Irreversibilities and Nonidealities in Desalination Systems by Karan H. Mistry S.M., Mechanical Engineering Massachusetts Institute of Technology, Cambridge, 2010 B.S., Mechanical Engineering University of California, Los Angeles, 2008 Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2013 c Massachusetts Institute of Technology 2013. All rights reserved. Author.............................................................. Department of Mechanical Engineering May 20, 2013 Certified by. John H. Lienhard V Collins Professor of Mechanical Engineering Thesis Supervisor Accepted by . David E. Hardt Chairman, Committee on Graduate Students 2 Irreversibilities and Nonidealities in Desalination Systems by Karan H. Mistry Submitted to the Department of Mechanical Engineering on May 20, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Abstract Energy requirements for desalination systems must be reduced to meet increasing global demand for fresh water. This thesis identifies thermodynamic limits for the energetic performance of desalination systems and establishes the importance of irreversibilities and solution composition to the actual performance obtained. Least work of separation for a desalination system is derived and generalized to apply to all chemical separation processes driven by some combination of work, heat, and chemical energy (fuel) input. At infinitesimal recovery, least work reduces to the minimum least work of separation: the true exergetic value of the product and a useful benchmark for evaluating energetic efficiency of separation processes. All separation processes are subject to these energy requirements; several cases relevant to established and emerging desalination technologies are considered. The effect of nonidealities in electrolyte solutions on least work is analyzed through comparing the ideal solution approximation, Debye-H¨uckel theory, Pitzer's ionic interaction model, and Pitzer-Kim's model for mixed electrolytes. Error introduced by using incorrect property models is quantified. Least work is a strong function of ionic composition; therefore, standard property databases should not be used for solutions of different or unknown composition. Second Law efficiency for chemical separation processes is defined using the min- imum least work and characterizes energetic efficiency. A methodology is shown for evaluating Second Law efficiency based on primary energy inputs. Additionally, entropy generation mechanisms common in desalination processes are analyzed to illustrate the effect of irreversibility. Formulations for these mechanisms are applied to six desalination systems and primary sources of loss are identified. An economics-based Second Law efficiency is defined by analogy to the energetic parameter. Because real-world systems are constrained by economic factors, a perfor- mance parameter based on both energetics and economics is useful. By converting all thermodynamic quantities to economic quantities, the cost of irreversibilities can be compared to other economic factors including capital and operating expenses. By applying these methodologies and results, one can properly characterize the energetic performance and thermodynamic irreversibilities of chemical separation 3 processes, make better decisions during technology selection and design of new systems, and critically evaluate claimed performance improvements of novel systems. Thesis Supervisor: John H. Lienhard V Title: Collins Professor of Mechanical Engineering 4 Acknowledgments The work presented in this thesis could not have been completed without the help and support of many individuals; I am extremely grateful for the guidance, advice, and support that I have received during my time at MIT. Professor John Lienhard, I owe you my deepest thanks for your continued support and encouragement over the past five years. Through your guidance, I have grown as a scientist, an engineer, and most importantly, as an analytical problem solver. In addition to my adviser, I am thankful for the feedback and guidance I have received from my doctoral committee: Alexander Mitsos, Evelyn Wang, and Mostafa Sharqawy. To all the members of our research group and the Rohsenow Kendall Heat Transfer Laboratory, and in particular, Ed, Prakash, Greg, Ronan, Jacob, and Leo, thank you for providing years worth of both intellectual discourse and lighthearted banter. I have truly enjoyed my time with the group and have found our interactions both intellectually stimulating and personally rewarding. To my family, Shaila and Hemant Mistry and Priyanjali Shah, thank you for always believing in me, and more importantly, for always being there to give me a kick in the right direction whenever I need it. I have been blessed with having a number of extremely close friends. Nick, working with you, both at UCLA and at MIT, has been an absolute pleasure. You were the first of my friends to truly challenge and push me academically and I eagerly look forward to any future projects we may have together. Ben and Amneet, you both have been invaluable in helping me deal with all of the challenges that life has thrown my way. I would like to thank the King Fahd University of Petroleum and Minerals for funding the research reported in this thesis through the Center for Clean Water and Clean Energy at MIT and KFUPM under project number R13-CW-10. Lastly, thank you to everyone that I have had the pleasure of working with while at MIT, including students, faculty, and staff, for making the past five years memorable. While I know I will miss MIT dearly, as this chapter of my life comes to a close, I am excited to see where the next chapter will lead me. |Karan (Rao) Mistry 5 6 The future belongs to those who can manipulate entropy; those who understand but energy will be only accountants. |Frederic Keffer Day after day, day after day, We stuck, nor breath nor motion; As idle as a painted ship Upon a painted ocean. Water, water, every where, And all the boards did shrink; Water, water, every where, Nor any drop to drink. |Samuel Taylor Coleridge The Rime of the Ancient Mariner 7 8 Contents Abstract 3 Acknowledgments 5 Contents 9 List of Figures 13 List of Tables 15 Nomenclature 17 1 Introduction 23 1.1 The growing water problem . 23 1.2 Current state of desalination research . 24 1.3 Energy requirements for desalination systems . 26 1.4 Research objectives and thesis overview . 27 1.4.1 Generalized least energy of separation . 27 1.4.2 Nonidealities in electrolyte solutions . 27 1.4.3 Second Law efficiency for separation processes . 28 1.4.4 Economic Second Law efficiency . 28 2 Generalized least energy of separation 29 2.1 Introduction . 30 2.2 Least work and least heat of separation . 30 2.3 Generalized least energy of separation . 33 2.4 Least work of separation . 38 2.5 Least heat of separation . 40 2.6 Least chemical energy (fuel) of separation . 43 2.6.1 Combustion . 43 2.6.2 Chemical disequilibrium . 45 2.6.3 Electrochemical reactions . 48 2.6.4 Limitations . 50 2.7 Least work of separation with an assist stream . 50 2.8 Conclusions . 55 9 3 Nonidealities in electrolyte solutions 57 3.1 Introduction . 58 3.2 Essential chemical thermodynamics . 59 3.2.1 Solvent . 60 3.2.2 Solutes . 60 3.3 Evaluation of activity coefficients . 62 3.3.1 Ideal solution . 62 3.3.2 Debye-H¨uckel theory and the Davies equation . 63 3.3.3 Pitzer ion interaction model for single electrolytes . 64 3.3.4 Pitzer-Kim model for mixed electrolytes . 65 3.3.5 Pitzer model with effective molality for mixed electrolytes . 66 3.3.6 Experimental data . 67 3.3.7 Empirical correlations . 70 3.4 Least work of separation . 70 3.4.1 Summary of derivation . 71 3.4.2 Mass basis . 71 3.4.3 Mole basis . 72 3.5 Feed water composition . 74 3.6 Aqueous sodium chloride . 74 3.6.1 Least work for an NaCl solution . 76 3.6.2 Error associated with ideal behavior approximation . 79 3.7 Mock seawater . 82 3.8 High valence electrolyte solution . 85 3.9 Comparison to seawater . 89 3.10 Conclusions . 91 4 Second Law efficiency for separation processes 95 4.1 Introduction . 96 4.2 Energetic performance parameters . 97 4.3 Exergetic value of product . 98 4.4 Second Law efficiency for a chemical separator . 100 4.5 Second Law efficiency for a desalination system operating as part of a cogeneration plant . 103 4.5.1 Desalination powered by work . 105 4.5.2 Desalination powered by heat . 106 4.5.3 Desalination powered by cogenerated heat and work . 108 4.6 Analysis of entropy generation mechanisms . 110 4.6.1 Flashing . 111 4.6.2 Flow through an expansion device without phase change . 112 4.6.3 Pumping and compressing . 113 4.6.4 Approximately isobaric heat transfer process . 115 4.6.5 Thermal disequilibrium of discharge streams . 116 4.6.6 Chemical disequilibrium of concentrate stream . 116 4.7 Application to desalination technologies . 117 4.7.1 Multiple effect distillation . 118 10 4.7.2 Multistage flash . 121 4.7.3 Direct contact membrane distillation . 124 4.7.4 Mechanical vapor compression . 127 4.7.5 Reverse osmosis . 129 4.7.6 Humidification-dehumidification . 133 4.8 Conclusions . 134 5 Economic Second Law efficiency 139 5.1 Introduction . 140 5.2 Second Law efficiency for a chemical separator . 141 5.3 Derivation of an economics-based Second Law efficiency . 143 5.3.1 Minimum cost of producing product . 144 5.3.2 Actual cost of producing product . 147 5.3.3 Generalized to cogeneration systems . 149 5.4 Application to various desalination systems . 149 5.4.1 Multistage flash and multiple effect distillation . 149 5.4.2 Reverse osmosis . 152 5.4.3 Membrane distillation . 161 5.5 Conclusions . 166 6 Conclusions 169 6.1 Generalized least energy of separation .