Optimization for Energy Systems and Supply Chains: Fundamentals and Applications 9781032146218, 9781032146225, 9781003240228

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Optimization for Energy Systems and Supply Chains To curb the impacts of rising CO2 emissions, the Intergovernmental Panel on Climate Change report states that a net zero target needs to be achieved by the year 2055. Experts argue that this is a critical time to make important and accurate decisions. Thus, it is essential to have the right tools to efficiently plan and deploy future energy systems and supply chains. Mathematical models can provide decision-makers with the tools required to make well-informed decisions relating to development of energy systems and supply chains. This book provides an understanding of the various available energy systems, the basics behind mathematical models, the steps required to develop mathematical models, and examples/case studies where such models are applied. Divided into two parts, one covering basics for beginners and the other featuring contributed chapters offering illustrative examples, this book: • Shows how mathematical models are applied to solve problems in energy systems and supply chains • Provides fundamentals of the working principles of various energy systems and their technologies • Offers basics of how to formulate and best practices for developing mathematical models, topics not covered in other titles • Features a wide range of case studies • Teaches readers to develop their own mathematical models to make decisions on energy systems This book is aimed at chemical, process, mechanical, and energy engineers.

Green Chemistry and Chemical Engineering Series Editor Sunggyu Lee Ohio University, Athens, Ohio, USA

Carbon-Neutral Fuels and Energy Carriers Nazim Z. Muradov and T. Nejat Veziroğlu

Oxide Semiconductors for Solar Energy Conversion: Titanium Dioxide Janusz Nowotny

Water for Energy and Fuel Production Yatish T. Shah

Managing Biogas Plants: A Practical Guide Mario Alejandro Rosato

The Water-Food-Energy Nexus: Processes, Technologies, and Challenges I. M. Mujtaba, R. Srinivasan, and N. O. Elbashir

Hemicelluloses and Lignin in Biorefineries Jean-Luc Wertz, Magali Deleu, Séverine Coppée, and Aurore Richel

Materials in Biology and Medicine Sunggyu Lee and David Henthorn

Resource Recovery to Approach Zero Municipal Waste Mohammad J. Taherzadeh and Tobias Richards

Hydrogen Safety Fotis Rigas and Paul Amyotte

Nuclear Hydrogen Production Handbook Xing L. Yan and Ryutaro Hino

Water Management: Social and Technological Perspectives Iqbal Mohammed Mujtaba, Thokozani Majozi, and Mutiu Kolade Amosa

Optimization for Energy Systems and Supply Chains: Fundamentals and Applications Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay

For more information about this series, please visit: https://www.routledge.com/ Green-Chemistry-and-Chemical-Engineering/book-series/CRCGRECHECHE

Optimization for Energy Systems and Supply Chains Fundamentals and Applications

Edited by

Viknesh Andiappan Denny K. S. Ng Santanu Bandyopadhyay

First edition published 2023 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2023 selection and editorial matter, Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay; individual chapters, the contributors Reasonable efforts have been made to publish reliable data and information, but the authors and publishers cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright. com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@ tandf.co.uk Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-14621-8 (hbk) ISBN: 978-1-032-14622-5 (pbk) ISBN: 978-1-003-24022-8 (ebk) DOI: 10.1201/9781003240228 Typeset in Times by codeMantra

Contents Series Preface ...........................................................................................................vii Preface.......................................................................................................................ix Foreword ...................................................................................................................xi Acknowledgments .................................................................................................. xiii Editors ...................................................................................................................... xv Contributors ...........................................................................................................xvii

Part a Fundamentals Chapter 1

Energy Systems and Supply Chains .....................................................3 Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay

Chapter 2

Optimization of Energy Systems and Supply Chains ........................ 15 Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay

Chapter 3

Formulating Generalized Mathematical Models ............................... 41 Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay

Part B applications Chapter 4

Mixed-Integer Linear Programming Model for the Synthesis of Negative-Emission Biochar Systems .................................................. 51 Beatriz A. Belmonte, Kathleen B. Aviso, Michael Francis D. Benjamin, and Raymond R. Tan

Chapter 5

A Comprehensive Guidance on Transitioning Toward Sustainable Hydrogen Network from Localized Renewable Energy System: Case Study of South Korea ...................................... 73 Juin Yau Lim and Bing Shen How

Chapter 6

An Optimization Framework for Polygeneration System Driven by Glycerine Pitch and Diesel ............................................................ 93 Wai Mun Chan and Irene Mei Leng Chew v

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Chapter 7

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Multi-Objective Optimization of TEG Dehydration Process to Mitigate BTEX Emission under Feed Composition Uncertainty .... 111 Rajib Mukherjee and Krystal Smith

Chapter 8

Constrained Production Planning with Parametric Uncertainties ... 133 Nitin Dutt Chaturvedi and Piyush Kumar Kumawat

Chapter 9

Linear Programming Models Based on the Input-Output Framework........................................................................................ 151 Raymond R. Tan, Kathleen B. Aviso, and Jui-Yuan Lee

Chapter 10 Optimisation of Oil Palm-Based Biodiesel Supply Chain: Upstream Stages ............................................................................... 169 Jaya Prasanth Rajakal and Yoke Kin Wan Chapter 11 Optimal Design of Islanded Distributed Energy Systems Incorporating Renewable Energy for Rural Africa: A Namibian Case Study ........................................................................................ 181 Kemi Jegede, Ishanki De Mel, Michael Short, and Adeniyi J. Isafiade Chapter 12 Multi-Objective Optimization for Energy Network Planning: Energy Storage and Distribution in Integrated Solar Powered Grids ................................................................................................. 201 Jayne San Juan, Amiel Ching, Charles Chua, Lorenzo Dyogi, and Charlle Sy Index ...................................................................................................................... 221

Series Preface Towards the late 20th century, the development of various environmentally friendly processes, techniques, and methodologies saw significant growth in the scientific community. The main driving forces for such growth were the rising awareness of sustainable development, more stringent environmental regulation, and increasing costs of raw materials and waste treatment. After several decades of development, we now broadly term these environmentally friendly processes, techniques, and methodologies as green/clean technologies. In the 21st century, the global community has experienced many extreme weather events such as prolonged drought, extreme heat, tornadoes, and wildfires. The scientific community believes that these extreme weather events are closely linked to climate change, and they are expected to increase in frequency and intensity in the future. Following the Paris Agreement and Glasgow Climate Pact, there is now an international commitment to limit the rise of global temperature to well below 2°C by end of this century and to pursue efforts to limit temperature increase to 1.5°C above pre-industrial levels. Hence, it is believed that green/clean technologies will have a much bolder role to play in combating the global climate change in the coming years. It is also worth mentioning that the United Nation Sustainable Development Goals (UNSDG) that were launched in 2015 define 17 important goals to transform the world by 2030. It is believed that some of these goals may be addressed with the development of green/clean technologies. These include: • Goal 6: Clean Water and Sanitation: Ensure access to water and sanitation for all • Goal 7: Affordable and Clean Energy: Ensure access to affordable, reliable, sustainable, and modern energy • Goal 12: Responsible Consumption and Production: Ensure sustainable consumption and production patterns • Goal 13: Climate Action: Take urgent action to combat climate change and its impacts The Green Chemistry and Chemical Engineering book series by CRC Press/Taylor & Francis focuses on the subset of green technologies dedicated to address the “2E” agenda, i.e., environment and energy. It involves the development of materials (e.g., catalysts, nanomaterials), methodologies (e.g., process optimization, footprint reduction, artificial intelligence), and processes (e.g., waste treatment) that will bring forth solutions to address pressing problems such as: • • • • • •

Greenhouse gas management and reduction Sustainable water production Wastewater treatment and recycling Circular economy and waste reduction Renewable energy Sustainable use of energy resources vii

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I am hopeful that this Green Chemistry and Chemical Engineering series will serve as a de facto source of reference materials and practical guides for academics and industrial practitioners looking to advance the discipline and aims of green chemistry and chemical engineering. Dominic C. Y. Foo Centre for Green Technologies University of Nottingham Malaysia

Preface “Ask not what your country can do for you, ask what you can do for your country” A profound and notable quote from an inaugural address delivered by John F. Kennedy. As President of the United States of America, it was one of his efforts to inspire his citizens to understand the importance of taking civil action and getting involved in public service. Such a quote still carries significant relevance in today’s context. Rising global greenhouse gas emission levels and climate change issues today have prompted us to pose the same argument as John F. Kennedy did in the past, but with a much deeper premise: Ask not what your planet can do for you, ask what you can do for your planet. Amid the vastly reported impacts of climate change, it is now crucial for us to rethink energy initiatives for the future. We should aggressively visualize new ways to operate in the energy sector and reduce carbon emissions. Since the Paris Agreement in 2015, nations worldwide have been developing policies for curbing carbon dioxide (CO2) emissions. To date, CO2 emissions are still a critical going issue. CO2 emissions in 2020 saw a significant dip compared to previous years. Experts argue that this was due to movement restrictions and lockdowns imposed in many countries to address the spread of COVID-19 virus. However, it is clear that we cannot rely on such extreme measures to curb CO2 emissions in the long term. This shows that we still have a lot to do to reduce CO2 emissions globally. More effective carbon reduction strategies must be put in place to cut CO2 emissions in the coming few decades. To curb the impacts of rising CO2 emissions, the Intergovernmental Panel on Climate Change (IPCC) report states that the emissions target needs to be net-zero by the year 2050. This would certainly require a rethinking of the way we deploy our energy systems and supply chains, considering energy transition efforts. These efforts take considerable time to materialize once decisions are made. Hence, it is now a critical time for us to make important and accurate decisions for our energy systems. We need the right tools for us to efficiently plan energy systems and supply chains and to avoid making costly judgments that will impact our future negatively. Mathematical models can provide us with the tools required to make wellinformed decisions. They have been widely used in aiding the decision-making process, modeling, and performance prediction related to energy systems and supply chains. Several books have been published on the use of sophisticated models for energy systems and supply chains. However, these books focus mainly on catering to advanced researchers. This led us to discover that there is a gap in addressing readers who are new to the research field and are keen to learn the basics behind developing mathematical models. Without understanding the basics, people are largely deprived of possibilities for using mathematical models meaningfully to solve issues in energy systems and supply chains. The recognition of this gap allowed us to conceptualize the idea for this book. This book aims to provide an understanding of the various available energy systems and supply chains, the basics behind mathematical models, the steps required to develop mathematical models, and examples/case studies where such models ix

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are applied. This book is divided into two parts. In the first part, we have the first three chapters (i.e., Chapters 1 – 3) written in a textbook format suitable for beginners interested to learn about mathematical models. Here, we adopted a strategy of teaching the basics and principles needed to develop basic mathematical models. This will be catered to advanced undergraduate students, postgraduate students, and new researchers keen on exploring this research field. In Chapter 1, we provide the essential concepts and understanding of the working principles of various energy systems and supply chains. A detailed account of the different configurations is described to give a solid foundation for readers. This is linked to Chapters 2 and 3, where essential basics and fundamentals on mathematical models and optimization, development of mathematical models, and the guiding principles when developing such models are covered. In the second part of the book, the remaining chapters contain an edited compilation of contributed chapters from different research groups and authors experienced in this research field. These chapters will provide the reader with illustrative examples and case studies to show how mathematical models are applied to solve problems in different energy systems and supply chains. The second part starts with Chapter 4 where Belmonte, Aviso, Benjamin, and Tan used mathematical models to synthesize optimal biochar systems. In Chapter 5, Lim, How, and Lin applied a mathematical model to the planning of sustainable hydrogen networks in South Korea. Meanwhile, Chapter 6 by Chan and Chew, discussed the application of a mathematical model to optimize polygeneration systems powered by glycerine-pitch and diesel. Following this, Mukherjee and Smith used a framework of mathematical models in Chapter 7 to optimize the economic and environmental sustainability of a TEG dehydration process. Then, Chapter 8 by Kumawat and Chaturvedi applied mathematical models to aggregate production planning for the steel industry in India. Chapter 9 by Tan, Aviso, and Lee pivoted to the macro-level perspective, where mathematical models were used to optimize the economic planning for Taiwan. Following suit, Rajakal and Wan demonstrated a mathematical model’s ability to develop sustainable land expansion strategies for palm-based biodiesel supply chains in Chapter 10. Next, Chapter 11 by Jegede, De Mel, Short, and Isafiade presented the use of a mathematical model to determine the optimal design of a decentralized renewable energy system in Namibia. Finally, Chapter 12 by San Juan, Ching, Chua, Dyogi, and Sy applied a mathematical model to optimize battery energy within the electrical distribution grid. We hope that the twelve chapters of this book provide readers with the foundations and inspiration to tackle problems in energy systems and supply chains using mathematical models. Viknesh Andiappan, Denny K. S. Ng, and Santanu Bandyopadhyay June 2022

Foreword Providing clean, affordable energy is necessary to support rising standards of living throughout the world while keeping environmental footprints within sustainable levels. There is also increasing pressure to curb fossil fuel use and ramp up low-carbon alternatives, particularly renewables, in order to manage climate change. Limiting mean global temperature to a safe level – no more than 2°C above the pre-industrial average – will actually require the world to cut net greenhouse gas emissions to zero by the middle of the 21st century. This goal will also require massive, concerted deployment of multiple carbon management measures, one of which is the widespread use of green energy. This unprecedented challenge will also require energy specialists of the near future to be well versed in computing techniques that can support the rapid greening of the energy sector. This book is intended to address this need by providing a comprehensive introduction to optimization models and their application to energy systems and supply chains. The book is divided into two main parts. The first part focuses on fundamentals and consists of three tutorial chapters written by the editors themselves. Chapter 1 (Energy Systems and Supply Chains) sets the tone by discussing the engineered systems that the world relies on to meet its energy needs. Chapter 2 (Optimization of Energy Systems and Supply Chains) discusses how optimization is a fundamental part of the effective planning, design, and operation of such systems. Then, Chapter 3 (Formulating Generalized Mathematical Models) delves into the mathematics of optimization models in the context of energy applications. These three chapters are designed to provide a textbook-style introduction into the subject matter which is then illustrated further in the latter half of the book. The second part of the book deals with applications and consists of nine contributed chapters by research teams from 15 different institutions in nine countries. The chapters provide a diversified but coherent illustration of how optimization models can be applied to energy-related problems. Chapter 4 (Mixed-Integer Linear Programming Model for the Synthesis of Negative-Emissions Biochar Systems) by Belmonte and colleagues shows the application of network optimization models for planning negative emissions systems that sequester carbon in biochar. Chapter 5 (A Comprehensive Guidance on Transitioning Toward Sustainable Hydrogen Network from Localized Renewable Energy System: Case Study of South Korea) by Lim and colleagues, on the other hand, considers the optimization of future hydrogen networks as part of energy systems with high renewable penetration. Both of these chapters consider macro-level modeling of large-scale systems. On the other hand, Chapter 6 (An Optimization Framework for Polygeneration System Driven by Glycerine Pitch and Diesel) by Chan and Chew considers the optimization of a dual-fuel system for efficient provision of multiple output streams. Chapter 7 (MultiObjective Optimization of TEG Dehydration Process to Mitigate BTEX Emissions under Feed Composition Uncertainty) by Mukherjee and Smith describes a model for the optimization of an industrial process and considers two complications that are often encountered in real-world systems – the presence of multiple objectives and the xi

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occurrence of uncertainty. Chapter 8 (Constrained Production Planning with Parametric Uncertainties) by Chaturvedi and Kumawat similarly considers how to deal with uncertainties that are encountered in the parameters of production planning models. Chapter 9 (Linear Programming Models Based on the Input-Output Framework) by Tan and colleagues describes a special class of optimization models based on Leontief’s wellestablished approach for representing economic networks; the economy-wide impacts of energy disruptions or transitions are also considered. The final three chapters deal with climate-related concerns. Chapter 10 (Optimization for Oil Palm-Based Biodiesel Supply Chain: Upstream Stages) by Rajakal and Wan considers the problem of minimizing land-use change resulting from capacity expansion in agro-industrial supply chains. Managing such expansion is critical to mitigating non-combustion greenhouse gas emissions. Then, Chapter 11 (Optimal Design of Islanded Distributed Energy Systems Incorporating Renewable Energy for Rural Africa: A Namibian Case Study) by Jegede and colleagues demonstrates the benefits of optimal design of decentralized energy production as a strategy for meeting the needs of remote communities in developing countries. Finally, Chapter 12 (Multi-Objective Optimization for Energy Network Planning: Energy Storage and Distribution in Integrated Solar Powered Grids) by Sy and colleagues describes a model for planning renewable energy systems where energy storage is a critical component. Together, these nine chapters provide the reader with a broad spectrum of potential applications of optimization models for energy systems and supply chains, while remaining consistent with the overall direction set by the first three didactic chapters. As conceived by the editors, this book provides a strong general introduction to the area of energy systems optimization using mathematical programming. The content is appropriate for graduate and senior-level undergraduate students in engineering and related disciplines, as well as researchers, practitioners, and lecturers. The careful balance between theory and practice guarantees an engaging journey for the reader who is intent on contributing to the inexorable greening of the world’s energy. Prof. Raymond R. Tan De La Salle University

Acknowledgments First and foremost, we wish to thank the authors who contributed their invaluable expertise in the form of chapters covering state-of-the-art developments in Energy Systems and Supply Chains. The value of this book is based primarily on their inputs. We are also grateful to the staff of CRC Press, who provided invaluable assistance throughout the process of publication. Finally, we would like to thank our family members for their support throughout our professional careers. In particular, Viknesh Andiappan would like to dedicate this book to his wife Aparna and their families. This book will not have been possible without their support and care. Denny K. S. Ng dedicates this book to his wife Pick Ling and children (Jenny, Kenny, and Penny) as well as family members for their support throughout his professional career. Santanu Bandyopadhyay would like to dedicate this book to his wife Sreyasi and son Ratul for their valuable support. “We all die. The goal isn’t to live forever, but to leave behind something that will.”

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Editors Viknesh Andiappan, PhD, is an Associate Professor at Swinburne University of Technology Sarawak Campus. His area of specialization centers on optimization of energy systems and supply chains. His research interests also include design and optimization of net-zero energy systems, synthesis of integrated biorefineries, industrial symbiosis planning, energy planning for greenhouse gas emission reduction, and sustainable agriculture planning. He spends his time working on mathematical programming, multi-objective optimization, input-output modeling, game theory models, process simulation, and process integration tools such as pinch analysis. Dr. Andiappan is well published and well cited for a young researcher (over 70 publications with an h-index of 15) and presented several papers at various conferences. In 2020, Dr. Andiappan was awarded the IBAE Young Researcher of the Year Award. He was also shortlisted as a finalist for the IChemE Young Researcher Malaysia Award in 2018 and 2019. Dr. Andiappan is also an editorial board member for internationally peer-reviewed journals such as Process Integration and Optimization for Sustainability (PIOS) and Frontiers in Sustainability (Sustainable Chemical Process Design). He is a member of the reviewer board for Processes Journal. In addition, he serves as a technical committee member for several conferences. Dr. Andiappan also collaborates closely with well-known international researchers from Malaysia, the Philippines, India, Japan, Taiwan, and United Kingdom. He led and completed a COVID-19 research grant, which worked on developing an economic analysis model to formulate postpandemic recovery strategies for the agro-industry in both Malaysia and the Philippines. He was awarded the IBAE Young Researcher of the Year Award in 2020 for his contributions and achievements in research. Aside from research, Dr. Andiappan is a Chartered Engineer and serves as a Chartered Engineer C&C Report evaluator for the Institution of Chemical Engineers (IChemE). He also serves as the vice-chair for the IChemE Palm Oil Processing Special Interest Group (POPSIG) and was previously the university roadshow coordinator. As the university roadshow director, he led efforts to promote the palm industry and the opportunities for chemical engineers as well as for young chemical engineering undergraduate students in universities around Malaysia. Denny K. S. Ng, PhD, is Head in the School of Engineering and Physical Sciences, Heriot-Watt University, Malaysia. Prof. Ng has well published over 220 papers with an h-index of 40, edited one book, and is the author of one book. He served as an editor in a number of international refereed journals (e.g., Process Integration and Optimization for Sustainability, Springer; Proceedings of the Institution of Civil Engineers – Waste and Resource Management; Processes, MDPI; Frontiers in Energy Research and Frontiers in Sustainability) and guest editor in a number of journals which include Process Safety and Environmental Protection, Elsevier. His areas of specialization include net-zero strategies, optimization of xv

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sustainable value chain of palm oil industry, energy management, resource conservation via process integration techniques, synthesis and analysis of biomass processing, and integrated biorefineries. He is a fellow of IChemE; a fellow of the Higher Education Academy; Chartered Engineer, Engineering Council; Professional Engineer, Malaysia; and Exco member of Young Scientist Network – Academy of Sciences Malaysia (YSN-ASM). He contributed to professional bodies actively. With his excellent contributions, he is listed as one of the Top 2% of scientists in their main subfield discipline in 2019 and 2021, Stanford List. He is recognized as Top Research Scientists Malaysia (TRSM) in 2018 and is the recipient of Ten Outstanding Young Malaysian Award (TOYM) 2017; Institution of Engineers, Malaysia Young Engineer Award 2015; and Global IChemE Young Chemical Engineer of the Year 2012. Prof. Ng also applied his R&D output in industrial consultation projects. Santanu Bandyopadhyay, PhD, is currently Praj Industries Chair Professor in the Department of Energy Science and Engineering, at the Indian Institute of Technology Bombay (IIT Bombay). His research interest includes process integration, pinch analysis, industrial energy conservation, modeling and simulation of energy systems, and design and optimization of renewable energy systems. Since 1994, Prof. Bandyopadhyay has been associated with and contributed toward various developmental, industrial, and research activities involving different structured approaches to process synthesis, energy integration and conservation, as well as renewable energy systems design. Before joining IIT Bombay, he worked for M/s Engineers India Limited, New Delhi. He is currently Co-Editor-in-Chief for Process Integration and Optimization for Sustainability (Springer Nature) as well as Associate Editor for Journal of Cleaner Production (Elsevier), Clean Technologies and Environmental Policy (Springer Nature), and South African Journal of Chemical Engineering (Elsevier). He is a fellow of the Indian National Association of Engineering (INAE).

Contributors Viknesh Andiappan Faculty of Engineering, Computing and Science Swinburne University of Technology, Jalan Simpang Tiga Kuching, Malaysia Kathleen B. Aviso Chemical Engineering Department De La Salle University Manila, Philippines

Irene Mei Leng Chew School of Engineering Monash University Malaysia Selangor, Malaysia Amiel Ching Industrial and Systems Engineering Department De La Salle University Manila, Philippines

Santanu Bandyopadhyay Department of Energy Science and Engineering Indian Institute of Technology Bombay Mumbai, India

Charles Chua Industrial and Systems Engineering Department De La Salle University Manila, Philippines

Beatriz A. Belmonte Chemical Engineering Department University of Santo Tomas Manila, Philippines

Ishanki De Mel Department of Chemical and Process Engineering University of Surrey Guildford, United Kingdom

Michael Francis D. Benjamin Chemical Engineering Department University of Santo Tomas Manila, Philippines Wai Mun Chan School of Engineering Monash University Malaysia Selangor, Malaysia Nitin Dutt Chaturvedi Department of Chemical and Biochemical Engineering Indian Institute of Technology Patna Bihar, India

Lorenzo Dyogi Industrial and Systems Engineering Department De La Salle University Manila, Philippines Bing Shen How Faculty of Engineering, Computing and Science Swinburne University of Technology Sarawak, Malaysia Adeniyi J. Isafiade Department of Chemical Engineering University of Cape Town Cape Town, South Africa

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Kemi Jegede Department of Mining and Process Engineering Namibian University of Science and Technology Windhoek, Namibia and Department of Chemical Engineering University of Cape Town Cape Town, South Africa

Jaya Prasanth Rajakal School of Computer Science and Engineering Taylor’s University, Lakeside Campus Subang Jaya, Malaysia

Piyush Kumar Kumawat Department of Chemical and Biochemical Engineering Indian Institute of Technology Patna Bihar, India

Michael Short Department of Chemical and Process Engineering University of Surrey Guildford, United Kingdom

Jui-Yuan Lee Department of Chemical Engineering and Biotechnology National Taipei University of Technology Taipei, Taiwan

Krystal Smith Department of Chemical Engineering The University of Texas Permian Basin Odessa, Texas

Juin Yau Lim Department of Environmental Science and Engineering Kyung Hee University Gyeonggi, Korea Rajib Mukherjee Department of Chemical Engineering The University of Texas Permian Basin Odessa, Texas Denny K. S. Ng School of Engineering and Physical Sciences Heriot-Watt University Malaysia Wilayah Persekutuan, Malaysia

Jayne San Juan Industrial and Systems Engineering Department De La Salle University Manila, Philippines

Charlle Sy Industrial and Systems Engineering Department De La Salle University Manila, Philippines Raymond R. Tan Chemical Engineering Department De La Salle University Manila, Philippines Yoke Kin Wan Department of Chemical and Environmental Engineering University of Nottingham Malaysia Semenyih, Malaysia and School of Computer Science and Engineering Taylor’s University, Lakeside Campus Subang Jaya, Malaysia

Part A Fundamentals

1

Energy Systems and Supply Chains Viknesh Andiappan Swinburne University of Technology

Denny K. S. Ng Heriot-Watt University Malaysia

Santanu Bandyopadhyay Indian Institute of Technology Bombay

CONTENTS 1.1 1.2 1.3

Introduction ......................................................................................................3 Energy Supply Chains ......................................................................................4 Energy Systems ................................................................................................ 6 1.3.1 Conventional Power Plants ...................................................................6 1.3.2 Cogeneration Systems ...........................................................................8 1.3.3 Trigeneration Systems...........................................................................8 1.3.4 Polygeneration Systems ...................................................................... 10 1.3.5 Hybrid and Renewable Energy Systems ............................................. 10 1.4 Process Systems Engineering ......................................................................... 13 References ................................................................................................................ 14

1.1

INTRODUCTION

Studies from the International Energy Agency (IEA) indicate that we are still faced with the challenge of mitigating global greenhouse gas (GHG) emission, particularly carbon dioxide (CO2). However, IEA studies also revealed a dip in CO2 emission in 2020. According to some, this may be attributed to reducing human activities due to lockdowns to address the COVID-19 pandemic, which started in early 2020. Nevertheless, the pandemic has taught us one lesson: we cannot rely on drastic measures such as lockdowns to curb CO2 emission in the long term. Most CO2 emission originate from using non-renewable fossil fuel energy resources as our primary energy sources. As of 2020, the global energy mix stands at 83.1% nonrenewable fossil fuel energy resources and 5.7% renewable energy resources (British Petroleum, 2021). These data show that we still have a lot to do regarding reducing global CO2 and other GHG emission. As global movement restrictions begin to loosen, more effective carbon reduction strategies must be implemented to reduce DOI: 10.1201/9781003240228-2

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CO2 emission in the coming few decades. To curb the impacts of rising CO2 emission, the Intergovernmental Panel on Climate Change (IPCC) stated that a net-zero emission target needs to be achieved by 2050 (IPCC, 2018). This provides us sufficient motivation to begin revaluating how we deploy our energy systems and supply chains. Experts argue that this is a critical time to make essential and accurate decisions as we cannot afford to make costly judgments. Future energy systems and supply chains need to be designed and operated differently. In fact, future energy systems and supply chains need to be optimized to achieve higher energy efficiencies and reduce emission. This must be coupled with renewable energy to avoid emission. The integration of these solutions requires careful and holistic decision-making. The first step to making informed decisions is to understand how energy systems and supply chains work. This chapter takes a closer look at energy supply chains and the state-of-the-art technologies used in energy systems. At the end of this chapter, we introduce a research domain that deals with the development of decision-making tools.

1.2

ENERGY SUPPLY CHAINS

To understand energy supply chains, let’s understand what a typical supply chain network is. A supply chain network is generally made up of several stages. These stages include suppliers, manufacturers, distribution centers, and customers (Beamon, 1998). A supply chain network shows how each stage is connected. The “connection” here refers to how each stage interacts with the others. Such interactions can be the movement of material and energy resources or the transmission and distribution of generated material and energy. Transportation modes such as trucks, tankers, ships, pipelines, and electric cables are typically considered to transport energy resources from the sources to the destination. However, the choice of transportation is dependent on the type of material and energy resources, cost, and distance of delivery. Figure 1.1 shows the stages found in a typical energy supply chain. The energy supply chain begins with the source where primary energy resources are harvested or extracted. Energy resources can be categorized into non-renewable energy resources (i.e., coal, natural gas, diesel) and renewable energy resources (i.e., biomass, solar, hydro, wind). Non-renewable energy resources refer to fossil fuels such as oil and gas extracted from wells and coal mines. The products from the extractions are then transported to energy systems to generate secondary energy sources such as petrol, diesel, liquified petroleum gas, and electricity. On the other hand, renewable energy resources can be in the form of biomass. Biomass can be obtained from agricultural products and waste collected from croplands and processing facilities. In this respect, biomass can be transported to energy systems to generate secondary energy. Solar and wind energies are other types of renewable energy resources. Unlike biomass, solar and wind do not require transportation. However, solar and wind need to be converted to a useful secondary form in locations with sufficiently high availability and intensity. The energy system refers to the system/facilities that use primary energy resources to produce secondary energy forms for the final energy services. Energy services refer to heating, power, cooling, lighting, cooking, and transportation. Depending on

Energy Systems and Supply Chains

FIGURE 1.1

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Energy supply chain.

the type of energy system, the secondary energy produced has to be transported and distributed to the end-users. For example, electricity is transmitted via transmission lines and then distributed to various end-users via distribution systems. These distribution systems involve transformers for change in voltage. Distribution transformers receive the high-voltage electricity from the transmission lines and distribute the lowvoltage electricity to the end-users such as residences and industry. Similarly, energy

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can be transported in other forms, such as natural gas, and liquefied petroleum gas, via gas pipelines or cylinders. In addition, other heating and cooling energy can then be transported via energy carriers (e.g., steam, water, heating oil) to the end-user using pipelines. Based on the forms of secondary energy produced, energy systems can be classified into conventional power plants, cogeneration systems, trigeneration systems, polygeneration systems, and hybrid and renewable energy systems. The following sections describe each type of energy system.

1.3 ENERGY SYSTEMS As shown in Figure 1.1, energy systems are the “heart” of an overall energy supply chain. These energy systems comprise several unit operations that produce energy for consumption. The following sub-sections dive deeper into the various classifications of energy systems.

1.3.1

Conventional Power Plants

In conventional energy supply chains, the facilities that produce electricity are known as power plants. Power plants convert various primary energy resources to generate electricity (secondary energy). Examples of power plants include gas-fired power plants, coal-fired power plants, biomass-fired power plants, hydropower plants, and many more. Regardless of the primary energy resource used, the technologies in thermal power plants are deployed in different configurations. These configurations can be the gas turbine/engine, steam, or combined cycles. The gas turbine/engine cycle relies on the high-temperature cycle, where primary energy resources are used to produce electricity; then some of the thermal energy is rejected as waste heat. Figure 1.2 shows an example of the gas cycle. In Figure 1.2, both gas turbines and gas engines are used to generate electricity. This is done by combusting gaseous energy resources at high temperatures to generate electricity. However, the waste heat generated from these technologies is typically released into the atmosphere. This is because the conversion

FIGURE 1.2

Example of gas turbine/engine cycle for power plants.

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process of heat to electricity is restricted by the laws of thermodynamics and generates waste heat. Figure 1.3 shows the configuration for the steam cycle. The steam cycle operates on the low-temperature cycle. In other words, the primary energy resource is used to produce heat first, a part of which is then converted to electricity. Examples of a steam cycle may include the use of steam boilers. In steam boilers, energy resources (i.e., natural gas, coal) are combusted, and the heat produced here is used to generate high-pressure steam. The high-pressure steam is then directed to a steam turbine, where electricity is produced. Electricity is produced by converting thermal energy from the high-pressure steam in the steam turbine. The steam then leaves the turbine at a lower pressure. The low-pressure steam is then condensed for reuse. Multiple cycles, such as the gas and steam cycles, may be combined to generate electricity more efficiently in combined cycle power plants (Miller, 2017). Figure 1.4 shows an example of a combined cycle power plant. As shown, the energy system follows the same operation as the gas cycle, but the waste heat is now utilized in a heat recovery steam generator to produce steam. The steam is then passed through a steam turbine to generate more electricity.

FIGURE 1.3

Example of steam cycle for power plants.

FIGURE 1.4

Example of combined cycles for power plants.

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FIGURE 1.5

1.3.2

Example of bottoming cycle for cogeneration systems.

Cogeneration systems

Note that power plants tend to operate with low energy efficiency, especially when the facility’s sole purpose is to produce electricity. On the other hand, cogeneration systems are often considered to improve the overall energy conversion efficiency. Cogeneration systems produce heat and power simultaneously, typically from a single primary energy resource. It is also known as a combined heat and power system (Wu and Wang, 2006). Cogeneration systems aim to utilize energy primary resources with higher efficiency. Such systems are suitable when both heat and electricity demands are present at the same location. Such systems are commonly used in industrial processes or residential areas with colder climates. Cogeneration systems can be configured in various ways such as the bottoming, topping, or combined cycles (Breeze, 2018). Figure 1.5 shows an example of a bottoming cycle in cogeneration systems. Its operation is similar to the steam cycle discussed in Section 1.3.1, with the only difference in the steam usage at the end. As shown in Figure 1.5, steam leaves the steam turbine at a lower pressure and is used for heating purposes (e.g., process heating, space heating). Unused steam is condensed for reuse. Figure 1.6 shows an example of the topping cycle for cogeneration systems. As shown, the topping cycle follows a similar operation to the gas turbine/engine cycle described in Section 1.3.1. However, in cogeneration systems, the waste heat is utilized in a heat recovery steam generator to produce low-grade heat (or low-pressure steam) for heating applications. Topping and bottoming cycles can also be combined in cogeneration systems. Such systems are known as combined cycle cogeneration systems (Rao, 2012). This variant extends the operation of the combined cycle power plant to provide a portion of the steam produced for heating purposes.

1.3.3

trigeneration systems

Trigeneration systems, otherwise known as combined cooling, heating, and power systems, are extensions of cogeneration systems. These systems essentially produce

Energy Systems and Supply Chains

FIGURE 1.6

9

Example of topping cycle for cogeneration systems.

additional cooling energy for space or industrial cooling requirements (Jradi and Riffat, 2014). Trigeneration systems commonly produce cooling energy using two primary technologies: vapor compression chiller and absorption chiller (shown in Figure 1.7). Vapor compression chillers work on the principle of using the vapor compression cycle to produce cooling energy. Such a cycle typically consists of four components: evaporator, compressor, condenser, and expansion valve (as shown in Figure 1.8). Based on Figure 1.8, heat is extracted from chilled water and is added to the refrigerant at constant pressure. Both refrigerant and chilled water do not mix and are separated by a solid wall in the evaporator. The refrigerant then leaves the evaporator as vapor and is compressed by a compressor (which requires electricity input) to high pressure and temperature. Here, the compressor is typically powered by the electricity produced from the cogeneration section (Figure 1.7a). The compressed refrigerant vapor is then sent to a condenser, where its heat is rejected to the outside cooling medium (e.g., cooling water, air). The refrigerant then leaves the condenser as liquid and is expanded in an expansion valve, where its pressure and temperature are reduced to the evaporator level. This cycle repeats to produce chilled water at the evaporator section continuously. On the other hand, absorption chillers utilize the remaining waste heat after heating and electricity generation to produce cooling energy. Unlike vapor compression chillers, the working principle for absorption chillers is the absorption cycle. In the absorption cycle (shown in Figure 1.9), the compressor in the vapor compression cycle is replaced with a chemical cycle. This chemical cycle consists of an absorber, pump, and regenerator. Instead of compressing the refrigerant vapor exiting the evaporator like in the vapor compression cycle, the absorption cycle dissolves the vapor in a liquid (the absorbent). The solution is then pumped to a higher pressure (with much less power input than a compressor). Finally, it uses heat input, typically waste heat, to evaporate the refrigerant vapor from the solution (Figure 1.7b).

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FIGURE 1.7 tion chiller.

1.3.4

Trigeneration system (a) with vapor compression chiller and (b) with absorp-

Polygeneration systems

Polygeneration systems are systems that extend the operations of trigeneration systems. These systems produce heat, power, and cooling, just like trigeneration systems. However, they also produce fuels or additional products. Polygeneration systems are also known as multi-energy or multi-vector energy systems due to their ability to produce other additional outputs (i.e., biofuels, chemicals, hydrogen, clean water) in addition to heating, power, and cooling energy (Mancarella, 2014). These systems would typically contain additional unit operations that utilize either primary energy sources or waste energy to produce additional output. In most cases, polygeneration systems contain thermochemical conversion pathways that produce syngas as an intermediate. In recent times, polygeneration systems have multiple input energy resources and multiple outputs. This makes the system flexible and improves adjustability. For example, Figure 1.10 shows an example of a polygeneration system, where hydrogen is produced due to using energy produced from units that make up a trigeneration system.

1.3.5

Hybrid and renewable energy systems

Hybrid and renewable energy systems produce various kinds of energy for residential and industrial consumption. However, hybrid and renewable energy systems are

Energy Systems and Supply Chains

FIGURE 1.8

Vapor compression cycle.

FIGURE 1.9

Absorption cycle.

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FIGURE 1.10

Optimization for Energy Systems and Supply Chains

Polygeneration system using natural gas.

unique due to the energy resources that are used as input. Hybrid energy systems utilize a combination of renewable and non-renewable energy resources to produce energy services (Shivarama Krishna and Sathish Kumar, 2015). The combination of renewable and non-renewable primary energy resources can be done via co-firing. Co-firing can be implemented in several ways: direct, indirect, and parallel. In direct co-firing, primary energy resources can be either mixed before the combustion chamber or fed separately into a combustion chamber (Aviso et al., 2020). For instance, biomass and coal can be co-fired in a steam boiler to help generate very high-pressure steam for electricity generation. Indirect co-firing is when energy resources are fired in different combustion chambers and mixed to generate energy (Aviso et al., 2020). For example, biomass and coal can be combusted in separate chambers. The gases produced from combustion will be mixed and fed into a steam boiler to generate steam. As for parallel co-firing, energy systems would utilize each energy resource in separate pathways (Aviso et al., 2020). For example, coal is combusted in steam boilers while biomass is used in a gasifier to produce syngas which is later fed into a separate boiler within the same system. Finally, there are alternative hybrid energy systems that do not rely on co-firing. Specific hybrid energy systems utilize renewable energy sources such as solar, wind, and hydro alongside non-renewable energy resources. These systems have pathways that generate energy through combustion and those that avoid combustion entirely under one roof. In this respect, these are not the conventional hybrid energy systems where energy resources are mixed before or after combustion. For example, solar intensity can be converted by concentrated solar panels to produce power. Such unit operations can be operated alongside coal-fired steam boilers within the same system. Renewable energy systems are systems that generate secondary energy exclusively from renewable energy resources. Thus, these systems consist of the unit operations discussed in Sections 1.3.1–1.3.5 but purely rely on renewable energy resources as input to generate heat, power, cooling, and other products. Sections 1.2 and 1.3 indicate that there are many options in energy systems and supply chains to consider for energy generation and distribution. Each system has a

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range of unit operations that may or may not be suitable for energy generation. In particular, energy systems and supply chains can be configured differently based on performance, sizes, costs, environmental impact, operational flexibility, scalability, transport routes, logistics, scheduling, and planning. In this respect, it can be challenging to determine optimal energy systems and supply chains for operation. Thus, decision-making tools are essential to ensuring that optimal technologies and transportation routes will be selected for energy systems and supply chains. The next section introduces a field that develops decision-making tools for systems known as process systems engineering (PSE).

1.4 PROCESS SYSTEMS ENGINEERING The field of PSE has a long-standing history of developing systematic methods to design and optimize energy systems and supply chains (Sargent, 2005; Stephanopoulos and Reklaitis, 2011). PSE is known to develop methods for process synthesis. Process synthesis is defined as “an act of determining the optimal interconnection of processing units as well as the optimal type and design of the units within a process system” (Nishida, 1981). As stated in its definition, process synthesis requires designers to find an optimum chemical process design that fulfills various aspects such as efficiency, sustainability, economics (El-Halwagi, 2017; Nishida, 1981). In this respect, several systematic methods have been developed to provide designers with a methodological framework for designing chemical processes (Biegler et al., 1997; Douglas, 1988; El-Halwagi, 2006; Seider et al., 2004; Stephanopoulos and Reklaitis, 2011). Specifically, these methods provide guidance in identifying the feasibility of a process before the actual design of its units. Prior to this, several alternatives are generated and evaluated based on design decisions and constraints. After ranking by specific performance criteria, the most convenient options are refined and optimized. By applying these systematic methods, quasioptimal targets for process units can be set well ahead of their detailed sizing (Dimian et al., 2014). Systematic methods developed in PSE are not just limited to process synthesis. As shown in reviews presented by Barnicki and Siirola (2004), Cecelja et al. (2011), Grossmann and Daichendt (1996), Li and Kraslawski (2004), and Westerberg (2004), systematic methods have also been developed for the synthesis of energy systems and supply chains. These methods used mathematical optimization to optimize the selection of technologies in energy systems (Ünal et al., 2015). This book aims to provide entry-level access to the basics of mathematical optimization in energy systems and supply chains. This will be covered in two parts (i.e., A and B). Part A starts with Chapter 2, where a detailed account of how we can develop mathematical optimization (models) to optimize energy systems and supply chains is provided. Following this, Chapter 3 recommends best practices for writing generalized mathematical equations. Part A is complemented further by Part B of this book. Part B contains nine contributed chapters, showcasing the range of applications for mathematical optimization.

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REFERENCES Aviso, K.B., Sy, C.L., Tan, R.R., Ubando, A.T., 2020. Fuzzy optimization of carbon management networks based on direct and indirect biomass co-firing. Renew. Sustain. Energy Rev. 132, 110035. Barnicki, S.D., Siirola, J.J., 2004. Process synthesis prospective. Comput. Chem. Eng. 28, 441–446. Beamon, B.M., 1998. Supply chain design and analysis: Models and methods. Int. J. Prod. Econ. 55, 281–294. Biegler, L.T., Grossmann, I.E., Westerberg, A.W., 1997. Systematic Methods of Chemical Process Design. Hoboken, NJ: Prentice Hall PTR. Breeze, P., 2018. Combined Heat and Power. Academic Press, London. British Petroleum, 2021. Statistical Review of World Energy 2021, BP Energy Outlook 2021. Cecelja, D.F., Kokossis, P.A., Du, D., 2011. Integration of ontology and knowledge-based optimization in process synthesis applications, in: Pistikopoulos, E.N., Georgiadis, M.C., Kokossis, A.C. (Eds.), Computer Aided Chemical Engineering. Elsevier, New York, pp. 427–431. Dimian, A.C., Bildea, C.S., Kiss, A.A., 2014. Integrated Design and Simulation of Chemical Processes, 2nd ed. Elsevier, Amsterdam. Douglas, J.M., 1988. Conceptual Design of Chemical Processes. McGraw‐Hill, New York. El-Halwagi, M.M., 2006. Process Integration. Academic Press. El-Halwagi, M.M., 2017. Sustainable Design through Process Integration, 2nd ed. Elsevier, Cambridge, MA. Grossmann, I.E., Daichendt, M.M., 1996. New trends in optimization-based approaches to process synthesis. Comput. Chem. Eng. 20, 665–683. IPCC, 2018. Summary for Policymakers. Cambridge University Press, Cambridge, UK and New York. Jradi, M., Riffat, S., 2014. Tri-generation systems: Energy policies, prime movers, cooling technologies, configurations and operation strategies. Renew. Sustain. Energy Rev. 32, 396–415. Li, X., Kraslawski, A., 2004. Conceptual process synthesis: Past and current trends. Chem. Eng. Process. Process Intensif. 43, 583–594. Mancarella, P., 2014. MES (multi-energy systems): An overview of concepts and evaluation models. Energy 65, 1–17. Miller, J., 2017. The combined cycle and variations that use HRSGs, in: Eriksen, V.L. (Ed.), Heat Recovery Steam Generator Technology. Woodhead Publishing Limited, pp. 17–43. Doi: 10.1016/b978-0-08-101940-5.00002-6. Nishida, N., 1981. A review of process synthesis. AIChE J. 27, 321–351. Rao, A.D., 2012. Combined Cycle Systems for Near-Zero Emission Power Generation. Woodhead Publishing Limited, Cambridge. Sargent, R., 2005. Process systems engineering: A retrospective view with questions for the future. Comput. Chem. Eng. 29, 1237–1241. Seider, W.D., Seader, J.D., Lewin, D.R., 2004. Product and Process Design Principles: Synthesis, Analysis and Evaluation, 2nd ed. John Wiley & Sons, Ltd. Shivarama Krishna, K., Sathish Kumar, K., 2015. A review on hybrid renewable energy systems. Renew. Sustain. Energy Rev. 52, 907–916. Stephanopoulos, G., Reklaitis, G.V., 2011. Process systems engineering: From Solvay to modern bio- and nanotechnology. A history of development, successes and prospects for the future. Chem. Eng. Sci. 66, 4272–4306. Ünal, A.N., Ercan, S., Kayakutlu, G., 2015. Optimisation studies on tri‐generation a review (1).pdf. Int. J. Ener 39, 1311–1334. Westerberg, A.W., 2004. A retrospective on design and process synthesis. Comput. Chem. Eng. 28, 447–458. Wu, D.W., Wang, R.Z.Ã., 2006. Combined cooling, heating and power : A review. Progress Energy Combust. Sci. 32, 459–495.

2

Optimization of Energy Systems and Supply Chains Viknesh Andiappan Swinburne University of Technology

Denny K. S. Ng Heriot-Watt University Malaysia

Santanu Bandyopadhyay Indian Institute of Technology Bombay

CONTENTS 2.1 Introduction .................................................................................................... 15 2.2 Methodology of Mathematical Optimization ................................................. 16 2.3 Illustrative Example ........................................................................................ 22 2.4 Conclusion ...................................................................................................... 38 Further Reading ....................................................................................................... 38

2.1

INTRODUCTION

As mentioned in the previous chapter, process systems engineering (PSE) offers a range of process synthesis methods. In PSE literature, mathematical optimization is among the methods widely used in designing energy systems and supply chains. Before we look into how mathematical optimization is done, it is important for us to understand key terminologies that will be used regularly in this chapter. These key terminologies include: • Model: A mathematical representation or description of a unit operation, process, system, or sub-system. • Modeling: The act of building a model. It is where the behavior and performance of each unit operation, process, or system are represented using mathematical equations. The end product of modeling is a mathematical model. • Simulation: The act of solving a model to study the behavior and performance of a unit operation, process, or system. DOI: 10.1201/9781003240228-3

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• Optimization: The act of changing and adjusting variables in a model to determine the “best” performance or design for a given unit operation, process, or system. The terminologies play a significant role in shaping our understanding of mathematical optimization. Mathematical optimization is typically performed using the steps shown below (Biegler et al., 1997; Hendry et al., 1973):

This chapter aims to provide a detailed account of the steps mentioned above. First, Section 2.2 provides a clear methodology for mathematical optimization. This methodology is then demonstrated via an illustrative example in Section 2.3. The purpose of the illustrative example is to allow readers to relate the theoretical knowledge in this chapter alongside a demonstrated example.

2.2 METHODOLOGY OF MATHEMATICAL OPTIMIZATION This section provides a detailed description of the steps needed in mathematical optimization. The ensuing sub-sections offer a step-by-step guide on how mathematical models can be developed for optimization. Step 1: Developing superstructure of possible connections for unit operations The first step in mathematical optimization is to develop a superstructure. A “superstructure” diagram displays all possible connections between various unit operations considered for an energy system. It is essentially a visual representation of a network with potential process configurations that need to be optimized. It is worth noting that a superstructure can also be used to enumerate several possible unit operations and their alternative system configurations, process integration, operating modes, and other important matters in an energy system (Liu et al., 2011; Westerberg, 1991; Yeomans and Grossmann, 1999). Several publications from renowned PSE researchers have divided superstructure development into a few stages (Grossmann and Sargent, 1978; Mencarelli et al., 2020). The general steps of developing a superstructure are described further in the following:

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FIGURE 2.1 (a) Listing of raw materials and final products (b) Inclusion of unit operations to utilize raw materials and to produce final products.



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FIGURE 2.2 (a) Forward and backward branching (b) Matching.

FIGURE 2.3

Inclusion of interception.

(Pham and El-Halwagi, 2012). At the same time, those unit operations that can produce final products from these intermediate products are also to be connected (Figure 2.2a). This is called backward branching (Pham and El-Halwagi, 2012). The branching exercises here may lead to some matches in intermediate products. Therefore, these branches can be easily connected to form complete pathways in the superstructure (Figure 2.2b).

Optimization of Energy Systems and Supply Chains

Step 2: Collecting data for unit operations specified in the superstructure After Step 1, we need to collect data on the unit operations specified in our superstructure. These data may include (but are not limited to) input-tooutput ratios, efficiencies, yields, conversions, cost of raw materials, cost of unit operations per unit flow or capacity, utility requirements per unit flow, and emission factors. These data will be used in Steps 4 and 5 to determine the performance of each unit operation. However, there would be occasions where data is not readily available for a given unit operation, e.g., new technologies or technologies with limited published literature. In this respect, there are several ways to go about addressing this: • Assumptions are usually made when there is a lack of data. For example, a boiler’s capital cost is given ranges instead of exact values due to differences in capacity requirements. Therefore, a boiler’s cost is then extrapolated, assuming the relationship between the capacity and capital cost of the equipment is linear. Alternatively, assumptions can be made based on benchmarks with similar unit operations used in other applications. • Heuristics or experience can be helpful in cases where data are not available in the literature. • Fundamental calculations based on first principles can be performed to generate simplified data. For example, it may be challenging to obtain data on the conversion of a general boiler as this highly varies based on the manufacturer’s design. Hence, fundamental heat transfer calculations can be done to determine the general conversion. • Simulation packages can also be used to estimate the performance of certain unit operations. The results from such simulation can act as data for us to include. It is also essential to note that the data collection step is important in determining the rigor of a mathematical model will consider. For instance, if we collect simplified data, the eventual model will take a simplified form as well. This may be useful in cases where estimations would be required. However, if the goal is to determine accurate insights, then the data collected must also be reflective. It would be fair to say that a mathematical model is only as good as its data input. However, extremely accurate data and models may pose challenges in computational effort. The most rigorous data and models often require highly complex computational effort to generate solutions. Such cases may take up a lot of time to collect accurate data and involve lengthy durations to generate solutions. This may not suit those who require quick insights to make informed decisions. Hence, a trade-off between simplification and accuracy is required. One must consider factors such as the desired level of accuracy, the urgency to obtain solutions, and the resources available to operate highly complex computational systems. Step 3: Modeling unit operations in the superstructure The cornerstone of mathematical optimization is the development of a mathematical model. The mathematical model is built based on the superstructure developed in the previous step. Here, a series of equations and

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inequalities are formulated to represent the behavior of the unit operations shown in the superstructure. These equations represent the relationships between the inputs and the outputs of a given unit operation, production flows, and costs. In addition, these equations contain variables and parameters. Variables are quantities assumed to vary during calculations. In other words, variables are unknowns that will be varied and determined upon optimization to determine the “best” performance for a given system. For example, if we are interested in knowing what the optimal capacity would be for a given energy system, the capacity is deemed as the variable. It is worth noting that the number of variables in the model determines the computational time required to find solutions. Thus, there are several strategies that can be used to reduce the complexity of models: • Reduce the number of variables by replacing them with fixed parameters • Set boundaries or ranges for each variable to reduce complexity • Decompose the model into several parts, i.e., solving smaller-sized models in series instead of a large-sized one Aside from the number of variables, the nature of the model can significantly impact its computational time. For instance, models could be linear, non-linear, mixed-integer linear, or mixed-integer non-linear in nature. Linear models contain equations that express a linear relationship between its input and output. These equations are often simplified correlations that can be solved in quick durations but lack rigor. Non-linear models are usually deemed more accurate models than their linear counterparts. This is because most real-life applications exhibit non-linear behaviors. However, the downside of non-linear models is that they require longer solving times and may require more labor-intensive algorithms to generate solutions. Many researchers have developed techniques to linearize non-linear equations in the past, but this chapter will not cover this. Nevertheless, the decision to model unit operations in an energy system highly depends on the modeler’s accuracy and computational speed preference. Parameters, on the other hand, are fixed coefficients. Fixed coefficients can come in the form of conversion factors, emission factors, are even cost factors, to name a few. However, these coefficients very much depend on what are the elements we wish to keep constant to allow other elements to be included as variables. Mathematical models can also be categorized into deterministic or nondeterministic models. Deterministic models are essentially models that assume a steady-state condition. In other words, it assumes that the data collected as parameters are fixed and do not change based on time or scenario. Meanwhile, non-deterministic models may contain parameters that are uncertain or vary based on probability. The modeling approach would highly depend on whether the decision-maker is keen to optimize an energy system based on a steady-state scenario or under uncertainty. As this book is catered for beginners in the field, the focus of this chapter will be on deterministic models.

Optimization of Energy Systems and Supply Chains

Regardless of the nature and category of a mathematical model, it can be formulated and built on various commercial optimization software platforms. The choice of software may depend on preference, pricing, features, user-friendliness, computing requirements, and built-in algorithms. Examples of commercial software include (but are not limited to) Microsoft Excel Solver, GAMS, LINGO, AIMMS, and MATLAB. In addition, software such as process-graph or p-graph possesses built-in features that enable users to generate and optimize superstructures simultaneously. Before choosing software, we need to know how we could write equations for a mathematical model. This is covered in Section 2.3, where an illustrative example illustrates the step-by-step procedure to develop a mathematical model. However, it is unlikely for publications in PSE research to present equations in the format shown in Section 2.3. In fact, they often (if not always) use generalized mathematical equations equipped with symbols and notations to represent the superstructure mathematically. Examples of these can be found in papers (Andiappan et al., 2014; Leong et al., 2019; Tay et al., 2011). The purpose of these generalized equations is to provide a generic framework for other researchers to use as a guide in the future, allowing them to replicate the concept in their work. Nevertheless, beginners need to understand what these symbols and notations mean before being able to follow them as a guide. Chapter 3 will expand on this further by describing recommended ways to write generalized equations and best practices when doing so. Step 4: Setting objective function and constraints Once the behavior and performance of each unit operation in the superstructure are mathematically modeled, additional constraints must be set. These constraints can be in the form of equations or inequalities (as shown below).

h( x ) = 0 g( x ) ≤ 0

Equality Constraint Inequality Constraint

Typical examples of such constraints may include (but are not limited to) a target on product demands, a limit on available raw materials, and feasible operating ranges for a unit operation. These constraints define the relationship between the decision variables, whose values are determined by optimizing (e.g., minimizing or maximizing) the model according to a specific optimization objective (Baños et al., 2011; Edgar et al., 2001; Floudas, 1995). The optimization objective here is known as the objective function. If the objective function is exclusively formulated for a single criterion (e.g., economic performance), it is typically considered single-objective optimization (Savic, 2002). Other examples of objective functions may include maximizing yield, maximizing energy efficiency, maximizing profit, minimizing the number of processing steps, minimizing cost, and minimizing environmental impact.

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By default, all models are optimized based on a single objective. In other words, each mathematical model can only consider one objective or objective function at a time. This indicates that mathematical models cannot simultaneously have two or more objective functions. Several approaches have been developed to consider two or more objectives within a single model to address this. These approaches fall under the category known as multi-objective optimization. Some examples of multi-objective optimization approaches include Pareto optimization, weight-sum, ε-constraint, fuzzy optimization, and evolutionary multi-objective algorithms. For further information on the basics behind multi-objective optimization, readers are directed to Andiappan (2017). Step 5: Optimization and generating solutions When the objective function is set, the final step is to solve the model and generate solutions. The solving of a mathematical model here refers to optimization. As mentioned earlier, optimization is done by adjusting the variables in a model to determine the “best” performance or solutions. To solve a mathematical model, several algorithms are available depending on the mathematical nature of the model (e.g., linear, mixed-integer linear, non-linear, and mixed-integer non-linear). In most commercial optimization software, there are a set of algorithms working in the background to solve the models that we developed and generate solutions accordingly. Algorithms are essentially a sequence of instructions and procedures used to solve mathematical problems. For more details on algorithms, readers are directed to papers such as Andiappan (2017) for further reading. The solution of the optimization would represent the optimal configuration of the energy system. The optimal system, in this sense, may refer to the unit operations with the highest yield, the highest energy efficiency, the simplest, the minimum cost, the maximum profit, and so on, depending on the objective function set in Step 4. Since mathematical optimization optimizes a superstructure and reduces it to the optimal set of unit operations, it explicitly determines the topology of energy systems. The following section provides an illustrative example to demonstrate the steps described in Section 2.3.

2.3

ILLUSTRATIVE EXAMPLE

In this illustrative example, let us consider an energy system that is expected to either utilize biomass or palm oil mill effluent and eventually produce final outputs such as electricity, medium pressure steam, and methanol. This example is desired to determine the optimal energy system configuration with the highest profit margin. The first step to developing a mathematical model is to put together a superstructure. Step 1: Developing superstructure of possible connections for unit operations i. Enumerating possible raw materials, final products, and unit operations As mentioned previously, this step lists out the raw materials and desired final products. For this example, biomass and palm oil mill effluent are

Optimization of Energy Systems and Supply Chains

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FIGURE 2.4 Raw materials and final products.

FIGURE 2.5 Inclusion of unit operations to utilize raw materials and to produce final products.

listed as raw materials (Figure 2.4). Meanwhile, electricity, medium pressure steam, and methanol are included as the final products in the superstructure (Figure 2.4). The unit operations that utilize biomass and palm oil mill effluent are included in the superstructure. For example, a pyrolysis unit is added to use biomass, while the anaerobic digestion unit is included for the palm oil mill effluent (POME) (Figure 2.5). As for the final products, steam turbine and methanol synthesis units are added to the superstructure (Figure 2.5).

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FIGURE 2.6

Forward and backward branching.

FIGURE 2.7

Inclusion of matches.

FIGURE 2.8 Including of interceptions.

 



Optimization of Energy Systems and Supply Chains

 

Step 2: Collecting data for unit operations specified in the superstructure Once the superstructure has been finalized, data must be collected for each unit operation. This may include data related to performance, cost, and material prices. Such data can be compiled from a variety of sources. For this example, data was obtained from journal papers and textbooks. Tables 2.1 and 2.2 show the data collected for this example. These data will be used in Step 3 as part of the equation development process. Step 3: Modeling unit operations in the superstructure Based on Steps 1 and 2, a mathematical model can now be formulated in modeling software, as introduced in the previous section. The equations for the model were developed and coded in commercial optimization software, i.e., LINGO v18*. The following provides an overview of how each equation was written for this example. This overview offers a guide based on each section of the superstructure developed in Step 1. We start with the pyrolysis unit shown in Figure 2.9. The left side of Figure 2.9 shows the labels given to each flow. F_Biomass, F_SG_PYRO, and F_M_PYRO represent the flows to and from the pyrolysis unit. The right side of Figure 2.9 shows the equations used to represent the conversion occurring in the pyrolysis unit. C_PYRO_SG and C_PYRO_M are conversion factors for syngas and methane, respectively. Similarly, this is done for the anaerobic digestion unit, as shown in Figure 2.10. Meanwhile, Figure 2.11 shows how the distribution and summation of methane flow are represented in equations. Next, Figure 2.12 shows the equations formulated for the boiler and the steam reformer conversion. The summation of the syngas flow is shown in Figure 2.13. This includes the syngas produced at the pyrolysis unit and the steam reformer. The syngas is then fed into the methanol synthesis unit, where Figure 2.14 shows the equations representing its conversion to methanol.

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TABLE 2.1 Compilation of Performance and Cost Data for Each Unit Operation Collected Data Unit Operation Pyrolysis

Anaerobic digestion Boiler

Conversion (Output/Input) 0.155 kg Syngas/kg Biomass, 0.005 kg Methane/kg Biomass (Hanif et al., 2016) 0.20 kg Methane/kg POME (Ng et al., 2013) 5.5 kg High-pressure steam/kg Methane (Andiappan et al., 2014)

Steam 0.90 kg Syngas/kg Methane reformer (Basye and Swaminathan, 1997) Steam turbine 0.0194 kWh Electricity/kg Highpressure steam, 1 High-pressure steam/kg Mediumpressure steam (Andiappan et al., 2014) Methanol 0.937 kg Methanol/kg Syngas synthesis (Andiappan et al., 2016) a

CAPEX Factor (Cost/Input)

Annualized CAPEX Factora (Cost/Input.year)

162.8 $/ (kg/h Biomass) (Sadhukhan et al., 2014)

21.2 $/ (kg/h Biomass).y

35.8 $/ (kg/h POME) (Sadhukhan et al., 2014) 87.5 $/ (kg/h Highpressure steam) (Foong et al., 2020) 56.7 $/ (kg/h Methane) (Steinberg, 1989) 6100 $/ kW Electricity (Andiappan et al., 2014)

4.7 $/ (kg/h POME).y 11.4 $/ (kg/h High-pressure steam).y 7.4 $/ (kg/h Methane).y 793 $/ (kW Electricity).y

40 $/ (kg/h Methanol) (Sadhukhan et al., 2014)

5.2 $/ (kg/h Methanol).y

CAPEX factors are annualized by multiplying CAPEX factors with an assumed annualizing factor of 0.13/year.

TABLE 2.2 Compilation of Pricing Data for Raw Materials and Products Raw Material or Product

Material Pricing Factor (Cost/Material)

Biomass

0.0046 $/kg (Andiappan et al., 2016) – 0.0667 $/kWh (Andiappan et al., 2016) 0.046 $/kg (Andiappan et al., 2016) 0.805 $/kg (Andiappan et al., 2016)

POME Electricity Medium-pressure steam Methanol

Following Figures 2.9–2.14, the cost equations were written based on the flow variables of each unit operation. This is shown in Figure 2.15. In addition, the prices for raw materials and products were included in the model to determine the economic performance of the synthesized

Optimization of Energy Systems and Supply Chains

FIGURE 2.9 Equations for pyrolysis unit.

FIGURE 2.10 Equation for anaerobic digestion unit.

FIGURE 2.11

Equations for distribution and summation of methane flow.

FIGURE 2.12 Equations for boiler and steam reformer units.

27

28

Optimization for Energy Systems and Supply Chains

FIGURE 2.13 Equation for summation of syngas.

FIGURE 2.14 Equations for steam turbine and methanol synthesis units.

FIGURE 2.15 Cost equations for all units.

Optimization of Energy Systems and Supply Chains

FIGURE 2.16 Constraints included for feed flow.

system. Economic equations that calculate the expenditure for materials and total revenue in the energy system shall be included. This will be shown in the next step. Step 4: Setting objective function and constraints The objective function of this illustrative example is to maximize the system’s profit margin. We can determine the optimal configuration with maximum profit margin by doing this. Meanwhile, additional constraints such as the limit of available feed for biomass and POME were included in the model. These constraints function as boundaries for the flow rate that could be utilized in the unit operations. This is shown in Figure 2.16. The values for these limits can be seen in the complete list of equations below. These equations are coded in the commercial optimization software, i.e., LINGO Version 18. A demo version of the LINGO software can be downloaded for free from www.lindo.com. The complete code used in LINGO is as follows: !Model; !Objective Function; Max = Margin; !Conversion Data; C_PYRO_SG = 0.155; C_PYRO_M = 0.005; C_AD_M = 0.20; C_Boiler_HPS = 5.5; C_SR_SG = 0.90; C_MSYN_MEOH = 0.937; C_HST_MPS = 1; C_HST_Elec = 0.0194; !Raw Material Availability; F_Biomass_av = 100000; F_POME_av = 100000; !Cost Data; CF_PYRO = 21.2; !162.82; CF_AD = 4.7; !0.018 ; CF_Boiler = 11.4; !87.5 ; CF_SR = 7.4; !150 ;

29

30

Optimization for Energy Systems and Supply Chains

CF_HST = 793; !610 ; CF_MSYN = 40; !172.57 ; !Pricing Data; P_MPS = 0.046; P_MEOH = 0.805; P_Elec = 0.0667; P_Biomass = 0.0046; !Constraints; F_Biomass_av >= F_Biomass; F_POME_av >= F_POME; !Equations; !Conversion in Pyrolysis; F_SG_PYRO = F_Biomass * C_PYRO_SG; F_M_PYRO = F_Biomass * C_PYRO_M; !Conversion in Anaerobic Digestion; F_M_AD = F_POME * C_AD_M; !Distribution of Methane from Pyrolysis; F_M_PYRO = F_M_PYRO_Boiler + F_M_PYRO_SR; !Distribution of Methane from Anaerobic Digestion; F_M_AD = F_M_AD_Boiler + F_M_AD_SR; !Mixing of Methane at Boiler and Steam Reformer; F_M_Boiler = F_M_PYRO_Boiler + F_M_AD_Boiler; F_M_SR = F_M_PYRO_SR + F_M_AD_SR; !Mixing of Syngas at MEOH Synthesis; F_SG_MSYN = F_SG_PYRO + F_SG_SR; !Conversion at Boiler and Steam Reformer; F_HPS = F_M_Boiler * C_Boiler_HPS; F_SG_SR = F_M_SR * C_SR_SG; !Conversion to MEOH; F_MEOH = F_SG_MSYN * C_MSYN_MEOH; !Conversion at Steam Turbine; F_Elec = F_HPS * C_HST_Elec; F_MPS = F_HPS * C_HST_MPS; !Cost Equations; !Pyrolysis; Cost_PYRO = F_Biomass * CF_PYRO; !Anaerobic Digestion; Cost_AD = F_POME * CF_AD; !Boiler; Cost_Boiler = F_MPS * CF_Boiler; !Steam Reformer; Cost_SR = F_M_SR * CF_SR; !High Pres Steam Turbine; Cost_HST = F_Elec * CF_HST;

Optimization of Energy Systems and Supply Chains

31

!Methanol Synthesis; Cost_MSYN = F_MEOH * CF_MSYN; !Profit and Expenditure; TotalAnnualizedCost = Cost_PYRO + Cost_AD + Cost_Boiler + Cost_SR + Cost_HST + Cost_MSYN; TotalRev = (F_Elec * P_Elec + F_MPS * P_MPS + F_MEOH * P_MEOH) * AOT; TotalExp = (F_Biomass * P_Biomass) * AOT; !Annual Operating Time; AOT = 8000; Margin = TotalRev - TotalExp - TotalAnnualizedCost; @free(Margin);

The last four lines of the code above indicate the equations that calculate the total cost of equipment, total revenue from products, and total material expenditure. The final equation indicates the equation to determine the profit margin by subtracting the total cost of equipment and the total material expenditure from the total revenue from products. Step 5: Solving model and generating solutions After adding the equations into LINGO, the model can be solved to generate an optimal solution. The results generated in LINGO are shown as follows: Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Model Class:

0.1971697E+09 0.000000 0 0.17 LP

Total variables:

27

Nonlinear variables:

0

Integer variables:

0

Total constraints: Nonlinear constraints:

26 0

Total nonzeros: Nonlinear nonzeros:

63 0

Variable MARGIN C_PYRO_SG C_PYRO_M C_AD_M C_BOILER_HPS C_SR_SG

Value 0.1971697E+09 0.1550000 0.5000000E-02 0.2000000 5.500000 0.9000000

32

Optimization for Energy Systems and Supply Chains C_MSYN_MEOH C_HST_MPS C_HST_ELEC F_BIOMASS_AV F_POME_AV CF_PYRO CF_AD CF_BOILER CF_SR CF_HST CF_MSYN P_MPS P_MEOH P_ELEC P_BIOMASS F_BIOMASS F_POME F_SG_PYRO F_M_PYRO F_M_AD F_M_PYRO_BOILER F_M_PYRO_SR F_M_AD_BOILER F_M_AD_SR F_M_BOILER F_M_SR F_SG_MSYN F_SG_SR F_HPS F_MEOH F_ELEC F_MPS COST_PYRO COST_AD COST_BOILER COST_SR COST_HST COST_MSYN TOTALANNUALIZEDCOST TOTALREV AOT TOTALEXP

0.9370000 1.000000 0.1940000E-01 100000.0 100000.0 21.20000 4.700000 11.40000 7.400000 793.0000 40.00000 0.4600000E-01 0.8050000 0.6670000E-01 0.4600000E-02 100000.0 100000.0 15500.00 500.0000 20000.00 0.000000 500.0000 0.000000 20000.00 0.000000 20500.00 33950.00 18450.00 0.000000 31811.15 0.000000 0.000000 2120000. 470000.0 0.000000 151700.0 0.000000 1272446. 4014146. 0.2048638E+09 8000.000 3680000.

The results above suggest that the optimal solution had a maximum profit margin of $205 million/y. Figure 2.17 summarizes the optimal flows for each unit operation in the optimum solution. For this case, the biomass and POME were fully utilized. This required both pyrolysis and anaerobic digestion units to be selected. However, all methane produced by the pyrolysis and anaerobic digestion units was fed only to the steam reformer. This means that the boiler and steam turbine units were not chosen.

Optimization of Energy Systems and Supply Chains

33

FIGURE 2.17 Optimal solution for an illustrative example.

The methane entering the steam reformer was converted to syngas and added to the syngas from pyrolysis for further processing in the methanol synthesis unit. Lastly, methanol is produced as the final product in the methanol synthesis unit. Apart from presenting the optimal solution, Figure 2.17 also highlights that the boiler and steam turbine route was not chosen. This gives us an insight that such a route does not offer a higher profit margin compared to the selected system. However, we may repeat this step with a different unit price for biomass to conduct a sensitivity analysis and understand the impact of its price on the optimal solution. By varying the biomass price, it was found that only when the price of biomass is lower than 0.12 $/kg, the pyrolysis will be chosen alongside the anaerobic digester. In other words, the pyrolysis unit will not be favorable when the biomass price is 0.12 $/kg or higher. These insights are very useful for practical analysis and planning. Further analysis can be done if other aspects such as energy consumption, and emission are considered in the model. The example here can also be extended to consider supply chain elements. In Chapter 1, we learned that energy resources can be transported from one stage of the energy supply chain to another stage using different modes of transportation. These transportation modes have unique costs based on distance. Let us revisit Figure 2.16. The equations and representations in Figure 2.16 can be updated to consider the sourcing and transportation of biomass to the energy system. Figure 2.18 shows two possible sources at different locations (i.e., A and B) and distance from the energy system. The first two equations in Figure 2.18 represent the limits in which biomass can be sourced from location A and B, respectively. F_Biomass_av_A and F_ Biomass_av_A are the amount of available biomass at locations A and B. The third equation in Figure 2.18 expresses the total amount of biomass sourced from A and B that will enter the pyrolysis unit. From here, the transportation elements can be introduced. The cost factors CTA and CTB in Figure 2.18 indicate the cost required to transport a kg of biomass per unit distance. CTA and CTB are then included alongside the distances in the fourth equation in Figure 2.18 to determine total transportation cost. The LINGO code shown earlier is updated with the equations in Figure 2.18. The following code shows the updated LINGO code.

34

Optimization for Energy Systems and Supply Chains

FIGURE 2.18 Equations for transportation cost.

!Model; !Objective Function; Max = Margin; !Conversion Data; C_PYRO_SG = 0.155; C_PYRO_M = 0.005; C_AD_M = 0.20; C_Boiler_HPS = 5.5; C_SR_SG = 0.90; C_MSYN_MEOH = 0.937; C_HST_MPS = 1; C_HST_Elec = 0.0194; !Raw Material Availability; F_Biomass_av_A = 100000; F_Biomass_av_B = 100000; F_POME_av = 100000; !Cost Data; CF_PYRO = 21.2; CF_AD = 4.7; CF_Boiler = 11.4; CF_SR = 7.4; CF_HST = 793; CF_MSYN = 40; !Cost of Transporting Biomass; CTA = 0.06; CTB = 0.02; !Distance in km; DA = 2; DB = 4; !Pricing Data;

Optimization of Energy Systems and Supply Chains P_MPS = 0.046; P_MEOH = 0.805; P_Elec = 0.0667; P_Biomass = 0.0046; !Constraints; F_Biomass_av_A >= F_Biomass_A; F_Biomass_av_B >= F_Biomass_B; F_POME_av >= F_POME; F_Biomass_A + F_Biomass_B = F_Biomass; !Equations; !Conversion in Pyrolysis; F_SG_PYRO = F_Biomass * C_PYRO_SG; F_M_PYRO = F_Biomass * C_PYRO_M; !Conversion in Anaerobic Digestion; F_M_AD = F_POME * C_AD_M; !Distribution of Methane from Pyrolysis; F_M_PYRO = F_M_PYRO_Boiler + F_M_PYRO_SR; !Distribution of Methane from Anaerobic Digestion; F_M_AD = F_M_AD_Boiler + F_M_AD_SR; !Mixing of Methane at Boiler and Steam Reformer; F_M_Boiler = F_M_PYRO_Boiler + F_M_AD_Boiler; F_M_SR = F_M_PYRO_SR + F_M_AD_SR; !Mixing of Syngas at MEOH Synthesis; F_SG_MSYN = F_SG_PYRO + F_SG_SR; !Conversion at Boiler and Steam Reformer; F_HPS = F_M_Boiler * C_Boiler_HPS; F_SG_SR = F_M_SR * C_SR_SG; !Conversion to MEOH; F_MEOH = F_SG_MSYN * C_MSYN_MEOH; !Conversion at Steam Turbine; F_Elec = F_HPS * C_HST_Elec; F_MPS = F_HPS * C_HST_MPS; !Cost Equations; !Pyrolysis; Cost_PYRO = F_Biomass * CF_PYRO; !Anaerobic Digestion; Cost_AD = F_POME * CF_AD; !Boiler; Cost_Boiler = F_MPS * CF_Boiler; !Steam Reformer; Cost_SR = F_M_SR * CF_SR; !High Pres Steam Turbine; Cost_HST = F_Elec * CF_HST;

35

36

Optimization for Energy Systems and Supply Chains

!Methanol Synthesis; Cost_MSYN = F_MEOH * CF_MSYN; !Profit and Expenditure; TotalAnnualizedCost = Cost_PYRO + Cost_AD + Cost_Boiler + Cost_SR + Cost_HST + Cost_MSYN; TotalRev = (F_Elec * P_Elec + F_MPS * P_MPS + F_MEOH * P_MEOH) * AOT; TotalExp = (F_Biomass * P_Biomass) * AOT; TotalTransportCost = (F_Biomass_A * DA * CTA + F_Biomass_B * DB * CTB) * AOT; !Annual Operating Time; AOT = 8000; Margin = TotalRev - TotalExp - TotalAnnualizedCost - TotalTransportCost; @free(Margin);

The model is then solved, and the results are shown below. Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Model Class:

0.1331697E+09 0.000000 0 0.17 LP

Total variables: Nonlinear variables: Integer variables:

30 0 0

Total constraints: Nonlinear constraints:

29 0

Total nonzeros: Nonlinear nonzeros:

71 0

Variable MARGIN C_PYRO_SG C_PYRO_M C_AD_M C_BOILER_HPS C_SR_SG C_MSYN_MEOH C_HST_MPS C_HST_ELEC F_BIOMASS_AV_A

Value 0.1331697E+09 0.1550000 0.5000000E-02 0.2000000 5.500000 0.9000000 0.9370000 1.000000 0.1940000E-01 100000.0

37

Optimization of Energy Systems and Supply Chains F_BIOMASS_AV_B F_POME_AV CF_PYRO CF_AD CF_BOILER CF_SR CF_HST CF_MSYN CTA CTB DA DB P_MPS P_MEOH P_ELEC P_BIOMASS F_BIOMASS_A F_BIOMASS_B F_POME F_BIOMASS F_SG_PYRO F_M_PYRO F_M_AD F_M_PYRO_BOILER F_M_PYRO_SR F_M_AD_BOILER F_M_AD_SR F_M_BOILER F_M_SR F_SG_MSYN F_SG_SR F_HPS F_MEOH F_ELEC F_MPS COST_PYRO COST_AD COST_BOILER COST_SR COST_HST COST_MSYN TOTALANNUALIZEDCOST TOTALREV AOT TOTALEXP TOTALTRANSPORTCOST

100000.0 100000.0 21.20000 4.700000 11.40000 7.400000 793.0000 40.00000 0.6000000E-01 0.2000000E-01 2.000000 4.000000 0.4600000E-01 0.8050000 0.6670000E-01 0.4600000E-02 0.000000 100000.0 100000.0 100000.0 15500.00 500.0000 20000.00 0.000000 500.0000 0.000000 20000.00 0.000000 20500.00 33950.00 18450.00 0.000000 31811.15 0.000000 0.000000 2120000. 470000.0 0.000000 151700.0 0.000000 1272446. 4014146. 0.2048638E+09 8000.000 3680000. 0.6400000E+08

Figure 2.19 shows the optimal solution generated from the updated model. As shown, the optimal system remained the same for the energy system. However, biomass was sourced and transported from location B to the energy system. This is because the total cost of transportation for this route was cheaper compared to the alternative in location A.

38

Optimization for Energy Systems and Supply Chains

FIGURE 2.19 Optimal solution for illustrative example with transportation considerations.

For this case, it is assumed that the cost of factors CTA and CTB apply to one type of transport mode. If multiple transport options need to be considered, additional nodes can be included in the superstructure. Consider a case where trucks and pipelines are possible transport options. In this case, one node must be assigned to the truck node from source to the destination and another node for pipeline. These additional nodes can then be modeled using the same concept described above. The above extension serves as an entry-level example on the concept of including supply chain considerations. It must be noted that supply chains can grow in complexity depending on the aspects considered in the model. Nevertheless, the concept in this chapter can be expanded upon and applied to other transport modes such as grid connections and pipelines.

2.4 CONCLUSION This chapter provided an overview of the steps to develop a mathematical model and optimize energy systems. An illustrative example was also presented to provide a detailed guide on how a mathematical model can be developed and used to develop insights. It is worth noting that the model developed for the example was simplified for demonstration purposes. Readers are welcome to add more considerations such as energy consumption and emission, into the model to develop further insights.

FURTHER READING Readers are encouraged to refer to Pham and El-Halwagi (2012) for examples on development superstructures. In addition to this, Ünal et al. (2015) provide an overview of applications for mathematical optimization in energy systems. Meanwhile, the background on linear, non-linear, mixed-integer linear, and mixed-integer nonlinear models can be found in Andiappan (2017). Andiappan (2017) also provides a comprehensive review of deterministic and non-deterministic models. Andiappan, V., 2017. State-of-the-art review of mathematical optimisation approaches for synthesis of energy systems. Process Integr. Optim. Sustain. 1, 165–188. Andiappan, V., Ng, D.K.S., Bandyopadhyay, S., 2014. Synthesis of biomass-based trigeneration systems with uncertainties. Ind. Eng. Chem. Res. 53, 18016–18028. Andiappan, V., Tan, R.R., Ng, D.K.S., 2016. An optimization-based negotiation framework for energy systems in an eco-industrial park. J. Clean. Prod. 129, 496–507.

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Baños, R., Manzano-Agugliaro, F., Montoya, F.G., Gil, C., Alcayde, A., Gómez, J., 2011. Optimization methods applied to renewable and sustainable energy: A review. Renew. Sustain. Energy Rev. 15, 1753–1766. Basye, L., Swaminathan, S., 1997. Hydrogen Production Costs – A Survey. U.S. Department of Energy Office of Scientific and Technical Information, Maryland USA. Biegler, L.T., Grossmann, I.E., Westerberg, A.W., 1997. Systematic Methods of Chemical Process Design. Hoboken, NJ: Prentice Hall PTR. Edgar, T.F., Himmelblau, D.M., Lasdon, L.S., 2001. Optimization of Chemical Processes. Boston, MA: McGraw-Hill. Floudas, C.A., 1995. Nonlinear and Mixed-Integer Optimization, Handbook of Applied Optimization. Cary, NC: Oxford University Press. Foong, S.Z.Y., Chong, M.F., Ng, D.K.S., 2020. Strategies to promote biogas generation and utilisation from palm oil mill effluent. Process Integr. Optim. Sustain. Doi: 10.1007/ s41660-020-00121-y Grossmann, I.E., Sargent, R.W.H., 1978. Optimum design of chemical plants with uncertain parameters. AIChE J. 24, 1021–1028. Hanif, M.U., Capareda, S.C., Iqbal, H., Arazo, R.O., Baig, M.A., 2016. Effects of pyrolysis temperature on product yields and energy recovery from co-feeding of cotton gin trash, cow manure, and microalgae: A simulation study. PLoS One 11, 1–11. Hendry, J.E., Rudd, D.F., Seader, J.D., 1973. Synthesis in the design of chemical processes. AIChE J. 19, 1–15. Leong, H., Leong, H., Foo, D.C.Y., Ng, L.Y., Andiappan, V., 2019. Hybrid approach for carbon-constrained planning of bioenergy supply chain network. Sustain. Prod. Consum. 18. Doi: 10.1016/j.spc.2019.02.011 Liu, P., Georgiadis, M.C., Pistikopoulos, E.N., 2011. Advances in energy systems engineering. Ind. Eng. Chem. Res. 50, 4915–4926. Mencarelli, L., Chen, Q., Pagot, A., Grossmann, I.E., 2020. A review on superstructure optimization approaches in process system engineering. Comput. Chem. Eng. 136, 106808. Ng, R.T.L., Ng, D.K.S., Tan, R.R., 2013. Systematic approach for synthesis of integrated palm oil processing complex. Part 2: Multiple owners. Ind. Eng. Chem. Res. 52, 10221–10235. Pham, V., El-Halwagi, M., 2012. Process synthesis and optimization of biorefinery configurations. AIChE J. 58, 1212–1221. Sadhukhan, J., Kok Siew, N., Martinez-Hernandez, E., 2014. Biorefineries and Chemical Processes: Design, Integration and Sustainability Analysis, 1st ed. Wiley, Sussex. Savic, D., 2002. Single-objective vs. multiobjective optimisation for integrated decision support, in: International Congress on Environmental Modelling and Software. International Environmental Modelling & Software Society Lugano, Switzerland, p. 119. Steinberg, M., 1989. Modern and prospective technologies for hydrogen production from fossil fuels. Int. J. Hydrogen Energy 14, 797–820. Tay, D.H.S., Ng, D.K.S., Sammons, N.E., Eden, M.R., 2011. Fuzzy optimization approach for the synthesis of a sustainable integrated biorefinery. Ind. Eng. Chem. Res. 50, 1652–1665. Ünal, A.N., Ercan, S., Kayakutlu, G., 2015. Optimisation studies on tri‐generation a review (1).pdf. Int. J. Ener 39, 1311–1334. Westerberg, A.W., 1991. Process engineering, perspectives in chemical engineering, research and education, in: Clark K. Colton (ed.) Advances in Chemical Engineering. Amsterdam: Elsevier, pp. 499–523. Yeomans, H., Grossmann, I.E., 1999. A systematic modeling framework of superstructure optimization in process synthesis. Comput. Chem. Eng. 23, 709–731.

3

Formulating Generalized Mathematical Models Viknesh Andiappan Swinburne University of Technology

Denny K. S. Ng Heriot-Watt University Malaysia

Santanu Bandyopadhyay Indian Institute of Technology Bombay

CONTENTS 3.1 3.2 3.3

Introduction .................................................................................................... 41 Recommended Practices................................................................................. 42 General Representations and Equations ......................................................... 43 3.3.1 Conversion .......................................................................................... 43 3.3.2 Branching Points.................................................................................44 3.3.3 Summing Points.................................................................................. 45 3.3.4 Other Aspects .....................................................................................46 3.4 Conclusion ...................................................................................................... 47 Further Reading ....................................................................................................... 47 References ................................................................................................................ 48

3.1 INTRODUCTION Generic mathematical equations have several components: index, labels, variable/ parameter symbols, and notations. An index represents a set of elements. The elements here may include input materials, intermediate materials, final outputs, technologies, and emission. For example, suppose an index i may be used to represent the input material in a system. In that case, i = 1 may refer to a certain input material (i.e., biomass), i = 2 may be a different input material (i.e., coal), and this can go up to i = I input materials. This applies to intermediates and outputs, where other indices such as k and p are used, respectively. Similarly, indices can be used to describe technologies or process units too. For example, index j can be used below to represent technologies at the first layer. The following layer of technologies is represented by index j’. This is to indicate the difference between the first and second layers. However, more layers can be added depending on one’s preference and the needs for the model. More indices must be assigned to every additional layer considered in such instances. DOI: 10.1201/9781003240228-4

41

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Optimization for Energy Systems and Supply Chains

Apart from indices, mathematical equations consist of variables and parameters. As mentioned in Chapter 2, variables are unknowns that need to be varied and determined, while parameters are fixed known coefficients. Lastly, mathematical equations have notations that express various mathematical operations. It is common to see PSE research present notations such as ∑, ∈ and ∀. The notation “∑” represents the summation of elements while “∈” is used to describe the subset of elements. The “∀” symbol reads as “for all”. For example, if the notation is written as “∀ i ∈ N” after an equation, it would mean that the equation is applicable “for all values of i belonging to set N”. In some of the modeling equations, you may see “.” between variables or parameters. Such a symbol represents “multiply”. A more detailed list of mathematical notations can be found in the following source (https://www.rapidtables.com/math/symbols/Basic_Math_Symbols.html). For this chapter, we will examine those that are typically used in the context of PSE research.

3.2

RECOMMENDED PRACTICES

Before writing general equations, it is important to take note of some recommended practices. These recommended practices offer a systematic way to write these equations. This, in turn, provides a structured way for others to read and understand the role that each equation plays in the mathematical model. First, it is recommended that mathematical equations be written in the following format shown in Figures 3.1 and 3.2.

FIGURE 3.1 Recommended format for presenting parameters in mathematical equations.

FIGURE 3.2 Recommended format for presenting variables in mathematical equations.

Formulating Generalized Mathematical Models

43

The general rule is to express anything that is fixed or constant (parameters) as non-italic, while variable (those that vary) is presented in italic form. As shown in Figure 3.1, “F” is an example of a symbol used to indicate a material’s flow rate. In this case, “F” is considered a constant parameter because it is non-italic. Labels or names are recommended to be placed above as a superscript and made non-italic. Labels or names are used to provide non-mathematical information such as “Total”, “New”, and “Available”. These are information that are not mathematical in nature but provide distinguishing information. We will see this being applied later in Section 3.4.4. Meanwhile, the index is expected to be placed in italic form since it can vary depending on its set size. Figure 3.2 shows how variables can be presented in mathematical equations. Most features are similar to Figure 3.1 except for the format in “F”. In the case where “F” is a variable, it is recommended to write it in italic form. The recommendations shown in Figures 3.1 and 3.2 provide a solid start to developing equations. The following section describes various examples of how general equations can be developed.

3.3

GENERAL REPRESENTATIONS AND EQUATIONS

The relationship between inputs and outputs can be represented using simple block diagrams. The figures below show different block representations readers may come across. These block diagrams may come in handy when developing general equations.

3.3.1

Conversion

Figure 3.3 shows a representation of a conversion step, where process j converts input i into several outputs p. A good example of this is the pyrolysis unit in Section 2.3, where biomass flows into the pyrolysis unit to produce syngas and methane. The “raw” equations are written as follows:

FIGURE 3.3

General conversion process.

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Optimization for Energy Systems and Supply Chains



In Eq. (3.1), Fj, p represents the flow rate of the output p in technology j. The output is determined by multiplying the input flow rate Gj, i with the fixed conversion coefficient C i, j, p. This takes the shape of a typical conversion process of input i to output p via technology j. It is important to note that Eq. (3.1) is written specifically for product p = 1. Equation (3.2) presents the equation for product p = 2, while Eq. (3.3) describes the flow rate for p = P. In short, Eqs. (3.1)–(3.3) is done for all p. We can see that multiple equations must be written to represent its operation for just this section alone. This may be tedious to present to a larger audience; hence a more generalized form needs to be considered. The generic equation for this will take the form of: l

Fj , p =

∑G

i, j

Ci , j , p ⋅ ∀j∀p

(3.4)

i=1

The “∀j∀p” indicates that this Eq. (3.4) must be applied for all technology j and output p. To verify if the equation is written correctly, it is good practice to check the consistency of indices on both sides. The general rule is to ensure that both sides have the same “active” indices. On the left side of Eq. (3.4), indices j and p are active. The same applies to the right side of Eq. (3.4). But what about the index i? Index i l   is no longer active due to the summation with respect to i  ie.,  . The “i = 1”  i=1 

∑

l

and “I” in the

∑ symbol mean the summation is done for elements from i = 1 to i=1

i = I. Equation (3.1) shows a relevant example where terms from i = 1 until i = I are summed. As a result, the index i is not factored as an active index. Since both sides of Eq. (3.4) have the same active indices, we can then proceed to include “∀j∀p” based on those active indices. It is also worth noting that the concept above is not restricted to only conversion processes. Separation or purification processes can also follow this concept, but the conversion coefficient is modified to become a separation coefficient. The separation coefficient represents the efficiency of separation.

3.3.2

branCHing Points

Branching points are points where materials are split and can be distributed to different places (Figure 3.4). In the case below, output p is produced by technology j in the first layer and can be distributed to the second layer where technologies j’ are available. In theory, the actual equation would be written as follows: Fq=1, p=1 = Fq=1, j =1, p=1 + Fq=1, j = 2, p=1 +  + Fq=1, j = J , p=1

(3.5)

Formulating Generalized Mathematical Models

45

FIGURE 3.4 Branching points.

FIGURE 3.5

Summing points.

However, the general form would like Eq. (3.6): J

Fq , p =

∑F

q , j, p

⋅ ∀q∀p

(3.6)

j=1

At times, Eq. (3.6) can take the form of an inequality instead. However, inequalities can be included in cases where the consumption of the entire flow is not necessary. For example, this may be applicable when there is a high amount of available feed flow, and it is not expected to be completely used for processing. It is not common to apply this in intermediate processes as it will imply that there’s a possibility of unused intermediates.

3.3.3

summing Points

Summing points are points at which materials from different sources are added to each other. As shown in Figure 3.5, material i is generated at the first layer of technologies j and can be mixed prior to being processed by technology j’.

46

Optimization for Energy Systems and Supply Chains

For this representation, the expanded equation can be written as: Fj =1,i =1, j′=1 + Fj = 2,i =1, j′=1 +  + Fj = J ,i =1, j′=1 = Fj′=1,i =1

(3.7)

Therefore, the generalized version is: J

∑F

= Fj′,i ⋅ ∀j ′∀p

j ,i , j′

(3.8)

j=1

3.3.4

otHer asPeCts

Aside from flow rates, a mathematical model may have other aspects being evaluated too. These aspects may include emission, cost, and energy consumption. In most cases, these aspects vary based on the total flow rate entering or leaving a given unit operation. Let us consider cost as an example. The cost of a unit operation is dependent on its size, which often can be related to the flow rate. Cost can be broken down into several subcomponents, but for this example, we will consider capital expenditure (CAPEX) and operating expenditure (OPEX) only. Ideally, we would assign different symbols to CAPEX and OPEX. However, if we want to express them via a standardized symbol, labels can be used to differentiate them. Equations (3.9) and (3.10) are examples of how labels differentiate aspects with similar symbols. = ( Fj =1,p=1 + Fj =1,p=1 +  + Fj =1,p= P ) C Cj =APEX COSTCAPEX j =1 1 COSTOPEX = ( Fj =1,p=1 + Fj =1,p=1 +  + Fj =1,p= P ) C OPEX j =1 j =1

(3.9) (3.10)

As shown, both CAPEX and OPEX use the “COST” symbol. The difference is in the labels “CAPEX” and “OPEX”. The “C” coefficient in both equations refers to the cost factor per unit flow rate. Meanwhile, the term ( Fj =1,p=1 + Fj =1,p=1 +  + Fj =1,p= P ) refers to the total flow rate leaving a technology j = 1. To make these equations more generalized, they can be written as Eqs. (3.11) and (3.12), respectively. P

CAPEX j

COST

=

∑F

j, p

C CAPEX α j ⋅ ∀j j

(3.11)

p=1

P

OPEX j

COST

=

∑F

j, p

C OPEX ⋅  ∀j   j

(3.12)

p=1

Note that αj in Eq. (3.11) is the annualizing factor for each technology j. For both equations, index p is inactive due to the summation. This leaves both sides having

47

Formulating Generalized Mathematical Models

the same active index j. This means Eqs. (3.11) and (3.12) must be applied to every technology j. Following this, Eq. (3.13) sums both CAPEX and OPEX equations to represent the total cost. In this case, the index j is no longer active as the summation is with respect to j. J

COST TOTAL =

∑ j=1

J

COSTjCAPEX +

∑ COST

OPEX j

(3.13)

j =1

This concept can be extended and applied to equations for other aspects too. The general representations above serve as guidance in developing generalized equations. These rules can be used to represent complex superstructures.

3.4

CONCLUSION

This chapter provided the basics for writing generalized equations. As mentioned previously, this chapter serves as a guide for readers to develop generalized equations for their own work. This chapter ends the first part of this book. Chapters in the second half focus on the applications of mathematical models to optimize various case studies involving energy systems and supply chains. Those chapters are part of an edited compilation contributed by different research groups around the globe. The second half begins with Chapter 4, where Belmonte, Aviso, Benjamin, and Tan used mathematical models to synthesize optimal biochar systems. In Chapter 5, Lim, How, and Lin applied a mathematical model to the planning of sustainable hydrogen networks in South Korea. Meanwhile, Chapter 6 by Chan and Chew discussed the application of a mathematical model to optimize polygeneration systems powered by glycerine-pitch and diesel. Following this, Mukherjee and Smith used a series of mathematical models in Chapter 7 to optimize the economic and environmental sustainability of a TEG dehydration process. Then, Chapter 8 by Kumawat and Chaturvedi applied mathematical models to aggregate production planning for the steel industry in India. Chapter 9 by Tan, Aviso, and Lee pivoted to the macrolevel perspective, where mathematical models were used to optimize the economic planning for Taiwan. Following suit, Rajakal and Wan demonstrated a mathematical model’s ability to develop sustainable land expansion strategies for palm-based biodiesel supply chains in Chapter 10. Next, Chapter 11 by Jegede, De Mel, Short, and Isafiade presented the use of a mathematical model to determine the optimal design of a decentralized renewable energy system in Namibia. Finally, Chapter 12 by San Juan, Ching, Chua, Dyogi, and Sy applied a mathematical model to optimize battery energy within the electrical distribution grid.

FURTHER READING Readers are directed to contributions by Stoecker (1989), Meier (1984), Nayak et al. (2015), and Stricker (1985) for examples of generalized mathematical equations written for energy systems and supply chains.

48

Optimization for Energy Systems and Supply Chains

REFERENCES Meier, P., 1984. Energy Systems Analysis for Developing Countries. Munich: Springer-Verlag Berlin Heidelberg. Nayak, J.K., Kedare, S.B., Banerjee, R., Bandyopadhyay, S., Desai, N.B., Paul, S., Kapila, A., 2015. A 1 MW national solar thermal research cum demonstration facility at Gwalpahari, Haryana, India. Curr. Sci. 109, 1445–1457. Stoecker, W., 1989. Design of Thermal Systems, 3rd ed. New York: McGraw-Hill. Stricker, S., 1985. Optimizing Performance of Energy Systems. New York: McGraw-Hill.

Part B Applications

4

Mixed-Integer Linear Programming Model for the Synthesis of Negative-Emission Biochar Systems Beatriz A. Belmonte University of Santo Tomas

Kathleen B. Aviso De La Salle University

Michael Francis D. Benjamin University of Santo Tomas

Raymond R. Tan De La Salle University

CONTENTS 4.1 4.2 4.3 4.4 4.5

Introduction .................................................................................................... 52 Negative-Emission Biochar Systems .............................................................. 54 Methodology ................................................................................................... 54 Case Study 1: Synthesis of Bioenergy Plant with Biochar Production........... 55 Case Study 2: Synthesis of Bioenergy Plant Producing Multi-grade Biochars ...................................................................................... 59 4.6 Conclusion ......................................................................................................64 4.7 Further Reading .............................................................................................. 65 4.8 Density and Calorific Value of Process Streams ............................................ 65 References ................................................................................................................ 65 Appendix .................................................................................................................. 68

DOI: 10.1201/9781003240228-6

51

52

Optimization for Energy Systems and Supply Chains

4.1 INTRODUCTION It is well known that climate change is one of the major environmental crises that humanity is facing. The concentration of greenhouse gas in the atmosphere is continuously increasing, and the world is still behind schedule in meeting the targets of the Paris Agreement. Considering that climate impacts are becoming inescapable, there is an immediate need for all countries to commit to net zero emission by 2050. Such climate transition is still possible if comprehensive plans, supportive policies, and most importantly, effective technologies will be immediately employed. Some researchers have asserted the necessity to deploy negative emission technologies (NETs) to stabilize the global climate (Haszeldine et al., 2018). Among the NETs, biochar-based carbon sequestration emerges as promising for scale-up in the near future since it is cost-effective (Belmonte et al., 2019a) and utilizes mature technologies (Tan, 2019). Biochar is considered a NET since it can store carbon dioxide in soil for hundreds of years (Woolf et al., 2010). It is produced via thermochemical conversion of biomass. This process simultaneously produces green energy such as bio-oil that can be processed as transportation fuel, and syngas that can be used as fuel for stationary applications such as industrial plants. The biochar consists of mostly recalcitrant carbon that can remain in soil when biochar is used for soil amendment. Various life cycle assessments applied to a biochar production system show that utilizing waste biomass results in climate mitigation (Matuštík et al., 2022). Biochar has a potential to sequester 130 Gt CO2 until 2100 (Woolf et al., 2010). The physicochemical properties of biochar (e.g., specific surface area, porosity, pH, cation exchange capacity, carbon content) vary depending on the type of feedstock and operational conditions (pyrolysis temperature, heating rate, and residence time) during biomass conversion. The extent to which biochar can amend specific soil quality issues largely depends on these properties. In addition, the reason why some biochar applications appear as ineffective in soil amendment is due to the addition of unsuitable biochar to the soil (Tan et al., 2017). It is, therefore, important to produce biochar that is tailored with relevant physical properties to fit local soil conditions. For example, the pyrolysis of coconut shell biomass at 600°C had produced biochar with 93.9% carbon content among the different biochars produced from various crop residues (Windeatt et al., 2014), which is suitable for arid soil (Belmonte et al., 2019a). When the carbon content of arid soil is increased via the application of high-carbon content biochar, the water holding capacity increases (Novak et al., 2012). Wood biochar has the advantage of higher porosity compared with other feedstocks (Marousek et al., 2021). Biochar with high porosity can increase the capacity of infertile soil to retain moisture and nutrients (Belmonte et al., 2019a). Porous biochar is also suitable for hard soils since it has the capacity to enhance plant root growth (Kazemi Shariat Panahi et al., 2020). High-temperature pyrolysis of biomass that contains aromatic lignin, aliphatic alkyls, and ester groups results in biochars with higher surface area (Tomczyk et al., 2020) that can increase the nutrient holding capacity of degraded soil. It also shows that as the pyrolysis temperature increases, biochar’s alkalinity (pH) also

Synthesis of Negative-Emission Biochar Systems

53

increases (Li et al., 2019). Acidic soil can strongly benefit from the liming effects of biochar on its pH (Belmonte et al., 2019b). Biochars that are derived from mineral-rich biosolids have higher cation exchange capacity (Kazemi Shariat Panahi et al., 2020) that are suitable for sandy soil (Belmonte et al., 2019a). Application of unsuitable biochars into the soil could possibly raise the greenhouse gas emission from the soil, reduce soil nutrients, and can negatively impact the biological properties of the soil (Kazemi Shariat Panahi et al., 2020). Therefore, there is a need to enhance the efficacy of biochar via the designer biochar concept to customize biochar that can address the specific conditions of the soil to which it is added (Ding et al., 2016). The application of biochar promotes environmental sustainability and supports circular economy objectives. Production of biochar from residual biomass and its application to soil is a good waste management strategy and can reduce the utilization of fertilizer and water for irrigation which further translates into economic gains for farmers. The energy co-products generated simultaneously with biochar further displace the consumption of fossil fuels which in turn offset the emission from these nonrenewable resources. A pyrolysis-biochar system applied to an olive farm uses its semi-solid waste to produce liquid and gas fuels from biochar production to fulfill its energy requirement and generates an electricity surplus that can be sold to the grid while the biochar is used for soil amendment (Zabaniotou et al., 2015). The utilization of biochar is perceived to support sustainable development goals (SDGs) such as zero hunger (SDG2), affordable and clean energy (SDG7), responsible consumption and production (SDG12), and climate action (SDG13). It is, therefore, necessary to standardize and optimize the production and application of biochar which can be seen as an environmentally sustainable way to mitigate climate change (Neogi et al., 2021). Biochar production for carbon sequestration can be integrated with a multi-functional bioenergy system to generate biofuels alongside biochar, bio-oil, and syngas. When multi-functional bioenergy system is integrated with biochar production, the whole system can achieve a negative carbon footprint (Ubando et al., 2014). This integrated system can also be a subunit of a biochar-based carbon management network (Belmonte et al., 2018) for the generation of biochars tailored to address specific soil quality issues. The main goal of this work is to design and optimize a bioenergy system, which simultaneously generates biochar, using mathematical programming. Mathematical programming can facilitate the development of a model for a particular system. The mixed-integer linear programming (MILP) model previously developed (Belmonte et al., 2019a) is applied here for the synthesis of a negative-emission bioenergy system. This chapter is organized as follows. The succeeding Section 4.2 describes the bioenergy system that is being considered here. Section 4.3 discusses the model formulation. Two hypothetical case studies are given in Sections 4.4 and 4.5 to demonstrate how the mathematical model is used to design and synthesize bioenergy systems. Conclusions are presented in Section 4.6. Section 4.7 recommends papers for further reading. Other pertinent data used in the case studies are presented in Section 4.8. The mathematical programming codes are then presented in the Appendix.

54

4.2

Optimization for Energy Systems and Supply Chains

NEGATIVE-EMISSION BIOCHAR SYSTEMS

The bioenergy system being considered here consists of multiple process units. Each process unit consumes input materials (e.g., different biomass feedstocks) to generate the final product outputs (i.e., bio-oil, biochar, and biofuels). There are also internal demands for the generated energy (i.e., syngas and electricity) needed to produce the final products to be sold in the market. Each process unit is defined by a fixed proportion of input and output materials or energy. Each stream (input or output) has a corresponding unit cost and carbon footprint. Each process unit has a unique capital cost. The cost data are needed to compute the profitability of the system, while the carbon footprint of each stream is used to compute the net carbon footprint of the whole integrated system. Due to the different factors that need to be considered, the design of such system would require optimization. The hypothetical case studies in Sections 4.4 and 4.5 give the detailed features of the system.

4.3

METHODOLOGY

The mathematical model that is employed for the synthesis of integrated biochar systems is an MILP model that is based on the previous formulation (Belmonte et al., 2019a) and is defined by the following equations:

The variable x generally corresponds to the design variable, such as the sizes of equipment, pressures, or temperatures. In this system, x is the process unit capacity vector bounded by lower (x L) and upper (xU) values, y is the final or net output stream vector bounded by lower (yL) and upper (yU) limits, c is the stream unit cost vector, v is the variable capital unit cost coefficient vector, f is the fixed capital unit cost

Synthesis of Negative-Emission Biochar Systems

55

coefficient vector, b is the process unit selection vector consisting of binary variables, CRF is the capital recovery factor, A is the process matrix that is made up of coefficients describing the average fixed proportion of input and output flows of materials and energy in every process unit, z is the stream carbon footprint coefficient vector, CF is the net or final carbon footprint of the system, and M is an arbitrary large number. The objective is to maximize the profitability of the integrated biochar system (Eq. 4.1). The profit is computed by calculating first the revenues from the sales of products and costs of purchased inputs (cTy). Then, the total annual capital cost (variable and fixed) is subtracted from the revenues to solve for the annual profit. The model includes linear expressions of material and energy balances that correspond to the process streams (Eq. 4.2) where matrix A can be based from the system’s historical data. The process unit selection vector consisting of binary variables (Eq. 4.5) is used (Eq. 4.6) to denote if the process unit exists (b = 1) or not (b = 0). The required capacities of the process units take non-negative values (Eq. 4.7). The net carbon footprint of the biochar system (Eq. 4.8) can also be predicted by accounting for the carbon footprint of the individual net output streams (y). It is important to mention that the input of biomass to the system takes negative values in y, thus allowing for the corresponding carbon footprint to be accounted for. Near-optimal alternative solutions can also be determined via the addition of integer-cut constraints in the original formulation (Voll et al., 2015). The succeeding hypothetical case studies illustrate how the model can be applied in integrated biochar systems for negative carbon emission.

4.4

CASE STUDY 1: SYNTHESIS OF BIOENERGY PLANT WITH BIOCHAR PRODUCTION

The hypothetical bioenergy plant consists of several process units as illustrated in Figure 4.1. The pyrolysis unit produces syngas, bio-oil, and biochar via thermal decomposition of biomass material (coconut shell) in an inert environment. The

FIGURE 4.1 Block diagram of process units in Case Study 1.

56

Optimization for Energy Systems and Supply Chains

electricity demand of the plant is being supplied by the combined heat and power (CHP) unit using syngas as an input. Fermentation units I and II generate bioethanol and biobutanol from corn stover. The bioreactor unit also utilizes corn stover to produce biohydrogen. Extracted bran oil from rice bran is being used to produce biodiesel via the process of transesterification. Figure 4.1 also presents the input and output flow of material and energy for each process unit. Table 4.1 gives the process matrix (A) for the bioenergy plant. Each column shows the relative proportions of material and energy streams in a particular process equipment unit. The positive coefficient indicates that the stream is being produced, while the negative coefficient denotes that the stream is being consumed by the process unit. For example, −4.06 MW of energy input (syngas) is needed to produce 1 MW of electricity (output) from CHP. The process flowsheet of the bioenergy plant is presented in Figure 4.2. Other

TABLE 4.1 Process Matrix for Case Study 1 Process Unita Product Stream

CHP

Syngas (MW) −4.06 Electricity 1.00 (MW) Rice bran 0.00 (kg/s) Coconut shell 0.00 (kg/s) Corn stover 0.00 (kg/s) Bio-oil (kg/s) 0.00 Biochar (kg/s) 0.00 Bioethanol 0.00 (MW) Biobutanol 0.00 (MW) Biohydrogen 0.00 (MW) Biodiesel 0.00 (MW) Reference Carvalho et al. (2012) a

Pyrolysis

Fermentation Fermentation I II Bioreactor Transesterification

3.59

0.00

0.00

0.00

0.00

−0.06

−0.00087

−0.0114

−0.166

−0.00003

0.00

0.00

0.00

0.00

−0.0015

−1.00

0.00

0.00

0.00

0.00

0.00

−0.00131

−0.0018

−0.0003

0.00

0.44 0.28 0.00

0.00 0.00 0.00579

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00

0.00

0.001

0.00

0.00

0.00

0.00

0.00

0.00305

0.00

0.00

0.00

0.00

0.00

0.009

Windeatt et al. (2014)

Kazi Baral and Shah Zhang Lei et al. (2010) et al. (2010) (2016) et al. (2013)

Some adapted values were converted to specified units.

57

Synthesis of Negative-Emission Biochar Systems

FIGURE 4.2 Bioenergy plant flowsheet for Case Study 1.

TABLE 4.2 Capital Cost Coefficients for Case Study 1 Process Unit

Fixed Cost

Variable Cost/ (MW)

Reference

CHP Pyrolysis

$432,790 $714,924

$1,073,033 $3,434,623

$5,185,749 $2,382,267 $65,948,914 $16,449

$1,450 $2,241 $10,492 $5.912

Sy et al. (2016) Badger et al. (2011) Granatstein et al. (2009) Peters et al. (2003)a Peters et al. (2003)a Peters et al. (2003)a Peters et al. (2003)a

Fermentation I Fermentation II Bioreactor Transesterification a

Computed based on cost estimation rules by Peters et al. (2003).

pertinent data that were used are given in Section 4.8. Table 4.2 shows the capital cost data used in the case study. The capital cost of each equipment is assumed to be a linear function of its capacity. It is further assumed that the bioenergy plant is operating 8,000 h/y. The CRF used is 0.08 (i.e., approximately 5% interest per annum for 20 years). The capital costs of fermentation (I and II), bioreactor, and transesterification units are computed based on cost estimation rules by Peters et al. (2003). Table 4.3 shows the final output values of the streams and the corresponding selling price. As can be seen in Eq. (4.5) taking bioethanol as an example, the final output value should be less than or equal to 5 MW. The bioenergy plant requires syngas as

58

Optimization for Energy Systems and Supply Chains

TABLE 4.3 Demand of Process Streams and Selling Price for Case Study 1 Final Output Streams

Lower

Upper

Selling Price

Syngas (MW) Electricity (MW) Rice bran (kg/s) Coconut shell (kg/s) Corn stover (kg/s) Bio-oil (kg/s) Biochar (kg/s) Bioethanol (MW) Biobutanol (MW) Biohydrogen (MW) Biodiesel (MW)

0 0 −7.967 −1,163 −24.24 7.59 3.709 0 0 0 0

0 0 0 0 0

n/a n/a $0.3125/kg $0.032/kg $0.1006/kg $0.09/kg $2.7/kg $1.1731/L $0.984/L $52.805/m3 $0.9582/L

a

∞ ∞ 5 10 5 15

Reference for the Selling Pricea

Lazaro (2019) Belmonte et al. (2019a) Thompson and Tyner (2014) Belmonte et al. (2019a) Ahmed et al. (2016) Kazi et al. (2010) Meramo-Hurtado et al. (2020) Zhang et al. (2013) Corpuz (2019)

Some adapted values were converted to specified units.

TABLE 4.4 Carbon Footprint per Product for Case Study 1 Products Syngas (kg/MW) Electricity (kg/MW) Rice bran (kg/kg) Coconut shell (kg/kg) Corn stover (kg/kg) Bio-oil (kg/kg) Biochar (kg/kg) Bioethanol (g/MJ) Biobutanol (g/MJ) Biohydrogen (kg/MW) Biodiesel (kg/MW)

Carbon Footprint 0 0 0.008 0.017 0.008 0 −3.86 44.9 79 0 0

Reference Ubando et al. (2014) Ubando et al. (2014) Ubando et al. (2014) Tan et al. (2009) Ubando et al. (2014) Ubando et al. (2014) Belmonte et al. (2018) Mekonnen et al. (2018) Väisänen et al. (2016) Ubando et al. (2014)

energy fuel to generate electricity, biochar, bio-oil, bioethanol, biobutanol, biohydrogen, and biodiesel. Table 4.4 gives the carbon footprint of each product. The case study demonstrates the applicability of the model previously described herein. The objective of the case study is to maximize the profitability of the bioenergy plant. Solving Eqs. (4.1)–(4.8) results in an optimal solution which excludes the transesterification unit as illustrated in Figure 4.3. The final output values of the optimal configuration are 206.87 kg/s of bio-oil, 131.65 kg/s of biochar, 5 MW of bioethanol, 10 MW of biobutanol, and 5 MW of biohydrogen. The plant consumes 470.17 kg/s of

Synthesis of Negative-Emission Biochar Systems

FIGURE 4.3

59

Optimal bioenergy plant configuration for Case Study 1.

coconut shell and 19.42 kg/s of corn stover. The maximum profit is $1,031,668 × 107/y. The corresponding carbon footprint attained by the system is −499 kg/s (−14.37 Mt/y). What if the optimal solution may not be feasible to implement due to some practical constraints not accounted for in the mathematical model such as space limitation and other sustainability issues (e.g., cost and equipment reliability)? The generation of near-optimal solutions may help find alternative solutions for implementation. This methodology may also reveal insights that can lead to better decision-making. Integer cuts are then used to determine near-optimal solution alternatives. Table 4.5 presents the generated near-optimal solutions alongside the optimal solution. Results show that the CHP and the pyrolysis units are important since they are all included in all solutions. On the other hand, all generated solutions excluded the transesterification unit. As profitability decreases, the carbon footprint also decreases. Comparing the objective function values obtained in solutions 2, 3, and 4 with the profitability value achieved in the optimal solution, it can be observed that the percentage difference is within 0.029%. Compared to the optimal solution, the near-optimal solutions are less complex since 2–3 process units are excluded from the synthesized bioenergy plant.

4.5

CASE STUDY 2: SYNTHESIS OF BIOENERGY PLANT PRODUCING MULTI-GRADE BIOCHARS

The second example is used to demonstrate a bioenergy plant that simultaneously produces multi-grade biochars with other bioenergy products previously mentioned in Case Study 1. Two more pyrolysis units are added in the previous plant configuration

60

Optimization for Energy Systems and Supply Chains

TABLE 4.5 Generated Optimal and Near-Optimal Solutions for Case Study 1

Rank Optimum Second Third Fourth Fifth Sixth Seventh Eighth

Profit (109 $/y) 10,316.68 10,316.66 10,313.73 10,313.71 2.965255 2.965254 2.949297 2.949296

Process Unit Capacity (MW) Carbon Footprint Fermen- FermenTransesteri(Mt/y) CHP Pyrolysis tation I tation II Bioreactor fication −14.37 −14.35 −10.16 −10.14 −4.232 −4.232 −4.211 −4.211

415.7 414.9 293.4 292.6 123.1 123.1 122.3 122.3

470.2 469.3 331.9 330.9 139.2 139.2 138.3 138.3

863.1 0.0 863.1 0.0 863.1 863.1 0.0 0.0

10,000 10,000 0.0 0.0 10,000 10,000 10,000 10,000

1,639.3 1,639.3 1,639.3 1,639.3 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

FIGURE 4.4 Bioenergy plant flowsheet for Case Study 2.

(Case Study 1). Figure 4.4 presents the new plant flowsheet. As can be seen, the three pyrolysis units are producing different grades of biochar that are specifically tailored to address certain soil quality limitations. The rice husk biochar pyrolyzed at 600°C can increase the pH of acidic soil (Belmonte et al., 2019a). Coconut shell biochar pyrolyzed at 600°C and 300°C can increase the carbon and cation exchange capacity (CEC) of arid and sandy soil, respectively (Belmonte et al., 2019a). The assumed demand for multi-grade biochars and other energy products including the selling price is given in Table 4.6. The input and output streams for the additional pyrolysis units are shown in Figure 4.5. Table 4.7 gives the process matrix data. The capital

61

Synthesis of Negative-Emission Biochar Systems

TABLE 4.6 Demand of Process Streams and Selling Price for Case Study 2 Final Output Streams

Lower

Upper

Selling Price

Syngas (MW) Electricity (MW) Rice husk (kg/s) Rice bran (kg/s) Coconut shell (kg/s) Corn stover (kg/s) RH bio-oil (kg/s) RH biochar (kg/s) CS 600 bio-oil (kg/s) CS 600 biochar (kg/s) CS 300 bio-oil (kg/s) CS 300 biochar (kg/s) Bioethanol (MW) Biobutanol (MW) Biohydrogen (MW)

0 0 −64.52 −7.967 −1,163 −24.24 0 0 7.59 3.709 1.56 3.31 5 10 5

0 0 0 0 0 0 12.78 12.95 ∞ ∞ ∞ ∞ ∞ ∞ ∞

n/a n/a $0.029/kg $0.3125/kg $0.032/kg $0.1006/kg $0.057/kg $1.541/kg $0.09/kg $2.7/kg $0.068/kg $2.425/kg $1.1731/L $0.984/L $52.805/m3

15

∞

$0.9582/L

Biodiesel (MW)

Reference

Belmonte et al. (2019a) Lazaro (2019) Belmonte et al. (2019a) Thompson and Tyner (2014) Belmonte et al. (2019a) Belmonte et al. (2019a) Belmonte et al. (2019a) Ahmed et al. (2016) Belmonte et al. (2019a) Belmonte et al. (2019a) Kazi et al. (2010) Meramo-Hurtado et al. (2020) Zhang et al. (2013) Corpuz (2019)

FIGURE 4.5 Additional pyrolysis units producing different grades of biochar for Case Study 2.

62

Optimization for Energy Systems and Supply Chains

TABLE 4.7 Process Matrix for Case Study 2 Product Stream

Process Unita I

II

III

IV

Syngas (MW) −4.06 3.59 2.79 0.23 Electricity 1.00 −0.06 −0.06 −0.06 (MW) Rice husk 0.00 0.00 0.00 −1.00 (kg/s) Rice bran 0.00 0.00 0.00 0.00 (kg/s) Coconut shell 0.00 0.00 −1.00 −1.00 (kg/s) Corn stover 0.00 0.00 0.00 0.00 (kg/s) RH bio-oil 0.00 0.00 0.34 0.00 (kg/s) RH biochar 0.00 0.00 0.39 0.00 (kg/s) CS 600 bio-oil 0.00 0.44 0.00 0.00 (kg/s) CS 600 0.00 0.28 0.00 0.00 Biochar (kg/s) CS 300 bio-oil 0.00 0.00 0.00 0.19 (kg/s) CS 300 0.00 0.00 0.00 0.70 biochar (kg/s) Bioethanol 0.00 0.00 0.00 0.00 (MW) Biobutanol 0.00 0.00 0.00 0.00 (MW) Biohydrogen 0.00 0.00 0.00 0.00 (MW) Biodiesel 0.00 0.00 0.00 0.00 (MW) Reference Carvalho Windeatt Windeatt Prabhakar et al. et al. et al. et al. (1986) (2012) (2014) (2014) a

V

VI

VII

VIII

0.00

0.00

0.00

0.00

−0.00087 −0.0114

−0.166 −0.00003

0.00

0.00

0.00

0.00

0.00

0.00

0.00

−0.0015

0.00

0.00

0.00

0.00

−0.0003

0.00

−0.00131 −0.0018 0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00579

0.00

0.00

0.00

0.00

0.001

0.00

0.00

0.00

0.00

0.00305

0.00

0.00

0.00

0.00

0.009

Zhang et al. (2013)

Lei et al. (2010)

Kazi et al. Baral and (2010) Shah (2016)

I – CHP, II – Pyrolysis 1, III – Pyrolysis 2, IV – Pyrolysis 3, V – Fermentation I, VI – Fermentation II, VII – Bioreactor, VIII – Transesterification.

63

Synthesis of Negative-Emission Biochar Systems

TABLE 4.8 Carbon Footprint per Product for Case Study 2 Products

Carbon Footprint

Reference

0 0 0.04 0.008 0.017 0.008 0 −2.0 0 −3.86 0 −3.43 44.9 79 0 0

Ubando et al. (2014) Ubando et al. (2014) Liu et al. (2016) Ubando et al. (2014) Tan et al. (2009) Ubando et al. (2014) Ubando et al. (2014) Belmonte et al. (2018) Ubando et al. (2014) Belmonte et al. (2018) Ubando et al. (2014) Belmonte et al. (2018) Mekonnen et al. (2018) Väisänen et al. (2016)

Syngas (kg/MW) Electricity (kg/MW) Rice husk (kg/kg) Rice bran (kg/kg) Coconut shell (kg/kg) Corn stover (kg/kg) RH bio-oil (kg/kg) RH biochar (kg/kg) CS 600 bio-oil (kg/kg) CS 600 biochar (kg/kg) CS 300 bio-oil (kg/kg) CS 300 biochar (kg/kg) Bioethanol (g/MJ) Biobutanol (g/MJ) Biohydrogen (kg/MW) Biodiesel (kg/MW)

Ubando et al. (2014)

TABLE 4.9 Generated Optimal and Near-Optimal Solutions for Case Study 2 Rank

Profit Carbon (109 $/y) Footprint (Mt/y)

Optimum Second

32,430.4 31,642.8

a

−36.61 −35.90

Process Unit Capacity (MW)a I

II

III

IV

V

VI

VII

VIII

1,044.2 1,154.6 33.2 8.2 863.1 10,000 5,154.2 1,636.4 1,021.4 1,154.6 0.0 8.2 863.1 10,000 5,029 1,636.4

I – CHP, II – Pyrolysis 1, III – Pyrolysis 2, IV – Pyrolysis 3, V – Fermentation I, VI – Fermentation II, VII – Bioreactor, VIII – Transesterification.

cost data of all process units, including the additional pyrolysis units, are the same as in Case Study 1 (Table 4.2). Other pertinent data that were used are given in Section 4.8. Table 4.8 gives the carbon footprint for each product. Case Study 2 uses the same assumptions as in Case Study 1. The optimization was done and generated two solutions (one optimal and one near-optimal), as shown in Table 4.9. The optimized bioenergy plant generates a profit of 324,304 × 108 $/yr. Figure 4.6 illustrates the optimal solution superstructure. As can be observed, the optimal solution includes all the process units originally present in Figure 4.4. The bioenergy plant produces 12.95 kg/s rice husk biochar (RH biochar), 11.29 kg/s RH bio-oil, 323.28 kg/s coconut shell biochar pyrolyzed at

64

Optimization for Energy Systems and Supply Chains

FIGURE 4.6

Optimal bioenergy plant configuration for Case Study 2.

600°C (CS-600 biochar), 508 kg/s CS-600 bio-oil, 5.76 kg/s coconut shell biochar pyrolyzed at 300°C (CS-300 biochar), 1.56 kg/s CS-300 bio-oil, 5 MW of bioethanol, 10 MW of biobutanol, 15.72 MW of biohydrogen, and 15 MW of biodiesel. The optimized bioenergy plant utilizes 33.21 kg/s rice husk biomass, 2.40 kg/s rice bran biomass, 1,162.79 kg/s coconut shell biomass, and 20.51 kg/s corn stover biomass. The production of biochar from the three pyrolysis units in the optimal solution results in a carbon footprint of −1,271.22 kg/s (−36.61 Mt/y). Meanwhile, the generated nearoptimal solution offers a less complex configuration with the exclusion of pyrolysis unit II. However, this results in a slight reduction in negative carbon footprint (−1,246.64 kg/s) and profitability ($316,428 × 108/yr).

4.6

CONCLUSION

An MILP model was applied for the synthesis of a bioenergy plant with biochar production to attain negative carbon emission. The model was demonstrated with two case studies. Since limitations may exist during implementation, near-optimal solutions were also generated to support decision-making for the selection of the final plant configuration. Two hypothetical case studies were used to illustrate the applicability of the model. Both case studies demonstrate that certain design features can be considered during the selection process. In addition, the production of customized biochars integrated into the plant design can address the quality issues of the different types of soil to achieve favorable results when biochar is applied. The MILP model employed in this work can further be applied in the synthesis of other NETs such as enhanced weathering networks and to consider other footprints that accompany the selection of the technology. Parametric uncertainties can be integrated into the basic model through non-deterministic formulations based on fuzzy, stochastic, or robust optimization.

65

Synthesis of Negative-Emission Biochar Systems

4.7

FURTHER READING

A broad introduction to the NET research landscape can be found in the review paper of Minx et al. (2018), while their costs and benefits are compared in a companion article (Fuss et al., 2018). The generic MILP for process synthesis was first proposed by Grossmann and Santibanez (1980). Their seminal work is the basis of all mainstream MILP formulations used in process synthesis applications. Optimization models allow the identification of the best solutions to any given model. However, examination of near-optimal solutions may have engineering value as well. This point is discussed in more detail by Voll et al. (2015). Alternatives to MILP models may also be used for optimal process synthesis. For example, process graph methodology has proven to be a viable alternative for many applications (Friedler et al., 2019).

4.8

DENSITY AND CALORIFIC VALUE OF PROCESS STREAMS

Streams

Reference

Calorific Value

Reference

Syngas Electricity Rice husk Rice bran Coconut shell Corn stover RH bio-oil RH biochar CS 600 Bio-oil CS 600 Biochar CS 300 Bio-oil CS 300 Biochar Bioethanol 790 kg/m3 Chen et al. (2019)

15.5 MJ/kg 3,000 kcal/kg 17.2 MJ/kg 16.5 MJ/kg 13.69 MJ/kg 19.3 MJ/kg 19.75 MJ/kg 33.7 MJ/kg 16 MJ/kg 30.238 MJ/kg 26.4 MJ/kg

Windeatt et al. (2014) Zafar (2021) Windeatt et al. (2014) Lizotte et al. (2015) Yusup et al. (2015) Windeatt et al. (2014) Rout et al. (2016) Windeatt et al. (2014) Granatstein et al. (2009) Prabhakar et al. (1986) “Bioethanol – European Biomass Industry Association,” n.d. Aparicio et al. (2020) Fatehizadeh et al. (2018) “Biodiesel Chemistry Tutorial,” (n.d.)

Biobutanol Biohydrogen Biodiesel

Density

12 g/L Sindhu et al. (2019) 0.09 g/L Fatehizadeh et al. (2018) 0.88 g/mL “Biodiesel Chemistry Tutorial,” (n.d.)

29.2 MJ/L 122 kJ/g 33 MJ/L

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APPENDIX Lingo Code for Case Study 1 Model: !Capacities !x1, !x2, !x3, !x4,

of the Process Units (MW); CHP; Pyrolyis; Fermentation I; Fermentation II

Synthesis of Negative-Emission Biochar Systems

!Final output values converted to MW; y1 = 0; y2 = 0; -100 < y3; y3 < 0; @FREE(y3); -20000 < y4; y4 < 0; @FREE(y4); -400 < y5; y5 < 0; @FREE(y5); y6 > 150; y7 > 125; y8 < 5; y9 < 10; y10 < 5; y11 < 15; !PROFIT converted to $/y; PROFIT = (717017.2084*y3 + 53581.39535*y4 + 175592.7273*y5 + 131240.5063*y6 + 2307418.398*y7 + 1615650.173*y8 + 970520.5479*y9 + 2.0613E+12*y10 + 836247.2727*y11) - ((1073033*x1*0.08) + (3434623*x2*0.08) + (1450*x3*0.08) + (2241*x4*0.08) + (10492*x5*0.08) + (5.91*x6*0.08) + (382500*b1*0.08) + (631850*b2*0.08) + (5185749*b3*0.08) + (2382266*b4*0.08) + (65948913*b5*0.08) + (16449*b6*0.08));

69

70

Optimization for Energy Systems and Supply Chains

!Maximize profit; max = PROFIT; !CF = negative carbon footprint converted to kg/s; CF = (y3/12.552*0.008) + (y4/17.2*0.017) + (y5/16.5*0.008) + (y7/33.7*3.86) - (y8/26.4*1.18) - (y9/2433*192); x1 15; -1000 < y3; y3 < 0; @FREE(y3); y7 < 175; y8 < 250; y11> 25; y12> 100; !PROFIT converted to $/y; PROFIT = (717017.2084*y4 + 53581.39535*y5 + 175592.7273*y6 + 131240.5063*y9 + 2307418.398*y10 + 1615650.173*y13+ 970520.5479*y14 + 2.0613E+12*y15 + 836247.2727*y16 + 53883.87097*y3 + 119912.3448*y7 + 2287670.103*y8 + 122400*y11 + 2309676.566*y12) -((1073033*x1*0.08) + (3434623*x2*0.08) + (3434623*x3*0.08) + (3434623*x4*0.08) + (1450*x5*0.08) + (2241*x6*0.08) + (10492*x7*0.08) + (5.91*x8*0.08) + (432790*b1*0.08) + (714924*b2*0.08) + (714924*b3*0.08) + (714924*b4*0.08) + (5185749*b5*0.08) + (2382266*b6*0.08) + (65948913*b7*0.08) + (16449*b8*0.08)); !Maximize profit; max = PROFIT;

72

Optimization for Energy Systems and Supply Chains

!CF = negative carbon footprint converted to kg/s; CF = (y4/12.552*0.008) + (y5/17.2*0.017) + (y6/16.5*0.008) + (y10/33.7*3.86) - (y13/26.4*1.18) - (y14/2433*192) + (y3/15.5*0.04) + (y8/19.3*2) + (y12/30.238*3.43); x1 ε do Solve optimization model Min Cost Set Budget = cost Solve optimization model Max Eff Set Eff target = eff i = i +1 if cost>Cost max Cost max = cost if env