These variables equal 1 if the transportation links between the corresponding components are established and 0 if they are not. The amounts of materials transported between the components of a biorefinery SC are constrained by upper limits as follows: harvesting sitesplant Mm;h;ph;t

harvesting sitesplant # ymm;h;ph;t

harvesting sitesplant Mupperm;h;ph

’mAM;

hAH;

phAPH;

tAT (3.16)

harvesting sitesmain Mm;h;t

harvesting sitesmain # ymm;h;t

plantmain Mm;ph;t plantmain Pk;ph;t plantmarket Pk;ph;mk;t

harvesting sitesmain Mupperm;h

plantmain # ymm;ph;t

plantmain Mupperm;ph

’mAM;

plantmain # ypk;ph;t

plantmain Pupperk;ph

’kAK;

plantplantmarket market # ypk;ph;mk;t Pupperk;ph;mk mainmarket Pk;mk;t

’mAM;

mainmarket # ypk;mk;t

’kAK;

mainmarket Pupperk;mk

phAPH;

phAPH;

phAPH; ’kAK;

hAH;

tAT (3.17)

tAT

(3.18)

tAT

mkAMK;

mkAMK;

(3.19)

tAT

tAT

(3.20)

(3.21)

The amounts of materials shipped between the SC components are also limited by lower bounds: harvesting sitesplant Mm;h;ph;t

harvesting sitesplant $ ymm;h;ph;t

harvesting sitesplant Mlowerm;h;ph

’mAM;

hAH;

phAPH;

tAT (3.22)

harvesting sitesmain Mm;h;t

harvesting sitesmain $ ymm;h;t

harvesting sitesmain Mlowerm;h

’mAM;

hAH;

tAT (3.23)

Optimal Planning and Site Selection 43 plantmain Mm;ph;t plantmain Pk;ph;t plantmarket Pk;ph;mk;t

plantmain $ ymm;ph;t

plantmain Mlowerm;ph

’mAM;

plantmain $ ypk;ph;t

plantmain Plowerk;ph

’kAK;

plantplantmarket market $ ypk;ph;mk;t Plowerk;ph;mk mainmarket Pk;mk;t

mainmarket $ ypk;mk;t

’kAK;

mainmarket Plowerk;mk

phAPH;

phAPH;

phAPH; ’kAK;

tAT

(3.24)

tAT

mkAMK;

mkAMK;

(3.25)

tAT

(3.26)

tAT

(3.27)

For each type of transportation link established between two SC components, the corresponding transportation time (time spent transporting the material) is calculated by Eqs. (3.28)(3.33). The transportation activity is assumed incapable of changing the properties the shipped materials. Thus, the amount of material that leaves the origin component equals the amount that is received by the destination component between two interconnected SC components, as shown in Eqs. (3.28)(3.33). However, the material transport flow between these components leaves the origin component at time t harvesting sitesharvesting sitesplantplantplantmain- ! plant main main main market market Mm;h;ph;t and arrives at the , Mm;h;t , Mm;ph;t , Pk;ph;t , Pk;ph;mk;t , and Pk;mk;t

destination component at a later time plantmarket Pek;ph;mk;t ,

and

mainmarket Pek;mk;t

harvesting sitesplant Mem;h;ph;t

,

harvesting sitesmain Mem;h;t

,

plantmain Mem;ph;t

,

plantmain Pek;ph;t

,

! . Therefore, the transportation time, ttransp, is given by the

difference between the leaving and receiving time associated with each transportation link established in the SC. harvesting sitesplant Mm;h;ph;t

harvesting sitesplant 5 Mem;h;ph;t1ttransp

harvesting sitesmain Mm;h;t plantmain Mm;ph;t plantmain Pk;ph;t

’mAM;

harvesting sitesmain 5 Mem;h;t1ttransp

plantmain 5 Mem;ph;t1ttransp plantmain 5 Pek;ph;t1ttransp

hAH; ’mAM;

’mAM; ’kAK;

phAPH;

hAH;

phAPH;

phAPH;

tAT

tAT

tAT

tAT

(3.28)

(3.29)

(3.30)

(3.31)

44

Chapter 3 plantmarket Pk;ph;mk;t

plantmarket 5 Pek;ph;mk;t1ttransp mainmarket Pk;mk;t

’kAK;

mainmarket # Pek;mk;t1ttransp

phAPH;

’kAK;

mkAMK;

mkAMK;

tAT

tAT

(3.32)

(3.33)

3.3.12 Processing Constraints The proposed model considers the distribution of biomass processing. Therefore, it includes a set of distributed secondary plants and only one central plant, but all available production technologies can be used in both types of plants. Distributed biomass processing potentially alleviates feedstock transportation costs by processing biomass in secondary plants that are located near the harvesting sites. To account for economies of scale, the conversion technologies costs follow power law functions that dictate decreasing unit production costs with increasing plant capacity. Therefore, nonlinear cost functions are linearized over different intervals between given processing limits to obtain a linear problem (Fig. 3.5). Constraints (3.34) and (3.35) are used to guarantee that the total amount of product k produced from raw material m through technology r in a secondary plant ph at time period t is lower than the upper bound and greater than the lower bound of the technology capacity: processing processing Mm;k;r;ph;t # ymprocessing m;k;r;ph;t Mupperm;k;r;ph;t

’mAM;

kAK;

rAR;

phAPH;

tAT (3.34)

processing processing Mm;k;r;ph;t $ ymprocessing m;k;r;ph;t Mlowerm;k;r;ph;t

’mAM;

kAK;

rAR;

phAPH;

tAT (3.35)

Figure 3.5 Example for considering different unit processing costs. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 45 These equations introduce the binary variable ymprocessing m;k;r;ph;t to model the selection of production technology. This binary variable takes the value of 1 if a production technology r is selected to produce product k using feedstock m in a secondary plant ph at time period t. If the technology is not selected, the binary variable equals 0. A large number of possible production technologies may be comprised of several processing steps to convert diverse biomass feedstocks into multiple biofuels and bioproducts. This situation results in a highly complex nonlinear optimization problem to design and planning multiproduct biorefinery SCs. Therefore, the proposed model assumes that the conversion of feedstock m into product k can be described using a fixed production yield or conversion factor for each production technology r to enforce the linearity of the problem. This assumption results in Eq. (3.36), which models the production technologies available in each secondary plant ph: processing Pproduced m;k;r;ph;t1tprocessing 5 αm;k;r Mm;k;r;ph;t

’mAM;

kAK;

rAR;

phAPH;

tAT (3.36)

where αm;k;r is the yield or conversion factor of product k converted from a unit quantity of biomass feedstock m with production technology r. Like the secondary plants, the production rate of product k by technology r in the main plant using feedstock m at time period t is bounded by the lower and upper limits of the technology capacity, as stated in Eqs. (3.37) and (3.38): processing main Mm;k;r;t

processing processing main main # ymm;k;r;t Mupperm;k;r

’mAM;

kAK;

rAR;

tAT

(3.37)

processing main Mm;k;r;t

processing processing main main $ ymm;k;r;t Mlowerm;k;r

’mAM;

kAK;

rAR;

tAT

(3.38)

processing main ymm;k;r;t

where is a binary variable equals 1 if the production technology r is selected to produce product k from feedstock m in the main processing plant over each time period t. Finally, the set of functions given by Eq. (3.39) models the performance of each production technology r available in the main plant to produce product k from feedstock m over each time period t: producedmain Pm;k;r;t1tprocessing

processing main 5 αm;k;r Mm;k;r;t

’mAM;

kAK;

rAR;

tAT

Examples of available production technologies are given by Huber, Iborra, and Corma (2006); these authors presented reviews of a variety of technologies that have been developed to convert a large number of biomass feedstocks into diverse biofuels and biochemicals. These technologies include, among others, hydrolysis, fermentation,

(3.39)

46

Chapter 3

hydrogenation, fast pyrolysis, and liquefaction. Saxena, Seal, Kumar, and Goyal (2008) presented a review to highlight several thermochemical processes that convert biomass into hydrogen-rich gas. Furthermore, Saxena, Adhikari, and Goyal (2009) highlighted various biochemical processes to convert biomass into biological hydrogen gas and ethanol. Several reports have also identified the top-valued products from bioresources; in this context, Werpy, Petersen, Aden, Bozell, and Holladay (2004) screened several potential candidates to obtain syngas from sugars, while Holladay, Bozell, White, and Johnson (2007) showed results for refining lignin. In addition, several technological and economic evaluations have been reported that analyze different conversion technologies for bioresources to produce bioethanol. For example, the fermentation by Zymomonas mobilis and Saccharomyces to convert sugar to ethanol was reported by Dutta, Dowe, Ibsen, Schell, and Aden (2010). Kazi et al. (2010) reported a technological and economic analysis to obtain ethanol from cellulosic materials through biochemical routes. A similar analysis for the thermochemical conversion of lignocellulosic biomass to ethanol by acetic acid was reported by Zhu and Jones (2009). The production of biodiesel from algal oil was reported by Pokoo-Aikins, Nadim, Mahalec, and El-Halwagi (2010).

3.3.13 Availability Constraints The feedstocks for processing plants can be obtained from a variety of biomass resources. In addition, while increasing the capacity generally lowers the unit production costs, the size of biorefineries can be constrained by feedstock availability. In fact, the production
 produced capacity Mm;h;t for each biomass feedstock m of harvesting site h at time period t is 0 1 upper

B produced C constrained by an upper limit @Mm;h;t A, which can be obtained from the statistical records of biomass feedstock availabilities for the involved harvesting sites. This constraint is defined as follows: upper produced ypmm;h;t Mm;h;t

produced $ Mm;h;t ;

’mAM;

hAH;

tAT

(3.40)

This equation uses the binary variable ypmm;h;t , which takes the value of 1 if bioresource m available at harvesting site h is selected as the raw material over time period t. If the bioresource is not selected, this variable equals 0. It should be noted that the biomass resources at the considered harvesting sites already have different uses, so the proposed model assumes the additional production of biomass resources to meet the raw material demands of biorefining plants. Therefore, the land use for the additional biomass production is considered to calculate the ecoindicator-99 corresponding to each type of biomass feedstock.

Optimal Planning and Site Selection 47

3.3.14 Start and End Storage Constraints An additional constraint ensures that the problem can be solved for any period of time and that it can be coupled with other time periods. Thus, if the problem is solved for a period of 12 months, it also could be solved for 24, 36, months, etc. This is an important constraint to ensure that the process can be performed over a realistic time frame. It states that the total inventory of raw materials and products at the end of the period (Ss;l;last t ) at the storage facilities should be equal to the total storage inventory at the beginning of the period (Ss;l;0 ): Ss;l;CARDðtÞ 5 Ss;l;0 ;

’sAS;

lAL

(3.41)

3.3.15 Objective Functions The mathematical model presented above aims to simultaneously optimize the economic, environmental, and social performance of the biorefinery SC, which are stated as follows. 3.3.15.1 Economic objective function The economic objective is to maximize the net profit of the biorefinery SC, which represents the difference between the income (i.e., sales of products) and the total cost. The total cost includes the processing, transportation, and storage costs of feedstocks and products. The net profit is given by the following relationship:

Profit 5

XXX k

2

XX m

2

plant

storage market Ckk;mk

ph

k

2

2

m

h

XX

main Ctmm;h;t

storage plant

harvesting sitesplant Ctmm;h;ph;t

harvesting sites-

main

main

t

r

2

XXX k

ph

t

h

storage main

Ckk

harvesting sitesplant

Mm;h;ph;t XXXX k

Ctkk;ph;t Pk;ph;t 2

main

Cmm;h

k

t plant-

X

ph

main Mm;h;t

plant-

2

Ckk;ph

storage

t

ph

harvesting sites-

2

XX m

k

XXXX

mk

h

main

Cmm

produced Cmproduced Mm;h;t m;h;t

t

h

storage

m

XXXXX m

X

2

Cmm;ph

XXX k

2

m storage

XXX m

2

t

ph

XX k

2

mk

sold Ckk;mk;t Psold k;mk;t 2

XXX

mk

processing processing Cm;k;r;ph;t Mm;k;r;ph;t

ph

plant-

plant-

market market Ctkk;ph;mk;t Pk;ph;mk;t

t

mk

main-

main-

market

market

Ctkk;mk;t Pk;mk;t

t

2

XXXX m

k

r

processing main Cm;k;r;t

processing main

Mm;k;r;t

t

(3.42)

48

Chapter 3

sold where Ckk;mk;t is the unit price for products, Cmproduced is the unit cost for raw materials, m;h;t storage main Cmm;h ,

storage plant Cmm;ph ,

storage main Cmm

and and are the unit costs for the storage of raw material at harvesting sites, secondary processing plants and main processing plant, respectively. These costs have a fixed component (independent of the amount of raw material) and a variable component (that depends on the amount of raw material). Furthermore,

storage plant Ckk;ph

,

storage main Ckk

,

storage market Ckk;mk

and are the costs for the storage of products in harvesting sites, secondary processing plants and main processing plant, respectively. These costs also have a fixed harvesting sitesharvesting sitesplant main l component (Csmfs;l ) and a variable component. Ctmm;h;ph;t , Ctmm;h;t , plantplantmainmarket main market Ctkk;ph;mk;t , Ctkk;ph;t , and Ctkk;mk;t are the unit transportation costs for raw materials and processing Cm;k;r;ph;t

processing main Cm;k;r;t

products in the established transportation links. Finally, and are the unit processing costs for hubs and central processing facilities, respectively. It should be noted that a distributed system is designed to reduce the transportation costs associated with the SC, and the model takes into account the economies of scale for the production technologies. 3.3.15.2 Environmental objective function The environmental objective function measures the environmental impact through the ecoindicator-99. The ecoindicator-99 is based on the life cycle assessment technique first proposed by Geodkoop and Spriensma (2001), and this indicator can be applied to any substance, process, or activity to consider its global environmental impact (see Guinee et al., 2002). The ecoindicator-99 method focuses on the damage; this method is continuously updated and considers 11 impact categories, which are divided into three damage categories. A specific weight factor is assigned to each category to obtain a global damage factor. These three damage categories are: 1. Damage to human health due to: a. Carcinogens b. Organic substances that damage in breathing c. Inorganic substances that damage in breathing d. Climate change e. Depletion of the ozone layer

Optimal Planning and Site Selection 49 2. Damage to the ecosystem due to: a. Toxic substances b. Acidification and eutrophication c. Use and land conversion 3. Damage to resources extraction: a. Mineral resources b. Fossil fuels In this context, factors known as ecoindicators, which are related to the substances and processes involved in the complete SC, can be determined. The factors are weighted based on three perspectives (i.e., hierarchical, egalitarian, and individualist). The hierarchy perspective considers that incurred damages can be avoided by good management. This perspective also assumes that the fossil fuels can be replaced. The egalitarian perspective considers that fossil fuels cannot be replaced and that catastrophic events could happen. Finally, in the individualist perspective the fossil fuel supply is unlimited. The ecoindicator99 units can be determined for each process prior to the SC optimization. The environmental objective function accounts for the ecoindicator-99 of raw material production, product manufacturing, product use, and the transportation of materials between SC components. This function is stated as follows: XXX XXX material produced EI 5 EcoIndproduct Psold EcoIndraw Mm;h;t k;mk;t 1 m k k

1

ph

h

ph

mk

k

plant

harvesting sitesplant

EcoIndmm;h;ph

Mm;h;ph;t

t harvesting sitesmain EcoIndmm;h

mk

harvesting sitesmain

Mm;h;t

plant-

plant-

market market EcoIndkk;ph;mk Pk;ph;mk;t

k main-

market EcoIndkk;mk

mainmarket

Pk;mk;t 1

m processing main

EcoIndm;k;r;t

ph

plantmain EcoIndkk;ph

k

r

plantmain

Pk;ph;t

t

XXXXX

t

r

1

XXX

t

XXXX m

t

h

harvesting sites-

t

XXX k

1

m

XXXX k

1

h

XXX m

1

t

XXXX m

1

mk

ph

processing EcoIndprocessing m;k;r;ph;t Mm;k;r;ph;t

t

processing main

Mm;k;r;t

t

(3.43)

50

Chapter 3

material where EcoIndproduct is the unit ecoindicator-99 for the use of product k, and EcoIndraw m k is the unit ecoindicator-99 for the production of raw material m (this unit ecoindicator homehomeplant main includes the used of land for biomass production). EcoIndmm;h;ph and EcoIndmm;h are the unit ecoindicators-99 for the transportation of raw material m from harvesting site h to plantmarket processing plant ph and the main processing facilities, respectively. EcoIndkk;ph;mk , plantmainmain market EcoIndkk;ph , and EcoIndkk;mk are the unit ecoindicators-99 for the transportation of products from hubs to markets, hubs to central plant and central plant to markets,

EcoIndprocessing m;k;r;ph;t

processing main EcoIndm;k;r;t

respectively. Finally, and are the unit processing ecoindicators-99 for hubs and central facilities, respectively. The relationship between the production levels and environmental impact are assumed to be linear because the main environmental impacts are usually associated with the amount of processed materials. This association arises because the environmental impact is almost independent from the size of the selected equipment that processes the raw materials, but it significantly depends on the total consumed raw materials. For land conversion, Geodkoop and Spriensma (2001) suggested using conversion data only for cases where natural areas are converted into non-natural areas. The ecoindicator-99 predictions are poor for highly biodiverse land because the damage factors are based on empirical observations of the number of plant species per area type; the damage factors may also have considerable uncertainties in agricultural and urban areas. The damage factor estimates the conversion of natural to arable areas, which approximates agricultural regions; these damage factors were reported by Geodkoop and Spriensma (2001). The environmental performance of the biorefinery SC represents the environmental dimension of sustainability. However, it can also be used to indirectly assess the social impact because the environmental impact is based on the ecoindicator-99, which includes the damage to human health and resources that may involve some social impacts. Furthermore, this objective function considers the entire scope of environmental impact measured through the life cycle of the SC. In addition, the model formulation can incorporate different ways to determine the environmental impact (e.g., it could be interesting to include the methodology reported by Cucek, Klemes, & Kravanja, 2012). 3.3.15.3 Social objective function Furthermore, the model considers the social impact through the number of jobs generated by harvesting sitesharvesting sites raw material  plant main the raw material production SIm , transportation SIm;h;ph , SIm;h ,

Optimal Planning and Site Selection 51 plantmain SImk;ph

,

plantmarket SIk;ph;mk ,

plantmain SIk;ph

,

mainmarket SIk;mk

0

!

B , and processing @SIprocessing m;k;r;ph;t ;

processing main SIm;k;r;t

1 C A. This

objective is difficult to incorporate because the jobs produced have varying impact. For example, the jobs generated in the biomass crop fields impact society differently than the jobs associated with a processing plant, which requires a variety of employees with different educational backgrounds. However, this objective is very important because it can yield a more integrated vision of the biorefinery SC performance before a decision is made. Consequently, the social dimension of sustainability is integrated in the proposed model by considering that a distributed biomass processing system may represent an advantage for generating jobs in different areas. In this study, the Jobs and Economic Development Impact methodology (JEDI, 2012), the IMPLAN model (IMPLAN, 2012), and information reported by different governmental institutions were used to account for the number of jobs generated for any process or product in the entire life cycle. The social objective function measured by the number of jobs generated in the entire life cycle of the SC is stated as follows:

SI 5

XXX m

1

harvesting sites-

mk

k

main Mm;h;t

1

mk

plant-

market market SIk;ph;mk Pk;ph;mk;t

XXX

t

k main-

market SIk;mk

mainmarket

Pk;mk;t 1

t

r

1

main

SIm;k;r;t

ph plant-

main SIk;ph

k

r

harvesting sitesplant

Mm;h;ph;t plant-

main SImm;ph

plantmain

Mm;ph;t

t plantmain

Pk;ph;t

t

XXXXX m

processing

ph

plant

SIm;h;ph

XXX m

plant-

harvesting sites-

t

ph

harvesting sites-

main SIm;h

XXXX m

h

t

XXX k

1

ph

produced Mm;h;t 1

m

XXXX k

1

h

material

t

XXX m

1

h

SIraw m

XXXX

ph

processing SIprocessing m;k;r;ph;t Mm;k;r;ph;t

t

processing main

Mm;k;r;t

t

(3.44) The relationship between social impact and production level was assumed to be linear because the unit social values depend on location (i.e., regional considerations) and each location has upper and lower limits for the allowed activities in the SC. Although the general behavior is not linear, the linear approximation is a reasonable representation for the considered case study in a given interval between lower and upper limits.

52

Chapter 3

3.3.16 Remarks on the Model It is important to highlight the following features of the proposed model: •

•

• •

•

The mathematical formulation is a multiobjective, multiperiod mixed-integer linear programming problem (MILP), where the objective functions are the simultaneous maximization of the net profit (Eq. 3.42), minimization of the environmental impact (Eq. 3.43), and the maximization of the social benefit through the number of jobs generated in the entire SC (Eq. 3.44). The proposed approach explicitly accounts for the economies of scale of the production technologies and distributed biomass processing to reduce the transportations costs of raw materials. This method also includes the optimal processing plant locations and capacities, as well as the optimal selection of a number of processing technologies to obtain multiple products using a variety of biomass feedstocks. The model explicitly considers the seasonal dependence of potential feedstock bioresources for the biorefinery SC. The proposed optimization approach is based on a deterministic framework. To incorporate changes in the parameters and unit costs in the model, only the most probable scenario based on statistical projections can be considered. To include the fluctuations in the parameters and unit cost data properly, formal stochastic optimization approaches should be used. In this context, the proposed model can be extended to incorporate the stochastic scenario. The time periods used in the considered planning problem (i.e., long-term decision level) can exceed some task processing times (i.e., short-term decision level). However, the proposed model divides the planning horizon into time periods of equal size, where aggregated production is planned by assuming that the tasks must begin and end at a specified time point. For example, for a time horizon of 1 year, there are twelve 1month time periods. To illustrate this case, consider an available transport capacity of 400 tons/day. For modeling purposes, the transportation activity is assumed to persist for 1 month. Therefore, the total of 12,000 tons are shipped at the end of each time period. In this case, dividing the time horizon into hours (i.e., 8760 time periods) is more realistic, but this division drastically increases the number of variables in the model. Thus, the short-term scheduling for each planning period of the time horizon is considered in the present chapter to avoid a prohibitive number of time periods, which may yield an unsolvable problem.

To solve the multiobjective, multiperiod MILP and identify the trade-offs between the three objectives considered, the following approach is used: First, limits to clearly visualize the relation between the objectives on two planes must be obtained because it is difficult to illustrate their trade-offs in a Pareto curve with more than two dimensions. A general description of the solution approach is shown in Fig. 3.6, which can be described as

Optimal Planning and Site Selection 53 Pareto curve with more than two objectives

Difficult to present the relation between objectives

The solution is presented in several pareto curves with two dimensions It is necessary to generate limits for:

Maximum limit for profit

Minimum limit for environmental impact

Maximum limit for social impact

Upper limit for environmental impact

Lower limit for profit

Lower limit for profit

Lower limit for generated jobs

Upper limit for environmental impact

Lower limit for generated jobs

Environmental impact

Environmental impact

Generated jobs

Profit

Generated jobs

With obtained limits is possible to produce these pareto curves

Profit

Figure 3.6 General representation for the solution approach. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

follows: First, the problem is solved to maximize the net profit (Eq. 3.42) without considering the environmental impact (Eq. 3.43) or social benefits (Eq. 3.44). This solution provides information about the maximum net profit, as well as an upper limit for the environmental impact and a lower limit for the social impact. The MILP problem for

54

Chapter 3

minimizing the environmental impact given by Eq. (3.43) is then solved without including the other two objectives defined by Eqs. (3.42) and (3.44). This solution yields the minimum environmental impact and limits for the lower net profit. Next, the MILP problem is solved to only maximize the social impact (Eq. 3.44). This solution also provides lower limits for the net profit and upper limits for the environmental impact. Finally, using the limits obtained in the previous steps, the constraint method (see Diwekar, 2003) is implemented to determine the Pareto solutions for the three considered objectives. The GAMS code for the model of this chapter is given in the Appendix B.

3.4 Case Study The proposed methodology was applied to a case study to establish a distributed biorefinery system in Mexico. The raw materials could be produced and processed in six different places, while the products could be sold in five different locations; the resulting site distribution can be seen in Fig. 3.7. The spatial distribution of biomass production and processing sites is based on the recently updated SAGARPA-SIAP (Mexican System of Information about Agriculture and Fishing) (2011) and SEMARNAT (Mexican Ministry of Environmental and Natural Resources) (2012) databases. In addition, historical data available for biomass production from used land were considered to estimate the biomass availability data in locations where the land is not being used. The monthly product demands were based on data from PEMEX (Mexican Ministry of Oil from Mexico) (2010). This case involves a set of nine bioresources (wood chips, commercial wood, sugarcane, corn grain, sorghum grain, sweet sorghum, sunflower, African palm oil, and Jatropha) available in Mexico, which can be used as feedstocks to obtain two products (bioethanol and biodiesel). In addition, four different processing technologies are available (gasification and biosynthesis, hydrolysis and fermentation, gasification and chemical synthesis, and transesterification). The conversion factors for the four different processing technologies shown in Table 3.1 were taken from data by Chouinard-Dussault, Bradt, Ponce-Ortega, and El-Halwagi (2011) for bioethanol and Santiban˜ez-Aguilar, Gonza´lez-Campos, PonceOrtega, Serna-Gonza´lez, and El-Halwagi (2011) for other bioproducts. In addition, each bioresource considered has an associated production cost, environmental impact, and number of jobs generated as a result of production. Furthermore, the availability for each bioresource in the different places depends on the region and season because climates can change drastically throughout the year in such countries as Mexico, which considerably affects the availability of bioresources. The bioresource data are shown in Tables 3.2 and 3.3. For the presented case study, the time horizon is divided into months to avoid additional complexities in the solution approach.

Optimal Planning and Site Selection 55

Figure 3.7 Problem statement for the biorefinery SC in Mexico: (A) harvesting places; (B) markets; and (C) processing plants. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014. Table 3.1: Conversion factors for different production technologies available to transform raw materials into products Product

Raw Material

Processing Route

Mass Ratio

Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Biodiesel Biodiesel Biodiesel

Wood chips Wood chips Wood chips Sugarcane Corn grain Sorghum grain Sweet sorghum African palm oil Jatropha Sunflower

Pretreatment, acid hydrolysis, and fermentation Gasification and biosynthesis Gasification and chemical synthesis Pretreatment, acid hydrolysis, and fermentation Pretreatment, acid hydrolysis, and fermentation Pretreatment, acid hydrolysis, and fermentation Pretreatment, acid hydrolysis, and fermentation Extraction and transesterification with methanol Extraction and transesterification with methanol Extraction and transesterification with methanol

0.1669 0.2625 0.1887 0.0592 0.3149 0.2999 0.0553 0.2064 0.3268 0.2850

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

56

Chapter 3 Table 3.2: Unit costs, ecoindicator-99 and jobs for each feedstock considered

Raw Material

Cost US$ (ton)

Ecoindicator-99 (ton)

Jobs (ton) Yielded

Wood chips Commercial wood Sugarcane Corn grain Sorghum grain Sweet sorghum African palm Jatropha Sawflower

86.60 60.62 28.98 207.40 167.77 31.11 66.31 110.40 269.07

211.12 169.32 12.14 199.78 250.56 41.84 14.61 14.61 614.38

2.9925E 2 04 2.9925E 2 04 7.6652E 2 03 6.3356E 2 07 1.9000E 2 07 1.9000E 2 07 2.9925E 2 04 2.9925E 2 04 1.9000E 2 07

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Similarly, the demand for biofuels in Mexico significantly depends on the season in different markets. Tables 3.4 and 3.5 present the annual demands for bioethanol and biodiesel in each market considered, respectively. Table 3.6 presents the unit ecoindicator99 for the use of bioethanol and biodiesel as biofuels. Tables 3.7 and 3.8 show the data for the transportation of raw materials and products. These data include the unit cost, distance, ecoindicator-99, and generated jobs for each material. These values were obtained using the methodology reported by Geodkoop and Spriensma (2001) and information taken from the Mexican Ministry of Communication and Transportation (SCT). The data were generated by the GREET 1.8d software, which is a platform that considers the energy consumption and emissions associated with the production and use of transportation fuels. The SCT provided important information about distance between the SC components, road conditions, and fuel consumption associated with transportation in Mexico. The model consists of 16,167 binary variables, 130,769 continuous variables, and 180,779 constraints. It was coded in the GAMS software, a high-level modeling system for mathematical programming and optimization. Each point on the Pareto curve was solved in an average of 2.2 seconds of CPU time by a 2.60GHz i73720QM processor with 6 GB of RAM using the solver CPLEX, which is a GAMS solver that can quickly solve large optimization problems (Brooke, Kendrick, Meeruas, & Raman, 2018). Fig. 3.8 shows the Pareto curve for this case study that considers only the net profit and environmental impact. Two sections are identified in this figure. In the first section, the profit increases drastically in response to small increases in the environmental impact; whereas in the second section the profit increases only slightly with respect to increases in the environmental impact. As shown in this figure, increases in the net profit and ecoindicator-99 also increase the total number of jobs because net profit correlates positively with raw materials processing and products production. This relationship results in an increase in the total number of jobs and environmental impact. Both sections show a natural trade-off between net profit and

Table 3.3: Feedstock availability for different locations during the year in tons Raw material Sugarcane

Corn

Sorghum

Sweet sorghum

Sunflower

Wood Chips

Home 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

January

February

March

April

May

June

July

August

53,3008 395,977 77,5646 529,242 744,649 558,202 389,363 0 3,025,668 1,094,683 2,184,954 166,9491 1,334,888 282,295 113,518 0 2,748,833 1,116,699 1,470,949 1,820,716 752,872 366,686 110,452 0 0 0 0 0 0 0 0 0 6,219,260 4,458,579 5,769,145 5,178,078 3,426,659 682,132 1,384,818 0 594,493 258,901 348,528 296,504 370,420 0 0 0 194 222 29,763 84,305 1,785,225 3,224,777 89,881 3778 11,805 58,713 62,752 65,346 57,243 64,597 16,306 12,392 1319 255 5180 78,290 37,821 10,311 8037 1079 0 0 0 0 270 1705 0 1419 9633 15,896 30,375 108,580 237,199 85,922 242,639 19,0775 0 0 0 1490 1289 914 1307 478 0 1000 9466 215,244 8045 23,186 394,771 59,919 0 747 7864 27,216 13,364 10,315 3773 597 896 16 1993 15,101 7849 3680 428 492 0 0 0 0 0 19,066 4400 10,059 480 0 19,865 85,780 45,188 1,893,824 501,646 1821 0 0 0 0 0 0 0 0 7625 58,755 12,414 84,221 25,722 45,410 48,943 199,258 0 0 4787 1852 1060 1095 0 220 17,786 6151 38,791 113,274 9782 10,491 3519 3409 0 0 0 0 180 50,413 39,083 475,238 0 595 2755 4600 7115 0 2725 4000 0 0 0 225 1105 233 447 4743 17,786 7898 60,908 357,586 32,251 45,087 402,063 64,145 0 0 0 0 0 0 0 0 480 0 19,865 85,780 45,188 1,893,824 501,646 1821 896 16 1993 15,101 7849 22,746 4828 10,551 7625 59,350 15,169 88,821 33,017 95,823 90,751 678,496 0 0 0 0 0 0 0 0 5084 5084 5084 5084 5084 5084 5084 5084 1701 1701 1701 1701 1701 1701 1701 1701 3311 3311 3311 3311 3311 3311 3311 3311 4213 4213 4213 4213 4213 4213 4213 4213 779 779 779 779 779 779 779 779 779 779 779 779 779 779 779 779

September October November December 0 0 0 0 0 0 7337 4203 225 0 45,317 170 44,783 130 2959 1243 9927 0 424,088 317 5476 304,165 7289 1148 50,706 0 9927 4202 735,542 0 5084 1701 3311 4213 779 779

0 0 0 0 0 0 281,066 223,921 603,659 241,622 304,867 55,190 7791 1117 456,005 22,183 881 13,641 227,577 406 229,133 346,089 3581 2256 238,447 0 14,522 478,188 577,247 0 5084 1701 3311 4213 779 779

Annual

0 0 3,926,087 0 0 9,705,497 0 0 8,387,207 0 0 0 0 0 27,118,671 0 0 1,868,846 111,428 224,323 5,842,299 497,902 460,400 1,535,580 1,787,921 2,580,913 5,115,010 1,047,587 110,359 1,402,962 1,056,438 615,297 2,942,938 612,789 995,510 1,669,137 80,092 103,934 948,231 7023 17,127 89,273 959,629 519,013 1,968,061 52,547 27,017 136,515 87,819 329,187 297,6418 191,951 41,774 247,366 332,236 184,921 1,651,170 1039 365 11,141 257,755 307,985 1,003,552 253,728 183,950 1,652,846 16,410 4560 53,630 3046 5933 19,136 345,909 429,411 2,052,197 0 0 0 279,770 370,961 3,223,784 1,012,176 546,030 2,104,576 602,374 373,431 3,357,646 0 0 0 5084 5084 61,006 1701 1701 20,408 3311 3311 39,730 4213 4213 50,559 779 779 9354 779 779 9354

(Continued)

Table 3.3: (Continued) Raw material Commercial Wood

African palm

Jatropha

Home

January

February

March

April

May

June

July

August

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

September October November December 1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

1841 616 1199 1525 282 282 0 24,517 0 0 6129 0 0 44,150 44,150 44,150

Annual 22,087 7389 14,384 18,304 3386 3386 0 294,204 0 0 73,548 0 0 529,800 529,800 529,800

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 59 Table 3.4: Bioethanol demand in each market during the year in tons Period

1

2

3

4

5

January February March April May June July August September October November December Annual

181,960 121,307 90,980 75,817 75,817 60,653 60,653 75,817 75,817 90,980 121,307 181,960 1,213,068

81,091 54,061 40,545 33,788 33,788 27,030 27,030 33,788 33,788 40,545 54,061 81,091 540,606

114,146 76,097 57,073 47,561 47,561 38,049 38,049 47,561 47,561 57,073 76,097 114,146 760,970

95,858 63,905 47,929 39,941 39,941 31,953 31,953 39,941 39,941 47,929 63,905 95,858 639,054

70,515 47,010 35,257 29,381 29,381 23,505 23,505 29,381 29,381 35,257 47,010 70,515 470,098

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. ElHalwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Table 3.5: Biodiesel demand in each market during the year in tons Period

1

2

3

4

5

January February March April May June July August September October November December Annual

25,709 51,419 38,564 19,282 16,068 16,068 12,855 12,855 12,855 16,068 16,068 192,82 257,093

13,482 26,963 20,223 10,111 8426 8426 6741 6741 6741 8426 8426 10,111 134,817

20,469 40,938 30,703 15,352 12,793 12,793 10,234 10,234 10,234 12,793 12,793 15,352 204,689

17,289 34,578 25,933 12,967 10,806 10,806 8644 8644 8644 10,806 10,806 12,967 172,889

12,631 25,261 18,946 9473 7894 7894 6315 6315 6315 7894 7894 9473 126,307

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. ElHalwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Table 3.6: Ecoindicator-99 for the products considered Product

Ecoindicator-99 (ton)

Ethanol Biodiesel

32.12 10.15

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

60

Chapter 3

Table 3.7: Parameters for the transportation of products from processing plants to markets Processing Hub Tula (main plant)

Salamanca

Cadereyta

Cd. Madero

´n Minatitla

Salina Cruz

Distance (km) Cost US$ (ton) Ecoindicator-99 (ton) Type of Transport Market 178.0 914.8 532.3 2550.8 1046.9 380.3 702.9 277.1 2518.9 1889.9 1020.5 26.0 898.9 2262.5 2530.1 615.6 601.5 788.7 2814.9 1806.4 597.2 1461.7 1139.0 3380.8 1034.4 819.7 1684.2 1361.5 2620.0 1339.9

1.4992E 2 11 2.8206E 2 08 4.4844E 2 11 7.8653E 2 08 8.8199E 2 11 3.2038E 2 11 2.1672E 2 08 2.3341E 2 11 7.7667E 2 08 1.5922E 2 10 3.1466E 2 08 2.1904E 2 12 2.7716E 2 08 6.9761E 2 08 2.1315E 2 10 1.8982E 2 08 5.0671E 2 11 2.4319E 2 08 8.6796E 2 08 1.5218E 2 10 5.0315E 2 11 1.2315E 2 10 9.5956E 2 11 1.0424E 2 07 8.7145E 2 11 6.906E 2 11 1.4189E 2 10 5.1976E 2 10 1.0002E 2 09 1.1288E 2 10

0.1459 0.7500 0.4365 2.0915 0.8584 0.3118 0.5763 0.2272 2.0653 1.5496 0.8367 0.0213 0.7370 1.8551 2.0746 0.5048 0.4932 0.6467 2.3081 1.4811 0.4897 1.1985 0.9339 2.7720 0.8481 0.6721 1.3810 1.1163 2.1482 1.0986

Duct Tank truck Duct Tank truck Duct Duct Tank truck Duct Tank truck Duct Tank truck Duct Tank truck Tank truck Duct Tank truck Duct Tank truck Tank truck Duct Duct Duct Duct Tank truck Duct Duct Duct Tank ship Tank ship Duct

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Table 3.8: Data for the transportation of products from the main plan to processing hubs Distance (km) 226.3 872.5 531.2 642.3 870.8

Cost US$ (ton)

Ecoindicator-99 (ton)

Processing Hub

1.9061E 2 11 7.3501E 2 11 4.4753E 2 11 5.4109E 2 11 7.3359E 2 11

0.18551029 0.71536049 0.43556587 0.52661965 0.7139748

Salamanca Cadereyta Cd. Madero Minatitla´n Salina Cruz

From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. ElHalwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

environmental impact because a reduction in the latter objective can only be achieved by compromising the net profit of the biorefinery SC. Furthermore, each point of the Pareto curve entails a specific SC configuration along with a corresponding set of planning decisions.

Optimal Planning and Site Selection 61

Figure 3.8 Pareto curve between annual profit and environmental impact for different penalties due to unsatisfied demand. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

In addition, the analysis considered different penalties if demands were not satisfied, which consequently decreases net profit for the same environmental impact. Moreover, the number of jobs generated remains constant for a given environmental impact. When the penalty for the unsatisfied demand is considered, the economic benefit is negative on the left side of the Pareto curves. Conversely, the environmental impact and the number of generated jobs increase when the net economic profit is fixed. This is an effect of the social objective on the economic perspective. This increase is more noticeable on the right side of the Pareto curves shown in Fig. 3.8. The number of generated jobs increases until a maximum value in the Pareto curves is reached; the feedstocks selected at these points are wood chips and sorghum for ethanol production, and Jatropha and African palm for biodiesel production. It is important to analyze the types of jobs generated because their social impacts differ. For example, the social impact of jobs generated for producing raw materials (located in marginal areas in such countries as Mexico) differs from that of jobs generated for transporting materials and manufacturing products. Fig. 3.9 shows the distribution of jobs generated for some of the Pareto solutions shown in Fig. 3.8, which depends on the type of feedstocks processed, generated products, and the type of transportation used. Fig. 3.9 indicates that the majority of jobs are generated for the processing step, which primarily benefits the locations where the hubs and central processing facilities are installed. For the Pareto solutions that do consider the number of generated jobs as objective (because this is

62

Chapter 3

Figure 3.9 Percentage of the number of jobs of different types for points of the Pareto curve Profit-EI of Fig. 3.8. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo SernaGonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

a fixed parameter because solutions exclusively consider the trade-offs between economic and environmental objectives), most of the jobs generated strongly depend on the processing steps and transportation tasks. Therefore, the number of jobs generated tends to be independent of the biomass production at harvesting sites, where it is most important to have a large social impact. Conversely, when the net profit decreases, the number of jobs tends to be concentrated on biomass production tasks, which positively impacts the rural societies of developing countries such as Mexico, where agricultural areas are the poorest. After analyzing the Pareto curves of the case involving trade-offs between economic and environmental objectives (without constraining the social objective), the next analysis maximizes the social benefit while minimizing the environmental impact for different fixed values of the minimum net profit between 0 and US$4 3 107. Fig. 3.10 shows the resulting Pareto curves for this scenario. Here, the social benefit is highly significant, generating up to 23,000 jobs. The number of jobs generated strongly depends on the environmental impact if Environmental Impact (EI) is low (i.e., , 0.7 3 108) and the net profit is lower than 4 3 107 US$/year. In addition, the number of jobs generated correlates positively with the environmental impact (Fig. 3.10). This effect positively impacts the society due to the number of jobs generated, but negatively impacts the environment. Thus, a trade-off exists between these objectives. Conversely, the net profit inversely correlates with the number of jobs generated. Therefore, the economic and social objectives conflict with one another. Fig. 3.10 indicates the maximum social benefit and environmental impact for given values of the net profit, which is very useful information to support the optimal selection of biorefinery SCs. Fig. 3.11 shows the distribution of the number of jobs generated when the social benefit is maximized and the environmental impact is minimized for different values of the minimum

Optimal Planning and Site Selection 63 Pareto curves jobs vs EI

25,000

Generated jobs (jobs/year)

This is a region with negative profit 20,000

Prof it greater than zero

15,000

A

Prof it greater than 2x107 US$/year

10,000

5000

0 0.00E + 00

Prof it greater than 4x107 US$/year

1.00E + 08

2.00E + 08

3.00E + 08

4.00E + 08

5.00E + 08

6.00E + 08

7.00E + 08

Environmental impact (ecoindicator99/year)

Figure 3.10 Pareto curve for the social benefit versus environmental impact for the minimum annual profit. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo SernaGonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Figure 3.11 Profiles of number of jobs generated considering net profit constraints. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

64

Chapter 3

net profit. It should be noted that biomass production is the main contributor to the number of jobs generated when the net profit constraint is relaxed; whereas the number of generated jobs associated with processing plants is higher when the net profit constraint is stricter for a given environmental impact because the amount of feedstock processed increases. An increase in the use of sugarcane and a little of sorghum respect to the Pareto curves for the maximum net profit versus minimum environmental impact (i.e., solutions of Fig. 3.8), where these biomass feedstocks are not included in the optimal solutions. Fig. 3.12 shows the Pareto sets of optimal solutions for the number of jobs generated versus the maximum net profit for given values of the environmental impact. These results clearly indicate that both objectives are in conflict: improving the social benefit decreases the net profit and vice versa. This figure indicates that the number of generated jobs is a decreasing near-linear function of the net profit, attaining its lowest values for large net profits and low environmental impacts. Furthermore, the social benefit decreases as the penalty for unmet demand decreases when the environmental impact is constant. Finally, Fig. 3.13 shows the Pareto curves for maximizing the generated jobs and minimizing the environmental impact for different values of the minimum net profit considering diverse penalties for the unsatisfied demand. The results show that when the

Figure 3.12 Pareto curve for the social benefit versus the annual profit. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 65 Pareto curves jobs vs EI with penalty for unmet demand

Generated jobs (jobs/year)

25,000

This is a region with negative profit 20,000

15,000

Prof it greater than zero without penalty

Prof it greater than 2x107 US$/year with 0.5% of penalty

10,000

5000

Jobs decrease while the penalty increases

Prof it greater than 4x107 US$/year with 1% of penalty

The EI increases while the penalty increases

0 0.00E + 00 1.00E + 08 2.00E + 08 3.00E + 08 4.00E + 08 5.00E + 08 6.00E + 08 7.00E + 08

Environmental impact (ecoindicator99/year)

Figure 3.13 Pareto curve for the maximization of the social benefit and the minimization of the environmental impact considering penalizations due to unsatisfied demand. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

penalty increases, the generated jobs decrease for the same environmental impact. In addition, if the number of generated jobs is fixed, the environmental impact increases significantly when the penalization for the unsatisfied demand increases.

3.5 Discussion The trade-offs between the three objectives of sustainability considered in this work can be analyzed using the aforementioned figures. The Pareto set of optimal solutions helps decision makers to choose the solution that best satisfies sustainable criteria. For example, an optimal solution can be selected from the Pareto curve shown in Fig. 3.10, which illustrates the tradeoffs between the number of jobs generated (objective not addressed in previous reported approaches, e.g., Bowling et al., 2011) and the environmental impact. While the Pareto front has a significant slope if the environmental impact is low (i.e., EI , 0.7 3 108), the remainder of the solution curve levels off. These results suggest that the solution at point A is one of the most promising alternatives to generate a significant number of jobs without overly compromising the environmental impact of the biorefinery SC. At this point, the number of jobs is 13,000, the environmental impact is 1 3 108 ecoindicator-99 points and the net profit

66

Chapter 3

is US$2 3 107. The geographical distribution (i.e., optimal locations) of the harvesting sites, markets, and processing plants for solution A are given in Fig. 3.14. Here, only four harvesting sites, two processing facilities, and four markets are selected. The SC configuration and site selection of the solution for point A are depicted in Fig. 3.15. This figure shows the number and type of processing plants installed along with the chosen feedstocks, obtained products, as well as their distribution throughout the SC are shown. Only harvesting sites 3, 4, 5, and 6 are involved in supplying biomass to processing plants. Fig. 3.15 shows the interaction between feedstocks and products for different biomass production methods, processing techniques, and market places over the entire time span considered in the analysis. The optimal SC configurations are identical over all periods. Furthermore, the biorefinery SC in Fig. 3.15 has a distributed topology, which properly accounts for the economies of scale and reduction in transportation costs. This accuracy can be achieved because processing hub 1 and the central processing plant appear in the optimal solution, using different raw materials and producing different products over the entire time span considered. The economies of scale associated with the production technologies have not been considered in most of the previously reported methodologies for biorefinery SCs (e.g., You, Tao, Graciano, & Snyder, 2012).

Figure 3.14 Studied region indicating the selected locations of the harvesting sites, markets, and processing plants. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 67

Figure 3.15 SC configuration for solution A. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

In addition, Figs. 3.16 and 3.17 show the main feedstocks used in the different processing facilities for bioethanol and biodiesel production, respectively. The main feedstocks represented in these figures are sorghum and sugarcane to obtain bioethanol

68

Chapter 3 (A) Amount of raw material sent from harvesting sites to plants (tons)

600,000

500,000

400,000

300,000

200,000

100,000

0 ry ry rch pril ua rua a A n M b Ja Fe

(B) Amount of raw material sent from harvesting sites to plants (tons)

10,000

ay

M

ne Ju

ly er st er er er Ju ugu mb ob mb emb t c e A ve ec O pt D No Se

8000

Wood chips from harvesting site 3 to hub 1

6000

Wood chips from harvesting site 3 to main Wood chips from harvesting site 4 to main Sorghum from harvesting site 4 to main

4000

Sorghum from harvesting site 5 to hub 1 Wood chips from harvesting site 5 to main Sorghum from harvesting site 5 to main Wood chips from harvesting site 6 to main

2000

Sugar cane from harvesting site 6 to main

0 ril ay ne uly ust ber ber ber ber ry ry ch J ug ua rua ar Ap M Ju o n M b A ptem Oct ovem cem Ja Fe e N De S

Figure 3.16 Feedstocks used for ethanol production in different processing plants for solution A: (A) general view and (B) zoom of this figure. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 69

Figure 3.17 Feedstocks used for biodiesel production in different processing plants for solution A. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

and Jatropha for the production of biodiesel, as reported by Santiban˜ez-Aguilar et al. (2011). At point A, bioethanol is sent only to market 1 (which is the greatest consumer), whereas biodiesel is sent from the different processing plants to all markets except market 4, which is far from the harvesting sites of feedstocks and processing facilities (Figs. 3.18 and 3.19). Furthermore, the generated jobs are diversified for the most decentralized solution; thus, many places are benefited by the resultant diverse jobs for biomass production and transportation. However, the associated cost for the entire SC may increase because the majority of processing plants are distributed throughout the system. While the social benefit decreases for the most centralized solutions because the jobs are not distributed in the region considered, the number of jobs associated with transportation also decreases. Nevertheless, the economic objective function benefits because the capital and operational costs for the processing facilities are reduced. The environmental impact is not relevant to this analysis. Finally, these results were obtained without numerical complications, and the proposed methodology considers different scenarios and compensations for the involved objectives, a feature that is very useful for decision makers.

Figure 3.18 Bioethanol distribution for solution A. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Figure 3.19 Biodiesel distribution for solution A. From Jose´ Ezequiel Santiban˜ez-Aguilar, J. Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Medardo Serna-Gonza´lez, Mahmoud M. El-Halwagi, Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives, Journal of Cleaner Production, 2014.

Optimal Planning and Site Selection 71

3.6 Concluding Remarks This chapter has presented a model to design and plan sustainable distributed biomass processing systems that manufacture multiple products optimally using a variety of biomass feedstocks and diverse production technologies. The problem was mathematically formulated as a multiobjective, multiperiod problem that seeks to maximize the net profit, minimize the environmental impact and maximize the number of jobs generated by implementing the biorefinery SC. The environmental impact was measured using the ecoindicator-99, which includes the recent advances in life cycle analysis. The ε-constraint method was applied to obtain the trade-offs between the three objectives considered. The model incorporates important features that should be considered when implementing a biorefinery SC. These features include (1) the simultaneous consideration of economic, environmental, and social objectives; (2) variations in the availability and cost of bioresources throughout the year; (3) diverse production technologies to produce multiple products using a variety of biomass feedstocks that are geographically distributed; and (4) distributed biomass processing to reduce transportation costs and include the effects of economies of scale on the performance of the biorefinery SC through the installation of preprocessing hubs and central processing facilities. The application of the proposed model was illustrated with a case study for a multiproduct biorefinery SC in Mexico. The solutions obtained by our approach indicated that this model can provide Pareto curves to evaluate the complex trade-offs between the economic, environmental, and social objectives of sustainability considered for biorefinery SCs. In addition, the Pareto solutions can provide valuable insights for decision makers to select the solution that shows the best compromise among the considered objectives. The results of the case study show that cost-effective solutions can be obtained in Mexico by choosing feedstocks that are available year-round and without significantly affecting the environment. From an economic point of view, wood chips are selected as the feedstock to produce ethanol because of their low cost in relation to the value of the ethanol. However, sugarcane and sorghum present more environmentally friendly feedstocks to produce ethanol because of their lower overall ecoindicator-99. For the production of ethanol, sugarcane and sorghum yield the most important social benefits. Similarly, biodiesel production from Jatropha showed significant social benefits. All of these sources created a significant number of jobs in rural regions. This feature is notably important in such countries as Mexico, where the rural regions that produce biomass are the poorest. Finally, results show that fossil fuels can be partially replaced by biofuels obtained from different feedstocks. Further research is needed to include changes in the biomass properties in our approach because such changes can require additional biomass pretreatment to homogenize the mass and energy potential of the material. Such properties include the bulk density and moisture during storage and transportation in the SC. The water requirements for biomass production

72

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can also be integrated into the proposed model to consider the effects of specific crops placement on the water quality of the corresponding watershed. Finally, future extensions of this work should incorporate the variability of uncertain parameters (i.e., life cycle inventory of emissions) to obtain solutions that perform well in all possible scenarios.

3.7 Nomenclature 3.7.1 Sets M K R H PH MK T

Set Set Set Set Set Set Set

that contains the raw materials for products processing routes that contains the harvesting sites that contains the secondary processing plants that contains the markets that contains the periods of time

3.7.2 Indexes m k r h ph mk t

Index to Index to Index to Index to Index to Index to Index to

indicate the indicate the indicate the indicate the indicate the indicate the indicate the

contained contained contained contained contained contained contained

elements elements elements elements elements elements elements

into into into into into into into

the the the the the the the

set set set set set set set

M K R H PH MK T

3.7.3 Parameters αm;k;r Cksold k;mk;t produced

Cmm;h;t

storage main

Cmm;h

storage plant

, Cmm;ph

storage main Cmm storage plant Ckk;ph

,

storage main Ckk

,

,

Efficiency factor for the  conversion of the raw material m to  product k through the processing route tonne product=tonne raw material Unit cost for the product k in the market mk in the period of time t   US$=tonne product Unit cost to the production of raw material m in the harvesting site h in the period of time t US$=tonne raw material Costs for the storage of feedstock m in the harvesting site h, hub ph, and main plant ðUS$Þ

Costs for the storage of product k in the hub ph, main plant, and the market mk, respectively ðUS$Þ

storage market Ckk;mk

(Continued)

Optimal Planning and Site Selection 73 (Continued) harvesting sitesplant Ctmm;h;ph;t

Unit cost for the transportation  of feedstock m from the harvesting site h to the hub ph in the period of time t US$=tonne raw material

harvesting sitesmain

Unit cost for the transportation offeedstock m from the harvesting site h to the  main plant in the period of time t US$=tonne raw material

Ctmm;h;t

plantmarket Ctkk;ph;mk;t

Unit cost for the transportation of product k from the hub ph, to the market mk  in the period of time t US$=tonne product

plantmain

Unit cost for the transportation of product k from the hub ph to the main plant  in the period of time t US$=tonne product

mainmarket Ctkk;mk;t

Unit cost for the transportation of product k from   the main plant to the market mk in the period of time t US$=tonne product

Ctkk;ph;t

processing main

processing

Cm;k;r;ph;t , Cm;k;r;t product

EcoIndk EcoIndraw m

material

harvesting sitesplant EcoIndmm;h;ph harvesting sitesmain

EcoIndmm;h

plantmarket EcoIndkk;ph;mk plantmain

EcoIndkk;ph

mainmarket EcoIndkk;mk processing EcoIndm;k;r;ph;t

processing main

EcoIndm;k;r;t upper produced Mm;h;t demand Pk;mk;t upper

lower Pm;k;r;l , Pm;k;r;l upperl

Smlowerl , Sms;l s;l raw material SIm

harvesting sitesplant SIm;h;ph

Unit costs for processing to produce product k from feedstock m through processing route r, in the secondary and main plants in the period of time t   US$=tonne raw material   Unit ecoindicator-99 to use the product k ecoindicator-99=tonne product m Unit ecoindicator-99 to produce the feedstock  ecoindicator-99=tonne raw material Unit ecoindicator-99 for  the transportation of feedstock m from  harvesting site h to secondary plant ph ecoindicator-99=tonne raw material Unit ecoindicator99 for the transportation of feedstock   m from harvesting site h to main plant ecoindicator-99=tonne raw material Unit ecoindicator-99 for the transportation of product k from secondary plant ph   to market mk ecoindicator-99=tonne product Unit ecoindicator-99 for the transportation of the product k from the secondary plant ph to the main plant ecoindicator-99=tonne product Unit ecoindicator-99  for the transportation of the product k from the main plant to the market mk ecoindicator-99=tonne product Unit ecoindicator-99 to produce the product k from the feedstock m through the processing route r at the period of time  t in the secondary plant ecoindicator99=tonne raw material Unit ecoindicator-99 to produce the product k from the feedstock m through the processing route r at the period of time  t in the main plant ecoindicator-99=tonne raw material Maximum production of feedstock m that can be producedin the harvesting site h at the period of time t tonne raw material=each month mk at the end of period of time t Demand of product k in the market  tonne product=each month Upper and lower processing limits for the feedstock m to product k through the processing route r in the location l Lower and upper storage limits of the material s in la localization l (tonne)   Jobs generated to produce the feedstock m job=tonne raw material Jobs generated to transport the feedstock m from the harvesting site h to the   secondary plant ph job=tonne raw material (Continued)

74

Chapter 3 (Continued)

harvesting sitesmain SIm;h

Jobs generated m from the harvesting site h to the  to transport the feedstock  main plant job=tonne raw material

plantmain

Jobs generated to transport the feedstock m from the secondary processing  facilities to main plant job=tonne raw material

SImm;ph plantmain SIk;ph plantmarket SIk;ph;mk mainmarket SIk;mk

processing

Jobs generated  to transport theproduct k from the secondary plant ph to the market mk job=tonne product Jobs generated  to transport the  product k from the secondary plant ph to the main plant job=ton product the product k from the main plant to the market mk Jobs generated to transport  job=tonne product processing main

SIm;k;r;ph;t , SIm;k;r;t

Jobs generated to produce product k from feedstock m through processing route r at period of time t in the secondary and main plants, respectively job=tonne raw material

3.7.4 Variables harvesting sites

Mm;h;t

produced

Mm;h;t

harvesting sitesplant

Mm;h;ph;t

Feedstock m accumulated at theend of the period of time t in the harvesting site h ton raw material=each month site h at the end of time t Feedstock m produced in the harvesting  ton raw material=each month Feedstock m transported  from the harvesting site h to the  secondary plant ph at the end of the period of time t ton raw material=each month

harvesting sitesmain

Feedstock m transported from the harvesting siteh to the main plant at the end of the  period of time t ton raw material=each month

plant

Feedstock m accumulated at theend of period of time t in the secondary plant ph  ton raw material=each month Feedstock  m arrived from the harvesting site  h to the secondary plant. ph at the end of period t ton raw material=each month

Mm;h;t

Mm;ph;t harvesting sitesplant

Mem;h;ph;t

processing

Mm;k;r;ph;t Mmain m;t plantmain

Mem;ph;t

harvesting sitesmain

Mem;h;t

procesing main

Mm;k;r;t plant

Pk;ph;t

produced

Pm;k;r;ph;t

Feedstock m processed in the hub ph through the processing route r to produce  the product k at the end of the period of time t ton raw material=each month Feedstock m accumulated at theend of period of time t in the main plant  ton raw material=each month Feedstock m arrived from the hub   ph at the end of the period of time t ton raw material=each month Feedstock m arrived from the harvesting site h at the end of the period of time   ton raw material=each month Feedstock m processed in the mainplant through the processing route  r to produce the product k at the end of the time t ton raw material=each month Product k accumulated in thesecondary plant ph at the end of the period of time t  tonne product=each month Product k produced from the feedstock m through the processing   route r in the hub ph at the end of the period of time t tonne product=each month (Continued)

Optimal Planning and Site Selection 75 (Continued) Product k accumulated in themain plant at the end of the period of time t  tonne product=each month Product k produced from the feedstock m through the processing route r in the main   plant at the end of the time t tonne product=each month

main Pk;t producedmain

Pm;k;r;t

plantmain Pek;ph;t

Product k arrived from the hub   ph to the main plant at the end of period of time t tonne product=each month

mainmarket Pk;mk;t plant-market Pek;ph;mk;t

Product  k transported from the main plant to the market mk at the end of period of time t tonne product=each month Product k arrived from the secondary plant ph at the end of period of time t   tonne product=each month Product k arrived from the main   plant at the end of period of time t tonne product=each month Product k sold in the market mk   at the end of period of time t tonne product=each month Material s stored in location l in the period of time  t tonne product or raw material=each month

main-market Pek;mk;t sold Pk;mk;t l Ss;l;t

3.7.5 Binary Variables l necesary

yss;l ysls;l;t

ym;l1;l2;t ym;k;r;l;t ypmm;h;t

Binary variable to define if the store of material s in the localization l is necessary in any period of time t Binary variable to define if the storage of material s in the localization l is necessary in a specific period of time t Binary variable to define if the transportation of the material m is done from the localization l1 to l2 in a period of time t Binary variable to define if the processing in the localization l is necessary to produce the product k from the feedstock m through the processing route k in the period of time t Binary variable to define if the production of feedstock m in the harvesting site h is necessary in any period of time t

3.7.6 Boolean Variables Ysls;l;t

Boolean variable to define if the storage of material s is necessary in the localization l in a period of time t

References Bowling, I. M., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2011). Facility location and supply chain optimization for a biorefinery. Industrial and Engineering Chemistry Research, 50(10), 62766286. Brooke, A., Kendrick, D., Meeruas, A., & Raman, R. (2018). GAMS-language guide. Washington, DC: GAMS Development Corp.

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Castro, P. M., & Grossmann, I. E. (2006). An efficient MILP model for the short-term scheduling of single stage batch plants. Computers and Chemical Engineering, 30(67), 10031018. Chouinard-Dussault, P., Bradt, L., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2011). Incorporation of process integration into lifecycle analysis for the production of biofuels. Clean Technologies and Environmental Policy, 13(5), 673685. Cucek, L., Klemes, J. J., & Kravanja, Z. (2012). A review of footprint analysis tools for monitoring impacts on sustainability. Journal of Cleaner Production, 34, 920. Diwekar, U. M. (2003). Introduction to applied optimization. Norwell, MA: Kluwer Academic Press. Dutta, A., Dowe, N., Ibsen, K. N., Schell, D. J., & Aden, A. (2010). An economic comparison of different fermentation configurations to convert corn stover to ethanol using Z. mobilis and Saccharomyces. Biotechnology Progress, 26(1), 6472. Geodkoop, M., & Spriensma, R. (2001). The ecoindicator 99, a damage oriented for lifecycle impact assessment: methodology report and manual for designers. Technical report, PRe Consultants, Amersfoort. The Netherlands. Guinee, J. B., Gorree, M., Heijungs, R., Huppes, G., Kleijn, R., de Koning, A., . . . Huijbregts, M. A. J. (2002). Handbook on lifecycle assessment: operational guide to the ISO standards. Dordrecht, The Netherlands: Kluwer Academic Publishers. Holladay, J. E., Bozell, J. J., White, J. F., & Johnson, D. (2007). Top value-added chemicals from biomass. Volume II: Results of screening for potential candidates from biorefinery lignin. Report No. PNNL-16983. Pacific Northwest National Laboratory. Washington, DC. Huber, G. W., Iborra, S., & Corma, A. (2006). Synthesis of transportation fuels from biomass: Chemistry, catalysts, and engineering. Chemical Reviews, 106(9), 40444098. IMPLAN. (2012). Economic impact analysis. Minnesota IMPLAN Group LLC. MIG Inc. Available from www. implan.com/. JEDI (2012). Job and economic development impact model. Denver, Colorado, USA. ,www.nrel.gov/analysis/ jedi/.. Kazi, F., Fortman, J., Anex, R., Kothandaraman, G., Hsu, D., Aden, A., & Dutta, A. (2010). Techno-economic analysis of biochemical scenarios for production of cellulosic ethanol. Golden, CO: National Renewable Energy Laboratory, NREL/TP-6A2-46588, Denver, USA. Maravelias, C. T., & Grossmann, I. E. (2003). New general continuous-time state-task network formulation for short-term scheduling of multipurpose batch plants. Industrial and Engineering Chemistry Research, 42 (19), 30563074. PEMEX. (2010). Memory of work 2010. Annual report for the Mexican Ministry of Oil. Mexico City, Mexico. ,www.pemex.com/files/content/Version_completa_memoria_de_labores_2010.pdf.. Pokoo-Aikins, G., Nadim, A., Mahalec, V., & El-Halwagi, M. M. (2010). Design and analysis of biodiesel production from algae grown through carbon sequestration. Clean Technologies and Environmental Policy, 12(3), 239254. Ponce-Ortega, J. M., Jimene´z-Gutie´rrez, A., & Grossmann, I. E. (2008). Optimal synthesis of heat exchanger networks involved isothermal process streams. Computers and Chemical Engineering, 32(8), 19181942. SAGARPA-SIAP. (2011). Mexican system of information about agriculture and fishing. Advance of planting and harvesting for Mexico. Mexico City, Mexico. ,www.siap.gob.mx/index.php?option 5 com_wrapper &view 5 wrapper&Itemid 5 347.. Santiban˜ez-Aguilar, J. E., Gonza´lez-Campos, J. B., Ponce-Ortega, J. M., Serna-Gonza´lez, M., & El-Halwagi, M. M. (2011). Optimal planning of a biomass conversion system considering economic and environmental aspects. Industrial and Engineering Chemistry Research, 50(14), 85588570. Santiban˜ez-Aguilar, J.E., Gonza´lez-Campos, J.B., Ponce-Ortega, J.M., Serna-Gonza´lez, M., & El-Halwagi, M.M. (2014). Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives. Journal of Cleaner Production, 65, 270294.

Optimal Planning and Site Selection 77 Saxena, R. C., Adhikari, D. K., & Goyal, H. B. (2009). Biomass-based energy fuel through biochemical routes: A review. Renewable and Sustainable Energy Reviews, 13(1), 167178. Saxena, R. C., Seal, D., Kumar, S., & Goyal, H. B. (2008). Thermo-chemical routes for hydrogen rich gas from biomass: A review. Renewable and Sustainable Energy Reviews, 12(3), 19091927. SEMARNAT. (2012). Mexican Ministry of Environmental and Natural Resources. Forest Almanac 2011. General council for social communication, General direction for land and forest management. Mexico City, Mexico. ,www.semarnat.gob.mx/tramites/gestionambiental/forestalsuelos/Anuarios/Anuario% 20Forestal%202006.pdf.. Werpy, T., Petersen, G., Aden, A., Bozell, J., & Holladay, J. (2004). Top value added chemicals from biomass, volume I: Results of screening for potential candidates from sugars and synthesis gas. Washington, DC: Pacific Northwest NationalLaboratory (PNNL) and National Renewable Energy Laboratory (NREL). You, F., Tao, L., Graciano, D. J., & Snyder, S. W. (2012). Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with lifecycle assessment and inputoutput analysis. AIChE Journal, 58(4), 11571180. Zhu, Y., & Jones, S. (2009). Techno-economic analysis for the thermochemical conversion of lignocellulosic biomass to ethanol via acetic acid synthesis. Richland, WA: Pacific Northwest National Laboratory, [PNNL-18483].

Further Reading INE. (2012). Final report for the integrated analysis for the technologies and option for sustainability and options for the bioenergy in Mexico. Mexico City, Mexico. ,www2.ine.gob.mx/descargas/cclimatico/ e2008e_bioenergia.pdf..

CHAPTER 4

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 4.1 Introduction Water hyacinth causes severe ecological problems. Several strategies have been proposed to eliminate this plant, but most of them have not been economically attractive. This chapter proposes a general superstructure and mathematical programming model for the sustainable elimination of water hyacinth through a distributed biorefining network. The proposed model optimizes the selection of the products, siting and sizing for the processing facilities and the selection of the markets while accounting for technical and economic constraints. A case study for the central part of Mexico is used to show the applicability of this proposed holistic approach. Results show that an optimally synthesized distributed biorefining network is capable of the sustainable and economic elimination of water hyacinth from contaminated water bodies while generating value. Additionally, the results shown through Pareto curves allow the identification of a set of optimal solutions featuring trade-offs between economic and environmental objectives (see Fig. 4.1).

4.2 Outline of the Model Formulation Water hyacinth can be considered as a raw material used to produce some products because it includes biomass in its structure; in addition, this plant has a lot of water. The water hyacinth is a source of clean water and dry biomass that can be obtained when the plant is processed. The removed water has some pollutants, so it has to be treated to eliminate them and yield clean water. Therefore, as can be seen in Fig. 4.2, the processing of water hyacinth contributes to clean water bodies and, at the same time, generates biomass and clean water that are valuable. The proposed model is based on the superstructure presented in Fig. 4.3, which also considers the representation shown in Fig. 4.4, where there are several places (rivers and lakes) distributed over a given region (as can be seen in Fig. 4.1) that have huge amounts of water hyacinth. In the optimization formulation, a superstructure must be constructed to include the Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00004-3 © 2019 Elsevier Inc. All rights reserved.

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Figure 4.1 Schematic representation of the distribution of sources and sinks of the problem. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Figure 4.2 Representation of the potential uses of water hyacinth obtained from the water bodies. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Figure 4.3 Superstructure for the distributed supply chain based on water hyacinth. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

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Figure 4.4 Representation for the distributed supply chain based on water hyacinth. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

possible places to locate the secondary and central processing facilities, the possible water bodies to be treated and the possible consumers. The water bodies to be treated are the places infested by water hyacinth, and the central processing facilities can be located in the places where there are huge amounts of available water hyacinth and are close to industrialized zones; whereas the secondary processing facilities can be located near water bodies infested by the water hyacinth and far from industrialized zones. Usually, the secondary processing facilities are smaller than the central processing facilities, and the unit processing costs for the central processing plants are lower than the ones for secondary processing plants. The consumers are selected considering the demands for the products that can be produced by the system. The produced clean water can be sent to consumers by pipelines whereas the chemical products and biofuels can be sent by truck, train or pipeline (if they are liquids) to consumers. To efficiently solve this problem, this chapter proposes to use the water hyacinth as a biomass source to produce biofuels and other products that can be used to satisfy the energetic requirements and specific demands of products generated for places in a given region. Therefore, the addressed problem in this chapter can be defined as follows: given a set of water bodies (s) with specified amounts of water hyacinth which can be used to produce

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 83 different products with known demands (k) to be distributed in several markets. The problem then consists of determining the location for the processing facilities (i) and their sizes, the technologies used (j), the requirements of water hyacinth in the different places (m) and the distribution of the products (p). The objective is to find the optimal distributed biorefinery system that simultaneously minimizes the overall net cost (or maximizes the net profit), while maximizing the percentage of the eliminated water hyacinth in order to control its growth in different water bodies.

4.3 Model Formulation Before we present the model formulation, we define the following indexes: s represents the water bodies that are sources of water hyacinth, i processing facility, j corresponds to biomass processing technologies available, p corresponds to the bioproducts, k is used to represent the markets for the bioproducts, n is used to define the technologies used to treat the recovered water, c is used to define the pollutants present in the recovered water and m represents the water consumers. The proposed model will combine the supply chain and water networks optimization models for the optimal design of a water hyacinth-based biorefinery in a distributed macroscopic system. The proposed model is stated as follows.

4.3.1 Mass Balance for the Harvesting of Water Hyacinth Two main methods are used to control water hyacinth: chemical control and mechanical control. Some of the advantages of mechanical control are: (1) the removal of superfluous nutrients, (2) immediate control without significant damage to the ecosystem and (3) it is suitable for open flowing as well as closed water systems. However, mechanical control is associated with high energy consumption due mainly to the power requirements for harvesting. Thus, one of the most important factors for the mechanical control of the water hyacinth is the large cost of harvesting, which is location-dependent. The water hyacinth used at source s (Fwhs) can be harvested and processed to extract biomass (Fbs) and water (Fws). The harvesting technology can extract the biomass from the water hyacinth with a given efficiency (Zwhs) as follows: Fwhs UZwhs 5 Fbs ;

sAS

(4.1)

In the same way, the harvesting technology can extract the water content in the water hyacinth with a given efficiency (Zws) as follows: Fwhs UZws 5 Fws ;

sAS

(4.2)

84

Chapter 4

4.3.2 Availability of the Harvested Water Hyacinth The harvested water hyacinth must be lower or equal than the maximum available water hyacinth ðFwhs max Þ at source s as Eq. (4.3) shows: Fwhs # Fwhs max ;

sAS

(4.3)

In this chapter, a mechanical method is considered for harvesting water hyacinth. As was mentioned above, this method is widely used due to its advantages, although it is too expensive and time consuming (Gunnarsson & Petersen, 2007). There are several machines for harvesting water hyacinth; for example, a conveyor-chopper, single conveyor and modified clamshell bucket. These machines have a maximum limit of harvesting and efficiency at obtaining water hyacinth. Several data for the water hyacinth harvesting process have been reported (Pham, Holtzapple, & El-Halwagi, 2010).

4.3.3 Mass Balance for the Splitters Before the Processing Plants The dry biomass extracted from water hyacinth in each location s ðFbs Þ can be segregated to the processing facility located in place i ðfbhub s;i Þ and to the central facility
andcendirected  fbs to treat it and to obtain the final products: X cen Fbs 5 fbhub sAS (4.4) s;i 1 fbs ; iAI

4.3.4 Balances for Mixers Before the Processing Facilities The total biomass flow rate inlet to the processing facility i and sent to the different bioconversion technologies j ðfbjhub i;j Þ is equal to the sum of the biomass distributed from the different harvesting places s ðfbhub s;i Þ as follows: X X fbhub 5 fbjhub s;i i;j sAS

’iAI

(4.5)

jAJ

4.3.5 Balances for the Technologies Used in the Processing Facilities In each processing facility, there are available several technologies that can be used to transform the biomass to final products. For example, the biomass from water hyacinth can be fermented to produce bioethanol; this process has been modeled previously (Chuang et al., 2011; Isarankura-Na-Ayudhya, Tantimongcolwat, Kongpanpee, Prabkate, & Prachayasittikul, 2007; Mishima et al., 2008; Nigam, 2002) and the technical performance and associated costs have been determined. The technologies available for the fermentation

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 85

Figure 4.5 General approach to produce ethanol from water hyacinth. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.


 of the water hyacinth are characterized with known conversion factors αhub that represent j;p the mass of product (i.e., p 5 bioethanol) produced for a given amount of biomass from water hyacinth. The general approach for the fermentation of water hyacinth to produce ethanol has been reported (Ganguly, Chatterjee, & Dey, 2012) and is shown in Fig. 4.5. The MixAlco process (Forrest, Hernandez, & Holtzapple, 2010; Kim & Holzapple, 2005; Lo´pez & Bocco, 2000; Mosier et al., 2005) is an interesting technology that can be used to produce a mixture of mixed alcohols through fermentation, thermal conversion and hydrogenation from biomass (see Fig. 4.6). This technology has been accurately modeled and optimized to determine its conversion efficiency (SENER, 2012) (i.e., the amount of mixed alcohols obtained from a given amount of biomass, αhub j;p . Anaerobic digestion is a biological process by which organic matter is degraded in the absence of oxygen producing biogas (Gunnarsson & Petersen, 2007). The biogas produced can be used to generate energy or electricity. This has been an interesting option to produce energy and reduce reliance on fossil fuels. An advantage is that water hyacinth can be easily degraded because it has a high content of fermentable matter that can be transformed into biogas. The digestion of this plant can solve the problems caused by its excessive growth in water bodies. However, this treatment has some especial technical requirements that are difficult to implement in rural areas. The general process is shown in Fig. 4.7. On the other hand, the water hyacinth can be treated to produce compost by aerobic decomposition. The compost is an interesting product in which agriculture plays a

86

Chapter 4

Figure 4.6 MixAlco process to yield bioethanol from water hyacinth. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Figure 4.7 Producing biogas through anaerobic digestion from water hyacinth. From Jose´ Ezequiel Santiban˜ezAguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

significant part. It is important to note that in this case the high moisture content of water hyacinth is an advantage, because the preparation of 1 t of compost needs about 2700 L of water (Gunnarsson & Petersen, 2007) that can be obtained from water hyacinth. Another option to obtain a useful product from water hyacinth is deoxy-liquefaction (Lu, Wang, & Yang, 2009). Deoxy-liquefaction is a process where biomass can be converted

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 87 into liquid fuel indirectly through gasification to syngas followed by catalytic conversion and direct liquefaction. In this process, most of the oxygen in biomass is released in the form of CO and CO2. There is about 2.9% oxygen contained in the oil. This process is classified as a hydrothermal process, and is an alternative to increasing the energy content in biomass. Direct burning is another option to use water hyacinth; however, this plant has a moisture content of about 90% and when its moisture is reduced, the energy density is close to 15.23 MJ/ kg. This option can be used at small scale at places near water bodies to produce energy. Therefore, the optimization approach must select the type of technology used (j) in each processing facility (i) to produce the different products (p). This is modeled through the following relationships: hub hub fbjhub i;j Uαj;p 5 wprodi;j;p ;

’iAI; jAJ; pAP

(4.6)

4.3.6 Balances for the Mixers Before the Central Processing Facilities The total biomass flow rate
inlet to  the central processing facilities and sent to the different bioconversion technologies fbcen is equal to the sum of the biomass distributed from the s cen different harvesting places s ðwbj Þ as follows: X X fbcen wbcen (4.7) s 5 j sAS

jAJ

4.3.7 Balances for the Technologies of Central Processing Facilities In central processing facilities, there are several bioconversion technologies j available for cen transforming the biomass ðwbcen j Þ and to produce different products ðwprodj;p Þ with a given efficiency ðαcen j;p Þ that can be optimized previously. The advantage of the central facility is to account for the economies of scale and to reduce the capital and operational costs associated to big units. This is modeled as follows: cen cen wbcen j Uαj;p 5 wprodj;p ;

’jAJ; pAP

(4.8)

4.3.8 Balances for the Splitters After Each Processing Facility The products p obtained in the processing facility i ðwprodhub i;j;p Þ using different technologies j are segregated and directed to the consumers located in different places k ðgprodhub i;j;p;k Þ: X wprodhub gprodhub ’iAI; jAJ; pAP (4.9) i;j;p 5 i;j;p;k ; kAK

88

Chapter 4

It should be noted that the outlet flow rates in this equation are optimization variables and thus it is not required to include explicitly split fractions (the previous explanation also applies to all the splitters modeled in the optimization formulation).

4.3.9 Balances for the Splitters After the Central Processing Facilities The products p obtained in the central processing facilities ðwprodcen j;p Þ using different technologies j are segregated and directed to the consumers located in different places k ðgprodcen j;p;k Þ: X wprodcen gprodcen ’jAJ; pAP (4.10) j;p 5 j;p;k ; kAK

4.3.10 Balances for the Markets The product p inlet to the market in place k ðGcon p;k Þ is equal to the products sent from all hub preprocessing plants ðgprodi;j;p;k Þ and the central processing facilities ðgprodcen j;p;k Þ: XX X con gprodhub gprodcen ’pAP; kAK (4.11) i;j;p;k 1 j;p;k 5 Gp;k ; iAI jAJ

jAJ

4.3.11 Demands for the Consumers The flow rate for each product p inlet to the market k ðGcon p;k Þ must be lower than the conMax maximum demand in each location ðGp;k Þ: con Gcon p;k # Gp;k

Max

;

’pAP; kAK

(4.12)

4.3.12 Balances for the Water Treatment in Each Source The water extracted from water hyacinth in each source ðFws Þ is sent to a set of treatment
 technologies n fwts;n to eliminate given pollutants to make it suitable for specific uses: X fwts;n ; ’ sAS (4.13) Fws 5 nAN

4.3.13 Water Treatment Technology in Each Source There are available several treatment technologies n to eliminate the pollutants c for the water extracted from water hyacinth with given efficiencies γn;c , relating this way the inlet

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 89 out composition to the water treatment technologies Zwin i;c with the outlet composition Zwi;n;c as follows:
 in ’sAS; nAN; cAC (4.14) Zwout s;n;c 5 Zws;c U 1 2 γ n;c ;

4.3.14 Mass Balance for the Splitters After the Water Treatment Water extracted from water hyacinth
from source s and treated with technology n can be sent to the water consumer m hws;n;m , modeled as follows: X hws;n;m ; ’sAS; nAN (4.15) fWTs;n 5 mAM

4.3.15 Mass Balance for the Mixers Before Each Water Consumer
 The total water flow rate directed to the water
consumer m H is equal to the sum of W s;m  the water flow rate from any treatment unit n hws;n;m : X hws;n;m 5 HWs;m ; ’sAS; mAM (4.16) nAN

4.3.16 Component Balance for the Mixers Before Each Water Consumer The following balances are required to determine the components present in the water directed to the consumers ðZwcon s;m;c Þ:  X con hws;n;m UZwout ’sAS; mAM; cAC (4.17) s;n;c 5 HWs;m UZws;m;c ; nAN

It is important to note that Eq. (4.17) is a nonlinear relationship since it has a bilinear term, formed by the product of the composition of pollutant in the discharge of the water con treatment
 units ðZws;m;c Þ and the total water flow rate directed to the water consumers HWs;m . This is the only nonlinear relationship in the model.

4.3.17 Demand for Water Consumers Each water consumer m has a specific maximum water demand ðHwmax Þ. This constraint is i;m written as follows: ; HWs;m # Hwmax s;m

’sAS; mAM

(4.18)

90

Chapter 4

4.3.18 Constraints for the Water Quality for Each Consumer There are specific constraints for the concentration of some pollutants c in each  watermax  consumer depending on the use; therefore, the maximum water concentration Zwcon for s;m;c each consumer is stated as follows: max

con Zwcon s;m;c # Zws;m;c ;

’sAS; mAM; cAC

(4.19)

4.3.19 Operational Cost for the Processing Facilities The operational cost for the processing facilities ðCostHubop i;j Þ depends on the treated flow op Þ and the associated unit cost ðβ hub Þ for each rate of biomass from water hyacinth ðfbhub j i;j source i and processing technology j: hub op hub CostHubop ; i;j 5 fbji;j Uβ j

’iAI; jAJ

(4.20)

4.3.20 Capital Cost for the Processing Facilities The capital cost for the processing facilities ðCostHubcap i;j Þ are determined considering hub hub σ nonlinear functions with fixed ðAi;j Þ and variable terms ðBhub i;j Uðfbi;j Þ Þ, where σ is usually between 0.6 and 0.9 to account for the economies of scale. In this work, the second nonconvex term is replaced by a set of linear segments as follows: hub hub CostHubcap i;j 5 Ai;j 1 Bfi;j ;

’iAI; jAJ

(4.21)

And the term ðBfi;jhub Þ is modeled through the following disjunction: 3 2 hub Yi;j;q 7 6 hubmin hub hubmax 7 fb # fb # fb 36 7 6 i;j;q i;j i;j;q 7; iAI; jAJ 6 hub hub 7 q6 A 5 a i;j i;j;q 5 4 hub hub hub Bfi;j 5 bi;j;q Ufbi;j Previous disjunction is reformulated as follows. First, only one linear segment can be selected: X yhub ’iAI; jAJ (4.22) i;j;q 5 1; qAQ

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 91 Then, each continuous variable is disaggregated as follows: X fbjhub dfbhub ’iAI; jAJ i;j 5 i;j;q ;

(4.23)

qAQ

Ahub i;j 5

X

dAhub i;j;q ;

’iAI; jAJ

(4.24)

’iAI; jAJ

(4.25)

qAQ

Bfi;jhub 5

X

dBhub i;j;q ;

qAQ

Then, the relationships are stated in terms of the disaggregated variables as follows: min

max

hub hub hub hub fbhub i;j;q Uyi;j;q # dfbi;j;q # fbi;j;q Uyi;j;q ; hub hub dAhub i;j;q 5 ai;j;q Uyi;j;q ;

’iAI; jAJ; qAQ

’iAI; jAJ; qAQ

(4.26) (4.27)

hub hub dBhub i;j;q 5 bi;j;q Udfbi;j;q ;

’iAI; jAJ; qAQ (4.28)
 In the previous disjunction, for a given treated flow rate fbhub i;j;q , Eq. (4.26) is used to activate the corresponding binary variable; then, just one binary variable ðyhub i;j;q Þ can take a value of one because of Eq. (4.22). Next, the disaggregated variables are calculated through Eqs. (4.27) and (4.28). It should be noted that only the disaggregated variables for the active segment q are able to take values greater than zero and these are assigned to the original continuous variables through Eqs. (4.234.25). It is noteworthy that the advantage of using disjunctive formulations is the easy representation and reformulation of complicated logical relationships; the disjunctive formulation does not affect the solution strategy because the corresponding algebraic reformulation is the one that is solved.

4.3.21 Operational Cost for the Central Processing Facilities The operational cost for the central processing facilities ðCostCenop j Þ depends on the treated op cen Þ flow rate of biomass from the water hyacinth ðwbj Þ and the unit cost associated ðβ cen j for each processing technology j: cen op cen CostCenop ; j 5 wbj Uβ j

’jAJ

(4.29)

4.3.22 Capital Cost for the Central Processing Facilities The capital cost for the central processing facilities ðCostCencap j Þ are determined considering Þ and variable parts in the same way than for preprocessing facilities as follows: the fixed ðAcen j cen cen CostCencap j 5 Aj 1 Bfj ;

’jAJ

(4.30)

92

Chapter 4

And the term ðBfjcen Þ is modeled through the following disjunction. 3 2 cen Yj;q 7 6 min cen cenmax 7 3 6 wbcen 6 j;q # wbj # wbj;q 7; jAJ 7 cen q6 Acen 5 4 j 5 aj;q cen cen cen Bfj 5 bj;q Uwbj Previous disjunction is reformulated as follows: X ycen j;q 5 1;

’jAJ

(4.31)

qAQ

wbcen j 5

X

dwcen j;q ;

’jAJ

(4.32)

qAQ

Acen j 5

X

dAcen j;q ;

’jAJ

(4.33)

’jAJ

(4.34)

qAQ

Bfjcen 5

X

dBcen j;q ;

qAQ min

max

cen cen Uycen Uycen wbcen j;q # dwj;q # wbj;q j;q ; j;q cen cen dAcen j;q 5 aj;q Uyj;q ;

’jAJ; qAQ

’jAJ; qAQ

cen cen dBfj;q 5 bcen j;q Udwj;q ;

’jAJ; qAQ

(4.35) (4.36) (4.37)

The explanation for previous relationships is similar to the one corresponding to the distributed processing facilities.

4.3.23 Operational Cost for the Water Treatment Units op The operational s;n Þ depends on the water flow
cost  for the water treatment units ðCostWT wt op rate treated fwts;n and the unit cost associated ðβ s;n Þ for each treatment unit n: wt op CostWTop s;n 5 fwts;n Uβ s;n ;

’sAS; nAN

(4.38)

4.3.24 Capital Cost for the Water Treatment Units The capital costs for the water treatment units ðCostWTcap s;n Þ are determined considering the Þ and variable parts in the same way than for distributed processing facilities as fixed ðAWT s;n follows: WT WT CostWTcap s;n 5 As;n 1 Bfs;n ;

’sAS; nAN

(4.39)

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 93 WT And the term ðBfi;n Þ is modeled through the following disjunction: 3 2 WT Ys;n;q 6 min max 7 # fwts;n # fwts;n;q 7 3 6 fwts;n;q 7; ’sAS; nAN; qAQ 6 7 6 WT WT q4 As;n 5 as;n;q 5 WT WT Bfs;n 5 bs;n;q Ufwts;n

Previous disjunction is reformulated to obtain: X ywt ’sAS; nAN s;n;q 5 1; qAQ

fwts;n 5

X

dfwts;n;q ;

’sAS; nAN

(4.40) (4.41)

qAQ

Awt s;n 5

X

dAwt s;n;q ;

’sAS; nAN

(4.42)

’sAS; nAN

(4.43)

qAQ

wt 5 Bfs;n

X

wt dBfs;n;q ;

qAQ min max wt Uywt fwts;n;q s;n;q # dfwts;n;q # fwts;n;q Uys;n;q ;

dAwt s;n;q

wt 5 awt s;n;q Uys;n;q ;

’sAS; nAN; qAQ

’sAS; nAN; qAQ

wt 5 bwt dBfs;n;q s;n;q Udwts;n;q ;

’sAS; nAN; qAQ

(4.44) (4.45) (4.46)

The explanation for previous relationships is like the one corresponding to the distributed processing facilities.

4.3.25 Harvesting Cost The water hyacinth harvesting cost ðCostHarvestingÞ is determined
based on the amount harvested ðFwhs Þ and the associated unit harvesting cost β Harvesting for each location s as s follows: X CostHarvesting 5 Fwhs Uβ Harvesting (4.47) s sAS

It should be noted that the unit harvesting costs depend on the place because the difficulty associated with this operation is different for each location. It should be noted that an important factor included in the harvesting costs is the energy required.

4.3.26 Water Transportation Cost The water transportation cost consists of the transportation of untreated and treated water Transp Transp considering the unit costs βwts;n and βwts;n;m , respectively: XX XX X Transp Transp CostTransWater 5 fwts;n Uβwts;n 1 hwts;n;m Uβwts;n;m (4.48) sAS nAN

sAS nAN mAM

94

Chapter 4

4.3.27 Biomass Transportation Cost The biomass transportation cost ðCostTransBMÞincludes the biomass transportation cost from the source to the processing facilities ðβbhubTransp Þ and to the central processing s;i facilities ðβbcenTransp Þ: s X XX Transp Transp fbhub Uβbhub 1 fbcen (4.49) CostTransBM 5 s;i s;i s Uβbcens sAS iAI

sAS

4.3.28 Products Transportation Cost The transportation cost for the products includes the one corresponding to the transportation of products from the processing facilities ðβhubprodTransp i;j;p;k Þ and from the central processing Transp facilities ðβcenprodj;p;k Þ: XXXX Transp CostTransProd 5 gprodhub i;j;p;k Uβhubprodi;j;p;k iAI jAJ pAP kAK

1

XXXX

Transp gprodcen i;j;p;k Uβcenprodj;p;k

(4.50)

iAI jAJ pAP kAK

4.3.29 Total Operational Cost The total operational cost ðCostOperationalÞ is given by the sum of the associated costs with the operation of the distributed processing facilities ðCostHubop i;j Þ, central processing op Þ and water treatment units ðCostWT Þ: facilities ðCostCenop j s;n XX X XX op CostOperational 5 CostHubop 1 CostCen 1 CostWTop (4.51) i;j j s;n iAI jAJ

jAJ

sAS nAN

4.3.30 Total Capital Cost The total capital cost ðCostCapitalÞ includes the associated costs for the distributed cap processing facilities ðCostHubcap i;j Þ, central processing facilities ðCostCenj Þ and water cap treatment units ðCostWTs;n Þ: X XX XX CostHubcap CostCencap CostWTcap (4.52) CostCapital 5 i;j 1 j 1 s;n iAI jAJ

jAJ

sAI nAN

4.3.31 Total Sales The total sales ðSalesProdÞ correspond to the sales of the products and water as follows: XX XX prod SalesProd 5 Gcon β 1 Hws;m β wat (4.53) p;k p m pAP kAK

In Eq. (4.53),

β prod p

and

β wat m

sAS mAM

are the unit prices for the products p and water m, respectively.

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 95

4.3.32 Total Net Annual Cost (Negative of Total Net Profit) The total net annual cost for the overall system ðTAC Þ (which is equal to the negative of the total net annual profit) includes the water hyacinth harvesting cost ðCostHarvestingÞ plus the transportation cost associated with the water ðCostTransWaterÞ, biomass ðCostTransBMÞ and products ðCostTransProdÞ, plus the operational ðCostOperationalÞ and capital costs ðCostCapitalÞ, minus the total sales ðSalesProdÞ and the tax credit ðTAXCreditÞ. Therefore, the total net annual cost is stated as follows: TAC 5 CostHarvesting 1 CostTransWater 1 CostTransBM 1 CostTransProd 1 CostOperational 1 KF UCostCapital

(4.54)

2 SalesProd 2 TAXCredit

4.3.33 Percentage of Eliminated Water Hyacinth In this study, the environmental objective function is to maximize the percentage of eliminated water hyacinth. This function is environmentally representative because it indicates how much water hyacinth is eliminated from water bodies. The percentage of eliminated water hyacinth is defined as follows: P Fwhs consume 5 100 P s max (4.55) Fwh s s The General Algebraic Modeling System (GAMS) code for this model is presented in Appendix C.

4.4 Remarks on the Model •

•

•

The optimization problem consists of minimizing the Total Annual Cost (TAC) [given by Eq. (4.54)] and maximizing the percentage of eliminated water hyacinth [given by Eq. (4.55)] subject to Eqs. (4.1)(4.53). To solve this multiobjective optimization model, the constraint method has been implemented; this way, to generate a set of Pareto solutions that trade off these two objectives, the problem for minimizing the TAC subject to relationships (4.1)(4.53) and subject to one of the following constraints consume $ ε or consume # ε must be solved for several values of ε. The first constraint allows generating a Pareto curve for high elimination of water hyacinth, while the second one is used to obtain a Pareto curve for low elimination of water hyacinth. The model considers simultaneously the supply chain for the bioproducts obtained from water hyacinth, the remediation of the water bodies and the recycle and reuse of the recovered water. The optimization model simultaneously optimizes the selection of bioconversion technologies for the water hyacinth and the water treatment; it also takes into account

96

•

•

•

Chapter 4 the optimization of the size and location for the distributed processing and central processing facilities to account for the economies of scale; in addition, the model considers which products should be selected (bioproducts and type of water) and the optimal distribution for the products in the different markets. This optimization model could be very useful to solve an environmental problem (controlling water hyacinth in water bodies) and, at the same time, to obtain economic benefits due to revenues from sale of products (bioproducts and water). For modeling the splitters only mass balances are required, which state that the flow of the inlet stream is equal to the flows of the outlet streams. It is noteworthy that the flows of the outlet streams are optimization variables (i.e., the outlet flow rates are determined by the optimization process) and, therefore, it is not required to include a split fraction because it is implicit in the optimization process. If the number of potential places to install central and distributed processing facilities is big enough, the associated number of binary variables can be increased significantly. In this case, also the Central Processing Unit (CPU) time required to solve the problem increases exponentially. If this CPU time is huge enough, a prescreening approach can be implemented to eliminate potential places that may not be promissory (i.e., water bodies with a small amount of water hyacinth, places far from the consumers, etc.).

4.5 Results To show the applicability of the proposed methodology, a case study from Mexico is used. This case is considered because the central part of Mexico has a lot of water bodies highly infested with water hyacinth; therefore, the sustainability of these systems is at risk. Several approaches have been proposed and some of them implemented to solve this problem (including several chemical and physical treatments) without good results (some of them are very expensive; others have severe adverse adjacent impacts and others are not efficient to eliminate the water hyacinth). To apply the proposed methodology in such region, first the potential harvesting sites are identified as the water bodies seriously infested with water hyacinth. Thus, the Lake of Chapala is one of the harvesting sites proposed, since it is the most important lake of Mexico and is also infested with water hyacinth. This lake is very close to Guadalajara, the second biggest city of Mexico. Other site is the Balsas River, which is one of the greatest rivers in the central part of Mexico. This river supplies cooling water to the most important thermo-electric plant in the state of Michoacan in Mexico. In addition, the Lakes of Patzcuaro and Cuitzeo are proposed as harvesting sites. These lakes are close to the cities of Patzcuaro and Morelia, respectively; the Lake of Patzcuaro has an endemic species of fish named white fish and tourism and fishing are the most important activities in this region. Also, the lake of Yuriria is an important lake of the state of Guanajuato infested with water hyacinth. In this regard, these harvesting sites are very important water bodies in the considered system. Furthermore, the refinery candidates correspond to the main cities around such water bodies, since the objective of a distributed

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 97 system is to decrease the costs (manly transportation costs) and, hence, the transportation distances must be short. Besides, the demand zones are located in cities around the water bodies, because these locations have a given demand of biofuels, water, and chemicals among other products. Fig. 4.1 shows the water bodies polluted with water hyacinth and Table 4.1 presents the available biomass of water hyacinth for each place considered in this example. In addition, Fig. 4.1 also shows the places that demand some bioproducts (in this case, the bioproducts considered are ethanol, mixed alcohols, biogas, fertilizers and biomass for heating) and Table 4.2 presents the demand at each place for such products. Table 4.3 gives the water demand for each place with the quality constraints for the pollutants considered. The treatment technologies available for obtaining water from water hyacinth are given in Table 4.4, which also shows the removal efficiency for each technology [in this case only Cr(VI) is considered as the only pollutant in water; however, the study can be Table 4.1: Available biomass from water hyacinth for each water body Wet Biomass Production (t/ha year)

Water Body Chapala Patzcuaro Cuitzeo Yuriria Sayula Atotonilco Balsas

1530 1530 1530 1530 1530 1530 1530

Annual Wet Biomass Production Infested Area (ha) (t/year)

Reference for Infested Area

4500 3037 9628 5820 4548 1508 1,719,220

Government of Jalisco, 2011 ´, 2003 Rodrı´guez-Trejo & Ducoing-Chaho ´pez & Bocco, 2000 Lo Instituto Nacional de Ecologı´a, 2012a,b,c,d,e Instituto Nacional de Ecologı´a, 2012a,b,c,d,e Instituto Nacional de Ecologı´a, 2012a,b,c,d,e Instituto Nacional de Ecologı´a, 2012a,b,c,d,e

6,887,903 4,648,569 14,737,052 8,908,355 6,961,374 2,308,213 2,631,516,762

From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Table 4.2: Demands for each product at each place (PEMEX, 2010; SENER, 2012) Product Consumer Morelia Lazaro Cardenas Guadalajara Queretaro Leon Patzcuaro Celaya Zamora Uruapan Yuriria Cuitzeo Zacapu

Ethanol (t/year) 40,512 9933 212,523 44,548 79,798 4877 78,071 31,014 52,554 11,796 4704 12,241

Biogas (t/year) 706 173 3705 777 1391 85 1361 541 916 206 82 213

Acetic Acid (t/year) 797 195 4179 876 1569 96 1535 610 1034 232 93 241

Compost (t/year) 799 20 419 88 157 96 154 61 104 23 9 24

HCF* (t/year) 465 114 2441 512 917 56 897 356 604 135 54 141

Energy (GJ/year) 20,382 4998 106,923 22,413 40,147 2454 39,279 15,604 26,441 5935 2367 6159

*HCF (High Caloric Fuel). From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

98

Chapter 4

Table 4.3: Water demand for each water consumer and quality required (CONAGUA, 2012; NOM-001-ECOL-1996) Water Consumer

Water Demand (hm3/year)

Morelia Lazaro Cardenas Guadalajara Queretaro Leon Patzcuaro Celaya Zamora Uruapan Yuriria Cuitzeo Zacapu

141 23 496 104 186 17 91 36 61 14 5 14

Maximum Concentration Pollutant (Mass Fraction)

Use

5.00 3 10207 1.00 3 10206 1.00 3 10206 1.00 3 10206 1.00 3 10206 5.00 3 10207 1.00 3 10206 5.00 3 10207 5.00 3 10207 5.00 3 10207 5.00 3 10207 1.00 3 10206

Public Industrial Industrial Industrial Industrial Public Industrial Public Public Public Public Industrial

From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Table 4.4: Efficiency at removing the pollutant for each technology considered Technology to Eliminate Cr(VI)

Efficiency

Ion exchange resins Ion exchange Mexican clinoptilolite Electroplating HA 216

Reference 0.99 0.2 0.5

(70) (71) (72)

From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Table 4.5: Efficiencies for the processing technologies Product

Technology

Ethanol

Acid hydrolysis and fermentation, 10% sulfuric acid Acid hydrolysis and fermentation, 1% sulfuric acid Anaerobic digestion Composting MixAlco process Deoxy-liquefaction Cogeneration

Ethanol Biogas Compost Acetic acid High caloric fuel Energy

Conversion Factor

Units

Reference

0.19

g/dry g

0.35

g/dry g

(6) and (7) (7)

291 0.7 0.3 0.05

mL/dry g g/dry g g/dry g g/dry g

(23) (24) (20) (61)

15.23

kJ/dry g

(61)

From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

extended to include additional pollutants]. Table 4.5 presents the efficiency needed to obtain the products for the different technologies considered. On the other hand, the biomass is transported in truck by highways (since transportation by truck is the most

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 99 widely used in this zone of Mexico); the unit biomass transportation costs are shown in Table 4.6. The water is transported by pipelines and costs about US$1.63/m3 transported water for a distance of 500 m. Using these data, the model formulation was coded in GAMS and consists of 210 binary variables, 8054 continuous variables and 2958 constraints. The problem was solved using a computer with an i7 processor at 2.2 GHz with 6 GB of RAM. Notice that the MINLP (mixed integer nonlinear programming) problem has to be solved several times to determine the Pareto curve TAC versus the percentage of eliminated water hyacinth. Therefore, good initial guesses are required to properly solve the MINLP problem. Also, notice that there is a bilinear term in Eq. (4.17), which introduces nonconvexities into the model of the problem. Therefore, it is necessary to propose a solution strategy to generate good initial values, since the quality of the solution for the full MINLP problem depends on the starting point of the optimization. If the starting point were bad, the conventional MINLP solvers (e.g., DIscrete and Continuous OPTimizer (DICOPT), Branch-And-Reduce Optimization Navigator (BARON), and Standard Branch and Bound (SBB) could fail to provide a feasible solution or converge to a local optimum far from the optimal global. To generate an effective initialization of variables, the following strategy is proposed. First, a simplified MILP (mixed integer linear programming) problem is formulated and solved to obtain good initial guesses for the binary variables. This problem does not include Eq. (4.17), which is the only expression in the model that contains nonlinear terms. Then, an analysis to determine the best values for the percentage of eliminated water hyacinth was carried out to obtain initial guesses for the continuous variables. In this analysis, values for the eliminated water hyacinth between 0.5 and 4 times of the solution provided by the RMINLP (relaxed mixed integer nonlinear programming) problem were tested (RMINLP corresponds to the case when the binary variables are transformed into continuous variables). This sensitivity analysis showed that the best value to provide good initial guesses corresponds to 3. Using the initial guesses thus obtained for integer and continuous variables, the original MINLP problem is solved without complication. The suggested solution strategy to solve this problem was implemented in the modeling language GAMS. First, the MILP problem is solved using the solver CPLEX. The solution of the MILP problem provides the values of the integer variables that are used to solve the RMINLP problem using any one of the solvers CONOPT, Modular In-core Nonlinear Optimization System (MINOS) or Sparse Nonlinear OPTimizer (SNOPT). After that, the amount of eliminated water hyacinth is specified as three times the eliminated water hyacinth corresponding to the RMINLP solution in order to solve the MINLP with DICOPT. If the previous strategy produces an infeasible solution, then it is necessary to use the solver CPLEX for solving the MILP problem and the solver BARON for solving the RMINLP problem and the original MINLP problem. The problem was solved for different levels of the constraints to get the Pareto curve; each point of the Pareto curve consumes from 1.39 to 4.73 seconds when the solver CONOPT, MINOS or SNOPT are used to solve the RMINLP problem, from 0.172 to 0.218 seconds when the solver CPLEX is used to

Table 4.6: Transportation costs for biomass from water hyacinth sources to processing plants (based on a constant transportation cost of US$0.079/t km to transport biomass on highway) Water Body

Chapala

Patzcuaro

Cuitzeo

Yuriria

Sayula

Atotonilco

Balsas

Processing Plant

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Distance (km)

Transp US$/t

Morelia Lazaro Cardenas Leon Queretaro Guadalajara Celaya Zamora Uruapan Yuriria Cuitzeo Zacapu

284 555

22.44 43.85

59 263

4.66 20.78

34 341

2.69 26.94

64 378

5.06 29.86

394 427

31.13 33.73

297 476

23.46 37.60

250 67

19.75 5.29

253 359 48 299 152 261 301 272 214

19.99 28.36 3.79 23.62 12.01 20.62 23.78 21.49 16.91

259 244 282 194 132 57 117 88 65

20.46 19.28 22.28 15.33 10.43 4.50 9.24 6.95 5.14

178 161 275 109 159 141 30 1 99

14.06 12.72 21.73 8.61 12.56 11.14 2.37 0.08 7.82

145 139 306 67 188 172 1 30 130

11.46 10.98 24.17 5.29 14.85 13.59 0.08 2.37 10.27

329 456 111 415 203 304 408 379 321

25.99 36.02 8.77 32.79 16.04 24.02 32.23 29.94 25.36

329 358 111 317 143 244 315 284 228

25.99 28.28 8.77 25.04 11.30 19.28 24.89 22.44 18.01

456 439 434 389 270 168 314 283 259

36.02 34.68 34.29 30.73 21.33 13.27 24.81 22.36 20.46

From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 101 solve the MILP problem, from 2.76 to 3.12 seconds when the solver DICOPT is used to solve the MINLP problem and, finally, from 548.28 to 1203 seconds when the solver BARON is used to solve the RMINLP as well as the MINLP problems. The general solution procedure is presented in Fig. 4.8. In addition, the problem was solved for several tax credits, which is a subvention for eliminating water hyacinth from the sources. In this case, four tax credits were considered (0, 0.1, 0.3 and 0.5US$/t eliminated water hyacinth). For each tax credit, a Pareto curve was obtained, which are shown in Figs. 4.9 and 4.10.

Figure 4.8 Solution procedure of the addressed problem. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a PonceOrtega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

102 Chapter 4 3.00E + 07

Harvesting cost

0 Tax credit 0.1 Tax credit

2.00E + 07 E

Total annual cost (US$/year)

1.00E + 07

0.3 Tax credit 0.5 Tax credit

al annu total reases d n a c cost cinth in ya sting arve water h h e h d t e t n a e e min tw e be n the eli renc diffe ses whe e h T ea decr cost

0.00E + 00

–1.00E + 07

–2.00E + 07

The tax credit has units of US$/t Harvested water hyacinth

D

–3.00E + 07

–4.00E + 07 C

The curves are subjected to Percent eliminated of WH ≥ ε

–5.00E + 07

–6.00E + 07 20

22

24

26

28

30

32

34

36

38

40

42

44

Percent eliminated water hyacinth

Figure 4.9 Pareto curves for alternative 1 (TAC versus percentage of eliminated water hyacinth). From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

It is important to note that the harvesting cost for the stand-alone operation that only eliminates the water hyacinth is always greater than the TAC for the integrated process, since in this case the plant is not used to obtain various products. On the other hand, when the water hyacinth is considered as raw material to obtain a set of products, it is possible to generate solutions attractive economically (which means that the harvesting cost is lower than the sales for the products manufactured). As can be seen in Fig. 4.9 for alternative 1, the TAC increases when the eliminated water hyacinth increases. This leads to a decrease in the difference between the harvesting cost and the total annual cost, while the eliminated water hyacinth increases. The part of the Pareto curves for negative TAC represents attractive solutions (i.e., the net profit is positive because it is equal to 2 TAC). On the other hand, in Fig. 4.10, the Pareto curves are opposites because the TAC begins at a value of zero and decreases while the harvesting cost increases. The maximum amount of eliminated

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 103 Harvesting cost 1.00E + 07

Total annual cost (US$/year)

0.00E + 00 The total annual cost always is lower than the harvesting cost

The tax credit has units of US$/t Harvested water hyacinth

–1.00E + 07 A

The total annual cost decreases when the eliminated water hyacinth increases

–2.00E + 07

–3.00E + 07

B

–4.00E + 07

The curves are subjected to Percent eliminated of WH ≤ ε

0 Tax credit 0.1 Tax credit 0.3 Tax credit 0.5 Tax credit

C

–5.00E + 07

–6.00E + 07 0

2

4

6

8

10

12

14

16

18

20

22

Percent eliminated water hyacinth

Figure 4.10 Pareto curves for alternative 2 (TAC versus % eliminated water hyacinth). From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

water hyacinth is about 22%, and is represented with the letter C, for a tax credit of zero. The point C in Fig. 4.10 is the same solution represented as point C in Fig. 4.9. As can be observed, the point C represents an inflexion point in the curve for the TAC. The difference between Figs. 4.9 and 4.10 is that Fig. 4.9 is based on alternative 1 to solve the problem (high elimination of water hyacinth), whereas Fig. 4.10 represents the case when the elimination of water hyacinth is low. A set of points were selected to observe the change of the TAC with respect to the harvesting cost; for example, in point A the harvesting cost is US$2,564,582 and the TAC is US$ 2 1.72 3 107, which means the difference between the TAC and the harvesting cost is about 700% of the harvesting cost. This is explained by the large sales revenue from the different products produced. On the other hand, in point C the percentage of this difference is about 400%. Finally, in point E the difference between the harvesting cost and the sale of products represents about 40% of the harvesting cost. Other analysis can be done when each point is shown based on the percentage of water hyacinth eliminated from each water body. Because the total percentage can be high, however, it can be low at a specific water body.

104 Chapter 4

Figure 4.11 Representation of eliminated water hyacinth at each source and overall. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Fig. 4.11 shows the individual consumption of water hyacinth at each source. The main water body for this case study is Lake of Chapala, so it is selected to consider the specific elimination of water hyacinth with different percentages. For example, point A represents an elimination of 30% of the water hyacinth in this lake, whereas in point C almost 100% of the water hyacinth is eliminated from this water body. On the other hand, the second water body most important for this system is the Balsas River because it has a large amount of this plant; however, this river is located close to the west coast and far from other water bodies and cities and thus the elimination of water hyacinth from the Balsas River is selected only in point E. Notice in Fig. 4.9 that this point has high consumption of water hyacinth, but it also has greater TAC with respect to the other solutions. In addition, in the addressed problem the water bodies corresponding to the lakes of Patzcuaro, Cuitzeo and Yuriria are important because they are the closest ones to the main cities and are related to significant economic activities. Fig. 4.12 shows the distribution for the satisfied demands of products at the different consumer places for the points indicated in Figs. 4.9 and 4.10, which show that compost

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 105

Figure 4.12 Distribution of the satisfied demands of products at different consumer sites for the points indicated in Figs. 4.9 and 4.10. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

106 Chapter 4 and energy are the main products since in all points their demands are fully satisfied. Ethanol does not appear in cities like Patzcuaro, Lazaro Cardenas, Queretaro and Leon. Notice that the maximum demand satisfied for ethanol is at point E and that High Fuel Caloric also appears at this point. Furthermore, the MixAlco process is used in point C to produce acetic acid. An analysis was also done to identify the impact of the produced clean water on the minimization of total annual cost including several tax credits and two alternatives for produced water. The first option is when a low production of water is required and the second option is for a high production of clean water. The behavior is similar to the analysis corresponding to the harvested water hyacinth. The harvesting cost is always greater than the total annual cost, which means that in this case there is always a positive net profit (or that the TAC is negative). There is an inflexion point between these two options, which is represented as point C in Figs. 4.13 and 4.14. Notice in Fig. 4.13 that the TAC decreases when the tax credit increases, and this effect is more significant in this second option because in this case the Pareto curves always have positive net profits. Fig. 4.13 (option 1) also shows that the Pareto curves for the point when the TAC of zero corresponds to an amount of produced water of zero.

Figure 4.13 Pareto curves for the TAC versus produced water (alternative 1). From Jose´ Ezequiel Santiban˜ezAguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 107

Figure 4.14 Pareto curves for the TAC versus the produced water (alternative 2). From Jose´ Ezequiel Santiban˜ezAguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

At this point, from the previous analysis the following important questions appear: Where is the water hyacinth for the production of clean water coming from? and Where should the clean water produced be distributed? Fig. 4.15 shows the distribution of the water bodies for the different points on the Pareto curves of Figs. 4.13 and 4.14. Fig. 4.15 also shows the distribution of the extracted clean water from the different water bodies to the water consumers. It is important to note that the produced water in a specific water body should be used by the closest water consumer, because in these cases the water transportation cost is lower. Also, the number of selected water bodies increases when the amount of produced clean water is maximized.

4.6 Concluding Remarks This chapter has presented a new formulation for the cleaning of water bodies of water hyacinth and the value-added processing through a distributed biorefinery system that produces several bioproducts (including biofuels and specialty chemicals) and clean water. The optimization model is formulated as a multiobjective optimization problem that

108 Chapter 4

Figure 4.15 Distribution of water bodies and water consumers selected for the different points in the Pareto curves of Figs. 4.13 and 4.14. From Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, J. Betzabe Gonza´lez-Campos, et al, Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, ACS Sustainable Chemistry & Engineering, 2013.

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 109 simultaneously considers the minimization of the total annual cost and the maximization of the amount eliminated of water hyacinth from the water bodies (or the maximization for the production of clean water) while satisfying technical and environmental constraints. The results were shown through Pareto curves to represent the trade-offs between the contradicting objectives and to allow determining the solution that best satisfies the specific requirements. The proposed approach impacts the sustainability of the water hyacinth processing system in three dimensions: economic, social and environmental. The economic criterion consists of the maximization of the profit due to the processing of the eliminated water hyacinth. The environmental dimension is based on the cleaning of water bodies infested with water hyacinth. The social dimension consists of providing benefits to the local population such as appropriate conditions for human activities on water bodies and the possibility of jobs at the harvesting sites. The application of the proposed methodology to a case study of one of the most important hydrologic regions in Mexico shows that it is useful to generate solutions to clean water bodies, to obtain clean water and to produce several biofuels and specialty chemicals with positive net profits. Therefore, the proposed methodology shows that a distributed biorefinery system can be an economical and sustainable option to eliminate the water hyacinth from water bodies. Finally, the proposed model is general and can be applied to any case of interest with the proper input data. In addition, the proposed model can be extended to consider other plants considered as pollutants in water bodies.

4.7 Nomenclature 4.7.1 Parameters aWT s;n;q

Unit fixed capital costs for the water treatment units accounting for the limits given Unit fixed capital costs for the processing facilities accounting for the limits given

ahub i;j;q acen j;q bWT s;n;q bhub i;j;q bcen j;q

Unit fixed capital costs for the central processing facilities accounting for the limits given Unit variable capital costs for the water treatment units accounting for the limits given Unit variable capital costs for the processing facilities accounting for the limits given Unit variable capital costs for the central processing facilities accounting for the limits given Unit variable cost for the distributed processing facilities j

Bhub i;j min

; fbhub fbhub i;j;q i;j;q

max

min max fwts;n;q ; fwts;n;q

Maximum and minimum limits for the amount of processed biomass in the processing facilities Maximum and minimum limits for the amount of processed biomass in the water treatment units (Continued)

110 Chapter 4 (Continued) Fwhmax s Max Gcon p;k Hmax ws;m

The amount of water hyacinth available in the place of source Maximum amount of product p to the market k

βj

Maximum water demand in the market m Maximum and minimum limits for the amount of processed biomass in the central processing facilities Efficiency to extract water from the water hyacinth in the source s Inlet composition of the pollutant to the water treatment technologies Outlet composition of the pollutant to the water treatment technologies Maximum composition of pollutant in the discharged water to the markets Efficiency to extract biomass from the water hyacinth in the source s Efficiency factor in the processing facility for the technology j for the conversion of dry biomass to produce p Efficiency factor in the central processing facility for the technology j for the conversion of dry biomass to product p Unit operational cost associated to the route j and the central processing facility Unit operational cost associated to the source i and the water treatment units Unit operational cost associated to the technology j in the processing facility

β Harvesting s βbcenTransp s Transp βbhubs;i

Unit harvesting costs for each location s Unit transportation cost of biomass from the source s to the central processing facility Unit transportation cost for biomass from the source s to the processing facility i

min max wbcen ; wbcen j;q j;q

Zws in Zws;c out Zws;n;c conmax Zws;m;c Zwhs αhub j;p αcen j;p cen op

βj op β wt s;n

hub op

Transp

βcenprodj;p;k

Transp βhubprodi;j;p;k Transp βwts;n Transp βwts;n;m

σ γ n;c

Unit transportation cost for products from the centralizer to the markets Unit transportation cost for products from the processing facilities to the markets Untreated water unit cost Treated water unit cost Exponent to consider the economies of scale Efficiency to eliminate the pollutant c from the extracted water from the water hyacinth

4.7.2 Variables Ahub i;j Acen j AWT s;n Bfi;jhub Bfj cen WT Bfs;n op CostHubi;j cap CostHubi;j op CostCenj cap CostCenj op CostWT s;n

Fixed capital cost for the processing facilities Fixed cost for the capital cost of the central processing facilities Fixed cost of the capital cost of the water treatment units Term used to linearize the capital costs for the processing facilities Term used to linearize the capital costs for the central processing facilities Term used to linearize the capital costs for the water treatment units Operational cost for the processing facilities Capital cost for the processing facilities Operational cost for the central processing facilities Capital cost for the central processing facilities Operational cost for the water treatment units (Continued)

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 111 (Continued) CostWT cap s;n CostCapital CostHarvesting CostOperational CostTransBM CostTransProd CostTransWater dAhub i;j;q dAcen j;q dAwt s;n;q dBhub i;j;q dBcen j;q wt dBfs;n;q dfbhub i;j;q dfwts;n;q cen dwj;q Fbs fbhub s;i fbcen s fbjhub i;j Fws Fwhs fwts;n gprodhub i;j;p;k gprodcen j;p;k Gcon p;k hws;n;m HWs;m NetProfit SalesProd wbcen j wprodhub i;j;p wprodcen j;p con Zws;m;c

Capital cost for the water treatment units Total capital cost Water hyacinth harvesting cost Total operational cost Biomass transportation cost Products transportation cost Water transportation cost Disaggregated variable used for the fixed part of the capital costs in the processing facilities Disaggregated variable used for the fixed part of the capital costs in the central processing facilities Disaggregated variable for the fixed capital costs for the water treatment units Disaggregated variable used for the variable part of the capital costs in the processing facilities Disaggregated variable used for the variable part of the capital costs in the centralizers Disaggregated variable for the variable capital costs for the water treatment units Disaggregated variable used for the processed biomass Disaggregated variable for the biomass processed in the water treatment units Disaggregated variable used for the processed biomass in the central processing facilities Amount of extracted biomass Amount of dry extracted biomass in the location s that is directed to the processing facility located in place i Amount of dry extracted biomass in the location s that is directed to the central facility Amount of dry biomass in the processing facility i that is processed with technology j Amount of Amount of Amount of Amount of

extracted water water hyacinth used in the place of source s treated water by technology n product segregated and directed to the market k from processing facility i

Amount of product segregated and directed to the market k from the central facility Product p inlet to the market k Amount of water from the place s treated by technology n sent to the water consumer m Total water flow rate directed to the water consumer m Total net profit for the overall system Total sales correspond to the sales for the products Amount of distributed biomass to the technology j in the central processing facilities Amount of produced product p from biomass of the processing facility i by technology j Amount of produced product p from biomass of the central processing facility by route j Composition of pollutant in the discharged water to the consumers

112 Chapter 4

4.7.3 Binary Variables hub yi;j;q cen yj;q wt ys;n;q hub Yi;j;q cen Yj;q WT Ys;n;q

Binary variable used for the capital cost Binary variable used for the capital cost in the central processing facility Binary variable used in the capital cost in the water treatment units Boolean variable used in the capital costs Boolean variable in the capital costs for the central processing facility Boolean variable in the capital costs for the water treatment units

References Chuang, Y. S., Lay, C. H., Sen, B., Chen, C. C., K, G., Wu, J. H., Lin, C. S., & Lin, C. Y. (2011). Biohydrogen and biomethane from water hyacinth (Eichhornia crassipes) fermentation: Effects of substrate concentration and incubation temperature. International Journal of Hydrogen Energy, 36, 1419514203. CONAGUA. Overall availability per capita. Atlas digital del agua Me´xico. (2012). ,http://www.conagua.gob. mx/atlas/atlas.html?seccion 5 2&mapa 5 0#. Accessed March 2012. Forrest, A. K., Hernandez, J., & Holtzapple, M. T. (2010). Effect of temperature and pretreatment conditions on mixed-acid fermentation of water hyacinth using a mixed culture of thermophilic microorganisms. Bioresource Technology, 101(19), 75107515. Ganguly, A., Chatterjee, P. K., & Dey, A. (2012). Studies on ethanol production from water hyacinth—A review. Renewable and Sustainable Energy Reviews, 16, 966972. Government of Jalisco Programa Especial 21 Administracio´n y uso del agua. Primera Actualizacio´n. (2011). Gunnarsson, C. C., & Petersen, C. M. (2007). Water hyacinth as a resource in agriculture and energy production: A literature review. Waste Management, 27(1), 117129. Instituto Nacional de Ecologı´a. Watersheds in Mexico. (2012a). http://cuencas.ine.gob.mx/cuenca/ Accessed 28.12.12. Instituto Nacional de Ecologı´a. Watersheds in Mexico. Lerma Chapala. (2012b). http://cuencas.ine.gob.mx/ cuenca/12A02.html Accessed 28.12.12. Instituto Nacional de Ecologı´a. Watersheds in Mexico. Lago Atotonilco. (2012c). http://cuencas.ine.gob.mx/ cuenca/12D03.html Accessed 28.12.12. Instituto Nacional de Ecologı´a. Watersheds in Mexico. Lago Sayula. (2012d). http://cuencas.ine.gob.mx/cuenca/ 12D02.html Accessed 28.12.12. Instituto Nacional de Ecologı´a. Watersheds in Mexico. Rio Balsas. (2012e). http://cuencas.ine.gob.mx/cuenca/ 18A02.html Accessed 28.12.12. Isarankura-Na-Ayudhya, C., Tantimongcolwat, T., Kongpanpee, T., Prabkate, P., & Prachayasittikul, V. (2007). Apropiate technology for the bioconversion of water hyacinth (Eichhornia crassipes) to liquiq ethanol: Future prospects for community strengthening and sustainable development. EXCLI Journal, 6, 167176. Kim, S., & Holzapple, M. T. (2005). Lime pretreatment and enzymatic hydrolysis of corn stover. Bioresource Technology, 96(18), 19942006. Lo´pez, E., & Bocco, G. (2000). Cambio de uso de cobertura vegetal y uso del suelo en la cuenca de lago de Cuitzeo. Tesis Doctoral en Ciencias Biolo´gicas. Facultad de Ciencias. UNAM. Lu, W., Wang, C., & Yang, Z. (2009). The preparation of high caloric fuel (HCF) from water hyacinth by deoxy-liquefaction. Bioresource Technology, 100(24), 64516456. Mishima, D., Kuniki, M., Sei, K., Soda, S., Ike, M., & Fujita, M. (2008). Ethanol production from candidate energy crops: Water hyacinth (Eichhornia crassipes) and water lettuce (Pistia stratiotes L.). Bioresource Technology, 99(7), 24952500.

Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth 113 Mosier, N., Wyman, C., Dale, B., Elander, R., Lee, Y. Y., Holtzapple, M., & Ladisch, M. (2005). Bioresource Technology, 96(6), 673686. Nigam, J. N. (2002). Bioconversion of water-hyacinth (Eichhornia crassipes) hemicellulose acid hydrolysate to motor fuel ethanol by xylose-fermenting yeast. Journal of Biotechnology, 97, 107116. NOM-001-ECOL-1996. Upper and lower limits for pollutants for discharge of residual water in water bodies Diario Oficial de la Federacio´n, 1996. , http://dof.gob.mx/nota_detalle.php?codigo 5 4863829&fecha 5 06/ 01/1997 .. PEMEX. Memory of work 2010. ,http://www.pemex.com/files/content/Version_completa_memoria_de_labores_2010. pdf.. Pham, V., Holtzapple, M. T., & El-Halwagi, M. M. (2010). Techno-economic analysis of biomass to fuel via the MixAlco process. Journal of Industrial Microbiology & Biotechnology, 37(11), 11571168. Rodrı´guez-Trejo, E.; Ducoing-Chaho´, E. Evaluation between the factors and activities in the watershed of Patzcuaro, Michoaca´n. Universidad Auto´noma Metropolitana: Unidad Iztapalapa, 2003. Santiban˜ez-Aguilar, J.E., Ponce-Ortega, J.M., Gonza´lez-Campos, J.B., Serna-Gonza´lez, M., & El-Halwagi, M.M. (2013). Synthesis of Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth. ACS Sustainable Chemistry and Engineering, 1(2), 284305. SENER. Energy information system. (2012). ,http://sie.energia.gob.mx/sie/bdiController?action 5 login..

CHAPTER 5

Optimization of the Supply Chain Associated to the Production of Bioethanol From Residues of Agave From the Tequila Process in Mexico 5.1 Introduction The Mexican economy is highly dependent of the tequila industry where there are associated several residues of agave (i.e., the plant used to make tequila), which is lignocellulosic matter that can be used as feedstock for bioethanol production. The residues of agave are obtained in the harvesting sites located in several states of Mexico and from the tequila factories that are mainly located in two places in Mexico. Therefore, this chapter presents an optimization framework for designing a supply chain for the bioethanol production from residues of agave bagasse obtained in the tequila processing in Mexico; where central and distributed bioethanol processing plants are considered. The bioethanol production process in the central and distributed plants is modeled according to conversion factors for the different processing steps obtained from experimental data. The proposed optimization formulation also considers the total available agave and the bioethanol demanded in Mexico. Several scenarios are analyzed for the bioethanol production from agave bagasse in Mexico, where positive results are obtained from the reuse of residues of agave bagasse for the bioethanol production obtaining considerable profits and satisfying a significant demand of the gasoline required in the zone.

5.2 Problem Statement The proposed approach is based on Fig. 5.1, which shows the most important harvesting areas of agave in Mexico; these harvesting sites produce agave that can be separated in leaves and plant heads, where the leaves are transported to processing facilities and the plant heads are distributed to the tequila industries. In addition, it is possible to obtain bagasse as waste from the tequila industries; this waste can be transported to potential bioethanol processing

Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00005-5 © 2019 Elsevier Inc. All rights reserved.

115

116 Chapter 5

Figure 5.1 Schematic representation of supply chain of bioethanol production in Mexico from agave bagasse. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

facilities (details for this process are shown in Fig. 5.2) to be mixed with the bagasse from leaves according with Fig. 5.3, where the main sources to obtain agave bagasse represent the stalks in the cultivation areas and the bagasse obtained from the tequila industry; this agave bagasse is used to produce bioethanol in processing factories (see Fig. 5.2). Fig. 5.4 shows the steps that the biomass requires to be transformed to bioethanol. Note that there is a lot of water required in the production process. Finally, the produced bioethanol can be transported to different consumption regions located in the main cities of Mexico. To identify that processing system is considered as a distributed system (different locations for processing facilities, raw material suppliers and consumption regions), the superstructure shown in Fig. 5.5 is proposed. First, the agave bagasse from the harvesting areas and tequila and mezcal industries are used as feedstock in the central and/or distributed processing plants. These processing plants are based on Fig. 5.2 for bioethanol production. The differences between central and distributed processing facilities are the capacity and the

Figure 5.2 Bioethanol processing from agave bagasse. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Figure 5.3 Main sources of agave bagasse. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

118 Chapter 5

Figure 5.4 Steps for bioethanol production from agave bagasse. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

location. In this context, central processing facilities are located in industrialized zones where the capacity is larger and the processing is cheaper, which allows obtaining larger volumes of bioethanol. On the other hand, distributed processing facilities are located near cultivation areas, where there is less infrastructure and the processing capacity is lower, which means unit processing cost is greater (due to the economies of scale). In this context, distributed processing facilities help to reduce the transportation costs for raw materials, which is the main transportation cost involved in the supply chain; however, this distributed processing facilities increase the processing cost. This means the optimization model must determine the best compromise between these two options. There are two processing cost functions that depend on the capacity (one for the distributed plant and another for the central plant) and the location of the processing facilities.

Optimization of the Supply Chain Associated to the Production of Bioethanol 119

Figure 5.5 Proposed superstructure for optimizing the supply chain for a biorefinery based on residues of agave. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

The processing to obtain bioethanol considers conversion efficiencies ðαÞ for each step; these efficiencies are shown in Table 5.1. Note that these values were calculated according to experimental data obtained from a pilot plant and represent the ratio of the outlet mass produced per the inlet total mass processed in each process step.

5.3 Model Formulation Prior to formulating the mathematical model the following sets need to be defined: i represents a set for harvesting areas; j is an index used to define the distributed processing facilities; l is used to represent the central processing facilities; the sites for the industries for tequila production are associated with the index k; locations where products (bioethanol

120 Chapter 5 Table 5.1: Efficiencies of the bioethanol processing from residues of agave Step

Efficiency for Each Processing Step ðαÞ (Mass Produced/Mass Processed)

Mill (bagasse) (Juice) Sieve first step Sieve second step Fermentation Column (preconcentrate) Column (dehydrated)

0.537 0.463 0.8 0.52 0.39 0.99 0.99

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

and solid fuel) are consumed are defined by the index m; and finally the time periods are identified by the index t. The mathematical programing formulation is based on the superstructure shown in Fig. 5.5, whereas the bioethanol production facilities considered are based on the flowsheet presented in Fig. 5.2; the model accounts for the optimal design of the supply chain for the bioethanol production based on residues of agave from the tequila industry in Mexico and considering the available agave residues, presented as follows.

5.3.1 Mass Balances in Agave Cultivating Areas Plant heads ðFPlantHeadsi;t Þ, can be obtained from available agave ðFAgavei;t Þ which are the main raw materials for the tequila production considering a separation efficiency of zAHi , which is modeled as follows: FAgavei;t UzAHi 5 FPlantHeadsi;t ;

’iAI; tAT

(5.1)

Also, the stalks are important parts of the agave ðFTotalLeavesBagassei;t Þ that currently are considered as wastes but can be raw materials used for producing bioethanol. The amount of stalks that can be obtained from the agave is determined as follows: FAgavei;t UzALi 5 FTotalLeavesBagassei;t ;

’iAI; tAT

(5.2)

where zALi is the separation factor for the stalks. The total amount of agave bagasse obtained from the stalks in the agave growing areas is sent to the distributed and central process facilities for bioethanol production: X FTotalLeavesBagassei;t 5 FLeavesBagasseDistributed i;j;t jAJ

1

X lAL

FLeavesBagasseCentral ; i;l;t

’iAI; tAT

(5.3)

Optimization of the Supply Chain Associated to the Production of Bioethanol 121

5.3.2 Maximum Available Agave The maximum agave that can be used is limited by the following constraint: FAgavei;t # FAgaveMax i;t ;

’iAI; tAT

(5.4)

where FAgaveMax represents the maximum agave available in the agricultural areas. In this i;t chapter, the maximum available agave in the cultivation areas is considered as an optimization variable, since the proposed model includes the possibility to increase the cultivation area to satisfy a greater demand based on the available area in the zone. Therefore, FAgaveMax is calculated considering the current available agave in this area at i;t 0 1 Currently

Possible

available C increasing B any period of time @FAgavei;t A multiplied by a possible increment Inci;t

as follows:

0

1

Currently Possible available B increasing C Max FAgavei;t 5 FAgavei;t @1 1 Inci;t A;

’iAI; tAT

(5.5)

Possible increasing Inci;t

It should be noted that the variable is fixed to zero for the case when the possibility of increasing is not considered, and for other cases it is limited to the available area in the zone at each period of time t.

5.3.3 Mass Balances in Tequila Industry This balance determines the inlet flow rate to the tequila processing facilities   FPlantHeadsTequilaIndustry ; in this way, the amount of agave plant heads from the i;k;t   harvesting areas i FPlantHeadsi;t is equal to the agave plant heads distributed for the tequila production in all facilities k at any period t. The inlet flow rate to the tequila processing factories is used to determine the amount of bagasse that can be obtained as waste from the tequila industry at any period of time: X FPlantHeadsi;t 5 FPlantHeadsTequilaIndustry ; ’iAI; tAT (5.6) i;k;t kAK

  The total flow rate of plant heads FTotalPlantHeadsTequilaIndustry from growing areas i that is k;t processed by the tequila industry k for yielding tequila at any time period t is stated as follows: X 5 FPlantHeadsTequilaIndustry ; ’kAK; tAT (5.7) FTotalPlantHeadsTequilaIndustry k;t i;k;t iAI

122 Chapter 5

5.3.4 Residues of Agave Bagasse From the Tequila Industry   This balance determines the total amount of tequila bagasse FTequilaBagassek;t that is obtained from the tequila processing factories; the obtained bagasse depends on the total   agave plant heads in the tequila industry FTotalPlantHeadsTequilaIndustry and an efficiency k;t factor ðzCookedk Þ as follows: FTequilaBagassek;t 5 FTotalPlantHeadsTequilaIndustry UzCookedk ; ’kAK; tAT (5.8) k;t   The total amount of agave bagasse from the tequila industry FTequilaBagassek;t is sent to     the distributed FBagasseTequilaDistributed and central FBagasseTequilaCentral processing k;j;t k;l;t facilities for producing bioethanol at any time period t: X X FBagasseTequilaDistributed 1 FBagasseTequilaCentral FTequilaBagassek;t 5 k;j;t k;l;t ; ’kAK; tAT jAJ

lAL

(5.9)

5.3.5 Mass Balances in Distributed Processing Plants for Bioethanol Production These balances take into account the total amount of bagasse in the distributed processing   plants FTotalBagasseDistributed , which is equal to the flow rate of the stalk bagasse j;t     Distributed FLeavesBagassei;t and the plant heads bagasse FBagasseTequilak;j;t used to obtain bioethanol: 5 FTotalBagasseDistributed j;t

X

FBagasseTequilaDistributed k;j;t

kAK

1

X

FLeavesBagasseDistributed ; i;j;t

’jAJ; tAT

(5.10)

iAI

The total bagasse flow rate in the distributed processing facilities is considered for the bioethanol production, using the process shown in Fig. 5.2. All the considered steps have   efficiency factors αstepPlant shown in Table 5.1, which are based on the data obtained p from the pilot plant. The involved steps in the bioethanol production are described in Eqs. (5.11)(5.23). These equations are similar for the central and distributed processing facilities; for this reason, these equations are grouped using the index Plant for both facilities. This way, the set P is the union of J and L ðP 5 J , LÞ.

Optimization of the Supply Chain Associated to the Production of Bioethanol 123 In this process, the agave bagasse in the plants is preprocessed to decrease the particle size through a milled process, because a small particle size is required to improve the process to obtain carbohydrates that can be transformed to bioethanol: Plant FTotalBagassePlant 5 FMillPlant p;t UαMillp p;t ;

’pAP; tAT

(5.11)

On the other hand, during the process of milling it is possible to obtain juices rich in sugars that then can be processed to produce bioethanol: Plant FTotalBagassePlant 5 FJuicePlant p;t UαJuicep p;t ;

’pAP; tAT

(5.12)

In addition, the flow rate from milling is treated in a hydrolysis reactor to break the chain of cellulose and hemicellulose; this step is associated with an efficiency factor to process the lignocellulosic material to yield a mix of compounds that can be separated. Plant FMillPlant 5 FReactorPlant p;t UαReactorp p;t ;

’pAP; tAT

(5.13)

After the first reactor, a mix of hydrolyzed and nonhydrolyzed compounds is separated through a filter, where the hydrolyzed part is sent to a fermentation tank and the nonhydrolyzed part is directed to a second hydrolysis reactor to obtain additional fermentable materials. The separation after the first reactor is modeled in Eqs. (5.14) and (5.15): Plant FReactorPlant 5 FFiltered1Plant p;t UαFiltred1p p;t ; Plant FReactorPlant 5 FFiltered2Plant p;t UαFiltered2p p;t ;

’pAP; tAT

(5.14)

’pAP; tAT

(5.15)

There is another filtering section to treat the effluent from the second hydrolysis reactor.   obtained from Eq. (5.17) is conducted The fermentable material FFilteredSecondPlant p;t to one fermentation process and the other part is considered as solid fuel   FFuelSolidPlant that is a byproduct in the global bioethanol production process and is p;t given by Eq. (5.18): Plant FFiltered2Plant 5 FReactor2Plant p;t UαReactor2p p;t ;

’pAP; tAT

Plant FReactor2Plant 5 FFilteredSecondPlant p;t UαFilteredsecond1p p;t ;

’pAP; tAT

(5.16) (5.17)

Plant 5 FFuelSolidPlant ’pAP; tAT (5.18) FReactor2Plant p;t UαFilteredSecond2p p;t ;   Fermentable materials FFermentationPlant are juices from primary agave bagasse p;t     FJuicePlant , effluents from the first FFiltered1Plant and second p;t p;t   FFilteredSecondPlant hydrolysis reactors (here we only consider the hydrolyzed part); p;t

124 Chapter 5 these fermentable materials are directed to a fermentation process to obtain bioethanol from sugar, and the produced bioethanol is sent to a distillation column that is known as the concentrator column: Plant Plant Plant FFermentationPlant p;t 5 FJuicep;t 1 FFiltered1p;t 1 FFilteredSecondp;t ;

’pAP; tAT (5.19)

Plant Plant FFermentationPlant p;t UαFermentationp;t 5 FColumn1p;t ;

’pAP; tAT

(5.20)

Materials from the concentrator column are sent to a second column that is used to dehydrate the bioethanol because one of the most important problems in using bioethanol as fuel is the humidity content. After the dehydrator column, the product is stored in a tank that allows satisfying and distributing adequately the product to consumers: Plant FColumn1Plant 5 FColumn2Plant p;t αDestilationp p;t ; Plant FColumn2Plant 5 FStockPlant p;t αDehydratedp p;t ;

’pAP; tAT ’pAP; tAT

(5.21) (5.22)

Finally, to take into account the storage of bioethanol in the plants at any time period t   FTankPlant , we consider the stored bioethanol in the previous time period t 2 1 p;t     Plant FTankPlant plus the bioethanol obtained from any processing facility FStock minus p;t21 p;t   , which is stated as follows: the sent bioethanol to markets FprodBioethanolPlant p;t Plant Plant Plant FTankPlant p;t 5 FTankp;t21 1 FStockp;t 2 FprodBioethanolp;t ;

’pAP; tAT

(5.23)

5.3.6 Distribution of Products From Processing Plants to Markets These balances take into account the total flow rate of the bioethanol obtained from the distributed and central processing plants; furthermore, the flow rate of solid fuel that is obtained in the processing is considered (this solid fuel is a byproduct that can be economically attractive). The total products obtained from the processing plants   Plant FprodBioethanolPlant , are collected and sent to the markets for sale p;t ; FFuelSolidp;t   Plant ; gprodSolidFuel gprodBioethanolPlant p;m;t p;m;t , and these relationships are stated as follows: FprodBioethanolPlant p;t 5

X mAM

gprodBioethanolPlant p;m;t ;

’pAP; tAT

(5.24)

Optimization of the Supply Chain Associated to the Production of Bioethanol 125 X

FFuelSolidPlant p;t 5

gprodSolidFuelPlant p;m;t ;

’pAP; tAT

(5.25)

mAM

Additional equations are required   to establish that the products in markets GBioethanolm;t ; GSolidFuelm;t are equal to the products obtained from distributed   ; gprodSolidFuelDistributed gprodBioethanolDistributed and central j;m;t j;m;t   Central processing facilities: gprodBioethanolCentral i;m;t ; gprodSolidFueli;m;t X

gprodBioethanolDistributed 1 j;m;t

jAJ

X

X

gprodBioethanolCentral i;m;t 5 GBioethanolm;t ;

’mAM; tAT

lAL

gprodSolidFuelDistributed 1 j;m;t

jAJ

X

(5.26) gprodSolidFuelCentral i;m;t 5 GSolidFuelm;t ;

’mAM; tAT

lAL

(5.27)

5.3.7 Product Demands

    Min Eqs. (5.43) to (5.46) impose limits for the maximum GMax and minimum G limits m;t m;t for demands in the markets: GBioethanolm;t # GBioethanolMax m;t ; GSolidFuelm;t # GSolidFuelMax m;t ; GBioethanolm;t $ GBioethanolMin m;t ; GSolidFuelm;t $ GSolidFuelMin m;t ;

’mAM; tAT ’mAM; tAT ’mAM; tAT ’mAM; tAT

(5.28) (5.29) (5.30) (5.31)

5.3.8 Cost of the Distributed Bioethanol Processing Plants The operational cost for the distributed and central processing plants is calculated according to the cost of the involved equipment in the plants as follows: 1 0 Reactor CoperDistMill 1CoperDistReactor2 1CoperDistSieve 1 p 1CoperDistp p p C XB 1CoperDistTank 1CoperDistTank2 1CoperDistColumn 1A @ 1CoperDistSieve2 p p p p CostPlantOP 5 1CoperDistTankA 1CoperDistColumn2 jAJ p p ’pAP (5.32)

126 Chapter 5 where the individual cost for each unit depends on a unitary cost for the amount of processed material in each unit: X CoperPlantMill 5 UCostPlantOpMill UFTotalBagassePlant ’pAP p p p;t ; tAT

5 CoperPlantReactor p CoperPlantReactor2 5 p

X

X

(5.33)

UCostPlantOpReactor UFMillPlant p p;t ;

’pAP

(5.34)

UCostPlantOpReactor2 UFfiltered2Plant p p;t ;

’pAP

(5.35)

tAT

tAT

CoperPlantSieve2 5 p

X

UCostPlantOpSieve2 UFReactor2Plant p p;t ;

’pAP

(5.36)

tAT

X

5 CoperPlantSieve p

UCostPlantOpSieve UFReactorPlant p p;t ;

’pAP

(5.37)

tAT

CoperPlantTank 5 p

X

  Plant UCostPlantOpTank U Ffiltered1Plant ; p p;t 1 FJuicep;t

tAT

5 CoperPlantTank2 p

X

UCostPlantOpTank2 UFFermentationPlant p p;t ;

tAT

CoperPlantColumn 5 p

X

UCostPlantOpColumn UFColumn1Plant p p;t ;

’pAP

’pAP ’pAP

(5.38) (5.39) (5.40)

tAT

5 CoperPlantColumn2 p

X tAT

5 CoperPlantTankA p

UCostPlantOpColumn2 UFColumn2Plant p p;t ; X

UCostPlantOpTankA UFStockPlant p p;t ;

’pAP

(5.41)

’pAP

(5.42)

tAT

The capital cost accounts for the fixed and variable costs for each unit in the distributed and central processing plants: 1 0 Mill Reactor 1 CPlantReactor2 p X B CPlantp 1 CPlantp C 1 CPlantSieve2 1 CPlantTank CostPlantCAP 5 KF A ’pAP (5.43) @ 1CPlantSieve p p p Column Column2 TankA pAP 1CPlantp 1 CPlantp 1 CPlantp Additional constraints in distributed and central plants are needed to calculate the capacity that is used to obtain the variable part of the capital cost for the processing units. This should be considered into a disjunctive formulation because the fixed part of the cost is only considered when the unit exists. Furthermore, the capacity for each unit

Optimization of the Supply Chain Associated to the Production of Bioethanol 127 must consider the maximum flow rate for all the time periods considered in the supply chain: FTotalBagasseCAPPlant $ FTotalBagassePlant p p;t ; FMillCAPPlant $ FMillPlant p p;t ;

’pAP; tAT

(5.44)

’pAP; tAT

(5.45)

$ Ffiltered2Plant Ffiltered2CAPPlant p p;t ;

’pAP; tAT

(5.46)

FReactorCAPPlant $ FReactorPlant p p;t ;

’pAP; tAT

(5.47)

FReactor2CAPPlant $ FReactor2Plant p p;t ;

’pAP; tAT

(5.48)

FFermentationCAPPlant $ FFermentationPlant p p;t ; ’pAP; tAT

(5.49)

$ FColumn1Plant FColumn1CAPPlant p p;t ;

’pAP; tAT

(5.50)

FColumn2CAPPlant $ FColumn2Plant p p;t ;

’pAP; tAT

(5.51)

$ FStockPlant FStockCAPPlant p p;t ;

’pAP; tAT

(5.52)

For the optimal location of processing facilities, the following disjunction is proposed (where the unit data are shown in Table 5.2, and these costs include the capital and is used to determine the optimal location for the operating costs). The binary variable yPlant p distributed and central plants. Table 5.2: Unit fixed and variable costs for the equipment in processing plants Distributed Plant Equipment Mill Reactor 1st stage Reactor 2nd stage Sieve 1st stage Sieve 2nd stage Fermentation tank Distillation column Dehydrated column Stock tank

Unit Fixed Cost (USD)

Unit Variable Cost (USD/kg)

Central Plant Unit Fixed Cost (USD)

Unit Variable Cost (USD/kg)

93,500 200,000 225,000

0.063 0.074 0.081

140,250 30,000 337,500

0.057 0.069 0.076

115,000 120,000 105,000

0.057 0.062 0.053

172,500 180,000 150,750

0.053 0.055 0.048

320,000

0.083

480,000

0.078

310,000

0.087

465,000

0.081

98,500

0.06

147,750

0.055

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

128 Chapter 5 2

3

YpPlant

7 6 MIN 7 6 FTotalBagasseCAPPlant # FTotalBagasseCAPPlant p p 7 6 7 6 Plant PlantMAX 7 6 FTotalBagasseCAPp # FTotalBagasseCAPp 7 6 7 6 6 CPlantMill 5 CFixPlantMill 1 CVarPlantMill UFFTotalBagasseCAPPlant 7 p p p p 7 6 7 6 Reactor Reactor Reactor Plant 7 6 CPlant 5 CFixPlant 1 CVarPlant UFMillCAP p p p p 7 6 6 Reactor2 Reactor2 Plant 7 7 6 CPlantReactor2 5 CFixPlant 1 CVarPlant UFfiltered2CAP p p p p 7 6 7 6 Sieve Sieve Sieve Plant CPlantp 5 CFixPlantp 1 CVarPlantp UFReactorCAPp 7 6 7 6 7 6 Sieve2 Sieve2 Sieve2 Plant CPlant 5 CFixPlant 1 CVarPlant UFReactor2CAP 7 6 p p p p 7 6 6 CPlantTank 5 CFixPlantTank 1 CVarPlantTank UFFiermentationCAPPlant 7 7 6 p p j p 7 6 6 CPlantColumn 5 CFixPlantColumn 1 CVarPlantColumn UFColumn1CAPPlant 7 7 6 p p p p 7 6 Column2 Column2 Column2 Plant 6 CPlant 5 CFixPlantp 1 CVarPlantp UFColumn2CAPp 7 p 5 4 TankA TankA TankA Plant CPlantp 5 CFixPlantp 1 CVarPlantp UFStockCAPp 3 2 :YpPlant 7 6 6 FTotalBaggaseCAPPlant 5 0 7 p 7 6 7 6 Mill 7 6 CPlantp 5 0 7 6 7 6 Reactor 7 6 50 CPlantp 7 6 7 6 CPlantReactor2 5 0 7 6 p 7 6 7 6 CPlantSieve 5 0 36 7; ’pAP p 7 6 Sieve2 7 6 50 CPlantp 7 6 7 6 Tank 7 6 CPlantp 5 0 7 6 7 6 Column 7 6 CPlant 5 0 p 7 6 7 6 Column2 7 6 CPlant 5 0 p 5 4 5 0 CPlantTankA p The previous disjunction is reformulated as follows; the binary variable yPlant is one when p the distributed or central plant is installed; otherwise, the binary variable is zero. Then, the distributed or central plant is installed when the amount of treated agave bagasse is between given upper and lower limits: Min

UyPlant # FTotalBagasseCAPPlant ; FTotalBagassePlant p p p

’pAP

(5.53)

Optimization of the Supply Chain Associated to the Production of Bioethanol 129 FTotalBagasseCAPPlant # FTotalBagasseCAPPlant p p

Max

UyPlant ; p

’pAP

(5.54)

is used to calculate the capital cost for each processing unit, The binary variable yPlant p where the fixed part of the capital cost is multiplied by the binary variable and the variable part is equal to a unitary cost multiplied by the greatest flow rate processed in all periods of time. It should be noted that the capital cost function usually has an exponent between 0.6 and 0.8 in the variable part to account for the economies of scale. That is, the economies of scale state that there is no linear relationship between the capacity and cost. However, this formulation may represent numerical complications for solving large nonlinear and nonconvex optimization problems. In the analyzed case study, the above-mentioned formulation yields problems that are difficult to solve without good initial guesses. It should be noted that it is not simple to obtain these good initial guesses. Instead, the nonlinear behavior for the capital cost functions can be linearized in several segments, as was presented by Bowling, Ponce-Ortega, and El-Halwagi (2011). To obtain these linear relationships, only upper and lower bounds with respect to the capacity for the linear segments are required. In this chapter, proper upper and lower bounds for the capacity for the units involved were considered to obtain linear relationships for the capital cost functions (it should be noted that these limits for central processing plants are greater than the ones for distributed processing plants); the model accounts for the economies of scale and at the same time the model formulation can be easily solved. Plant Plant CPlantMill 5 CFixPlantMill 1 CVarPlantMill ; p p Uyp p UFTotalBagasseCAPp

CPlantReactor 5 CFixPlantReactor UyPlant 1 CVarPlantReactor UFMillCAPPlant ; p p p p p

’pAP (5.55) ’pAP

CPlantReactor2 5 CFixPlantReactor2 UyPlant 1 CVarPlantReactor2 UFfiltered2CAPPlant ; p p p p p

(5.56)

’pAP (5.57)

5 CFixPlantSieve UyPlant 1 CVarPlantSieve UFReactorCAPPlant ; CPlantSieve p p p p p 5 CFixPlantSieve2 UyPlant 1 CVarPlantSieve2 UFReactor2CAPPlant ; CPlantSieve2 p p p p p

’pAP

(5.58)

’pAP (5.59)

CPlantTank 5 CFixPlantTank UyPlant 1 CVarPlantTank UFFiermentationCAPPlant ; p p p p p

’pAP (5.60)

130 Chapter 5 CPlantColumn 5 CFixPlantColumn UyPlant 1 CVarPlantColumn UFColumn1CAPPlant ; p p p p p

’pAP (5.61)

5 CFixPlantColumn2 UyPlant 1 CVarPlantColumn2 UFColumn2CAPPlant ; CPlantColumn2 p p p p p

’pAP (5.62)

5 CFixPlantTankA UyPlant 1 CVarPlantTankA UFStockCAPPlant ; CPlantTankA p p p p p

’pAP

(5.63)

The operational cost of the central processing plants is calculated in a similar way as for the distributed processing facilities; the main differences between distributed and central processing plants are their capacity, since the economies of scale are considered; in addition, the central processing facilities are associated with a different binary variable that is used to determine if any central plant should be installed. The capital cost for the central processing plants are calculated as a sum of the capital costs for each unit, with a fixed term and a variable term that depends on the amount of processed material.

5.3.9 Transportation Cost for Stalks to Distributed and Central Plants

  and This cost involves a unitary charge for bagasse transportation UCostTranspLeavPlant i;p   Plant the distance from the growing areas to the plant di;p : CostTranspLeavesPlant 5

XXX

Plant Plant UCostTranspLeavPlant i;p Udi;p UFLeavesBagassei;p;t

iAI pAP tAT

(5.64)

5.3.10 Transportation Cost From the Tequila Industries to Distributed and Central Bioethanol Processing Plants The transportation cost associated with the bagasse transported from the tequila industries to the central and distributed processing plants accounts for the unit transportation cost ðUCostTranspBagÞ, the associated distance ðd Þ and the transported bagasse ðFBagasseTequilaÞ: XXX Plant Plant CostTranspBagassePlant UCostTranspBagPlant Teq 5 k;p Udk;p UFBagasseTequilak;p;t kAK pAP tAT

(5.65)

Optimization of the Supply Chain Associated to the Production of Bioethanol 131

5.3.11 Transportation Cost for Products This cost involves the transportation cost for the products obtained in the distributed and central processing plants that are sent to the markets; two products are obtained, bioethanol and solid fuel, and the cost is calculated as follows: CostTranspProdBioethanol XXX Dist 5 gprodBioethanolDistributed UUCostTranspBioDist j;m;t j;m;t Udj;m jAJ mAM tAT

1

XXX

(5.66) Central Cent gprodBioethanolCentral l;m;t UUCostTranspBiol;m;t Udl;m

lAL mAM tAT

CostTranspProdSolidFuel XXX Dist 5 gprodSolidFuelDistributed UUCostTranspSolidDist j;m;t j;m;t Udj;m jAJ mAM tAT

1

XXX

(5.67) Central Cent gprodSolidFuelCentral l;m;t UUCostTranspSolidl;m;t Udj;m

lAL mAM tAT

To annualize the transportation cost for bagasse and products, the sum of all time periods is considered.

5.3.12 Objective Function The objective function is maximizing the profit, which accounts for the sales minus the costs. The total cost takes into account all the costs involved in the proposed model, including the operational cost, the capital cost and the transportation cost for distributed and central processing plants: TotCost 5

!

CostPlantOP 1 CostPlantCAP 1 CostTranspLeavesPlant 1CostTranspBagassePlant Teq 1 CostTranspProdBioethanol 1 CostTranspProdSolidFuel

(5.68) On the other hand, the total sales include the sales for bioethanol and solid fuel in the markets. In this case, the amount sold in each market over each time period is multiplied by the unitary price: ! XX XX Bioethanol SolidFuel TotSales 5 GBioethanolm;t Uβ m 1 GSolidFuelm;t Uβ m (5.69) mAM tAT

mAM tAT

132 Chapter 5 Finally, the total annual profit is determined by the difference between total sales and costs. PROFIT 5 TotSales 2 TotCost

(5.70)

5.4 Case Study The proposed mathematical model will be applied to a case study in Mexico, since this is the main region where agave is cultivated and where the tequila and mezcal industries are located (see Fig. 5.1). Table 5.3 shows the available agave in this region; this information has been reported by the Mexican government through its website with the current reports of agricultural species (SAGARPA, 2013). The demand for gasoline in the States of Mexico is shown in Table 5.4. These data represent the total consumption, but the mathematical formualtion developed in this chapter can determine the demand that can be satisfied considering that the gasoline can be replaced by bioethanol (SENER, 2012). The model considers nine agricultural areas for agave cultivation (Guanajuato, Zacatecas, Jalisco, Michoaca´n, Morelos, Nayarit, Oaxaca, Puebla and Zacatecas). The current tequila factories are located in six places (Tequila 1, Tequila 2, Pe´njamo, Oaxaca, Morelos and Zacatecas). Three central processing facilities for bioethanol production have been considered (Tequila, Oaxaca and Irapuato), and six distributed bioethanol processing facilities (Chilpancingo, Morelia, Cuernavaca, Tepic, Puebla and Fresnillo). Using these data and taking into account the possible installation of distributed and central bioethanol processing plants, the next step is to solve the model to find the optimal distribution for the supply chain of bioethanol from agave residues in Mexico. The model for this case study has 12,534 continuous variables, 9 binary variables and 7189 constraints; this model was coded in the GAMS software and solved through the solver CPLEX (Brooke, Kendrick, Meeraus, & Raman, 2018). Several scenarios were analyzed to identify the applicability of the proposed methodology. Scenario A considers the economic solution with a constraint for the satisfied demand of bioethanol equal to 1% of the total demand of gasoline in each consumption site. Scenario B considers the case where the bioethanol demand is not limited in any Table 5.3: Agave available in Mexico (SAGARPA, 2013) 1 2 3 4 5 6 7 8 9

Cultivation Area

Production (Tonne/Year)

Guanajuato Guerrero Jalisco Michoaca´n Morelos Nayarit Oaxaca Puebla Zacatecas

88,597 6435 1,091,736 67,210 16,801 36,545 329,411 25,174 29,560

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Optimization of the Supply Chain Associated to the Production of Bioethanol 133 Table 5.4: Gasoline demand in Mexico (SENER, 2012) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

State

Gasoline Consumption (Tonne/Year) 3 1023

Aguascalientes Baja California N Baja California S Campeche Coahuila Colima Chiapas Chihuahua Distrito Federal Durango Guanajuato Guerrero Hidalgo Jalisco Me´xico Michoaca´n Morelos Nayarit ´n Nuevo Leo Oaxaca Puebla Quere´taro San Luis Potosı´ Sinaloa Sonora Tabasco Tamaulipas Veracruz ´n Yucata Zacatecas

493.62 1632.15 353.45 186.06 504.31 841.10 796.67 1251.03 4079.28 756.28 1349.26 535.85 978.99 1601.33 2146.21 1148.62 599.99 183.81 1773.62 565.34 1305.18 829.44 644.05 1093.20 981.38 727.91 1204.99 1762.23 1012.26 326.71

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

market. For each scenario, the Pareto curves are presented to take into account the behavior between the agave consumption versus the net annual profit; in addition, a comparison of both scenarios is presented to show the best economic solution between the profit and demand of bioethanol. Furthermore, Scenario C considers the case where it is possible to increase the cultivation area to satisfy greater bioethanol demand; in this Scenario C the additional land and water for agave cultivation is considered.

5.4.1 Scenario A (Economic Solution With a Constraint of 1% for the Bioethanol Demand in Each Consumption Site) The optimal solution for Scenario A determines the installation of two central plants (Central 1 at the city of Tequila in the State of Jalisco and Central 2 at the city of Oaxaca in the State of

134 Chapter 5 Oaxaca); no distributed plants were selected. Central processing plant 1 receives bagasse from cultivation area 3 (located in the State of Jalisco) with a flow rate of 4.32 3 108 kg of bagasse per year and from cultivation area 6 (located in the State of Nayarit) with a flow rate of 1.11 3 107 kg/year. Central processing plant 2 is fed from the growing area 7 (near the city of Oaxaca) with a flow rate of 1.32 3 108 kg/year. Also, the central processing plants are fed with tequila bagasse; tequila industry 1 (located in the city of Tequila) and tequila industry 2 (also located in the city of Tequila) feed a flow rate of bagasse to the central processing plant 1 at 1.12 3 108 and 1.21 3 107 kg/year, respectively. Central processing plant 2 is fed with a flow rate of 3.08 3 108 kg/year of tequila agave from the tequila industry 4 (located in the city of Oaxaca). In this case, the bioethanol production is 1.79 3 108 kg of bioethanol/year and 1.38 3 108 kg of bioethanol/year for central processing plants 1 and 2, respectively. The obtained bioethanol is sent to all markets (the flow rates are shown in Table 5.5). In addition, Table 5.5: Bioethanol distribution for the optimal solution of Scenario A Processing Plant

Market

Flow (Tonne/Year) 3 1023

Central 1

1 (Aguascalientes) 2 (Baja California Norte) 3 (Baja California Sur) 5 (Coahuila) 6 (Colima) 8 (Chihuahua) 10 (Durango) 11 (Guanajuato) 14 (Jalisco) 15 (Me´xico) 16 (Michoaca´n) 18 (Nayarit) ´n) 19 (Nuevo Leo 22 (Quere´taro) 23 (San Luis Potosı´) 24 (Sinaloa) 25 (Sonora) 27 (Tamaulipas) 30 (Zacatecas) 4 (Campeche) 7 (Chiapas) 9 (Distrito Federal) 12 (Guerrero) 13 (Hidalgo) 15 (Me´xico) 17 (Morelos) 20 (Oaxaca) 21 (Puebla) 26 (Tabasco) 28 (Veracruz) 29 (Yucata´n)

4.94 16.30 3.53 5.04 8.41 12.50 7.56 13.50 16.00 8.82 11.50 1.84 17.70 8.29 6.44 10.90 9.81 12.10 3.27 1.86 7.97 40.80 5.36 9.79 12.60 6.00 5.65 13.10 7.28 17.60 10.10

Central 2

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Optimization of the Supply Chain Associated to the Production of Bioethanol 135 Fig. 5.6 shows the graphical representation for the supply chain. The optimal distribution was generated with the constraint of 1% for the satisficed demand; this constraint is subjected to the demand stated in each market and thus the bioethanol is consumed in all markets, but the portion consumed in each market is different due to the demand. For the best economic solution for Scenario A, 85% of the total available agave bagasse was consumed. The optimal distribution presents a total annual profit of 1.5337 3 108 USD/year, with sales and costs of 3.72646 3 108 USD/year and 2.1927 3 108 USD/year, respectively. In the bioethanol production, the agave waste can be used as solid fuel, adding an important monetary value; this waste provides 2.1645 3 106 USD/year of the total sales. It should be noted that the major contribution for the costs is the operational cost in the central processing plants with a value of 1.9630 3 108 USD/year, since the residual bagasse cost is not considered for this case. Furthermore, the transportation cost for biomass and products is lower than the operational cost in central processing plants, which is 7 3 105 to 9 3 106 USD/year due to the lower density of the agave bagasse and the transportation cost for products is lower (It should be noticed that products are transported via pipelines). Also, it should be noted that the distribution for the supply chain states that the bioethanol production is cheaper in central processing facilities, although this configuration is not sufficient to obtain the total bioethanol consumed.

Figure 5.6 Optimal economic solution for Scenario A. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

136 Chapter 5 Comparision of both curves 2.00E+08

Prof it (USD/year)

1.80E+08 1.60E+08 1.40E+08 1.20E+08 1.00E+08 8.00E+07 6.00E+07 4.00E+07 2.00E+07 0.00E+00 0.00E+00

1.00E+08

2.00E+08

3.00E+08

4.00E+08

Total demand (kg/year) Without restrictions

With restrictions

Figure 5.7 Pareto curves for Scenarios A and B. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ezAguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Scenario A was chosen because it allows satisfying the biofuel demands in all markets, and represents a geographically distributed solution. Additionally, this scenario only considers the current available agave, which is realistic. Furthermore, the proposed approach can obtain a set of Pareto solutions like that shown in Fig. 5.7 to balance profit and demand in this scenario. Notice that the profit increases when the satisfied demand increases. Two cases are selected for analyzing this Pareto curve. Case 1. (40% of consumed agave). This scenario accounts for the installation of the central processing plant 1. This plant receives 2.56 3 108 kg/year of bagasse from cultivation area 3 (Jalisco) and 1.46 3 107 kg/year from growing area 6 (Nayarit). Also, the tequila industries 1 and 2 (both located in Tequila, Jalisco) feed the central processing plant with a bagasse flow rates of 9.97 3 107 and 1.03 3 108 kg/year, respectively; with this total flow rate central processing plant 1 produces 1.49 3 108 kg/year of bioethanol. The distribution of the bioethanol obtained in these markets is shown in Fig. 5.8, and the associated profit is 7.4806 3 107 USD/year. Case 2. (75% of consumed agave). For this scenario, the optimal distribution considers the installation of central processing plants 1 and 3. Central processing plant 1 is fed from cultivation area 6 (Nayarit) with a flow rate of 1.46 3 107 kg/year of agave bagasse; central processing plant 3 receives bagasse from cultivation areas 1, 3 and 4 with bagasse flow rates of 3.54 3 107, 4.37 3 108 and 1.35 3 107 kg/year, respectively. Furthermore, tequila industries 1 and 2 provide bagasse flow rates of 2.83 3 108 and 6.26 3 107 kg/year to central processing plant 1. Tequila industry 3 provides a bagasse flow rate of 3.52 3 107 kg/year to central

Optimization of the Supply Chain Associated to the Production of Bioethanol 137

Figure 5.8 Distribution of bioethanol for Case 1 of Scenario A. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

processing plant 3. According to the total flow rate in each central processing plant, it is possible to obtain 1.13 3 108 kg/year of bioethanol from central processing plant 1 and 1.66 3 108 kg/year of bioethanol from central processing plant 3. Fig. 5.9 shows the distribution of the bioethanol obtained in the considered markets for this case 2, and the associated profit is 1.3949 3 108 USD/year.

5.4.2 Scenario B (Solution Without Constraint for the Demand of Bioethanol in the Markets) In this scenario, the model is solved without constraints for demands in markets. The optimal economic solution for this scenario selects the installation of central processing facilities 1, 2 and 3, and distributed processing facility 3. Table 5.6, shows the agave bagasse from the cultivation areas and tequila industries feeding each central and distributed processing plant; in addition, Table 5.7 shows the bioethanol obtained from each processing plant. The flow rates of the obtained bioethanol are sent to the different markets; however, in this scenario there is not a constraint to satisfy any demand in the markets; for this reason, in the optimal solution the plants send bioethanol to the nearest markets, as is shown in Fig. 5.10. In addition, the satisfied demand in some markets is around 50% in some periods; nonetheless,

Figure 5.9 Distribution of bioethanol for Case 2 of Scenario A. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014. Table 5.6: Agave bagasse fed for the plants in Scenario B

Processing Plant Central 1 (Tequila) Central 2 (Oaxaca) Central 3 (Irapuato)

Distributed 3 (Cuernavaca)

Cultivation Area

Flow rate (Tonne/Year) 3 1023

3 (Jalisco) 6 (Nayarit) 9 (Zacatecas) 7 (Oaxaca)

143.00 14.60 7.88 132.00

1 (Guanajuato) 3 (Jalisco) 4 (Michoaca´n) 9 (Zacatecas) 2 (Guerrero) 5 (Morelos) 8 (Puebla)

35.40 294.00 26.90 3.94 2.57 6.72 10.10

Tequila Industry

Flow Rate (Tonne/Year) 3 1023

1 (Tequila, Jal.) 2 (Tequila, Jal.)

70.60 124.00

4 (Oaxaca, Oax)

228.00

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Optimization of the Supply Chain Associated to the Production of Bioethanol 139 Table 5.7: Produced bioethanol for the optimal solution in Scenario B Processing Plant

Bioethanol Produced (Tonne/Year) 3 1023

Central 1 (Tequila) Central 2 (Oaxaca) Central 3 (Irapuato) Distributed 3 (Cuernavaca)

113 113 113 327

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Figure 5.10 Optimal economic solution for Scenario B. From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

the satisfied demand during the considered time span is around 10% to 20%. The obtained profit is 1.8541 3 108 USD/year for the given supply chain configuration. Fig. 5.7 shows the Pareto curve for this scenario; note that the profit increases when the satisfied demand increases. Fig. 5.7 also shows the comparison between both Pareto curves. The main difference between both solutions is the configuration of the supply chains. The

140 Chapter 5 amount of harvested agave is very similar as well as the obtained profit, then a change in the supply chain should affect the transportation cost of raw materials and products. However, the behavior of both Pareto curves is very similar; consequently, the transportation cost does not have a significant effect on the net profit for the analyzed case study.

5.4.3 Scenario C (Increasing the Cultivation Area) A third scenario is also considered; in this case, the possibility of increasing the agave cultivation areas in order to increase the satisfied bioethanol demand is considered. This scenario also provides an analysis of the profitability of the use of the agave bagasse in bioethanol production. This scenario was considered because the agave production is not sufficient to satisfy the total bioethanol demand; the agave is also a perennial plant and requires 5 years for growing. In this context, it is necessary to implement an optimal planning to determine the location where agave cultivation is feasible or required. To consider a change in the availability of agave, the upper limit for the variable Possible increasing Inci;t

[see Eq. (5.5)] was changed from 1 to 6; with this change, the amount of available agave was increased from 100% to 600% more of the currently available agave. It is important to note that the amount of utilized agave can be different from the available agave for given harvesting sites. The cost for the production of the new agave must also be taken into account. An example of this variable is given as follows: • • •

If it takes the value of zero, the increment is 0% (the available agave is equal to the current amount of agave). If it takes the value of one, he increment is 100% (the available agave is equal to double the current amount of agave). The parameter should be changed until 6 for this case study. In other words, the available agave can be up to 7 times the current amount of agave.

According to the obtained results, the maximum bioethanol demand that can be satisfied is about 3.8% of the total demand of gasoline with an increment of 400% of the available agave. Currently, the gasoline is mixed with bioethanol for use in vehicles, with the most common composition being 90% to 10%, although this concentration depends on the country. In this context, the satisfied demand is almost 40% of the total bioethanol demand. However, the increment in the cultivation areas requires more used land, land conversion, irrigation water and water due to the increase in the bioethanol production. Table 5.8 shows the required surface for the agave cultivation as well as the bioethanol production; it is important to note that the model incorporates constraints for the additional cultivation areas depending on the available cultivation land (the model can also determine the additional water required for cultivating the additional agave). Table 5.9 shows the amount of water

Optimization of the Supply Chain Associated to the Production of Bioethanol 141 Table 5.8: Additional land required for the agave increase in Scenario C Maximum Increment %

100

200

300

400

500

600

New Area (Ha)

New Area (Ha)

New Area (Ha)

New Area (Ha)

New Area (Ha)

New Area (Ha)

3 1023

3 1023

3 1023

3 1023

3 1023

3 1023

1.03 0.07 12.40 0.18 0.19 0.42 3.81 0.29 0.34

2.05 0.15 24.86 1.56 0.39 0.85 7.63 0.58 0.68

3.08 0.22 22.94 2.34 0.58 1.27 11.42 0.87 1.03

4.10 0.30 18.60 3.11 0.78 1.69 12.63 1.17 1.37

5.13 0.37 15.47 3.89 0.97 2.12 12.63 1.46 1.71

6.16 0.45 12.34 4.67 1.17 2.54 12.63 1.75 2.05

Cultivation Area 1 2 3 4 5 6 7 8 9

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

Table 5.9: Water utilized for agave in Scenario C Maximum Increment %

100

200

Used

Used 3

Cultivation Area 1 2 3 4 5 6 7 8 9

300

400

Used 3

500

Used 3

600

Used 3

Used 3

Water (m )

Water (m )

Water (m )

Water (m )

Water (m )

Water (m3)

3 1023

3 1023

3 1023

3 1023

3 1023

3 1023

5028 365 60,761 889 953 2074 18,693 1429 1677

10,055 730 121,814 7628 1907 4148 37,385 2857 3355

15,083 1096 112,421 11,442 2860 6221 55,941 4286 5032

20,110 1461 91,141 15,256 3814 8295 61,881 5714 6710

25,138 1826 75,801 19,069 4767 10,369 61,881 7143 8387

30,165 2191 60,462 22,883 5720 12,443 61,881 8571 10,064

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

needed to produce bioethanol when the possibility of increasing the agave production is considered, according to the produced bioethanol from each plant. The water for irrigation was approximated with the monthly precipitation for good agave production, which is around 600800 mm of water. Results for this scenario show that the needed water is from 365 3 103 to 122 3 106 m3; in this case, the needed water depends mainly on the increased area required for the agave production. The water required for processing is shown in Table 5.10. In this case, the amount of utilized water does not change significantly because

142 Chapter 5 Table 5.10: Water utilized for agave increment in Scenario C for bioethanol production Increment

Plant C1 C2 C3 D1 D2 D3 D4 D5 D6

1

2

3

4

5

6

Process Water (m3)

Process Water (m3)

Process Water (m3)

Process Water (m3)

Process Water (m3)

Process Water (m3)

3 1023

3 1023

3 1023

3 1023

3 1023

3 1023

568 568 568 0 0 358 0 0 254

568 568 568 29 358 358 358 358 358

568 568 568 331 358 358 358 358 358

568 568 568 358 358 358 358 358 358

568 568 568 358 358 358 358 358 358

568 568 568 358 358 358 358 358 358

From Pascual Eduardo Murillo-Alvarado, Jose´ Ezequiel Santiban˜ez-Aguilar, Jose´ Marı´a Ponce-Ortega, et al, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, Industrial & Engineering Chemistry Research, 2014.

the processing plants are operating to the maximum allowed capacity to obtain the most bioethanol for the best economic solution.

5.5 Concluding Remarks This chapter has presented a study for the optimal planning of the sustainable use of agave residues obtained in the tequila production in Mexico. This chapter proposed the use of lignocellulosic residues from the processing of tequila to obtain biofuels (bioethanol and solid fuel). The study included the development of an optimization formulation for the supply chain, where several harvesting sites, tequila factories and markets for the biofuels were considered. Furthermore, the optimization model involves the optimization for the selection of distributed and central processing facilities, the transportation and the economies of scale associated to the supply chain. Experimental data from a pilot plant for obtaining bioethanol from agave residues was included in the optimization formulation. The optimization formulation considers the maximization for the profit accounting for the sales for the bioethanol and solid fuel in the markets minus the total costs associated with harvesting, processing and transportation in the supply chain. Several scenarios were analyzed. Results show that the bioethanol production from agave bagasse is a feasible way to obtain biofuels. For the current situation, the results show that it is possible to satisfy around 10% of the total demand of bioethanol of Mexico; and for some specific cities it is possible to satisfy about 40% and 50% of the bioethanol demand in some seasons of the year, and with a considerable obtained profit for processing this residue from the tequila industry. Furthermore, the proposed approach was applied to determine the additional agave as well as land and water required to satisfy greater bioethanol demand in Mexico. Results show

Optimization of the Supply Chain Associated to the Production of Bioethanol 143 that the possible satisfied bioethanol demand is around 40% in most of the considered markets, although requires the consumption of large amounts of water and a significant amount of additional cultivation land. Finally, no numerical complications were observed in the application of the proposed approach, which is general and can be applied to different biomass and biofuel types.

5.6 Nomenclature 5.6.1 Indexes i j k l m t p

Index for agave cultivation areas Index for distributed bioethanol processing plants Index for tequila industry Index for central bioethanol processing plants Index for markets Index for time period Distributed or central processing plants

5.6.2 Sets

I J K L

M P T

Set Set Set Set Set Set Set

for for for for for for for

agave cultivation area i distributed bioethanol processing plant j tequila industry k central bioethanol processing plant l market m for bioethanol and solid fuel central and distributed processing plants time period t

5.6.3 Parameters αDehydrated αDistillation αFermentation αFiltered1 αFiltered2 αFilteredsecond1 αFilteredsecond2 αReactor αReactor2 αSieve

Efficiency for dehydration Efficiency for distillation Efficiency for fermentation Efficiency for filtration at first stage of filtration Efficiency for filtration at first stage of filtration to obtain the amount of material directed to the second hydrolysis reactor Efficiency for second filtration process at second stage to obtain the fermentable material Efficiency for second filtration to obtain the solid fuel Efficiency for reaction at first stage of hydrolysis Efficiency for reaction process at second stage Efficiency for milling (Continued)

144 Chapter 5 (Continued) αSieveJuice β Bioethanol m β SolidFuel m CFixPlantColumn p

Efficiency for milling for the juice obtained Bioethanol price in market m Solid fuel price in market m Fixed cost for distillation column

CFixPlantColumn2 p

Fixed cost for dehydrated column

CFixPlantMill p CFixPlantReactor p CFixPlantReactor2 p CFixPlantSieve p CFixPlantSieve2 p CFixPlantTank p CFixPlantTank2 p CFixPlantTankA p CVarPlantColumn p CVarPlantColumn2 p CVarPlantMill p CVarPlantReactor p CVarPlantReactor2 p CVarPlantSieve p CVarPlantSieve2 p CVarPlantTank p CVarPlantTankA p CVarPlantTank2 p Plant di;p Plant dk;p Plant dp;m FAgaveMAX i;t GBioethanolMAX m;t GBioethanolMIN m;t GSolidFuelMax m;t GSolidFuelMin m;t

Fixed cost for milling Fixed cost for reactor Fixed cost for reactor of the second stage Fixed cost for sieve Fixed cost for sieve of the second stage Fixed cost for tanks Fixed cost for tanks of the second stage Fixed cost for stock tank Unit variable cost for distillation column Unit variable cost for dehydrated column Unit variable cost for mill Unit variable cost for reactor Unit variable cost for reactors of the second stage Unit variable cost for sieve Unit variable cost for sieve of the second stage Unit variable cost for tanks Unit variable cost for stock tank Unit variable cost for tanks of the second stage Distance from cultivation area i to plant p Distance from tequila industry k to plant p Distance from plant p to market m

KF UCostPlantOpColumn p

Maximum agave available in cultivation area i Maximum demand of gasoline in market m Minimum demand of gasoline in market m Maximum demand of solid fuel in market m Minimum demand of solid fuel in market m Factor used to annualize the capital costs Unit operating cost for distillation column

UCostPlantOpColumn2 p

Unit operating cost for dehydrated column

UCostPlantOpMill p UCostPlantOpReactor p UCostPlantOpReactor2 p UCostPlantOpSieve p UCostPlantOpSieve2 p UCostPlantOpTank p UCostPlantOpTank2 p

Unit operating cost for mills Unit operating cost for reactors Unit operating cost for reactors of second stage Unit operating cost for sieves Unit operating cost for sieve of second stage of plants Unit operating cost for tanks Unit operating cost for tanks of second stage (Continued)

Optimization of the Supply Chain Associated to the Production of Bioethanol 145 (Continued) UCostPlantOpTankA p UCostTranspBag UCostTranspBio UCostTranspLeav UCostTranspSolid zAHi zALi zCookedk

Unit operating cost for stock tanks Unit transportation cost from tequila industry kto plants Unit transportation cost from plants to market k Unit transportation cost from cultivation area i to plants Unit transportation cost from plants to market k Efficiency for agave plant heads in cultivation area i Efficiency for agave bagasse in cultivation area i Efficiency for agave bagasse in tequila industry k

5.6.4 Variables CPlantColumn p

Capital cost for the columns

CPlantColumn2 p CPlantMill p CPlantReactor p CPlantReactor2 p

Capital cost for the second columns

CPlantSieve p

Capital cost for the sieves

CPlantSieve2 p CPlantTank p CPlantTankA p CPlantTank2 p

Capital cost for the second stage of sieves

CoperPlantColumn p CoperPlantColumn2 p CoperPlantMill p CoperPlantReactor p CoperPlantReactor2 p CoperPlantSeive p CoperPlantSeive2 p CoperPlantTank p CoperPlantTankA p CoperPlantTank2 p CAP

Operating cost for the columns

CostPlant CostPlantOP CostTranspBagasseCentral Teq CostTranspBagasseDist Teq CostTranspLeavesDist CostTranspLeavesDist CostTranspProdBioethanol CostTranspProdSolidFuel GBioethanolm;t

Capital cost for the mills Capital cost for the reactors Capital cost for the second stage of reactors

Capital cost for the tanks Capital cost of the stock tanks Capital cost of the second tanks Operating cost for the second stage of columns Operating cost for the mills Operating cost for the reactors Operating cost for the second stage of reactors Operating cost for the sieves Operating cost for the second stage of sieves Operating cost for the tanks Operating cost for the stock tanks Operating cost for the second stage of tanks Total capital cost for the processing plants Total operational cost for the processing plants Cost for transportation of agave bagasse from the tequila factories to central processing plants Cost for transportation of agave bagasse from the tequila factories to distributed plants Cost for the transportation of the bagasse to central processing plants Cost for the transportation of the bagasse to distributed processing plants Transportation cost of the bioethanol to markets Transportation cost of the solid fuel to markets Total bioethanol flow rate sent to the market m (Continued)

146 Chapter 5 (Continued) gprodBioethanol gprodSolidFuel GSolidFuelm;t FBagasseTequila FColumn1Plant p;t

Bioethanol flow rate sent from plants to markets Solid fuel flow rate sent from plants to markets Total solid fuel sent to the market m Bagasse flow rate sent from the tequila industry k to processing plants Flow rate inlet to the distillation column

FColumn2Plant p;t

Flow rate inlet to the dehydrated column

FFermentationPlant p;t FFIlteredsecondPlant p;t Ffiltered1Plant p;t Ffiltered2Plant p;t FFuelSolidPlant p;t

Flow rate inlet to the fermentation process

FPlantHeadsi;t TequilaIndustry FPlantHeadsi;k;t

Flow rate of agave plant heads in cultivation area i Flow rate of plant heads from cultivation area i in tequila industry k

FMillPlant p;t

Flow rate in mill process

FprodBioethanolPlant p;t

Flow rate of bioethanol produced in plants

FReactorPlant p;t

Flow rate in reaction process in plants

FReactor2Plant p;t

Flow rate in reaction of the second stage in plants

FStockPlant p;t FTankPlant p;t

Amount of bioethanol obtained in distributed or central plants

FTequilaBagassek;t

Total flow rate of bagasse in tequila industry k Total flow rate of bagasse in plants

Flow rate inlet to the filter of the second stage Flow rate outlet to the fist filter Flow rate outlet to the first filter sent to second stage of hydrolysis Flow rate of solid fuel obtained

Flow rate in stock tank in plants

FTotalBagassePlant p;t

Tequila Industry

FTotalHeadsk;t FTotalLeavesBagassei;t FTotalLeavesBagasse PROFIT TotCost TotSales yp

Total flow rate of plant heads in tequila industry k Flow rate of agave bagasse in cultivation area i Flow rate of bagasse in cultivation area i sent to plants Total annual profit Total annual cost Total annual sales Binary variable for the existence of the distributed or central processing plants

References Bowling, I. M., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2011). Facility location and supply chain optimization for a biorefinery. Industrial and Engineering Chemistry Research, 50(10), 62766286. Brooke, A., Kendrick, D., Meeraus, A., & Raman, R. (2018). ,www.gams.com. GAMS A user’s guide. Washington, DC: GAMS Development Corporation. Murillo-Alvarado, P.E., Santiban˜ez-Aguilar, J.E., Ponce-Ortega, J.M., Castro-Montoya, A.J., Serna-Gonza´lez, M., & El-Halwagi, M.M. (2014). Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico. Industrial and Engineering Chemistry Research, 53(13), 55245538. SAGARPA-SIAP. Mexican system of information about agriculture and fishing. Advance of planting and harvesting for Mexico. (2013). Mexico City: Mexico. ,http://www.siap.gob.mx/index.php? option 5 com_wrapper&view 5 wrapper&Itemid 5 350.. SENER. Mexican secretary of energy. Potential and viability for the use of bioethanol and biodiesel for transportation in Mexico. (2012). ,http://sie.energia.gob.mx/bdiController.do?action 5 temas..

CHAPTER 6

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains Under Uncertainty 6.1 Introduction Biofuels are attractive alternatives for satisfying today’s energy demand in a more sustainable way than with fossil fuels. In order to establish a biorefinery system, it is necessary to optimally plan the entire supply chain, covering aspects such as selection of feedstocks, location and capacity of biorefineries, processing technologies selected, amount of products produced, and transportation flows. In this context, some of the parameters, including the availability of biomass and the demands of products and prices, are difficult to predict, as they can change drastically over the different seasons of the year as over the years. To address this challenge, this chapter presents a mathematical programming model for the optimal planning of a distributed system of biorefineries that considers explicitly the uncertainty associated with the supply chain. The capabilities of the proposed approach are demonstrated through its application in a case study to the production of biofuels in Mexico with multiple raw materials and products.

6.2 Problem Statement The optimal planning of a distributed supply chain based on biomass conversion considering the dependence over time of the involved variables as well as the uncertainty associated with the raw material price is addressed in this chapter. As shown in Fig. 6.1, the distributed system takes into account a set of suppliers, processing facilities, and consumers. The time horizon is divided into time periods of equal length. In every period, decisions on the distribution of raw materials and products, processing of feedstock and selling of final products must be made considering uncertain future prices. The problem we aim to solve can be formally stated as follows. We are given the availability of the raw material, the upper and lower limits for the capacity of the processing plants, the transportation limits, the set of products to be produced and the set of the raw material to be selected as well as several scenarios for the raw material price. The Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00006-7 © 2019 Elsevier Inc. All rights reserved.

147

148 Chapter 6 From suppliers

Processing activity Route 1

Raw material flow

Route 2

Products flow

Route r

Suppliers

Processing facilities

To consumers

Final decision

Consumers

Each one of the perdiods of time

Secondary

Risk

Cumulative probability curves

Financial risk curve Main

Figure 6.1 Superstructure for the proposed methodology. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

goal of the analysis is to find the optimal supply chain configuration, including the associated planning decisions that optimize the expected economic performance and minimize the associated risk.

6.3 Mathematical Model Formulation The mathematical model is comprised of mass balance constraints, capacity limitations, and objective function equations. The notation used is as follows. Index h represents the harvesting sites involved in the distributed system, index ph denotes the processing facilities to process the biomass and index mk is used for the consumers of products. On the other hand, index m represents the different raw materials, while k is used for the considered products. In addition, index r is defined for the processing routes used in plants, while index q denotes the economies of scale for the different processing facilities. Finally, index t represents the time periods and index s the uncertain scenarios. The model is a two-stage stochastic programming one, where first-stage variables represent the network topology while second-stage ones denote planning decisions. A set of scenarios with equal probability of occurrence are considered. Without loss of generality, the parameter values in each scenario are generated via sampling on probability functions. The full set of mass balances and constraints of the model are described in detail in the supplementary material. In essence, the model contains several cosntraints as well as

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 149 continuous and binary variables. Continuous variables are related with the amounts of raw material and products to be transported, processed, or produced as well as inventory levels for the materials involved in the supply chain. Regarding binary variables, they are used to represent the selection of a level of capacity, processing technology, an interval for the processing, sets of constraints are considered: Availability of raw material, maximum product demand, transportation, and processing limits are used to limit the values of the continuous variables and define the value of the binary variables. Concerning the objective function, the model must optimize two different objectives. On the one hand, the expected profit, and on the other a risk metric that allows controlling the variability of the profit distribution in the scenarios considered in the analysis.

6.4 Objective 1: Expected Profit
 The expected profit E½profit is the first objective function, calculated as the sum of the individual values of the net annual profit in each scenario (Profits ) multiplied with the corresponding probability of occurrence (Probs ): X E½profit 5 Probs UProfits (6.1) s

6.5 Objective 2: Worst Case for the Net Annual Profit To control the variability of the objective function in the uncertain parameter space, we incorporate in the objective function the worst case of the net annual profit (WC), defined as the smallest value of the net annual profit across all scenarios (Profits ): WC # Profits ;

’sASCENARIOS

(6.2)

The model can be expressed in compact form as follows:   max E½profit; WC s:t: hðx; yÞ 5 0 gðx; yÞ # 0 xAℝ; yAf0; 1g where x represents the continues variables as the amounts of feedstock and products and the inventory levels, and y represents the binary variables to select the processing capacity, interval for the transportation amounts, and the processing technology. The model can be solved by any standard multiobjective optimization algorithm. In this work, without loss of generality, we apply the epsilon-constraint method since it is possible to generate information for both objectives and their solutions, which is based on the solving of the

150 Chapter 6 original problem considering only one objective subject to several lower limit values for the other objective to obtain the complete Pareto curve. In this chapter, the model from Chapter 2, Involving Environmental Aspect in the Strategic Planning of a Biomass Conversion System, is used (only the stochastic analysis is different).

6.6 Results and Discussion The mathematical model is applied to two case studies for biofuel production in Mexico. Both cases consider as uncertain parameters the raw materials price. However, in the first case the raw material price is modeled through a geometric Brownian motion that assumes uncorrelated uncertain parameters. In the second case, the uncertain parameters follow correlated multivariate lognormal distributions. Both distributions are based on historical information to obtain the mean and variance values taken from the Mexican Ministry of Agriculture. The case studies consider 9 raw materials, which are produced in 6 different distributed suppliers, 4 processing routes, 5 distributed secondary processing plants, and 1 centralized processing facility. Furthermore, biodiesel and bioethanol are the main products to be distributed in the 5 consumption regions. A time horizon of 1 year divided into 12 months is considered.

6.6.1 Distribution of Raw Material Price Without Correlation Fig. 6.2 shows the distribution for the raw material prices determined through the geometric Brownian motion. In this case, there is no correlation between the parameters. Table 6.1 shows the price of the raw material from historical information and the prediction for 2014, which is taken as reference year. Also, the mean and standard deviation for the lognormal distribution are shown. The model was implemented in GAMS as a mixed-integer linear programming problem and solved with CPLEX. It contains 53,194 continuous variables, 18,320 binary variables, and 67,268 equations. The solution time ranges from 17 to 29 seconds on a computer with processor Intel Core i7
4700MQ at 2.4 GHz with 24 GB of RAM depending on the instance being solved. Fig. 6.3 shows the Pareto curve that trades off the expected profit versus the worst case. As can be seen, the worst cases (minimum profit over all scenarios) can be improved but at the expense of sacrificing the expected performance. Several sections in the Pareto curve can be identified. Each point of Fig. 6.3 represents a different configuration of the supply chain and may be associated with a risk curve (described later in this section). Fig. 6.4 shows the cumulative probability curves for the uncorrelated distribution associated with the maximum expected profit solution and the maximum worst-case solution (minimum risk solution). Fig. 6.4 also shows an upper bound curve that has been constructed from the optimal profits attained in each scenario. Hence, the upper bound

Figure 6.2 Distribution of the raw material price through geometric Brownian motion. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., MoralesRodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

152 Chapter 6 Table 6.1: Historical information of the raw material price and statistical data for the geometric Brownian distribution (US$/ton for prices) Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Mean log normal Std log normal 2014

Wood Chips

Wood

Sugarcane

Corn Grain

28.59 44.62 36.59 32.79 38.54 70.09 53.97 53.40 80.06 88.87 86.60 0.192

57.19 89.24 73.19 65.57 77.09 140.18 107.93 106.79 160.13 177.74 173.20 0.142

50.57 42.36 38.29 33.36 47.24 34.90 57.95 38.97 52.36 47.79 58.23 0.096

0.290

0.290

0.302

98.95

252.85

50.01

Sorghum Sweet Grain Sorghum

African Palm Jatropha Safflower

240.63 197.53 190.60 237.31 199.92 242.58 261.30 211.26 245.90 295.01 357.57 0.066

123.52 120.18 117.74 109.83 143.55 176.09 207.36 159.96 179.73 277.60 259.12 0.070

27.78 25.07 25.73 27.14 28.53 30.80 37.98 29.17 34.81 40.08 39.84 0.059

21.89 34.16 28.02 25.11 29.51 53.67 41.32 40.89 61.31 68.05 66.31 0.242

43.43 67.76 55.58 49.80 58.54 106.45 81.96 81.10 121.60 134.97 131.52 0.092

184.21 210.53 208.61 207.12 214.40 216.10 332.57 310.91 343.97 449.91 459.59 0.062

0.177

0.202

0.139

0.290

0.290

0.152

372.83

214.41

31.54

95.32

151.61

315.29

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Figure 6.3 Pareto curve showing the financial risk of the implementation of a supply chain topology for the uncorrelated data (expected profit vs worst case for profit). From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 153

Figure 6.4 Cumulative probability curves for the uncorrelated distribution. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

curve does not reflect any realistic solution, but rather an ideal case implementing a waitand-see strategy. It is possible to observe that the probability to obtain at least a given value of profit is different in each solution. For comparison purposes, let us have a look at three profit targets: 4.05 3 102, 4.4 3 102, and 4.65 3 102 millions US$/year, for which the probabilities of showing a profit value below them are 5%, 38%, and 90% with the riskiest curve, in solutions with a minor risk 3%, 54%, and 99%, respectively. In other words, there is a larger probability to get a high profit value with the maximum risk solution, but there is also a larger probability to get a low profit value with the minimum risk solution. Fig. 6.5 presents the net annual profit of each scenario for the maximum expected profit and worst-case solutions. It is possible to see that the maximum values for the profit are given at the 97th scenario, while the minimum net profit values are given at the 77th scenario for both cases. For the maximum risk solution the maximum net profit is equal to 4.86 3 102 millions US$/year, the worst case is equal to 3.90 3 102 millions US$/year and

154 Chapter 6

Figure 6.5 Net annual profit for each scenario for the highest and lowest risk solutions for the uncorrelated distribution. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

the expected profit is equal to 4.45 3 102 millions US$/year, while for the minimum risk solution the maximum net profit is equal to 4.68 3 102 millions US$/year, the worst case of profit is equal to 3.90 3 102 millions US$/year and the expected profit is equal to 4.38 3 102 millions US$/year. Table 6.2 shows the raw material prices for the two scenarios (77th and 97th) as well as information with respect to the minimum, maximum, and mean values. As can be seen, the 97th scenario has a price of sugarcane significantly above the mean value, a price of jatropha under the mean value and the price of the sweet sorghum above the mean value. On the other hand, the 77th scenario presents a price of sugarcane significantly under the mean value, a price of jatropha near the mean value and a price of sweet sorghum above the mean value. It is worth noting that the solution produced by the model selects these raw materials (Figs. 6.5 and 6.6), maybe because the price of jatropha is under the mean value in the 97th scenario and the price of jatropha in the 77th scenario is only 5.05% larger respect to the mean value while the other prices of raw materials to produce biodiesel are from 22.77% larger than the mean value (safflower) up to 63.39% larger than the mean value (African palm). The same case works for the price of sugarcane. Besides the sweet sorghum price for both cases (77th and 97th) always is larger than the mean value, although the price is lower than other raw materials.

Table 6.2: Raw material prices for the scenarios with the highest and lowest value for profit for uncorrelated distribution 77th Scenario Value US $/ton Wood chips Wood Sugarcane Grain corn Sorghum grain Sweet Sorghum African Palm Jatropha Safflower

% to Mean

97th Scenario Value US $/ton

% to Mean

Min Value US $/ton

Mean Value US$/ton

Max Value US $/ton

189.91

60.01

71.18

2 40.03

58.73

118.69

244.09

307.70 52.66 356.73 265.75

2 4.26 2 18.96 2 12.16 2 10.74

430.97 97.03 378.79 303.12

34.10 49.33 2 6.73 1.81

138.80 34.76 179.16 184.79

321.38 64.98 406.13 297.73

730.49 125.28 620.77 500.20

59.10

29.17

50.37

10.10

32.11

45.75

60.04

179.74

63.39

71.88

2 34.66

50.46

110.01

228.73

199.28 539.31

5.05 22.77

164.25 497.16

2 13.42 13.18

86.70 296.24

189.70 439.28

308.06 570.67

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Figure 6.6 Frequency histogram for the net annual profit for the solutions with the highest and lowest risk for the uncorrelated distribution of the raw material price. From Santiban˜ez-Aguilar, J. E., GuillenGosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

156 Chapter 6 Fig. 6.6 shows the frequency histogram for the net annual profit of the different analyzed cases. Fig. 6.5A and B show that the best value for the profit in the maximization of the expected profit is larger than the best value of profit in the maximization of the worst case; however, the worst value for the profit in Fig. 6.5A is lower than the worst profit in Fig. 6.5B. Fig. 6.7 also shows the configuration of the supply chain for the maximum expected profit solution. It is important to observe that the supplier allocated in the Northwest region is not selected in any case because that region is too far from the others and the transportation cost increase significantly. Also, notice that biodiesel is produced only in Salamanca and Tula, mainly because these processing facilities are allocated in the center of the country and the biodiesel is easily distributed to the different consumers. Notice that the raw

Figure 6.7 Configuration of the supply chain for the riskiest solution for the uncorrelated raw material price. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 157 materials for bioethanol production are sugarcane and sweet sorghum and for biodiesel mainly Jatropha. On the other hand, the supply chain configuration for the maximum Worst Case (WC) solution is presented in Fig. 6.8. It is worth noting that the Northwest supplier is not selected in any case; furthermore, there is no biodiesel production in any processing facility. Additionally, some of the interconnections of the supply chain change. For example, in this configuration there is no transportation of sugarcane from the Northeast supplier, and the processing plant in Salina Cruz does not distribute any product to consumers located in the South. Table 6.3 shows the percentage of fulfilled demand for ethanol and biodiesel for high risk case and low risk case. It should be noticed that the demand satisfied changes drastically

Figure 6.8 Configuration of the supply chain for the solution with the lowest risk for the uncorrelated raw material price. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

158 Chapter 6 between the extreme solutions. It can be seen that there the demand of biodiesel is not fulfilled in the maximum WC solution. Furthermore, the amount of ethanol produced decreases for the Center and Northeast markets, which have two of the three biggest cities in Mexico. On the other hand, the amount of ethanol delivered to the Center West, Northwest, and South markets is greater in the maximum expected profit solution. Table 6.4 also presents the amounts and percentages with respect to the maximum availability of raw material used in the supply chain for both cases. It is worth noting that Table 6.3: Percentage of fulfilled demand of products for the uncorrelated distribution for the solutions with highest and lowest risk Product

Consumer

Required Demand 3 106 Ton

High Risk % Fulfilled

Low Risk % Fulfilled

Ethanol

Center Northeast Center West Northwest South Center Northeast Center West Northwest South

1.21 0.54 0.76 0.64 0.47 0.26 0.13 0.20 0.17 0.13

30.26 46.42 13.83 0.00 19.78 2.84 0.00 12.14 0.23 43.63

19.58 39.84 24.64 0.92 36.15 0.00 0.00 0.00 0.00 0.00

Biodiesel

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Table 6.4: Amount of biomass used for the solution with the highest and lowest risk solution

Highest risk solution

Lowest risk solution

Raw Material

Supplier

Amount Used ( 3 106 ton)

Maximum Available ( 3 106 ton)

% Used

Sugarcane Sugarcane Sugarcane Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Jatropha Jatropha Sugarcane Sugarcane Sugarcane Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum

Center West East Center South Center West Northeast East Center Center West Northeast Center West East Center South Center West Northeast East Center

0.02 0.40 0.21 0.01 0.36 0.35 0.05 0.02 0.12 0.15 0.02 0.40 0.21 0.01 0.36 0.35 0.05 0.02

8.39 27.12 1.87 0.01 1.00 1.65 0.05 0.02 0.53 0.53 8.39 27.12 1.87 0.01 1.00 1.65 0.05 0.02

0.29 1.46 11.23 100.00 36.33 21.38 100.00 100.00 22.50 28.12 0.29 1.46 11.23 100.00 36.33 21.38 100.00 100.00

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 159 the main raw material used to produce ethanol is sweet sorghum, because its price is almost constant and lower than the other raw materials. In addition, jatropha is used to obtain biodiesel, although this raw material shows large variability, but it is cheaper than the African palm or the safflower.

6.6.2 Case With Correlated Values Fig. 6.9 illustrates the distribution for the raw material prices through a multivariate lognormal random distribution with correlated values. The correlations were determined from historical data presented previously in Table 6.1. It is worth noting that the geometric Brownian distribution is a lognormal distribution of the ratio of the raw material price for two different periods, with one used as the reference price. For that reason, the correlation of the ratio of the raw material price for two periods of time was done (e.g., price of 2001/ price of 2000, price of 2002/price of 2001, etc.) considering a reference price (price of 2015) to compare with the uncorrelated distribution. Table 6.5 shows the correlation matrix used to obtain the correlated distribution. It can be seen that there are positive and negative correlation factors. Similar to the first case study (uncorrelated values), the model was implemented in GAMS as a mixed-integer linear programming problem and solved with CPLEX. It contains 53,194 continuous variables, 18,320 binary variables and 67,268 equations. However, in this case the solution time ranges from 90 to 150 seconds on a computer with the same specs as before depending on the instance being solved. The Pareto curve associated with the worst value of profit and the expected value of profit for the correlated uncertain data is presented in Fig. 6.10. It is possible to identify several sections along this Pareto curve. Section A is allocated between points 1 and 2, and the main differences between these points is that the interconnections between the processing facilities to markets for the bioethanol distribution change drastically from point 1 to point 2, and the biodiesel production decreases in point 2 with respect to point 1. On the other hand, section C is characterized by an increment in the bioethanol production in the secondary processing facilities, a decrement in the bioethanol production in the main processing facility and there is no biodiesel production in the point 4, although more raw materials are utilized to obtain ethanol. Fig. 6.11 shows the cumulative probability and the net annual profit when the optimization approach is solved for the maximization of the expected profit and the maximization of the worst case for the profit. The figure also shows an upper bound curve constructed from the optimal profits attained in each scenario. Hence, the upper bound curve does not reflect any realistic solution, but rather an ideal case implementing a wait-and-see strategy.

Figure 6.9 Distribution of the raw material price through correlated multivariable normal random distribution. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 161 Table 6.5: Correlation matrix for the correlated distribution

1 2 3 4 5 6 7 8 9

Wood Chips

Wood Sugarcane

Corn Grain

Sorghum Grain

Sweet Sorghum

African Palm

1.00 0.90 2 0.27 0.04 0.23 2 0.01 0.90 0.90 2 0.20

0.90 1.00 2 0.27 0.04 0.23 2 0.01 0.90 0.90 2 0.20

0.04 0.04 0.09 1.00 0.30 0.62 0.04 0.04 0.16

0.23 0.23 0.30 0.30 1.00 0.68 0.23 0.23 0.52

2 0.01 2 0.01 0.64 0.62 0.68 1.00 2 0.01 2 0.01 0.64

0.90 0.90 2 0.27 0.04 0.23 2 0.01 1.00 0.90 2 0.20

2 0.27 2 0.27 1.00 0.09 0.30 0.64 2 0.27 2 0.27 0.59

Jatropha Safflower 0.90 0.90 2 0.27 0.04 0.23 2 0.01 0.90 1.00 2 0.20

2 0.20 2 0.20 0.59 0.16 0.52 0.64 2 0.20 2 0.20 1.00

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Figure 6.10 Pareto curve showing the financial risk of the implementation of a supply chain topology for the correlated data (expected profit vs worst case for profit). From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Similarly to Fig. 6.4, three values for the net annual profit were selected as follows: 4.3 3 102 millions US$/year, 4.55 3 102 millions US$/year, and 4.75 3 102 millions US $/year. From each one of the profit targets it is possible to illustrate the probabilities to obtain a profit below them, which are 7%, 47%, and 98% with the riskiest curve, in solutions with a minor risk 10%, 51%, and 99%, respectively. The different values for the net profit for the highest and lowest risk alternatives are shown in Fig. 6.12. As can be seen, the maximum values for the net profit were obtained in the 9th

Figure 6.11 Cumulative probability curves for the correlated distribution. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Figure 6.12 Net annual profit for each scenario for the highest and lowest risk solutions for the correlated distribution. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 163 and 88th scenarios for the riskiest and lowest risk curves while the minimum values for the net profit correspond to the 85th scenario in both cases. For the maximum risk solution, the maximum profit is equal to 4.8 3 102 millions US$/year, the worst case is equal to 4.03 3 102 millions US$/year and the expected profit is equal to 4.54 3 102 millions US $/year, while for the minimum risk the maximum profit it is 4.79 3 102 millions US$/year, the worst case is equal to 4.13 3 102 millions US$/year and the expected profit is equal to 4.52 3 102 millions US$/year. Table 6.6 illustrates the value for the raw material price for the different aforementioned scenarios (9th, 88th, and 85th) for the correlated distribution as well as a comparison with their maximum, minimum, and mean values. It is worth noting that the selected raw materials in the highest risk solution are sweet sorghum and sugarcane, because the price of these raw materials have values lower than the other raw materials. Regarding the solution with the lowest risk, this solution considers wood chips, the wood chips are added in the list of raw materials chosen in the solution with the lowest risk because sugarcane presents a high value of its price and a low value of the wood chips price when the data are correlated (see Table 6.5 and Fig. 6.9). Fig. 6.13 shows the histogram for the value of the net annual profit for the solutions from the maximization of the expected profit and the maximization of the worst case when the data are correlated. Notice that the values of profit for the correlated data are distributed in a shorter range than the values of profit for the uncorrelated data. One reason for this behavior is because the selected raw materials in the case of correlated data present negative correlations, which causes limited behavior for the value of profits. Table 6.6: Raw material prices for the scenarios with the highest and lowest value for profit for correlated multivariable distribution Scenario 85th Value US $/ton Wood chips Wood Sugarcane Grain corn Sorghum grain Sweet sorghum African palm Jatropha Safflower

Scenario 9th

Min Value US $/ton

Mean Value US $/ton

Max Value US $/ton

174.38 39.59 416.22 37.07 27.74 2 51.82 296.80 2 26.62 202.30 2 13.79

53.75 140.97 27.74 280.75 121.62

124.92 303.64 57.57 404.46 234.64

241.74 664.94 130.86 621.05 402.19

24.52 2 27.46

24.52

33.80

44.18

87.62 2 30.71 96.40 2 23.76 167.16 32.20 101.76 2 41.17 131.30 2 24.10 261.97 51.45 466.76 37.61 276.23 2 18.56 251.74 2 25.78

58.03 74.93 224.50

126.45 172.98 339.19

265.37 289.58 466.76

% to Mean

Value US $/ton

Scenario 88th

% to Mean

74.39 2 40.45 80.77 2 35.34 181.59 2 40.20 243.86 2 19.69 130.86 127.31 37.40 2 35.04 382.60 2 5.41 348.70 2 13.79 253.34 7.97 172.82 2 26.35 40.13

18.73

26.19 2 22.52

Value US $/ton

% to Mean

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

164 Chapter 6

Figure 6.13 Frequency histogram for the net annual profit for the solutions with the highest and lowest risk for the correlated distribution of the raw materials price. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Fig. 6.14 represents the supply chain configuration when the expected profit is maximized. It is worth noting that the configuration of the supply chain presents some important differences between the uncorrelated and correlated data. For example, the fulfilled demands change for all markets. The first important change is in the consumers located in the center for the ethanol demand from 30.26% for the uncorrelated case until only 22.28% for the correlated case. The second variation occurred in the consumer located in the South since the uncorrelated case has a fulfilled biodiesel demand of 43.63% and the correlated case does not have any percentage for the satisfied biodiesel demand. Also, the interconnection for the market located in Northwest region does not receive any product since this region does not have any connection with processing facilities. Finally, Fig. 6.15 shows the general configuration of the supply chain for the lowest risk solution. Here, it is possible to see that the biodiesel is produced in the main processing facility and there are more selected raw materials available, sweet sorghum, sugarcane, and wood chips, to produce ethanol. Furthermore, the satisfied demand is almost the same in all markets, although the biodiesel fulfilled demand increases up to 22.48% in the South.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 165

Figure 6.14 Configuration of the supply chain for the riskiest solution for the correlated raw materials price. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Table 6.3 shows that the demand changes drastically between the extreme solutions. As can be seen, the demand of biodiesel is not fulfilled in the maximum WC solution. Furthermore, the amount of ethanol produced decreases for the Center and Northeast markets, which have two of the three biggest cities in Mexico. On the other hand, the amount of ethanol delivered to the Center West, Northwest, and South markets is greater in the maximum expected profit solution. Table 6.7 lists the percentages of satisfied demand for the different markets and products for the extreme solutions when the raw material prices are correlated. Effects of the correlation of the data can be seen. One of the main effects is the selection of more raw materials for the

166 Chapter 6

Figure 6.15 Configuration of the supply chain for the solution with the lowest risk for the correlated raw materials price. From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

solution with the lowest risk. Another direct effect is the change in the biodiesel production, because the biodiesel production in the uncorrelated case is given in the highest risk solution but in the correlated case it is given in the lowest risk solution (Table 6.8).

6.7 Concluding Remarks This chapter has presented a strategy to optimize distributed systems of biomass conversion under uncertainty. The problem was modeled in mathematical terms as a two-stage stochastic mixed-integer linear programming problem that seeks to optimize the expected profit and worst case simultaneously.

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 167 Table 6.7: Percentages of fulfilled demand of products for the correlated distribution for the solutions of highest and lowest risk Product

Consumer

Required Demand 3 106 Ton

High Risk % Fulfilled

Low Risk % Fulfilled

Ethanol

Center Northeast Center West Northwest South Center Northeast Center West Northwest South

1.21 0.54 0.76 0.64 0.47 0.26 0.13 0.20 0.17 0.13

22.28 41.76 19.98 0.00 35.77 0.00 0.00 0.00 0.00 0.00

22.54 47.76 21.41 0.06 27.95 4.73 0.00 3.96 0.00 22.48

Biodiesel

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

Table 6.8: Amount of biomass used for the solution with the highest and lowest risk solution for the correlated data

Highest risk solution

Lowest risk solution

Raw Material

Supplier

Amount Used ( 3 106 ton)

Maximum Available ( 3 106 ton)

% Used

Sugarcane Sugarcane Sugarcane Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Wood chips Wood chips Sugarcane Sugarcane Sugarcane Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Sweet sorghum Jatropha

Center West East Center South Center West Northeast East Center Northeast Center Center West East Center South Center West Northeast East Center Northeast

0.02 0.40 0.21 0.01 0.36 0.35 0.05 0.02 0.03 0.01 0.02 0.40 0.21 0.01 0.36 0.35 0.05 0.02 0.15

8.39 27.12 1.87 0.01 1.00 1.65 0.05 0.02 0.06 0.02 8.39 27.12 1.87 0.01 1.00 1.65 0.05 0.02 0.53

0.29 1.46 11.23 100.00 36.33 21.38 100.00 100.00 47.16 45.82 0.29 1.46 11.23 100.00 36.33 21.38 100.00 100.00 28.12

From Santiban˜ez-Aguilar, J. E., Guillen-Gosa´lbez, G., Morales-Rodriguez, R., Jime´nez-Esteller, L., Castro-Montoya, A. J., & Ponce-Ortega, J. M. (2016). Financial risk assessment and optimal planning of biofuels supply chains under uncertainty. BioEnergy Research, 9(4), 1053
1069.

According to the obtained results, the distribution of the uncertain data can affect significantly the selection of raw materials, products, and interconnections between supply nodes. In the uncorrelated case, the maximum profit solution uses sugarcane, sweet sorghum, and jatropha, while the maximum WC selects only sugarcane and sweet sorghum

168 Chapter 6 and there is no biodiesel production. In the correlated case, the maximum profit solution uses sugarcane and sweet sorghum, while the maximum WC selects sugarcane, sweet sorghum, jatropha, and wood chips. In both cases, the correlated and uncorrelated one, it is possible to reduce the risk associated with the supply chain operation by properly adjusting the design and planning decisions. This is accomplished by the inventory levels, amounts of transported materials, types and amounts of used raw materials, as well as the type of product to be produced. Our tool is intended to facilitate the task of decision makers concerning the identification of robust alternatives for the production, storage, and delivery of biofneuels to the final customers.

6.8 Nomenclature 6.8.1 Variables operating C facilities

Operating cost in secondary processing facilities

operating C main

Operating cost in the main processing facility

capital facilities

Capital cost in secondary processing facilities

Cm;k;r;ph capital main Cm;k;r distributed CT hs-facilities

Transportation cost of raw material from harvesting sites to secondary processing facilities

distributed CT hs-main

Transportation cost of raw material from harvesting sites to the main processing facility

distributed

CTm plant-main distributed CT plant-main distributed

CT facilities-mk distributed CT main-mk storage-raw harv-sites

Cm;h storage facilities Cmm;ph storage main Cmm

Capital cost in the main processing facility

Transportation cost of product from secondary processing plants to the main processing facility Transportation cost of product from secondary processing plants to the main processing facility Transportation cost of product from secondary processing plants to consumers Transportation cost of product from the main processing plant to consumers Storage cost of raw material in the harvesting sites Storage cost of raw material in the secondary processing plants Storage cost of raw material in the main processing facility

(Continued)

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 169 (Continued) storage facilities

Ck;ph storage main Ck storage market Ck;mk raw material Costs   E profit prod Mm;h;t

storage harv-sites

Mm;h;t distributed hs-facilities Mm;h;ph;t distributed hs-main Mm;h;t storage facilities Mm;ph;t distributed hs-facilities Mem;h;ph;t distributed plant-main Mm;ph;t processed facilities Mm;k;r;ph;t processed facilities Mdism;k;r;ph;t;q storage main

Mm;t distributed hs-main Mem;h;t distributed plant-main Mem;ph;t processed main Mm;k;r;t processed main Mdism;k;r;t;q

Storage cost of product in the secondary processing facilities Storage cost of product in the main processing plant Storage cost of product in the consumers Production cost for raw material Expected net annual profit Amount of produced biomass m in the harvesting site h over the period of time t Amount of stored biomass m in the harvesting site h over the period of time t Amount of distributed biomass m from the harvesting site h to the secondary processing facility ph over the period of time t Amount of distributed biomass m from the harvesting site h to the main processing facility over the period of time t Amount of stored biomass m in the secondary processing plant ph over the period of time t Amount of arrived biomass m from the harvesting site h to the secondary processing facility ph over the period of time t Amount of distributed biomass m from the secondary processing facility ph to the main processing facility over the period of time t Amount of processed biomass m in the secondary processing facility ph by the processing technology r to obtain the product k over the period of time t Discretized amount for accounting the economies of scale for the processed biomass m in the secondary processing facility ph by the processing technology r to obtain the product k over the period of time t Amount of stored raw material m in the main processing plant over the period of time t Amount of raw material m sent from the harvesting site h to the main processing plant over the period of time t Amount of raw material m sent from the secondary processing plant ph to the main processing plant over the period of time t Amount of processed biomass m in main facility by the processing technology r to obtain the product k over the period of time t Discretized amount for accounting the economies of scale of processed biomass m in main facility by the processing technology r to obtain the product k over the period of time t (Continued)

170 Chapter 6 (Continued) storage facilities

Pk;ph;t obtained facilities Pm;k;r;ph;t distributed facilities-mk Pk;ph;mk;t distributed plant-main Pk;ph;t storage main Pk;t obtained main Pm;k;r;ph;t distributed main-mk Pk;mk;t distributed plant-main Pek;ph;t storage market Pk;mk;t distributed facilities-mk Pek;ph;mk;t distributed main-mk Pek;mk;t sold Pk;mk;t sold Pk;mk;t Profits sale Revenue products WC

Amount of stored product k in the secondary processing facility ph over the period of time t Amount of produced product k in the secondary processing facility ph by the processing route r and from the raw material m over the period of time t Amount of distributed product k from the secondary processing facility ph to the consumer mk over the period of time t Amount of distributed product k from the secondary processing facility ph to the main facility over the period of time t Amount of stored product k in the main processing plant over the period of time t Amount of produced product k in the main process facility by the processing route r and from the raw material m over the period of time t Amount of distributed product k from the main processing facility to the consumer mk over the period of time t Amount of distributed product k that arrives from the secondary processing facility ph to the main facility over the period of time t Amount of stored product k in the consumer mk over the period of time t Amount of distributed product k that arrives from the secondary processing facility ph to the consumer mk over the period of time t Amount of distributed product k that arrives from the main processing facility to the consumer mk over the period of time t Amount of sold product k in the market mk over the period of time t Amount of sold product k in the market mk over the period of time t Net annual profit Revenue for sale of products Worst case for the net annual profit

6.8.2 Binary Variables time facilities

ym;k;r;ph;t;q capital facilities ym;k;r;ph;q time main ym;k;r;t;q

Binary variable with dependence over time that is used to consider the economies of scale in the processing activity for the secondary processing facilities Binary variable without dependence over time that is used to consider the economies of scale in the processing activity for the secondary processing facilities Binary variable with dependence over time that is used to consider the economies of scale in the processing activity for the main processing facility (Continued)

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 171 (Continued) capital main

ym;k;r;q distributed hs-facilities ym;h;ph;t distributed hs-main ym;h;t distributed plant-main ymm;ph;t distributed plant-main yk;ph;t distributed facilities-mk yk;ph;mk;t distributed main-mk yk;mk;t storage harv-sites ycapm;h storage facilities ymcapm;ph storage main ymcapm storage facilities ycapk;ph storage main ycapk storage market ycapk;mk storage harv-sites ym;h;t storage facilities ymm;ph;t storage main ymm;t storage facilities yk;ph;t storage main yk;t storage market yk;mk;t

Binary variable without dependence over time that is used to consider the economies of scale in the processing activity for the main processing facility Binary variable to define the transportation activity of raw material from the harvesting site to the secondary processing facility Binary variable to define the transportation activity of raw material from the harvesting site to the main processing facility Binary variable to define the transportation activity of raw material from the secondary processing facility to the main processing facility Binary variable to define the transportation activity of products from the secondary processing facility to consumers Binary variable to define the transportation activity of products from the secondary processing facility to consumers Binary variable to define the transportation activity of products from the main processing facility to consumers Binary variable to define the storage activity of raw material in the harvesting site Binary variable to define the storage activity of raw material in the secondary processing plants Binary variable to define the storage activity of raw material in the main processing plants Binary variable to define the storage activity of product in the secondary processing plants Binary variable to define the storage activity of product in the main processing plant Binary variable to define the storage activity of product in the consumers Binary variable to define the storage activity of raw material in the harvesting site accomplished in a given time period t Binary variable to define the storage activity of raw material in the secondary processing plants accomplished in a given time period t Binary variable to define the storage activity of raw material in the main processing plants accomplished in a given time period t Binary variable to define the storage activity of product in the secondary processing plants accomplished in a given time period t Binary variable to define the storage activity of product in the main processing plant in a given time period t Binary variable to define the storage activity of product in the markets in a given time period t

172 Chapter 6

6.8.3 Parameters conversion factor

αm;k;r capital facilities Am;k;r;ph;q capital main Am;k;r;q storage-raw harv-sites Am;h storage facilities Amm;ph storage main Amm storage facilities Ak;ph storage main Ak storage market Ak;mk capital facilities Bm;k;r;ph;q capital main Bm;k;r;q storage-raw harv-sites Bm;h storage facilities Bmm;ph storage main Bmm storage facilities Bk;ph storage main Bk storage market Bk;mk sale product Ck;mk;t

Conversion factor for the production of product k from the raw material m through the technology r Unitary fixed cost for the capital cost of the processing facilities Unitary fixed cost for the capital cost of the main process facility Unitary fixed cost for the capital cost of the storage activity in the harvesting site Unitary fixed cost for the capital cost of the storage activity of raw material in the secondary processing facilities Unitary fixed cost for the capital cost of the storage activity of raw material in the main processing facility Unitary fixed cost for the capital cost of the storage activity of product in the secondary processing facilities Unitary fixed cost for the capital cost of the storage activity of product in the main processing facility Unitary fixed cost for the capital cost of the storage activity of product in the consumers Unitary variable cost for the capital cost of the processing facilities Unitary variable cost for the capital cost for the main process facility Unitary variable cost for the capital cost of the storage activity in the harvesting site Unitary variable cost for the capital cost of the storage activity of raw material in the secondary processing facilities Unitary variable cost for the capital cost of the storage activity of raw material in the main processing facility Unitary variable cost for the capital cost for the storage activity of product in the secondary processing facilities Unitary variable cost for the capital cost for the storage activity of product in the main processing facility Unitary variable cost for the capital cost for the storage activity of product in the consumers Unitary price of product over the period of time t

(Continued)

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 173 (Continued) maximum H periods

Maximum number of periods for the time horizon

KF

Factor used to annualize the capital cost Upper limit for the produced biomass m in the harvesting site h and the period of time t Upper limit for the processed biomass m in the secondary facility ph and the period of time t

UPP

Mavailable m;h;t

UPPER

processed facilities

Mm;k;r;ph;q processed facilities LOWER Mm;k;r;ph;q processed main UPPER Mm;k;r;q processed main LOWER Mm;k;r;q distributed hs-facilities UPPER Mm;h;ph distributed hs-facilities LOWER Mm;h;ph distributed hs-main UPPER Mm;h distributed hs-main LOWER Mm;h distributed plant-main UPPER Mm;ph distributed plant-main LOWER Mm;ph storage harv-sites UPPER Mm;h storage harv-sites LOWER Mm;h storage facilities UPPER Mm;ph storage facilities LOWER Mm;ph storage main UPPER Mm storage main LOWER Mm

Lower limit for the processed biomass m in the secondary facility ph over the period of time t Upper limit for the processed biomass m in the main processing facility over the period of time t Lower limit for the processed biomass m in the main process facility over the period of time t Upper limit for the transportation of biomass m from harvesting sites to secondary processing facilities Lower limit for the transportation of biomass m from harvesting sites to secondary processing facilities Upper limit for the transportation of biomass m from harvesting sites to the main processing facility Lower limit for the transportation of biomass m from harvesting sites to the main processing facility Upper limit for the transportation of biomass m secondary processing facilities to the main processing facility Lower limit for the transportation of biomass m from secondary processing facilities to the main processing facility Upper limit for the storage of raw material m in the harvesting sites Lower limit for the storage of raw material m in the harvesting sites Upper limit for the storage of raw material m in the secondary processing facilities Lower limit for the storage of raw material m in the secondary processing facilities Upper limit for the storage of raw material m in the main processing facility Lower limit for the storage of raw material m in the main processing facility

(Continued)

174 Chapter 6 (Continued) distributed plant-main

Pk;ph distributed plant-main LOWER Pk;ph distributed facilities-mk UPPER Pk;ph;mk distributed plant-main LOWER Pk;ph distributed main-mk UPPER Pk;mk distributed plant-main LOWER Pk;ph storage facilities UPPER Pk;ph storage facilities LOWER Pk;ph storage main UPPER Pk storage main LOWER Pk storage market UPPER Pk;mk storage market LOWER Pk;mk Probs demand Pk;mk;t operating facilities UCm;k;r;ph;t operating main UCm;k;r;t distributed hs-facilities UCT m;h;ph distributed hs-main UCT m;h distributed plant-main UCTmm;ph distributed plant-main UCT k;ph UPPER

Upper limit for the transportation of product k secondary processing facilities to the main processing facility Lower limit for the transportation of product k from secondary processing facilities to the main processing facility Upper limit for the transportation of product k from secondary processing facilities to the markets Lower limit for the transportation of product k from secondary processing facilities to the markets Upper limit for the transportation of product k from the main processing facility to the markets Lower limit for the transportation of product k from the main processing facility to the markets Upper limit for the storage of product k in the secondary processing facilities Lower limit for the storage of product k in the secondary processing facilities Upper limit for the storage of product k in the main processing facility Lower limit for the storage of product k in the main processing facility Upper limit for the storage of product k in the consumers Lower limit for the storage of product k in the consumers Probability for each scenario Required product k in the market mk over the period of time t Unitary operating cost for the secondary processing facilities Unitary operating cost for the main processing facility Unitary transportation cost of raw material from harvesting sites to secondary processing facilities Unitary transportation cost of raw material from harvesting sites to the main processing facility Unitary transportation cost of raw material from secondary processing plants to the main processing facility Unitary transportation cost of product from secondary processing plants to the main processing facility (Continued)

Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains 175 (Continued) distributed facilities-mk

UCT k;ph;mk distributed main-mk UCT k;mk storage-raw harv-sites UCm;h;t storage facilities UCmm;ph;t storage main UCmm;t storage facilities UCk;ph;t storage main UCk;t storage market UCk;mk;t raw material UCm;s

Unitary transportation cost of product from secondary processing plants to consumers Unitary transportation cost of product from the main processing plant to consumers Unitary storage cost of raw material in the harvesting sites Unitary storage cost of raw material in the secondary processing facilities Unitary storage cost of raw material in the main processing facility Unitary storage cost of product in the secondary processing facilities Unitary storage cost of product in the main processing facility Unitary storage cost of product in the consumers Unitary price for the raw material for each scenario s

CHAPTER 7

Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives 7.1 Introduction Biomass is a renewable resource and has attractive characteristics for energy production. But a supply chain based on biomass is subject to several uncertain factors that can drastically affect the final supply chain configuration. Therefore, this work presents a new approach for the optimal planning under uncertain price of feedstock into a biomass conversion system involving simultaneously economic and environmental issues. The environmental impact was measured using the ecoindicator99 method and the economic aspect was the net annual profit. On the other hand, the uncertain raw material price was considered by stochastic generation of scenarios using the Latin Hypercube method followed by implementation of the Monte-Carlo method, where a deterministic optimization problem was solved for each one of the scenarios to select the structure of the more robust supply chain relying on statistical data. The proposed approach was applied to a case study for a distributed biorefinery system in Mexico. The results show that the supply chain topology is affected by the uncertainty in the raw material price; however, the values of the environmental and economic objectives do not present significant changes. Additionally, it is possible to observe that the selected feedstocks are associated with high risk because of the value of the objective functions.

7.2 Problem Statement The problem addressed in this chapter is the optimal planning under uncertainty of a distributed supply chain of biorefineries considering environmental and economic aspects and taking into account the mass balances and constraints with dependence over time. Therefore, the problem consists of determining the set of raw materials, products, facilities and processing technologies of a distributed system focused on biomass processing to get

Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00007-9 © 2019 Elsevier Inc. All rights reserved.

177

178 Chapter 7 the best economic and environmental benefits accounting for the involved uncertainties. The proposed mathematical approach takes into account the following aspects: • • • •

Three sets of potential facilities: suppliers, processing plants and consumers. Three sets of materials: feedstocks, products and byproducts. Two types of processing stages: The processing of raw material to final products and byproducts, and the processing of the byproducts stream to obtain the final products. Several samplings of the raw material price to contemplate the uncertainties involved in the bioresources.

Furthermore, the proposed mathematical approach involves a strategy to select the topology to obtain the best values for the economic and environmental objectives with the use of appropriate tools to find deterministic solutions based on statistical analysis.

7.3 Mathematical Formulation To explain the proposed mathematical model, first we define the indexes used in the formulation. Index h is used for the suppliers or harvesting sites, index ph represents the secondary processing plants and index mk denotes the markets. In addition, indexes m and k illustrate the raw materials and products. The processing routes are represented by index r for the first processing stage and index sr for the second processing stage. Moreover, the proposed approach is a multiperiod model and index t is required to describe each one of the periods of time. Finally, index q is used for the economies of scale and the scenarios are represented by index s.

7.3.1 Availability of Raw Material The raw material produced in the harvesting sites is limited due to the fact that biomass production depends on the season of the year. The amount of produced biomass by the
 prod suppliers h Mm;h;t must be lower than the maximum amount of available biomass to be
 for all periods of time. produced UPP M available m;h;t UPP

prod M available $ Mm;h;t ; m;h;t

’mABIOMASS; hAHARVSITES; tAPERIODS

(7.1)

7.3.2 Mass Balances in the Suppliers Several activities can be developed at the harvesting sites, including the distribution of raw materials to the processing plants, the biomass production and the storage of raw materials.

Stochastic Design of Biorefinery Supply Chains 179 0 Thus, the stored biomass at the harvesting site h for the period of time t

storage B harv-sites @Mm;h;t

1 C A is


 prod equal to the produced biomass Mm;h;t minus the distributed biomass to the processing 0 1 distributed

distributed

hs-main C B hs-facilities and Mm;h;t plants @Mm;h;ph;t A plus the stored raw materials in the previous period

0 of time

storage B harv-sites @Mm;h;t21

storage harv-sites Mm;h;t

1 C A.

prod 5 Mm;h;t

2

X

distributed hs-facilities Mm;h;ph;t

distributed hs-main 2 Mm;h;t

storage harv-sites 1 Mm;h;t21

;

ph

mABIOMASS; ’ hAHARVSITES; tAPERIODS (7.2)

7.3.3 Mass Balances in the Processing Facilities The proposed mathematical model takes into account two types of processing plants (main and secondary processing plants) as well as two types of materials (feedstocks and products). Then, the first mass balance corresponds to the raw material balance in the secondary processing facilities, where the stored biomass in the processing plants 0 1 0 1 storage

distributed

B facilities C B hs-facilities C @Mm;ph;t A is equal to the biomass flow rate from the harvesting sites @Mem;h;ph;t A, 0 minus the raw materials flow sent to the first stage of processing 0 stored biomass in the previous period of time

storage facilities Mm;ph;t

5

X h

distributed hs-facilities Mem;h;ph;t

2

XX k

r

processed B facilities @Mm;k;r;ph;t

1 C A plus the

1

storage B facilities C @Mm;ph;t21 A.

processed facilities Mm;k;r;ph;t

storage facilities 1 Mm;ph;t21 ;

mABIOMASS; ’ phAFACILITIES; tAPERIODS (7.3)

180 Chapter 7 The product mass balance in the secondary processing plants states that the stored product 0 1 0 1 storage

yield

B facilities C B facilities C in the secondary plants @Pk;ph;t A is equal to that produced in the plant @Pk;ph;t A 0 minus the product distributed to the markets 0 previous period of time

storage facilities Pk;ph;t

storage B facilities @Pk;ph;t21

yield facilities 5 Pk;ph;t

2

distributed B facilities-mk @Pk;ph;mk;t

1 C A plus the one stored in the

1 C A.

X

distributed facilities-mk Pk;ph;mk;t

storage facilities 1 Pk;ph;t21

kAPRODUCTS; ’ phAFACILITIES; tAPERIODS

;

mk

(7.4)

In addition, the mass balances for the main processing facilities are considered in the mathematical model, which are defined in a similar way as for the secondary processing plants. storage main Mm;t

5

X

distributed hs-main Mem;h;t

2

h storage main Pk;t

XX k

yield main 5 Pk;t

2

X

processed main Mm;k;r;t

storage main 1 Mm;t21 ;

r distributed main-mk Pk;mk;t

storage main 1 Pk;t21

;

’

mk

’

mABIOMASS; tAPERIODS

kAPRODUCTS; tAPERIODS

(7.5)

(7.6)

7.3.4 Mass Balances in the Markets It is also necessary to consider an equation for the mass balance in the markets. The stored 1 0 storage

B market C product in the market in the period of time t @Pk;mk;t A is equal to the product arrived 0 from the processing plants

distributed B facilities-mk @Pek;ph;mk;t

and

distributed main-mk Pek;mk;t

1 C A, minus the sold product, plus

the stored product in the previous period of time. storage market Pk;mk;t

5

X ph

distributed facilities-mk Pek;ph;mk;t

distributed main-mk 1 Pek;mk;t

2 Psold k;mk;t

storage market 1 Pk;mk;t21 ;

kAPRODUCTS; ’ mkAMARKETS; tAPERIODS

(7.7)

Stochastic Design of Biorefinery Supply Chains 181

7.3.5 Demand Constraint An important constraint is the one for used to save resources and limit the
the demand  sold production. Thus, the sold product Pk;mk;t should be lower than the maximum demand in
each market Psold k;mk;t . demand Psold k;mk;t # Pk;mk;t ;

’kAPRODUCTS; mkAMARKETS; tAPERIODS

(7.8)

7.3.6 Relationships for the Input
Output of the Distributed Material We also need to consider some relationships for the input-output of the distributed material between the different entities of the supply chain. These constraints allow contemplating the transportation time because the material leaves an entity in the period of time t 2 1 1 0 distributed

distributed

distributed

distributed

hs-main facilities-mk main-mk C B hs-facilities @Mm;h;ph;t21 ; Mm;h;t21 ; Pk;ph;mk;t21 ; Pk;mk;t21 A and arrives at another entity in the

0 period of time t

distributed B hs-facilities @Mem;h;ph;t

;

distributed hs-main Mem;h;t ;

distributed facilities-mk Pek;ph;mk;t

;

distributed main-mk Pek;mk;t

1 C A. These

relationships are required to transport biomass from the suppliers to processing facilities, and products from the facilities to markets. Thus, the period of time t-1 is equal to the last period of the horizon when the constraints are applied to the first period of time t. This guarantees that the mathematical model can be used in a sequential way with two horizons of time. distributed hs-facilities Mm;h;ph;t21 distributed hs-main Mm;h;t21

distributed hs-main 5 Mem;h;t

distributed facilities-mk Pk;ph;mk;t21 distributed main-mk Pk;mk;t21

distributed hs-facilities 5 Mem;h;ph;t ;

;

;

mABIOMASS; hAHARVSITES; phAFACILITIES; tAPERIODS

’mABIOMASS; hAHARVSITES; tAPERIODS

distributed facilities-mk 5 Pek;ph;mk;t

distributed main-mk 5 Pek;mk;t

’

;

’

kAPRODUCTS; phAFACILITIES; mkAMARKETS; tAPERIODS

’kAPRODUCTS; mkAMARKETS; tAPERIODS

(7.9)

(7.10)

(7.11)

(7.12)

182 Chapter 7

7.3.7 Transportation Limits and Transportation Costs The model considers binary variables for the transportation of materials to determine where and when the materials are distributed. Subsequently, the distributed amounts of materials 1 0 distributed

distributed hs-main Mm;h;t ;

B hs-facilities @Mm;h;ph;t ;

0

distributed facilities-mk Pk;ph;mk;t

distributed

hs-facilities B transportation limit @ LOWER Mm;h;ph ;

distributed LOWER main-mk Pk;mk

0

distributed B hs-facilities @ym;h;ph;t ;

0

LOWER

are greater than a lower

distributed distributed hs-main LOWER facilities-mk Mm;h ; Pk;ph;mk ;

! multiplied by the binary variable for the transportation

distributed hs-main ym;h;t ;

distributed B hs-facilities @Mm;h;ph;t ;

;

distributed main-mk C Pk;mk;t A

distributed facilities-mk yk;ph;mk;t ;

distributed hs-main Mm;h;t ;

1

distributed main-mk C yk;mk;t A.

distributed facilities-mk Pk;ph;mk;t ;

Moreover, the distributed amounts of materials

distributed main-mk Pk;mk;t

! are lower than an upper transportation limit

0

distributed distributed distributed distributed B UPPER hs-facilities UPPER hs-main UPPER facilities-mk UPPER main-mk Mm;h;ph ; Mm;h ; Pk;ph;mk ; Pk;mk @

0 binary variable for the transportation

distributed B hs-facilities @ym;h;ph;t ;

distributed hs-main ym;h;t ;

!

distributed facilities-mk yk;ph;mk;t ;

multiplied by the 1

distributed main-mk C yk;mk;t A.

The

types of transportation are: transportation of raw materials from suppliers to processing plants and final products from processing plants to markets. It is important to note that the density of the types of biomass has already been considered here, because the transportation limits are based on the mass of biomass and the volume depending on the Mexican norms for transportation in which the maximum amount to be transported by truck is around 20
40 t for each truck. The volume of each truck is until 96 m3. Thus, the number of trucks to be utilized is defined by the volume limit and the mass limit, which directly affects the unitary transportation cost for each type of biomass. LOWER

distributed hs-facilities Mm;h;ph

distributed hs-facilities Uym;h;ph;t

distributed hs-facilities # Mm;h;ph;t

;

’

mABIOMASS; hAHARVSITES; phAFACILITIES; tAPERIODS (7.13)

Stochastic Design of Biorefinery Supply Chains 183

LOWER

distributed distributed hs-main hs-main Mm;h Uym;h;t

distributed hs-main # Mm;h;t ;

’mABIOMASS; hAHARVSITES; tAPERIODS (7.14)

LOWER

LOWER

distributed distributed facilities-mk facilities-mk Pk;ph;mk Uyk;ph;mk;t

distributed distributed main-mk main-mk Pk;mk Uyk;mk;t

distributed hs-facilities Mm;h;ph;t distributed hs-main Mm;h;t

#

#

UPPER

UPPER

distributed facilities-mk # Pk;ph;mk;t ;

distributed main-mk # Pk;mk;t ;

’

distributed distributed hs-facilities hs-facilities Mm;h;ph Uym;h;ph;t ;

distributed distributed hs-main hs-main Mm;h Uym;h;t ;

’

kAPRODUCTS; phAFACILITIES; mkAMARKETS; tAPERIODS (7.15)

kAPRODUCTS; mkAMARKETS; tAPERIODS ’

mABIOMASS; hAHARVSITES; phAFACILITIES; tAPERIODS

(7.16)

(7.17)

’mABIOMASS; hAHARVSITES; tAPERIODS (7.18)

distributed facilities-mk Pk;ph;mk;t distributed main-mk Pk;mk;t

distributed distributed facilities-mk facilities-mk Pk;ph;mk Uyk;ph;mk;t ;

#

UPPER

#

UPPER

distributed distributed main-mk main-mk Pk;mk Uyk;mk;t ;

’

’

kAPRODUCTS; phAFACILITIES; (7.19) mkAMARKETS; tAPERIODS

kAPRODUCTS; mkAMARKETS; tAPERIODS

(7.20)

It is worth including the transportation cost because this cost can define the configuration of the macrostructure of the supply chain. Thus, the transportation cost 0 1 distributed

@Ctransp hs-facilities ; Ctransp

distributed hs-main

; Ctransp

0

distributed facilities-mk

distributed

; Ctransp

distributed main-mk A

is equal to a

distributed

hs-facilities hs-main B unitary transportation cost @UCtranspm;h;ph ; UCtranspm;h ;

distributed facilities-mk UCtranspk;ph;mk

0

distributed B hs-facilities @Mm;h;ph;t ;

;

distributed main-mk UCtranspk;mk

distributed hs-main Mm;h;t ;

!

distributed facilities-mk Pk;ph;mk;t

multiplied by the amount of transported material 1

;

distributed main-mk C Pk;mk;t A.

The unitary transportation cost

184 Chapter 7 depends on the distance between the places in the supply chain as well as the type of material (biomass or product).

Ctransp

distributed hs-facilities

5

XXXX m

Ctransp

distributed hs-main

5

h

Ctransp

distributed facilities-mk

5

Ctransp

distributed hs-main UCtranspm;h

#

ph

mk

distributed hs-main UMm;h;t

(7.22)

distributed facilities-mk UCtranspk;ph;mk

distributed facilities-mk UPk;ph;mk;t

(7.23)

t

mk

XXX k

(7.21)

t

XXXX k

distributed main-mk

h

distributed hs-facilities UMm;h;ph;t

t

ph

XXX m

distributed hs-facilities UCtranspm;h;ph

distributed main-mk UCtranspk;mk

distributed main-mk UPk;mk;t

(7.24)

t

7.3.8 Processing Stages in the Processing Facilities In all processing facilities there are two processing stages and both stages depend on each other. The first processing step states that the product obtained in the first step at period of 0 1 stage 1

stage 1

main C B facilities time t @Pm;k;r;ph;t and Pm;k;r;t A is equal to the biomass distributed to the different

1

0 processing technologies at the period of time t 2 1

processed B facilities @Mm;k;r;ph;t21

and 0

multiplied by a conversion factor for the processing technologies

stage 1 facilities Pm;k;r;ph;t

stage 1 main Pm;k;r;t

conversion factorstage1 5 αm;k;r

conversion factorstage1 5 αm;k;r

processed facilities UMm;k;r;ph;t21 ;

processed main UMm;k;r;t21

;

’

’

processed main C Mm;k;r;t21 A

conversion B factor stage 1 @αm;k;r

1 C A.

mABIOMASS; kAPRODUCTS; rATECH1 phAFACILITIES; tAPERIODS (7.25)

mABIOMASS; kAPRODUCTS; rATECH1 tAPERIODS

(7.26)

Stochastic Design of Biorefinery Supply Chains 185 The produced product in the first processing stage is mixed considering the type of product k to obtain the total amount of product from the first stage. Thus, the total produced product 0 1 stage 1

stage 1

facilities main B k @Ptotalk;r;ph;t and Ptotalk;r;t

C A in the first processing stage is equal to the sum of the 0

yield product from all raw materials m

stage 1 facilities Ptotalk;r;ph;t

5

X

stage 1 B facilities @Pm;k;r;ph;t

5

1 C A:

stage 1 facilities Pm;k;r;ph;t ;

’

kAPRODUCTS; rATECH1 phAFACILITIES; tAPERIODS

(7.27)

stage 1 main Pm;k;r;t

’

kAPRODUCTS; rATECH1 tAPERIODS

(7.28)

m stage 1 main Ptotalk;r;t

and

stage 1 main Pm;k;r;t

X

;

m

Subsequently, the total product from the first processing stage is distributed to the different processing routes for the second processing stage, because the amount of yield product from the first stage is related to the flow of the byproduct stream to be sent to the second stage. The next constraint states that the product flow from the first stage 1 0 stage 1

stage 1

facilities main B @Ptotalk;r;ph;t and Ptotalk;r;t

C A is equal to the sum of the feedstock for the second

0 processing stage

stage 1 facilities Ptotalk;r;ph;t

stage 2 facilities B @Pfeedk;sr;ph;t

5

X

and

stage 2 facilities Pfeedk;r;sr;ph;t ;

m stage 1 main Ptotalk;r;t

5

X m

stage 2 main Pfeedk;sr;t

’

1 C A.

kAPRODUCTS; rATECH1; srATECH2 phAFACILITIES; tAPERIODS

stage 2 main Pfeedk;r;sr;t

;

’

kAPRODUCTS; rATECH1 srATECH2; tAPERIODS

(7.29)

(7.30)

Once the distributed product is obtained for the different technologies of the second stage 0 1 stage 2

stage 2

facilities main C B @Pfeedk;r;sr;ph;t and Pfeedk;r;sr;t A, it is possible to calculate the yield product for the

186 Chapter 7 0 second stage

stage 2 B facilities @Pk;r;sr;k0 ph;t

1

stage 2 main C Pk;r;sr;k0 ;t A.

and

0 This is done through a factor

conversion B factorstage2 @αk;r;sr;k0

1 C A to

obtain the product from the second stage. stage 2 facilities Pk;r;sr;k0 ph;t

stage 2 main Pk;r;sr;k0 ;t

conversion stage 2 factorstage2 facilities 5 αk;r;sr;k0 UPfeedk;r;sr;ph;t ;

’

conversion stage 2 factorstage2 main 5 αk;r;sr;k0 UPfeedk;r;sr;t ;

’

kAPRODUCTS; rATECH1; srATECH2 k0 APRODUCTS; phAFACILITIES; tAPERIODS (7.31)

kAPRODUCTS; rATECH1; srATECH2 k0 APRODUCTS; tAPERIODS

(7.32)

Finally, with the total product from the first and second stages it is possible to calculate the total product yield in the processing facilities, which states that the total product yield in 1 0 yield

yield

main C B facilities the processing facilities @Pk;ph;t and Pk;t A is equal to the sum of the product in the

1

0 first

stage 1 facilities B @Ptotalk;r;ph;t

and

stage 1 main C Ptotalk;r;t A

1

0 and second

stage 2 B facilities @Pk0 ;r;sr;k;ph;t

and

stage 2 main C Pk0 ;r;sr;k;t A

processing

stages. yield facilities Pk;ph;t

5

X

stage 1 facilities Ptotalk;r;ph;t

1

r

XXX r

k0

sr

stage 2 facilities Pk0 ;r;sr;k;ph;t ;

’

kAPRODUCTS; phAFACILITIES; tAPERIODS (7.33)

yield main Pk;t

5

X r

stage 1 main Ptotalk;r;t

1

XXX r

sr

k0

stage 2 main Pk0 ;r;sr;k;t ;

’kAPRODUCTS; tAPERIODS (7.34)

7.3.9 Processing Constraints for the First Stage To consider the economies of scale, we need to discretize the processed raw material for the first and second stages in several intervals to transform the capital cost function in a lineal equation. For that reason, the raw material for each processing facility

Stochastic Design of Biorefinery Supply Chains 187 0

processed B facilities @Mm;k;r;ph;t

1

;

processed main C Mm;k;r;t A

is equal to the sum of the discretized raw material flow for each 0

one of the economies of scale

processed facilities Mm;k;r;ph;t

5

X

processed facilities B @Mdism;k;r;ph;t;q ;

processed facilities Mdism;k;r;ph;t;q ;

q

processed main Mm;k;r;t

5

X

processed main Mdism;k;r;t;q

;

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; tAPERIODS

(7.35)

mABIOMASS; kAPRODUCTS; rATECH1; tAPERIODS

(7.36)

’

q

1

processed main C Mdism;k;r;t;q A.

Other constraints are included for the processing technologies since the processing technologies are limited by the economies of scale. In this context, there are several intervals for the processing technologies associated with the binary variables. These binary variables allow working with the nonlinear functions of the economies of scale in a simple way. Each one of the binary variables is activated when the processed amount is between the given lower and upper limits. For that reason, the amount of raw material used in each 1 0 processed

processed

facilities main C B processing route in the first stage @Mdism;k;r;ph;t;q ; Mdism;k;r;t;q A is greater than the lower

0 B limit @

processed facilities LOWER Mm;k;r;ph;q ;

processed main LOWER Mm;k;r;q

0 processing in the first stage

capital B facilities @ym;k;r;ph;t;q ;

1 C A multiplied by a binary variable for the 1

capital main C ym;k;r;t;q A.

0 in each processing route in the first stage

Also, the amount of raw material used

processed facilities B @Mdism;k;r;ph;t;q ;

1

processed main C Mdism;k;r;t;q A

is lower than the

188 Chapter 7 0 B upper limit @

processed facilities UPPER Mm;k;r;ph;q

1

;

processed main C UPPER Mm;k;r;q A

0 processing in the first stage

LOWER

processed facilities Mm;k;r;ph;q

processed facilities Mdism;k;r;ph;t;q

LOWER

#

processed main Mm;k;r;q

processed main Mdism;k;r;t;q

#

capital B facilities @ym;k;r;ph;t;q ;

capital facilities Uym;k;r;ph;t;q

UPPER

capital main Uym;k;r;t;q

UPPER

1

capital main C ym;k;r;t;q A.

processed facilities # Mdism;k;r;ph;t;q ;

processed facilities Mm;k;r;ph;q

capital facilities Uym;k;r;ph;t;q ;

processed main # Mdism;k;r;t;q

processed main Mm;k;r;q

multiplied by a binary variable for the

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; tAPERIODS; qAECON

(7.37)

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; tAPERIODS; qAECON

(7.38)

;

’

mABIOMASS; kAPRODUCTS; (7.39) rATECH1; tAPERIODS; qAECON

capital main Uym;k;r;t;q ;

’

mABIOMASS; kAPRODUCTS; (7.40) rATECH1; tAPERIODS; qAECON 0

It is important to note that the sum of these binary variables

capital B facilities @ym;k;r;ph;t;q ;

1

capital main C ym;k;r;t;q A

with

respect to the interval q is equal to 1, because only one binary variable for one interval q can be activated. X

capital facilities ym;k;r;ph;t;q

5 1;

q

X q

capital main ym;k;r;t;q 5 1;

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; tAPERIODS

(7.41)

mABIOMASS; kAPRODUCTS; rATECH1; tAPERIODS

(7.42)

’

Additionally, the proposed model should consider other constraints and binary variables without dependence on the time to be activated if one of the binary variables with

Stochastic Design of Biorefinery Supply Chains 189 dependence of the time is one. For that reason, the next constraints are proposed to ensure 0 1 capital

capital

capital B facilities @ym;k;r;ph;t;q ;

capital main C ym;k;r;t;q A.

main C B facilities that the binary variable for the first processing stage @y2m;k;r;ph;q ; y2m;k;r;q A is activated

0 when any of the binary variables takes the value of 1

1

These

constraints also depend on the maximum number of periods (Hmax): capital facilities y2m;k;r;ph;q

capital facilities ym;k;r;ph;t;q ;

X

#

t capital main y2m;k;r;q

#

X

capital main ym;k;r;t;q ;

’

t capital facilities HmaxUy2m;k;r;ph;q $

X

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; qAECON

(7.43)

mABIOMASS; kAPRODUCTS; rATECH1; qAECON

(7.44)

capital facilities ym;k;r;ph;t;q ;

t capital main HmaxUy2m;k;r;q

$

X

capital main ym;k;r;t;q ;

’

t

mABIOMASS; kAPRODUCTS; ’ rATECH1; phAFACILITIES; qAECON

(7.45)

mABIOMASS; kAPRODUCTS; rATECH1; qAECON

(7.46)

Furthermore, the capital cost is taken into account for both processing steps. The capital 0 1 capital

capital

main C B facilities cost for the first processing step @Cm;k;r;ph ; Cm;k;r A is equal to a fixed capital cost

0

capital B facilities @Am;k;r;ph;q ;

capital main Am;k;r;q

1 C A multiplied by the binary variable for the first stage without 0

dependence over the time 0

capital B facilities @Bm;k;r;ph;q ;

capital main Bm;k;r;q

capital B facilities @ym;k;r;ph;q ;

capital main ym;k;r;q

1 C A, plus a unitary cost multiplied

1 C A by the upper limit of the processing to consider the capacity of the

190 Chapter 7 0 B processing activity in the interval q @

processed facilities UPPER Mm;k;r;ph;q

0 binary variable for the processing activity capital facilities Cm;k;r;ph

X

5 KF U

capital B facilities @ym;k;r;ph;q ;

1

;

capital main ym;k;r;q

capital capital facilities facilities Am;k;r;ph;q Uym;k;r;ph;q

q

1

processed facilities UPPER Mm;k;r;ph;q

X

processed main C UPPER Mm;k;r;q A

capital capital facilities facilities UBm;k;r;ph;q Uym;k;r;ph;q

!

;

multiplied by the

1 C A:

mABIOMASS; kAPRODUCTS; ’ (7.47) rATECH1; phAFACILITIES

q

capital main Cm;k;r

X

5 KF U

capital main Am;k;r;q

capital main Uym;k;r;q

q

1

processed capital main main UPPER Mm;k;r;q UBm;k;r;q

X q

0

Also, the processing cost @C 1 0 operating

operating

facilities main B @UCm;k;r;ph;t ; UCm;k;r;t

0 first stage

processed B facilities @Mm;k;r;ph;t

C

operating facilities

; C

capital main Uym;k;r;q

operating main

!;

mABIOMASS; ’ kAPRODUCTS; rATECH1

(7.48)

1 A, which is equal to the unitary cost

C A multiplied by the amount the raw material processed in the 1

;

processed main C Mm;k;r;t A,

operating facilities

5

XXXXX m

C

operating main

is also considered:

5

r

k

k

r

(7.49)

t

ph

XXXX m

operating processed facilities facilities UCm;k;r;ph;t UMm;k;r;ph;t

t

operating main UCm;k;r;t

processed main UMm;k;r;t

(7.50)

Stochastic Design of Biorefinery Supply Chains 191

7.3.10 Processing Constraints for the Second Stage The second processing stage is modeled in a similar way as the first processing stage. Thus, the processed feedstock flow rate for the second processing step 1 0 stage 2

stage 2

facilities main C B @Pfeedk;r;sr;ph;t ; Pfeedk;r;sr;t A is equal to the sum of several discretized feedstock flow rates

0

stage 2 facilities B @Pdfeedk;r;sr;ph;t;q ;

for the intervals of production capacity

stage 2 facilities Pfeedk;r;sr;ph;t

5

X

stage 2 facilities Pdfeedk;r;sr;ph;t;q ;

’

q

1

stage 2 main C Pdfeedk;r;sr;t;q A:

kAPRODUCTS; rATECH1; srATECH2 phAFACILITIES; tAPERIODS (7.51)

stage 2 main Pfeedk;r;sr;t

5

X

stage 2 main Pdfeedk;r;sr;t;q ;

q

’

kAPRODUCTS; rATECH1; srATECH2 tAPERIODS

(7.52)

Also, the processing limits are applied to the second processing stage. Therefore, the constraints consider binary variables for the activation of the second processing step 0 1 0 1 stage 2

stage 2

stage 2

stage 2

facilities main C facilities main C B B @yfeedk;r;sr;ph;t;q ; yfeedk;r;sr;t A as well as upper @uppPfeedk;r;sr;ph;t;q ; uppPfeedk;r;sr;t A and

0 lower processing limits

stage 2 facilities B @lowPfeedk;r;sr;ph;t;q ;

1

stage 2 main C lowPfeedk;r;sr;t A:

stage 2 facilities Pdfeedk;r;sr;ph;t;q

stage 2 stage 2 facilities facilities $ lowPfeedk;r;sr;ph;q Uyfeedk;r;sr;ph;t;q ;

kAPRODUCTS; rATECH1; ’ srATECH2; phAFACILITIES; tAPERIODS; qAECON (7.53)

stage 2 facilities Pdfeedk;r;sr;ph;t;q

stage 2 stage 2 facilities facilities # uppPfeedk;r;sr;ph;q Uyfeedk;r;sr;ph;t;q ;

kAPRODUCTS; rATECH1; ’ srATECH2; phAFACILITIES; tAPERIODS; qAECON (7.54)

192 Chapter 7

stage 2 stage 2 stage 2 main main main Pdfeedk;r;sr;t;q $ lowPfeedk;r;sr;q Uyfeedk;r;sr;t;q ;

’

kAPRODUCTS; rATECH1; srATECH2; tAPERIODS; qAECON

(7.55)

stage 2 stage 2 stage 2 main main main Pdfeedk;r;sr;t;q # uppPfeedk;r;sr;q Uyfeedk;r;sr;t;q ;

’

kAPRODUCTS; rATECH1; srATECH2; tAPERIODS; qAECON

(7.56)

To select only one of the intervals for the capacity, the sum of the binary variables for the second 0 1 stage 2

stage 2

facilities main C B processing step @yfeedk;r;sr;ph;t;q ; yfeedk;r;sr;t;q A with respect to the interval q is equal to 1:

X

stage 2 facilities yfeedk;r;sr;ph;t;q

5 1;

kAPRODUCTS; rATECH1; ’ srATECH2; phAFACILITIES; tAPERIODS

(7.57)

stage 2 main yfeedk;r;sr;t;q

5 1;

’

kAPRODUCTS; rATECH1; srATECH2; tAPERIODS

(7.58)

q

X q

It should be noted that the facility siting for the second step is necessary if at least one of the binary variables for the processing with dependence of the time 0 1 stage 2

stage 2

facilities main C B @yfeedk;r;sr;ph;t;q ; yfeedk;r;sr;t;q A is activated. Thus, two constraints are proposed for each

processing facility in the second processing stage, which ensure that if at least one of the binary variables for the second step with dependence over time 0 1 stage 2

stage 2

facilities main C B @yfeedk;r;sr;ph;t;q ; yfeedk;r;sr;t;q A takes the value of 1, then the binary variable for the

0 processing in that step without dependence over time

stage 2 facilities B @y2feedk;r;sr;ph;q ;

1

stage 2 main C y2feedk;r;sr;t;q A

is

equal to 1. Moreover, no matter whether all binary variables with dependence over time

Stochastic Design of Biorefinery Supply Chains 193 0

stage 2 facilities B @yfeedk;r;sr;ph;t;q ;

1

stage 2 main C yfeedk;r;sr;t;q A

take the value of zero, the binary variable without

0 dependence over time

stage 2 facilities y2feedk;r;sr;ph;q

stage 2 facilities B @y2feedk;r;sr;ph;q ;

#

stage 2 facilities yfeedk;r;sr;ph;t;q ;

X t

stage 2 main y2feedk;r;sr;t;q

X

#

1

stage 2 main C y2feedk;r;sr;t;q A

kAPRODUCTS; rATECH1; ’ srATECH2; phAFACILITIES; qAECON

(7.59)

kAPRODUCTS; rATECH1; srATECH2; qAECON

(7.60)

kAPRODUCTS; rATECH1; ’ srATECH2; phAFACILITIES; qAECON

(7.61)

stage 2 main yfeedk;r;sr;t;q ;

’

t

stage 2 facilities HmaxUy2feedk;r;sr;ph;q

$

X

stage 2 facilities yfeedk;r;sr;ph;t;q ;

t

stage 2 main HmaxUy2feedk;r;sr;t;q

$

X

stage 2 main yfeedk;r;sr;t;q ;

is equal to zero.

’

t

kAPRODUCTS; rATECH1; srATECH2; qAECON

(7.62)

Also, the capital cost is defined for the second processing step, which is the sum of a fixed cost multiplied by the binary variable for the processing in the second step without dependence over time, plus a unitary cost multiplied by the processing capacity as well as the binary variable to define when the processing is done. capital facilities C2k;r;sr;ph

5 KF U

X

capital stage 2 facilities facilities A2k;r;sr;ph;q Uy2feedk;r;sr;ph;q

q stage 2 capital stage 2 X facilities facilities facilities 1 uppPfeedk;r;sr;ph;q UB2k;r;sr;ph;q Uy2feedk;r;sr;ph;q q

!

kAPRODUCTS; rATECH1; ;’ srATECH2; phAFACILITIES (7.63)

194 Chapter 7

capital main C2k;r;sr

X

5 KF U

capital main A2k;r;sr

stage 2 main Uy2feedk;r;sr;q

q

1

X

stage 2 main uppPfeedk;r;sr;q

capital main UB2k;r;sr

stage 2 main Uy2feedk;r;sr;q

kAPRODUCTS; ; ’ rATECH1; srATECH2;

!

q

(7.64) Finally, the operational cost is defined by a unitary cost for each processing technology in the second processing step multiplied by the amount of feedstock processed in the processing step.

C2

operating facilities

5

XXXXX r

k

C2

operating main

5

sr

r

sr

stage 2 facilities UPfeedk;r;sr;ph;t

(7.65)

t

ph

XXXX k

operating facilities UC2k;r;sr;ph;t

operating main UC2k;r;sr;t

stage 2 main UPfeedk;r;sr;t

(7.66)

t

7.3.11 Storage Modeling The mathematical model considers constraints for the storage limits in the different facilities of the supply chain. To determine if there is material stored in any facility, it is necessary to include binary variables, which are activated when the stored amount of material is between an upper and a lower limit. Thus, the 1 0 storage

storage

storage

storage

storage

storage

facilities main facilities main market C B harv-sites stored amount of material @Mm;h;t ; Mm;ph;t ; Mm;t ; Pk;ph;t ; Pk;t ; Pk;mk;t A

is lower than the upper storage limit storage main UPPER Mm ;

storage UPPER facilities Pk;ph

;

UPPER

storage UPPER main Pk

storage harv-sites Mm;h

;

;

UPPER

storage UPPER market Pk;mk

storage facilities Mm;ph

! multiplied by the

binary variable to define if there is storage in any period of time t 0 1 storage

storage

storage

storage

storage

storage

;

facilities main facilities main market C B harv-sites ; ymm;ph;t ; ymm;t ; yk;ph;t ; yk;t ; yk;mk;t A: @ym;h;t

Stochastic Design of Biorefinery Supply Chains 195 storage harv-sites Mm;h;t storage facilities Mm;ph;t

#

#

UPPER

UPPER

storage main Mm;t storage facilities Pk;ph;t

#

#

#

storage storage facilities facilities Mm;ph Uymm;ph;t

UPPER

UPPER

storage main Pk;t storage market Pk;mk;t

UPPER

storage storage harv-sites harv-sites Mm;h Uym;h;t ;

storage storage facilities facilities Pk;ph Uyk;ph;t

#

UPPER

storage market Pk;mk;t

;

(7.67)

mABIOMASS; phAFACILITIES; tAPERIODS

(7.68)

’mABIOMASS; tAPERIODS

(7.69)

kAPRODUCTS; phAFACILITIES; tAPERIODS

(7.70)

’kAPRODUCTS; tAPERIODS

(7.71)

’

; ’

storage storage main main Pk Uyk;t ;

storage storage market market Pk;mk Uyk;mk;t

!

;

’kAPRODUCTS; MARKETS; tAPERIODS (7.72)

Also, the stored amount of material storage main Pk;t ;

;

storage storage main main Mm Uymm;t

mABIOMASS; hAHARVSITES; tAPERIODS

’

storage harv-sites Mm;h;t ;

storage facilities Mm;ph;t

is greater than the lower storage limit

storage facilities LOWER Mm;ph ;

storage main LOWER Mm ;

storage LOWER facilities Pk;ph

;

;

storage main Mm;t ;

LOWER

storage LOWER main Pk

;

storage facilities Pk;ph;t ;

storage harv-sites Mm;h

;

storage LOWER market Pk;mk

!

multiplied by the binary variable to determine if there is storage in any period of time t 0 1 storage

storage

storage

storage

storage

storage

facilities main facilities main market C B harv-sites ; ymm;ph;t ; ymm;t ; yk;ph;t ; yk;t ; yk;mk;t A: @ym;h;t

storage harv-sites Mm;h;t

storage facilities Mm;ph;t

$

$

LOWER

LOWER

storage storage harv-sites harv-sites Mm;h Uym;h;t ;

storage storage facilities facilities Mm;ph Uymm;ph;t

;

mABIOMASS; hAHARVSITES; tAPERIODS

(7.73)

mABIOMASS; phAFACILITIES; tAPERIODS

(7.74)

’

’

196 Chapter 7 storage main Mm;t storage facilities Pk;ph;t

$

storage main Pk;t storage market Pk;mk;t

$

$

LOWER

LOWER

$

storage storage main main Mm Uymm;t

storage storage facilities facilities Pk;ph Uyk;ph;t ;

LOWER

LOWER

’

storage storage main main Pk Uyk;t ;

storage storage market market Pk;mk Uyk;mk;t ;

;

’mABIOMASS; tAPERIODS

(7.75)

kAPRODUCTS; phAFACILITIES; tAPERIODS

(7.76)

’kAPRODUCTS; tAPERIODS

(7.77)

’kAPRODUCTS; MARKETS; tAPERIODS (7.78)

Since the mathematical model is a multiperiod approach, the storage may be carried out by all periods of time as well as the initial time, which is the same as the final period. To include the capital cost for the storage activity, the model includes other binary variables without dependence on the time 0 1 storage

storage

storage

storage

storage

storage

facilities main facilities main market C B harv-sites ; ym2m;ph ; ym2m ; y2k;ph ; y2k;t ; y2k;mk;t A and the storage @y2m;h;

activity is modeled in a similar way as for other activities in the formulation. Thus, there are constraints to ensure that the storages are constructed when the storage is needed in at least one period of time: storage harv-sites y2m;h

#

X

storage harv-sites ym;h;t

;

’mABIOMASS; hAHARVSITES

(7.79)

’mABIOMASS; phAFACILITIES

(7.80)

t storage facilities ym2m;ph

#

X

storage facilities ymm;ph;t ;

t storage main ym2m

#

X

storage main ymm;t ;

’mABIOMASS

(7.81)

t storage facilities y2k;ph

#

X t

storage facilities yk;ph;t ;

’kAPRODUCTS; phAFACILITIES

(7.82)

Stochastic Design of Biorefinery Supply Chains 197 storage main y2k;t

#

storage main yk;t ;

X

’kAPRODUCTS

(7.83)

’kAPRODUCTS; MARKETS

(7.84)

t storage market y2k;mk;t

X

#

storage market yk;mk;t ;

t storage harv-sites HmaxUy2m;h

X

$

storage harv-sites ym;h;t

;

’mABIOMASS; hAHARVSITES

(7.85)

t storage facilities HmaxUym2m;ph

$

X

storage facilities ymm;ph;t ;

’mABIOMASS; phAFACILITIES

(7.86)

t storage main HmaxUymm

X

$

storage main ymm;t ;

’mABIOMASS

(7.87)

t storage facilities HmaxUy2k;ph

$

X

storage facilities yk;ph;t ;

’kAPRODUCTS; phAFACILITIES

(7.88)

storage main yk;t ;

’kAPRODUCTS

(7.89)

’kAPRODUCTS; MARKETS

(7.90)

t storage main HmaxUy2k;t

$

X t

storage market HmaxUy2k;mk

$

X

storage market yk;mk;t ;

t

As the storage cost is significant for the entire supply chain, this cost is given by all types of storage (raw material and products in suppliers, processing plants and markets). Thus, the storage cost for each type 1 0 storage
raw

storage

storage

storage
raw B harv
sites @Am;h

storage facilities Amm;ph

storage

storage

storage

facilities main facilities main market C B harv
sites ; Cmm;ph ; Cmm ; Ck;ph ; Ck ; Ck;mk A is equal to a @Cm;h

0 fixed cost

;

;

storage main Amm ;

storage facilities Ak;ph

by the binary variable associated with the storage

;

storage main Ak ;

storage market Ak;mk

1 C A multiplied

198 Chapter 7 0

storage B harv
sites @y2m;h

;

storage facilities ym2m;ph

;

storage main ym2m

0 variable cost

storage
raw B harv
sites @Bm;h

;

storage facilities y2k;ph

;

storage facilities Bmm;ph

;

storage main y2k;t

;

storage main Bmm

0

;

;

storage facilities Bk;ph

storage UPPER facilities Pk;ph

storage
raw

storage UPPER main Pk

;

0 variable linked to the storage

storage B harv
sites @y2m;h

;

;

UPPER

storage UPPER market Pk;mk

storage facilities ym2m;ph

;

;

storage market Bk;mk

storage facilities Mm;ph

1 C A

;

! multiplied by the binary

storage facilities y2k;ph

0

C A plus a unitary

storage main Bk

;

harv
sites B multiplied by the capacity of storage @ UPPER Mm;h ;

storage main UPPER Mm ;

1

storage market y2k;mk;t

;

storage main y2k;t

storage
raw

;

storage market y2k;mk;t

1 C A,

storage

harv
sites facilities B plus the sum over time of a unitary operational cost @UCm;h;t ; UCmm;ph;t ;

storage main UCmm;t

;

storage facilities UCk;ph;t

0 unit

storage
raw B harv
sites @Mm;h;t

storage
raw harv
sites Cm;h

;

1

storage facilities Mm;ph;t

;

;

storage market UCk;mk;t

storage main Mm;t

storage
raw harv
sites Am;h

5 KF U

1

;

storage main UCk;t

;

! multiplied by the amount stored for each

storage facilities Pk;ph;t

;

storage main Pk;t

storage
raw harv
sites t Mm;h;t

1 C A:

storage harv
sites Uy2m;h

storage
raw storage
raw storage harv
sites harv
sites harv
sites UPPER Mm;h UBm;h Uy2m;h

P

;

storage market Pk;mk;t

! ;’

mABIOMASS; hAHARVSITES

storage
raw harv
sites UUCm;h;t

(7.91)

Stochastic Design of Biorefinery Supply Chains 199 storage facilities Cmm;ph

storage storage facilities facilities Amm;ph Uym2m;ph

5 KF U

storage facilities UPPER Mm;ph

1

1

X

storage facilities Mm;ph;t

storage facilities UBmm;ph

storage facilities Uym2m;ph

! ; ’

mABIOMASS; phAFACILITIES

storage facilities UUCmm;ph;t

t

(7.92) storage main Cmm

storage storage main main Amm Uym2m

5 KF U

storage storage main main UPPER Mm UBmm

1

X

1

storage main Mm;t

storage main Uym2m

! ;

’mABIOMASS

storage main UUCmm;t

t

(7.93) storage facilities Ck;ph

5 KF U

1

1

storage storage facilities facilities Ak;ph Uy2k;ph

storage UPPER facilities Pk;ph

X

storage facilities UBk;ph

storage facilities Uy2k;ph

! ;

’

kAPRODUCTS; phAFACILITIES

storage storage facilities facilities Pk;ph;t UUCk;ph;t

t

(7.94) storage main Ck

storage storage main main Ak Uy2k

5 KF U

1

1

storage UPPER main Pk

X t

storage storage main main UBk Uy2k

storage storage main main Pk;t UUCk;t

! ;

’mABIOMASS (7.95)

200 Chapter 7

storage market Ck;mk

storage storage market market Ak;mk Uy2k;mk

5 KF U

1

1

storage storage market UPPER market Pk;mk UBk;mk

X

storage market Pk;mk;t

storage market Uy2k;mk

! ;

’

kAPRODUCTS; mkAMARKETS

storage market UUCk;mk;t

t

(7.96)

7.3.12 Revenue From Selling Products The income from selling products is equal to a unitary selling price multiplied by the amount of sold products in each market. sale

Revenue products 5

XXX k

sold UCdemand k;mk UPk;mk;t

(7.97)

t

mk

7.3.13 Raw Material Production Cost The produced raw material cost is equal to a unitary production cost multiplied by the amount of produced raw material at each harvesting site:

Cost

raw material

5

XXX m

raw material UCm;h

prod UMm;h;t

(7.98)

t

h

7.3.14 Economic Objective Function The economic objective function (Profit) is given by the total annual profit, which considers 0 1 sale

the income for selling products @Revenue products A minus the raw material production cost 0 @Cost

raw material

0

1 A, minus the capital

capital B facilities @Cm;k;r;ph

0 cost for the processing facilities @C

operating facilities

;

capital main Cm;k;r

; C

operating main

;

capital facilities C2k;r;sr;ph

; C2

;

operating facilities

capital main C2k;r;sr

1 C A and operating 1

; C2

operating main A

for both

Stochastic Design of Biorefinery Supply Chains 201 0

storage-raw storage storage storage facilities main facilities B harv-sites processing stages, minus the storage @Cm;h ; Cmm;ph ; Cmm ; Ck;ph ;

storage main Ck ;

storage market Ck;mk

!

0

distributed

and transportation cost @Ctransp hs-facilities ; Ctransp

distributed hs-main

;

! distributed

Ctransp facilities-mk ; Ctransp

distributed main-mk

sale

: raw

Profit 5 Revenue products 2 Cost material capital capital capital X X X X facilities X X X main XXXX facilities 2 Cm;k;r;ph 2 Cm;k;r 2 C2k;r;sr;ph m

2 2 2

k

r

m

ph

r

k

capital operating operating XXX main facilities C2k;r;sr 2 C 2 C main r sr k storage-raw storage X X harv-sites XX facilities Cm;h 2 Cmm;ph 2 m m ph h storage X X facilities Ck;ph k ph

2 Ctransp 2 Ctransp

distributed hs-facilities distributed facilities-mk

2

storage X main Ck k

2 Ctransp

2

k

2 C2 X

r

operating facilities

sr

ph

2 C2

operating main

storage main Cmm

m

storage X X market Ck;mk k mk

distributed hs-main

2 Ctransp

distributed main-mk

(7.99)

7.3.15 Environmental Objective The environmental objective considers the environmental impact assessed using the ecoindicator 99 method. Thus, the overall environmental impact is equal to the impact of the 0 1 raw

material B prod C production of raw materials @UEcom UMm;h;t A plus the impact of the use of products

0

use products B @UEcok

1 C UPsold k;mk;t A plus the impact of processing in the processing facilities

202 Chapter 7 0

operating

stage 2

operating

facilities facilities main B @UEcok;r;sr;ph UPfeedk;r;sr;ph;t ; UEcok;r;sr

operating processed main main UEcom;k;r UMm;k;r;t ;

distributed facilities-mk UEcok;ph;mk

stage 2 main UPfeedk;r;sr;t ;

distributed facilities-mk UPk;ph;mk;t

!

;

distributed main-mk UEcok;mk

distributed main-mk UPk;mk;t

distributed distributed hs-facilities hs-facilities B UMm;h;ph;t @UEcom;h;ph

distributed hs-main UEcom;h

distributed hs-main UMm;h;t

0 impact of transportation

operating processed facilities facilities UEcom;k;r;ph UMm;k;r;ph;t ;

;

plus the 1 C A. It

should be noted that each environmental impact is equal to a unitary ecoindicator value multiplied by the amount of material associated with a given activity. use raw XXX products material prod sold EI 5 UEcok UPk;mk;t 1 UEcom UMm;h;t m t k mk t h operating stage 2 operating stage 2 XXXXX XXXX facilities facilities main main 1 UEcok;r;sr;ph UPfeedk;r;sr;ph;t 1 UEcok;r;sr UPfeedk;r;sr;t r sr ph t r sr t k k

XXX

1

m

1

k

r

ph

distributed distributed distributed distributed XXX hs-facilities hs-facilities hs-main hs-main UEcom;h;ph UMm;h;ph;t 1 UEcom;h UMm;h;t t m t h

XXXX m

1

operating processed operating processed XXXX facilities facilities main main UEcom;k;r;ph UMm;k;r;ph;t 1 UEcom;k;r UMm;k;r;t t m r t k

XXXXX

h

ph

distributed distributed distributed distributed XXX facilities-mk facilities-mk main-mk main-mk UEcok;ph;mk UPk;ph;mk;t 1 UEcok;mk UPk;mk;t t k mk t

XXXX k

ph

mk

(7.100)

7.4 Solution Approach Fig. 7.1 shows, in a general way, the proposed solution strategy, divided into several steps as follows.

7.4.1 Definition of the Superstructure The definition of the superstructure is used to determine the processing technologies, products, raw materials, location of facilities as well as other parameters associated (processing limits, demands, transportation limits) with the supply chain.

Stochastic Design of Biorefinery Supply Chains 203

Figure 7.1 General representation of the proposed solution strategy for the addressed problem. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

7.4.2 Identification of the Parameters Under Uncertainty The second step consists of identifying the parameters and variables with significant uncertainty based on historical information and published literature. The data allow determining some statistical information such as standard deviation, which is essential in the next step.

7.4.3 Sampling for Uncertain Parameters During the third stage, a sampling of N scenarios for the uncertain parameters is done. Here, we use the Latin Hypercube Sampling (LHS) method. The LHS method requires upper and lower bounds to provide the samples; thus, the standard deviation is employed. In the fourth step a Monte-Carlo simulation is performed, which allows us to obtain an optimal solution solving a deterministic problem for each sample parameter.

7.4.4 Solving of the Associated Deterministic Optimization Problem As noted, several scenarios were generated for the uncertain parameters, and a deterministic optimization problem for each of the scenarios is solved. Each of the deterministic models can be expressed in compact form as follows. Maximization of net annual profit and minimization of the overall environmental impact (maximization of the negative value of the environmental impact).   Max ProfitðEq: ð99ÞÞ; 2 EIðEq: ð100ÞÞ Subject to  hðx; yÞ 5 0 Eqs: ð1Þ 2 ð98Þ gðx; yÞ # 0

204 Chapter 7 xAℝ; yAf0; 1g where x represents the continuous variables as the flow rate of feedstock and products, the inventory levels, the processed raw material, etc. Furthermore, y represents the binary variables to select the capacity of the processing stages as well as to define if a material is transported or stored. As can be seen, the previous problem is a multiobjective optimization problem that can be solved by any standard multiobjective optimization algorithm. Here, the epsilon constraint method was applied. This method is based on solving the original problem considering only one of the objectives subject to an upper limit for the environmental impact. The solving of that problem for different values for the upper limit between a minimum and a maximum value of environmental impact can generate the Pareto curve. Thus, the problem to be solved for each one of the scenarios is given by:   Max ProfitðEq: ð99ÞÞ Subject to EIðEq: ð100ÞÞ # ε  hðx; yÞ 5 0 Eqs: ð1Þ 2 ð98Þ gðx; yÞ # 0 xAℝ; yAf0; 1g Once the previous problem is solved, it is possible to determine the optimal solution for the net annual profit as well as the supply chain topology. It should be noted that each deterministic problem is subject to a constraint for the upper limit in the function for the environmental impact.

7.4.5 Comparison Between Different Supply Chain Topologies Once the deterministic problems are solved, the fifth step compares the topology of the supply chain of each solution to select the more flexible topology based on the statistical data. In order to understand how the optimal solutions of the supply chain compare to each other, the entire supply chain can be divided in several stages (see Fig. 7.2): the transportation of biomass from suppliers to plants, biomass processing by the first processing stage, byproducts processing through the second processing stage and transportation of final products from plants to consumers. Each section of the supply chain is identified and the complete supply chain is obtained when at least one option of each part of the supply chain is selected (see Fig. 7.2).

Stochastic Design of Biorefinery Supply Chains 205

Figure 7.2 Representation of the different sections of the supply chain. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

Then, the number of times that each section is repeated is calculated to obtain the maximum number of occurrences to get the value of a repetition factor, which is equal to the number of repetitions divided by the maximum number of repetitions. Thus, the sum of the repetitions factors for each topology is compared each other and the selected topology is the optimal solution with largest value of the total repetition factor. Fig. 7.3 shows two examples of this procedure. Case A represents the situation when at least one of the complete structures is repeated and the selected structure is the structure with the largest mode value. In this case, to select the exact topology, the structure with the best value of the economic objective function is chosen. On the other hand, case B is used when all supply chain structures are different, and the selected structure corresponds to the optimal solution in scenario 1, because sections 1 and 2 at least is repeated twice to get a total repetition factor of 4. It should be noted that the final result in case A considers the topology with the largest mode value; however, if all topologies are completely different (case B), the selected topology is the one with the largest number of interconnections in the different steps.

7.4.6 Changing of the Upper Limit for the Environmental Impact The sixth stage consists of changing the value of the upper limit to the environmental impact and then going back to step 4 to generate the complete Pareto curve.

206 Chapter 7

Figure 7.3 Explanation of the method to select the topology from the set of deterministic solutions. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

7.4.7 Standardized Regression Coefficients Additionally, step 7 is used to perform a statistical analysis based on the standardized regression coefficients method to identify the contribution of each uncertain parameter or variable in the selected objectives or factors (Morales-Rodriguez, Meyer, Gernaey, & Sin, 2011). The seventh stage can be useful to do predictions about the behavior of the supply chain topology when the price or availability of some raw material changes (Sin, Gernaey, & Lantz, 2010).

7.5 Case Study A nationwide case study for a supply chain in Mexico considering uncertainties in the raw material prices was used to illustrate the proposed solution strategy and mathematical approach. The case study consists of 6 suppliers, 6 processing facilities and 5 consumers. Also, 9 raw materials, 5 products, 13 processing technologies for the first processing stage and 10 processing routes for the second processing stage were selected for the case study. Table 7.1 presents these options, which could be selected through the use of the mathematical model. Regarding the products obtained from the different processing routes, the data for bioethanol and biodiesel production (ratio between the amount of produced product and the raw material used) from different raw materials used in the case study were

Stochastic Design of Biorefinery Supply Chains 207 Table 7.1: Description of the case study Possible Locations for Facilities Suppliers

Processing Plants

Markets

Northwest

Salamanca

Center

South

Cadereyta

North east

Center west

Cd. Madero

Center west

Northeast

Minatitlan

North west

East

Salina Cruz

South

Center

Tula

Materials Raw Materials Wood chips Corn grain African palm

Wood Sorghum grain Jatropha

Products Sugar cane Sweet sorghum Safflower

Bioethanol Biodiesel

Xylitol Lactic acid

Butanol

Processing Route First Stage Pretreatment acid hydrolysis and fermentation Fermentation with immobilized acetobutylicum L-intermedius NRRL B-3693

Pretreatment gasification and biosynthesis Fermentation with suspended acetobutylicum

Pretreatment extraction and transesterification ABE fermentation

Processing Route Second Stage Fermentation with immobilized acetobutylicum L-intermedius NRRL B-3693

Fermentation with suspended acetobutylicum Acid fermentation

ABE fermentation

From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

208 Chapter 7 Table 7.2: Historical data for the raw material prices, USD/metric-ton Year 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 %Dev base value Upper limit Lower limit

Wood Chips

Wood

Sugar Cane

Corn Grain

Sorghum Grain

Sweet Sorghum

African Palm

28.59 44.62 36.59 32.79 38.54 70.09 53.97 53.40 80.06 88.87 86.60 25.58

57.19 89.24 73.19 65.57 77.09 140.18 107.93 106.79 160.13 177.74 173.20 25.58

50.57 42.36 38.29 33.36 47.24 34.90 57.95 38.97 52.36 47.79 58.23 14.99

240.63 197.53 190.60 237.31 199.92 242.58 261.30 211.26 245.90 295.01 357.57 13.67

123.52 120.18 117.74 109.83 143.55 176.09 207.36 159.96 179.73 277.60 259.12 22.12

27.78 25.07 25.73 27.14 28.53 30.80 37.98 29.17 34.81 40.08 39.84 14.16

21.89 34.16 28.02 25.11 29.51 53.67 41.32 40.89 61.31 68.05 66.31 25.58

43.43 67.76 55.58 49.80 58.54 106.45 81.96 81.10 121.60 134.97 131.52 25.58

184.21 210.53 208.61 207.12 214.40 216.10 332.57 310.91 343.97 449.91 459.59 21.91

108.75

217.50

66.96

406.44

316.43

45.48

83.27

165.16

560.30

64.45

128.90

49.50

308.70

201.81

34.20

49.35

97.88

358.88

Jatropha Safflower

From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

obtained from Santiban˜ez-Aguilar, Gonza´lez-Campos, Ponce-Ortega, Serna-Gonza´lez, and El-Halwagi (2014). The data, including the reactive conversion for the production of xylitol, have been reported in several works; for example, the data used for obtaining xylitol from glucose via acid fermentation were obtained from Granstro¨m, Izumori, and Leisola (2007), and using Candida mogii from Tochampa et al. (2005). Also, the data from a review study for different microorganisms to produce xylitol via fermentation were obtained from Chen, Jiang, Chen, and Qin (2010). The data used to obtain biobutanol with immobilized cells of clostridium acetobutylicum were obtained from Chen et al. (2013), and the data used to obtain biobutanol through the acetone-butanol-ethanol (ABE) fermentation were reported by Jones and Wood (1986), whereas Sukumaran, Gottumukkala, Rajasree, Alex, and Pandey (2011) reported improved information. The data for lactic acid via lactobacillus intermedius NRRL B-3693 were obtained from Saha and Nakamura (2003). As noted, the uncertain parameter is the raw material price. Thus, Table 7.2 shows the raw material prices from 2002 to 2012, the upper and lower limits for the distributions and the deviation with respect to the base value (data from 2012), which is the standard deviation of all periods of time divided by the base value that was employed to perform the LHS sampling to generate the needed scenarios. Fig. 7.4 shows that the samplings are distributed uniformly in the given interval for the raw material price. This can be seen because the diagonal represents the frequency histogram for the different raw material prices, and this histogram looks like a uniform distribution. The points in Fig. 7.4 show the different

Stochastic Design of Biorefinery Supply Chains 209

Figure 7.4 Distribution of the raw material prices for the case study. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

combinations of values for a raw material price with respect to another feedstock price. Notice that the uniform distribution allows illustrating the effect of the uncertainty in the raw material price for a more representative space (combinations distributed more), although it is possible to obtain combinations with a lower possibility of occurring. In addition, it is possible to observe that the number of samplings was adequate for all the proposed raw materials and no correlation was included in the samplings, since the entire space was utilized.

210 Chapter 7

Figure 7.5 Dataflow and computer-aided tools integration. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

7.6 Computer-Aided Tools The dataflow and software integration are illustrated in Fig. 7.5. The standard deviation was calculated using Excel. This information was sent to MATLAB to perform the sampling using the LHS method. The problem was formulated as a mixed-integer linear programming (MILP) model in GAMS, which solved each of the samples automatically as a deterministic problem and sent back the values of the objective function to MATLAB. Note that a software synergy (Ferris, Jain, & Dirkse, 2010) was accomplished to facilitate the handling of data from MATLAB to GAMS and vice versa.

7.7 Results and Discussion The model was solved as discussed in the previous section using a computer with a processor Intel Core i7-4700MQ at 2.40 GHz with 24 GB of RAM. The average CPU time for solving each one of the MILP problems was 12 minutes (one MILP problem for each scenario), and for the statistical analysis of the solutions it was 70 minutes. Each one of the MILP problems consists of 1,152,679 constraints, 779,791 continuous variables and 200,660 binary variables. The Pareto curve for the economic and environmental objective functions are shown in Fig. 7.6. It should be noted that each point considers the more flexible topology of the supply chain with respect to 100 samples, which is selected according to the proposed method. It is possible to distinguish two regions in the Pareto curve. In the first one, the environmental impact does not increase quickly but the economic objective profit increases from 0 to 400 M US$/year. The second one shows that the economic profit increases from 400 M US$/year up to almost 600 M US$/year, while the environmental impact changes

Stochastic Design of Biorefinery Supply Chains 211

Figure 7.6 Pareto curve between the environmental impact and the net annual profit. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

from almost 125 M Eco points per year up to 275 M Eco points. In order to explain the Pareto curve behavior, several points are selected. Fig. 7.6 also shows the Pareto front for the deterministic case (mean values). Notice that the behavior for the relationship between the environmental and economic objective is very similar to the Pareto curve for the stochastic case, which illustrates that the deterministic solution (dashed line) provides good approximation to the values for the environmental and economic objectives. However, the main advantage of the proposed approach is the evaluation of N different samplings before reporting a solution for the objective functions since the supply chain topology from the deterministic case is optimal for a specific set of data. Nevertheless, the deterministic solution can be poor for other sets of data. The supply chain topology for points A and C are shown in Fig. 7.7. It should be noted that there is no difference in the macrostructure of the supply chain because the same suppliers, processing plants and consumers as well as their interconnections were selected. On the other hand, the raw materials for the biodiesel and lactic acid were not chosen probably because the variations in the prices of the raw materials are very high and the system is not able to support these variations. Furthermore, it can be seen that the xylitol demand is almost satisfied because the required demand is lower than the other products and the supply chain considers the possibility of producing xylitol from the residue streams of other processing technologies. Additionally, the main effect on the environmental impact is caused by increasing the bioethanol and biobutanol production since the fulfilled demand of these products increases drastically from point A to point C.

212 Chapter 7

Figure 7.7 Macrostructures selected for points A and C of the Pareto curve of Fig. 7.6. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

Stochastic Design of Biorefinery Supply Chains 213

Figure 7.8 Configuration of the processing technologies for the plant located in Salamanca for points A and C of Fig. 7.6. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lezCampos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

The selected processing technologies also change from point A to point C. Fig. 7.8 shows the configuration of the processing technologies for the plant located in Salamanca. This figure depicts that at point A the butanol is produced via three technologies in the first processing stage and only two technologies in the second stage, while the butanol

214 Chapter 7

Figure 7.9 Dependence of the economic objective function on the uncertain parameters. From Jose´ Ezequiel Santiban˜ez-Aguilar, Ricardo Morales-Rodriguez, Janett Betzabe Gonza´lez-Campos, Jose´ Marı´a Ponce-Ortega, Stochastic design of biorefinery supply chains considering economic and environmental objectives, Journal of Cleaner Production, 2016.

production at point C is performed through three technologies in the first stage and four technologies in the second one. Additionally, the ethanol is obtained from one route in the first stage and two routes in the second processing step for both points. This indicates that the changes in the interconnections between the different processing stages cause an increase in the profit as well as the environmental impact. Fig. 7.9 depicts the contribution of the different uncertain raw material prices to the economic objective function for the different points of the Pareto curve. Point A represents a point with low environmental impact and the main contribution to the economic profit was the sugarcane and sweet sorghum prices. This means that variations in the price for these raw materials affect the objective function. For that reason, selection of these raw materials in the supply chain can present a major risk due to the uncertainty of these parameters. In addition, it can be seen that at the other points the sweet sorghum price

Stochastic Design of Biorefinery Supply Chains 215 presents a significant contribution, although it is a raw material with high conversion to products and also was one of the most important raw materials in the previous work by Santiban˜ez-Aguilar et al. (2014). The solutions with this feedstock represent a major risk because the sweet sorghum price introduces most of the uncertainty in these cases. It should be noted that all the contributions are lower than 0.7 for the β 2 factor, which indicates that the net annual profit does not depend significantly on one or two raw materials; however, these raw materials can change the value of the net annual profit.

7.8 Concluding Remarks This chapter proposed a new method for the supply chain optimization of biorefinery systems under uncertainty. The uncertainty was considered by stochastic generation of samplings done through the Latin Hypercube method, which allowed a uniform distribution of the uncertain parameters along the full uncertain space. Additionally, the presented approach is able to select a topology for the supply chain to illustrate the trade-offs between economic and environmental objectives. A case study for predicting biofuels in Mexico was presented, and the results show that it is possible to satisfy the biofuel demands in a sustainable way accounting for the involved uncertainty thought a robust supply chain, which is identified through the proposed approach. Furthermore, the results show that the behavior of the profit values for the stochastic case is not associated with the behavior of the raw material price because the histogram of the profit is like a normal distribution while the histograms of all raw material prices are uniform distributions. This study also presented the integration of different computer-aided tools and methods facilitating the implementation of the proposed method.

7.9 Nomenclature 7.9.1 Indexes m h k, k’ mk ph q r sr t

Index used to represent the raw materials Index used to represent the harvesting sites Indexes used to denote the possible products Index used for the markets Index used for the secondary processing plants Index used for the economies of scale Index used to define the processing technologies in the first processing stage Index used for the processing routes in the second processing stage Index used for the periods of time

216 Chapter 7

7.9.2 Variables Symbols used for the costs associated to the activities in the supply chain (e.g., capital cost, storage cost, operating cost)

C, C2, Cm raw

Cost material Ctransp EI M Mdis P Pdfeed Ptotal, Pfeed Profit

Symbol for the raw material production cost This is used for the transportation cost for each transportation type Overall environmental impact assessed through the Eco-Indicator99 method Symbol used to define the amount of raw material for the different activities in the supply chain (e.g., biomass production, biomass transportation, biomass processing) Variable used in the reformulations of the disjunctions presented in the paper for the activities, in which the biomass is involved Symbol used to express the amount of product for the activities in the supply chain (e.g., product storage, product transportation, product selling) Representation used to discretize the amount of processed product in the second processing stage Variables used for the amount of obtained product from the different processing stages Net annual profit for the implementation of the system

sale

Revenue products y, y2, yfeed, y2feed, ym

Revenue for selling of products Symbols used for the binary variables of the model (storage, transportation, processing, selecting of equipment)

7.9.3 Parameters conversion factorstage1

αm;k;r

Parameters used to denote the conversion factors for the different processing stages ,

conversion factorstage2

αk;r;sr;k0 A, A2, Am B, B2, Bm Hmax KF lowPfeed, uppPfeed M

P UC, UC2, UCm UCtransp UEco

Characters used to identify the fixed capital cost for the processing technologies and processing facilities Symbols used to denote the unitary variable capital cost for the processing technologies and processing facilities Parameter used to represent the value of the maximum number of periods Symbol that represents the annualization factor for the capital costs Lower and upper limits for the processing activity in the second processing stage Symbol used to represent the value of the parameters for the activities associated to the biomass in the supply chain (e.g., availability, maximum and minimum processing, maximum and minimum transportation) Symbol used for the parameters associated to the products in the supply chain (e.g., product demand, product transportation, product storage) Representations for the unitary cost for the activities of the supply chain (e.g., processing of biomass and intermediate products) Representation for the unit transportation cost for each transportation type Symbol used for the unit values for the Eco-Indicator99 for the different activities of the supply chain

Stochastic Design of Biorefinery Supply Chains 217

References Chen, X., Jiang, Z. H., Chen, S., & Qin, W. (2010). Microbial and bioconversion production of D-xylitol and its detection and application. International Journal of Biological Sciences, 6(7), 834. Chen, Y., Zhou, T., Liu, D., Li, A., Xu, S., Liu, Q., & Ying, H. (2013). Production of butanol from glucose and xylose with immobilized cells of Clostridium acetobutylicum. Biotechnology and Bioprocess Engineering, 18(2), 234
241. Ferris, C. F., Jain, R., & Dirkse, S. (2010). GDXMRW: Interfacing GAMS and MATLAB. ,http://pages.cs. wisc.edu/Bferris/matlab/gdxmrw.pdf. Consulted on December, 2015. Granstro¨m, T. B., Izumori, K., & Leisola, M. (2007). A rare sugar xylitol. Part I: The biochemistry and biosynthesis of xylitol. Applied Microbiology and Biotechnology, 74(2), 277
281. Jones, D. T., & Wood, R. D. (1986). Acetone-butanol rementation revisited. Microbiology Reviews, 50(4), 484
524. Morales-Rodriguez, R., Meyer, A. S., Gernaey, K. V., & Sin, G. (2011). A framework for model-based optimization of bioprocesses under uncertainty: Identifying critical parameters and operating variables. Computer-Aided Chemical Engineering, 29, 1455
1459. Saha, B. C., & Nakamura, L. K. (2003). Production of mannitol and lactic acid by fermentation with Lactobacillus intermedius NRRL B-3693. Biotechnology and Bioengineering, 82(7), 864
871. Santiban˜ez-Aguilar, J. E., Gonza´lez-Campos, J. B., Ponce-Ortega, J. M., Serna-Gonza´lez, M., & El-Halwagi, M. M. (2014). Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives. Journal of Cleaner Production, 65, 270
294. Santiban˜ez-Aguilar, J.E., Morales-Rodriguez, R., Gonza´lez-Campos, J.B., & Ponce-Ortega, J.M. (2016). Stochastic design of biorefinery supply chains considering economic and environmental objectives. Journal of Cleaner Production, 136, 224
245. Sin, G., Gernaey, K. V., & Lantz, A. E. (2010). Good modeling practice for PAT applications: propagation of input uncertainty and sensitivity analysis. Biotechnology Progress, 25, 1043
1053. Sukumaran, R. K., Gottumukkala, L. D., Rajasree, K., Alex, D., & Pandey, A. (2011). Butanol fuel from biomass: Revisiting ABE fermentation. Biofuels: Alternative feedstocks and conversion processes. (pp. 571
586). Amsterdam: Academic Press. Tochampa, W., Sirisansaneeyakul, S., Vanichsriratana, W., Srinophakun, P., Bakker, H. H., & Chisti, Y. (2005). A model of xylitol production by the yeast Candida mogii. Bioprocess and Biosystems Engineering, 28(3), 175
183.

CHAPTER 8

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 8.1 Introduction The implementation of supply chains (SCs) based on biomass conversion requires the exploration of various aspects, including the selection of processing technologies, configuration of the SC, portfolio of products as well as the feedstock selection. One important feature of this system is that the composition of the available biomass changes drastically throughout the year because it depends significantly on the climatic conditions. Thus the dynamic behavior of this process is an important issue that must be considered. This chapter presents a dynamic optimization model for the optimal planning of a distributed biorefinery system taking into account the time dependence of the involved variables and parameters. In addition, this chapter incorporates a model predictive control methodology to obtain the behavior of the storage and order of the SC, where the objective function is the difference between the required and satisfied demands in the markets. Therefore this study considers relevant issues such as the multiple available biomass feedstocks at various harvesting sites, the availability and seasonality of biomass resources, potential geographical locations for processing plants that produce multiple products using diverse production technologies, economies of scale for the production technologies, demands and prices of multiple products in each consumer, locations of storage facilities, and a number of transportation modes between the SC components. The model was applied to a case study for a distributed biorefinery system in Mexico, where the SC configuration and operating conditions were optimized involving its rigorous dynamic behavior. Furthermore, the solutions obtained by the model illustrate that the SCs based on biomass conversion are seriously affected by the availability of bioresources over the time.

8.2 Problem Statement The problem addressed in this chapter involves the optimal planning of a SC based on biomass processing considering as objective function the maximization of the satisfied demand to regulate the dynamic behavior of the SC through a nonlinear model predictive Strategic Planning for the Sustainable Production of Biofuels. DOI: https://doi.org/10.1016/B978-0-12-818178-2.00008-0 © 2019 Elsevier Inc. All rights reserved.

219

220 Chapter 8 control (NLMPC) method. As shown in Fig. 8.1, the SC includes a set of suppliers, multiproduct processing facilities, distribution centers, and consumers. The SC can produce biofuels and other specialty chemicals from different types of biomass that are available from a number of potential supplier allocations. The suppliers have given capacities for producing raw materials that change over the time. Thus Fig. 8.1 shows the network superstructure with possible flow links between its components since the SC considers two types of flows. On the one hand, the flow of raw material and products between the different locations of the SC. On the other hand, the superstructure (see Fig. 8.1) allows the information flows among the diverse locations; for instance, the raw material can be distributed from the suppliers to the processing facilities and the information can be sent from the processing facilities to the suppliers.

Figure 8.1 Superstructure for the dynamic supply chain based on biomass conversion. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixedinteger dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 221 Furthermore, the superstructure shows that each processing plant can use different production technologies to obtain multiple products from several raw materials. Thus the processing plants are modeled in terms of a set of production routes that determine multiple output materials (biofuels and other chemicals) from several potential input materials (biomass). Additionally, each element of the SC is modeled in a dynamic way to take into account the storage for the different materials.

8.3 Mixed-Integer Dynamic Mathematical Optimization Model The following indexes are used in the model formulation. The considered locations are the ones associated with suppliers, processing plants, and distribution centers, denoted by the indexes s, ph, and dc, respectively. Additionally, the index m is used for raw materials and the index p denotes products. Moreover, the processing technologies are given by the index r and the economies of scale are specified by the index q. Finally, the finite elements are denoted by the index e and the orthogonal collocation points are represented by the index o.

8.3.1 Raw Material Inventory at Suppliers


 suppliers ðtÞ is modeled through a differential The raw material inventory at the suppliers Im;h
 prod equation that takes into account the production rate of raw material in suppliers Mm;h ðt Þ as well as the from the
 raw material that is transported
 suppliers to the processing facilities h2ph h2main Mm;h;ph ðtÞ and the main process plant Mm;h ðtÞ : h i suppliers ðtÞ d Im;h X h2ph prod h2main ðtÞ 2 Mm;h;ph ðtÞ 2 Mm;h ðtÞ; ’mAM; hAH (8.1) 5 Mm;h dt phAPH

8.3.2 Raw Material Inventory at Processing Facilities


 rm2plants The change in the raw material inventory at the processing facilities Im;ph ðtÞ is equal to the sum of the transportation rate from the suppliers to the processing plants ! processing
 route h2ph Mem;h;ph ðtÞ minus the total raw material that is used for processing Mm;r;ph ðtÞ in order to obtain the products: h i rm2plants processing d Im;ph ðt Þ X route X h2ph Mem;h;ph ðtÞ 2 Mm;r;ph ðtÞ; 5 dt rAR hAH

’mAM; phAPH

(8.2)

222 Chapter 8

8.3.3 Raw Material Inventory at Main Processing Facility In the same way, the change in the inventory at the main processing facility  rm2main Im ðtÞ is defined by the sum of the raw material rate from the supplier to the main
 ð t Þ minus the raw material that is distributed to the processing routes plant Meh2main m;h ! main2processing route

ðt Þ :

Mm;r

  main2processing X X route d Imrm2main ðtÞ h2main ðtÞ; 5 Mem;h ðtÞ 2 Mm;r dt rAR hAH

’mAM

(8.3)

8.3.4 Product Inventory at Processing Facilities On the other hand, the products can be stored in the processing plants. Thus the change in
 pr2plants ðtÞ is equal to the rate in which the product is produced the product inventory Ik;ph ! processing route

Pk;r;ph

ðtÞ

minus the rate in which the product is transported to the distribution


 ph2dc centers Pk;ph;dc ðtÞ : h i pr2plants ðt Þ d Ik;ph dt

5

X rAR

processing route Pk;r;ph

ðtÞ 2

X

Pph2dc k;ph;dc ðtÞ;

’kAK; phAPH

(8.4)

dcADC

8.3.5 Product Inventory at Main Processing Facility The definition of the product inventory for the main processing facility is determining in a similar way than for the distributed facilities. Thus the production rate and the transportation to the distribution centers are defined by the main processing plant: h i main2processing d Ikpr2main ðtÞ X X route Pk;r ðt Þ 2 Pmain2dc ðtÞ; ’kAK (8.5) 5 k;dc dt rAR dcADC

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 223

8.3.6 Product Inventory at Distribution Centers


 distr2centers The change in the product inventory for the distribution centers Ik;dc ðtÞ depends on the velocity at which theproduct arrives from the processing plants

 main2dc sale Peph2dc ð t Þ; Pe ð t Þ and the velocity at which the product is sold P ð t Þ : k;dc k;dc k;ph;dc h i distr2centers d Ik;dc ðtÞ X ph2dc main2dc ðtÞ 1 Pek;dc ðtÞ 2 Psale 5 Pek;ph;dc ’kAK; dcADC (8.6) k;dc ðtÞ; dt phAPH

8.3.7 Continuity of the Inventories at the Beginning and End of the Time Horizon In order to guarantee the continuity of the inventories for each horizon of time, the inventory level of any material in any location at the beginning of the horizon  
 locations ðtÞ has to be equal to the inventory level for the same location and Imaterials;locations t50 
  locations ðtÞ material at the end of the considered horizon Imaterials;locations : t5Horizon

  locations ðtÞ Imaterials;locations

t50

  locations 5 Imaterials;locations ðtÞ

t5Horizon

;

’M , KAMATERIALS; H , PH , DC , MAINALOCATIONS (8.7)

8.3.8 Raw Material Orders From General Facilities to Suppliers Additionally, the model allows transmitting information about the behavior and requirement of the SC between the different locations. This information is transmitted through orders from a superior to another inferior location. The variation of the order from the facilities to
 s2facilities the suppliers Om;h;ph ðtÞ is given by the raw material requirement from the processing
 plants to the suppliers Rqfacilities m;h;ph ðt Þ minus the raw material that is sent from the suppliers
 h2ph ðt Þ : to satisfy the raw material requirements in the processing plants Mm;h;ph h i d Os2facilities ðtÞ m;h;ph dt

h2ph 5 Rqfacilities m;h;ph ðtÞ 2 Mm;h;ph ðt Þ;

’mAM; hAH; phAPH

8.3.9 Raw Material Orders From the Main Facility to Suppliers

(8.8)


 The raw material orders from the main facility to suppliers Os2main ð t Þ is given by the
m;h main requirements from the main facility to the suppliers Rqm;h ðtÞ minus the raw material that

224 Chapter 8 is received in the main plant to fulfill the raw material demands in the main plant
 h2main ðtÞ : Mm;h h i s2main d Om;h ðtÞ dt

h2main 5 Rqmain ðtÞ; m;h ðtÞ 2 Mm;h

’mAM; hAH

(8.9)

8.3.10 Product Orders From the Distribution Centers to the Facilities The distribution centers require products from the processing facilities; in this context, the variation in the product order from the distribution centers to the processing facilities
 ph2dc ðtÞ is equal to the product requirement in the distribution centers from the Ok;ph;dc
 ð Þ minus the product that arrives to the distribution centers processing facilities Rqph2dc t k;ph;dc
 ph2dc Pk;ph;dc ðtÞ : h i ph2dc d Ok;ph;dc ðt Þ dt

ph2dc ðtÞ 2 Pph2dc 5 Rqk;ph;dc k;ph;dc ðtÞ;

’kAK; phAPH; dcADC

(8.10)

8.3.11 Product Orders From the Distribution Centers to the Main Facility The variation of the product orders from distribution centers to the main processing plant

 main2dc ð t Þ is given by the total product requirement Rq ð t Þ minus the product Omain2dc k;dc k;dc
 ð t Þ : that is transported to the distribution centers to satisfy the product demand Pmain2dc k;dc h i d Omain2dc ð t Þ k;dc dt

5 Rqmain2dc ðtÞ 2 Pmain2dc ðtÞ; k;dc k;dc

’kAK; dcADC

(8.11)

8.3.12 Product Orders From Consumers to the Distribution Centers It is worth noting that each distribution center has a specific consumer. Thus the distribution
center can fulfill the demand through the flow rate
that is sent  to the final dc consumer Psale ð t Þ ; additionally, the consumer requirement Rq ð t Þ is given by: k;dc k;dc h i d Odc k;dc ðtÞ sale ’kAK; dcADC (8.12) 5 Rqdc k;dc ðt Þ 2 Pk;dc ðtÞ; dt

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 225

8.3.13 Continuity of the Inventories at the Beginning and End of the Horizon The continuity of the orders at the end of the horizon should be guaranteed. Thus the value of orders of any material from one location to another location is equal when the time is equal to zero and at the end of the time horizon:   ’M , KAMATERIALS;   locations Olocations ð t Þ 5 O ð t Þ ;  materials;loc1;loc2 materials;loc1;loc2  H , PH , DC , MAINALOC1; LOC2 t50 t5Horizon (8.13)

8.3.14 Availability of Raw Material


 prod The raw material production in any harvesting site in any time Mm;h ðtÞ is limited by a
 ð Þ because the raw material t maximum value for the raw material production max M prod m;h production depends on the time for the climatic conditions: max

prod M prod m;h ðt Þ $ Mm;h ðtÞ;

8.3.15 Constraints for the Demand The product demand that can be satisfied in demand of any product in a market for each

’mAM; hAH






a market Psale k;dc ðtÞ
demand time Pk;dc ðtÞ :

Pdemand ðtÞ $ Psale k;dc k;dc ðt Þ;

(8.14)

is limited by the total

’kAK; dcADC

(8.15)

8.3.16 Constraints to Control the Orders From Consumers to Distribution Centers The main control actions are the level of the orders from consumers to distribution centers
Odc k;dc ðtÞ ; in this context, the level of the order for the first orthogonal point for any finite element is equal to the second orthogonal point for the same finite element. Additionally, the level of the orders for the third orthogonal point is equal to zero for any finite element, because the response time of the SC is equal to the size of each finite element (i.e., if the product demand is not satisfied at the end of the finite element the order is fixed to zero for the next finite element):   dc   Odc ’kAK; dcADC (8.16) k;dc ðt Þ tAðo51Þ 5 Ok;dc ðt Þ tAðo52Þ ;   (8.17) Odc ’kAK; dcADC k;dc ðtÞ tAðo53Þ 5 0;

226 Chapter 8

8.3.17 Constraints for Transported Flow Rate at the Outlet and Inlet Locations The model formulation includes several constraints for the transported flow rates between the locations. The transportation flow rate from location 1 to location 2 for any finite element and orthogonal collocation point is equal to the transportation flow rate to the inlet of location 2 for the next orthogonal collocation point (see Eqs. 8.188.21). It is important to note that for the last orthogonal collocation point in the last finite element, the next orthogonal point is the first orthogonal collocation point for the first finite element (see Eqs. 8.228.25).     h2ph ðtÞ 5 Meh2ph ð t Þ ; ’mAM; hAH (8.18) Mm;h;ph m;h;ph  tAf ðe;oÞ

 h2main  ðtÞ Mm;h

tAf ðe;oÞ

  ph2dc ðtÞ Pk;ph;dc

tAf ðe;o11Þ

  5 Meh2main ð t Þ  m;h

  ph2dc 5 Pek;ph;dc ðtÞ

tAf ðe;oÞ

tAf ðe;o11Þ

tAf ðe;o11Þ

 main2dc  ðtÞ Pk;dc

tAf ðe;oÞ

  5 Pemain2dc ð t Þ  k;dc



;

tAf ðe;o11Þ



 5 Meh2ph ; m;h;ph ðt Þ t50

t5Horizon

t50

  ph2dc ðtÞ Pk;ph;dc

t5Horizon

  Pmain2dc ð t Þ  k;dc

  5 Meh2main ð t Þ  m;h

  ph2dc 5 Pek;ph;dc ðtÞ

t5Horizon

t50

’mAM; hAH

’kAK; phAPH; dcADC

 h2ph ðtÞ Mm;h;ph t5Horizon

 h2main  Mm;h ðtÞ

;

;

;

’kAK; dcADC ’mAM; hAH

;

’mAM; hAH

’kAK; phAPH; dcADC

 main2dc  5 Pek;dc ðtÞ

t50

;

’kAK; dcADC

(8.19) (8.20) (8.21) (8.22) (8.23) (8.24) (8.25)

8.3.18 Transportation Limits There are enforced transportation limits for the flow rates between the different locations because the transportation activity cannot be done in an unlimited way; this is, the transportation rate is limited for the transportation equipment (a car, a truck, etc.). In this context, Eqs. (8.26)(8.33) are used to define the minimum and maximum transportation flow rates between the different locations. h2ph h 2 ph h2ph ðtÞ # MAX M m;h;ph Uym;h;ph ðtÞ; Mm;h;ph h2main h 2 main h2main Mm;h ðtÞ # MAX M m;h Uym;h ðtÞ;

’mAM; hAH ’mAM; hAH

(8.26) (8.27)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 227 MAX ph 2 dc ph2dc Pph2dc P k;ph;dc Uyk;ph;dc ðtÞ; k;ph;dc ðtÞ #

’kAK; phAPH; dcADC

main2dc 2 dc main2dc Pk;dc ðtÞ # MAX P main Uyk;dc ðtÞ; k;dc h2ph h 2 ph h2ph Mm;h;ph ðtÞ $ MIN M m;h;ph Uym;h;ph ðtÞ; h2main h 2 main h2main ðtÞ $ MIN M m;h Uym;h ðtÞ; Mm;h MIN ph 2 dc ph2dc P k;ph;dc Uyk;ph;dc ðtÞ; Pph2dc k;ph;dc ðt Þ $

’kAK; dcADC ’mAM; hAH ’mAM; hAH

’kAK; phAPH; dcADC

main2dc 2 dc main2dc ðtÞ $ MIN P main Uyk;dc ðtÞ; Pk;dc k;dc

’kAK; dcADC

(8.28) (8.29) (8.30) (8.31) (8.32) (8.33)

8.3.19 Processing


 main2produced The obtained products Pproduced ð t Þ; P ð t Þ in the processing facilities are equal k;m;r;ph k;m;r ! processing main2processing product

to the distributed raw materials

Mm;k;r;ph

product

; Mm;k;r

ðtÞ

multiplied by a


 conversion factor αconversion . It is worth noting that the time difference between the m;k;r beginning of processing and the obtaining of products is equal to the time from one orthogonal collocation point to another. Eqs. (8.34)(8.36) represent the processing for the secondary processing facilities and Eqs. (8.378.39) model the processing in the main facilities. processing route Mm;r;ph

ðtÞ 5

X

processing product Mm;k;r;ph ðtÞ;

’mAM; rAR; phAPH

(8.34)

kAK processing  product  conversion Mm;k;r;ph ðtÞ αm;k;r

tAf ðe;oÞ

  5 Pproduced ð t Þ  k;m;r;ph

processing route Pk;r;ph ðtÞ 5

X

tAf ðe;o11Þ

Pproduced k;m;r;ph ðtÞ;

;

’mAM; kAK; rAR; phAPH (8.35)

’kAK; rAR; phAPH

(8.36)

mAM main2processing route Mm;r

ðtÞ 5

X

main2processing product Mm;k;r

ðtÞ;

’mAM; rAR

(8.37)

kAK main2processing  product  conversion αm;k;r Mm;k;r ðtÞ tAf ðe;oÞ

  5 Pmain2produced ð t Þ  k;m;r

tAf ðe;o11Þ

;

’mAM; kAK; rAR (8.38)

228 Chapter 8 main2processing route Pk;r ðtÞ 5

X

Pmain2produced ðtÞ; k;m;r

’kAK; rAR

(8.39)

mAM

8.3.20 Economies of Scale for Processing Facilities Two disjunctions are used for modeling the economies of scale for the operating and capital costs of the proposed SC. The first disjunction states that processing is necessary over the ! processing time; this possibility is determined by the binary variable

time route ym;k;r;ph;q

ðtÞ , which has a

dependence of the time. If the raw material were processed in the period of time t the ! processing binary variable

time route ym;k;r;ph;q

ðtÞ

takes the value of 1 for this period of time. Moreover,

another disjunction is used to calculate the capital cost; in this case, the binary variable processing ! route

ym;k;r;ph;q

is not a function of time and it is only activated when at least one of the first

binary variables

processing ! time route ym;k;r;ph;q

is equal to 1; otherwise, the binary variable is equal to

zero. The two disjunctions for the secondary processing facilities are formulated as follows: 3 2 processing

6 time route Y m;k;r;ph;q ðtÞ 6 6 6 processing processing 6 3t6 product route UPP 6 Mm;k;r;ph ðtÞ # M m;k;r;ph;q 6 6 processing processing 4 route product LOW Mm;k;r;ph $ M m;k;r;ph;q 2

7 7 7 7 7 7; 7 7 7 5

’mAM; kAK; rAR; phAPH

3

processing route 6 7 3q4 Ym;k;r;ph;q 5; CAP processing CAP FIX VAR Cm;k;r;ph;q 5 Cm;k;r;ph;q 1 Cm;k;r;ph;q U M m;k;r;ph;

’mAM; kAK; rAR; phAPH

Previous disjunctions are reformulated with the purpose of solving the mathematical programming model; it is important to note that the sum of the binary variables

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 229 processing ! route ym;k;r;ph;q

with respect to the interval for the economies of scale is equal to 1 because

only one interval should be selected. X

processing route ym;k;r;ph;q

5 1;

’mAM; kAK; rAR; phAPH

qAQ

The raw material that is sent to processing for all the times processing product dis Mm;k;r;ph;q

sections

! ðtÞ

processing ! route LOW Mm;k;r;ph;q

bounds

that are limited between upper

! processing product Mm;k;r;ph ðtÞ

processing processing product route UPP M m;k;r;ph;q ðtÞ # M m;k;r;ph;q

dis

processing processing processing product route LOW time route M m;k;r;ph;q ðtÞ $ M m;k;r;ph;q U y m;k;r;ph;q ðtÞ; processing product Mm;k;r;ph ðtÞ 5

X



dis

time

processing route y m;k;r;ph;q ðtÞ;

processing product Mm;k;r;ph;q

qAQ

ðtÞ;

and lower

processing time route ym;k;r;ph;q

! processing product dis Mm;k;r;ph;q ðtÞ

dis

is discretized in q

processing ! route UPP Mm;k;r;ph;q

when the value of the binary variable

to 1; otherwise, the value for the discretized variable

(8.40)

! ðtÞ

is equal

is equal to zero:

’mAM; kAK; rAR; phAPH; qAQ

(8.41)

’mAM; kAK; rAR; phAPH; qAQ

(8.42)

’mAM; kAK; rAR; phAPH

(8.43)

Additionally, the capital cost for the processing facilities depends on the maximum treated amount in a given processing plant, the maximum processed raw material is discretized, and it has to be greater than all discretized variables: X CAP processing CAP 2 dis processing M m;k;r;ph 5 M m;k;r;ph;q ; ’mAM; kAK; rAR; phAPH (8.44) qAQ

dis

processing product M m;k;r;ph;q

ðtÞ # CAP 2 dis M processing m;k;r;ph;q ;

’mAM; kAK; rAR; phAPH; qAQ

(8.45)

230 Chapter 8 CAP 2 dis

processing route processing UPP M m;k;r;ph;q # M m;k;r;ph;q




processing route Uym;k;r;ph;q

;

’mAM; kAK; rAR; phAPH; qAQ (8.46)



CAP depends on two parts: a fixed cost Then, the capital cost Cm;k;r;ph;q

processing ! route FIX Cm;k;r;ph;q Uym;k;r;ph;q

plus another part that is influenced by the maximum amount treated for a given processing
 VAR UCAP M processing facility Cm;k;r;ph;q : m;k;r;ph CAP Cm;k;r;ph;q

processing route FIX 5 Cm;k;r;ph;q Uym;k;r;ph;q

VAR 1 Cm;k;r;ph;q U

CAP

processing Mm;k;r;ph ;

’mAM; kAK; rAR; phAPH; qAQ

(8.47)

Finally, there are two additional relationships ! for the binary variables. These relationships ensure that the binary variable ! variables

processing time route ym;k;r;ph;q

ðtÞ

processing route ðMaxPeriodsÞUym;k;r;ph;q

$

processing route ym;k;r;ph;q

is equal to 1 if and only if one of the binary

is equal to 1: X

processing time route ym;k;r;ph;q

ðtÞ;

’mAM; kAK; rAR; phAPH; qAQ

tAf ðe;oÞ

(8.48) processing route ym;k;r;ph;q

#

X

processing time route ym;k;r;ph;q ðtÞ;

’mAM; kAK; rAR; phAPH; qAQ

(8.49)

tAf ðe;oÞ

On the other hand, the processing in the main facility is modeled in a similar way as the processing in secondary processing plants. First, the disjunctions are stated as follows: 3 2 main 2 processing

6 time route Y m;k;r;q ðtÞ 6 6 6 main2processing main 2 processing 3t6 route UPP 6 M product ðtÞ # M m;k;r;q 6 m;k;r 6 main2processing main 2 processing 4 route product Mm;k;r $ LOW M m;k;r;q

7 7 7 7 7; 7 7 7 5

’mAM; kAK; rAR

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 231 2

main2processing route 6 Ym;k;r;q 3q4 main2CAP main2FIX main2VAR CAP main 2 processing Cm;k;r;q 5 Cm;k;r;q 1 Cm;k;r;q U M m;k;r

3 7 5;

’mAM; kAK; rAR

Previous disjunctions are reformulated as follows: X

main2processing route ym;k;r;q

5 1;

’mAM; kAK; rAR

(8.50)

qAQ main2processing product Mm;k;r;q

ðtÞ #

UPP

main2processing product Mm;k;r;q

ðtÞ $

LOW

dis

dis

main2processing route Mm;k;r;q

U

time

main2processing route Mm;k;r;q

U

time

main2processing product Mm;k;r ðt Þ 5

X

dis

main2processing route ym;k;r;q

ðtÞ;

main2processing route ym;k;r;q

ðtÞ;

main2processing product Mm;k;r;q

ðtÞ;

’mAM; kAK; rAR; qAQ (8.51) ’mAM; kAK; rAR; qAQ (8.52)

’mAM; kAK; rAR

(8.53)

’mAM; kAK; rAR; qAQ

(8.54)

qAQ

dis

main 2 processing product 2 processing M m;k;r;q ðtÞ # CAP 2 dis M main ; m;k;r;q CAP

main2processing Mm;k;r 5

X

CAP 2 dis

2 processing M main ; m;k;r;q

’mAM; kAK; rAR

(8.55)

qAQ

CAP 2 dis

main2processing route main2processing UPP Mm;k;r;q # Mm;k;r;q

main2processing route Uym;k;r;q

;

’mAM; kAK; rAR; qAQ (8.56)

main2processing route main2CAP main2FIX Cm;k;r;q 5 Cm;k;r;q Uym;k;r;q

main2processing main2VAR CAP 1 Cm;k;r;q U Mm;k;r ;

’mAM; kAK; rAR; qAQ (8.57)

232 Chapter 8 main2processing route ðMaxPeriodsÞUym;k;r;q

X

$

main2processing time route ym;k;r;q ðtÞ;

’mAM; kAK; rAR; qAQ

tAf ðe;oÞ

(8.58) main2processing route ym;k;r;q

#

X

time

main2processing route ym;k;r;q ðtÞ;

’mAM; kAK; rAR; qAQ

(8.59)

tAf ðe;oÞ

8.3.21 Storage Modeling The storage activity is divided in six different types: the raw material storage in suppliers

 suppliers rm2plants ðtÞ , the raw material storage in secondary processing plants Im;ph ðtÞ as well Im;h   as the raw material storage in the main processing facility Imrm2main ðtÞ . Also, the product
 pr2plants can be stored in the two types of processing facilities Ik;ph ðtÞ; Ikpr2main ðtÞ and finally,
 distr2centers ðtÞ . The stored amount of the product is stored in the distribution centers Ik;dc material is defined by the inventory level in the different locations and these inventories are limited by upper (see Eqs. 8.608.65) and lower limits (see Eqs. 8.668.71). In comparison with the relationships between the binary variables for the economies of scale (see Eqs. 8.48, 8.49, 8.58, and 8.59), there are two types of binary variables for the storage related by Eqs. (8.72)(8.83). There are binary variables depending on
rm 2 plants 2 plants 2 main 2 main ðtÞ; time ym;ph ðtÞ; time yrm ðtÞ; time y pr ðtÞ; time y pr ðtÞ; and time time ysuppliers m k;ph k m;h
time distr 2 centers ðtÞÞ and time-invariant binary variables ysuppliers y k;dc ; yrm2plants ; yrm2main ; m m;h m;ph pr2plants distr2centers ; ypr2main ; and yk;dc Þ: yk;ph k suppliers Im;h ðtÞ # UPP I suppliers Utime y suppliers ðtÞ; m;h m;h rm2plants 2 plants time rm 2 plants ðtÞ # UPP I rm U y m;ph ðtÞ; Im;ph m;ph

’mAM; hAH ’mAM; phAPH

2 main time rm 2 main Imrm2main ðtÞ # UPP I rm U ym ðtÞ; m pr2plants 2 plants time pr 2 plants Ik;ph ðtÞ # UPP I pr U y k;ph ðtÞ; k;ph

(8.60) (8.61)

’mAM

(8.62)

kAK; phAPH

(8.63)

2 main time pr 2 main U yk ðtÞ; Ikpr2main ðtÞ # UPP I pr k distr2centers 2 centers time distr 2 centers Ik;dc ðtÞ # UPP I distr U y k;dc ðtÞ; k;dc

kAK

(8.64)

kAK; dcADC

(8.65)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 233 suppliers Im;h ðtÞ $ LOW I suppliers Utime y suppliers ðtÞ; m;h m;h

’mAM; hAH

rm2plants 2 plants time rm 2 plants ðtÞ $ LOW I rm U y m;ph ðtÞ; Im;ph m;ph

’mAM; phAPH

2 main time rm 2 main U ym ðtÞ; Imrm2main ðtÞ $ LOW I rm m pr2plants 2 plants time pr 2 plants Ik;ph ðtÞ $ LOW I pr U y k;ph ðtÞ; k;ph

(8.66) (8.67)

’mAM

(8.68)

kAK; phAPH

(8.69)

2 main time pr 2 main U yk ðtÞ; Ikpr2main ðtÞ $ LOW I pr k

kAK

distr2centers 2 centers time distr 2 centers Ik;dc ðtÞ $ LOW I distr U y k;dc ðtÞ; kAK; dcADC k;dc X time suppliers $ y m;h ðtÞ; ’mAM; hAH ðMaxPeriodsÞUysuppliers m;h

(8.70) (8.71) (8.72)

tAf ðe;oÞ

X

ðMaxPeriodsÞUyrm2plants $ m;ph

time rm 2 plants y m;ph ðtÞ;

’mAM; phAPH

(8.73)

tAf ðe;oÞ

X

ðMaxPeriodsÞUyrm2main $ m

time rm 2 main ym ðtÞ;

’mAM

(8.74)

’kAK; phAPH

(8.75)

tAf ðe;oÞ

ðMaxPeriodsÞUypr2plants $ k;ph

X

time pr 2 plants y k;ph ðtÞ;

tAf ðe;oÞ

$ ðMaxPeriodsÞUypr2main k

X

time pr 2 main yk ðtÞ;

’kAK

(8.76)

’kAK; dcADC

(8.77)

tAf ðe;oÞ

X

ðMaxPeriodsÞUydistr2centers $ k;dc

time distr 2 centers y k;dc ðtÞ;

tAf ðe;oÞ

ysuppliers # m;h

X

time suppliers y m;h ðtÞ;

’mAM; hAM

(8.78)

’mAM; phAPH

(8.79)

tAf ðe;oÞ

yrm2plants # m;ph

X

time rm 2 plants y m;ph ðtÞ;

tAf ðe;oÞ

X

yrm2main # m

time rm 2 main ym ðtÞ;

’mAM

(8.80)

’kAK; phAPH

(8.81)

tAf ðe;oÞ

ypr2plants # k;ph

X

time pr 2 plants y k;ph ðtÞ;

tAf ðe;oÞ

ykpr2main #

X tAf ðe;oÞ

time pr 2 main yk ðtÞ;

’kAK

(8.82)

234 Chapter 8 ydistr2centers # k;dc

X

time distr 2 centers y k;dc ðtÞ;

’kAK; dcADC

(8.83)

tAf ðe;oÞ

8.3.22 Operating Cost The operational cost is equal to a unitary operational cost by the processing flow rate of the raw material

processing product Mm;k;r;ph

processing plant Cm;k;r ;

ðtÞ;

processing main Cm;k;r

main2processing product Mm;k;r;ph

! multiplied !

ðtÞ , which

depends on the type of raw material m, the yielded product k, the used technology r, the processing facility as well as the time. It should be noted that this relationship is discretized over time in various orthogonal collocation points (o) and a given  number of finite  elements (e). For this reason, in order to calculate the total operating cost C OPERATIONAL , we need to integrate the individual operational cost with respect to the time as well as the sum of the individual operational cost for all raw materials, products, processing plants, and processing routes. t5HORIZON ð

C OPERATIONAL

5 t50 t5HORIZON ð

1 t50

processing plant Cm;k;r

X XX X

processing product UMm;k;r;ph

ðtÞdt

mAM kAK rAR phAPH

X XX

processing main2processing main product Cm;k;r UMm;k;r;ph

(8.84) ðtÞdt

mAM kAK rAR

8.3.23 Total Capital Cost   The total capital cost C CAPITAL is equal to the sum of the individual plants
 CAP main2CAP ; Cm;k;r;q Cm;k;r;ph;q : C CAPITAL 5

X XX X X mAM kAK rAR phAPH qAQ

CAP Cm;k;r;ph;q 1

X XXX

main2CAP Cm;k;r;q

(8.85)

mAM kAK rAR qAQ

8.3.24 Transportation Cost The transportation cost is determined by a unitary transportation cost per distance and the  amount of transported material Cmrm ; Ckp multiplied by the distance between the
 h2ph ph2dc h2main main2dc and the transported flow rate for a ; dh;main ; dph;dc ; dmain;dc considered locations dh;ph

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 235
 h2ph h2main main2dc given value of time Mm;h;ph ðtÞ; Mm;h ðtÞ; Pph2dc ð t Þ; P ð t Þ . For this reason, it is k;dc k;ph;dc necessary to carry out the integral with respect to the time to obtain the total transportation   cost C TRANSPORTATION . t5HORIZON ð

C

5

TRANSPORTATION

t50 t5HORIZON ð

t50 t5HORIZON ð

t50 t5HORIZON ð

t50

XX X

h2ph h2ph Cmrm Udh;ph UMm;h;ph ðtÞdt

mAM hAH phAPH

XX

h2main h2main ðtÞdt Cmrw Udh;main UMm;h

mAM hAH

X X X

(8.86) ph2dc Ckp Udph;dc UPph2dc k;ph;dc ðt Þdt

kAK phAPH dcADC

X X

main2dc Ckp Udmain;dc UPmain2dc ðtÞdt k;dc

kAK dcADC

8.3.25 Storage Cost   The storage cost CSTORAGE is divided in two parts: the first part considers the capital cost for storage and the second part considers the operational cost for storage that depends on the inventory level over time. The capital cost for storage considers a fixed part, which is equal to zero in all cases plus a term that depends on the maximum amount of the stored material for all time. This term takes into account a unitary
 suppliers rm2plants pr2plants pr2main rm2main distr2centers ; Csm;ph ; Csm ; Csk;ph ; Csk ; Csk;dc storage cost Csm;h
2 plants multiplied by the maximum inventory level UPP I suppliers ; UPP I rm ; m;h m;ph UPP rm 2 main UPP pr 2 plants UPP pr 2 main UPP distr 2 centers Im ; I k;ph ; Ik ; I k;dc Þ

and the binary variable for the  rm2plants pr2plants pr2main rm2main distr2centers ; y ; y ; y ; y ; y . existence of the storage ysuppliers m k;dc k m;h m;ph k;ph


It is worth noting that the binary variable for the existence of storage is equal to 1 if
2 plants ðtÞ; time y rm ðtÞ; and only if at least one of the binary variables time y suppliers m;h m;ph pr 2 plants time rm 2 main ym ðtÞ; time y k;ph ðtÞ; time y kpr 2 main ðtÞ;

time distr 2 centers y k;dc ðtÞÞ

is equal to 1 for all

the time horizons. On the other
hand, the operational costs from the storages involve the integral with respect to  rm2main OP the time OP Cssuppliers ; OP Csrm2plants ; OP Csm ; Cspr2plants ; OP Cspr2main ; OP Csdistr2centers k;dc m;h m;ph k;ph k

236 Chapter 8


suppliers rm2plants multiplied by the level inventory for the different types of storage Im;h ðtÞ; Im;ph ðtÞ; pr2plants pr2main rm2main distr2centers Im ðtÞ; Ik;ph ðtÞ; Ik ðtÞ; Ik;dc ðtÞÞ.

ð8:87Þ

8.3.26 Net Annual Profit The net annual profit ðPROFIT  which is equal  saleÞconsiders the revenue for selling
products, sale the cost to a unitary product price C multiplied by the sold product Pk;dc ðtÞ , minus

k  prod prod ð Þ of raw material production Cm;h , multiplied by the produced raw material M t m;h   CAP the annualized total capital cost KF UC  , minus the total minus   operational cost TRANSPORTATION C OPERATIONAL , minus the transportation cost C , and minus the total  STORAGE  storage cost C . t5HORIZON ð

PROFIT

5 t50

X X kAK dcADC

t5HORIZON ð

Cksale UPsale k;dc ðt Þdt 2 t50

XX

prod prod Cm;h UMm;h ðtÞdt

mAM hAH

2 KF UC CAP 2 COPERATIONAL 2 CTRANSPORTATION 2 CSTORAGE

8.3.27 Control Product Demand   The control objective function
CTRLDEMAND is equal to the square of the difference 
sale ð t Þ and the sold product P ð between the product demand Pdemand k;dc k;dc tÞ .

(8.88)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 237 t5HORIZON ð

CTRL

DEMAND

5 t50

i2

X X h demand sale dt Pk;dc ðtÞ2Pk;dc ðtÞ

(8.89)

kAK dcADC

This objective function is proposed to minimize the value of the difference between the demanded and sold product because an adequate parameter to assess the behavior of a SC is the control of the satisfied demand. This is an appropriate objective because this objective allows modifying the inventory levels and orders to get the maximum satisfied demand of a product. However, the gross profit changes with each control cycle because the solution of the SC is changed, which means the economic objective function is difficult to evaluate with the final configuration of the SC considering the proposed methodology.

8.4 Nonlinear Model Predictive Control Approach In this chapter, a strategy based on NLMPC is used because it allows us to take into account online implementation of the optimal control polices considering the presence of disturbances in a robust way. Mathematically the NLMPC problem addressed can be described as follows: Minimize

W ðx; uÞ ðNLMPCÞ subject to dx 5 f ðx; uÞ dt hðx; uÞ # 0 xL # x # xU uL # u # uU

where x is the state vector given for the distributed flow rate between the different allocations, as well as the production and consumption rate of products and raw materials, respectively; u is the vector of manipulated variables taken in this work as the inventories and the orders for the different considered places; W represents the objective function given by Eq. (8.89); f is the map representing the dynamic process behavior; and the system of constraints is given by h. Fig. 8.2 shows a representation of the parts of the NLMPC approach, where the manipulated variables, state variables, and variables to control are defined. Fig. 8.3 shows the basic idea behind the NLMPC approach: we would like to reach a target objective represented by Ysp using a set of values of the control actions u(t). The control action is divided into a set of time intervals. We assume that at the end of each interval the measurement of the target value Yk will be available. Then, when the measurement Yk is available, a set of dynamic optimization problems for the present time interval tk and for a given number of future time intervals tk11, tk12,. . .tnt is solved. It is important to note that n is the number of prediction intervals. The value of this number is set by trial and error and it influences the stability of the control strategy.

238 Chapter 8

Figure 8.2 Schematic representation of the proposed NLMPC approach for supply chains. NLMPC, Nonlinear model predictive control. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio FloresTlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Figure 8.3 NLMPC approach. Tnu is the number of control horizon intervals, Tnt is the number of predictions _ horizon intervals, ysp is the target set point, and y i are the values of the output-controlled variable obtained by applying input-manipulated variables denoted by ui. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Even when the control problem is solved for several control horizons giving rise to the control actions uk11, uk12,. . .unt, only the first one uk is applied to the underlying dynamic system. The remaining control actions are discarded. When a new measurement becomes available, the whole optimization process is repeated, advancing by one the control horizon

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 239 until the target value of the controlled variables is reached. It is worth noting that the proposed strategy (NLMPC) can take care of disturbances affecting the process and may be suitable for online computation depending on the computational cost of the presented approach, which depends on the number of finite elements and orthogonal points (number of variables and equations). In other words, the computational cost depends on the specific case study. In the next section, a detailed explanation about transforming the mixed-integer dynamic optimization (MIDO) problem into an MINLP is presented.

8.5 Solution Approach for the MIDO Problem The solution approach to the MIDO problem for the optimization of supply change is described as follows. The dynamic model described in terms of ordinary differential equations is fully discretized using the transcription approach (see Biegler, 2010). Thus the original MIDO problem is transformed into an MINLP problem whose solution can be obtained, in principle, by the standard methods that are available today. In particular, in this work the discretization of the underlying dynamic system is carried out through the use of the orthogonal collocation method on finite elements. Commonly, dynamic models are obtained by applying the first principles of mass, energy, and momentum balance relationships. In most cases, such dynamic models can be formulated as a set of differential-algebraic equations (DAE) as shown below: x_ 5 f ðx; y; uÞ;

xð0Þ 5 x0

0 5 gðx; y; uÞ

(8.90) (8.91)

where Eq. (8.90) represents the inventory and order balances in the differential equations of the MIDO problem, where x represents the states of the dynamic system defined in a semiexplicit form that for this specific case are the orders and inventory levels as function of the variables of the system. On the other hand, Eq. (8.91) symbolizes the equations of the algebraic system like the equations in the processing section of the mathematical formulation, some of the reformulated equations from disjunctions as well as the equations to obtain the main costs. Here, y represents the states of the algebraic system and u the manipulated variables. If we assume that the index of the DAE system is 1, then the initial conditions of the dynamic system are given by x0 , whereas similar initial conditions of the algebraic variables are obtained from Eq. (8.91). Moreover, additional constraints, which actually are not part of the DAE system, are commonly included in the MIDO problem to take care of constraints on product purity,

240 Chapter 8 Table 8.1: Summary of the presented MIDO problem MIDO Problem

Mathematical Formulation

Description

(8.90) (8.91)

(8.18.6), (8.88.12) (8.7), (8.13), (8.168.25), (8.348.40), (8.43), (8.44), (8.47), (8.50), (8.53), (8.55), (8.57), (8.848.89)

(8.92)

(8.14), (8.15), (8.268.33), (8.41), (8.42), (8.45), (8.46), (8.48), (8.49), (8.51), (8.52), (8.54), (8.56), (8.588.83)

Inventory and orders balances Equations in the processing section of the mathematical formulation, some reformulated equations from disjunctions as well as equations to obtain the main costs Minimum and maximum limits for transportation, storage and processing, and some relationships between the binary variables

From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

safety margins, bounds on some decision variables, etc. In general terms, this set of constraints reads as follows: hðx; y; uÞ # 0

(8.92)

In this case, relationship (8.92) denotes inequalities, for example, the minimum and maximum limits for transportation, storage and processing, and some relationships between binary variables. Table 8.1 summarizes the MIDO problem. As stated previously, in this work we will use the orthogonal collocation method on finite elements to discretize the underlying DAE system and the set of related constraints. In this approach, the solution space is divided into a set of e finite elements; within each finite element we assume that o internal collocation points will be used. Hence, x 5 x0e 1 he U

NP X

_ Ao ðτ ÞUx;

eANf

(8.93)

o51

where Nf is the number of finite elements, NP is the number of internal collocation points, he is the length of the finite elements e, τ is the scaled time coordinate normally bounded between [0,1], x0e is the value of the differential state at the beginning of the element j, x_ is the value of the first derivate of the differential state at the finite element j and the internal collocation point is o. Finally, Ao ðτ Þ is a polynomial in τof order NP , which reads as follows: ðτ Ao ðτ Þ 5 lk ðτ 0 Þdτ 0 (8.94) 0

where lk represents a basis function of the following Lagrange interpolation polynomial: lk ðτ Þ 5

τ 2 τ k0 τ k0 51;6¼k k 2 τ k0 NP

L

(8.95)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 241 Also, continuity between adjacent finite elements should be enforced: x0e11 5 x0e 1 he U

NP X

τ NP ;o Ux_o;e ;

e . 1; e # Nf

(8.96)

o51

Differential states are evaluated at each finite element e and each internal collocation point o:   (8.97) x_o;e 5 f xo;e ; yo;e ; uo;e Finally, the algebraic states y can also be evaluated using Lagrange polynomials as follows: y5

NP X

lk ðτ ÞUyo;e ;

eANf

(8.98)

o51

Once discretized, the solution to the resulting MINLP problem can be obtained using full space standard algorithms such as the discrete and continuous optimizer (DICOPT) or standard branch and bound (SBB) solvers available in the algebraic modeling language GAMS. Notice that DICOPT is based on the outer-approximation algorithm including the equality relaxation strategy; a detailed description can be found in Duran and Grossmann (1986), Kocis and Grossmann (1987), and Viswanathan and Grossmann (1990). Also, DICOPT is based on the assumption that the mixed-integer programming models can be solved efficiently while the nonlinear programming models can be expensive and difficult to solve. On the other hand, SBB is based on a combination of the standard branch and bound for mixed-integer linear programming, where one of the main assumptions is that the nonlinear programming problems can be solved quickly using a good restart procedure. DICOPT works better for models within an important and difficult combinatorial part, while SBB performs better for models with fewer discrete variables but more difficult nonlinear programming problems. It important to note that these solvers do no guarantee finding the global optimal solution; for the optimal solution of large-scale MINLP problems, decomposition approaches are normally required (see TerrazasMoreno, Flores-Tlacuahuac, & Grossmann, 2008).

8.6 Results The proposed methodology was applied to a case study to establish a distributed biorefinery system in Mexico. The raw materials can be produced in six different geographical regions as presented in Table 8.2, while the products are processed in six locations, five secondary processing plants and a main processing plant. The case involves a set of nine bioresources (wood chips, commercial wood, sugarcane, corn grain, sorghum grain, African palm, jatropha, and safflower). Furthermore, the availability of each bioresource in the different places depends on the region and season because weather conditions change drastically throughout the year in such countries as Mexico, which considerably affects the availability

242 Chapter 8 Table 8.2: Description of the geographical regions for the suppliers Geographical Region

Considered States

North West

Sinaloa, Sonora, Durango, Nayarit, Baja California, Baja California Sur

South

Chiapas, Tabasco, Campeche, Yucata´n, Quintana Roo, Oaxaca

West

´n, Jalisco, Guanajuato, Guerrero, Colima Michoaca

North

´n, Chihuahua, Zacatecas, Aguas Coahuila, Nuevo Leo Calientes

East

Veracruz, Puebla, Tamaulipas, Hidalgo, San Luis Potosı´

Center

Mexico City, Estado de Me´xico, Quere´taro, Tlaxcala, Morelos

Schematic Representation

From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

of bioresources. Two products are also considered (bioethanol and biodiesel). In addition, four different processing technologies are available (gasification and biosynthesis, hydrolysis and fermentation, gasification, chemical synthesis and transesterification). The conversion factors for the four different processing technologies shown were taken from Santiban˜ezAguilar, Gonza´lez-Campos, Ponce-Ortega, Serna-Gonza´lez, and El-Halwagi (2014). The discretized dynamic model consists of 335,402 continuous variables, 83,674 binary variables, and 412,988 constraints. It was coded in the GAMS software environment. This model was solved using a computer with two processors Intel Xenon e5345 at 2.40 GHz with 100 GB of RAM. The average CPU time for the solution of the MIDO model is approximately 48 hours using 20 finite elements. In this context, the CPU time was approximately 2.4 hours for each iteration of the NLMPC problem. However, the planning is done for an interval of 1 year. On the other hand, the quality of the solution is good since the mathematical model is almost linear (it is a quadratic programming problem). Although the multiplicity of solutions may be possible because the operational variables such as the amounts of distributed raw material or product change over time and a given amount transported in January may produce the same solution as another transported in September. Thus the solution of the mathematical programming model is a set of values for the operational and design variables that allow getting

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 243 Table 8.3: Behavior of the total annual profit for each control cycle Iteration of the Control Cycle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Total Expected Profit at the End of the Cycle (US$/year) 7.81 3 1006 4.48 3 1006 4.17 3 1006 4.81 3 1006 8.59 3 1006 2 1.41 3 1006 5.04 3 1006 2 1.74 3 1006 1.07 3 1007 4.26 3 1006 4.53 3 1006 1.07 3 1007 1.15 3 1007 5.17 3 1006 1.02 3 1007 5.24 3 1006 4.62 3 1006 3.66 3 1006 9.09 3 1006 1.37 3 1007

From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

a specific value of the objective. Notice that the objective function may take the same value within two or more different configurations. Table 8.3 shows the change in the gross profit with each control cycle. It shows that the total profit increases in most cases since the profit is corrected when the control actions are implemented in each control cycle. Also, it is possible to note that in some cases the expected total profit is negative for the change of the SC configuration at the end of the iteration of the control cycle. Fig. 8.4 shows the behavior of the raw material inventories for the suppliers; it is important to note that there are inventories only for three raw materials (wood chips, sorghum grain, and sweet sorghum) because the others raw materials are consumed and produced at the same rate. Additionally, for most of the suppliers, the raw material inventory is not constant, because the requirements continuously change; however, for the sorghum grain at the East supplier the inventory is almost at steady state conditions from the first third of the year. In addition, the value of the sorghum grain inventory is the greatest with respect to the supplier inventories. The raw material inventories at the processing facilities are presented in Figs. 8.58.7. Figs. 8.5 and 8.6 and show the inventories for the raw materials utilized for bioethanol production. The selected raw materials for bioethanol production are wood chips, sugarcane, sorghum grain, sweet sorghum, and corn grain. It should be noted that the objective function is focused on satisfying the demand. However, environmental and

244 Chapter 8

Figure 8.4 Raw material inventories for the suppliers. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 245

Figure 8.5 Wood chips, sugarcane, and corn grain inventories for the processing. From Jose´ Ezequiel Santiban˜ezAguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

246 Chapter 8

Figure 8.6 Sweet sorghum and sorghum grain inventories for the processing facilities. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixedinteger dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

economic objectives are not considered as in the paper by Santiban˜ez-Aguilar et al. (2014). For this reason, most of the raw materials have to be utilized to obtain a major amount of bioethanol. Fig. 8.5 illustrates the behavior for the wood chips, sugarcane, and corn grain, where the stored amount of wood chips is intermittent for most of the processing plants. However, the inventory in the main processing facility is almost constant over the year, although it is smaller than other inventory levels. Additionally, the inventory level behaviors for sugarcane and corn grain are similar, but the inventory level for the sugarcane is approximately 80% greater than the inventory level of corn grain. The inventory levels for the sugarcane and corn grain present a continuous decreasing over time for all secondary processing facilities, and for the main processing facilities the inventory for these raw materials is constant. Fig. 8.6 shows the inventory level for sorghum grain and sweet sorghum at the processing facilities. For the case of sorghum grain in the secondary processing plants, the inventory

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 247

Figure 8.7 Safflower and jatropha inventories for the processing facilities. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

level presents an increment at the beginning and a continuous decrement through the horizon time. Furthermore, the inventory level for sorghum grain at the main processing facility is almost constant. Alternatively, Fig. 8.6 presents the stored sweet sorghum in the secondary processing plants within a uniform decrement from the beginning of the time horizon to the end of the time horizon. Finally, Fig. 8.7 illustrates the raw material inventory for the biodiesel production, where the inventory levels show some intermittent pulses in the horizon. Table 8.4 shows the amount of raw materials used in the processing plants. As can be seen, the main raw material used to produce bioethanol is sugarcane (35%), and the second raw material is sweet sorghum (25.8%). In addition, the processing facility with higher use of raw materials for bioethanol production is the facility located in Salamanca. This is because this processing plant is located near the suppliers with the highest sugarcane and sweet sorghum production. On the other hand, the main raw material for the biodiesel production

Table 8.4: Selected raw materials in the processing plants Salamanca Tons (1023)

Cadereyta %

Tons (1023)

Cd. Madero %

Tons (1023)

Minatitlan %

Tons (1023)

Salina Cruz %

Tons (1023)

Tula %

Tons (1023)

Total %

Tons (1023)

%

Bioethanol Production Wood chips Comm. wood Sugarcane Corn grain Sorghum grain Sweet sorghum

8.95 0

7.9 0

17.31 0

14.5 0

11.34 0

11.3 0

12.67 0

10.7 0

12.54 0

11.2 0

4.68 0

6.9 0

67.48 0

10.7 0

40.99 20.32 11.63

36.1 17.9 10.3

41.13 19.92 12.14

34.5 16.7 10.2

38.22 15.10 10.54

37.9 15.0 10.5

45.33 20.16 10.51

38.2 17.0 8.9

43.87 20.58 10.50

39.2 18.4 9.4

11.70 16.81 11.60

17.3 24.8 17.1

221.2 112.9 66.92

35.0 17.9 10.6

31.54

27.8

28.65

24.0

25.56

25.4

29.91

25.2

24.32

21.8

22.96

33.9

163.0

25.8

0 0.0 100.0

1.78 2.78 4.14

20.5 32.0 47.5

0.71 3.48 1.49

12.5 61.3 26.2

2.50 10.88 8.94

11.2 48.7 40.1

Biodiesel Production African palm Jatropha Safflower

0 2.66 0.83

0 76.2 23.8

0.009 1.44 0.70

0.4 67.0 32.6

0 0.52 0.70

0 42.4 57.6

0 0 1.09

From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 249 is jatropha (48.7%) and safflower. The biodiesel production is also very different for each processing facility; for example, the plant located in Minatitlan is based on safflower, but the plants located in Tula and Cadereyta are mainly based on jatropha. Fig. 8.8 presents the bioethanol demand results for the different markets, where 41% of the demand can be met by the South consumers and 60.5% by the East consumers. It is important to note that the required demand for the East consumers is approximately three times the required demand for the South consumers, which shows that the optimal SC configuration is focused on satisfying the places with high demand. Further, the satisfied demand takes the maximum value at the beginning and end of the year for all consumers, which corresponds to the highest value of the required demand for the consumers. The bioethanol inventory levels for the processing facilities and the distribution centers are presented in Fig. 8.9. The case of the processing plants is shown in Fig. 8.9A, where the behavior is very similar for all processing plants. Also, the inventory levels take their maximum values at the beginning and end of the year. These behaviors coincide with the maximum values for the satisfied demand; in other words, the bioethanol availability for the processing facilities is high because the bioethanol production is sufficient to satisfy most of the required demand for the consumers. However, this behavior is limited by the response time of the SC. Similarly, the bioethanol inventory levels for the distribution centers are presented in Fig. 8.9B. It should be noted that the inventory for the East

Figure 8.8 Fulfilled demand for bioethanol for different consumers. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

250 Chapter 8 distribution center presents a high value from week 31 to week 49. This indicates that the bioethanol demand for the East consumers is almost satisfied in this period of time, although this value decreases to meet the demand until the end of the year. Fig. 8.10 presents the satisfied biodiesel demand for all consumers. As can be seen, the maximum percentage of satisfied biodiesel demand is 79.9% for the Northeast consumers,

Figure 8.9 Bioethanol inventory levels for the processing facilities and the distribution centers. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Figure 8.10 Fulfilled demand for biodiesel for different consumers. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixed-integer dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 251

Figure 8.11 Biodiesel inventory levels for the processing facilities and the distribution centers. From Jose´ Ezequiel Santiban˜ez-Aguilar, Martı´n Rivera-Toledo, Antonio Flores-Tlacuahuac, Jose´ Marı´a Ponce-Ortega, A mixedinteger dynamic optimization approach for the optimal planning of distributed biorefineries, Computers & Chemical Engineering, 2015.

while the minimum percentage of satisfied biodiesel demand is 56.6% for the East consumers. However, the East consumers have the maximum required demand and the Northeast consumers require the minimum biodiesel demand. Thus the optimal solution for the SC distributes the biodiesel uniformly to all consumers. In other words, the amount of biodiesel distributed to the consumers is similar, although the required biodiesel demand is different for the consumers. Finally, the stored biodiesel for the processing facilities is shown in Fig. 8.11A, while Fig. 8.11B presents the inventory level for the biodiesel in the distribution centers. The inventory level for the biodiesel in the processing plants is very intermittent. However, the stored biodiesel in the distribution centers presents the highest value at the beginning of the year for all distribution centers mainly because the maximum satisfied and required biodiesel demands take their maximum values at this period. The importance of this approach can be seen by comparing these results with the results obtained in the work reported by Santiban˜ez-Aguilar et al. (2014). Both present mathematical formulations for the optimal planning for distributed biorefinery systems; however, the work by Santiban˜ez-Aguilar et al. (2014) was focused on economic, environmental, and social objectives, and does not consider any control approach. On the one hand, in Santiban˜ez-Aguilar et al. (2014) the obtained annual profit was of US$2 3 107/year. Thus the SC configuration took into account only four suppliers, two processing facilities and four markets. Moreover, the bioethanol is only distributed to the East consumers with a satisfied demand of 5.77%. In addition, the biodiesel is transported to the West, Northeast, and East consumers with satisfied demands of 48%, 18%, and 58%, respectively. These values of satisfied demands are lower than the current results, mainly because the dynamic model was done using finite differences and the production, distribution of products, and raw materials are found at the end of the intervals. Furthermore, the selected raw materials

252 Chapter 8 for the production of biofuels are sugarcane, sorghum, and wood chips for bioethanol and jatropha and African palm for biodiesel. It is important to note that the approach by Santiban˜ezAguilar et al. (2014) does not consider the possible changes over time for the demand and cannot modify the distribution of the materials as a function of the response of the SC. On the other hand, in the current work the total profit is evaluated while the control actions are done. Thus the maximum expected annual profit is US$1.37 3 107/year. Here the five processing facilities selected for the bioethanol production and Minatitlan, Salina Cruz, Tula, and Salamanca are chosen for the biodiesel production. Moreover, the satisfied demands for bioethanol and biodiesel present a high percentage for all consumers, because the objective in the current work is to maximize the satisfied demand of the products. Additionally, the present work allows modifying the inventory levels and orders to increase the satisfied demand. The selected raw materials were wood chips, sugarcane, corn grain, sorghum, and sweet sorghum for bioethanol production and jatropha and safflower for biodiesel production. It is worth noting that the distribution of raw materials and products as well as the processing and inventory levels were modeled in a continuous form. For this reason, the percentage of satisfied demand is larger than the one reported by Santiban˜ez-Aguilar et al. (2014).

8.7 Conclusions This chapter presented a MIDO formulation to obtain the optimal configuration of a distributed biomass processing system. This model can select the processing technologies, processing facilities, manufactured products, and utilized raw materials to maximize the satisfied product demand for consumers. The addressed problem includes important features that should be taken into account in a biomass conversion system, such as the time-variant nature of the involved variables as well as the parameters, the diverse production technologies used to produce multiple products using a variety of biomass feedstocks that are geographically distributed and the distributed biomass processing needed to reduce transportation costs and to include the effects of economies of scale on the performance of the biorefinery system. The control of the SC was done through a NLMPC methodology, considering as controlled variable the difference between the total required and satisfied demands for the different consumers. The model was applied to a case study for a distributed biorefinery system in Mexico. The results show that it is possible to find the optimal configuration and behavior of the SC considering the involved dynamic behavior in a rigorous way. Furthermore, the solutions obtained by solving the MIDO formulation illustrate that the SCs based on biomass conversion are significantly affected by the availability of bioresources since the inventory levels in the different places are intermittent. In addition, the satisfied demand depends on the raw materials and products. Finally, future extensions of this work should incorporate other objectives such as environmental and social aspects, in addition to also considering uncertainty in the model and product demands.

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 253

8.8 Nomenclature 8.8.1 Parameters αconversion m;k;r Cmrm p Ck Cksale

prod

Cm;h

suppliers

Csm;h

rm2plants Csm;ph Csrm2main m pr2plants Csk;ph pr2main Csk Csdistr2centers k;dc OP suppliers Csm;h OP rm2plants Csm;ph OP rm2main Csm OP pr2plants Csk;ph OP pr2main Csk OP distr2centers Csk;dc FIX Cm;k;r;ph;q VAR Cm;k;r;ph;q main2FIX Cm;k;r;q main2VAR Cm;k;r;q processing plant Cm;k;r processing main Cm;k;r h2ph

dh;ph

h2main dh;main ph2dc

dph;dc

main2dc dmain;dc UPP suppliers Im;h UPP rm2plants Im;ph UPP rm2main Im UPP pr2plants Ik;ph UPP pr2main Ik UPP distr2centers Ik;dc

Conversion factor for the processing to get the product k through the route r and from the raw material m Unit transportation cost for the raw materials Unit transportation cost for the products Unit price of the products Unit production cost for the different raw materials in the suppliers Unit raw material storage cost in suppliers Unit raw material storage cost in secondary processing plants Unit raw material storage cost in main processing plant Unit product storage cost in secondary processing plants Unit product storage cost in the main processing plant Unit product storage cost in the distribution centers Unit operational cost for the raw material stored in suppliers Unit operational cost for the raw material stored in secondary processing plants Unit operational cost for the raw material stored in main processing plant Unit operational cost for the product stored in secondary processing plants Unit operational cost for the product stored in the main processing plant Unit operational cost for the product stored in the distribution centers Unit fixed cost for the capital of secondary processing plants Unit variable unitary cost for the capital of secondary processing plants Unit fixed cost for the capital of main processing plant Unit variable cost for the capital of main processing plant Unit operational cost for the secondary processing facilities Unit operational cost for the main processing facility Distance between the supplier s and the secondary processing plant ph Distance between the supplier s and the main processing plant Distance between the secondary processing plant ph and the distribution center dc Distance between the main processing plant and the distribution center dc Upper limit for the raw material storage in suppliers Upper limit for the raw material storage in secondary processing plants Upper limit for the raw material storage in the main processing plant Upper limit for the product storage in the secondary processing plants Upper limit for the product storage in the main processing plant Upper limit for the product storage in the distribution centers (Continued)

254 Chapter 8 (Continued) LOW suppliers Im;h LOW rm2plants Im;ph LOW rm2main Im LOW pr2plants Ik;ph LOW pr2main Ik LOW distr2centers Ik;dc

KF

prod

max

Mm;h ðt Þ demand ðt Þ Pk;dc MAX

h2ph Mm;h;ph

MAX

Mh2main m;h

MAX ph2dc Pk;ph;dc MAX main2dc Pk;dc MIN

Mm;h;ph

MIN

Mh2main m;h

UPP

h2ph

processing route

Mm;k;r;ph;q

LOW

UPP

processing route

Lower limit for the raw material storage in secondary processing plants Lower limit for the raw material storage in the main processing plant Lower limit for the product storage in the secondary processing plants Lower limit for the product storage in the main processing plant Lower limit for the product storage in the distribution centers Factor to annualize the capital cost Maximum raw material production rate in the supplier h Maximum required demand that can satisfy a distribution center dc Upper limit for the transportation flow rate of raw material from the suppliers to the processing facilities Upper limit for the transportation flow rate of raw material from the suppliers to the main processing facility Upper limit for the transportation flow rate of product from the processing facilities to the distribution centers Upper limit for the transportation flow rate of product from the main processing facility Lower limit for the transportation flow rate of raw material from the suppliers to processing facilities Lowe limit for the transportation flow rate of raw material from the suppliers to the main processing facility Upper processing limit for the processing in the secondary processing facilities Lower processing limit for the processing in the secondary processing facilities

Mm;k;r;ph;q

main2processing route Mm;k;r;q

LOW

Lower limit for the raw material storage in suppliers

main2processing route

Upper processing limit for the processing in the main processing facility Lower processing facilities for the processing in the main processing facility

Mm;k;r;q

MIN ph2dc Pk;ph;dc MIN main2dc Pk;dc

Lower limit for the transportation flow rate of product from the processing facilities to the distribution centers Lower limit for the transportation flow rate of product from the main processing facility to the distribution centers

8.8.2 Binary Variables h2ph

ym;h;ph ðt Þ h2main ðt Þ ym;h ph2dc

yk;ph;dc ðt Þ

Binary variable used to determine if the transportation between supplier and processing plants is carried out Binary variable used to determine if the transportation between supplier and main processing facility is carried out Binary variable used to define if the transportation between secondary plants and distribution centers is done (Continued)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 255 (Continued) Binary variable used to define the existence of the transportation between main plants and distribution centers Binary variable used to define the existence of the processing in the secondary plants independent of the time

main2dc yk;dc ðt Þ processing route

ym;k;r;ph;q suppliers

ym;h

rm2plants

ym;ph

ymrm2main pr2plants

yk;ph

pr2main

yk

distr2centers yk;dc processing route ym;k;r;ph;q ðt Þ time suppliers ym;h ðt Þ time

time

ym;ph

time

ymrm2main ðt Þ

time

yk;ph

time

yk

time

distr2centers yk;dc ðt Þ

rm2plants

pr2plants

pr2main

ðt Þ

ðt Þ

ðt Þ

Binary variable used to determine the existence of the suppliers independent of the time Binary variable used to determine the existence of the secondary processing plants independent of the time Binary variable used to determine the existence of the processing plants independent of the time Binary variable used to determine the existence of the processing plants independent of the time Binary variable used to determine the existence of the processing plants independent of the time Binary variable used to determine the existence of the distribution centers independent of the time Binary variable used to determine the existence of the processing plants in a given time period

raw material stored in the

Binary variable used to determine the existence of the suppliers in a given time period Binary variable used to determine the existence of the secondary processing plants in a given time period Binary variable used to determine the existence of the processing plant in a given time period Binary variable used to determine the existence of the processing plants in a given time period Binary variable used to determine the existence of the processing plant in a given time period Binary variable used to determine the existence of the processing plants in a given time period

raw material stored in the

raw material stored in the raw material stored in the main product stored in the secondary product stored in the main product stored in the processing in the secondary

raw material stored in the raw material stored in the main product stored in the secondary product stored in the main processing in the secondary

8.8.3 Variables CAP Cm;k;r;ph;q main2CAP Cm;k;r;q C CAPITAL C OPERATIONAL C TRANSPORTATION C STORAGE CTRLDEMAND CAP processing M m;k;r;ph CAP 2 dis CAP

processing

M m;k;r;ph;q

main 2 processing M m;k;r

Capital cost for the secondary processing plants Capital cost for the main processing plant Capital cost for the supply chain Total operational cost for the processing plants Total transportation cost for the supply chain Total storage cost for the supply chain Control objective function Capacity for the secondary processing facilities Discretized capacity for the secondary processing plants Capacity for the main processing facility (Continued)

256 Chapter 8 (Continued) CAP 2 dis

dis

main 2 processing

M m;k;r;q

processing product Mm;k;r;ph;q

ðt Þ Mh2main m;h h2ph

Mem;h;ph ðt Þ processing route

Mm;r;ph

Discretized raw material that is processed in the secondary processing facilities used to consider the economies of scale

ðt Þ

main2processing product dis Mm;k;r;q suppliers ðt Þ Im;h rm2plants ðt Þ Im;ph ð tÞ Irm2main m pr2plants ðt Þ Ik;ph pr2main ðt Þ Ik Idistr2centers ðt Þ k;dc prod Mm;h ðt Þ h2ph Mm;h;ph ðt Þ

Discretized capacity for the main processing plant

ðt Þ

Discretized raw material that is processed in the main processing facility used to consider the economies of scale Raw material inventory level in the suppliers Raw material inventory level in the secondary plants Raw material inventory level in the main plant Product inventory level in the secondary processing facilities Product inventory level in the main processing facilities Product inventory level in the distribution centers Produced raw material rate in the suppliers Distributed raw material flow rate from the suppliers to secondary processing plants Distributed raw material flow rate from the suppliers to main processing plant Inlet raw material flow rate from the suppliers to secondary processing plants Raw material flow rate that is processed in the processing facilities

ðt Þ

ðt Þ Meh2main m;h main2processing route ðt Þ Mm;r ðt Þ Os2facilities m;h;ph ðt Þ Os2main m;h ph2dc Ok;ph;dc ðt Þ main2dc ðt Þ Ok;dc ð t Þ Odc k;dc Olocations materials;loc1;loc2 ðt Þ processing route ðt Þ Pk;r;ph ph2dc

Inlet raw material flow rate from the suppliers to the main processing plant Raw material flow rate that is processed in the processing facilities Order from the secondary processing facilities to suppliers Order from the main processing facility to suppliers Order from distribution centers to secondary processing plants Order from distribution centers to the main processing plant Order from consumers to distribution centers General form for the orders for any material, from an allocation loc1 to another allocation loc2 Obtained product k from the processing route r in the secondary processing facilities

Pk;ph;dc ðt Þ

Distributed product from distribution centers to secondary processing plants

main2processing route Pk;r main2dc ðt Þ Pk;dc ph2dc Pek;ph;dc ðt Þ

Obtained product k from the processing route r in the main processing facility ðt Þ

main2dc ðt Þ Pek;dc sale Pk;dc ðt Þ produced

Pk;m;r;ph ðt Þ main2produced

Pk;m;r

ðt Þ

Distributed product from distribution centers to the main processing plants Inlet product flow rate in the distribution centers from the secondary processing plants Inlet product rate in the distribution centers from the main processing plant Sold product in the distribution centers Produced product flow rate in the secondary processing plants Product flow rate in the main processing plant (Continued)

Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries 257 (Continued) PROFIT Rqfacilities m;h;ph ðt Þ

Net annual profit for the supply chain Required raw material in the secondary processing facilities from suppliers

Rqmain m;h ðt Þ

Required raw material in the main processing facility from suppliers Required product in the distribution centers from the secondary processing facilities Required product in the distribution centers from the main processing facility Required product in the consumers from the distribution centers General form for the inventory levels for any material in any location

ph2dc

Rqk;ph;dc ðt Þ ðt Þ Rqmain2dc k;dc Rqdc k;dc ðt Þ Ilocations materials;locations ðt Þ

References Biegler, L. T. (2010). Nonlinear programming: Concepts, algorithms and applications to chemical engineering.. Philadelphia, PA: SIAM. Duran, M. A., & Grossmann, I. E. (1986). An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming, 36(3), 307339. Kocis, G. R., & Grossmann, I. E. (1987). Relaxation strategy for the structural optimization of process flow sheets. Industrial and Engineering Chemistry Research, 26(9), 18691880. Santiban˜ez-Aguilar, J. E., Gonza´lez-Campos, J. B., Ponce-Ortega, J. M., Serna-Gonza´lez, M., & El-Halwagi, M. M. (2014). Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives. Journal of Cleaner Production, 65, 270294. Santiban˜ez-Aguilar, J. E., Rivera-Toledo, M., Flores-Tlacuahuac, A., & Ponce-Ortega, J. M. (2015). A mixedinteger dynamic optimization approach for the optimal planning of distributed biorefineries. Computers and Chemical Engineering, 80, 3762. Terrazas-Moreno, S., Flores-Tlacuahuac, A., & Grossmann, I. E. (2008). A Lagrangean heuristic for the scheduling and control of polymerization reactors. AIChE Journal, 54(1), 163182. Viswanathan, J., & Grossmann, I. E. (1990). A combined penalty function and outer-approximation method for MINLP optimization. Computers and Chemical Engineering, 14(7), 769782.

APPENDICES

Code Used in the Book Appendix A GAMS Code for Model of Chapter 2, Environmental Aspects in the Strategic Planning of a Biomass Conversion System A.1 Introduction This appendix provides the GAMS code for the model presented in Chapter 2, Environmental Aspects in the Strategic Planning of a Biomass Conversion System, for the strategic planning of producing biofuels. The code considers the data of the addressed case study in Chapter 2, Environmental Aspects in the Strategic Planning of a Biomass Conversion System, but it can be used to implement different cases and solve different problems for the strategic planning of producing biofuels, with the relevant data.

A.2 GAMS Code for Chapter 2, Environmental Aspects in the Strategic Planning of a Biomass Conversion System

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Appendix B GAMS Code for Model of Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives B.1 Introduction This appendix presents the GAMS code for the model presented in Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives, the strategic plan for producing biofuels. In this model, the multiobjective optimization approach incorporates simultaneous economic, environmental and social objectives in the site selection and supply chain optimization. The code considers the data of the addressed case study in Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental, and Social Objectives. However, this model can be used to implement different cases and solve different problems for the strategic planning for producing biofuels, with the relevant data.

B.2 GAMS Code for Chapter 3, Optimal Planning and Site Selection for Distributed Multiproduct Biorefineries Involving Economic, Environmental and Social Objectives

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Appendix C GAMS Code for Model of Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth C.1 Introduction This appendix presents the GAMS code for the model presented in Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth, the strategic planning of biorefineries based on the harvesting of water hyacinth to eliminate this pollutant plant from lakes and rivers and to simultaneously obtain different value-added products (including pure water). The code considers the data of the addressed case study in Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth. However, this model can be used to implement different cases and solve different problems for the strategic planning of producing biofuels, with the relevant data.

C.2 GAMS Code for Chapter 4, Distributed Biorefining Networks for the Value-Added Processing of Water Hyacinth

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Appendix D GAMS Code for Model of Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico D.1 Introduction This appendix provides the GAMS code for the model presented in Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, the strategic planning of biorefineries based on residues from agave, the plant used to make tequila. The code considers the data of the case study in Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, but this model can be used to implement different cases and solve different problems for the strategic planning for producing biofuels, with the relevant data.

D.2 GAMS Code for Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico

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Appendix E GAMS Code for Model of Chapter 6, Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains under Uncertainty E.1 Introduction This appendix gives the GAMS code for the model presented in Chapter 6, Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains under Uncertainty, the strategic planning of biorefineries involving financial risk with uncertainty. This code considers the data of the addressed case study in Chapter 5, Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico, but it can be used to implement different cases and solve different problems for the strategic planning for producing biofuels, with the relevant data.

E.2 GAMS Code for Chapter 6, Financial Risk Assessment and Optimal Planning of Biofuels Supply Chains under Uncertainty

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Appendix F GAMS and MATLAB Code for Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives F.1 Introduction This appendix presents the approach implemented for solving the problem addressed in Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, the strategic planning of biorefineries with uncertainty. The code considers the data of the addressed case study in Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives. However, it can be used to implement different cases and solve different problems for the strategic planning for producing biofuels, with the relevant data.

F.2 GAMS Code for Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives

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F.3 MATLAB code for Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, SUPPLYCHAIN.m

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F.4 MATLAB Code for Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, STRUCTURS2.m

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F.5 MATLAB Code for Chapter 7, Stochastic Design of Biorefinery Supply Chains Considering Economic and Environmental Objectives, mesesiguales.m

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Appendix G GAMS Code for Model of Chapter 8, Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries G.1 Introduction This appendix presents the approach implemented for solving the problem addressed in Chapter 8, Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries, the strategic planning of biorefineries through a dynamic optimization approach. The code considers the data of the addressed case study in Chapter 8, Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries. However, this model can be used to implement different cases and solve different problems for the strategic planning for producing biofuels, with the relevant data.

G.2 GAMS Code for Chapter 8, Mixed-Integer Dynamic Optimization for Planning Distributed Biorefineries

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Index Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.

A Acetone-butanol-ethanol (ABE) fermentation, 208 Additional constraints, 239 240 Agave available in Mexico, 132t bagasse, 123 bioethanol processing, 117f fed for plants, 138t residues from Tequila industry, 122 sources, 117f steps for bioethanol production, 118f cultivation, 132 133 mass balances in agave cultivating areas, 120 maximum available agave, 121 Anaerobic digestion process, 85 Availability constraints, 46

B Bagasse. See also Agave—bagasse stalk, 122 transportation, 130 Balsas River, 96 99 BARON. See Branch-And-Reduce Optimization Navigator (BARON) Binary variables, 56 59, 128 129, 170 171, 187 188, 194 195, 230 Biodiesel, 150, 158 fulfilled demand for different consumers, 250f

inventory levels for processing facilities and distribution centers, 251f production, 206 208, 247 Bioethanol, 150 demand in consumption site, 133 137 in markets, 137 139 distributed and central bioethanol processing plants, 130 fulfilled demand for different consumers, 249f inventory levels for processing facilities and distribution centers, 250f production, 115, 118f, 119 120, 206 208 mass balances in distributed processing plants, 122 124 Biofuels, 1 technologies for, 2 3 Biogas, 85, 86f Biomass, 1, 177 biomass-based SCs, 1 2 crop fields, 32 processing, 177 178 production, 178 Biomass conversion system availability and feedstock used cost for biofuel production, 20t case study, 16 23 cost and demand of products, 20t cost of byproducts, 20t

507

GAMS code, 259 265 mathematical model, 10 15 optimization model, 9 sensitivity analysis, 23 24 solution strategy, 15 16 solutions of cases, 22t, 23t, 24t superstructure for optimal planning of biorefinery production system, 10f Biomass transportation cost (CostTransBM), 94 Bioprocessing industry, 1 2 Biorefineries, 1, 29 30, 147 Biorefinery supply chains, stochastic design of. See also Distributed multiproduct biorefineries case study, 206 209, 207t computer-aided tools, 210 GAMS code for, 415 464 historical data for raw material prices, USD/metric-ton, 208t indexes, 215 mathematical formulation, 178 202 MATLAB code mesesiguales.m, 471 STRUCTURS2.m, 467 470 SUPPLYCHAIN.m, 465 466 parameters, 216 problem statement, 177 178 solution approach, 202 206, 203f changing of upper limit for environmental impact, 205 comparison between supply chain topologies, 204 205

508 Index Biorefinery supply chains, stochastic design of (Continued) identification of parameters under uncertainty, 203 sampling for uncertain parameters, 203 solving of associated deterministic optimization problem, 203 204 standardized regression coefficients, 206 superstructure, 202 variables, 216 Bioresources, 54 Boolean variable, 38 Branch-And-Reduce Optimization Navigator (BARON), 99

C Capital cost, 127 128, 193 194 for central processing facilities, 91 92 for processing facilities, 90 91, 229 230 for storage, 235 for water treatment units, 92 93 Central bioethanol processing plants, transportation cost from Tequila industries to, 130 Central processing plant, 124 126 Central Processing Unit (CPU), 96 Chemical control of water hyacinth, 83 Compost, 86 Computer-aided tools, 210 dataflow and, 210f Concentrator column, 123 124 CONOPT solver, 99 101 Constraint(s), 11 to control orders from consumers to distribution centers, 225 for demand, 225 method, 15 for transported flow rate at outlet and inlet locations, 226

Continuity of inventories at beginning and end of time horizon, 223, 225 Continuous variables, 148 149 Control actions, 225 226 objective function, 236 237 product demand, 236 237 Conventional MINLP solvers, 99 Conversion factors, 9, 16, 17t, 18t, 241 242 “Corporate Integration of Voluntary Initiatives for Sustainability” framework, 3 4 Correlated values, case with, 159 166 amount of biomass for solution, 167t configuration of supply chain for riskiest solution, 165f, 166f correlation matrix for correlated distribution, 161t cumulative probability curves for correlated distribution, 162f distribution of raw material price, 160f frequency histogram for net annual profit, 164f net annual profit, 162f Pareto curve showing financial risk, 161f percentages of fulfilled demand of products, 167t raw material prices for scenarios, 163t Correlation, raw material price distribution without, 150 159 CostTransBM. See Biomass transportation cost (CostTransBM) CPLEX Solver, 56 59, 99 101 CPU. See Central Processing Unit (CPU) Cultivation area, 139 141 additional land for agave, 140t water utilized for agave, 141t Cumulative probability, 159 curves, 150 153, 153f, 162f

D DAE. See Differential-algebraic equations (DAE) Damage factor, 50 Demand constraint, 181 Deoxy-liquefaction process, 86 87 Deterministic optimization problem, 203 204 DICOPT. See DIscrete and Continuous OPTimizer (DICOPT) Differential-algebraic equations (DAE), 239 Direct burning process, 87 DIscrete and Continuous OPTimizer (DICOPT), 99, 241 Discretized dynamic model, 242 Disjunctions, 228, 230 232 Distributed bioethanol processing plants, 125 130, 127t transportation cost from Tequila industries to, 130 Distributed biorefining networks for water hyacinth GAMS code for, 301 318 model formulation, 79 95 results, 96 107 Distributed multiproduct biorefineries biodiesel distribution, 70f case study, 54 65 bioethanol demand in market, 59t feedstock availability, 57t parameters for products transportation, 60t problem statement for biorefinery SC in Mexico, 55f profiles of number of jobs generated considering net profit constraints, 63f unit costs, ecoindicator-99 and jobs for feedstock, 56t feedstocks for biodiesel production, 69f for ethanol production, 68f GAMS code for, 266 300

Index model formulation, 32 54 availability constraints, 46 constraints for total product sales, 37 example for production chain, 33f mass balances for harvesting sites, 34 mass balances for main plant, 36 mass balances for markets, 37 mass balances for processing hubs, 35 objective functions, 47 51 processing constraints, 44 46 products in hubs, 35 36 products in main plant, 36 37 raw materials in hubs, 35 raw materials in main plant, 36 remarks on model, 52 54, 53f start and end storage constraints, 47 storage constraints, 38 41 transportation constraints, 41 44 Pareto curve between annual profit and environmental impact, 60t for social benefit maximization and environmental impact minimization, 65f for social benefit vs. annual profit, 64f Pareto set of optimal solutions, 65 66 problem statement, 30 32 SC configuration, 67f selected locations of harvesting sites, markets, and processing plants, 66f structure for each processing plant, 31f Distributed processing facilities, 119 120 plants, 124 126 for bioethanol production, 122 124 Distributed system, 116 118

Distribution centers constraints to control orders from consumers to, 225 product inventory at, 223 product orders from distribution centers to facilities, 224 from distribution centers to main facility, 224 Diverse assessment frameworks, 3 4 Diverse production technologies, 29 30 Dry biomass, 84 Dynamic model, 239 Dynamic optimization, 219

E Ecoindicator-99, 13 15, 21t, 22t, 48 50, 56 59 Ecoindicators, 49 50 Economic objective function, 9, 12 13, 47 48, 200 201, 214f GAMS code for, 266 300 Economic solution with constraint of 1% for bioethanol demand, 133 137 bioethanol distribution for optimal solution, 134t distribution of bioethanol, 137f, 138f optimal economic solution, 135f Pareto curve, 136f Economies of scale for processing facilities, 228 232 Egalitarian perspectives, 49 50 Environmental assessment, 13 14 Environmental impact (EI), 1 3, 12, 15, 29 30, 62 changing of upper limit for, 205 minimization, 9 Environmental indicators, 2 3 Environmental objective function, 13 15, 48 50, 201 202 GAMS code for, 266 300 Epsilon-constraint method, 29 30, 149 150 Ethanol, 158 Expected profit, 149

509

F Feedstocks, 9 maximum availability for, 11 Fermentable material, 123 124 Financial risk assessment and optimal planning of biofuels supply chains binary variables, 170 171 biofuels, 147 case with correlated values, 159 166 distribution of raw material price without correlation, 150 159 expected profit, 149 GAMS code for, 375 414 mathematical model formulation, 148 149 parameters, 172 175 superstructure for proposed methodology, 148f variables, 168 170 worst case for net annual profit, 149 150 Frequency histogram for net annual profit, 155f, 156, 164f

G GAMS code. See General Algebraic Modeling System code (GAMS code) Gasoline, 132 133 General Algebraic Modeling System code (GAMS code), 18, 54, 95, 210, 242 for biomass conversion system, 259 265 for distributed multiproduct biorefineries, 266 300 for financial risk assessment and optimal planning of biofuel supply chains, 375 414 for mixed-integer dynamic optimization model, 472 504 for optimization of supply chain associated to production of bioethanol, 319 374

510 Index General Algebraic Modeling System code (GAMS code) (Continued) for stochastic design of biorefinery supply chains, 415 464 for water hyacinth, 301 318 General facilities to suppliers, raw material orders from, 223 General optimization model, 1 2 Geometric Brownian motion, 150, 159 Global bioethanol production process, 123 Greenhouse gas emissions (GHGE), 1 GREET 1.8d software, 56

H Harvested water hyacinth availability, 84 Harvesting cost of water hyacinth, 93 Hierarchical perspectives, 49 50 Holistic approach, 79 Hydrolyzed compound, 123 Hypercube method, 177

I Impact factors, 17 18 IMPLAN model, 50 51 Indexes, 10, 142, 215, 221 Individualist perspectives, 49 50 Inlet flow rate, 121 Input output of distributed material, relationships for, 181 Intel Xenon e5345 processors, 242 “Interlinked issues and dimensions”, 3 4

J Jatropha, 60 61, 67 69 Jobs and Economic Development Impact methodology (JEDI), 50 51

L Lagrange interpolation polynomial, 240 241 Lake of Chapala, 96 99

Lake of Patzcuaro, 96 99 Latin Hypercube Sampling method (LHS method), 203 Life cycle assessment technique, 29 30 Lignocellulosic matter, 115

M Markets bioethanol demand in, 137 139 mass balances in, 180 products distribution from processing plants to, 124 125 Mass balances, 11 in agave cultivating areas, 120 in distributed processing plants for bioethanol production, 122 124 for harvesting sites, 34 for main plant, 36 for markets, 37 in markets, 180 in processing facilities, 179 180 for processing hubs, 35 for splitters before processing plants, 84 in suppliers, 178 179 in Tequila industry, 121 for water hyacinth harvesting, 83 limit, 182 183 Material balance, 11 Mathematical formulation, 52 biorefinery supply chains, 178 202 availability of raw material, 178 demand constraint, 181 economic objective function, 200 201 environmental objective, 201 202 processing constraints, 186 194 processing stages in processing facilities, 184 186

raw material production cost, 200 relationships for input output of distributed material, 181 revenue from selling products, 200 storage modeling, 194 200 transportation limits and costs, 182 184 Mathematical model, 10 15 economic objective function, 12 13 environmental objective function, 13 15 formulation, 148 149 mass balances, 11 maximum availability for feedstocks, 11 maximum processing limits, 12 maximum products demand, 11 12 objective functions, 12 Mathematical programming model, 147 MATLAB code for stochastic design of biorefinery supply chains mesesiguales.m, 471 STRUCTURS2.m, 467 470 SUPPLYCHAIN.m, 465 466 Maximum availability for feedstocks, 11 Maximum available agave, 121 Maximum processing limits, 12 Maximum products demand, 11 12 Mechanical control of water hyacinth, 83 Mexican economy, 115 Mexico agave available in, 132t gasoline demand in, 133t supply chain in, 206 208 Mezcal industry, 116 118 MIDO. See Mixed-integer dynamic optimization (MIDO) MILP model. See Mixed-integer linear programming model (MILP model) Ministry of Agriculture, 16 17

Index Ministry of Economy, 16 17 Ministry of Energy, 16 17 Ministry of Environment, 16 17 MINLP. See Mixed integer linear programming (MINLP) MINOS. See Modular In-core Nonlinear Optimization System (MINOS) MixAlco process, 85, 86f Mixed integer linear programming (MINLP), 99 Mixed-integer dynamic mathematical optimization model, 221 237 availability of raw material, 225 behavior of total annual profit for each control cycle, 243t constraints to control orders from consumers to distribution centers, 225 for demand, 225 for transported flow rate at outlet and inlet locations, 226 continuity of inventories at beginning and end of time horizon, 223, 225 control product demand, 236 237 economies of scale for processing facilities, 228 232 geographical regions for suppliers, 242t net annual profit, 236 NLMPC, 237 239 operating cost, 234 problem statement, 219 221 processing, 227 228 product inventory at distribution centers, 223 at main processing facility, 222 at processing facilities, 222 product orders from consumers to distribution centers, 224 from distribution centers to facilities, 224 raw material inventory at main processing facility, 222 at processing facilities, 221

at suppliers, 221 raw material orders from general facilities to suppliers, 223 from main facility to suppliers, 223 224 results, 241 252 safflower and jatropha inventories, 247f solution approach for MIDO problem, 239 241 storage cost, 235 236 storage modeling, 232 234 sweet sorghum and sorghum grain inventories, 246f total capital cost, 234 transportation cost, 234 235 limits, 226 227 wood chips, sugarcane, and corn grain inventories, 245f Mixed-integer dynamic optimization (MIDO), 239 GAMS code for, 472 504 presented MIDO problem, 240t solution approach for, 239 241 Mixed-integer linear programming model (MILP model), 1 2, 52 54, 210 Mixed-integer nonlinear programming optimization model, 1 2 Mobilis, 45 46 Model formulation, 32 54 predictive control, 219 Modular In-core Nonlinear Optimization System (MINOS), 99 101 Monte-Carlo method, 177, 203 Multiobjective optimization approach, 2 3, 9, 204 Multiperiod MILP, 52 Multisite system model, 29 30

N Net annual profit, 153 154, 154f, 162f, 236 WC for, 149 150 Nonhydrolyzed compound, 123

511

Nonlinear behavior for capital cost functions, 129 130 Nonlinear model predictive control method (NLMPC method), 219 220, 237 239, 238f

O Objective functions, 12, 131 132, 242 Operating cost, 127 128, 234 Operational cost, 194 for central processing facilities, 91 for processing facilities, 90 for storage, 235 for water treatment units, 92 Optimal planning of SC, 219 220 Optimally synthesized distributed biorefining network, 79 Optimization, 3, 52, 87 case study, 132 141 agave available in Mexico, 132t cultivation area, 139 141 economic solution with constraint of 1% for bioethanol demand, 133 137 gasoline demand in Mexico, 133t solution without constraint for demand of bioethanol, 137 139 indexes, 142 Mexican economy, 115 model, 2 3, 9, 96, 119 132 cost of distributed bioethanol processing plants, 125 130 distribution of products from processing plants to markets, 124 125 mass balances in agave cultivating areas, 120 mass balances in distributed processing plants, 122 124 mass balances in Tequila industry, 121 maximum available agave, 121 objective function, 131 132

512 Index Optimization (Continued) product demands, 125 residues of agave bagasse from Tequila industry, 122 transportation cost for products, 131 transportation cost for stalks to distributed and central plants, 130 transportation cost from Tequila industries, 130 optimization-based automated targeting procedure, 1 parameters, 143 144 problem statement, 115 119 bioethanol processing from agave bagasse, 117f efficiencies of bioethanol processing, 120t sources of agave bagasse, 117f steps for bioethanol production from agave bagasse, 118f superstructure for optimizing supply chain, 119f sets, 143 of supply chain associated to production of bioethanol, 115 GAMS code for, 319 374 variables, 144 146 Orthogonal collocation method, 240 241

facilities, 186, 252 economies of scale for, 228 232 mass balances in, 179 180 processing stages in, 184 186 product inventory at, 222 raw material inventory at, 221 plants, 179 180 route, 9 technologies, 54 Product capacity, 191 demands, 125, 225 distribution from processing plants to markets, 124 125 inventory at distribution centers, 223 at main processing facility, 222 at processing facilities, 222 orders from consumers to distribution centers, 224 from distribution centers to facilities, 224 from distribution centers to main facility, 224 rate, 222 223 transportation cost, 131 of water hyacinth, 94 Profit, 12, 15 maximization, 9

P

Rapeseed, 21 Raw material(s) availability, 178, 225 inventories, 243 246, 244f at main processing facility, 222 at processing facilities, 221 at suppliers, 221 orders from general facilities to suppliers, 223 from main facility to suppliers, 223 224 price distribution without correlation, 150 159, 151f, 152f, 155t amount of biomass for solution, 158t

Parameters, 143 144, 172 175 Pareto curve, 18 19, 21 23, 24f, 62, 63f, 79, 150, 152f, 161f, 210 211, 211f macrostructures, 212f Pareto optimal solutions, 29 30 Pareto set of optimal solutions, 65 66 Pareto solution, 12, 13f PEMEX database, 54 Plant heads, 120 bagasse, 122 Processing constraints, 44 46, 186 194 costs, 16, 19t, 190 191

R

percentage of fulfilled demand of products, 158t in processing plants, 248t production cost, 200 Relaxed mixed integer nonlinear programming (RMINLP), 99 Residues of agave bagasse from Tequila industry, 122 Revenue from selling products, 200 RMINLP. See Relaxed mixed integer nonlinear programming (RMINLP)

S Saccharomyces, 45 46 SAGARPA-SIAP database, 54 Sampling for uncertain parameters, 203 SBB solvers. See Standard branch and bound solvers (SBB solvers) SC. See Supply chain (SC) Secondary processing plants, 180 Selling products, revenue for, 236 SEMARNAT database, 54 Sensitivity analysis, 23 24, 25f Sets, 32, 34f, 143 Shortcut method, 1 SNOPT. See Sparse Nonlinear OPTimizer (SNOPT) Social objective of environmental impact, 29 30 Social objective function, 50 51 GAMS code for, 266 300 Solid fuel, 124 Solution without constraint for bioethanol demand, 137 139 optimal economic solution, 139f produced bioethanol for optimal solution, 138t strategy, 15 16 Sparse Nonlinear OPTimizer (SNOPT), 99 101 Stalk bagasse, 122 Standard branch and bound solvers (SBB solvers), 99, 241

Index Standardized regression coefficients, 206 State-task network methodology, 32 Storage constraints, 38 41 cost, 235 236 modeling, 194 200, 232 234 Strategic planning, 1 3 Structural representation, 1 Superstructure, 202, 219 221 for dynamic supply chain based on biomass conversion, 220f Suppliers mass balances in, 178 179 raw material inventory at, 221 Supply chain (SC), 1, 29 31, 83, 147, 219 220 for bioethanol production, 115, 116f configuration, 156 157, 156f, 157f, 165f topology, 177 comparison between supply chain topologies, 204 205 section representation, 205f Sustainability, 3 4, 29 30 Sustainable development, 3 4 Systematic framework, 1 2

T TAC. See Total annual cost (TAC) Tequila industry, 115 118 mass balances in, 121 residues of agave bagasse from, 122 transportation cost from, 130 Time horizon, continuity of inventories at beginning and end of, 223, 225 Total annual cost (TAC), 95, 102 Total annual profit, 200 201 Total capital cost, 234 Total flow rate, 124 125 of plant heads, 121 122 Transportation, 182 183 constraints, 41 44 cost, 182 184, 234 235 for products, 131 for stalks to distributed and central plants, 130 from Tequila industries, 130

to distribution centers, 222 223 flows, 147 limits, 182 184, 226 227 Transported flow rate at outlet and inlet locations, constraints for, 226 Two-tiered sustainability equilibria, 3 4

U Uncertainty, identification of parameters, 203 Unitary production cost, 200 US energy SC network, 2 3

V Variables, 144 146, 168 170, 216 Volume limit, 182 183

W Water demand for water consumers, 89 network optimization models, 83 transportation cost, 93 treatment technology, 88 89 balances for, 88 Water hyacinth, 79 approach to produce ethanol from, 85f distribution of sources and sinks of problem, 80f GAMS code for, 301 318 model formulation, 79 95 availability of harvested water hyacinth, 84 balances for central processing facilities technologies, 87 balances for markets, 88 balances for mixers before central processing facilities, 87 balances for mixers before processing facilities, 84 balances for splitters after central processing facilities, 88

513

balances for splitters after each processing facility, 87 88 balances for technologies in processing facilities, 84 87 balances for water treatment in each source, 88 biomass transportation cost, 94 capital cost for central processing facilities, 91 92 capital cost for processing facilities, 90 91 capital cost for water treatment units, 92 93 component balance for mixers before each water consumer, 89 constraints for water quality for each consumer, 90 demand for water consumers, 89 demands for consumers, 88 harvesting cost, 93 mass balance for harvesting of water hyacinth, 83 mass balance for mixers before each water consumer, 89 mass balance for splitters after water treatment, 89 mass balance for splitters before processing plants, 84 operational cost for central processing facilities, 91 operational cost for processing facilities, 90 operational cost for water treatment units, 92 percentage of eliminated water hyacinth, 95 products transportation cost, 94 remarks on model, 95 96 total capital cost, 94 total net annual cost, 95 total operational cost, 94 total sales, 94 water transportation cost, 93 water treatment technology in each source, 88 89

514 Index Water hyacinth (Continued) representation for distributed supply chain based on, 82f obtaining from water bodies, 80f results, 96 107 available biomass from water hyacinth, 97t distribution of satisfied demands of products, 105f

distribution of water bodies and water consumers, 108f efficiencies for processing technologies, 98t Pareto curves, 102f, 103f Pareto curves for TAC vs. produced water, 106f, 107f representation of eliminated water hyacinth, 104f solution procedure of addressed problem, 101f

transportation costs for biomass, 100t superstructure for distributed supply chain, 81f Worst case (WC), 149, 157 for net annual profit, 149 150

X Xylitol demand, 211 production, 208