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Theoretical and experimental simulation of passive vacuum solar flash desalination

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Title:
Theoretical and experimental simulation of passive vacuum solar flash desalination
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English
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Abutayeh, Mohammad
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University of South Florida
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Tampa, Fla.
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Subjects / Keywords:
Solar energy
Seawater separation
Desalting
Distillation
Evaporation
Dissertations, Academic -- Chemical Engineering -- Doctoral -- USF   ( lcsh )
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bibliography   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Experimental and theoretical simulations of a novel sustainable desalination process have been carried out. The simulated process consists of pumping seawater through a solar heater before flashing it under vacuum in an elevated chamber. The vacuum is passively created and then maintained by the hydrostatic balance between pressure inside the elevated flash chamber and outdoor atmospheric pressure. The experimental simulations were carried out using a pilot unit built to depict the proposed desalination system. Theoretical simulations were performed using a detailed computer code employing fundamental physical and thermodynamic laws to describe the separation process, complimented by experimentally based correlations to estimate physical properties of the involved species and operational parameters of the proposed system setting it apart from previous empirical desalination models. Experimental and theoretical simulation results matched well with one another, validating the developed model. Feasibility of the proposed system rapidly increased with flash temperature due to increased fresh water production and improved heat recovery. In addition, the proposed desalination system is naturally sustainable by solar radiation and gravity, making it very energy efficient.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2010.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
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by Mohammad Abutayeh.
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Title from PDF of title page.
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Document formatted into pages; contains 268 pages.
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Includes vita.

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oclc - 646899493
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ABSTRACT: Experimental and theoretical simulations of a novel sustainable desalination process have been carried out. The simulated process consists of pumping seawater through a solar heater before flashing it under vacuum in an elevated chamber. The vacuum is passively created and then maintained by the hydrostatic balance between pressure inside the elevated flash chamber and outdoor atmospheric pressure. The experimental simulations were carried out using a pilot unit built to depict the proposed desalination system. Theoretical simulations were performed using a detailed computer code employing fundamental physical and thermodynamic laws to describe the separation process, complimented by experimentally based correlations to estimate physical properties of the involved species and operational parameters of the proposed system setting it apart from previous empirical desalination models. Experimental and theoretical simulation results matched well with one another, validating the developed model. Feasibility of the proposed system rapidly increased with flash temperature due to increased fresh water production and improved heat recovery. In addition, the proposed desalination system is naturally sustainable by solar radiation and gravity, making it very energy efficient.
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Theoretical and Experimental Simulation of Passive Vacuum Solar Flash Desalination by Mohammad Abutayeh A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemical & Biomedical Engineering College of Engineering University of South Florida Major Professor: D. Yogi Goswami Ph.D. Elias K. Stefanakos Ph.D. Scott W. Campbell Ph.D. John T. Wolan Ph.D. Thomas L. Crisman Ph.D. Date of Approval: March 23, 2010 Keywords: Solar Energy, Seawater Separa tion, Desalting, Distil lation, Evaporation Copyright 2010, Mohammad Abutayeh

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DEDICATION To the loving memory of my brother, Hussein

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ACKNOWLEDGEMENTS I would like to first thank Dr. D. Yogi Goswami for his ideas and research assistance that made this exploration possible. I would also like to express my gratitude to Dr. Elias K. Stefanakos for his prof essional leadership and generous support. Then, I would like to express my sincere appreciation to Dr. Scott W. Campbell for his tremendous knowledge that guided me throughout my career. I would also like to thank Dr. John T. Wolan for his valued sugge stions and support a ll through my studies. My thanks must also go to Dr. Thomas L. Crisman for his appreciated input and his well regarded encouragement. Finally, I would like to extend my deepest appreciation to my family and friends fo r their support a nd inspiration.

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i TABLE OF CONTENTS LIST OF TABLES...............................................................................................................v LIST OF FIGURES...........................................................................................................vi LIST OF SYMBOLS.......................................................................................................xiii ABSTRACT...................................................................................................................xviii CHAPTER 1. INTRODUCTION........................................................................................1 1.1 Overview...........................................................................................................1 1.2 Objective...........................................................................................................5 CHAPTER 2. DESALINATION.........................................................................................6 2.1 Conventional Desalination................................................................................6 2.1.1 Multiple Effect Evaporation..............................................................9 2.1.2 MultiStage Flash............................................................................10 2.1.3 Vapor Compression.........................................................................11 2.1.4 Indirect Contact Freezing.................................................................12 2.1.5 Reverse Osmosis..............................................................................13 2.1.6 ElectroDialysis...............................................................................14 2.2 Solar Desalination...........................................................................................15 2.2.1 Solar Distillation..............................................................................16 2.2.2 Solar Collectors................................................................................17 2.2.3 Thermal Energy Storage..................................................................18 2.2.4 Solar Ponds......................................................................................19 2.2.5 Photovoltaics....................................................................................20 CHAPTER 3. RESEARCH BACKGROUND..................................................................21 3.1 Renewable Energy Desalination Systems.......................................................21 3.2 Passive Vacuum Solar Desalination...............................................................22 3.3 Passive Vacuum Solar Flash Desalination......................................................23 3.4 Proposed Desalination System........................................................................24

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ii CHAPTER 4. THEORETICAL ANALYSIS....................................................................26 4.1 Process Description.........................................................................................26 4.2 Model Development........................................................................................28 4.2.1 Mass and Energy Balance................................................................29 4.2.2 Equilibrium Distribution Coefficients.............................................35 4.2.3 Adiabatic Flash................................................................................38 4.2.4 Heat Transfer...................................................................................40 4.2.5 Vacuum Volume..............................................................................44 4.2.6 Vacuum Pressure.............................................................................47 4.2.7 System Performance........................................................................51 4.2.8 Physical Properties...........................................................................54 4.3 Solution Algorithm.........................................................................................58 CHAPTER 5. EXPERIMENTAL ANALYSIS.................................................................61 5.1 Process Description.........................................................................................61 5.2 Experimental Apparatus..................................................................................63 5.3 Control Scheme...............................................................................................66 5.4 Data Acquisition.............................................................................................69 5.5 Operating Procedure.......................................................................................71 5.6 Experimental Design.......................................................................................73 CHAPTER 6. PARAMETRIC ANALYSIS......................................................................75 6.1 Analyses Synchronization...............................................................................75 6.2 Parameter Expressions....................................................................................76 6.3 Parameter Inputs.............................................................................................81 6.4 Equipment Specifications...............................................................................85 6.5 Simulation Specifications...............................................................................86 CHAPTER 7. DISCUSSION OF RESULTS....................................................................88 7.1 Discussion Guide............................................................................................88 7.2 Vacuum Erosion..............................................................................................90 7.3 Equilibrium Attainment..................................................................................97 7.4 Equilibrium Departure..................................................................................104 7.5 Heat Reclamation..........................................................................................111

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iii 7.6 Heater Size....................................................................................................118 7.7 Collector Size................................................................................................125 7.8 System Throughput.......................................................................................132 7.9 System Capacity............................................................................................139 7.10 Process Feasibility......................................................................................146 7.11 Condensing Efficiency................................................................................153 7.12 Recovery Efficiency....................................................................................160 7.13 Thermal Efficiency.....................................................................................167 7.14 Disambiguation...........................................................................................174 CHAPTER 8. CONCLUSION.........................................................................................175 8.1 Summary.......................................................................................................175 8.2 Outcome........................................................................................................176 8.3 Prospects.......................................................................................................180 REFERENCES................................................................................................................185 APPENDICES.................................................................................................................189 Appendix A. The operating procedure................................................................190 Appendix B. SUPERTRAPP code to generate Kvalues...............................195 Appendix C. Matlab code for FCT data regression..............................................202 Appendix D. Matlab code for NEA data regression............................................203 Appendix E. Matlab code for H2O data regression.............................................204 Appendix F. Matlab code for data regression.................................................205 Appendix G. Matlab code for HCN2 data regression...........................................206 Appendix H. Matlab code for HCO2 data regression..........................................207 Appendix I. Matlab code for HCAr data regression.............................................208 Appendix J. Matlab code for HCCO2 data regression..........................................209 Appendix K. Matlab code for PH2O sat data regression.........................................210 Appendix L. Sample TK Solver code for data mining.......................................211 Appendix M. Sample TK Solver code for model simulation.............................228 Appendix N. Experimental record......................................................................252 Appendix O. Experimental equipment specifications........................................253 Appendix P. Error analysis.................................................................................266

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iv ABOUT THE AUTHOR.......................................................................................End Page

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v LIST OF TABLES Table 1. Energy consumption of desalination systems [7]...............................................15 Table 2. Solar collectors [7]..............................................................................................17 Table 3. Sensible heat storage material [8].......................................................................18 Table 4. Latent heat storage material [8]..........................................................................18 Table 5. Spectral absorption of solar radiation in water [8].............................................19 Table 6. Experimental matrix...........................................................................................73 Table 7. Sea salt parameters [16] [31]..............................................................................82 Table 8. Seawater parameters [16] [31]............................................................................82 Table 9. Equipment dimensions........................................................................................85 Table 10. Heat transfer equipment parameters.................................................................85 Table 11. Simulation settings............................................................................................87 Table 12. Device and correlation errors..........................................................................266 Table 13. Propagation of error rules...............................................................................266

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vi LIST OF FIGURES Figure 1. Estimated water consumption of US counties for 2000 [1]................................3 Figure 2. Estimated energy consumption pe r capita of US states for 2001 [1]..................3 Figure 3. Estimated energy consumption pe r capita of Florida and the US [1]..................4 Figure 4. Monthly average daily solar insolation in the US [3]..........................................4 Figure 5. Global distribution of installed desalination capacity by technology [5]............8 Figure 6. Global distribution of installe d desalination capacity by region [5]...................8 Figure 7. Multiple effect evaporation.................................................................................9 Figure 8. Multistage flash...............................................................................................10 Figure 9. Mechanical vapor compression.........................................................................11 Figure 10. Indirect contact freezing..................................................................................12 Figure 11. Reverse osmosis..............................................................................................13 Figure 12. Electrodialysis...............................................................................................14 Figure 13. Solar distillation...............................................................................................16 Figure 14. Vertical cross section of a solar pond..............................................................19 Figure 15. Photovoltaic cell schematics............................................................................20 Figure 16. Photovoltaic system schematics......................................................................20 Figure 17. Passive vacuum solar desalination..................................................................22 Figure 18. Passive vacuum solar flash desalination..........................................................23 Figure 19. Singlestage solar flash desalination system...................................................25 Figure 20. Multistage solar fl ash desalination system....................................................25 Figure 21. Process schematics..........................................................................................28 Figure 22. Mass transfer operations..................................................................................30 Figure 23. Molecular tr ansfer operations..........................................................................33 Figure 24. Flow regimes...................................................................................................54 Figure 25. Developed model solution algorithm..............................................................59 Figure 26. Process and instrumentation diagram of the experimental unit.......................62

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vii Figure 27. 3tier mobile skids layout...............................................................................65 Figure 28. Feedback control loops of the experimental unit............................................66 Figure 29. Block diagram of the flash temperature feedback control loop......................68 Figure 30. Data acquisition structure................................................................................70 Figure 31. Data acquisition software................................................................................70 Figure 32. Overall view of the experimental unit.............................................................74 Figure 33. Countercurrent departure co rrection factor of condenser tube......................79 Figure 34. Nonequilibrium a llowance representation.....................................................79 Figure 35. Activity coefficient of water............................................................................80 Figure 36. Gas phase molecular content correction factor...............................................80 Figure 37. Henry's constant of nitrogen............................................................................82 Figure 38. Henry's constant of oxygen.............................................................................83 Figure 39. Henry's constant of argon................................................................................83 Figure 40. Henry's constant of carbon dioxide.................................................................84 Figure 41. Vapor pressure of water...................................................................................84 Figure 42. Modeled vacuum pressu re profiles at lower flow...........................................91 Figure 43. Experimental vacuum pre ssure profiles at lower flow....................................91 Figure 44. Modeled vacuum pressu re profiles at higher flow..........................................92 Figure 45. Experimental vacuum pre ssure profiles at higher flow...................................92 Figure 46. Vacuum pressure at 50C flash and lower flow..............................................93 Figure 47. Vacuum pressure at 50C flash and higher flow.............................................93 Figure 48. Vacuum pressure at 60C flash and lower flow..............................................94 Figure 49. Vacuum pressure at 60C flash and higher flow.............................................94 Figure 50. Vacuum pressure at 70C flash and lower flow..............................................95 Figure 51. Vacuum pressure at 70C flash and higher flow.............................................95 Figure 52. Vacuum pressure at 80C flash and lower flow..............................................96 Figure 53. Vacuum pressure at 80C flash and higher flow.............................................96 Figure 54. Modeled equilibrium temp erature profiles at lower flow................................98 Figure 55. Experimental equilibrium te mperature profiles at lower flow........................98 Figure 56. Modeled equilibrium temper ature profiles at higher flow..............................99 Figure 57. Experimental equilibrium te mperature profiles at higher flow.......................99

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viii Figure 58. Equilibrium temperature at 50C flash and lower flow.................................100 Figure 59. Equilibrium temperature at 50C flash and higher flow...............................100 Figure 60. Equilibrium temperature at 60C flash and lower flow.................................101 Figure 61. Equilibrium temperature at 60C flash and higher flow...............................101 Figure 62. Equilibrium temperature at 70C flash and lower flow.................................102 Figure 63. Equilibrium temperature at 70C flash and higher flow...............................102 Figure 64. Equilibrium temperature at 80C flash and lower flow.................................103 Figure 65. Equilibrium temperature at 80C flash and higher flow...............................103 Figure 66. Modeled concentrated brine te mperature profiles at lower flow...................105 Figure 67. Experimental concentrated brin e temperature profiles at lower flow...........105 Figure 68. Modeled concentrated brine te mperature profiles at higher flow.................106 Figure 69. Experimental concentrated brin e temperature profiles at higher flow..........106 Figure 70. Concentrated brine temperat ure at 50C flash and lower flow.....................107 Figure 71. Concentrated brine temperat ure at 50C flash and higher flow....................107 Figure 72. Concentrated brine temperat ure at 60C flash and lower flow.....................108 Figure 73. Concentrated brine temperat ure at 60C flash and higher flow....................108 Figure 74. Concentrated brine temperat ure at 70C flash and lower flow.....................109 Figure 75. Concentrated brine temperat ure at 70C flash and higher flow....................109 Figure 76. Concentrated brine temperat ure at 80C flash and lower flow.....................110 Figure 77. Concentrated brine temperat ure at 80C flash and higher flow....................110 Figure 78. Modeled preheat temper ature profiles at lower flow....................................112 Figure 79. Experimental preheat temp erature profiles at lower flow.............................112 Figure 80. Modeled preheat temperat ure profiles at higher flow...................................113 Figure 81. Experimental preheat temp erature profiles at higher flow............................113 Figure 82. Preheat temperature at 50C flash and lower flow........................................114 Figure 83. Preheat temperature at 50C flash and higher flow.......................................114 Figure 84. Preheat temperature at 60C flash and lower flow........................................115 Figure 85. Preheat temperature at 60C flash and higher flow.......................................115 Figure 86. Preheat temperature at 70C flash and lower flow........................................116 Figure 87. Preheat temperature at 70C flash and higher flow.......................................116 Figure 88. Preheat temperature at 80C flash and lower flow........................................117

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ix Figure 89. Preheat temperature at 80C flash and higher flow.......................................117 Figure 90. Modeled heat load profiles at lower flow......................................................119 Figure 91. Mined heat load profiles at lower flow..........................................................119 Figure 92. Modeled heat load profiles at higher flow.....................................................120 Figure 93. Mined heat load profiles at higher flow........................................................120 Figure 94. Heat load at 50C flash and lower flow........................................................121 Figure 95. Heat load at 50C flash and higher flow.......................................................121 Figure 96. Heat load at 60C flash and lower flow........................................................122 Figure 97. Heat load at 60C flash and higher flow.......................................................122 Figure 98. Heat load at 70C flash and lower flow........................................................123 Figure 99. Heat load at 70C flash and higher flow.......................................................123 Figure 100. Heat load at 80 C flash and lower flow......................................................124 Figure 101. Heat load at 80 C flash and higher flow.....................................................124 Figure 102. Modeled required solar colle ction area profiles at lower flow....................126 Figure 103. Mined required solar coll ection area profiles at lower flow........................126 Figure 104. Modeled required solar colle ction area profile s at higher flow...................127 Figure 105. Mined required solar coll ection area profiles at higher flow......................127 Figure 106. Required solar collection ar ea at 50C flash and lower flow......................128 Figure 107. Required solar collection ar ea at 50C flash and higher flow.....................128 Figure 108. Required solar collection ar ea at 60C flash and lower flow......................129 Figure 109. Required solar collection ar ea at 60C flash and higher flow.....................129 Figure 110. Required solar collection ar ea at 70C flash and lower flow......................130 Figure 111. Required solar collection ar ea at 70C flash and higher flow.....................130 Figure 112. Required solar collection ar ea at 80C flash and lower flow......................131 Figure 113. Required solar collection ar ea at 80C flash and higher flow.....................131 Figure 114. Modeled fresh water produc tion rate profiles at lower flow.......................133 Figure 115. Mined fresh water producti on rate profiles at lower flow...........................133 Figure 116. Modeled fresh water produc tion rate profiles at higher flow......................134 Figure 117. Mined fresh water producti on rate profiles at higher flow..........................134 Figure 118. Fresh water production rate at 50C flash and lower flow..........................135 Figure 119. Fresh water production rate at 50C flash and higher flow.........................135

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x Figure 120. Fresh water production rate at 60C flash and lower flow..........................136 Figure 121. Fresh water production rate at 60C flash and higher flow.........................136 Figure 122. Fresh water production rate at 70C flash and lower flow..........................137 Figure 123. Fresh water production rate at 70C flash and higher flow.........................137 Figure 124. Fresh water production rate at 80C flash and lower flow..........................138 Figure 125. Fresh water production rate at 80C flash and higher flow.........................138 Figure 126. Modeled fresh water produc tion amount profiles at lower flow.................140 Figure 127. Mined fresh water producti on amount profiles at lower flow.....................140 Figure 128. Modeled fresh water produc tion amount profiles at higher flow................141 Figure 129. Mined fresh water producti on amount profiles at higher flow....................141 Figure 130. Fresh water production amount at 50C flash and lower flow....................142 Figure 131. Fresh water production amount at 50C flash and higher flow...................142 Figure 132. Fresh water production amount at 60C flash and lower flow....................143 Figure 133. Fresh water production amount at 60C flash and higher flow...................143 Figure 134. Fresh water production amount at 70C flash and lower flow....................144 Figure 135. Fresh water production amount at 70C flash and higher flow...................144 Figure 136. Fresh water production amount at 80C flash and lower flow....................145 Figure 137. Fresh water production amount at 80C flash and higher flow...................145 Figure 138. Modeled prime energy cons umption profiles at lower flow.......................147 Figure 139. Mined prime energy consum ption profiles at lower flow...........................147 Figure 140. Modeled prime energy cons umption profiles at higher flow......................148 Figure 141. Mined prime energy consum ption profiles at higher flow..........................148 Figure 142. Prime energy consumption at 50C flash and lower flow...........................149 Figure 143. Prime energy consumption at 50C flash and higher flow..........................149 Figure 144. Prime energy consumption at 60C flash and lower flow...........................150 Figure 145. Prime energy consumption at 60C flash and higher flow..........................150 Figure 146. Prime energy consumption at 70C flash and lower flow...........................151 Figure 147. Prime energy consumption at 70C flash and higher flow..........................151 Figure 148. Prime energy consumption at 80C flash and lower flow...........................152 Figure 149. Prime energy consumption at 80C flash and higher flow..........................152 Figure 150. Modeled condenser effici ency profiles at lower flow.................................154

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xi Figure 151. Experimental condenser e fficiency profiles at lower flow..........................154 Figure 152. Modeled condenser effici ency profiles at higher flow................................155 Figure 153. Experimental c ondenser efficiency prof iles at higher flow.........................155 Figure 154. Condenser efficiency at 50C flash and lower flow....................................156 Figure 155. Condenser efficiency at 50C flash and higher flow...................................156 Figure 156. Condenser efficiency at 60C flash and lower flow....................................157 Figure 157. Condenser efficiency at 60C flash and higher flow...................................157 Figure 158. Condenser efficiency at 70C flash and lower flow....................................158 Figure 159. Condenser efficiency at 70C flash and higher flow...................................158 Figure 160. Condenser efficiency at 80C flash and lower flow....................................159 Figure 161. Condenser efficiency at 80C flash and higher flow...................................159 Figure 162. Modeled recovery effici ency profiles at lower flow...................................161 Figure 163. Experimental recovery ef ficiency profiles at lower flow............................161 Figure 164. Modeled recovery effici ency profiles at higher flow..................................162 Figure 165. Experimental recovery effi ciency profiles at higher flow...........................162 Figure 166. Recovery efficiency at 50C flash and lower flow......................................163 Figure 167. Recovery efficiency at 50C flash and higher flow.....................................163 Figure 168. Recovery efficiency at 60C flash and lower flow......................................164 Figure 169. Recovery efficiency at 60C flash and higher flow.....................................164 Figure 170. Recovery efficiency at 70C flash and lower flow......................................165 Figure 171. Recovery efficiency at 70C flash and higher flow.....................................165 Figure 172. Recovery efficiency at 80C flash and lower flow......................................166 Figure 173. Recovery efficiency at 80C flash and higher flow.....................................166 Figure 174. Modeled thermal effici ency profiles at lower flow.....................................168 Figure 175. Mined thermal efficien cy profiles at lower flow.........................................168 Figure 176. Modeled thermal effici ency profiles at higher flow....................................169 Figure 177. Mined thermal efficien cy profiles at higher flow........................................169 Figure 178. Thermal efficiency at 50C flash and lower flow.......................................170 Figure 179. Thermal efficiency at 50C flash and higher flow......................................170 Figure 180. Thermal efficiency at 60C flash and lower flow.......................................171 Figure 181. Thermal efficiency at 60C flash and higher flow......................................171

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xii Figure 182. Thermal efficiency at 70C flash and lower flow.......................................172 Figure 183. Thermal efficiency at 70C flash and higher flow......................................172 Figure 184. Thermal efficiency at 80C flash and lower flow.......................................173 Figure 185. Thermal efficiency at 80C flash and higher flow......................................173 Figure 186. Experimental and pseudo experimental data acquisition...........................174 Figure 187. Seawater conversion depe ndence on flash temperature..............................179 Figure 188. Prime energy consumption dependence on flash temperature....................179 Figure 189. Preparing to fill up the condenser................................................................190 Figure 190. Condenser full of fresh water......................................................................190 Figure 191. Preparing to fill up the evaporator...............................................................191 Figure 192. Evaporator full of seawater.........................................................................191 Figure 193. Switching the valve posit ions of the flash chamber....................................192 Figure 194. Flash chamber passively vacuumed............................................................192 Figure 195. Preparing to start the desalination process..................................................193 Figure 196. Desalination process taking place...............................................................193 Figure 197. Flash chamber vented to terminate vacuum................................................194 Figure 198. Flash chamber drained.................................................................................194

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xiii LIST OF SYMBOLS Nomenclature A area (cm2) / enthalpy parameter B enthalpy parameter BPE boiling point elevation (C) C enthalpy parameter CV flow coefficient D diameter (cm) / enthalpy parameter DL disturbance loop transfer function E energy flow (J/min) / enthalpy parameter f fanning friction factor F heat removal factor / counter current departure correction factor g gravity acceleration (cm/s2) h heat transfer coefficient (W/cm2C) H molar specific enthalpy (J/mol) H specific enthalpy (J/g) HC Henrys constant (bar) HF Henrys coefficient (C) I solar insolation (W/cm2) k thermal conductivity (W/cmC) K vaporliquid equilibrium di stribution coefficient / gain L length (cm) M flow rate (g/min) MW molecular weight (g/mol) n molar amount (mol) N molar flow rate (mol/min) / number of vertical rows NEA nonequilibrium allowance (C)

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xiv P pressure (bar) PA saturated pressure coefficient PB saturated pressure coefficient PC saturated pressure coefficient PD nominal pipe diameter (cm) PEC prime energy consumption PL equivalent pipe length (cm) / process loop transfer function Q heat input rate (J/min) r correlation coefficient R universal gas constant (barcm3/molC) Re Reynolds number S countercurrent departure parameter s Laplace domain frequency (1/sec) SG specific gravity T temperature (C) t time (min) TIC temperature contro ller transfer function U overall heat transfer coefficient (W/cm2C) V volume (cm3) W work output rate (J/min) x mole fraction in concentrated brine XA cross sectional area (cm2) y mole fraction in flashed vapor Z level or elevation (cm) z mole fraction before flash relativity factor / absorptance activity coefficient thickness (cm) P pressure drop (bar) t time increment (min) Tm logarithmic mean temperature difference (C)

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xv Error nonequilibrium allowance correlation parameter efficiency (%) viscosity (Poise) A viscosity coefficient B viscosity coefficient C viscosity coefficient D viscosity coefficient nonequilibrium allowance correlation parameter density (g/cm3) A density coefficient B density coefficient C density coefficient diffusion conductance parameter (gC/barmincm2) transmittance / time constant (sec) mass fraction in streams gas phase molecular content correction factor diffusion resistance parameter (bar) mass fraction in sea salt Subscripts 0 dead time Ar argon B brine water tank BO3 borate BP bubble point Br bromide C condenser / controller Ca calcium Cl chlorine CO2 carbon dioxide

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xvi CT condenser tube CV condenser vacuum D derivative DL disturbance loop DP dew point E flashed vapor EV evaporator vacuum F fluoride / fresh water tank H heater H2O water HCO3 bicarbonate HT heater tube I integral j representative stream K potsium Mg magnesium N2 nitrogen Na sodium NCG representative noncondensable gas O orifice O2 oxygen P pump PL process loop R recovery S seawater tank Salt sea salt SC solar collector SO4 sulfate Sr strontium T thermal V vacuum

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xvii W evaporator X seawater preheat Superscripts a accumulating C condensed vapor d diffusing i initial / inside id inside dirt in entering L latent o reference state / outside od outside dirt out existing sat saturated W concentrated brine w wall

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xviii THEORETICAL AND EXPERIMENTAL SIMULATION OF PASSIVE VACUUM SOLAR FLASH DESALINATION Mohammad Abutayeh ABSTRACT Experimental and theoretical simulati ons of a novel sustainable desalination process have been carried out. The simula ted process consists of pumping seawater through a solar heater before flashing it unde r vacuum in an elevated chamber. The vacuum is passively created and then ma intained by the hydrostatic balance between pressure inside the elevated flash ch amber and outdoor atmospheric pressure. The experimental simulations were carried out using a pilot unit built to depict the proposed desalination system. Theoretical simu lations were performed using a detailed computer code employing fundamental physical and thermodynamic laws to describe the separation process, complimented by experi mentally based correlations to estimate physical properties of the i nvolved species and operational pa rameters of the proposed system setting it apart from previous empirical desalination models. Experimental and theoretical simulation results matched well with one another, validating the developed model. Feasibility of the proposed sy stem rapidly increased with flash temperature due to increased fresh wa ter production and improved heat recovery. In addition, the proposed desalination system is naturally sustainable by solar radiation and gravity, making it very energy efficient.

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1 CHAPTER 1. INTRODUCTION 1.1 Overview Fresh water demand is persistently in creasing both as popul ations around the world keep growing and as existing fresh water reserves keep declining due to consumption and pollution. Figure 1 shows the estimated water consumption of US counties for 2000 [1]. Marine waters repres ent an infinite water source since 98 % of all global water is present in oceans; therefore, seawater desalination is the logical approach to meet rising fresh water demand. Energy demand is also continually in creasing due to relentless global industrialization. Oil and gas rema in the primary sources of energy for most of the world; however, their reserves are dwindling, production is pe aking, and consumption is harming the environment. Figure 2 illustrates the estimated energy consumption per capita of US states for 2001, while Figure 3 compares energy consumption per capita of Florida to the rest of the count ry for the past forty years [1]. Renewable energy sources are continually replenished by cosmic forces and can be used to produce sustainable and useful forms of energy with minimum environmental impact. Serious economic and social disruptions are unfolding over th e finite water and energy resources; hence, securing fresh wa ter supply and employing renewable energy sources will help avoid catast rophic conflicts, continue modern lifestyles, a nd circumvent global warming and environmental pollution [2].

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2 Desalination can be accomplished by separa tion techniques developed over the years to produce potable water. The most wi despread desalination methods are given in CHAPTER 2 Momentous amounts of energy are requi red in all desalination processes; therefore, reducing energy demand, as well as employing renewable energy, is imperative to developing viable desalination processe s. Various desalination systems driven by renewable energy have been developed over th e last few years; nonetheless, most have not yet been commercially implemented due to high capital cost associated with utilizing renewable energy. Solar radiation is a very appealing sour ce of energy because it is available at no cost; furthermore, exploiting it has no notable adverse effect on the environment. Plenty of research and development have been undertak en to utilize this free form of energy to develop more efficient sustainable proce sses such as water de salination and power generation. Figure 4 illustrates the US share of solar radiation [3]. Solar energy is intermittent and requires storage; however maximizing its use alongside developing energy efficient processes can greatly divers ify energy resources, save the environment, and reduce imposed social cost [4]. Solar desalination is essentially a smallscale duplicate of the natural hydrologic cycle that produces rain, which is the prim ary source of fresh water worldwide. Solar insolation is preferred over other renewable energy sources to drive desalination systems because its thermal energy can be directly applied to thermal desalination schemes without adverse energy conversion requirements that usually entail certain energy losses. In addition, thermal desalination schemes are more suitable than mechanical desalination schemes for largescale applic ations as will seen later.

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3 Estimated 2000 Water Consumption ( Million Gallons / Day ) Gulf of MexicoAtlantic Ocean Pacific Ocean Canada Mexico -70 -80 -80 -90 -90 -100 -100 -110 -110 -120 -120 -130 40 40 30 30 Pacific Ocean -150 -150 -160 -170 -180 -140 -130 70 60 50 Pacific Ocean -160 20Hawaii Alaska 02505007501,000 125 Miles 0230460690920 115 Miles 080160240 40 MilesCentral Meridian: -96 1st Std Parallel: 20 2nd Std Parallel: 60 Latitude of Origin: 40Albers Projection 0 50 50 100 100 200 200 300 300 400 400 500 500 1000 1000 1500 1500 3000 3000 6000 Figure 1. Estimated water consumption of US counties for 2000 [1] 2001 Energy Consumption Per Capita ( Million BTU ) Gulf of MexicoAtlantic Ocean Pacific Ocean Canada Mexico -70 -80 -80 -90 -90 -100 -100 -110 -110 -120 -120 -130 40 40 30 30 Pacific Ocean -150 -150 -160 -170 -180 -140 -130 70 60 50 Pacific Ocean -160 20Hawaii Alaska 02505007501,000 125 Miles 0230460690920 115 Miles 080160240 40 MilesCentral Meridian: -96 1st Std Parallel: 20 2nd Std Parallel: 60 Latitude of Origin: 40Albers Projection 200 225 225 250 250 275 275 300 300 325 325 350 350 400 400 500 500 600 600 800 800 1000 1000 1200 Figure 2. Estimated energy consumption per capita of US states for 2001 [1]

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4 0 100 200 300 400 500 600 7001960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000YearMillion BTU FL US Figure 3. Estimated energy consumption per capita of Florida and the US [1] Monthly Average Daily Total Radiation ( kW-hr / m^2-day ) Gulf of MexicoAtlantic Ocean Pacific Ocean Canada Mexico -70 -80 -80 -90 -90 -100 -100 -110 -110 -120 -120 -130 40 40 30 30 Pacific Ocean -150 -150 -160 -170 -180 -140 -130 70 60 50 Pacific Ocean -160 20Hawaii Alaska 02505007501,000 125 Miles 0230460690920 115 Miles 080160240 40 MilesCentral Meridian: -96 1st Std Parallel: 20 2nd Std Parallel: 60 Latitude of Origin: 40Albers Projection 0 2 2 4 4 6 6 8 8 10 Figure 4. Monthly average daily solar insolation in the US [3]

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5 1.2 Objective Developing an economicallyviable and environmentallyfriendly desalination system involves lowering its energy demand and employing renewable energy to drive its operation. In this study, the most common desa lination technique, multi stage flash, will be modified to have its system vacuum creat ed passively and to have its thermal energy requirements drawn from solar insolation. Th e proposed modifications are expected to further the feasibility and broaden the applicability of the desalination process. Creating vacuum conditions above liquids will increase their evaporation rates. This phenomenon can be integrated into a practical continuous desalination process by repeatedly flashing seawater in vacuumed ch ambers to produce water vapor that will be condensed to produce fresh water. Gravity can be used to balance hydrostatic pressure inside the flash chambers with the outdoor at mospheric pressure to maintain that vacuum, while low grade heat or solar radiation can be used to heat seawat er before flashing it. The objective of this study is to simulate theoretically and experimentally a solar flash desalination process under a hydrostati cally sustained vacuum and analyze its controlling variables. Theoretical simulation is accomplished by a rigorous computer code employing fundamental physical and th ermodynamic relationships to describe the process complimented by reliable empirical corr elations to estimate physical properties of the involved species and operational parameters of the proposed system. Experimental simulation is realized by constructing a pilot unit depicting the proposed desalination system. Theoretical and experimental simula tions will be run unde r various analogous conditions, and their results will be compared and anal yzed both to validate the developed model and to examine the feasibility of the proposed system.

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6 CHAPTER 2. DESALINATION 2.1 Conventional Desalination Desalination is very energy intensive and requires costly infrastructure; therefore; several desalination processes have been developed over the years to produce fresh water from seawater economically. These can be cl assified according to the applied separation scheme into thermal, physical, and chemical processes. Thermal desalination processes produce a fractional phase change of liquid seawater to either vapor or solid. The new phase is then separated from the bulk brine water producing fresh water, while the latent heat of phase change is reclaimed. Multiple effect evaporation, multistage flash, vapor compression, and indirect contact freezing are examples of thermal desalination processes. Physical desalination processes extract fresh water from s eawater by applying pressure or electric potential across a membrane. Either fresh water or solute ions travel through the semipermeable membrane due to the mechanically induced gradient yielding the desired separation. Reverse osmo sis, electrodialysis, and nanofiltration are examples of physical desalination processes. Chemical desalination processes extr act fresh water from seawater by precipitating its salts due to chemical re actions. These processes are less common because they are usually too expensive to produce fresh water. Ion exchange, gas hydrate, and liquidliquid extraction are examples of chemical desalination processes.

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7 Selecting a suitable desalination process requires several design considerations such as: startup time, seawater quality, se awater supply, maintenance requirements, energy efficiency, capital cost, operating cost, and other site specific factors [2]. Global distribution of these processes is illustrated categorically in Figure 5 and geographically in Figure 6 as percentages of total installed capacity [5]. Selecting a particular desalination proce ss also requires knowledge of its specific design limitations. Discussing the design limitati ons of different desalination processes is beyond the scope of this study, but such discussions are widely available in academic and business literature [6]. A brief summary of these limitations is provided here. The energy needed to recover fresh water from seawater increases with increased salinity; therefore, limiting recovery rates is one way to optimize the desalination process. Also, increasing process efficiency usually involves increasing equipment size, which entails capital cost increase. Optimum desi gn of desalination plants generally includes analyzing the tradeoff between energy and cap ital costs to minimize production costs. In addition, scaling is a major issue in desalina tion because it fouls mass and heat transfer surface areas, reducing both capacity and e fficiency. Scaling can be minimized by reducing the saturation limit of saline wate r via dropping the opera ting temperature and limiting the recovery rates in addition to chem ical pretreatment and lime soda softening. Finally, desired water quality directly influences which desalination path to take [6]. Desalination is a continually evolving field with many of its processes under research and development. In addition, a wide variety of cost effective hybrid processes are proposed as alternatives to the rather expensive common comm ercial processes. A brief discussion of the major desali nation processes is provided next.

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8 MultiStage Flash, 44.4 % Reverse Osmosis, 41.1 % ElectroDialysis, 5.6 % Vapor Compression, 4.3 % Multiple Effect Evaporation, 4.1 % Other, 0.5 % Figure 5. Global distribution of installe d desalination capacity by technology [5] Middle East, 49.1 % N. America, 16.2 % Europe, 13.3 % Asia, 11.2 % Africa, 5.1 % Caribbean, 3.5 % S. America, 0.8 % Australia, 0.8 % Figure 6. Global distribution of instal led desalination capacity by region [5]

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9 2.1.1 Multiple Effect Evaporation Originally developed in the 1820s for c oncentrating sugar in sugar cane juice, multiple effect evaporation was used for de salination in the 1950s, making it the oldest desalination process still in operation. Multip le effect evaporation has been combined with other desalination methods, such as va por compression, to increase its efficiency. Seawater is distributed to a sequence of vacuumed vessels, know n as effects, held at successively lower pressures. External h eat is supplied to the first effect, and the generated vapor of each effect supplies its latent heat of condensation to the next. Condensed vapor of each effect is then collected as the fresh water product. Multiple effect evaporation has a rela tively good thermal performance since external heating is only require d for the first effect, but its heat transfer tubes are very susceptible to scaling, making it a less attractive desalination option. Figure 7 provides a simple process flow diagram of the multiple effect evaporation desalination process [6]. Figure 7. Multiple effect evaporation

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10 2.1.2 MultiStage Flash Multistage flash is the most common de salination technique, accounting for over 40 % of the global capacity [5]. It has been coupled with ot her processes, such as solar heating and steam turbine power gene ration, to increase its efficiency. Seawater is moved through a sequence of vacuumed vessels, known as stages, held at successively lower pressures, where it is preheated. External heat is then supplied, heating the seawater to above its saturation point. Seawater is then successively passed from one stage to the next, where a small amou nt of water flashes to steam in each stage, and the remaining brine is forw arded to next stage for furt her flashing. The flashed steam of each stage condenses by losing its latent h eat of condensation to the entering seawater. The condensed vapor of each stage is then collected as the fresh water product. Multistage flash has a relatively low thermal performance due to bulk heating of seawater, but its heat transfer tubes are less susceptible to scaling because of that bulk heating, making it a more at tractive desalination option. Figure 8 provides a simple process flow diagram of the multistage flash desalination process [6]. Figure 8. Multistage flash

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11 2.1.3 Vapor Compression Seawater is preheated before entering a vacuumed vessel to be partially vaporized by the latent heat of a condensing steam obt ained via compressing vaporized water. The process is dubbed mechanical vapor comp ression if steam compression is done by a compressor or thermal vapor compression if steam compression is done by an ejector. Vapor compression has a relatively high thermal performance and can be applied in the desalination of extremely concentrated brines. Vapor compression is generally employed in small and medium capacity applications. Figure 9 provides a simple process flow diagram of the mechanical va por compression desalination process [6]. Figure 9. Mechanical vapor compression

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12 2.1.4 Indirect Contact Freezing Seawater is cooled by cold outgoing fres h water and brine before it enters the evaporator of a separate refr igeration cycle, known as the freezer, where it is partially frozen by evaporating refrigerant. Crystallized ice is separated from the brine before it enters the condenser of the refrigeration cy cle, known as the melter, where it melts by extracting its latent heat of fusion from c ondensing refrigerant. Cold outgoing fresh water and brine streams are used to cool the entering seawater in a heat exchanger. Indirect contact freezing has a relativel y high thermal performance and is less susceptible to scaling and corrosion due to its low temperature operation, but problems arise both from controlling solid s handling operations and from the uncertain reliability of refrigerant compressors due to increased risk of o il slugging at low pressures. Figure 10 provides a simple schematic of the indirect contact freezing de salination process [6]. Figure 10. Indirect contact freezing

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13 2.1.5 Reverse Osmosis Reverse osmosis is the most common de salination process nationally and the second most common internationally in terms of capacity. It is best used for brackish water and is usually combined with other fi ltration methods to incr ease its efficiency. Seawater is initially treated to adjust its pH and to free it from particulates that negatively impact the membrane structure. Seawater is th en pumped to a network of semipermeable membranes, separating fresh wa ter from concentrated brine. Seawater pressure is raised above its natural osmotic pressure, typically 25 bars, but is kept below the membrane tolerance pressure, typically between 60 and 80 bars, forcing pure water molecules through the membrane pores to the fresh water side. Sepa rated water is then treated and collected as the fresh water product, while the concentrated brine is rejected. Reverse osmosis is very efficient because the mechanical compression energy can be reclaimed from the rejected concen trated brine with a suitable turbine. Figure 11 provides a simple process flow diagram of the reverse osmosis desalination process [6]. Figure 11. Reverse osmosis

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14 2.1.6 ElectroDialysis Seawater is passed through an electrodialysis stack consisting of alternating layers of cationic and anionic ion exchange membranes in an electrical field. Cations and anions then migrate in opposite directions through ion selective membranes and away from the saline feed in response to applie d voltage across the electrodialysis stack, producing fresh water in the intermediary channels. The electrodialysis stack can be arranged in series to increase purification and in parallel to increase output. Electrodialysis is best used in brackish water applications and is usually combined with other filtr ation methods to increase its efficiency. Figure 12 provides a simple process flow diagram of the electrodialysis desalination process [6]. Figure 12. Electrodialysis

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15 2.2 Solar Desalination Extracting fresh water from seawater requi res a great deal of energy, both thermal and mechanical, as detailed in Table 1 [7]. Renewable energy dr iven desalination is becoming more viable despite its expensive infrastructure because it employs free natural energy sources and releases no harmful effluent s to the environment. Solar insolation is usually chosen over other renewable energy sources because its thermal energy can be directly applied to drive desa lination systems without irreve rsible energy conversion that involves inevitable energy loss according to the second law of thermodynamics. Solar desalination systems are classified into direct and indirect processes depending on the energy path to fresh water. Direct solar desalination systems combine solar energy collection and desalination in one process producing fresh water distillate by directly applying collected solar energy to seaw ater. Solar distillation using a solar still is an example of direct solar desalination. Indi rect solar desalination systems comprise two subsystems: a solar collection system and a desalination system. The solar collection subsystem is used either to co llect heat using solar collecto rs and supply it via a heat exchanger to a thermal desalination proces s or convert heat to electricity using photovoltaic cells to power a physical desalination process. The desalination subsystem can be any of the previously mentioned conventional desalination systems. Table 1. Energy consumption of desalination systems [7] Process Heat Input ( kJ / kg of product ) Power Input ( kJ / kg of product ) Prime Energy Consumption ( kJ / kg of product ) M E E 123 8149 MSF 294 9 338 VC 29 192 RO 18 120 ED 43 144

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16 2.2.1 Solar Distillation Seawater is placed in a blackened basin in side an air tight transparent structure where it evaporates due to ab sorption of solar radiation then condenses on the sloping structure by losing its late nt heat of condensation to the surroundings. Condensed droplets run down the cover to accumulating tr oughs to be collected as fresh water. Solar distillation is a small scale hydrol ogical cycle, and its efficiency is significantly dependent on mete orological limitations such as solar radiation, sky clearness, wind velocity, ambient temperat ure, and many others. Solar distillation requires large collection areas to maximize inso lation and is usually combined with other desalination methods to increase its efficiency. Figure 13 provides a simple process flow diagram of the solar distillation desalination process [6]. Figure 13. Solar distillation

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17 2.2.2 Solar Collectors The solar collection subsystem of an indirect solar desalination system is essentially a solar collector that absorbs inci dent solar radiation a nd transfers heat to a fluid flowing through it. The working fluid of the collector can either be a medium to transfer heat to the process or to a therma l energy storage reservoir, or it can be the seawater itself before going through a therma l desalination system. Solar collectors can be either stationary or tracking. Tracking solar collector s can be designed to go after the rays of sunlight by moving around either a single axis or double axes. Solar collectors can also be classifi ed as concentratin g and nonconcentrating types. The concentration ratio of a solar collec tor is the relative am ount of the solar flux on the receiver to flux on the aperture. Concen trating collectors ha ve a highly reflective surface to reflect and concentrate solar radi ation onto a receiver or an absorber, while nonconcentrating collectors have a highly absorptive surface with low emittance to maximize heat transfer to the working fluid. Solar collectors are chosen according to the desired process temperature. Table 2 includes an extensive list of solar collectors and their operational temperature ranges [7]. Table 2. Solar collectors [7] Tracking Collector Type Absorber Concentration Ratio Operational Range Flat plate Flat 1 300 C Evacuated tube Flat 1 5000 C Stationary Compound parabolicTubular 1 6040 C Compound parabolicTubular 5 6000 C Linear Fresnel Tubular 100 6050 C Parabolic trough Tubular 155 6000 C Singleaxis Cylindrical trough Tubular 100 6000 C Parabolic dish Point 1001000 100500 C Doubleaxis Heliostat field Point 1001500 1502000 C

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18 2.2.3 Thermal Energy Storage Thermal energy storage in various solid an d liquid media is used to synchronize energy supply and demand due to the intermittent nature of solar energy. Energy can be stored as sensible heat, as shown in Table 3, or as latent heat, as shown in Table 4 [8]. Thermal storage design depends on the temp erature range of the solar collection and desalination systems, charge and discharge rates, space, corrosivity, and many others. Table 3. Sensible heat storage material [8] Medium Range ( C ) ( kg / m3 ) Cp ( J / kg-C ) K ( W / m-C ) Water 00 1000 4190 0.63 Water 10 bar 00 881 4190 50 % ethylene glycol 00 1075 3480 Dowtherm A 1260 867 2200 0.12 Therminol 66 -93 750 2100 0.11 Draw salt 220540 1733 1550 0.57 Molten salt 142540 1680 1560 0.61 Liquid sodium 100760 750 1260 67.50 Cast iron Up to 1150 7200 540 42 Taconite 3200 800 Aluminum Up to 660 2700 920 200 Fireclay 210000 1000 1.01.5 Rock 1600 880 Table 4. Latent heat storage material [8] ( kg / m3 ) Cp ( kJ / kg-C ) Medium MP ( C ) HL ( kJ / kg ) Solid Liquid Solid Liquid k ( W / m-C ) LiClO3 3H2O 8.1 253 1720 1530 Na2SO4 10H2O 32.4 251 1460 1330 1.76 3.32 2.25 Na2S2O3 5H2O 48 200 1730 1665 1.47 2.39 0.57 NaCH3COO 3H2O 58 180 1450 1280 1.90 2.50 0.50 Ba(OH)2 8H2O 78 301 2070 1937 0.67 1.26 0.65 ( l ) MgNO3 6H2O 90 163 1636 1550 1.56 3.68 0.61 LiNO3 252 530 2310 1776 2.02 2.04 1.35 LiCO3 / K2CO3 505 345 2265 1960 1.34 1.76 LiCO3 / K2CO3 / Na2CO3 397 277 2300 2140 1.68 1.63 nTetradecane 5.5 228 825 771 0.15 nOctadecane 28 244 814 774 2.16 0.15 HDPE 126 180 960 900 2.88 2.51 0.36 Steric Acid 70 203 941 347 2.35 0.17 ( l )

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19 2.2.4 Solar Ponds Water absorbs solar radiation going through it causing its temperature to rise. The shorter the wave length of sunlight, the deeper it can penetrate the water column as shown in Table 5 [8]. Solar ponds are pools of water with a darkened bottom to maximize light absorption. They are designed to have increasing salinity w ith depth creating a density gradient that inhibits natural convection currents. Th e final outcome is a stratified pond with increasing temperature and salinity with dept h, as shown in Figure 14 [7]. Solar ponds function as both solar collect ors and thermal energy storage media. Table 5. Spectral absorption of solar radiation in water [8] Layer Depth Wavelength ( m ) 0 1 cm 10 cm 1 m 10 m 0.2.6 23.7 23.7 23.6 22.9 17.2 0.6.9 36.0 35.3 36.0 12.9 0.9 0.9.2 17.9 12.3 0.8 0.0 0.0 > 1.2 22.4 1.7 0.0 0.0 0.0 Total 100.0 73.0 54.9 35.8 18.1 Figure 14. Vertical cross section of a solar pond

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20 2.2.5 Photovoltaics Photovoltaic cells are made from common semiconductor compounds and can directly convert solar radiation into useful electricity, as shown in Figure 15 [8]. Cells are arranged to form modules that are combined to form panels Photovoltaic systems include an array of joined panels to produce the required electrical output, as shown in Figure 16 [8]. Photovoltaics can be employed independ ently or jointly with other sources to generate electricity needed to pow er physical desalination systems. Figure 15. Photovoltaic cell schematics Figure 16. Photovoltaic system schematics

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21 CHAPTER 3. RESEARCH BACKGROUND 3.1 Renewable Energy Desalination Systems Water and energy are the most essential i ngredients of a flourishing civilization. Fresh water and energy reserves are increasin gly exhausted as was mentioned earlier in CHAPTER 1 ; hence, seawater desalin ation using renewable en ergy sources is a very appealing research area. In addition, desali nation is an enormously energy exhaustive process making fossil fuel based conventiona l desalination methods extremely unpopular especially in light of the growing impact of environmental pollution and global warming. The worldwide capacity of desalination using renewable energy amounts to less than 1 % of that of conventional desalination due to high capital and maintenance costs associated with using renewable energy sources [9]. Several renewable energy driven desalination plants were de signed and constructed; however, most of them were geographically customized and bu ilt on pilot scale. A detailed record of renewable energy driven desalination plants was put together by Tzen and Morris [10]. Wind energy can be utilized to generate electricity via turbines to run physical and chemical desalination plan ts, while geothermal energy can be utilized to generate heat via underground heat excha ngers to run thermal desalina tion plants. Solar energy is the most promising renewable energy source du e to its ability to drive the more popular thermal desalination systems directly through solar collectors and to drive physical and chemical desalination systems i ndirectly through photovoltaic cells.

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22 3.2 Passive Vacuum Solar Desalination The passive vacuum desalination concept was initially developed and examined by Goswami and Kharabsheh [11]. Atmospheric pressure for ces seawater from a ground level tank into an elevated vacuumed ch amber through an inject ion pipe where water starts to evaporate due to solar energy supplied to the ch amber via a closed loop heat exchanger. The concentrated brine is then withdrawn through a withdrawal pipe annulus to the injection pipe to r ecover heat, while vapor moves towards a condenser due to a vapor pressure gradient through a finned pipe. Vapor then condenses by losing its latent heat of condensation to the ambient and flow s down to a fresh water tank due to gravity. The vacuum is maintained by the hydrostatic balance amongst all of the joined vessels. Figure 17 provides a simple illustration of the passive vacuum solar desalination process. Condenser Brine Water Fresh Water Sea Water Evaporator Figure 17. Passive vacuum solar desalination

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23 3.3 Passive Vacuum Solar Flash Desalination The prior passive vacuum solar process was modified to overcome the big size of the evaporator and its large level fluctuations Seawater is pumped through a condenser to preheat it before it enters a solar heater where it flashes into the vacuumed evaporator through an expansion orifice to produce water vapor and concentrated brine. The flashed vapor then condenses by losing its latent heat of condensation to the entering seawater in the condenser. The condensate and the concen trated brine flow down to ground tanks due to gravity, while the vacuum is naturally ma intained by the hydros tatic balance between the ground and the elevated vessels. Figure 18 provides a simple process flow diagram of the passive vacuum solar flash desalination process that was developed and examined theoretically by Goswami and Maroo [12]. Condenser Brine WaterFresh WaterSea WaterEvaporator Pump Heater Figure 18. Passive vacuum solar flash desalination

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24 3.4 Proposed Desalination System The proposed desalination system consists of a saline water tank, a concentrated brine tank, and a fresh water tank placed on ground level plus an evaporator and a condenser located at least ten meters above gr ound, as shown in Figure 19. The evaporatorcondenser assembly, or flash chamber, is initially filled with saline water that later drops into the ground tanks by gravity, cr eating a vacuum above the water surface in the unit without a vacu um pump. The vacuum is maintain ed by the hydrostatic pressure balance among all of the connected vessels. The ground tanks are open to the atmosphere, while the flash chamber is insulated and sealed to retain bot h heat and vacuum. In a continuous process, cool saline wa ter is pumped through the condenser to preheat it before it enters a solar heater and flashes into a vacuumed evaporator through an expansion orifice or a pressurer educing valve producing water vapor and concentrated brine. The water vapor then conde nses by losing its heat of condensation to the entering saline wa ter in the condenser. The fresh water condensate and concentrated brine flow down to the fresh water and brin e water tanks, respectively, due to gravity through linking pipes. Each of the fresh wate r and the brine water tanks has a discharge pipe located a few centimeters above the leve l of the inlet water pipes, keeping their levels constant to maintain th e vacuum in the flash chamber hydrostatically as well as to retrieve the fresh water product and reject the concentrating brine. Multistage flash desalination scheme of the proposed system can be achieved by flashing seawater in sequentially lower pressure flash chambers, as shown in Figure 20. Employing the multistage flash desalination scheme will result in more evaporation and better recovery of heat of condensation, resulting in more fresh water output.

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25 Figure 19. Singlestage solar flash desalination system Figure 20. Multistage solar flash desalination system

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26 CHAPTER 4. THEORETICAL ANALYSIS 4.1 Process Description The proposed desalination system with its designated stream labels is outlined in Figure 21. The desalination process includes tw o consecutive steps: a startup procedure and a continuous operation. The startup procedure is a simp le process invoked prior to running the continuous operation and will not be included in the model. The continuous operation is the essential part of the desali nation process, and a model will be built to simulate it. The valve positions shown depict the system in continuous operation mode. The startup procedure begins by separa tely pumping the condenser with fresh water and the evaporator with seawater, while their top valves are open and their bottom ones are closed until they are completely filled with water and free of air. Valve positions of both vessels of the flash chamber are then switched to let water drop under gravity, leaving behind a vacuum that is created without a vacuum pump. The continuous operation begins right af ter the initial startup procedure and it consists of pumping seawater through the condenser, preheat ing it before flowing it through the channels of a solar heater to reach a desired fl ash temperature. The desired flash temperature is controlled by manipulating the residence time of seawater in the solar heater by varying its flow rate in relation to availabl e solar insolation. Hot seawater then flashes into an insulated vacuumed ev aporator through an ex pansion orifice or a pressurereducing valve, producing wa ter vapor and concentrated brine.

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27 The produced water vapor flows to the condenser due to a vapor pressure gradient and condenses by losing its heat of condens ation to seawater passing through the condenser while concentrated brine rema ins in the evaporator. The fresh water condensate and concentrated brine flow down to the fresh water and brine water ground tanks, respectively, due to gravity through linki ng pipes that stretch down till just above the bottom of the tanks. The fresh water and the brine water ground tanks have discharge pipes positioned a few centimeters higher than the lip of the linking pipes, keeping their levels constant to maintain the vacuum in the flash chamber by the hydrostatic balance with the levels in the flash chamber. A comprehensive model will be developed to examine the dynamics of proposed continuous desalination operation. The model will employ fundamental laws to describe the process in addition to reli able empirical correla tions to estimate physical properties of the involved species and operational paramete rs of the proposed sy stem. The model will assume total steam condensation as well as quasi steady state operation, accounting for the build up of noncondensable gases in the fl ash chamber. The model will also account for the natural diffusion process of water va por occurring because of a vapor pressure gradient present between the hot and cold sides of the flash chamber. The model will include mass and energy balances around process equipment and geometrical formulas describing equipment layout and size. The RachfordRice method [13] will be employed to perform flash calcula tions, while Bernoulli's fluid equation will be used to perform hydrostatic balance relations. Thermodynamic equilibria and several physical property correlations will also be included in the model. In addition, an integrative equation of state will be us ed to express rising vacuum pressure.

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28 Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 21. Process schematics 4.2 Model Development Trace components in seawater may affect its kinetics but not its thermodynamic equilibrium; therefore, only major components will be considered in this theoretical analysis. The following subsections present a ll equations used in modeling the proposed system, while the next section sketches the solution algorithm. The nomenclature and engineer ing units of all variables used in the model are detailed at the beginning of this dissertation in the LIST OF SYMBOLS section. In addition, stream symbols that appear on the process flow diagram of Figure 21 are used as subscripts for different stream property va riables. Process equipment referred to in the model denote the pump, the condenser, the heater and the evaporator. The complete code with its input and output va lues can be found in the APPENDICES section.

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29 4.2.1 Mass and Energy Balance Salt balances around process equipment are given by P P S SM M (1) X X P PM M (2) H H X XM M (3) W W H HM M (4) Overall energy balances around pr ocess equipment are given by 0 out P in P P PE E W Q (5) a C out C in C C CE E E W Q (6) 0 out H in H H HE E W Q (7) d E out E in E E EE E E W Q (8) Energy flow inputs to pro cess equipment are given by S S in PH M E (9) L E E E P P in CH H M H M E (10) X X in HH M E (11) H H in EH M E (12) Energy flow outputs from process equipment are given by P P out PH M E (13) C C X X out CH M H M E (14) H H out HH M E (15) L E E E W W out EH H M H M E (16)

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30 Energy accumulation in the condenser due to noncondensable gases is given by a C a C a CH M E (17) Energy transmitted by the diffusing water molecules from the concentrated brine phase to the fresh water vapor phase is a ccounted for in the a bove energy input and output expressions; therefore, an offset term is included in the energy balance of the evaporator to neutralize the effect of that transmitted energy on the flashing process. In other words, offsetting transmitted energy of diffusing water molecules effectively altered the boundary of the above energy bala nce from the evaporator to expansion orifice. Figure 22 illustrates the ma ss transfer operations of the proposed system, where flash and diffusion operations occur in the evaporator. The transmitted energy of the diffusing water molecules offset term in the evaporator is given by L E E W d E d EH H H M E (18) Figure 22. Mass transfer operations

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31 Demisting is a standard unit operation in industry accomplished by devices called demisters that are fitted to process vessels to ensure a full remova l of liquid droplets from vapor streams. No demister was attached to the experimental unit and no demisting is considered in the model; however, flashed vapor can be safely assumed free from entrained brine droplets yiel ding zero salinity expressed by 0 C E (19) The experimental simulation wi ll be thoroughly discussed in CHAPTER 5 and its output will be comprehensively disclosed in CHAPTER 7 ; nonetheless, a significant observation regarding the produ ced amount of fresh water va por was made and needs to be mentioned here since it will be included in the model. The maximum amount of fresh water that can be produced by flashing seawater can be approximated by the expression [ MH ( HH HW ) / ( HE + HL E HW) ] dt which is obtained by conducting an energy balance around the expansion orifice assuming seawater to be a single component fluid and ignoring heat losses. Maximum amounts that can be produced were computed using experimental flow and temperature values, then they were compared to actual collected amounts. Actual amounts of fresh water produced at lower flash temperatures were considerably less th an predicted amounts by the single component flash calculation, indicating that a sizeable quantity of the fl ashed vapor condenses prematurely in the evaporator before making it to the condenser. In contrast the actual amounts of fresh water produced at higher flash temperatures were much more than predicted amounts by the single component flash cal culation, suggesting the presen ce of a diffusion process of vaporized water molecules from th e evaporator to the condenser.

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32 Bemporad [14] developed a correlation that es timates the diffusion rate of water vapor between two joined chambers under vacuum, where one chamber contains saline water and the other contains fresh water. Th e correlation was experimentally based with one empirical coefficient, and it identified the gradient PH2O / T as the driving force for diffusion. The correlation was slightly modi fied to properly correspond to the current experimental results yielding the following expression 15 273 15 273 54 0 12 2. T P T P XA MC C O H W W O H W E d E (20) Parameter serves as a diffusion coefficient, while parameter serves as a diffusion barrier and both can be adjusted using experimental results. The two parameters can be thought of as conductanc e and resistance terms, and it is imperative to reiterate that their obtained values pertain to the ge ometry of the experimental setup and should be readjusted whenever applied to different geometries using experimental records. The vapor pressures corresponding to the br ine and fresh water temperatures are needed to evaluate the above e xpression and can be calculated by [15] PC T PB PA exp PW W O H2 (21) PC T PB PA exp PC C O H2 (22) Flash and accumulation computations will be carried out on molar basis; therefore, a mole balance is included in the model to represent both operations by E W HN N N (23) a C C EN N N (24)

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33 The flash operation is the heart of the desalin ation process and will be thoroughly discussed later. The condensation operation is considered a quasis teady state operation where the formed noncondensable gases accumulate in the flash chamber, and all of the flashed water vapor condenses forming the fr esh water product. This quasisteady state operation is expressed by E O H a CN y N 21 (25) Note that the last equation can be replaced by NC = yH2O NE because total accumulation of noncondensable gases and total condensation of water vapor are interchangeable statements. Figure 23 represents a transformation of Figure 22 from mass to a molecular basis to correspond to the above mole balance and is accomplished by dividing the mass flow rate s by the stream molecular weights presented next. Figure 23. Molecular tr ansfer operations

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34 Mass flow rate and composition of pr ocess streams prior to flashing are considered constant, and their va lues will be input to the model H X P SM M M M (26) Both molar and mass flow rates are interchangeably used in this model to allow for flash and accumulation computations on a molar basis and for diffusion and production computations on a mass basis. They can be related using the average molecular weight of process streams that will be introduced later as follows H H HMW N M (27) d E W W WM MW N M (28) d E E E EM MW N M (29) d E C C CM MW N M (30) a C a C a CMW N M (31) Seawater is a solu tion of many salts and contains a small amount of dissolved gases. To simplify calculations, seawater salt will be treated as one substance with nitrogen, oxygen, argon, and ca rbon dioxide making up the disso lved gases. The average molecular weights of seawater salt and process streams are used in relating molar and mass flow rates and can be estimated by considering their major components as [16] F F Sr Sr BO BO Br Br HCO HCO K K Ca Ca Mg Mg SO SO Na Na Cl Cl SaltMW MW MW MW MW MW MW MW MW MW MW MW 3 3 3 3 4 41 (32) O H O H Salt Salt CO CO Ar Ar O O N N HMW z MW z MW z MW z MW z MW z MW2 2 2 2 2 2 2 2 (33)

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35 O H O H Salt Salt CO CO Ar Ar O O N N WMW x MW x MW x MW x MW x MW x MW2 2 2 2 2 2 2 2 (34) O H O H CO CO Ar Ar O O N N EMW y MW y MW y MW y MW y MW2 2 2 2 2 2 2 2 (35) O H CMW MW2 (36) O H CO CO Ar Ar O O N N a Cy MW y MW y MW y MW y MW2 2 2 2 2 2 21 (37) 4.2.2 Equilibrium Distribution Coefficients The distribution of noncondensable ga ses between the flashed vapor and concentrated brine in the flash chamber can be estimated by assuming equilibrium between the two phases. Salt is considered nonv olatile and therefore is not present in the flashed vapor. Henrys constants for noncondens able gases and satu ration pressure of water are needed to describe this assumed equilibrium. Henrys constants for the nonconde nsable gases are given by [17] 15 298 1 15 273 12 2 2. T HF exp HC HCE N o N N (38) 15 298 1 15 273 12 2 2. T HF exp HC HCE O o O O (39) 15 298 1 15 273 1 . T HF exp HC HCE Ar o Ar Ar (40) 15 298 1 15 273 12 2 2. T HF exp HC HCE CO o CO CO (41)

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36 The saturated pressure of water is given by [15] PC T PB PA exp PE O H2 (42) The equilibrium distribution coefficients are used in mass transfer computations to determine the distribution of chem icals between phases in equilibrium [18]. These are also known as the partition coefficients in th e literature or more commonly as Kvalues. The mentioned vaporliquid equilibrium distribution coefficient of species i is defined as Ki = yi / xi = i Pi sat / P. The Kvalue of seawater salt is zero due to its nonvolatility, wh ile those of the noncondensable gases as well as water can be approximated using the above temperaturebased correlations as follows V N N V N N N V N N N NP HC x P x HC x P P x y K2 2 2 2 2 2 2 2 2 (43) V O O V O O O V O O O OP HC x P x HC x P P x y K2 2 2 2 2 2 2 2 2 (44) V Ar Ar V Ar Ar Ar V Ar Ar Ar ArP HC x P x HC x P P x y K (45) V CO CO V CO CO CO V CO CO CO COP HC x P x HC x P P x y K2 2 2 2 2 2 2 2 2 (46) V O H O H O HP P K2 2 2 (47)

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37 Vaporliquid equilibrium distribution coefficients were obtained using the SUPERTRAPP program, an interactive computer code distributed by the National Institute of Standards and Technology that calculates thermodynamic properties of mixtures based on the PengRobinson equati on of state. SUPERTRAPP was employed to perform isobaric phase equili bria flash calculations for wa ter with an average content of noncondensable gas as reported in literature [16] at various temperatures to produce a dataset of Kvalues. Least squares regression was then used to fit the data to the above equilibrium equations by adjusting values of HCi, HFi, PA, PB, and PC producing correlation coefficients very close to unity as will be seen later in CHAPTER 6 The SUPERTRAPP code used in generating the vaporliquid equilibrium distribution coefficient data a nd the Matlab codes used in re gressing that data to adjust the vaporliquid equilibrium parameters are in the APPENDICES section. SUPERTRAPP simulations are fresh water based, and no salts were included in their flash calculations. To adjust phase equi libria computations of the current model for saline water, Kvalues are multiplied by a relativity parameter that can be defined as i = solubility in fresh water / solubility in seawater for solutes and H2O = seawater saturated pressure / fresh water saturated pressure for water. The relativity factor is a single constant obtained by averaging literature da ta given over the opera ting temperature range to simplify calculations [19]. Activity is a way for expressing the effec tive concentrations of species to account for their deviation from ideal behavior. Ac tivity can be applied to any concentration scales such as molality, molarity, or fractiona l scales; however, molar fraction is the most common concentration scale used in flash calculation.

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38 Activity accounts for deviations from ideal behavior by multiplying the concentration by an activity coefficient that can be experimentally determined or empirically computed using several available models. The value of an activity coefficient approaches unity as molecular inte ractions behave more ideally. The activity coefficient of water is needed to calculate its Kvalue. Experimental data can be used to perform adiabatic flas h calculations, generati ng activity coefficient data that are then used to find an act ivity coefficient correlation resembling P P fO H V O H 2 2 (48) 4.2.3 Adiabatic Flash The flash operation of the proposed desalination process is an adiabatic expansion operation where the temperature of seawater drops upon entering the flash chamber due to the drawn enthalpy of vaporization by the flashing water vapor, at taining a saturation temperature used in the above equilibrium calculations. Flash computations are carried out on a molar basis, and the molar compositi on of the stream entering the flash chamber can be calculated from the average com position of seawater re ported on mass basis [16] O H O H Salt H CO CO Ar Ar O O N N N N NMW MW MW MW MW MW MW z2 2 2 2 2 2 2 2 2 2 2 (49) O H O H Salt H CO CO Ar Ar O O N N O O OMW MW MW MW MW MW MW z2 2 2 2 2 2 2 2 2 2 2 (50)

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39 O H O H Salt H CO CO Ar Ar O O N N Ar Ar ArMW MW MW MW MW MW MW z2 2 2 2 2 2 2 2 (51) O H O H Salt H CO CO Ar Ar O O N N CO CO COMW MW MW MW MW MW MW z2 2 2 2 2 2 2 2 2 2 2 (52) O H O H Salt H CO CO Ar Ar O O N N Salt H SaltMW MW MW MW MW MW MW z2 2 2 2 2 2 2 2 (53) The molar composition of the concentrated brine is given by 2 2 2 2N N E W H N NK N N N z x (54) 2 2 2 2O O E W H O OK N N N z x (55) Ar Ar E W H Ar ArK N N N z x (56) 2 2 2 2CO CO E W H CO COK N N N z x (57) W H Salt SaltN N z x (58) O H O H E W H O H O HK N N N z x2 2 2 2 (59) Similarly, the molar composition of the flashed vapor is given by 2 2 2 2N N N NK x y (60)

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40 2 2 2 2O O O OK x y (61) Ar Ar Ar ArK x y (62) 2 2 2 2CO CO CO COK x y (63) O H O H O H O HK x y2 2 2 2 (64) Fraction summations are given by 12 2 2 2 O H H CO Ar O N (65) 12 2 2 2 O H Salt CO Ar O Nz z z z z z (66) 12 2 2 2 O H Salt CO Ar O Nx x x x x x (67) 12 2 2 2 O H CO Ar O Ny y y y y (68) 4.2.4 Heat Transfer Computing temperatures of streams exiting the flash chamber properly is essential in accurately evaluating performance of the proposed desalination system; therefore, heat transfer calculations are in cluded in the model, complimenting the above energy balance to solve for those temperatures. Heat transfer calculations are included to estimate the amount of heat transferred from the condens ing vapor to the ente ring seawater feed through the condenser tube as well as the heat loss from both compartments of the flash chamber through the walls of the condenser and evaporator. The condenser is exposed to maximize heat loss, while the evaporator is insulated to minimize heat loss, and the entire flash ch amber is vacuum sealed. The vapor pressure gradient between the two compartments of the flash chamber is the dr iving force of vapor transfer from the hot evaporator to the cold condenser to produce fresh water.

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41 The condenser will be modeled as a shell and tube heat exchanger, both where the cold seawater is flowing inside a coiled t ube placed in an exposed shell and where the flashed vapor is condensing on the outer surfac e of that coiled tube by losing its latent heat of condensation to the entering cold seaw ater. The evaporator will be modeled as an insulated vessel, where heated seawater is flashing producing fres h water vapor that moves to the condenser due to lower va por pressure through a connecting duct. Heat transfer is a complex process, particularly when phase change is involved. Heat transfer can come about in different modes; however, the current model will use the overall heat transfer appro ach to simplify computations. The inside and outside fluid film coeffi cients can be estimated by the following correlations that were developed speci fically for water and stagnant air [20] as well as evaporating and condensing steam [15] CT X X CT X i CTD T . D M h 02 0 35 1 10 0525 38 0 4 (69) 25 0 3 2725 0. X E CT CT X CT X X L E o CTT T D N k H g h (70) 25 0 3 213 1. E C C C C L E i CT T L k H g h (71) 25 00448 0. C E o CL T T h (72) 25 0 3 213 1. E E W W W L E i ET T L k H g h (73) 25 00448 0. E E o EL T T h (74)

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42 The overall heat transfer coefficient is a simplified parameter used in gauging overall convective and conductive resistance to heat transfer. Overall heat transfer coefficients are computed by the following correlations [20] CT CT CT w CT CT CT id CT CT CT CT i CT CT CT CT od CT o CT CTD D Ln k D h D D h D D h h U 2 1 1 1 (75) C C C w C C C id C C C C i C C C C od C o C CD D Ln k D h D D h D D h h U 2 1 1 1 (76) E E E w E E E id E E E E i E E E E od E o E ED D Ln k D h D D h D D h h U 2 1 1 1 (77) Heat transfer area is assumed to be equal to that of the inner surface of the heat transfer medium, with the end sections ignor ed; therefore, heat exchange surface areas are given by the following geometrical relationships CT CT CTL D A (78) C C CL D A (79) E E EL D A (80) The log mean temperature difference is a logarithmic average of the temperature difference between the hot and cold streams of a heat exchanger. It represents the driving force for heat transfer in heat exchangers, si nce that heat transfer is directly proportional to its value. The log mean temperatur e difference expressi ons are given by X E P E P X CTT T T T Ln T T Tm (81) C E E C CT T T T Ln T T Tm (82)

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43 W E E W ET T T T Ln T T Tm (83) The countercurrent departure parameters are dimensionless ratios used in correcting the log mean temperature di fference expressions and are given by P E P X CTT T T T S (84) T T T T SE C C (85) T T T T SE W E (86) The heat transferred from the condensing vapor to the entering seawater, as well as the heat loss from the condenser a nd from the evaporator, are given by CT CT CT CT P P X XTm F A U H M H M 60 (87) C C C C CTm F A U Q 60 (88) E E E E ETm F A U Q 60 (89) The countercurrent departure correction f actors are dimensionless variables used in correcting log mean temperature difference expressions. The count ercurrent departure correction factors are widely av ailable in literatu re as lookup charts for many types of heat exchangers and can be computed empi rically as functions of countercurrent departure parameters S f FCT CT (90) S f FC C (91) S f FE E (92)

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44 The vapor pressure of seawater is 1.84 % lower than that of pure water at the same temperature due to nonvolatile salts, and th erefore, the boiling point of seawater is slightly higher than that of fresh water. This phenomenon is known as the boiling point elevation or vapor pressure depression. Boili ng point elevation is a function of salinity and does not depend on properties of solute or solvent [14]. The temperature of seawater drops upon entering the flash chamber to attain equilibrium; however, equilibrium is not always fully achieved. This phenomenon is known as the nonequilibrium allowance, and it depends on several factors such as flash temperature, flow rates, concentrated brine depth, and chamber geometry. Correlations for boiling point elevation [21] and nonequilibrium allowance [22] can be incorporated into the model to account for flash efficiency as follows NEA BPE T TE W (93) 4.2.5 Vacuum Volume All vessels will be modeled as right circular cylinders with specified dimensions. The fresh water and the brine water tanks are equipped with discharge pipes located slightly above the level of the inlet water pipes, keeping thei r levels constant. Conversely, levels of the seawater tank, as well as conde nser and evaporator, are constantly changing during operation; therefore, they need to be computed and include d in the model. The level of the feed seawater tank is used in calculating the ver tical discharge pressure head that will be used in determining the pumpi ng requirements, while levels of the condenser and evaporator are used in calculating the v acuum volume that will be used in calculating the vacuum pressure.

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45 The circular cross sectional areas of thes e vessels are needed to calculate their levels and are determined by 24S SD XA (94) 24E ED XA (95) 24C CD XA (96) The level of the seawater tank decreases with time because of the continuous pumping of seawater to the process, and it can be geometrically computed by S S S i S SXA dt M Z Z (97) If the seawater flow rate remains consta nt during operation, th e numerator of the second term of the above equation simplifies to MS dt = MS t The level in the condenser is hydrostatically balanced with the level in the fresh water tank. Since the level in the fresh water tank is kept constant, the vacuum pressure inside the flash chamber is the only variable controlling the level in the condenser. The level in the condenser decrea ses as vacuum pressure incr eases due to noncondensable gases building up in the flash chamber. The initial and the dynamic levels in the condenser can be estimated using Bernoulli's fluid equation given by F C C C i V i CZ PL g P P P Z 610 (98) F C C C V CZ PL g P P P Z 610 (99)

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46 Similarly, the level in the evaporator is hydrostatically balanced with the level in the brine water tank. Since the level in the br ine water tank is kept constant, the vacuum pressure inside the flash chamber is the only variable controlling the level in the evaporator. The level in the ev aporator decreases as vacuum pressure increases due to noncondensable gases building up in the flash chamber. The initial and the dynamic levels in the evaporator can be estimated using Bernoulli's fluid equation given by B W W W i V i EZ PL g P P P Z 610 (100) B W W W V EZ PL g P P P Z 610 (101) The initial and the dynamic volumes of the vacuum in the condenser depend on corresponding initial and dynamic levels of the condenser. They are geometrically computed by subtracting corresponding fresh wa ter volume from total volume of the right circular horizontal cylin der condenser as follows 2 1 2 22 2 1 4 8i C C i C i C C C i C C C C i CVZ D Z Z D D Z sin Arc D D L V (102) 2 1 2 22 2 1 4 8C C C C C C C C C C CVZ D Z Z D D Z sin Arc D D L V(103) Initial and the dynamic volumes of the vacuum in the evaporator depend on corresponding initial and dynamic levels of the evaporator. They are geometrically computed by subtracting the corresponding br ine water volume from total volume of the right circular horizontal cyli nder evaporator as follows

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47 2 1 2 22 2 1 4 8i E E i E i E E E i E E E E i EVZ D Z Z D D Z sin Arc D D L V (104) 2 1 2 22 2 1 4 8E E E E E E E E E E EVZ D Z Z D D Z sin Arc D D L V(105) Vacuum volume is the total space occupied by vapor in the flash chamber and can be computed by adding the vapor space of both condenser and evaporator to the volume of the connecting duct and subt racting the volume of the coiled tube of the condenser. Therefore, the initial and dynamic v acuum volumes can be calculated by 2 24CT CT E E i CV i EV i VD L PD PL V V V (106) 2 24CT CT E E CV EV VD L PD PL V V V (107) 4.2.6 Vacuum Pressure Seawater flow rate and the flash temperat ure are the only controlled variables of the proposed continuous desalination operation, and their effects on the system will be analyzed later. Seawater flow rate dete rmines the amount of noncondensable gases accumulated, while the flash temperature dete rmines the equilibriu m temperature reached inside the flash chamber in line with the above mass and energy balance. The accumulated amount of noncondensable gases and the reached equilibrium temperature, as well as the calculated v acuum volume, determine vacuum pressure according to any equation of state. It is im perative to express the vacuum pressure properly to simulate the proposed continuous desalination operation accurately because of the profound impact of vacuum pressure on the outcome of the flash operation.

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48 The ideal gas model describes fluid propert ies without considering molecular size or intermolecular attractions; therefore, its accuracy diminishes at higher pressures and lower temperatures. Low vacuum pressure ma rginalizes the effect of molecular size, while the fairly high flash temperature, manifested in higher thermal kinetic energy, weakens the relative importance of intermolecu lar attractions. Consequently, the ideal gas law becomes a suitable equation of state to express rising vacuum pressure inside the flash chamber due to build up of nonconde nsable gases in the flash chamber. Initial vacuum pressure is an input value and should be very cl ose to or equal to the saturated pressure of water at ambien t conditions, while the initial vacuum volume can be determined by the above mentioned re lations, knowing initial levels in the flash chamber. The gas phase primarily consists of water molecules at first, and their amount can then be estimated by ) T ( R V P ni V i V i V15 273 (108) Noncondensable gas molecules progressively accumulate in the flash chamber, and their amount must be added to the ini tial amount computed above to express the dynamic amount of molecules in the gas phase as dt N n na C i V V (109) Initial and the dynamic saturated pressures of water are needed to express vacuum pressure in a little while. Th e dynamic saturated pressure of water is given above as a function of dynamic equilibrium temperature, while initial saturated pre ssure of water is a function of ambient temperatur e and can be calculated by [15] PC T PB PA exp Pi O H2 (110)

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49 The vacuum pressure needs to be specified to proceed with the flash calculations ultimately leading to convergence of the whole model; therefore, the simulation is executed incrementally, where the computed vacuum pressure of one time increment becomes the input vacuum pressure to th e next time increment. The known initial vacuum pressure value is input to the first time increment to initialize this progression. This scheme is known as the Iterative and Incremental Development in the art of software development. Consequently, the in cremented vacuum pressure is expressed by i O H O H V E V t VP P V ) T ( R n P2 215 273 (111) t t V VP P (112) To illustrate the Iterative and Increm ental Development concept as it pertains to the current model, consider the ensuing paradigm. The known initial vacuum pressure is fed to the computer code as dynamic vacuum pr essure of the first in crement resulting in a solution for the dynamic vacuum pressure of th e second increment that is then fed to the computer code resulting in a solution for the vacuum pressure of the third increment, and so forth until the last increment is reached. The dynamic quantity of molecules in th e gas phase incorpor ates accumulated noncondensable gas molecules plus water molecu les present at the initial ambient point; however, there are more water molecules in the gas phase not acc ount for due to the temperature increase from ambient to equi librium. Consequently the second term on right hand side of the vac uum pressure expression, PH2O Pi H2O, is added to correct the dynamic amount of water molecules in the gas phase by accounting for the increase in vapor pressure due to te mperature rise from am bient to equilibrium.

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50 The model assumes total accumulation of noncondensable gases in the flash chamber; however, water vapor dissolves a sm all quantity of noncondensable gases as it condenses. In addition, average values for se awater content of disso lved gases are input to the model, as the real seawater content of dissolved gases is indefinite and could be somewhat different from the average values. Moreover, the true vaporliquid equilibrium for carbon dioxide involves more than just the afore mentioned Kvalues due to presence of several carbonates in seawater that ar e also in equilibrium with carbon dioxide. Consequently, a correction factor for th e dynamic amount of molecules in the gas phase is included in the vacuum pressure expr ession. Experimental da ta can be used to perform adiabatic flash calculati ons, generating correction factor data that are then used to find a correction factor correlation resembling P P fO H V 2 (113) Other expressions of vacuum pressure can be worked out, but it is very important for the expressed vacuum pressure to match e xperimental values clos ely due to its strong impact on the outcome of the si mulation as mentioned earlier. Operating pressure inside the flash cham ber has to be between the dew point and the bubble point to carry out a successful flash separati on. Dew point and bubble point pressures are estimated by O H O H O H CO CO CO Ar Ar Ar O O O N N N V BPK z K z K z K z K z P P2 2 2 2 2 2 2 2 2 2 2 2 (114) O H O H O H CO CO CO Ar Ar Ar O O O N N N DP VK z K z K z K z K z P P2 2 2 2 2 2 2 2 2 2 2 2 (115)

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51 4.2.7 System Performance Pressure drop is a design parameter us ed in accounting for pr essure reduction due to friction. Total pressure drop of seawater flow from the seawater tank to flash chamber can be determined by summing up the pressure drops of each upstream pipe CT HT H X P SP P P P P P P (116) If a throttling valve is used to control fl ow rate of seawater, the pump will run at full capacity, and work exerted on seawater by the pump is a direct function of the power of the pump, that is WP = 44742 HPP. If a variablefrequency drive is used to control flow rate of seawater, the pump will run at modulated speeds, and work exerted on seawater by the pump is a function of the head pressure. The proposed desalination system will consider a variablefrequency drive to control flow rate of seawater due to its superior energy efficiency over a throttling valve; therefore, work exerted on seawater by the pump can be estimated using Bernoulli's fluid equation as P V O S P PP P P Z Z g M W 10 107 (117) An appropriate circulation pump can be selected from the catalog of any process equipment manufacture based on required flow rate and tota l head. Selecting the pump will set many parameters including its power and suction force. The procedure of selecting a pump or any requi red piece of equipment for the process is beyond the scope of this analysis; however, equipment sizi ng is a common straightforward practice. Formulae for sizing pumps, valves, vessels, pipes, expansion orifices, and many other process equipment are abundantly available in literature [23].

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52 A solar heater is employed in the propos ed desalination system to heat the preheated seawater coming out of the cond enser further before flashing it in the evaporator. Solar heating can be accomplished in a variety of ways; however, the present model assumes the heater to be a singleglazed flatplate solar collector directly heating seawater flowing through its absorbing tubes. Solar insolation is geographically refere nced and continually varying due to dynamic solar angles. In addition, solar insola tion incident on the collector varies with plate geometry, sky clearness, ground reflectivity, and ma ny other factors. Average values for a generic singlegl azed flatplate solar collecto r will be used to simplify comparison among the different simulation scenarios. The solar insolation area of the collector needed to meet the required heating load can be found using the HottelWhillierBliss correlation [8] T T U I F Q AX SC SC SC SC H SC 60 (118) Solar heating is usually accomplished indirectly by an intermediary heat exchanger that transfers heat from a solar collector loop to a pro cess loop. The proposed desalination system drops this intermediary heat exchanger by flowi ng seawater directly through the absorbing tubes of th e solar collector; therefore, increasing the efficiency and reducing the cost of the solar heater. On the ot her hand, this direct heating scheme has its drawbacks by increasing the risk of corro sion and scale formation causing equipment damage and inhibiting heat transf er. HermannKoschikowskiRommel [24] developed corrosionfree solar collectors for thermal desa lination systems use composed of a series of coated glass tubes mounted inside a convent ional flat-plate solar collector enclosure; therefore, flowing seawater directly through the collector is a viable alternative.

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53 Condenser efficiency is defined as the percent of the ratio of the temperature gradient on the cold tube side to the temp erature gradient on the hot shell side as % T T T TC E P X C100 (119) Heat recovery efficiency is defined as the percent of total enthalpy change that was essentially accomplished by reclaiming heat from the condensing vapor as % H H H HS H S X R100 (120) Thermal efficiency of the proposed desalina tion system is defined as the percent of the total thermal energy supplied that was actually used to vaporize water as % H M H H MH H L E E E T100 (121) Prime energy consumption is a very importa nt parameter in evaluating feasibility of any desalination system and is defined as the ratio of the amount of energy exhausted to the amount of fresh water produced. The to tal amount of energy exhausted is the heat supplied by the heater plus power supplied by the pump. Prime energy consumption can be expresse d as a constantly shifting parameter by PEC = ( QH + WP ) / MC on instantaneous basis; however it is typically desired to express prime energy consumption as a singl e value attained on a totalized basis by integrating the implicated dynamic process variables over the entire operating period. Total prime energy consumption of the proposed unit is given by dt M dt W dt Q PECC P H (122)

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54 4.2.8 Physical Properties Laminar flow is a smooth flow pattern, wh ere fluid layers are flowing in parallel concentric cylindrical layers without any interlayer mixing in a manner determined by the viscosity of the fluid [25]. Turbulent flow is a rough flow pattern, where fluid particles are randomly fluctuating in transverse to the general flow direction in a manner determined by inertial forces of the fluid [25]. Figure 24 illustrates th e streaming profile of both flow regimes. Flow Flow TurbulentLaminar Figure 24. Flow regimes Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces and is used to classi fy different flow regimes as either laminar or turbulent. Laminar flow behavior occurs at low Reynolds numbers, while turbulent flow behavior occurs at high Re ynolds numbers. The critical Reynolds number of 2300 is generally accepted as the midpoi nt of the transition range between laminar and turbulent flows in cylindrical pipes. Reynolds number of process streams is given by j j j jPD M Re 15 (123)

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55 The pressure of a flowing fluid inside a pipe inevitably drops due to gravity and wall drag. This pressure drop and loss can be approximated depending on the flow pattern by the HagenP oiseuille equation: Pj = 6.79 10-7 ( j PLj Mj ) / ( j PDj 4 ) for laminar or by the Moody equation: Pj = 9.01 10-10 ( fj PLj Mj 2 ) / ( j PDj 5 ) for turbulent flows [15], where f is the dimensionless Fanning Friction Factor available in literature as a function of both Reynolds number and pipe roughness. The current desalination process will be designed to include streams exhibiting laminar flow conditions to simplify experimental simulati ons later; hence, the model will employ the HagenPoiseuille equation to estimate averag e pressure drops of process streams as 4 710 79 6j j j j j jPD M PL P (124) Thermal conductivity is a property that ga uges heat conduction ability of a given substance. Dependence of thermal conductivity on temperature relates to the freedom of movement molecules enjoy; therefore, ther mal conductivity varies with temperature in fluids but remains fairly constant in solids. Thermal conductivities of process streams are calculated empirically by the Caldwell Relation [26] 610 1656.2364 T 0585 0. T 17.1335 5711.16 kj 2 j j j (125) Furthermore, thermal conductivities of flashing water vapor and accumulating noncondensable gases are not required but can be calculated empirically by [27] e 1 T 1.8 7 3.8912e T 1.8 10 5.8518e T 1.8 12 2.2744e kj 2 j 3 j E4 6943 32 32 32 (126) 6 3.9333e T 6 1.0184e T 10 4.8574e T e 1 kj 2 j 3 j a C15 273 15 273 15 273 13 5207 (127)

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56 The stream densities used in several correlation s above will be calculated by an empirical relationship experi mentally developed by the Rosenstiel School of Marine and Atmospheric Science at the University of Miami to calculate density of seawater as a function of temperature and salinity [28]. Densities of proces s streams are given by 9 7 5 310 39 5 10 25 8 10 64 7 10 09 4 82 0 T T T T Aj j j j j (128) j j jT . T B 6 4 310 6546 1 10 0227 1 10 72466 5 (129) j j j j j jT T T T T . . C 9 6 4 3 210 54 6 10 12 1 10 10 10 9 10 79 6 (130) j j j j j j j. B A C 48314 0 1000 1000 84 9992 1 (131) Stream viscosities used in several corre lations above will be calculated by an empirical relationship that was experimentally developed to calcula te the viscosity of seawater as a function of temperature and salinity [29]. Viscosities of process streams are given by j jT . A 5 410 185 5 10 0675 1 (132) j jT . B 5 310 3 3 10 591 2 (133) j j j. C 5413 553 (134) 93 89 20 10 827 1 20 1709 12 310 01002 0. T T T jj j j. D (135) j j j j j jD C B C A 5 01 (136) stream enthalpies used in the energy ba lances above will be calculated by an empirical relationship that was experimentally developed to calcula te heat capacity of seawater as a function of temperature and salinity [30] as follows

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57 04881 0 7532 14 7823 6 2045 4 1624 0 0310 0 0007 0 10 5367 8 6853 1 0530 02 2 2 3 4 2. T . T . T . Hj j j j j j j j j j (137) Seawater flashes in the ev aporator producing water vapo r that acquires its latent enthalpy of vaporization from the concentrat ed brine. Then, the produced water vapor condenses in the condenser by losing its latent enthalpy of condensation to the entering saline water. Latent enthalpy of vaporization and the latent enthalpy of condensation are numerically equal but have opposite signs and can be estimated by [27] 20042 0 9535 1 2101 2496E E L ET T . H (138) Nitrogen, oxygen, argon, a nd carbon dioxide are the only noncondensable gases considered in the model, since they make up more than 99.9 % of the total dissolved gases in seawater [19]. The US National Institute of Standards and Technology provides the following correlation to calculate molar enthalpy of noncondensable gases [31] NCG E NCG E NCG E NCG E NCG E NCG NCGF e T E e T e D T e C T e B T A H 3 1 15 273 6 1 15 273 9 4 15 273 6 3 15 273 3 2 15 2734 3 2 (139) Overall enthalpy of the accumulating nonc ondensable gases can be computed by adding molar enthalpies of each composing species weighted on a waterfree basis, in relation to the assumption of total condensation of flashed water vapor. In addition, the average molecular weight of the accumulating gases referenced before was employed to convert its enthalpy units from molar to mass based. Thus, overall enthalpy of accumulating noncondensable gases is given by a C O H CO CO Ar Ar O O N N a CMW y H y H y H y H y H 2 2 2 2 2 2 21 (140)

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58 4.3 Solution Algorithm A computer code featuri ng the above equations, pl us other correlations and parameters given later in CHAPTER 6 can be found in the APPENDICES section along with sample input and output values of proc ess variables. Computer code execution is incremental due to timebased numerical integration used above to account for accumulation of noncondensable gases in the flash chamber, while convergence process is iterative due to interdependence of equa tions of the model. The increment size should be carefully selected to simplify convergence and reduce processing without jeopardizing the integrity of the simulation. A concise block diagram outlining the general scheme to solve the above model is shown in Figure 25. Time is embedded in the model by flow rates of different streams; moreover, integration operations of the model are based on small time increments that evenly divide the entire run. Ambient temperature and pr essure, as well as physical properties and geometrical dimensions of process pipes and vessels, are input to the model. Universal values such as gas constant and gravity acce leration, plus seawater composition and the molecular weights of the involved species, ar e also input to the model. Parameters for enthalpy and vaporliquid equili brium relations, as well as average values for a generic singleglazed flatplate solar collector are also supplied to the code. Flash temperature is a controlled variable and will be supplied to code as a single set value. Initial vacuum pressure is a known quantity and will also be supplied to code to launch the simulation process. Initial vacuum pressure will be fed to the first increment, producing vacuum pressure for the second in crement producing the vacuum pressure for the third increment and so forth.

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59 Figure 25. Developed model solution algorithm

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60 The mass and energy balance simultaneously solves with mass and heat transfer relations, as well as enth alpy and nonequilibrium allowan ce correlations. Mass and energy balance indirectly solves with the pump work relation via density and pressure drop correlations and with molecular weight relations via RachfordRice calculations. Mass and energy balance provides inputs for density, viscosity, and pressure drop correlations, producing outputs that are fed to the pump work relation and Bernoulli's fluid equation. In addition, mass and ener gy balance provides inputs for thermal conductivity correlations used in heat transfer calculations and for efficiency relations that use those inputs along with other inputs from the enthal py correlations to evaluate system performance. The mass and energy ba lance also provides input values for the HottelWhillierBliss correlation to estimate solar collection area needed and for an integrator that totalizes system variables be fore forwarding them both to the prime energy consumption function and to Bernoulli's fluid equation. Mass and energy balance and the Rachfo rdRice calculations are linked via molecular weight relations and concurrently so lve for equilibrium temperature that is fed to vaporliquid equilibrium rela tions, a vapor pressure corre lation, and an equation of state. The equation of state estimates system vacuum pressure before it is lagged and forwarded to vaporliquid equilibrium relations where Kvalues are generated and fed to RachfordRice calculations to calculate the rate of accumulation of noncondensable gases that is integrated and fed back to the equation of state to calculate the pressure of the next time increment. The lagged system pr essure is also fed to Bernoulli's fluid equation, where tank levels ar e calculated and forwarded to geometrical relations to compute volume of the vacuum before fo rwarding it to the equation of state.

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61 CHAPTER 5. EXPERIMENTAL ANALYSIS 5.1 Process Description A small pilot unit has been built to simulate the propos ed continuous desalination system described previously experimentally. Figure 26 outlines a general process and instrumentation diagram of the small pilo t unit. Experimental simulations were performed inside a laboratory to simplify operation and main tenance. Due to this indoor process, solar heating was hard to implement due to lack of solar insolation, and passive vacuum was difficult to produce due to limited elevation. Solar heating is widely used in seve ral applications, including desalination systems as was mentioned in CHAPTER 2 ; therefore, replicating it with an electric heater is considered acceptable, since the concept of solar heating does not require further proof. In addition, vacuum was passively ge nerated by Goswami and Kharabsheh [11] for their desalination unit as was mentioned in CHAPTER 3 ; therefore, producing it with a vacuum pump is considered acceptable since the phenomenon of passive vacuum generation using gravity has been experimentally established. Placing the flash chamber at a low eleva tion in the experimental unit removed hydraulic head of the proposed unit; thus, a circulation pump is no longer required to pass seawater through the unit. The pressure difference between the vacuumed flash chamber and open seawater feed tank becomes the driving force of seawater flow, which was manually controlled by manipulating valve positions.

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62 Figure 26. Process and instrumentati on diagram of the experimental unit

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63 5.2 Experimental Apparatus The entire experimental unit is mounted on threetier mobile skids built from slotted and unslotted stru ts with linking joints and brackets as shown in Figure 27. The three tiers are connected by four upright ba rs, the bottom two tiers include plywood for weight distribution, and the bottom tier is outfitted with four wheels for mobility. The seawater feed tank is a 50gallon opentop, horizontal polyethylene trough placed on the bottom tier of skids. The c ondenser is a 40gallon paintedsteel, upright cylinder, while the evaporator is a 40gallon galvanizedsteel upright cylinder, and they are both placed on the middle tier of the skid s directly above the seawater feed tank. Condenser, evaporator, and 2 Yshaped CPVC pipe connecti ng them from the top make up the flash chamber. The condenser was cut open around its upper sectio n to install a 4 m long copper pipe coiled to provide the necessary condensing surface, then welded back to its original shape. In addition, a small hole was drilled at the bottom of the condenser to retrieve the condensed water. The evaporator and the 2 Yshaped CPVC pipe are wrapped with sheets of insolating mate rial to minimize heat loss. The condenser and evaporator have discharge pipes that drain into the seawater feed tank. The heater is a 4.5 kW zincplated, copper electric heating elem ent placed inside a copper shell, where seawater coming out of the condenser passes through it on its way to be flashed in the evaporator. A HP vacuum pump is piped to the evaporator to create the initial vacuum, and a polypr opylene needle valve, V7 in Figure 26, is placed right before the evaporator to function as an expansion orifice for the incoming heated seawater to be flashed. The CPVC pipe is used in connecting all of the above equipment as well as several CPVC and copper pipe fittings.

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64 Several instruments have been integrated into the experimental unit to manage system variables as shown in Figure 26. These are used in monitoring and controlling system vacuum, seawater flow, and flash temperature, as well as monitoring temperature of each process stream. Nomenclature used in the P&ID of Figure 26 is consistent with the International Society of Automation symbol standards. Pressure indicator PI is a liquidfilled analog vac uum gauge, while pressure element PE is a highprecision vacuum transmitte r. The PI was used to help establish the initial system vacuum and to monitor its gra dual erosion. The PE was used to continually supply the value of the system vacuum to a data acquisition system. Flow indicator FI is an acrylic inline flowmeter, while quantitative element QE is a glass 500 ml graduated cy linder. The FI was used to help establish and monitor the seawater flow through the system. The quantita tive element QE was used to collect and measure the amount of fresh water produ ced at the end of each experiment. Temperature elements TE10, TE11, TE 12, TE13, and TE14 are singleoutput, while temperature element TE15 is dualoutput diameter TType thermocouples. All used to supply the value of the temperature of each process stream continually to a data acquisition system. In addition, TE15 is used to supply the temperat ure controller with the value of its controlled variable. Pressure controller PC and flow controller FC are im aginary pressure and flow manual controllers, while temperature in dicating controller TI C is an LEDequipped digital PID automatic controll er. Regulators V1 and V4 are , while regulators V2, V3, V5, and V6 are full port ball valves. De tailed descriptions of all of the above apparatus taken from their vendors are in the APPENDICES section.

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65 Figure 27. 3tier mobile skids layout

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66 5.3 Control Scheme The three feedback control loops pertaini ng to system vacuum, seawater flow, and flash temperature shown in Figure 26 are replicated in Figure 28 in isolation to clarify their control techniques. System vacuum and seawater flow are manually adjusted, while flash temperature is automatically controlled. The system vacuum feedback control loop is invoked prior to running the experiment to attain the desired initial vacuum It consists of measuring the vacuum with pressure indicator PI while the vacuum pu mp is running. Once the desired vacuum set point SP is reached, hand switch HS is manua lly switched off to shut down motor M of the vacuum pump, which remains s hut during the entire experiment. The seawater flow feedback control l oop is invoked at the beginning of the experiment to attain the desired seawater flow rate, which remains constant throughout the experiment. It consists of measuring flow with flow indicator FI, while manually manipulating the valve position of V5 until the desired flow rate set point SP is realized. The valve position is kept cons tant throughout the experiment. Figure 28. Feedback control l oops of the experimental unit

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67 The flash temperature feedback control l oop is constantly activ e to stabilize flash temperature during the experiment. It consis ts of measuring temp erature of seawater coming out of the heater with temperat ure element TE15, then supplying that measurement to temperature indicating controll er TIC that automatically manipulates the current input into the heat element of the heat er, effectively varying its heat output to the incoming seawater until the desired flash temperature set point SP is achieved. A simplified block diagram of the flas h temperature feedback control loop is given in Figure 29. The assigned arro ws SP, E, CO, TO, and U are the frequencydomain Laplace transform functions of the set point, error, controller output, transmitter output, and disturbance signa ls, respectively. Block TIC represents the transfer function of the digital PID automatic temperature controller given generically as s s K ) s ( TICD I C 1 1 (141) Automatic temperature controller TIC is equipped with an automatic tuning ability that was used to tune its parameters during a dry run, yiel ding the following values PB = 20 % TO / % CO KC = 100 / PB = 5 % CO / % TO I = 60 seconds D = 2 seconds The cycle time or total period that contro ller output cycles on and off when the controlled variable is within the PB was se t to 1 second. In addition, a derivative approach control of 2.5 PB was used to remove derivative action at system startup. The failsafe mode of the controller was se t to turn off SP upon input signal loss.

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68 Block PL represents the transfer f unction of the process loop between the controlled and manipulated variables, which is usually represented by a first order model with dead time compensation as follows 10 s s t EXP K ) s ( PLPL PL (142) Block DL represents the transfer func tion of the disturbance loop between the controlled variable and distur bance, which is usually represented by a first order model with dead time compensation as follows 10 s s t EXP K ) s ( DLDL DL (143) Block PL and block DL are actually comb inations of several transfer functions that were lumped into a single first order model to simplify representing the dynamic response of the process. Block PL merges a se quence of transfer func tions characterizing thermocouple TE15, the heating process, an d electric heater. Block DL merges a sequence of transfer functi ons characterizing thermocoupl e TE15 and flowing process. The automatic tuning ability of controller TIC is based on obtaining the parameters of the first order models represen ting block PL and block DL. Figure 29. Block diagram of the flas h temperature feedback control loop

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69 5.4 Data Acquisition A data acquisition system designed to sa mple and record process variables was assembled and attached to the experimental apparatus. Configuration of the data acquisition system is illustrated in Figure 30. Pressure element PE outputs an analog current signal corr esponding to system vacuum with a range from 4 mA to fiel dbus module FBM1 through a 2wire cable. Temperature elements TE10, TE11, TE12, TE13, TE14, and TE15 output analog voltage signals corresponding to system temperatures each with a range from -0.001.01 mV to fieldbus module FBM2, through thermocouple extension wires. Fieldbus module FBM1 is a multiplexing signal conditioner, where the analog current signal of pressure element PE is converted to a corresponding analog voltage signal with a range from 1 V. Fieldbus module FBM2 is a multiplexing signal conditioner, where the analog voltage signals of temperature elements TE10, TE11, TE12, TE13, TE14, and TE15 are converted to corres ponding analog volta ge signals with a range of 1 V. The conditioned analog outpu t signals of fieldbus modules FBM1 and FBM2 are multiplexed via multiplexer MUX, which is a DC ribbon connecting cable. Analog to digital converter ADC is a 16bit data acquisi tion system that converts continuous analog signals supplied by multiple xer MUX to discrete digital signals and forwards them to humanmachine interface HM I through an enhanced parallel port LPT cable. Humanmachine interface HMI is a notebook PC running a data acquisition software that converts acquired data fr om its conditioned voltage units to its corresponding physical attributes The data acquisition software also displays and stores the acquired data for later analysis as shown in Figure 31.

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70 Figure 30. Data acquisition structure Figure 31. Data acquisition software

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71 5.5 Operating Procedure Operation of the experimental unit cl osely resembled that of the proposed desalination system described in CHAPTER 4 Initial vacuum was created by running the vacuum pump until a reasonable vacuum was reached. Running the vacuum pump further will trap moisture in its oil reservoi r significantly inhibiti ng its performance. Synthetic seawater was pr epared by mixing 13 pounds of commercialgrade sea salt with 40 gallons of tap water. The seawater mix was stirred well before each experiment to ensure full solution of sea salt. The seawater trough has a large open surface that enhances evaporat ion; therefore, small amounts of fresh water were often added before running experiments to reach a 40gallon level mark in the trough. Temperature indicating controll er TIC is not interlocked with seawater flow; thus, ensuring seawater flow through th e electric heater is a very critical safety measure. Regulators V5 and V6, plus needle valve V7, are instruments that control seawater flow. The valve position of needle valve V7 was kept constant at about 90 % open for all runs, because narrowing valve position caused fl ow oscillations regardless of the valve positions of regulators V5 and V6. The valve po sition of regulator V6 was used to start and stop the experiment; theref ore, it was toggle d between fully open and fully close. Valve position of regulator V5 was used to manipulate the flow as was mentioned above. Pressure element PE is calibrated by the manufacture, while Fieldbus module FBM2 contains a builtin co ld junction compensation that automatically calibrates thermocouple outputs. In addition, data acquis ition software wais set to execute one scan per second and to average every ten scans to reduce signal noise. The acquired data were saved to an assigned ASCII formatted file on the Humanmachine interface HMI.

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72 The experimental unit must be kept mo tionless during operation due to its high center of gravity, while its normal operating procedure is as follows 1. Start data acquisition system 2. Open regulator V2 fully 3. Start vacuum pump until desired vacuum is reached 4. Close regulator V2 fully 5. Stop vacuum pump 6. Slowly open regulator V6 fully 7. Set seawater flow rate through regul ator V5 and flow indicator FI 8. Activate temperature indicating controller TIC 9. Trigger data recording function of data acquisition software 10. Run unit until the specified period of the experiment is reached 11. Stop data recording function of data acquisition software 12. Disable temperature indi cating controller TIC 13. Quickly close regulator V6 fully 14. Stop data acquisition system 15. Open regulator V1 to terminate the vacuum 16. Open regulator V3 to drain brine into the seawater trough 17. Open regulator V4 to drain fresh water into quantitative element QE 18. Record amount produced then dr ain into the seawater trough 19. Fully close regulator V1 20. Fully close regulator V3 21. Fully close regulator V4

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73 5.6 Experimental Design Experiments were conducted at anal ogous conditions to simplify design evaluation but with different values of the controlling va riables to enhance process analysis and modeling. All experiments were run for a period of three hours starting with an initial system vacuum of 0.14 bars. Expe riments were carried out at two different seawater flow rate ranges and at four different flash temper atures of 50, 60, 70, and 80 degrees centigrade. In addition, each experime nt was duplicated thr ee times to estimate its variation. Table 6 illustrates the experimental matrix, while Figure 32 gives an overall view of the experimental unit. Table 6. Experimental matrix Number Start Time Stop Time Initial PI (bar) FI (LPM) TIC SP (C) QE (ml) 1 2 3 50 4 5 6 60 7 8 9 70 10 11 12 lower flow around ~ 0.50 80 13 14 15 50 16 17 18 60 19 20 21 70 22 23 24 0.14 higher flow around ~ 0.70 80

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74 Figure 32. Overall view of the experimental unit

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75 CHAPTER 6. PARAMETRIC ANALYSIS 6.1 Analyses Synchronization Theoretical and experimental analyses mu st be synchronized to compare their outputs properly. The model developed in CHAPTER 4 holds for the proposed desalination system outlined in Figure 21; however, it needs to be modified to represent the experimental unit outlined in Figure 26 to validate its predictions. The flash chamber of the experimental un it is not elevated for passive vacuum generation, and levels of the flash chambe r are not hydrostatica lly balanced as was mentioned in CHAPTER 5 Vacuum is created before running the unit by a vacuum pump; furthermore, the flash chamber is clos ed during operation to maintain that vacuum, since it can not be maintained hydrostatica lly. Consequently, Be rnoulli's fluid equation can not be used to estimate initial and the dynamic levels in the evaporator and condenser. Initial levels are equal to zero as ve ssels are drained be fore operation while dynamic levels are functions of totalized, or integrated, inlet flows. Therefore, Equation 98 through Equation 101 are substituted with 0 i CZ (Alternate 98) C C C i C CXA dt M Z Z (Alternate 99) 0 i EZ (Alternate 100) E W W i E EXA dt M Z Z (Alternate 101)

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76 The condenser and evaporator are modeled as horizontallymounted right circular cylinders as can be seen in Figure 21; however, the conden ser and evaporator of the experimental unit are vertical lymounted right circular cy linders as can be seen in Figure 26. Consequently, the geometry of the v acuum volume needs to adapt; therefore, Equation 102 through Equation 105 are substituted with i C C C i CVZ L XA V (Alternate 102) C C C CVZ L XA V (Alternate 103) i E E E i EVZ L XA V (Alternate 104) E E E EVZ L XA V (Alternate 105) The experimental unit does not include a feed pump as was mentioned in CHAPTER 5 ; therefore, Equation 117 is substituted with 0PW (Alternate 117) 6.2 Parameter Expressions The model developed in CHAPTER 4 along with the above alternate equations were coded and executed using ex perimental temperature, pressure, and flow rate values as inputs generating pseudoexperimental data of model parameters. This data mining process is used to uncover patterns in model parameters so they can be properly expressed in the model via correlatio ns obtained using non linear regression. The countercurrent departure correction fact or for the condenser tube is used to correct its log mean temperature difference to solve accurately for the temperature of preheated seawater before it enters the heater, which is essential for estimating prime energy consumption and efficiency of the condenser and heat recovery.

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77 A correlation for the countercurrent depa rture correction factor for the condenser tube is obtained by regressing the mined data as shown in Figure 33 yielding 4 3 2CT CT CT CT CTS 4.2518 + S 6.1629 S 2.9102 + S 0.1655 + 0.0293 F (Alternate 90) The countercurrent departur e correction factor for th e condenser is used to correct its log mean temperatur e difference to solve for the temperature of the condensed fresh water accurately; however, experimental data show that the temperature of the condensed fresh water remained rather cons tant with a value about two degrees above ambient regardless of how high the equilibriu m temperature was. This outcome is most likely due to a good heat rejection by the cond enser, in addition to the fact that the amount of cool seawater flowing through the condenser tube vastly exceeds that of the condensing water vapor outsi de the condenser tube. Consequently, a correlation for the counterc urrent departure co rrection factor for the condenser will be replaced by T TC2 (Alternate 91) The countercurrent departure correction f actor for the evaporator is used in correcting its log mean temperature differenc e to estimate its heat loss accurately. Temperatures of the flashed vapor and con centrated brine diverge due to boiling point elevation and nonequilibrium allowance as mentioned in CHAPTER 4 as well as a small amount of heat loss from the insulated evaporator. To simplify calculations, heat loss from the evaporator is ignored, and a correlation for the nonequilibrium allowance is obtained by regressi ng the experimental data as shown in Figure 34 yielding QE0 (Alternate 92)

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78 15 273 25 15 273 15 273 15 273 9154 5 1399 0 7785 2 3898 3 6836 13208 29 2. T T T Where exp . .H E W (Alternate 93) The activity coefficient of water is used to correct its molar fractions to solve for its Kvalue accurately. Theoretical expression s for activity coefficients of species in electrolyte solutions, such as seawater, are av ailable in literature but very challenging to implement due to the large number of interac tions present among all ions and molecules. Those interactions are characterized by pa rameters that in most cases must be experimentally determined. To simplify calculations, a correlation for the activity coefficient of water is obtained by regressing the mined data as shown in Figure 35 yielding O H V O HP P .2 20385 1 0020 0 (Alternate 48) The gas phase molecular content correcti on factor is used in correcting the equation of state to solve for the vacuum pre ssure accurately as was mentioned earlier in CHAPTER 4 It accounts for both gases dissolvi ng in the condensing water vapor and any possible discrepancy in the input seaw ater content of dissolved gases or the calculated vaporliquid equi librium for carbon dioxide. To simplify calculations, a correlation for gas phase molecular content correction factor is obtained by regressi ng the mined data as shown in Figure 36 yielding P P exp .O H V 22861 2 1 (Alternate 113) The Matlab codes used for regressing al l of the above mined data are found in the APPENDICES section.

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79 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SCTFCT.... = mined data = regression r = +0.9958603 Figure 33. Countercurrent departure co rrection factor of condenser tube 1.05 1.1 1.15 1.2 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 ( TH + 273.15 ) / ( 25 + 273.15 )( TW + 273.15 ) / ( TE + 273.15 ).... = experiment = regression r = +0.9487937 Figure 34. Nonequilibrium allowance representation

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80 1 1.5 2 2.5 3 3.5 4 4.5 5 1 1.5 2 2.5 3 3.5 4 4.5 5 PV / PH2OH2O.... = mined data = regression r = +0.9999999 Figure 35. Activity coefficient of water 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 PV / PH2O.... = mined data = regression r = +0.9914701 Figure 36. Gas phase molecular content correction factor

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81 6.3 Parameter Inputs Seawater is a solu tion of many salts and contains a small amount of dissolved gases as mentioned earlier in CHAPTER 4 Input parameters used for sea salt are given in Table 7, while input parameters used for seawater are given in Table 8. The molecular weights given in both ta bles are obtained from NIST [31], while mass fractions given in both tables are obtained fr om an oceanography manual [16]. In addition, the relativity factors given in Table 8 are found by averaging temperaturestamped data [19], while enthalpy parameters given in Table 8 are obtained from NIST [31]. As mentioned in CHAPTER 4 the SUPERTRAPP code was employed to perform isobaric phase equilibria flash calcula tions for water with an average content of noncondensable gas as reported in literature [16] at various temper atures to produce a dataset of Kvalues. SUPERTRAPP flash cal culations were executed at a constant pressure of 1 bar; therefore, the produced Kvalues are equivalent to Henry's constant for noncondensable gases and vapor pressure for water. The reported values of HCi and HFi [17] plus PA PB and PC [15] were used as initial guesses in Matlab least squares regression codes to adju st their values to best fit the produced Kvalue dataset to Henry's constant and vapor pr essure correlations. The SUPERTRAPP code used for ge nerating the Kvalue dataset and Matlab codes used for regressing them are in the APPENDICES section. The performed regressions yielded excellent results with correlation coefficients very close to unity as can be seen in Figure 37 through Figure 41. Better estimates of Kvalues denote better representation of the vaporliquid equilibrium, ultimately resulting in more reliable flash calculations.

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82 Table 7. Sea salt parameters [16] [31] MW MW MW Cl 35.45 0.55030 Ca 40.08 0.01180 BO3 58.81 0.00080 Na 22.99 0.30590 K 39.10 0.01110 Sr 87.62 0.00040 SO4 96.06 0.07680 HCO361.02 0.00410 F 19.00 0.00003 Mg 24.31 0.03680 Br 79.90 0.00190 Table 8. Seawater parameters [16] [31] MW A B C D E F HC HF PA PB PC N2 28.01 1.26E-05 1.21 26.0920 8.2188 -1.9761 0.1593 0.0444 -7.9892 8067573 -3546 O2 32.00 7.70E-06 1.22 29.6590 6.1373 -1.1865 0.0958 -0.2197 -9.8614 358815 -2209 Ar 39.94 4.00E-07 1.23 20.7860 2.83E-07 -1.46E-071.09E-08 -3.66E-08-6.1974 384073 -2308 CO2 44.01 2.20E-07 1.17 24.9974 55.1870 -33.6914 7.9484 -0.1366 -10.0851 10915 -445 Salt 3.50E-02 H2O 18.01 0.9816 30.0920 6.8325 6.7934 -2.5345 0.0821 -9.0546 13 4391 245 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 x 106 Temperature (C)HCN2 (bar)o = NIST = regression.... = Sander r = +0.9997174 Figure 37. Henry's constant of nitrogen

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83 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 105 Temperature (C)HCO2 (bar)o = NIST = regression.... = Sander r = +0.9995648 Figure 38. Henry's constant of oxygen 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 x 105 Temperature (C)HCAr (bar)o = NIST = regression.... = Sander r = +0.9996581 Figure 39. Henry's constant of argon

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84 0 10 20 30 40 50 60 70 80 90 100 0 2000 4000 6000 8000 10000 12000 Temperature (C)HCCO2 (bar)o = NIST = regression.... = Sander r = +0.9666632 Figure 40. Henry's constant of carbon dioxide 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 Temperature (C)Psat H2O (bar)o = NIST = regression.... = Geankoplis r = +0.9999635 Figure 41. Vapor pressure of water

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85 6.4 Equipment Specifications The seawater feed as we ll as brine and fresh water tanks are modeled as horizontal polyethylene troughs; moreover, the condenser and evaporat or are modeled as paintedsteel and galv anizedsteel upright cylinders, re spectively. The connecting pipes are modeled as CPVC with copper tubing us ed inside the condenser and heater. The condenser tube is a protracted copper tube vertically coiled inside the condenser in four loops, that is NCT = 4 Copper is not suited for seawater due to its corrosivity and should not be used in desalination systems; however for theoretical and shortterm experimental simulations, it is considered acceptable. Dimens ions and the heat transfer parameters of the experimental unit are given in Table 9 and Table 10, and these values will be input to the model as well. In addition, the model neglects any heat input by any pump as well as any work output by the heater, conde nser, or evaporator, that is QP = WC = WH = WE = 0 Table 9. Equipment dimensions Vessel D L Pipe D L Pipe D L Seawater 90 30 S 1.27 95 E 5.08 180 Brine Water 90 30 P 1.27 25 C 0.32 35 Fresh Water 90 30 X 1.27 60 CT 1.27 475 Evaporator 35 160 H 1.27 75 HT 1.27 13 Condenser 35 160 W 1.27 30 Table 10. Heat transfer equipment parameters hid hod kw Condenser Tube 0.20 0.50 0.125 3.810 Condenser 0.50 0.75 0.250 0.450 Evaporator 0.50 0.75 0.250 0.001

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86 The model also uses typical absorptance and transmittance values plus average heat transfer and removal factors pertaining to a singleglazed flatplate solar collector, in addition to a standard value for the intens ity of solar insolation, to estimate the solar collection area needed to meet the computed h eater load adequately. Explicitly declaring: I = 600 W/m2, FSC = 0.82, USC = 0.92 W/m2C, SC = 0.92, SC = 0.90 6.5 Simulation Specifications Model simulations will be carried out at conditions corresponding to those of the experimental simulations so they can be compared. Simulated operations will run for a period of three hours and will be modeled using one minute increments with the same initial seawater tank level and vacuum pre ssure. Simulations were carried out at two different seawater flow rate ranges and at four different flash temperatures. Mass flow rate of a fluid acr oss an orifice is given by M = CV ( P / SG ) The flow rate was manually adjusted during experiments using a ball valve. The valve position was kept constant for each flow rate range; however, flow rate slightly varied within each range due to varying fluid densi ties caused by different fluid temperatures and varying differential pressures across the valve caused by the different vacuum pressures. In addition, flow rates were pr ogressively decreasing during each experiment due to declining differential pressure cau sed by the increasing vacuum pressure. An average flow rate value was computed for each experiment and input to the corresponding model simulation as a constant value to simplify calculations. The average flow rate value was obtained by dividing the estimated amount of seawater transferred from the seawater feed tank by the duration of the experiment.

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87 The diffusion rate correlation given in CHAPTER 4 includes two adjustable parameters. Parameter serves as a diffusion coeffici ent and can be thought of as a conductance term, while parameter serves as a diffusion barri er and can be thought of as a resistance term. Both parameters were adjusted using the same code mentioned earlier for generating pseudoexperimental da ta of model parameters by arbitrarily assigning a value for parameter while tuning parameter to match the output amount of fresh water produced by the code to the ac tual amount of fresh water produced. It is important to point out once more that those obtained diffusion rate correlation parameter values pertain to the geometry of the cu rrent experimental setup and should be readjusted whenever applied to different ge ometries using new e xperimental records. The above mentioned experimental and adju sted simulation sett ings are given in Table 11 and will be input to the model. The experimental simulations were conducted in a laboratory; consequently, ambient conditions are considered accordingly, T = 20 C and P = 1.01325 bar Finally, temperature in the seawater feed tank is assumed equal to ambient, TS = T while common literature values were used for the universal gas constant and the gravity acceleration, R = 83.14472 barcm3/molC and g = 980.0665 cm/s2. Table 11. Simulation settings Simulation Zi S Pi V MS TH 1 24 0.14 496 50 2 0.118 2 24 0.14 474 60 2 0.150 3 24 0.14 453 70 2 0.120 4 24 0.14 388 80 2 0.019 5 24 0.14 711 50 2 0.135 6 24 0.14 690 60 2 0.197 7 24 0.14 668 70 2 0.229 8 24 0.14 582 80 2 0.103

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88 CHAPTER 7. DISCUSSION OF RESULTS 7.1 Discussion Guide Model and experimental results will be compared and discussed throughout this chapter. Model results are obtained by executing a code comprised of the equations given in CHAPTER 4 as well as the alternate equations and the parameter values given in CHAPTER 6 Experimental results correspond to two sets of experiments, where one set was conducted at lower seawater flow rates, and the other set was conducted at higher seawater flow rates. In addition, each set of experiments includes four variations of flash temperature, where each variation was duplicat ed three times to validate its outcome. So, each table value and figure curve given in this dissertation designated as an experimental result is in fact the averaged outcome of three matching experiments. The experimental matrix and conditions were provided earlier in Table 6 and Table 11. Experimental results will sometimes correspond to pseudo experimental data generated by a code comprised of the equations and the alternat e equations mentioned above, but with the mass and energy balance relations replaced by experimental temperature and pressure as well as flow rate values. Each figure will use a solid line to represent model data and a dotted line fitted with a translucent error ba nd to represent experimental data. A detailed error analysis can be found in the APPENDICES section. The figures will also indicate if the experimental data correspond to real e xperimental data or to pseudoexperimental data by dubbing the data as eith er experiment or mined, respectively, in their legend.

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89 The controlled variables of the current de salination system are seawater flow rate and flash temperature. Their effects on the de salination process will be analyzed through graphical representations of several system va riables that illustrate their dynamics during each simulation. Twelve timevarying system variables will be examined by a set of twelve figures provided for each one. Every se t includes four figures, each corresponding to a single flash temperature at lower seawater flow rates, as well as four figures, each corresponding to a single flash temperature at higher seawater flow rates. Furthermore, each figure will sketch two profiles, where one corresponds to model simulation, and the other corresponds to experimental simulation, both at analogous conditions. Each set also includes four figures, where the four different flash temperature profiles of each seawater flow rate range are joined on one figure fo r both model and experi mental simulations. The legend of each figure includes the corr elation coefficient that measures the linear dependence between the modeled and experimental datasets. The correlation coefficient is also known as the Pearson pr oduct moment correlation coefficient and is computed by dividing the covariance of two variables by the product of their standard deviations, yielding a value between -1 and +1 The computation process of the correlation coefficient is rather cumbersome ; however, it is available as a builtin function in many software packag es. A correlation coefficient of 0 indicates the total lack of correlation, while a co rrelation coefficient of -1 indicates a perfec t negative linear correlation and a correlation coefficient of +1 indicates a perfect positive linear correlation. A correlation coefficient less than -0.8 or greater than 0.8 typically indicates a strong correlation, while a co rrelation coefficient between -0.5 and +0.5 typically indicates a weak correlation.

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90 7.2 Vacuum Erosion System vacuum pressure accounts for the water vapor in addition to the accumulating noncondensable gases as was mentioned in CHAPTER 4 System vacuum gradually eroded for both seawater flow rates; moreover, it eroded a little faster at higher seawater flow rates. Vacuum pressure in creased with flash temperatures for both seawater flow rates, since vapor pressure is directly proportional to flashing temperature. The initial rapid increase of vacuum pressure was caused by the early rapid increase of water vapor pressure caused by th e early rapid increase of temperature inside the flash chamber. Vacuum pressure continued to increase afterwards but at a much lower rate due to slow accumulation of noncondensable gases. The rate of increase of vacuum pressure, PV / t was decelerating for higher flash te mperatures but was accelerating for lower flash temperatures for both seawater fl ow rates. This is especially obvious for higher flow experiments flashing at 50 C indicating that high er flow rates entail a higher rate of accumulation of noncondensable ga ses. Decreasing pressure at a given temperature increases vaporliquid equilibrium coefficient value resulting in more overall evaporation. Consequently, flashing seaw ater at lower flow ra tes slowed the rate accumulation of noncondensable gases, which decelerated vacuum erosion rate, resulting in more evaporation a nd more fresh water production. Model prediction of vacuum pressure rese mbled the experimental results but was generally lower, and the discre pancy increased with temperatur e. This is probably due to the constant seawater flow rate assumed by the model, while it was progressively decreasing during experiments due to the decl ining differential pressure caused by the eroding vacuum. Vacuum pressure profiles are shown in Figure 42 through Figure 53.

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91 0 20 40 60 80 100 120 140 160 180 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t (min)PV (bar) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 42. Modeled vacuum pressu re profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t (min)PV (bar) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 43. Experimental vacuum pr essure profiles at lower flow

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92 0 20 40 60 80 100 120 140 160 180 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t (min)PV (bar) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 44. Modeled vacuum pressu re profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t (min)PV (bar) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 45. Experimental vacuum pr essure profiles at higher flow

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93 Figure 46. Vacuum pressure at 50C flash and lower flow Figure 47. Vacuum pressure at 50C flash and higher flow

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94 Figure 48. Vacuum pressure at 60C flash and lower flow Figure 49. Vacuum pressure at 60C flash and higher flow

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95 Figure 50. Vacuum pressure at 70C flash and lower flow Figure 51. Vacuum pressure at 70C flash and higher flow

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96 Figure 52. Vacuum pressure at 80C flash and lower flow Figure 53. Vacuum pressure at 80C flash and higher flow

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97 7.3 Equilibrium Attainment The temperature of seawater drops from a set flash temperature to an equilibrium temperature corresponding to the system vacuum pressure as it enters the evaporator. Equilibrium temperature quickly increased, then mostly leveled for both seawater flow rates; moreover, it was higher to some extent at higher seawater flow rates. In addition, equilibrium temperatures increased with elev ated flash temperatures for both seawater flow rates in compliance with the energy balance around the evaporator. The equilibrium temperature was close to ambient at first; however, it rapidly increased as hot seawater was introduced to the evaporator, reaching a plateau comparable to the flash temperature for both seawater flow rates. Flash operation of the proposed desalination process is an adiabatic expa nsion, where temperature of seawater drops upon entering the flash chamber due to the drawn enthalpy of vaporization, forming fresh water vapor at an equilibrium status corresponding to the vacuum pressure. The model utilizes the Iterative and Incremental Development scheme as mentioned in CHAPTER 4 where the computed vacuum pressure of a previous time increment becomes the input vacuum pressure to the executing time increment, solving for the equilibrium temperature and vacuum pressure of the next time increment. The entire model execution progression is initia ted by the known initial vacuum pressure. The model prediction of equilibrium temperature resembled the experimental results but was slightly lower, and the disc repancy increased with temperature. This observation understandably matches that of vacuum pressure seen earlier, since the attained equilibrium temperature depends on the system vacuum pressure. Equilibrium temperature profiles are shown in Figure 54 through Figure 65.

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98 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TE (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 54. Modeled equilibrium temperature profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TE (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 55. Experimental equilibrium temperature profiles at lower flow

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99 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TE (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 56. Modeled equilibrium temperature profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TE (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 57. Experimental equilibrium temperature profiles at higher flow

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100 Figure 58. Equilibrium temperature at 50C flash and lower flow Figure 59. Equilibrium temperature at 50C flash and higher flow

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101 Figure 60. Equilibrium temperature at 60C flash and lower flow Figure 61. Equilibrium temperature at 60C flash and higher flow

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102 Figure 62. Equilibrium temperature at 70C flash and lower flow Figure 63. Equilibrium temperature at 70C flash and higher flow

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103 Figure 64. Equilibrium temperature at 80C flash and lower flow Figure 65. Equilibrium temperature at 80C flash and higher flow

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104 7.4 Equilibrium Departure Concentrated brine temperature is usually a bit lower than equilibrium temperature due to boiling point elevation and nonequilibrium allowance plus a small amount of heat loss from the insula ted evaporator as mentioned in CHAPTER 4 Concentrated brine temperature quickly increa sed then leveled for both seawater flow rates; moreover, it was slightly higher at lower seawater flow rates. In addition, concentrated brine temperatures increased with elevated flash temperatures for both seawater flow rates in compliance with the energy balance around the evaporator. The concentrated brine temperature was cl ose to ambient at first; however, it rapidly increased as hot seawater was intr oduced to the evaporat or, reaching a plateau parallel to equilibrium temperature for both seawater flow rates. The concentrated brine temperature remained lower than the equilibr ium temperature except for the lowest flash temperature for both seawater flow rates, wh ere concentrated brine temperature started lower but ended higher than equilibrium temperat ure. This can be attributed to some heat loss from the flashed water vapor along with diminishing vaporization rates as vacuum pressure rises at a relative low equilibrium temperature since the flashed vapor obtains its heat of vaporization from the concentrated brine. The model prediction of concentrated brine temperature resembled the experimental results but was slightly higher, with the discrepancy ri sing with increasing flash temperatures. This can be attributed to the neglected small amount of heat loss from the insulated hot evaporator to the cool ambiance combined with the imprecision of the nonequilibrium allowance corre lation used in the mode l. Concentrated brine temperature profiles are shown in Figure 66 through Figure 77.

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105 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TW (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 66. Modeled concentrated brine temperature profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TW (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 67. Experimental concentrated brin e temperature profil es at lower flow

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106 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TW (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 68. Modeled concentrated brine temperature profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TW (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 69. Experimental concentrated brin e temperature profiles at higher flow

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107 Figure 70. Concentrated brine temper ature at 50C flash and lower flow Figure 71. Concentrated brine temper ature at 50C flash and higher flow

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108 Figure 72. Concentrated brine temper ature at 60C flash and lower flow Figure 73. Concentrated brine temper ature at 60C flash and higher flow

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109 Figure 74. Concentrated brine temper ature at 70C flash and lower flow Figure 75. Concentrated brine temper ature at 70C flash and higher flow

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110 Figure 76. Concentrated brine temper ature at 80C flash and lower flow Figure 77. Concentrated brine temper ature at 80C flash and higher flow

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111 7.5 Heat Reclamation Cold incoming seawater is preheated in the condenser by hot water vapor condensing on the surface of the condenser tube before it enters the heater as mentioned in CHAPTER 4 The preheat temperature rapidly increased to reach a maximum early, before it slowly declined for both seawater flow rates; moreover, the preheat temperature attained at lower seawater flow rates, was hi gher. It increased with flash temperatures for both seawater flow rates since the amount a nd temperature of the condensing water vapor are directly proportional to flashing temperature. Hot water vapor condenses by losing its latent heat of condensation to the entering seawater in the condenser; hence, preh eat temperature indirect ly denotes the rate of water vaporization and condensation. The pr eheat temperature rapidly increased due to high initial rate of vaporiza tion caused by rapidly increasing equilibrium temperature at lower vacuum pressures, then it slowly declined due to the decreasing rate of vaporization caused by the stabilizing equilibrium temperature at rising vacuum pressures for both seawater flow rates as was shown previously. The preheat temperature profiles for both seawater flow rates are similar; how ever, they were higher for lower flow rates due to more condensation caused by more vaporization as will be seen later. Model prediction of preheat temperatur e loosely resembled the experimental results due to the inability of the condenser tu be heat transfer modul e to capture the rate of condensation. Modeling a heat transfer operation with a phase change is extremely complex, especially in the presence of noncondensable gases. The precision of the model in predicting the preheat temperature aff ects the quality of its evaluation of system performance. Preheat temper ature profiles are shown in Figure 78 through Figure 89.

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112 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TX (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 78. Modeled preheat temper ature profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TX (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 79. Experimental preheat te mperature profiles at lower flow

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113 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TX (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 80. Modeled preheat temper ature profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)TX (C) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 81. Experimental preheat temp erature profiles at higher flow

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114 Figure 82. Preheat temperature at 50C flash and lower flow Figure 83. Preheat temperature at 50C flash and higher flow

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115 Figure 84. Preheat temperature at 60C flash and lower flow Figure 85. Preheat temperature at 60C flash and higher flow

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116 Figure 86. Preheat temperature at 70C flash and lower flow Figure 87. Preheat temperature at 70C flash and higher flow

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117 Figure 88. Preheat temperature at 80C flash and lower flow Figure 89. Preheat temperature at 80C flash and higher flow

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118 7.6 Heater Size Preheated seawater coming out of the c ondenser is further heated by the solar heater to a set flash temperature as mentioned in CHAPTER 4 The heater load was fairly constant at lower flash temperatures but spiked, then rapidly decreased, reaching a minimum before it steadily increased at highe r flash temperatures for both seawater flow rates. Moreover, heater loads at lower seawat er flow rates were lower. The heater load increased with flash temperatures, reachi ng a maximum between 60 and 70 C, after which it decreased for both seawater flow ra tes due to improved heat recovery caused by increased condensation experienced at highe r flashing temperature as was mentioned. The heater load makes up nearly all energy input to the desalination system due to the relatively small pumping work; hence, curtailing it enhances the feasibility of the process. The heater load logically increased wi th flash temperature at first but started to decrease later at higher flash temperatur e due to improved heat recovery caused by increased condensation for both seawater fl ow rates. Increased vaporization and the subsequent condensation improve heat re covery manifested in higher preheat temperatures that reduce the temperature gr adient around the heater, ultimately reducing the heater load in line with the energy balan ce. The heater load profiles for both seawater flow rates are similar; however, they were lo wer for lower flow rates, since there was less volume to heat as well as the superior heat recovery as was seen earlier. Model prediction of heater load loos ely resembled the pseudoexperimental results due to the inexact preheat temperatur e calculation seen earlie r. The precision of the model in predicting the heater load affects the quality of its evaluation of system performance. Heater load profiles are shown in Figure 90 through Figure 101.

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119 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 14 x 104 t (min)QH (J/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 90. Modeled heat load profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 14 x 104 t (min)QH (J/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 91. Mined heat load profiles at lower flow

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120 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 14 x 104 t (min)QH (J/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 92. Modeled heat load profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 14 x 104 t (min)QH (J/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 93. Mined heat load profiles at higher flow

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121 Figure 94. Heat load at 50C flash and lower flow Figure 95. Heat load at 50C flash and higher flow

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122 Figure 96. Heat load at 60C flash and lower flow Figure 97. Heat load at 60C flash and higher flow

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123 Figure 98. Heat load at 70C flash and lower flow Figure 99. Heat load at 70C flash and higher flow

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124 Figure 100. Heat load at 80C flash and lower flow Figure 101. Heat load at 80C flash and higher flow

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125 7.7 Collector Size The heater is modeled as a singleglazed fl atplate solar collector directly heating seawater flowing through its absorbing tubes; moreover, it is sized by the solar collection area needed to meet the heater load computed by a correlation given in CHAPTER 4 [8]. The required solar collection area is directly proportional to the heater load, resulting in matching profiles of both variables. The require d solar collection area was fairly constant at lower flash temperatures, but spiked, th en rapidly decreased, reaching a minimum before it steadily increased at higher flash temperatures for both seawater flow rates; moreover, the required solar collection areas at lower seawater flow rates were lower. Required solar collection area increased w ith flash temperatures, reaching a maximum between 60 and 70 C, after which it decreas ed for both seawater flow rates due to improved heat recovery caused by increased co ndensation at higher fl ashing temperature. The required solar collection area increase d with flash temperature at first but started to decrease late r at higher flash temperature, matc hing the above detailed profile of heater load for both seawater flow rates. The required solar collection area profiles for both seawater flow rates were similar; however they were lower for lower flow rates due to reduced heater load, since there was le ss volume to heat as was seen earlier. Model prediction of required solar colle ction area did not closely resemble the pseudoexperimental results because of poorly estimated heater load values caused by inexact preheat temperature calculation as was mentioned earlier. Reliability of model estimates of the required solar collection ar ea depends on the accuracy of heater load computations, which relies on precision of preheat temperature computations. Required solar collection area profiles are shown in Figure 102 through Figure 113.

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126 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 x 104 t (min)ASC (cm2) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 102. Modeled required solar colle ction area profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 x 104 t (min)ASC (cm2) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 103. Mined required solar coll ection area profiles at lower flow

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127 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 x 104 t (min)ASC (cm2) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 104. Modeled required solar colle ction area profile s at higher flow 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 x 104 t (min)ASC (cm2) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 105. Mined required solar coll ection area profiles at higher flow

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128 Figure 106. Required solar collection area at 50C flash and lower flow Figure 107. Required solar collection area at 50C flash and higher flow

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129 Figure 108. Required solar collection area at 60C flash and lower flow Figure 109. Required solar collection area at 60C flash and higher flow

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130 Figure 110. Required solar collection area at 70C flash and lower flow Figure 111. Required solar collection area at 70C flash and higher flow

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131 Figure 112. Required solar collection area at 80C flash and lower flow Figure 113. Required solar collection area at 80C flash and higher flow

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132 7.8 System Throughput The fresh water produced is due to conde nsation of flashed and diffused water vapor moving from the evaporator to condenser as was mentioned in CHAPTER 4 Fresh water production rate was highest at first, then slowly decl ined for both seawater flow rates; moreover, it was generally higher for lower seawater flow rates. The difference between fresh water production rates of both s eawater flow rates is more significant at medium flash temperatures and seems to diminish at both low and high flash temperatures. Fresh water production rate in creased with flash temperatures for both seawater flow rates, since the amounts of flashing and diffusing water vapor are directly proportional to flashing temperat ure and the temperatureinduced vapor pressure gradient between the evaporator a nd condenser, respectively. Fresh water production rate was high at first due to the high initial rate of vaporization caused by the rapidly increasing equilibrium temperature at lower vacuum pressures, then it slowly declined due to th e decreasing rate of vaporization caused by the stabilizing equilibrium temperature at rising vacuum pressures, almost reaching a plateau comparable to the flash temperature for both seawater flow rates. Fresh water production rate profiles for both seawater flow rates are similar; however, they were higher for lower flow rates due to more condensation caused by more vaporization. Model prediction of fresh water producti on rate appropriately resembled the pseudoexperimental results due to adequa te prediction of sy stem vacuum and equilibrium temperature. Furthermore, adjusted parameters played a significant role in shifting the profile of fresh water production rate to match pseudoexperimental results. Fresh water production rate profiles are shown in Figure 114 through Figure 125.

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133 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 t (min)MC (g/min) TH = 60 C TH = 70 C TH = 80 C Figure 114. Modeled fresh water produc tion rate profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 t (min)MC (g/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 115. Mined fresh water produc tion rate profiles at lower flow

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134 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 t (min)MC (g/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 116. Modeled fresh water produc tion rate profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 t (min)MC (g/min) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 117. Mined fresh water producti on rate profiles at higher flow

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135 Figure 118. Fresh water production rate at 50C flash and lower flow Figure 119. Fresh water production rate at 50C flash and higher flow

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136 Figure 120. Fresh water production rate at 60C flash and lower flow Figure 121. Fresh water production rate at 60C flash and higher flow

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137 Figure 122. Fresh water production rate at 70C flash and lower flow Figure 123. Fresh water production rate at 70C flash and higher flow

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138 Figure 124. Fresh water production rate at 80C flash and lower flow Figure 125. Fresh water production rate at 80C flash and higher flow

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139 7.9 System Capacity The total amount of fresh water produced is calculated by nume rically integrating the dynamic fresh water production rate over th e entire operating period as was revealed in CHAPTER 4 Fresh water production amount was ri sing for both seawat er flow rates; moreover, it was generally higher for lower s eawater flow rates. The difference between fresh water production amounts of both seawater flow rates is more obvious at medium flash temperatures and diminishes at both low and high flash temp eratures corresponding to the fresh water production rate results The fresh water production amount increased with flash temperatures for both seawater flow rates in line with the fresh water production rate results due to enhanced eva poration rates at higher flash temperatures according to thermodynamic phase equilibria resulting in more fresh water production. The profile of fresh water production amount is not exactly linear, as it was rising at a higher rate at first due to the high initia l fresh water production rate, as seen earlier for both seawater flow rates. Fresh water production amount profile s for both seawater flow rates are similar; however, they were higher for lower seawater flow rates due to higher fresh water production rates, as seen earlier. Model prediction of fresh water produc tion amount properly resembled the pseudoexperimental results due to accurate portrayal of fres h water production rate as a result of adequate prediction of system v acuum and equilibrium temperature mentioned earlier; furthermore, adjusted parameters pl ayed a significant role in shifting the fresh water production rate profile to match pse udoexperimental results, resulting in good estimates of fresh water production amount. Fr esh water production amount profiles are shown in Figure 126 through Figure 137.

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140 0 20 40 60 80 100 120 140 160 180 0 1000 2000 3000 4000 5000 6000 t (min) MC dt (g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 126. Modeled fresh water produc tion amount profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 1000 2000 3000 4000 5000 6000 t (min) MC dt (g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 127. Mined fresh water produc tion amount profiles at lower flow

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141 0 20 40 60 80 100 120 140 160 180 0 1000 2000 3000 4000 5000 6000 t (min) MC dt (g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 128. Modeled fresh water produc tion amount profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 1000 2000 3000 4000 5000 6000 t (min) MC dt (g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 129. Mined fresh water produc tion amount profiles at higher flow

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142 Figure 130. Fresh water production amount at 50C flash and lower flow Figure 131. Fresh water production amount at 50C flash and higher flow

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143 Figure 132. Fresh water production amount at 60C flash and lower flow Figure 133. Fresh water production amount at 60C flash and higher flow

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144 Figure 134. Fresh water production amount at 70C flash and lower flow Figure 135. Fresh water production amount at 70C flash and higher flow

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145 Figure 136. Fresh water production amount at 80C flash and lower flow Figure 137. Fresh water production amount at 80C flash and higher flow

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146 7.10 Process Feasibility Feasibility of the proposed desalinati on system can be evaluated using its resulting prime energy consumption, defined as the ratio of the total amount of energy exhausted to total amount of fres h water produced, as mentioned in CHAPTER 4 Energy consumed is attributed to heat provided by the heater plus work supplied by the pump. The pumping work of the proposed desalination system was insignificant relative to the heater load whether the flow rate of seawat er was controlled with a throttling valve or a variablefrequency driv e; hence, the presented prime en ergy consumption computations ignore the pumping work, that is PEC QH dt / MC dt No economic analysis was performed in this venture, but the optimi zation process of the proposed desalination system lies within minimizing the prime en ergy consumption via maximizing production and minimizing heater load. Prime energy consumption steadily increas ed for both seawater flow rates; however, it was higher at higher seawater fl ow rates due to higher heater loads. It declined rapidly with flash temperature due to the increasing fresh water production and decreasing heater load due to the improve d heat recovery caused by the increased condensation associated with higher flash temperatures. In addition; the difference between prime energy consumption experience d at both seawater flow rates was more significant at low flash temperatures and di minished at higher flash temperatures. Model prediction of prime energy consump tion deteriorated w ith decreasing flash temperatures but improved with increasing flas h temperatures due to contrasting effects of poor heater load predic tion and good production amount prediction. Prime energy consumption profiles are shown in Figure 138 through Figure 149.

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147 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 7 8 9 10 x 104 t (min)PEC (J/g) TH = 60 C TH = 70 C TH = 80 C Figure 138. Modeled prime energy cons umption profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 7 8 9 10 x 104 t (min)PEC (J/g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 139. Mined prime energy cons umption profiles at lower flow

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148 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 7 8 9 10 x 104 t (min)PEC (J/g) TH = 60 C TH = 70 C TH = 80 C Figure 140. Modeled prime energy cons umption profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 7 8 9 10 x 104 t (min)PEC (J/g) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 141. Mined prime energy consum ption profiles at higher flow

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149 Figure 142. Prime energy consumpti on at 50C flash and lower flow Figure 143. Prime energy consumption at 50C flash and higher flow

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150 Figure 144. Prime energy consumpti on at 60C flash and lower flow Figure 145. Prime energy consumption at 60C flash and higher flow

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151 Figure 146. Prime energy consumpti on at 70C flash and lower flow Figure 147. Prime energy consumption at 70C flash and higher flow

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152 Figure 148. Prime energy consumpti on at 80C flash and lower flow Figure 149. Prime energy consumption at 80C flash and higher flow

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153 7.11 Condensing Efficiency Condenser efficiency describe s its heat transfer effectiveness and is defined as the ratio of the temperature gradient on the cold tube side to the temperature gradient on the hot shell side written as a percentage, that is C = [ ( TX TP ) / ( TE TC ) ] 100 % as was mentioned in CHAPTER 4 Condenser efficiency rapi dly increased to reach a maximum early before it slowly declined for both seawater flow rates; however, condenser efficiency attained at lower seaw ater flow rates was higher. The condenser efficiency increased with fl ash temperatures for both seaw ater flow rates, since the preheat temperature is directly proportional to the flashing temperature. The condenser efficiency indirectly conveys the percent of ava ilable heat that was utilized for preheating seawater. It rapidly in creased because of the rapidly rising preheat temperature due to the high initial rate of vaporization caused by rapidly increasing equilibrium temperature at lower vacuum pressu res, then it slowly declined because of the decreasing preheat temperature due to th e decreasing rate of vaporization caused by stabilizing equilibrium temperature at rising vacuum pressures for both seawater flow rates. The condenser efficiency profiles for both seawater flow rates are similar; however, they are higher for lower flow rates because of the higher preheat temperature experienced at lower seawater flow rates due to more condensation caused by more vaporization as seen before. Model prediction of condenser efficiency loosely resembled experimental results because of the loose depicti on of the preheat temperature due to the inability of the condenser tube heat transfer module of the model to capture the ra te of condensation. Condenser efficiency profiles are shown in Figure 150 through Figure 161.

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154 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)C (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 150. Modeled condenser effici ency profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)C (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 151. Experimental condenser e fficiency profiles at lower flow

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155 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)C (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 152. Modeled condenser effici ency profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)C (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 153. Experimental condenser e fficiency profiles at higher flow

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156 Figure 154. Condenser efficiency at 50C flash and lower flow Figure 155. Condenser efficiency at 50C flash and higher flow

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157 Figure 156. Condenser efficiency at 60C flash and lower flow Figure 157. Condenser efficiency at 60C flash and higher flow

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158 Figure 158. Condenser efficiency at 70C flash and lower flow Figure 159. Condenser efficiency at 70C flash and higher flow

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159 Figure 160. Condenser efficiency at 80C flash and lower flow Figure 161. Condenser efficiency at 80C flash and higher flow

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160 7.12 Recovery Efficiency Recovery efficiency is defined as the ra tio of seawater enthalpy change due to condensing water vapor to the overall enthalpy change required to attain the set flash temperature written as a percentage, that is R = [ ( HX HS ) / ( HH HS ) ] 100 % as was mentioned in CHAPTER 4 In other words, it is the pe rcent of total enthalpy change that was essentially accomplished by reclai ming heat from condensing vapor. Recovery efficiency rapidly increased to reach a maxi mum early before it slowly declined for both seawater flow rates; however, recovery e fficiency was higher at lower seawater flow rates. It increased with flash temperatures for both seawater flow rates, since preheat enthalpy is directly proportiona l to preheat temperature that is directly proportional to flashing temperature as seen earlier. Recovery efficiency directly expresses the percent of required heat that is reclaimed from condensing vapor. Recovery e fficiency rapidly increased because of rapidly rising preheat enthalpy due to rapidly rising preheat te mperature, then it slowly declined because of decreasing preheat enthal py due to decreasing preheat temperature. Recovery efficiency profiles for both seawater flow rates are similar; however, they were higher for lower flow rates because of hi gher preheat enthalpy due to higher preheat temperature experienced at lower seawater flow rates due to more condensation caused by more vaporization. Model prediction of recovery efficiency loosely resembled experimental results because of loose depiction of preheat temperat ure due to inability of the condenser tube heat transfer module of the model to captu re the rate of condensation. Recovery efficiency profiles are shown in Figure 162 through Figure 173.

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161 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)R (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 162. Modeled recovery effi ciency profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)R (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 163. Experimental recovery ef ficiency profiles at lower flow

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162 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)R (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 164. Modeled recovery effi ciency profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)R (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 165. Experimental recovery ef ficiency profiles at higher flow

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163 Figure 166. Recovery efficiency at 50C flash and lower flow Figure 167. Recovery efficiency at 50C flash and higher flow

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164 Figure 168. Recovery efficiency at 60C flash and lower flow Figure 169. Recovery efficiency at 60C flash and higher flow

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165 Figure 170. Recovery efficiency at 70C flash and lower flow Figure 171. Recovery efficiency at 70C flash and higher flow

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166 Figure 172. Recovery efficiency at 80C flash and lower flow Figure 173. Recovery efficiency at 80C flash and higher flow

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167 7.13 Thermal Efficiency Thermal efficiency of the desalination pr ocess is a performance measure defined as the ratio of heat used in vaporizing water to overall heat added to bulk seawater written as a percentage, that is T = [ ME ( HE + HL E ) / ( MH HH ) ] 100 % as was mentioned in CHAPTER 4 In other words, it is the percent of total thermal energy supplied that was actually used to vaporize water. Thermal efficiency rapidly increased to reach a maximum early before it slowly declined, then stabilized for both seawater flow rates; however, thermal efficiency was higher at lower seawater flow rates. The thermal efficiency increased with fl ash temperatures for both seaw ater flow rates, since the amounts and the temperatures of the water va por are directly proportional to the flashing temperature as seen earlier. Thermal efficiency rapidly increased because of rapidly increasing water vapor enthalpy due to its rising amount and temperatur e, and then it slowly declined, reaching a plateau because of slowly stabilizing water vapor enthalpy due to gradually declining vaporization rates, but gradually rising temper atures, of the water va por for both seawater flow rates. Thermal efficiency profiles for bo th seawater flow rates are similar; however, they were higher for lower flow rate s due to higher vaporization rates. Model prediction of thermal efficiency of the proposed desalination process properly resembled pseudoexperimental resu lts due to accurate portrayal of water vaporization rates; furthermore, adjusted para meters and correlations played a significant role in shifting vaporization rate profiles to match pseudoe xperimental results, resulting in excellent thermal efficiency estimates fo r the proposed desalination process. Thermal efficiency profiles are shown in Figure 174 through Figure 185.

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168 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)T (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 174. Modeled thermal effici ency profiles at lower flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)T (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 175. Mined thermal effici ency profiles at lower flow

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169 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)T (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 176. Modeled thermal effici ency profiles at higher flow 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 90 100 t (min)T (%) TH = 50 C TH = 60 C TH = 70 C TH = 80 C Figure 177. Mined thermal effici ency profiles at higher flow

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170 Figure 178. Thermal efficiency at 50C flash and lower flow Figure 179. Thermal efficiency at 50C flash and higher flow

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171 Figure 180. Thermal efficiency at 60C flash and lower flow Figure 181. Thermal efficiency at 60C flash and higher flow

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172 Figure 182. Thermal efficiency at 70C flash and lower flow Figure 183. Thermal efficiency at 70C flash and higher flow

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173 Figure 184. Thermal efficiency at 80C flash and lower flow Figure 185. Thermal efficiency at 80C flash and higher flow

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174 7.14 Disambiguation The preceding discussion included references to three different types of data as it examined profiles of twelve timevarying system variables. Model data refer to data obtained by running the developed model with its alternate equa tions and adjusted parameter values and expressions. Experiment al data refer to averaged temperature and pressure values recorded by the data acquisi tion system of three matching experiments; furthermore, experimental data also include observed values for seawater flow rate and fresh water amount. Pseudoexperimental data refer to results generated by a computer code composed of the developed model with its alternate equations but without adjusted parameter values and expressions; moreover, energy balance relati ons were deactivated, while experimental temperature and pressure, as well as recorded seawater flow rate and produced fresh water amount, were supplied to the computer code. The entire data mining procedure is illustrated in Figure 186. TE PV TX TC TW TP TH MUX MC SPFC SPPC SPTIC EXP Pseudoexperimental Experimental NonLinear Regression Parameter Expressions MS MW MX H NEA HX VPC WP VLE HWB k P EOS PEC BFE GR RR Figure 186. Experimental and pse udoexperimental data acquisition

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175 CHAPTER 8. CONCLUSION 8.1 Summary A flash desalination process sustainable by natural forces of solar radiation and gravity has been proposed. In addition, experi mental and theoretical simulations of the proposed desalination process have been car ried out. The proces s includes a startup procedure and continuous operation consis ting of pumping seaw ater through a solar heater before flashing it under vacuum in an elevated chamber. The vacuum is passively created and subsequently maintained by hydros tatic balance between pressure inside the elevated flash chamber and outdoor atmospheric pressure. Experimental simulations were carried out by a pilot unit de picting the proposed system but emulating solar heating and passive vacuum operations. Theoretical simulations were performed using a computer code comprising fundamental physical and thermodynamic laws plus numerous correlations and parameters. Experimental data were fed to an adapted computer code genera ting pseudoexperimental data; moreover, experimental and pseudoexperimental data were regressed, generating parametric values and correlations that were included in the developed computer model. Experimental and theoretical simulations were run at varyi ng operating conditions but at analogous circumstances, and their resu lts were compared and analyzed to validate the developed model. Feasibility of the prop osed system rapidly increased with flash temperature due to increased fresh wate r production and improved heat recovery.

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176 8.2 Outcome Experimental and pseudoexperimental da ta were regressed, generating four correlations given in CHAPTER 6 that were included in the model. In addition, a dataset of Kvalues was regressed to adjust parameter values of Henry's constant and vapor pressure correlations for noncondensab le gases and water, respectively. The developed correlation for the counterc urrent departure correction factor for the condenser tube yielded accep table results as was seen in CHAPTER 6 ; however, preheat temperature computed by the model using that develope d correlation yielded poor predictions as was seen in CHAPTER 7 The data mining code used the log mean temperature difference scheme to ge nerate pseudoexperimental data of FCT that were regressed to generate the aforementioned co rrelation. This observa tion suggests that the log mean temperature difference scheme is prob ably not the best option to model the heat transfer operation across the condenser tube Modeling a heat transfer operation with a phase change is extremely complex, especia lly in the presence of noncondensable gases. Precision of the model in predicting preheat temperature affects the quality of its evaluation of system performance as was seen in CHAPTER 7 The developed correlation for the nonequi librium allowance yielded average results as was seen in CHAPTER 6 ; consequently, equilibrium and concentrated brine temperatures computed by the model also yi elded average predictions as was seen in CHAPTER 7 Heat loss of the evaporator was ignored, while nonequilibrium allowance correlation and energy balance around the evapor ator were used to find equilibrium and the concentrated brine temperatures. This observation suggests that heat loss from the evaporator may need to be accounted for in the model.

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177 The developed correlation for the activity coefficient of water yielded excellent results as was seen in CHAPTER 6 The data mining code used the RachfordRice scheme along with experimental values of e quilibrium temperature and system pressure, plus average reported composition of seawater to generate pseudoexperimental data of H2O that were regressed to gene rate the previously mentioned correlation. In addition, the data mining code included parameter values of Henry's constant and vapor pressure correlations for noncondensable gases and water obtained using the SUPERTRAPP code from NIST [31] as was mentioned in CHAPTER 4 The RachfordRice scheme and SUPERTRAPP code, plus the reported com position of seawater, are well recognized in literature for their accuracy; ther efore, quality of the developed correlation for the activity coefficient of water is believed to be very high. The developed correlation for the gas pha se molecular content correction factor yielded good results, except for the case of highe r seawater flow rates flashing at 50 C as was seen in CHAPTER 6 The data mining code used the ideal gas law with experimental values of equilibrium temperature and system pressure, plus a straightforward formula for calculating dynamic vacuum volume to generate pseudoexperimental data of that were regressed to generate the previous correlation. This obs ervation suggests that flashing seawater at lower temperatures and high er flow rates rapidly increases the rate of accumulation of noncondensable gases. This phenomenon has been experimentally explored and theoretically modeled by Abtahi [32] via the molecular arrival rate concept. Results for seen in CHAPTER 6 indicate that deviation fro m ideal behavior increases with decreasing PV / PH2O values due to rising temperature gradient between the hot and the cold sides of the flash chamber. This observation was also confirmed by Abtahi [32].

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178 The results seen in CHAPTER 7 suggest that the proposed process becomes more feasible if operated at higher temperatures and more modera te flow rates. Higher flash temperatures will result in more evaporati on and subsequent condensation, resulting in more fresh water production. In addition, the increased amount of heat reclaimed from condensing vapor reduced overall heater load and thus required less solar collection area. The collective outcome of increased fresh water output and decreased heater load is a significant decrease in prime energy consump tion of the desalinati on unit, making it more economically viable. These obs ervations are quantified in Figure 187 and Figure 188 for seawater conversion efficiency and prime energy consumption, respectively. The results seen in CHAPTER 7 also suggest that most fresh water production occurs in the beginning of th e operation, where vacuum pre ssure is lowest. The current experimental simulations were launched at a reasonably low vacuum; however, a much lower vacuum can be achieved using less energy if the proposed method of creating a passive vacuum is implemented. The collec tive outcome of applying passive vacuum and solar heating schemes is a significant decr ease in prime energy c onsumption of the unit due to lower energy input and higher produc t output, furthering its feasibility. The efficiency of the unit can also be boosted by expl oiting the thermal energy of hot brine by either employing multistage sche mes or including heat recovery provisions to increase the amount of reclaimed heat, e ffectively reducing prime energy consumption. The temperature difference manifested in th e vapor pressure gradient between the two compartments of the flash chamber is the driving force of vapor transfer from the hot evaporator to the cold condenser; therefore, any attempt to exploit the thermal energy of the hot concentrated brine should be carefully applied as not to comp romise that gradient.

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179 40 45 50 55 60 65 70 75 80 85 90 0 1 2 3 4 5 6 7 8 9 10 TH (C)Conversion (%) = 100 MC dt / MS dt Lower flow Higher flow Figure 187. Seawater conversion de pendence on flash temperature 40 45 50 55 60 65 70 75 80 85 90 0 1 2 3 4 5 6 7 8 9 10 x 105 TH (C)PEC (J/g) Lower flow Higher flow Figure 188. Prime energy consumpti on dependence on flash temperature

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180 8.3 Prospects The results of this exploration demonstrat e great potential for application of the proposed desalination system, es pecially in light of grow ing energy and water demands. This section is aimed at offering recommenda tions for prospective researchers seeking to optimize and further feasibility of the proposed desalination system. CHAPTER 2 includes a brief overview of th e most common conventional and solar desalination methods. An immense numbe r of renewable energy driven desalination systems have been proposed and examined but never commercially materialized. The current study did not present those systems; ne vertheless, including them in the literature review of future research would be supporti ve of the novelty of the current system. In addition, corrosion and scaling are major chal lenges to all desalination systems; however, they were overlooked in this study to k eep the focus on simulation of the proposed desalination system, but they should be addressed in future investigations. Moving the experimental unit to an outdoor setting would enhance replication of the proposed system. An outdoor unit can be furn ished with a real solar heater and will enable the proposed passive vacuum generation by elevating the flash chamber to at least ten meters above ground. Implementing the proposed passive vacuum generation will also allow for much lower vacuums to be ach ieved using less energy, which translates to more fresh water production. In addition, v acuum erosion will be slower in an outdoor unit because vacuum volume will be increasing as system pressure increases due to the hydrostatic balance between the levels of the ground tanks a nd the flash chamber, which translates to more fresh water production due to lower pressures. Also, an outdoor unit will enable automatic flow control via a thro ttling valve or a variablefrequency drive.

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181 Accuracy of model output and pseudoexpe rimental data, as well as the precision of the regression, deeply rely on certainty of their input. There are slight discrepancies in literature when it comes to reporting seawater content; therefore, it is essential to investigate the seawater parameters given in CHAPTER 6 further, explicitly i and i, especially those pertaining to carbon dioxide due to its complex kinetics. Model convergence was difficult at times due to interdependence nature of its equations; therefore, other programming tools may be explored. In addition, the current model executes and integrat es using one minute incremen ts, yielding smooth results; however, easier convergence and smoother results can be obtained by decreasing increment size but that will also increase program run time. Heat transfer relations of the current model did not produc e very reliable results; consequently, they should be improved to predict heat loss of the flash chamber accurately as well as heat transfer across the condenser tube. Ri gorous heat transfer computations will result in better predicti ons of equilibrium and brine temperatures resulting in superior flash calculations. More rigorous heat transfer computations will also result in better predictions of preheat te mperature, resulting in enhanced performance evaluation due to regression of a more precise mined data. The log mean temperature difference method should be substituted with a more appropriate heat transfer model capable of handling the complexity of phase change operations. Experimental data should always be used to finetune the parameters of the employed heat transfer model. In addition, if heat transfer computations remained imprecise, adjusting local and overall heat transf er coefficients should be explored as an alternative to adjusting the parameters of the heat transfer model.

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182 Abtahi [32] hypothesized that the noncondens able gas molecules accumulating in the condenser tend to amass around the cold surface of the condenser tube, in essence forming an insulation layer that hampers heat transfer from the condensing water vapor. In addition, some heat transfer texts include mass transfer parameters within heat transfer coefficient correlations in condensers as they try to model the diffusion of water vapor molecules through the noncondensable gas layer. The current model assumes the total condens ation of flashed water vapor and uses a regressed molecular content correction fact or to account for rate of accumulation of noncondensable gases. Alternately, the di stribution of non-condensable gases among flashed vapor, concentrated brine, and c ondensed water in the flash chamber can be estimated by assuming equilibrium among the three phases [33]. This approach may be more valid, but will exacerbate computations and hinder convergence. A more accurate version of the correlation for the activity coefficient of water can be obtained by using a suitable activity coefficient model to write the activity coefficient formula, then adjusting its parameters usi ng the data mining code mentioned earlier in CHAPTER 6 and found in the APPENDICES section. The diffusion correlation developed in CHAPTER 4 includes two parameters that serve as conductance and resistance terms. In its current form, the model considers resistance to water vapor tran sfer to be pertinen t only to diffusing and not flashing vapor. It would be more prudent to remove the resistance term, then readjust the conductance term in accordance with reported values [14]. Afterward, a resistance term pertaining to diffusing and flashing water vapor should be in cluded in the model and adjusted using the data mining code mentioned in CHAPTER 6 and found in the APPENDICES section.

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183 The diffusion correlation development shou ld be carried out alongside the above mentioned molecular arrival rate concept modeled by Abtahi [32]. This approach will make the adjusted conductance and resistance terms more consistent with the complex mass and heat transfer operations, which wi ll ultimately result in improved vacuum pressure and preheat temperature predictions. Feasibility of the proposed desalination pr ocess should be simply investigated via prime energy consumption, PEC = ( QH + WP ) / MC and not vi a unnecessarily meticulous economic analyses. Process optimi zation is synonymous with prime energy consumption mitigation that is realized vi a minimizing the amount of energy exhausted or maximizing the amount of fresh water pr oduced. Most of the exhausted energy of all thermal desalination processes is due to heat and not to power input as was seen earlier in CHAPTER 2 and as confirmed by the current expe rimental and theoretical simulations; therefore, optimizing the propos ed desalination system shoul d specifically revolve around reducing heater load and amplifying fres h water production rate Detailed economic analyses can be performed by properly esti mating capital and operating costs; however, these analyses can be quite cumberso me and should be carefully employed. Seawater flash temperature is a set para meter; therefore, reducing heater load should be aimed for by increasing preheat temperature achieved via improved heat recovery in the condenser. Improving heat recovery in the condenser can be accomplished by improving the geometry of the condenser tube to harness the most of the latent heat of the condensing steam. Ther mally insulating the condenser should be investigated to see its c onsequences on directing conde nsing steam away from the condenser wall and more towards the condenser tube.

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184 Amplifying the fresh water production rate is thermodynamically controlled via increasing equilibrium temperature and lowering system pressure. With the exception of increasing flash temperature set point, increasing equilibrium temperature is accomplished by minimizing heat loss of the eva porator via enhanced thermal insulation. System pressure is always increasing because of the eroding vacuum due to build up of noncondensable gases in the flash chamber; however, initial system pressure is a controlled variable, and lowe ring it would lower system pressure all through the desalination process. The proposed met hod of passively creating vacuums should accomplish very low vacuum pressures, in e ffect equaling ambient water vapor pressure. In addition, fresh water production rate can be significantly enhanced by employing the multistage scheme outlined earlier in CHAPTER 4 The current model should be extended from simulating singlestage to multistage desalination schemes. In addition, a qualitative sensitivity analysis of model para meters should be executed to evaluate the outcome of their vari ation on model results. The proposed desalination system is m eant to be driven by solar energy and average values for a generic solar collector were used to estimate solar collection area. Detailed solar computations s hould be used instead of the av erage values to broaden the applicability of the model to different geogr aphies and different collectors. This would involve including several solar calculations that are widely available in literature [8]. Finally, experimental results discussed earlier have proven that some of the flashed vapor condenses prematurely in the ev aporator before making it to the condenser; therefore, resistan ce to vapor transfer from the evapor ator to condenser should be reduced to increase fresh water production and improve heat recovery.

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185 REFERENCES 1. National Atlas of the United States. Water Resources of the United States ; U. S. Geological Survey: Reston, VA, 2005. 2. Minton, P. E. Handbook of Evaporation Technology ; Noyes Publicat ions: Westwood, NJ, 1986. 3. Maxwell, E., George R., Wilcox S. Climatological Solar Radiation Model ; the National Climatic Data Center: Asheville, NC, 1998. 4. Culp, A. Principles of Energy Conversion ; McGraw Hill: New York, NY, 1991. 5. Wangnick, K. Worldwide Desalting Plants Inventory ; Report Number 15; International Desalination Asso ciation: Topsfield, MA, 1998. 6. Miller, J. E. Review of Water Resources and Desalination Technologies ; Materials Chemistry Department; Sandia National Laboratories: Albuquerque, NM, 2003. 7. Kalogirou, S. A. Seawater Desali nation Using Renewable Energy Sources, Progress in Energy and Combustion Science 2005, 31(3), pp 242. 8. Goswami, D. Y., Kreith, F., Kreider, J. F. Principles of Solar Engineering second edition; Taylor & Francis: Philadelphia, PA, 2000. 9. Delyannis, E. Historic Background of Desalination and Re newable Energies, Solar Energy 2003, 75(5), pp 357. 10. Tzen, E., Morris, R. Renewable Energy Sources for Desalination, Solar Energy 2003, 75(5), pp 375.

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186 11. AlKharabsheh, S. Theoretical and Experimental Analysis of Wa ter Desalination System Using Low Grade Solar Heat Doctoral Dissertation; University of Florida: Gainesville, Florida, 2003. 12. Maroo, S. C. Theoretical Analysis of Solar Driv en Flash Desalination System Based on Passive Vacuum Generation Master Thesis; University of Florida: Gainesville, Florida, 2006. 13. Rachford, H. H., Rice J. D. Procedure fo r Use of Electronic Digital Computers in Calculation Flash Vaporizat ion Hydrocarbon Equilibrium, Petroleum Technology 1952, 4, 9. 14. Bemporad, G. A. Basic Thermodynami c Aspects of a Solar Energy Based Desalination Process, Solar Energy 1995, 54 (2), pp 125. 15. Geankoplis, C. J. Transport Processes and Separation Process Principles ; Prentice Hall: Englewood Cliffs, NJ, 2003. 16. Turekian, K. K. Oceans ; Prentice Hall: Englewood Cliffs, NJ, 1968. 17. Sander, R. Compilation of Henry's Law Constant s for Inorganic and Organic Species of Potential Importance in Environmental Chemistry www.henryslaw.org 1999. 18. Perry, R. H., Green, D. Perrys Chemical Engineers Handbook ; McGrawHill: New York, NY, 1984. 19. Thibodeaux, L. J. Environmental Chemodynamics ; John Wiley & Sons: New York, NY, 1996. 20. Sinnott, R. K. Coulson and Richardsons Chemical Engineering ; Butterworth Heinemann: Oxford, UK, 1996. 21. E1Nashar, A. M., Qamhiyeh, A. A. Simulation of the SteadyState Operation of a MultiEffect Stack Seawater Distillation Plant, Desalination 1995, 101(3), pp 231.

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187 22. Miyatake, O., Murakami, K., Kawata, Y., Fujii, T. Fundamental Experiments with Flash Evaporation, Heat Transfer Japan Research 1973, 2(4), pp 89. 23. Coker, A. K. Chemical Process Design, Analysis, and Simulation ; Gulf Publishing: Houston, TX, 1995. 24. Hermann M., Koschikowski J., Rommel M. CorrosionFree Solar Collectors for Thermally Driven Seawater Desalination, Solar Energy 2002, 72(5), pp 415. 25. Granet, I. Fluid Mechanics ; Prentice Hall: Englewood Cliffs, NJ, 1996. 26. Caldwell, D. R. The Thermal Conductivity of Seawater, DeepSea Research 1974, 21, 131. 27. Chopey, N. P. Handbook of Chemical Engineering Calculations ; McGrawHill: New York, NY, 1994. 28. Millero, F. J., Poisson, A. Internationa l One Atmosphere Equation of State of Seawater, DeepSea Research 1981, 28, pp 625. 29. Sndermann, J. Numerical Data and F unctional Relationships in Science and Technology New Series Group V: Geophysics and Space Research, Oceanography 1986, 3(A), SpringerVerlag, Berlin, Germany. 30. Mamaev, O. I. TemperatureSalinity Analysis of World Ocean Waters ; translation from Russian by Burton, R. J.; Elsevier Scientific Publishing: Amsterdam, Netherlands, 1975. 31. Chase, M. W. NISTJANAF Themochemical Tables Journal of Physical and Chemical Reference, Number 9; American Chemical Society: Washington, DC, 1998. 32. Abtahi, H. Investigation of local pressure characteristics in gasloaded heat pipes, Proceedings of the ASME National Heat Transfer Conference Houston, TX, 1988; American Society of Mechanical Engin eers: New York, NY, 1988, A89 53251 23 34, pp 347.

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188 33. Abutayeh, M., Goswami, D. Y. Passive Vacuum Solar Flash Desalination, American Institute of Chemical Engineers [Online] 2009, pp 1547.

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189 APPENDICES

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190 Appendix A. The operating procedure Figure 189. Preparing to fill up the condenser Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 190. Condenser full of fresh water

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191 Appendix A (Continued) Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 191. Preparing to fill up the evaporator Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 192. Evaporator full of seawater

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192 Appendix A (Continued) Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 193. Switching the valve pos itions of the flash chamber Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 194. Flash chamber passively vacuumed

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193 Appendix A (Continued) Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 195. Preparing to star t the desalination process Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 196. Desalination process taking place

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194 Appendix A (Continued) Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 197. Flash chamber vented to terminate vacuum Brine Water Sea Water Make-Up Tank Condenser Evaporator Fresh Water Make-Up Tank Fresh Water S WCP X H E F B Solar Heater Figure 198. Flash chamber drained

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195 Appendix B. SUPERTRAPP code to generate Kvalues ************************************************************ NIST Standard Reference Database 4 * NIST THERMOPHYSICAL PROPERTIES OF HYDROCARBON MIXTURES * Program SUPERTRAPP Version 3.1, beta 1 * * Based on research sponsored by * the NASA Lewis Research Center, * the NIST Supercritical Fluid Property Consortium * and Standard Reference Data * * Marcia L. Huber * Physical and Chemical Properties Division * * Distributed by Standard Reference Data * National Institute of Standards and Technology * Gaithersburg, MD 20899 USA * * Copyright 2002 by the U.S. Secretary of Commerce * on behalf of the United States of America * All rights reserved. ************************************************************ For help in response to any question, enter "?". For a brief description of SUPERTRAPP, enter "?". Press enter to continue. Do you want to use default settings? (Y/N) (The default settings are whatever you last selected for units and file I/O.) How many components (maximum is 20, enter 0 to stop) ? 5 Enter the name of component 1 ? N2 Enter the name of component 2 ? O2 Enter the name of component 3 ? Ar Enter the name of component 4 ? CO2 Enter the name of component 5 ? H2O Enter the moles of nitrogen? 0.000892430051332573 Enter the moles of oxygen? 0.00043752734545909 Enter the moles of argon? 0.0000200300450676013 Enter the moles of carbon dioxide? 0.00409007248517348 Enter the moles of water? 107.121933077247 For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 288.15,1 2-Phase Flash results at T = 288.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.344128E-07 0.427495 0.427528 .12E+08 oxygen 0.408418E-05 0.409242E-06 0.189368 0.189267 .46E+06 argon 0.186974E-06 0.175174E-07 0.873203E-02 0.872798E-02 .50E+06 carbon dioxide 0.381795E-04 0.312301E-04 0.358131 0.356581 .11E+05 water 0.999949 0.999968 0.162738E-01 0.161498E-01 .16E-01 Molar Basis 1.00000 0.999981 0.194064E-04 Feed Fraction 18.0211 18.0208 34.4373 Molar Mass 0.762087E-03 0.742729E-03 0.998250 Comp. Factor, Z 54.7708 56.1983 0.418133E-01 D, mol/liter -287.426 -287.429 -145.202 H, kJ/mol 64.9348 64.9320 210.196 S, J/mol.K 76.7500 76.7509 32.3969 Cp, J/mol.K 1.26448 1.34988 Cp/Cv 3410.20 305.911 Sound Speed, m/s -0.193114E-01 0.496588 JT, K/bar 11292.3 171.639 Visc., uP 579.549 22.0159 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 293.15,1

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196 Appendix B (Continued) 2-Phase Flash results at T = 293.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.427090E-07 0.429025 0.429076 .10E+08 oxygen 0.408418E-05 0.460568E-06 0.187579 0.187490 .41E+06 argon 0.186974E-06 0.198371E-07 0.865197E-02 0.864843E-02 .44E+06 carbon dioxide 0.381795E-04 0.313748E-04 0.352284 0.350834 .11E+05 water 0.999949 0.999968 0.224604E-01 0.222965E-01 .22E-01 Molar Basis 1.00000 0.999981 0.193178E-04 Feed Fraction 18.0211 18.0208 34.2739 Molar Mass 0.754310E-03 0.735038E-03 0.998342 Comp. Factor, Z 54.3917 55.8178 0.410963E-01 D, mol/liter -286.753 -286.755 -144.235 H, kJ/mol 67.1288 67.1260 210.722 S, J/mol.K 75.6292 75.6301 32.4522 Cp, J/mol.K 1.19949 1.34891 Cp/Cv 3277.46 309.206 Sound Speed, m/s -0.201080E-01 0.483944 JT, K/bar 10054.1 173.823 Visc., uP 588.761 22.4243 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 298.15,1 2-Phase Flash results at T = 298.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.525102E-07 0.429422 0.429493 .82E+07 oxygen 0.408418E-05 0.514592E-06 0.185172 0.185096 .36E+06 argon 0.186974E-06 0.222940E-07 0.854277E-02 0.853976E-02 .38E+06 carbon dioxide 0.381795E-04 0.315055E-04 0.346245 0.344888 .11E+05 water 0.999949 0.999968 0.306178E-01 0.304033E-01 .31E-01 Molar Basis 1.00000 0.999981 0.192772E-04 Feed Fraction 18.0211 18.0208 34.0849 Molar Mass 0.746899E-03 0.727667E-03 0.998416 Comp. Factor, Z 54.0102 55.4377 0.404041E-01 D, mol/liter -286.086 -286.089 -143.669 H, kJ/mol 69.2517 69.2490 211.245 S, J/mol.K 74.5180 74.5188 32.5133 Cp, J/mol.K 1.14872 1.34788 Cp/Cv 3164.64 312.599 Sound Speed, m/s -0.209314E-01 0.474132 JT, K/bar 9000.45 175.802 Visc., uP 597.672 22.8360 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 303.15,1 2-Phase Flash results at T = 303.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.639249E-07 0.428310 0.428401 .67E+07 oxygen 0.408418E-05 0.570542E-06 0.182049 0.181984 .32E+06 argon 0.186974E-06 0.248543E-07 0.839976E-02 0.839729E-02 .34E+06 carbon dioxide 0.381795E-04 0.316181E-04 0.339991 0.338717 .11E+05 water 0.999949 0.999968 0.412514E-01 0.409730E-01 .41E-01 Molar Basis 1.00000 0.999981 0.193005E-04 Feed Fraction 18.0211 18.0208 33.8644 Molar Mass 0.739394E-03 0.720137E-03 0.998470 Comp. Factor, Z 53.6585 55.0934 0.397356E-01 D, mol/liter -285.463 -285.465 -143.617 H, kJ/mol 71.2038 71.2010 211.762 S, J/mol.K 73.5538 73.5546 32.5823 Cp, J/mol.K 1.11477 1.34678 Cp/Cv

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197 Appendix B (Continued) 3076.35 316.121 Sound Speed, m/s -0.216544E-01 0.467549 JT, K/bar 8098.85 177.528 Visc., uP 606.261 23.2528 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 308.15,1 2-Phase Flash results at T = 308.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.769946E-07 0.425229 0.425343 .55E+07 oxygen 0.408418E-05 0.627324E-06 0.178100 0.178049 .28E+06 argon 0.186974E-06 0.274689E-07 0.821784E-02 0.821594E-02 .30E+06 carbon dioxide 0.381795E-04 0.317072E-04 0.333489 0.332291 .11E+05 water 0.999949 0.999968 0.549638E-01 0.546051E-01 .55E-01 Molar Basis 1.00000 0.999981 0.194096E-04 Feed Fraction 18.0211 18.0208 33.6055 Molar Mass 0.729280E-03 0.709913E-03 0.998501 Comp. Factor, Z 53.5200 54.9800 0.390896E-01 D, mol/liter -285.087 -285.089 -144.212 H, kJ/mol 72.4338 72.4311 212.268 S, J/mol.K 73.5108 73.5116 32.6618 Cp, J/mol.K 1.12424 1.34556 Cp/Cv 3052.71 319.808 Sound Speed, m/s -0.215396E-01 0.464722 JT, K/bar 7323.15 178.947 Visc., uP 614.421 23.6766 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 313.15,1 2-Phase Flash results at T = 313.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.916537E-07 0.419638 0.419776 .46E+07 oxygen 0.408418E-05 0.683483E-06 0.173211 0.173173 .25E+06 argon 0.186974E-06 0.300721E-07 0.799164E-02 0.799034E-02 .27E+06 carbon dioxide 0.381795E-04 0.317661E-04 0.326694 0.325564 .10E+05 water 0.999949 0.999967 0.724650E-01 0.720057E-01 .72E-01 Molar Basis 1.00000 0.999980 0.196333E-04 Feed Fraction 18.0211 18.0208 33.2997 Molar Mass 0.719666E-03 0.700076E-03 0.998506 Comp. Factor, Z 53.3690 54.8624 0.384653E-01 D, mol/liter -284.712 -284.715 -145.607 H, kJ/mol 73.6397 73.6369 212.756 S, J/mol.K 73.4833 73.4841 32.7550 Cp, J/mol.K 1.13444 1.34419 Cp/Cv 3029.90 323.706 Sound Speed, m/s -0.214130E-01 0.466334 JT, K/bar 6652.37 179.992 Visc., uP 622.271 24.1101 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 318.15,1 2-Phase Flash results at T = 318.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.107669E-06 0.410902 0.411067 .38E+07 oxygen 0.408418E-05 0.737106E-06 0.167256 0.167232 .23E+06 argon 0.186974E-06 0.325762E-07 0.771537E-02 0.771471E-02 .24E+06 carbon dioxide 0.381795E-04 0.317855E-04 0.319543 0.318473 .10E+05

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198 Appendix B (Continued) water 0.999949 0.999967 0.945847E-01 0.939993E-01 .95E-01 Molar Basis 1.00000 0.999980 0.200118E-04 Feed Fraction 18.0211 18.0208 32.9372 Molar Mass 0.710577E-03 0.690609E-03 0.998482 Comp. Factor, Z 53.2022 54.7404 0.378617E-01 D, mol/liter -284.339 -284.341 -147.979 H, kJ/mol 74.8225 74.8197 213.214 S, J/mol.K 73.4714 73.4722 32.8654 Cp, J/mol.K 1.14539 1.34263 Cp/Cv 3007.94 327.872 Sound Speed, m/s -0.212745E-01 0.473293 JT, K/bar 6069.52 180.587 Visc., uP 629.807 24.5568 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 323.15,1 2-Phase Flash results at T = 323.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.124565E-06 0.398291 0.398487 .32E+07 oxygen 0.408418E-05 0.785728E-06 0.160097 0.160088 .20E+06 argon 0.186974E-06 0.348681E-07 0.738275E-02 0.738280E-02 .21E+06 carbon dioxide 0.381795E-04 0.317532E-04 0.311946 0.310930 .98E+04 water 0.999949 0.999967 0.122284 0.121540 .12E+00 Molar Basis 1.00000 0.999979 0.206030E-04 Feed Fraction 18.0211 18.0208 32.5064 Molar Mass 0.702055E-03 0.681498E-03 0.998424 Comp. Factor, Z 53.0148 54.6139 0.372780E-01 D, mol/liter -283.966 -283.969 -151.523 H, kJ/mol 75.9832 75.9804 213.624 S, J/mol.K 73.4754 73.4762 32.9972 Cp, J/mol.K 1.15716 1.34083 Cp/Cv 2986.83 332.379 Sound Speed, m/s -0.211239E-01 0.486828 JT, K/bar 5560.75 180.639 Visc., uP 637.027 25.0208 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 328.15,1 2-Phase Flash results at T = 328.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.141527E-06 0.380999 0.381229 .27E+07 oxygen 0.408418E-05 0.826198E-06 0.151580 0.151589 .18E+06 argon 0.186974E-06 0.368027E-07 0.698684E-02 0.698769E-02 .19E+06 carbon dioxide 0.381795E-04 0.316511E-04 0.303770 0.302803 .96E+04 water 0.999949 0.999967 0.156664 0.155721 .16E+00 Molar Basis 1.00000 0.999979 0.214936E-04 Feed Fraction 18.0211 18.0208 31.9935 Molar Mass 0.694172E-03 0.672728E-03 0.998326 Comp. Factor, Z 52.7999 54.4829 0.367137E-01 D, mol/liter -283.595 -283.598 -156.454 H, kJ/mol 77.1229 77.1200 213.961 S, J/mol.K 73.4953 73.4962 33.1549 Cp, J/mol.K 1.16979 1.33875 Cp/Cv 2966.57 337.320 Sound Speed, m/s -0.209608E-01 0.508656 JT, K/bar 5114.70 180.042 Visc., uP 643.930 25.5071 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma.

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199 Appendix B (Continued) 333.15,1 2-Phase Flash results at T = 333.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.157290E-06 0.358158 0.358430 .23E+07 oxygen 0.408418E-05 0.854500E-06 0.141528 0.141557 .17E+06 argon 0.186974E-06 0.381947E-07 0.651966E-02 0.652142E-02 .17E+06 carbon dioxide 0.381795E-04 0.314525E-04 0.294815 0.293892 .94E+04 water 0.999949 0.999967 0.198979 0.197782 .20E+00 Molar Basis 1.00000 0.999977 0.228202E-04 Feed Fraction 18.0211 18.0208 31.3818 Molar Mass 0.687051E-03 0.664287E-03 0.998177 Comp. Factor, Z 52.5465 54.3471 0.361680E-01 D, mol/liter -283.225 -283.228 -162.995 H, kJ/mol 78.2425 78.2394 214.188 S, J/mol.K 73.5315 73.5324 33.3432 Cp, J/mol.K 1.18333 1.33636 Cp/Cv 2947.16 342.819 Sound Speed, m/s -0.207850E-01 0.541296 JT, K/bar 4722.05 178.677 Visc., uP 650.515 26.0218 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 338.15,1 2-Phase Flash results at T = 338.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.170017E-06 0.328901 0.329223 .19E+07 oxygen 0.408418E-05 0.865497E-06 0.129726 0.129778 .15E+06 argon 0.186974E-06 0.388077E-07 0.597171E-02 0.597455E-02 .15E+06 carbon dioxide 0.381795E-04 0.311150E-04 0.284758 0.283878 .92E+04 water 0.999949 0.999968 0.250644 0.249120 .25E+00 Molar Basis 1.00000 0.999975 0.248116E-04 Feed Fraction 18.0211 18.0208 30.6511 Molar Mass 0.680907E-03 0.656162E-03 0.997966 Comp. Factor, Z 52.2366 54.2065 0.356408E-01 D, mol/liter -282.856 -282.858 -171.361 H, kJ/mol 79.3429 79.3396 214.254 S, J/mol.K 73.5839 73.5849 33.5673 Cp, J/mol.K 1.19785 1.33363 Cp/Cv 2928.60 349.043 Sound Speed, m/s -0.205963E-01 0.588638 JT, K/bar 4375.04 176.560 Visc., uP 656.778 26.5724 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 343.15,1 2-Phase Flash results at T = 343.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.177209E-06 0.292456 0.292840 .17E+07 oxygen 0.408418E-05 0.852608E-06 0.115916 0.115996 .14E+06 argon 0.186974E-06 0.383384E-07 0.533152E-02 0.533568E-02 .14E+06 carbon dioxide 0.381795E-04 0.305679E-04 0.273056 0.272223 .89E+04 water 0.999949 0.999968 0.313241 0.311289 .31E+00 Molar Basis 1.00000 0.999972 0.278789E-04 Feed Fraction 18.0211 18.0208 29.7758 Molar Mass 0.676138E-03 0.648342E-03 0.997674 Comp. Factor, Z 51.8386 54.0610 0.351317E-01 D, mol/liter -282.487 -282.490 -181.721 H, kJ/mol 80.4252 80.4215 214.085 S, J/mol.K

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200 Appendix B (Continued) 73.6530 73.6541 33.8314 Cp, J/mol.K 1.21342 1.33058 Cp/Cv 2910.91 356.232 Sound Speed, m/s -0.203943E-01 0.657058 JT, K/bar 4067.22 173.651 Visc., uP 662.720 27.1684 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 348.15,1 2-Phase Flash results at T = 348.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.175706E-06 0.248355 0.248816 .14E+07 oxygen 0.408418E-05 0.807485E-06 0.997923E-01 0.999089E-01 .12E+06 argon 0.186974E-06 0.364031E-07 0.458567E-02 0.459148E-02 .13E+06 carbon dioxide 0.381795E-04 0.296847E-04 0.258740 0.257968 .87E+04 water 0.999949 0.999969 0.388527 0.386000 .39E+00 Molar Basis 1.00000 0.999967 0.328354E-04 Feed Fraction 18.0211 18.0208 28.7214 Molar Mass 0.673540E-03 0.640815E-03 0.997272 Comp. Factor, Z 51.2911 53.9105 0.346411E-01 D, mol/liter -282.119 -282.122 -194.119 H, kJ/mol 81.4902 81.4859 213.573 S, J/mol.K 73.7388 73.7401 34.1379 Cp, J/mol.K 1.23010 1.32728 Cp/Cv 2894.09 364.745 Sound Speed, m/s -0.201789E-01 0.757657 JT, K/bar 3793.21 169.625 Visc., uP 668.338 27.8239 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 353.15,1 2-Phase Flash results at T = 353.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.161986E-06 0.196831 0.197385 .12E+07 oxygen 0.408418E-05 0.720114E-06 0.810616E-01 0.812226E-01 .11E+06 argon 0.186974E-06 0.325409E-07 0.372127E-02 0.372913E-02 .11E+06 carbon dioxide 0.381795E-04 0.282225E-04 0.239954 0.239281 .85E+04 water 0.999949 0.999971 0.478432 0.475112 .48E+00 Molar Basis 1.00000 0.999958 0.415005E-04 Feed Fraction 18.0211 18.0207 27.4376 Molar Mass 0.674910E-03 0.633572E-03 0.996706 Comp. Factor, Z 50.4623 53.7548 0.341701E-01 D, mol/liter -281.751 -281.754 -208.291 H, kJ/mol 82.5390 82.5336 212.554 S, J/mol.K 73.8415 73.8432 34.4836 Cp, J/mol.K 1.24796 1.32396 Cp/Cv 2878.14 375.167 Sound Speed, m/s -0.199497E-01 0.910718 JT, K/bar 3548.48 164.386 Visc., uP 673.632 28.5632 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. 358.15,1 2-Phase Flash results at T = 358.150 K and P = 1.00000 bar ----Component--------Feed----Liquid---Vapor-----Phi-----K-nitrogen 0.833055E-05 0.133193E-06 0.139622 0.140262 .10E+07 oxygen 0.408418E-05 0.580861E-06 0.596710E-01 0.598798E-01 .10E+06

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201 Appendix B (Continued) argon 0.186974E-06 0.263063E-07 0.273661E-02 0.274667E-02 .10E+06 carbon dioxide 0.381795E-04 0.256809E-04 0.212908 0.212416 .83E+04 water 0.999949 0.999974 0.585062 0.580665 .59E+00 Molar Basis 1.00000 0.999941 0.587112E-04 Feed Fraction 18.0211 18.0207 25.8425 Molar Mass 0.685034E-03 0.626603E-03 0.995858 Comp. Factor, Z 49.0224 53.5938 0.337217E-01 D, mol/liter -281.383 -281.387 -223.258 H, kJ/mol 83.5729 83.5654 210.774 S, J/mol.K 73.9614 73.9637 34.8491 Cp, J/mol.K 1.26709 1.32111 Cp/Cv 2863.07 388.563 Sound Speed, m/s -0.197064E-01 1.15016 JT, K/bar 3329.19 157.890 Visc., uP 678.600 29.4386 Th. Cond.,mW/m.K (VLE=PRS,PROPS=EXCST) For a list of available options, type ? Otherwise enter command or, if you wish to do a flash calculation, enter T(K) and P(bar) separated by a comma. stop

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202 Appendix C. Matlab code for FCT data regression % Non-Linear Least-Squares Regression of Condenser Tube Counter Current Departure Correction Factor a = 0.0293; b = 0.1655; c = 2.9102; d = 6.1629; e = 4.2518; T_P = Parameters(:,2); T_E = Parameters(:,5); T_X = Parameters(:,6); F_CT = Parameters(:,10); S_CT = ( T_X T_P ) ./ ( T_E T_P ); % Global Variables, Initial Guesses, & Options global S_CT F_CT; parameters =[a b c d e]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global S_CT F_CT; % a = parameters(1,1); % b = parameters(1,2); % c = parameters(1,3); % d = parameters(1,4); % e = parameters(1,5); % Fc_CT = a + b .* S_CT + c .* S_CT .^ 2 d .* S_CT .^ 3 + e .* S_CT .^ 4; % f = sum ( ( Fc_CT F_CT ) .^ 2 ); % Regression & Results, Fc_CT = Calculated Condenser Tube Counter Current Departure Correction Factor x=fminsearch('fun(x)',parameters,OPTIONS); a=x(1,1); b=x(1,2); c=x(1,3); d=x(1,4); e=x(1,5); a = 0.021965104279624; b = 0.275138363079761; c = 2.449155721049220; d = 5.436838343831495; e = 3.869806028493753; Fc_CT = a + b .* S_CT + c .* S_CT .^ 2 d .* S_CT .^ 3 + e .* S_CT .^ 4; r = corr2(F_CT,Fc_CT); r = 0.995860313403891; plot(S_CT(1:170),F_CT(1:170),'m:',S_CT(171:340),F_CT(171:340),'m:',S_CT(341:510),F_CT(341 :510),'m:',S_CT(511:680),F_CT(511:680),'m:',S_CT(681:850),F_CT(681:850),'m:',S_CT(851:102 0),F_CT(851:1020),'m:',S_CT(1021:1190),F_CT(1021:1190),'m:',S_CT(1191:1360),F_CT(1191:136 0),'m:',S_CT(1:170),Fc_CT(1:170),'k-',S_CT(171:340),Fc_CT(171:340),'k',S_CT(341:510),Fc_CT(341:510),'k-',S_CT(511:680),Fc_CT(511:680),'k',S_CT(681:850),Fc_CT(681:850),'k-',S_CT(851:1020),Fc_CT(851:1020),'k',S_CT(1021:1190),Fc_CT(1021:1190),'k-',S_CT(1191:1360),Fc_CT(1191:1360),'k-'),... axis([0 1 0 1]),xlabel('S_C_T'),ylabel('F_C_T'),gtext('^.^.^.^. = mined data'),gtext(' = regression'),gtext('r = +0.9958603')

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203 Appendix D. Matlab code for NEA data regression % Non-Linear Least-Squares Regression of Non-Equilibrium Allowance Ratio a = 1.6836; b = 3.3898; c = 2.7785; d = 0.1399; e = 5.9154; f = 29.3208; T0 = 273.15; Tr = 298.15; T_H = Parameters(:,7); T_E = Parameters(:,5); T_W = Parameters(:,4); R1 = ( T_H + T0 ) ./ Tr; R2 = ( T_W + T0 ) ./ ( T_E + T0 ); % Global Variables, Initial Guesses, & Options global R1 R2; parameters =[a b c d e f]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global R1 R2; % a = parameters(1,1); % b = parameters(1,2); % c = parameters(1,3); % d = parameters(1,4); % e = parameters(1,5); % f = parameters(1,6); % R2c = a .* R1 .^ 2 b .* R1 + c d .* exp ( e .* R1 .^ f ); % f = sum ( ( R2c R2 ) .^ 2 ); % Regression & Results, R2c = Calculated Non-Equilibrium Allowance Ratio x=fminsearch('fun(x)',parameters,OPTIONS); a=x(1,1); b=x(1,2); c=x(1,3); d=x(1,4); e=x(1,5); f=x(1,6); a = 1.346445189163027; b = 2.976010121977662; c = 2.674925159910569; d = 0.099408245751382; e = 11.939078418864948; f = 28.250917259494326; R2c = a .* R1 .^ 2 b .* R1 + c d .* exp ( e .* R1 .^ f ); r = corr2(R2,R2c); r = 0.948793730491143; plot(R1(1:170),R2(1:170),'m:',R1(171:340),R2(171:340),'m:',R1(341:510),R2(341:510),'m:',R 1(511:680),R2(511:680),'m:',R1(681:850),R2(681:850),'m:',R1(851:1020),R2(851:1020),'m:',R 1(1021:1190),R2(1021:1190),'m:',R1(1191:1360),R2(1191:1360),'m:',R1(1:170),R2c(1:170),'k',R1(171:340),R2c(171:340),'k-',R1(341:510),R2c(341:510),'k',R1(511:680),R2c(511:680),'k-',R1(681:850),R2c(681:850),'k',R1(851:1020),R2c(851:1020),'k-',R1(1021:1190),R2c(1021:1190),'k',R1(1191:1360),R2c(1191:1360),'k-'),... axis([1.05 1.20 0.92 1.02]),xlabel('( T_H + 273.15 ) / ( 25 + 273.15 )'),ylabel('( T_W + 273.15 ) / ( T_E + 273.15 )'),gtext('^.^.^.^. = experiment'),gtext(' = regression'),gtext('r = +0.9487937')

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204 Appendix E. Matlab code for H2O data regression % Non-Linear Least-Squares Regression of Water Activity Coefficient b = 0.0020; m = 1.0385; PA = 12.762946317344; PB = 4391.12942196166; PC = 245.367016018802; T_E = Parameters(:,5); P_V = Parameters(:,1); gamma_H2O = Parameters(:,8); P_H2O = exp ( PA PB ./ ( T_E + PC ) ); PoP = P_V ./ P_H2O; % Global Variables, Initial Guesses, & Options global PoP gamma_H2O; parameters =[b m]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global PoP gamma_H2O; % b = parameters(1,1); % m = parameters(1,2); % gammac_H2O = b + m .* PoP; % f = sum ( ( gammac_H2O gamma_H2O ) .^ 2 ); % Regression & Results, gammac_H2O = Calculated Water Activity Coefficient x=fminsearch('fun(x)',parameters,OPTIONS); b=x(1,1); m=x(1,2); b = 0.002040679931641; m = 1.038442953491211; gammac_H2O = b + m .* PoP; r = corr2(gamma_H2O,gammac_H2O); r = 0.999999864855922; plot(PoP(1:170),gamma_H2O(1:170),'m:',PoP(171:340),gamma_H2O(171:340),'m:',PoP(341:510),g amma_H2O(341:510),'m:',PoP(511:680),gamma_H2O(511:680),'m:',PoP(681:850),gamma_H2O(681:85 0),'m:',PoP(851:1020),gamma_H2O(851:1020),'m:',PoP(1021:1190),gamma_H2O(1021:1190),'m:',P oP(1191:1360),gamma_H2O(1191:1360),'m:',PoP(1:170),gammac_H2O(1:170),'k',PoP(171:340),gammac_H2O(171:340),'k-',PoP(341:510),gammac_H2O(341:510),'k',PoP(511:680),gammac_H2O(511:680),'k-',PoP(681:850),gammac_H2O(681:850),'k',PoP(851:1020),gammac_H2O(851:1020),'k-',PoP(1021:1190),gammac_H2O(1021:1190),'k',PoP(1191:1360),gammac_H2O(1191:1360),'k-'),... axis([1 5 1 5]),xlabel('P_V / P_H_2_O'),ylabel('\gamma_H_2_O'),gtext('^.^.^.^. = mined data'),gtext(' = regression'),gtext('r = +0.9999999')

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205 Appendix F. Matlab code for data regression % Non-Linear Least-Squares Regression of Fraction of NCG Molecules Accumulating a = 2.29; PA = 12.762946317344; PB = 4391.12942196166; PC = 245.367016018802; T_E = Parameters(:,5); P_V = Parameters(:,1); psi = Parameters(:,9); P_H2O = exp ( PA PB ./ ( T_E + PC ) ); PoP = P_V ./ P_H2O; % Global Variables, Initial Guesses, & Options global PoP psi; parameters =[a]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global PoP psi; % a = parameters(1,1); % psic = 1 a .* exp ( PoP ); % f = sum ( ( psic psi ) .^ 2 ); % Regression & Results, psic = Calculated Fraction of NCG Molecules Accumulating x=fminsearch('fun(x)',parameters,OPTIONS); a=x(1,1); a = 2.276134765625000; psic = 1 a .* exp ( PoP ); r = corr2(psi,psic); r = 0.991470128181259; plot(PoP(1:170),psi(1:170),'m:',PoP(171:340),psi(171:340),'m:',PoP(341:510),psi(341:510), 'm:',PoP(511:680),psi(511:680),'m:',PoP(681:850),psi(681:850),'m:',PoP(851:1020),psi(851: 1020),'m:',PoP(1021:1190),psi(1021:1190),'m:',PoP(1191:1360),psi(1191:1360),'m:',PoP(1:17 0),psic(1:170),'k-',PoP(171:340),psic(171:340),'k-',PoP(341:510),psic(341:510),'k',PoP(511:680),psic(511:680),'k-',PoP(681:850),psic(681:850),'k',PoP(851:1020),psic(851:1020),'k-',PoP(1021:1190),psic(1021:1190),'k',PoP(1191:1360),psic(1191:1360),'k-'),... axis([1 5 0 1.5]),xlabel('P_V / P_H_2_O'),ylabel('\psi'),gtext('^.^.^.^. = mined data'),gtext(' = regression'),gtext('r = +0.9914701')

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206 Appendix G. Matlab code for HCN2 data regression % Non-Linear Least-Squares Regression of Temperature-Henry's Constant % Data for Nitrogen Obtained from NIST's SUPERTRAPP Program at 1 bar T0 = 273.15; Tr = 298.15; HRl_N2 = 91973; HFl_N2 = 1300; T = [15 20 25 30 35 40 45 50 55 60 65 70 75 80 85]'; HC_N2 = [1.20E+07 1.00E+07 8.20E+06 6.70E+06 5.50E+06 4.60E+06 3.80E+06 3.20E+06 ... 2.70E+06 2.30E+06 1.90E+06 1.70E+06 1.40E+06 1.20E+06 1.00E+06]'; % Global Variables, Initial Guesses, & Options global T HC_N2; parameters =[HRl_N2 HFl_N2]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global T HC_N2; % HR_N2 = parameters(1,1); % HF_N2 = parameters(1,2); % HCc_N2 = HR_N2 .* exp ( HF_N2 .* ( ( 1 ./ ( T + 273.15 ) ) ( 1 ./ 298.15 ) ) ); % f = sum ( ( HCc_N2 HC_N2 ) .^ 2 ); % Regression & Results, HCc_N2 = Calculated Henry's Constant x=fminsearch('fun(x)',parameters,OPTIONS); HR_N2=x(1,1); HF_N2=x(1,2); HR_N2 = 8.0676e+006; HF_N2 = -3.5456e+003; HCc1_N2 = HR_N2 .* exp ( HF_N2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); HCc2_N2 = HRl_N2 .* exp ( HFl_N2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); r = corr2(HC_N2,HCc1_N2); r = 0.999717396687485; plot(T,HC_N2,'mo',T,HCc1_N2,'k-',T,HCc2_N2,'m:'),xlabel('Temperature (C)'),ylabel('HC_N_2 (bar)'),... axis([0 100 0 14e6]),gtext('o = NIST'),gtext(' = regression'),gtext('^.^.^.^. = Sander'),gtext('r = +0.9997174')

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207 Appendix H. Matlab code for HCO2 data regression % Non-Linear Least-Squares Regression of Temperature-Henry's Constant % Data for Oxygen Obtained from NIST's SUPERTRAPP Program at 1 bar T0 = 273.15; Tr = 298.15; HRl_O2 = 43154; HFl_O2 = 1700; T = [15 20 25 30 35 40 45 50 55 60 65 70 75 80 85]'; HC_O2 = [4.60E+05 4.10E+05 3.60E+05 3.20E+05 2.80E+05 2.50E+05 2.30E+05 2.00E+05 ... 1.80E+05 1.70E+05 1.50E+05 1.40E+05 1.20E+05 1.10E+05 1.00E+05]'; % Global Variables, Initial Guesses, & Options global T HC_O2; parameters =[HRl_O2 HFl_O2]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global T HC_O2; % HR_O2 = parameters(1,1); % HF_O2 = parameters(1,2); % HCc_O2 = HR_O2 .* exp ( HF_O2 .* ( ( 1 ./ ( T + 273.15 ) ) ( 1 ./ 298.15 ) ) ); % f = sum ( ( HCc_O2 HC_O2 ) .^ 2 ); % Regression & Results, HCc_O2 = Calculated Henry's Constant x=fminsearch('fun(x)',parameters,OPTIONS); HR_O2=x(1,1); HF_O2=x(1,2); HR_O2 = 3.5881e+005; HF_O2 = -2.2088e+003; HCc1_O2 = HR_O2 .* exp ( HF_O2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); HCc2_O2 = HRl_O2 .* exp ( HFl_O2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); r = corr2(HC_O2,HCc1_O2); r = 0.999564809550137; plot(T,HC_O2,'mo',T,HCc1_O2,'k-',T,HCc2_O2,'m:'),xlabel('Temperature (C)'),ylabel('HC_O_2 (bar)'),... axis([0 100 0 5e5]),gtext('o = NIST'),gtext(' = regression'),gtext('^.^.^.^. = Sander'),gtext('r = +0.9995648')

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208 Appendix I. Matlab code for HCAr data regression % Non-Linear Least-Squares Regression of Temperature-Henry's Constant % Data for Argon Obtained from NIST's SUPERTRAPP Program at 1 bar T0 = 273.15; Tr = 298.15; HRl_Ar = 40074; HFl_Ar = 1300; T = [15 20 25 30 35 40 45 50 55 60 65 70 75 80 85]'; HC_Ar = [5.00E+05 4.40E+05 3.80E+05 3.40E+05 3.00E+05 2.70E+05 2.40E+05 2.10E+05 ... 1.90E+05 1.70E+05 1.50E+05 1.40E+05 1.30E+05 1.10E+05 1.00E+05]'; % Global Variables, Initial Guesses, & Options global T HC_Ar; parameters =[HRl_Ar HFl_Ar]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global T HC_Ar; % HR_Ar = parameters(1,1); % HF_Ar = parameters(1,2); % HCc_Ar = HR_Ar .* exp ( HF_Ar .* ( ( 1 ./ ( T + 273.15 ) ) ( 1 ./ 298.15 ) ) ); % f = sum ( ( HCc_Ar HC_Ar ) .^ 2 ); % Regression & Results, HCc_Ar = Calculated Henry's Constant x=fminsearch('fun(x)',parameters,OPTIONS); HR_Ar=x(1,1); HF_Ar=x(1,2); HR_Ar = 3.8407e+005; HF_Ar = -2.3080e+003; HCc1_Ar = HR_Ar .* exp ( HF_Ar .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); HCc2_Ar = HRl_Ar .* exp ( HFl_Ar .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); r = corr2(HC_Ar,HCc1_Ar); r = 0.999658097432208; plot(T,HC_Ar,'mo',T,HCc1_Ar,'k-',T,HCc2_Ar,'m:'),xlabel('Temperature (C)'),ylabel('HC_A_r (bar)'),... axis([0 100 0 6e5]),gtext('o = NIST'),gtext(' = regression'),gtext('^.^.^.^. = Sander'),gtext('r = +0.9996581')

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209 Appendix J. Matlab code for HCCO2 data regression % Non-Linear Least-Squares Regression of Temperature-Henry's Constant % Data for Carbon Dioxide Obtained from NIST's SUPERTRAPP Program at 1 bar T0 = 273.15; Tr = 298.15; HRl_CO2 = 1652; HFl_CO2 = 2400; T = [15 20 25 30 35 40 45 50 55 60 65 70 75 80 85]'; HC_CO2 = [1.10E+04 1.10E+04 1.10E+04 1.10E+04 1.10E+04 1.00E+04 1.00E+04 9.80E+03 ... 9.60E+03 9.40E+03 9.20E+03 8.90E+03 8.70E+03 8.50E+03 8.30E+03]'; % Global Variables, Initial Guesses, & Options global T HC_CO2; parameters =[HRl_CO2 HFl_CO2]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global T HC_CO2; % HR_CO2 = parameters(1,1); % HF_CO2 = parameters(1,2); % HCc_CO2 = HR_CO2 .* exp ( HF_CO2 .* ( ( 1 ./ ( T + 273.15 ) ) ( 1 ./ 298.15 ) ) ); % f = sum ( ( HCc_CO2 HC_CO2 ) .^ 2 ); % Regression & Results, HCc_CO2 = Calculated Henry's Constant x=fminsearch('fun(x)',parameters,OPTIONS); HR_CO2=x(1,1); HF_CO2=x(1,2); HR_CO2 = 1.0915e+004; HF_CO2 = -445.1906; HCc1_CO2 = HR_CO2 .* exp ( HF_CO2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); HCc2_CO2 = HRl_CO2 .* exp ( HFl_CO2 .* ( ( 1 ./ ( T + T0 ) ) ( 1 ./ Tr ) ) ); r = corr2(HC_CO2,HCc1_CO2); r = 0.966663199694565; plot(T,HC_CO2,'mo',T,HCc1_CO2,'k-',T,HCc2_CO2,'m:'),xlabel('Temperature (C)'),ylabel('HC_C_O_2 (bar)'),... axis([0 100 0 1.2e4]),gtext('o = NIST'),gtext(' = regression'),gtext('^.^.^.^. = Sander'),gtext('r = +0.9666632')

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210 Appendix K. Matlab code for PH2O sat data regression % Non-Linear Least-Squares Regression of Temperature-Saturated Pressure % Data for Water Obtained from NIST's SUPERTRAPP Program at 1 bar PAl = 12; PBl = 3993; PCl = 234; T = [15 20 25 30 35 40 45 50 55 60 65 70 75 80 85]'; P_H2O = [1.60E-02 2.20E-02 3.10E-02 4.10E-02 5.50E-02 7.20E-02 9.50E-02 1.20E-01 ... 1.60E-01 2.00E-01 2.50E-01 3.10E-01 3.90E-01 4.80E-01 5.90E-01]'; % Global Variables, Initial Guesses, & Options global T P_H2O; parameters =[PAl PBl PCl]; OPTIONS(1)=0; % The Fun Function ( An m-File ) % function f=fun(parameters); % global T P_H2O; % PA = parameters(1,1); % PB = parameters(1,2); % PC = parameters(1,3); % PPC = exp ( PA ( PB ./ ( T + PC ))); % f = sum ( ( PPC P_H2O ) .^ 2 ); % Regression & Results, PsatPC = Calculated Saturated Pressure x=fminsearch('fun(x)',parameters,OPTIONS); PA=x(1,1); PB=x(1,2); PC=x(1,3); PA = 12.7629; PB = 4.3911e+003; PC = 245.3670; Pc1_H2O = exp ( PA ( PB ./ ( T + PC ))); Pc2_H2O = exp ( PAl ( PBl ./ ( T + PCl ))); r = corr2(P_H2O,Pc1_H2O); r = 0.999963505331023; plot(T,P_H2O,'mo',T,Pc1_H2O,'k-',T,Pc2_H2O,'m:'),xlabel('Temperature (C)'),ylabel('P^s^a^t_H_2_O (bar)'),... axis([0 100 0 0.7]),gtext('o = NIST'),gtext(' = regression'),gtext('^.^.^.^. = Geankoplis'),gtext('r = +0.9999635')

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211 Appendix L. Sample TK Solver code for data mining

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228 Appendix M. Sample TK Solver code for model simulation

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252 Appendix N. Experimental record Number Date Start Stop t (minutes) PEi (bar) VS i (Gallon) VS f (Gallon) MS (LPM) TIC (C) QE (ml) 1 4/24/09 3:20:00 PM 6:20:00 PM 180 0.140 40 17 0.48 50 30 2 4/25/09 1:15:00 PM 4:15:00 PM 180 0.140 40 17 0.48 50 15 3 4/26/09 2:09:00 PM 5:09:00 PM 180 0.140 40 17 0.48 50 36 4 4/27/09 12:55:00 PM 3:55:00 PM 180 0.140 40 18 0.46 60 345 5 4/28/09 12:42:00 PM 3:42:00 PM 180 0.140 40 18 0.46 60 350 6 4/29/09 12:37:00 PM 3:37:00 PM 180 0.140 40 18 0.46 60 360 7 4/30/09 1:17:00 PM 4:17:00 PM 180 0.140 40 19 0.44 70 2030 8 5/1/09 2:49:00 PM 5:49:00 PM 180 0.140 40 19 0.44 70 2050 9 5/2/09 1:07:00 PM 4:07:00 PM 180 0.140 40 19 0.44 70 2030 10 5/3/09 1:37:00 PM 4:37:00 PM 180 0.140 40 22 0.38 80 4880 11 5/4/09 1:17:00 PM 4:17:00 PM 180 0.140 40 22 0.38 80 4720 12 5/5/09 1:47:00 PM 4:47:00 PM 180 0.140 40 22 0.38 80 4560 13 5/15/09 1:13:00 PM 4:13:00 PM 180 0.140 40 7 0.69 50 13 14 5/16/09 1:04:00 PM 4:04:00 PM 180 0.140 40 7 0.69 50 25 15 5/17/09 2:24:00 PM 5:24:00 PM 180 0.140 40 7 0.69 50 27 16 5/18/09 12:24:00 PM 3:24:00 PM 180 0.140 40 8 0.67 60 190 17 5/19/09 12:30:00 PM 3:30:00 PM 180 0.140 40 8 0.67 60 205 18 5/20/09 12:59:00 PM 3:59:00 PM 180 0.140 40 8 0.67 60 200 19 5/21/09 12:24:00 PM 3:24:00 PM 180 0.140 40 9 0.65 70 1310 20 5/22/09 1:24:00 PM 4:24:00 PM 180 0.140 40 9 0.65 70 1180 21 5/23/09 1:39:00 PM 4:39:00 PM 180 0.140 40 9 0.65 70 1145 22 5/24/09 2:42:00 PM 5:42:00 PM 180 0.140 40 13 0.57 80 4995 23 5/25/09 1:04:00 PM 4:04:00 PM 180 0.140 40 13 0.57 80 4770 24 5/26/09 1:04:00 PM 4:04:00 PM 180 0.140 40 13 0.57 80 4365

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253 Appendix O. Experimental equipment specifications

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258 Appendix O (Continued)

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259 Appendix O (Continued)

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260 Appendix O (Continued)

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261 Appendix O (Continued)

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262 Appendix O (Continued)

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263 Appendix O (Continued)

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264 Appendix O (Continued)

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265 Appendix O (Continued)

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266 Appendix P. Error analysis Experimental data are directly measured a nd entail specific er rors provided by the manufacture of the measuring devices. In addition, physical properties determined by empirical relations also entail certain errors given by the developers of those correlations. Pseudoexperimental data are ge nerated using the experimental data and the empirically determined physical properties; consequently they entail indirect errors that are propagations of the direct errors of the e xperimental data and the physical properties. The errors associated with the previously mentioned devices a nd correlations are given in Table 12 while formulas to calculate th e propagation of erro r as functions of directly measured errors are given in Table 13. The rules of Table 13 can be multiplexed to represent the error of other vari ations as will be seen shortly. Table 12. Device and correlation errors Correlation Device ( g / cm3 ) H ( J / g ) TE ( C ) PE ( bar ) FI ( LPM ) QE ( cm3 ) Error 35 10-6 0.045 1.000 0.005 0.045 0.200 Table 13. Propagation of error rules Relationship Compounded Error Z = X + Y Z 2 = X 2 + Y 2 Z = X Y Z 2 = X 2 + Y 2 Z = X Y ( Z / Z ) 2 = ( X / X ) 2 + ( Y / Y ) 2 Z = X / Y ( Z / Z ) 2 = ( X / X ) 2 + ( Y / Y ) 2 Z = Xn ( Z / Z ) = n ( X / X ) Z = ln ( X ) Z = ( X / X ) Z = exp ( X ) ( Z / Z ) = X

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267 Many elements contribute to error in measurements; however the average error values given above in Table 12 are considered inclusive of all errors since experiments were conducted at matching laboratory condi tions and because a tr ue measurement can never be claimed. The dynamic errors of th e timevarying system variables that were graphically presented in CHAPTER 7 as error bands were com puted using the values of Table 12 and the rules of Table 13 to generate the following perturbations 045 0.FI (144) 2 0.QE (145) 005 0.PE PV (146) 1 TE T T TX W E (147) 610 35 E C H P (148) 045 0.H H H H HE H X P (149) TE T 2 (150) H H 2 (151) 2 1 2 2 2 FI MFI P P MP P (152) 2 1 2 2 2 FI MFI H H MH H (153) 2 1 2 2 2 FI MFI C C M MC C E (154)

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268 2 1 2 2 2 QE MQE C C MC C (155) 2 1 2 2 2 X H H P M H Q QH H M QP H H (156) 2 1 2 2 2 T T U I U Q AX SC SC SC T SC H Q SC AX H SC (157) 2 1 2 2 2 C M H Q PECM Q PECC H (158) 2 1 2 2 2100 100 C E T P X T CT T T TC (159) 2 1 2 2 2100 100 P H H P X H RH H H HR (160) 2 1 2 2 2 2 2100 100 H H H M E H E M RH M H MH H E E T (161) The above perturbations were included in the data mining code presented earlier to generate static error valu es for the primary variables and dynamic error values for the derived variables. The error va lues were then linked to their prospective variables to generate a translucent patch of error bars, or error bands around their profiles as was presented earlier in CHAPTER 7

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ABOUT THE AUTHOR Mohammad Abutayeh is originally from Kafr Sur, Palestine: a small West Bank village approximately thirty miles north of Je rusalem. He came to Am erica in search of a better life almost twenty years ago and has been calling it home since. He received a Bachelor of Science in Ch emical Engineering from the University of South Florida in 1997 with Cum Laude di stinction. He continued on obtaining his Master of Science in Chemical Engineering fr om the University of South Florida in 1999 where he wrote a thesis on predicting the citr ate solubleloss of th e dihydrate process. He then worked in several engineering areas designing process control systems, optimizing unit operations, customizing proce ss equipment, administering US patent laws, and many other functions. In addition, he successfully completed the Fundamentals of Engineering examination of the Florida Board of Professional Engineers, attended numerous seminars, and acquired several other certifications. He published several journa l articles and presented his thesis and dissertation research findings at national and internati onal venues. He graduated with a Doctor of Philosophy in Chemical Engineering from the University of South Florida in 2010 where he wrote a dissertation on simulating the passive vacuum solar flash desalination.