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A Cyclic electrodialysis process : investigation of closed systems Bass, Dieter 1976-02-21

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A CYCLIC ELECTRODIALYSIS PROCESS Investigation of Open Systems by MOHAMMED ELAMIEN ABU-GOUKH B.Sc. (Hons.), University of Khartoum, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1976 c\ Mohammed Elamlen Abu-Goukh, 1976 In presenting this thesis in partial fulfilment of the requirements f< an advanced degree at the University of British Columbia, I agree tha the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CK^AYU^AX IMtoLyw^ The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ABSTRACT Cyclic electrodialysis is a novel separation process in which a modified membrane stack is operated in a periodic unsteady-state manner. Repeated reversals of polarity could avoid the main problems encountered in conventional electrodialysis; fouling and scale formation on the membranes. In cyclic electrodialysis the standard electrodialysis stack is converted into an adsorption-desorption stack with only one set of flow channels, the other set being replaced by storage compartments. Thesr compartments are in the form of three-layer membranes consisting of an anion and a cation selective membrane enclosing a core of non- selective material. The depleted and enriched products are produced successively in the single set of channels instead of simultaneously in adjacent channels. The process is potentially applicable for commercial desalination of brackish water to make it potable, to remove harmful ions from discharge waters, or to concentrate ionic solutions for recovery of valuable materials. Previously reported experiments with aqueous NaCl solutions in a closed (batch) system showed that a large separation factor could be obtained in cyclic electrodialysis. Batch operation is somewhat analogous to total reflux in distillation. The present work extends the earlier work to potentially more useful operating conditions in which feed is supplied and product removed. A constant-rate model has been developed for the process and used extensively throughout the work as a simple and efficient tool to compare ii various operating cycles and modes of operation. Scattered articles in the literature on the resistance of an electrodialysis stack have been compiled to develop a stack resistance model. Good agreement was obtained between the model predictions and measured values of resistance. Experimental apparatus is described and the effects of the following eight system parameters are reported: (i) Demineralizing path length (ii) Production rate (iii) Pause time (iv) Applied voltage (v) Initial concentration (vi) No-pause operation (vii) Pure-pause operation (vii) Semi-symmetric operation Large separations were achieved for asymmetrical paused operation with long demineralizing path, long pause time, high applied voltage, low feed concentration and small production rate. Despite the strong trade-off between production rate and separation, a separation factor as high as 50 was obtained at the highest production rate used. This value is higher than that obtained in commercial plants currently in use. The process looks promising and is worth further consideration. iii TABLE OF CONTENTS Page ABSTRACT ii LIST OF TABLES viiLIST OF FIGURES xiiACKNOWLEDGEMENTS xx Chapter 1 INTRODUCTION AND GENERAL ........ 1 2 THEORY AND REVIEW 5 2.1 Desalting Processes .... 5 2.2 Some Economic Aspects of Selective and State-Change Processes 7 2.3 Electrodialysis 10 2.3.1 Electrodialysis Stack 14 2.3.2 Stack Size and Capacity . . . . . 16 2.4 Membrane Technology 19 2.4.1 Membrane Selectivity 21 2.4.2 Membrane Polarization 5 2.4.3 Scaling and Fouling of Membranes 30 2.5 Process Efficiency 32 2.5.1 Principal Energy Sinks 32.6 Variants of Electrodialysis 5 2.6.1 Transport Depletion 32.6.2 Electrogravitational Demineralization .... 38 iv Chapter Page 2.7 Cyclic Processes . 40 2.7.1 Electrosorption . . . 40 2.7.2 Cyclic Electrodialysis 42.7.3 Parametric Pumping 3 2.7.4 Cyclic Electrodialysis and Parametric Pumping . 46 3 SYSTEM MODELS 48 3.1 Stack Resistance Models 48 3.1.1 Non-ohmic Analysis . . 48 3.1.2 Ohmic Analysis 66 3.2 Mass Transfer Models 9 3.2.1 Equilibrium Model 71 3.2.2 Rate Models . 73 3.2.3 Comment on Constant-Rate Model' , . . 92 4 THE CYCLIC ELECTRODIALYSIS PROCESS - OBJECTIVES, TECHNIQUES AND APPARATUS . . , . . 93 4.1 Objectives of the Program ..... 93 4.2 Single Stack Operation .... 94 4.3 Back-to-Back Stack Configuration ..... 97 4.3.1 Open System Operation of a back-to-back configuration 94.4 Apparatus and Operation 114 4.4.1 Details of an ED Cell Design 118 4.5 Measuring and Recording 122 4.5.1 Concentrations, Current, Voltage and pH measurements4.5.2 Recording 127 5 EXPERIMENTAL RESULTS and DISCUSSION 128 v Chapter Page 5.1 Data-Collection 128 5.2 Experimental Designation 129 5.3 Main Survey Tables 130 5.4 Parameters and Modes of Operation Investigated .... 133 5.4.1 Effect of Demineralizing Path Length 147 5.4.2 Effect of Production Rate 172 5.4.3 Effect of Pause Time 173 5.4.4 Effect of Applied Voltage 192 5.4.5 Effect of Initial Concentration 208 5.4.6 No-Pause Operation , . . . . 208 5.4.7 Pure-Pause Operation . 223 5.4.8 Semi-Symmetric Operation 225.5 Comment on pH-Changes 227 5.6 Temperature Measurements » . . . . 243 5.7 Pressure Drop Measurements , . . . , 243 5.8 Probe Voltage, Apparent Resistance and Current Consumption 245.9 Voltage Efficiency 269 5.10 Current Density and Efficiency 265.11 Comments on Stack Resistance Models . 273 5.12 Comparison with Previous Work in Closed System .... 284 5.13 Reproducibility ......... 285 6 CONCLUSIONS and RECOMMENDATIONS ..... 288 NOMENCLATURE ..... 293 REFERENCES ..... 298 APPENDICES 304 vi Appendix Page A ELECTRODE SYSTEM ..... 304 A.l Electrodes Materials . , 304 A.2 Electrodes Reactions 30A.3 Electrode Polarization Effect on Power Consumption , . , 309 A. 4 Electrode Flow System . . , , 311 B THE CURRENT EFFICIENCY  313 C NERNST IDEALIZED MODEL OF WALL LAYERS 319 C.l The Flow Field in an Electrodialysis Cell 319 C.2 Nernst Model 31C.3 Some Derivations of the Model 320 C.3.1 Generalized Theory of Coupled Processes ......... 320 C.3.2 Ionic Fluxes 323 C.4 Wall Layer Thickness . . •. , 327 C.5 Conclusion ....... 328 D GRAPHICAL SOLUTION OF CONSTANT-RATE MODEL .......... 329 E COMPUTER PROGRAMS ..... 338 F THEORETICAL AND PRACTICAL ENERGY REQUIREMENTS FOR A DESALTING PROCESS ...... 359 F.l Minimum Work of Separation , 359 F.2 Practical Energy Requirements ...... 361 vii LIST OF TABLES Table Page I Classification of Main Desalting Processes ....... 6 II Total Number and Capacity of Desalting Plants exceeding 95 nrVday 8 III Large Electrodialysis Plants - Over 100,000 gpd .... 9 IV Technical Details of Benghazi (Libya) and Siesta Key (Florida) Electrodialysis Plants 18 V Reported Properties of Ion-Exchange Membranes ...... J.22 VI Conductivity and NaCl Concentration Ranges of BECKMAN Conductivity Cells (EL-VDJ) 323 VII Values of n in Experimental Designations Rna and Mna . , . . 131 VIII Values of a in Experimental Designations Rna and Mna ........ > 3 2 IX Compilation of Experiments with initial concentration (Cq) of 2000 ppm; 4-cell columns 134 X Compilation of Experiments with initial concentration (Cq) of 500 ppm; 4-cell columns 136 XI Compilation of Experiments with initial concentration (Cq) of 4000 ppm; 4-cell columns 138 XII Compilation of Experiments with initial concentration (Cq) of 2000 ppm; 8-cell columns 139 XIII Compilation of Experiments with initial concentration (Cq) of 500 ppm; 8-cell columns 141 XIV Compilation of. Experiments with initial concentration (Cq) of 4000 ppm; 8-cell columns 143 XV Duplicate Experiments to Test Reproducibility -Group R 145 viii Table Page XVI Duplicate Experiments to Test Reproducibility -Group M 146 XVII Effect of Production Rate on Separation; 4-cell columns; CQ - 500 ppm 148 XVIII Effect of Production Rate on Separation; 4-cell columns; Cq - 2000 ppm 150 XIX Effect of Production Rate on Separation; 4-cell columns; Cq - 4000 ppm 152 XX Effect of Production Rate on Separation; 8-cell columns; C - 500 ppm „ . 154 o XXI Effect of Production Rate on Separation; 8-cell columns; Cq - 2000 ppm 156 XXII Effect of Production Rate on Separation; 8-cell columns; Cq = 4000 ppm 158 XXIII Effect of Demineralizing Path Length on Separation; CQ = 500 ppm; A<J> = 20 V 160 XXIV Effect of Demineralizing Path Length on Separation; Cq = 500 ppm; A<|> = 30 V 162 XXV Effect of Demineralizing Path Length on Separation; Cq = 2000 ppm; A<j> = 20 V 164 XXVI Effect of Demineralizing Path Length on Separation; Cq = 2000 ppm; A<|> = 30 V 166 XXVII Effect of Demineralizing Path Length on Separation; Cq = 4000 ppm; A<j> = 20 V 168 XXVIII Effect of Demineralizing Path Length on Separation; CQ = 4000 ppm; A<|> = 30 V 170 XXIX Effect of Pause Time on Separation; 4-cell columns; C = 500 ppm 174 o XXX Effect of Pause Time on Separation; 4-cell columns; CQ = 2000 ppm 176 XXXI Effect of Pause Time on Separation; 4-cell columns; CQ - 4000 ppm 178 ix Table Page XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIV XLV XLVI XLVII Effect of Pause Time on Separation; 8-cell columns; Cq = 500 ppm 180 Effect of Pause Time on Separation; 8-cell columns; Cq = 2000 ppm 182 Effect of Pause Time on Separation; 8-cell columns; Cq = 4000 ppm 184 Effect of Pause Time on Separation; C = 500 ppm; Group M7 ° 186 Effect of Pause Time on Separation; C = 2000 ppm; Group M3 ° 188 Effect of Pause Time on Separation; C =; 4000 ppm; Group Mil ° 190 Effect of Applied Voltage on Separation; 4-cell columns; Cq = 500 ppm 193 Effect of Applied Voltage on Separation; 4-cell columns; Cq = 2000 ppm 195 Effect of Applied Voltage on Separation; 4-cell columns; Cq = 4000 ppm 197 Effect of Applied Voltage on Separation; 8-cell columns; Cq = 500 ppm 199 Effect of Applied Voltage on Separation; 8-cell columns; Cq = 2000 ppm 201 Effect of Applied Voltage on Separation; 8-cell columns; Cq - 4000 ppm 203 Effect of Feed Concentration on Separation; 4-cell columns; P.R. = 20 c.c./cycle 209 Effect of Feed Concentration on Separation; 4-cell columns; P.R. - 50 c.c./cycle 211 Effect of Feed Concentration on Separation; 4-cell columns; P.R. = 100 c.c./cycle 213 Effect of Feed Concentration on Separation; 8-cell columns; P.R. = 25 c.c./cycle 215 Table Page XLVIII Effect of Feed Concentration on Separation; 8-cell columns; P.R. ~ 50 c.c./cycle 217 XLIX Effect of Feed Concentration on Separation; 8-cell columns; P.R. = 100 c.c./cycle 219 L Comparison of Pause and No-Pause Operations 221 LI Comparison of Pure Pause with Mixed Mode Operations; Cq = 2000 ppm 224 LII Semi-Symmetric Operation; Cq = 2000 ppm . 226 LIII Comparison of Semi-Symmetric and Asymmetric Operations 228 LIV Average Product Concentrations in Arbitrary Units obtained under Semi-Symmetric and Asymmetric Operations 241 LV pH - Changes for some ED runs at various feed concentrations and operating conditions ... 242 LVI Pressure Drop Measurements 244 LVII Average Probe Voltage (Stack Voltage) over a complete cycle for various feed concentration and Applied Voltages 246 LVIII Variation of Probe Voltage along the Demineralization path during the depletion half cycle for various feed concentrations; A<|> = 30 V 253 LIX Variation of Current Consumption along the Demineralization Path during the depletion half cycle at various applied voltages; Cq - 2000 ppm 255 LX Variation of Current Consumption along the Demineralization Path during the depletion half cycle at various feed concentrations; A<j> = 30 V . 257 LXI Variation of Probe Voltage, Current, Resistance and Power Consumption along the demineralizing path; CQ - 500 ppm 259 LXII Variation of Probe Voltage, Current, Resistance and Power Consumption along the demineralizing path; Cq - 2000 ppm 260 xi Table Page LXIII Variation of Probe Voltage, Current, Resistance and Power Consumption along the demineralizing path; Cq = 4000 ppm 261 LXIV Effect of Initial Concentration on the Equivalent Resistance of ED Stack 262 LXV Variation of ED Stack resistance along the demineralizing path during the depletion half cycle at various applied voltages; CQ - 500 ppm 264 LXVI Voltage Efficiency 270 LXVII Overall Current Efficiency 272 LXVIII Equivalent Conductance and Diffusivity of aqueous sodium chloride solutions 275 LXIX Distribution of the predicted resistance of an ED stage between its resistive elements 280 LXX Values of Local Average Concentration, C and Measured Stage Resistance 282 LXXI Reproducibility - Group R; 4-cell columns 286 LXXII Reproducibility - Group M; 8-cell columns ....... 287 xii LIST OF FIGURES Figure Page 1 Comparison of energy costs for distillation and electrodialysis 11 2 Multiple-chamber alternate membrane electrodialysis cell 3 3 Exploded view of components in an electro-membrane stack 15 4 Dependence of counterion transport numbers and permselectivity upon external concentration 23 5a Ion transport across a permselective membrane 26 5b Concentration profile across a permselective membrane in an electrodialysis stack .... 26 6 The cation-neutral transport depletion process ..... 36 7 Electrogravitation with cation-selective membranes 39 8 Electrosorption Process . . 41 9a Diagram of column for direct mode P.P 45 9b Velocity and temperature at a point in the bed 4as a function of time 10 Simplified concentration profiles in an electrodialysis cell pair and the analogous electrical circuit .... 50 11 Diagram of the concentration profile and the diffusion layer on the dialysate side of an electrodialysis ion exchange membrane ..... 52 12a The concentration profiles (exponential) of both the dialysate and brine streams 55 12b The material balances of both the dialysate and brine streams 5xiii Figure • Page 13a Concentration distribution in a cation-exchange membrane. ZrCr is the concentration of fixed J charge in membrane 59 13b Schematic potential distribution through a cation-exchange membrane 59 14 Back emf due to concentration and polarization 63 15 Differential section of column , . . 70 16 Series connection of ED modules to approximate constant-rate operation , . , . , 74 17 Concentration profiles predicted by constant-rate model with equal ratesj continuous cyclic displacement of fluid and mass transfer ........ 77 18 Concentration profiles - interrupted current cycle . . . '. 80 19 Concentration profiles - interrupted flow cycle  84 20 . Concentration profiles predicted by constant-rate model-continuous cyclic displacement of fluid and mass transfer. The mass transfer cycle is 90° out-of-phase with the displacement cycle 36 21 Back-to-back operation of two units 88 22 Batch operation of cyclic electrodialysis process 94 23 Back-to-back operation of two cells 97 24 Developing concentration profile - two cells operating back-to-back in a closed system 98 25 Flow connections and valve timing sequence for symmetric operation ..... 100 26 Developing concentration profile, symmetric operation of an open system 103 27 Flow connections and valve timing sequence for semi-symmetric operation . . 105 28 Developing concentration profile, semi-symmetric operation of an open system 109 xiv Figure Page 29 Flow connections and valve timing sequence for asymmetric operation 110 30 Developing concentration profile, asymmetric operation of an open system 112 31 Electrodialysis Unit and Control Equipment . 114 32 Electrodialysis Cells in Back-to-Back Operation . . , . 115 33 A single stage with its two end-frames 118 34 A triple membrane-frame-spacer assembly , , . 118 35 Construction of single membrane-spacer assembly for an ED cell 119 36 Schematic diagram showing solution flows and instrumentation (Asymmetric operation) » 120 37 Current monitoring circuit . , . 125 38 Effect of production rate on separation. 4-cell column; initial cone. CQ - 500 ppm ' 149 39 Effect of production rate on separation. 4-cell column; initial cone. CQ = 2000 ppm 151 40 Effect of production rate on separation. 4-cell column; initial cone. CQ = 4000 ppm , . 153 41 Effect of production rate on separation. 8-cell column; initial cone. CQ = 500 ppm 155 42 Effect of production rate on separation. 8-cell column; initial cone. CQ = 2000 ppm 157 43 Effect of production rate on separation. 8-cell column; initial cone. CQ = 4000 ppm . 159 44 Effect of demineralizing path length on separation. CQ * 500 ppm, Acfi = 20 V 161 45 Effect of demineralizing path length on separation. CQ = 500 ppm, A<j> = 30 V 163 46 Effect of demineralizing path length on separation. CQ = 2000 ppm, A<() = 20 V 165 47 Effect of demineralizing path length on separation. Cn = 2000 ppm, A<j> = 30 V 167 xv Figure Page 48 Effect of demineralizing path length on separation. CQ a 4000 ppm, A<j> = 20 V '. 169, 49 Effect of demineralizing path length on separation. Cq = 4000 ppm, A<|> = 30 V 171 50 Effect of pause time on separation; 4-cell column; initial cone. CQ - 500 ppm 175 51 Effect of pause time on separation; 4-cell column; initial cone. Cq = 2000 ppm 177 52 Effect of pause time on separation; 4-cell column; initial cone. Cq * 4000 ppm 179 53 Effect of pause time on separation; 8-cell column; initial cone. Cq = 500 ppm 181 54 Effect of pause time on separation; 8-cell column; initial cone. CQ - 2000 ppm ........... 183 55 Effect of pause time on separation; 8-cell column; initial cone. Cq - 4000 ppm . . . . 185 56 Effect of pause time on separation. C = 500 ppm. Group M7 ° » 87 57 Effect of pause time on separation. C = 2000 ppm; Group M3 ° . 189 58 Effect of pause time on separation. C = 4000 ppm. Group Mil ° 191 59 Effect of applied voltage on separation. 4-cell column; initial cone. Cq - 500 ppm 194 60 Effect of applied voltage on separation. 4-cell column; initial cone. Cq = 2000 ppm ......... 196 61 Effect of applied voltage on separation; 4-cell column; initial cone. Cq = 4000 ppm - 198 62 Effect of applied voltage on separation. 8-cell column; initial cone. CQ = 500 ppm 200 63 Effect of applied voltage on separation. 8-cell column; initial cone. CQ - 2000 ppm 202 64 Effect of applied voltage on separation. 8-cell column; initial cone. CQ - 4000 ppm 204 xvi Figure 65 Variation of individual cost items making up the total processing cost Pace 207 66 Effect of feed concentration (CQ) on separation. 4-cell column; production rate -20 c.c./cycle 210 67 Effect of feed concentration (CQ) on separation. 4-cell column; production rate -50 c.c./cycle . 212 68 Effect of feed concentration (CQ) on separation. 4-cell column; production rate = 100 c.c./cycle 214 69 Effect of feed concentration (CQ) on separation. 8-cell column; production rate = 25 c.c./cycle , . . > 216 70 Effect of feed concentration (CQ) on separation. 8-cell column; production rate = 50 c.c./cycle .  . 218 71 Effect of feed concentration (CQ) on-separation. 8-cell column; production rate ~ 100 c.c./cycle . . , . 220 72 Comparison of pause and no-pause operations. 8-cell column; production rate - 50 c.c./cycle. .... 222 73 Pure pause operation (no power during circulation). 8-cell column; production rate - 50 c.c.cycle. Initial concentration CQ - 2000 ppm ....... ... 225 74 Comparison of semi-symmetric and asymmetric operations, 8-cell column; production rate - 100 c.c./cycle. Feed concentration Cq - 2000 ppm 229 75 Developing concentration profile; asymmetric operation of an open system with mass transfer during both pause and displacement periods. Dialysate product = brine product = 1/3 cell volume/cycle .... 234 76 Developing concentration profile; semi-symmetric operation of an open system with mass transfer during both pause and displacement periods. Dialysate product = brine product = 1/3 cell volume/cycle .... 240 77 Pressure drop vs. flow rate. 8-Stage ED stack ...... 245 xvii Figure 78 79 80 81 82 83 84 85 86 87 88 89 Page Average stack voltage (probe voltage) vs. applied voltage for various feed concentrations. Pause time T = 45 sec. Exp. group M3, H7 and Mil .... 247 Traces of probe voltage recording during a cycle at four points along the demineralizing path. Exp. M7F 248 Traces of current recording during a cycle at different points along the demineralizing path. Exp. M7F 249 Traces of probe voltage recording during a cycle at four points along the demineralizing path. Exp. M11F 250 Traces of current recording during a cycle at four points along the demineralizing path. Exp. M11F 251 Variation of stack voltage (probe voltage) along the demineralizing path for various feed concentrations. Exp. M7F and M11F 254 Variation of current consumption along the demineralization path at various applied voltages Cq = 2000 ppm, Exp. M3B, M3F and M3G 256 Variation of current consumption along the demineralization path at various feed concentrations. A* = 30 V; Exp. M3F, M7F and M11F 258 Effect of Initial Concentration on equivalent resistance of ED stack 263 Variation of stack resistance along the demineralization path during the depletion half cycle at various applied voltages. CQ - 500 ppm; Exp. M7F and M7G . Variation of apparent ED stack resistance along the demineralization path during the depletion half cycle using semi-log scale. A(J> = 30 V; Exp. M3F, M7F and M11F 265 267 Variation of apparent ED stack resistance along the demineralization path using semi-log scale CQ = 2000 ppm, Exp. M3B, M3F and M3G 268 xviii Figure Page 90 Equivalent conductance of aqueous sodium chloride solutions at 25°C 276 91 Diffusivity of aqueous sodium chloride solutions at 25°C 277 92 Discrepancy between predicted and measured value of an ED stage , , . 281 93 Variation of apparent resistance of an ED stage with the reciprocal of the average product concentration . . 283 xix ACKNOWLEDGEMENT I wish to thank Dr. D.W. Thompson, under whose direction this investigation was undertaken, for his unfailing help, invaluable ideas and encouragement in all stages of this work. Also thanks are due to the faculty and staff of Chemical Engineering Department of the University of British Columbia for their willing assistance and co-operation throughout these years. Highly appreciated is the assistance offered and the work performed by the personnel of the Workshop and the Stores of the same department . Also I am indebted to the staff of the U.B.C. Main Library and the Inter-library Loan section for their efficient service in providing and borrowing useful materials from other libraries. I am most grateful to Ms. Jane Winn for her expert typing of countless pages of strange symbols. Further thanks are due to the National Research Council and Environment Canada for their financial support. Finally, I must express my gratitude to my wife, Soad, for her sacrifices and continual support throughout this work. XX CHAPTER 1 Introduction and General Water is the most important chemical compound on Earth, When men settled down to agriculture and farming, they built their houses near potable water resources, such as rivers and lakes. Increasing the size of settlements augmented the needs of fresh water supply. The theoretical minimum water requirements, including agriculture, to sustain human life 3 are about 1.1 m per person per day, assuming that man can live on broad alone. The introduction of 0.5 kg of animal fat and protein to the ciief 3 increases the water requirement for subsistence to about 9.5 m pet person per day (Bradley, 1962). Increasing demand for water caused by the rising standard of living and by the increase in population, irresponsible wasting of water in many large cities, and above all pollution of natural water reserves with industrial waste and sewage, have brought many regions in various countries close to the critical point where existing resources can no longer satisfy the growing demand. The situation will become worse if adequate means are not adopted in time. Although the annual precipitation on Earth's surface might be sufficient, the uneven distribution of rainfall does not meet the human needs in all regions of the world. In several arid areas, existing water resources are saline, exceeding, the limit of potable water which is set as 1 2 500 mg/1 for total dissolved solids. Actually there are many communities in various countries which are still supplied with water containing over 1000 mg/1 total dissolved solids and sometimes up to 3000 mg/1. For such brackish and similar polluted waters treatment by distillation is not economically feasible and efforts have been made to resort to other processes such as electrodialysis. However, conventional electrodialysis has achieved only partial success in brackish water demineralization despite many theo retical advantages it offers over other processes. Under steady state operation, conventional electrodialysis is subject to mud and scale build-up on the membrane surfaces which may hinder the transfer of ions through the membranes, thus decreasing the capacity of the unit. The deposit may partially block flow channels, increasing pumping cost, and may react with and damage the membranes, reducing the selectivity and efficiency of the separation (Matz, 1965 and Korngold, 1970). Periodic current interruptions and/or reversals have been employed in standard electrodialysis plants to reduce polarization effects and deposition of particulates on the membranes (Matz, et al. , 1962; Calvit and Sloan, 1965). Based on current reversal technique, Lacey (1965, 1968) invented an electrosorption stack of much simpler construction than con ventional electrodialysis stacks. Electrosorption can be considered as a one-cycle process without reflux. This idea was further modified and developed into cyclic electrodialysis by Thompson and Bass (1972, 1974). Cyclic electrodialysis is a cyclic separation process which applies the periodic flow-reversal technique to an electrically driven electrosorption stack. The process has a wide field of potential applications such as: i) Brackish water demineralization ii) Brine production from sea water iii) Radioactive waste decontamination iv) Selective separation of monovalent salt from divalent and other polyvalent salts v) In the food industries it may be used for desalination of cheese whey and de-acidification of orange juice and treatment (mainly de-ashing) of sugars and syrups and related compounds vi) Other potential applications outside the food industry concern the treatment of leach solutions in- metallurgy, waste pickle-liquor recovery and waste sulfite-liquor recovery. Although cyclic electrodialysis may be most economical for the conversion of brackish waters (up to 10,000 ppm) to potable water of 500 ppm, nevertheless specific conditions can create other situations when the process could become unexpectedly economical. For example, there seems to be a 3 large potential demand for sea water conversion on the 2-5 m /h scale for tourist resorts. In these cases, the amortisation and interest charges tend to be very high and the utilisation factor is often as low as 33% per annum, Capital cost is therefore overwhelmingly the most important factor, and it appears that the process may provide the cheapest capital plant for meeting these requirements, although, at this salinity level, the power cost of cyclic electrodialysis would be higher than the other competitive processes. Cyclic electrodialysis has been investigated in a closed system and separation factors of several hundreds were reported for most of the runs with aqueous sodium chloride solutions (Bass, 1972). The present work is an extension of the previous work to an open system which represents a more useful mode of operation. The main objectives are to analyze the potential of the cyclic process on a continuous basis and to investigate systematically 4 the effect of the various design and operating parameters on the performance of the process. The present program makes a rather extensive study and exploration of the system within the design parameters and it provides information that should be useful in further study and in optimizing the system. CHAPTER 2 Theory and Review 2.1. Desalting Processes Desalting techniques potentially useful as commercial separation pro cesses may be classified into two general categories, as shown in Table I;; a) Processes that remove pure water from solution b) Processes that remove salts from solution The most developed process in category (a) is distillation. Freezing is a process currently being developed, while hydrate formation is still, in the experimental stage. Reverse osmosis, after a long period of membrane development, is entering the field of commercial operation. The latent heat for changing phase is an important factor in the overall economics of distillation processes while the degree of salinity of the raw water is of little importance. This process is therefore equally suitable for desalting seawater or brackish water. The same applies for freezing. However, the feed concentration is important in reverse osmosis, as the required counterpressure depends greatly upon the salt content of the raw water. The most developed process in category (b) is electrodialysis, and work has been done with ion exchange. The economics of these processes depends closely on the salt content of the raw water, which determines the amount of electric power required, or the consumption of chemicals needed 5 6 Table I Classification of Main Desalination Processes Processes that Separate Water from Solution Salts from Solution 1. Distillation Vertical tube evaporator Horizontal tube evaporator Multi-stage flash evaporator Vapor compression Solar evaporation 2. Reverse osmosis 3. Crystallization 1. Ionic processes Ion exchange Electrodialysis Transport depletion Osmionic Piezodialysis Electrochemical Biological Systems 2. Other processes Liquid-liquid extraction Freezing Hydrate formation 7 for the regeneration of the resins. Hence, these processes are more suitable for the purification of brackish waters. Table II shows the number and capacity of plants by process and by geographic location. (01Shaughnessy, 1973). Multi-stage flash evaporation accounts for 65% of the total capacity of the distillation plants. Two regions which represent large centres of desalting are the islands in the Caribbean Sea, and the Middle East, including countries around the Persian Gulf. A listing of most electrodialysis plants having a capacity of 100,000 gpd or more is given in Table III. It has also been reported that approxi mately 300 electrodialysis plants have been constructed and installed in the U.S.S.R. (Lynch and Mintz, 1972). 0 2.2. Some Economic Aspects of Selective and State-Change Processes Selective processes such as electrodialysis achieve separation without a change of phase of any component in the system. Such processes have economical advantages over state-change processes such as distillation and freezing. The methods of separation that rely on a change of state involve a high rate of energy circulation in the system, because the heat of fusion or vaporization of the solvent must be supplied. In general, this energy is many times larger than the energy theoretically needed to separate the salt from the solvent; and the energy required for vaporization or fusion must be recovered and reused to make such processes practical. The losses and inefficiencies in any system tend to be proportional to the energy Table II Total number and capacity of desalting plants exceeding 25000 gpd (95 m /day)* P = plants number; a = data in 1000 m3/day; b = data in Mgd. Geographic Total Electrodial sis Reverse Freezing Total desalination Location distillation plants ^ Osmosis Processes plant capacity P a b P a b P a b P a b P a b % United States ... 281 161.7 42.7 15 21.6 5.7 24 9.1 2.4 1 0.3 0.1 321 192.7 50.9 14.63 U.S. Territories 16 47.8 12.6 1 0.3 0.1 17 48.1 12.7 3.65 N. America except 13 32.5 8.6 1 1.1 0.3 14 33.6 8.9 2.56 South America ... 24 18.5 4.9 2 1.9 0.5 1 0.4 0.1 27 20.8 5.5 1.58 Caribbean 37 99.2 26.2 1 0.1 0.1 1 1.1 0.3 39 100.4 26.6 7.65 Europe Continental ... 102 174.9 46.3 12 16.3 4.3 2 0.2 0.1 1 0.4 0.1 117 191.8 50.8 14.60 England and 63 59.8 15.8 1 0.1 0 64 59.9 15.8 4.54 U*S«S*K* •••••••• 12 111.7 29.5 1 0.1 0 13 111.8 29.5 8.48 29 21.2 5.5 4 3.4 0.9 33 24.6 6.4 1.84 Middle East and Persian Gulf .. 77 405.0 107.0 18 8.7 2.3 1 0.1 0 96 413.8 109.3 31.41 55 92.8 24.5 10 22.0 5.8 65 114.8 30.3 8.71 5 4.5 1.2 1 0.1 0 6 4.6 1.2 0.34 Total Plants 714 61 33 4 812 324.8 18.7 4.0 0.4 347.9 Total 1000 m3/day 1229.7 70.8 15.0 1.4 1316.9 87.93 • 7.51 4.06 0.49 100.0 93.36 5.38 1.15 0.11 100.0 100.0 * From O'Shaughnessy, F.' , "Desalting Plant Inventory Kept. No. 4 (1973), ed. by the U.S. Office of Saline Water. Table III Large Electrodialysis Plants - Over 100,000 gpd* Plant Location Actual or Planned Year of Start-up Feedwater Salinity ppm Manufacturer Capacity Brindisi, Italy 1971 2,000 Ionics 1,300,000 Buckeye, Ariz. 1962 2,200 Ionics 650,000 Pantelleria, Italy 1971 4,500 Ionics 265,000 Siesta Key, Fla. 1969 1,300 Ionics 1,500,000 Aramco, Dhahran, Saudi Arabia 1961 2,700 Ionics 115,000 Bahrain Petroleum Co., Bahrain, Persian Gulf 1964 3,150 Ionics 100,000 Anaconda Copper Co., Chile 1970 2,200 Ionics 265,000 Industrial Co., Tex. 1969 2,500 Ionics 880,000 Automobile Factory, Bari, Italy 1970 2,000 Ionics 530,000 U.S. Army N.M. 1970 3,100 Ionics 100,000 Al Saudi Co., Al Khobar, Saudi Arabia 1967 2,800 Ionics 100,000 Gillette, Wyo. 1971 2,500 Ionics 1,500,000 Port Mansfield, Tex. 1965 2,400 Ionics 265,000 Ras Gharib, Egypt 1971 Ionics 113,000 El Adem, Libya 1971 Ionics 170,000 Bahrain Hospita, Bahrain 1971 Ionics 105,000 Benghazi, Libya Under construction 2,000 Wm. Boby Co. 5,000,000 Moshabei, Sadeh, Israel 1971 2,300 Tahal Consulting 1,250,000 Engineers Heinekens Brewery, Rotterdam, Netherlands 1968 1,100 Wm. Boby Co. 177,000 Zliten, Libya 1968 4,400 Wm. Boby Co. 105,000 Kazakstan, U.S.S.R. Under construction Unknown 500,000 * From Lynch and Mintz, J. Am. Water, 64^, 711 (1972) 10 circulation; and, to a first approximation at least, the energy needed to operate a distillation system will be a definite fraction of the heat of vaporization of the solvent and independent of the amount of solute present (Shaffer & Mintz, 1966). On the other hand, processes that are based, on selective transport require energy at a rate that varies with the theoretical minimum energy (Helmholtz free energy) needed to produce a desalted and concentrated stream from a saline feed water i.e. while the salinity does not affect the practical energy requirements for a process such as distillation, it does make a great deal of difference to a process such as electrodialysis. For further discussion on theoretical and actual energy requirements for a desalting process refer to Appendix F. The energy losses in the selective transport systems arise primarily as a result of the desire to maintain practical production rates; thus necessitates the use of substantial driving forces instead of infinitesimal forces, which would cause the processes to take place slowly and reverr.ibly. The net result of these considerations can best be seen by examining Figure 1, (Shaffer & Minrz, 1966) which compares the energies actually required for distillation and electrodialysis with the theoretical require ments at various salinities and fixed blowdown and product specifications. According to this graph distillation is more economical for de mineralizing high-salinity waters while electrodialysis is more attractive for brackish waters up to about 10,000 ppm. 2.3. Electrodialysis Electrodialysis is a selective transport process, in which the partial separation of the components of an ionic solution is induced by an electric current. The separation is accomplished by placing ion selective 11 2,000 4,000 10,000 20,000 40,000 FEED PPM FIGURE I Comparison of energy costs for distillation and electrodialysis of salt water. Basis : Average equivalent weight of sait =60 ;btowdown concentration £=two times feed concentration ^distillation to produce pure water; and electrodialysis to produce 0-005-N (300-ppm ) product . (A) Theoretical energy for electrodialysis }(B) theoretical energy for distillation-, (C) estimated actual energy for electrodialysis •, and (D)estimated actual energy for distillation- (Spiegler, 1966)-12 membranes across the path of the current flow. The process takes advantage of the ability of the membranes to discriminate between differently charged ions and the origin of separation lies in this membrane's selectivity. If non-selective membranes that are permeable to ions (e.g. cellophane) are used in electrodialysis processes, electrolytes can be separated from non-electrolytes. On the other hand, with membranes that are more permeable to univalent ions than to multivalent ions, electrodialysis can be used to simultaneously separate and concentrate univalent ions from solutions containing mixtures of uni- and multivalent electrolytes. Electrodialysis differs fundamentally from the great majority of electrochemical processes in that it does not utilize the electrode reactions. Electrodes do, of course, have to be incorporated in an electro dialysis plant, but they serve the purely ancillary purpose of applying the EMF. They are in fact a necessary evil, since they involve a great deal of extra complication in the design and operation of the plant. A pioneer book on electrodialysis, edited by Wilson (1960), describes the process and the use of ion exchange membranes in water desalting. Chapters in books by Tuwiner (1962), Spiegler (1962, 1966 a), Sporn (1966), Popkin (1968) and Kuhn (1971) also describe electrodialysis mainly as a desalination process. Lacey and Loeb (1972) consider various applications of the process such as concentration of electrolytes in dilute solutions, processing of cheese whey and recovery of constituents from pulping liquors. Recently Hwang and Kammermeyer (1975) have reviewed the process. The electrodialysis process uses cells consisting of many (at least three) compartments formed alternatively by an anion exchange membrane and a cation exchange membrane placed between an anode and a cathode as shown in Figure 2. Demineralized Water Electrode Reaction .•MA A j 1 Cone * t * ? ? ? Raw Water — Feed H2 O O O Cathode r\ o o c $0 Concentrate Brine Electrode ^ Reaction .9 Products ° 02, ci2 O O I - Anode ° I +-o" FIGURE 2 Multiple-chamber alternate-membrane electrodialysis.cell. A,the anion_selective membrane; C,the cation_selective membrane. Transport numbers are shown above or below arrows. 14 The saline water feed is pumped through the compartments of the membrane stack and, when a direct current potential is applied, cations . migrate toward the cathode and anions migrate toward the anode. Cations pass easily through the cation-permeable membrane and are blocked from further transfer by the anion-permeable membrane. Similarly, anions have free passage through the anion-permeable membrane and are stopped at the cation permeable membrane. As a result the adjacent cells become alter nately diluting and concentrating compartments. 2.3.1. Electrodialysis Stack The essential elements of a membrane stack are: (a) a large number of ion-permeable membranes arranged in the correct order. (b) gaskets and spacers to provide sealing between compartments and to maintain proper distances between membranes. (c) manifold systems to direct feed, product and waste streams into and out of the compartments without leakage. (d) electrodes and conductors. (e) a pair of strong presses to hold the above-mentioned parts in place. The multicell electrodialysis stacks are normally assembled in the same fashion as a plate-and-frame filter press (Figure 3). In addition to the stack, which is the actual part that effects the desalination, electrodialysis plants consist of: I Hydraulic equipment and auxilaries such as pipes, pumps, valves, filters, raw water supply, concentrate disposal. FIGURE 3 Exploded view of components In an electromembrane stack. 16 II A power supply with transformers and rectifiers and associated electrical and control instrumentation. 2.3.2. Stack Size and Capacity (i) Cell size Electrodialysis cell dimensions are limited only by the availability of suitably sized membrane sheets and the practicability of handling the gaskets and membrane materials, Weiner and co-workers at the University of California have developed a 10-foot-long stack to study polarization effects (Weiner, et al., 1964). In order to increase desalination and to reduce operating costs, the area of each cell-pair should be as large as practicable. One of the size limitations is the fact that membrane stacks need, at periodic intervals, to be dismantled in order to remove solid deposits formed during operation. It is necessary that the stack should be relatively small in order to be conveniently handled. In addition, large size membranes which are generally mechanically weak, tend to tear and break more readily during handling. The practice today is to limit the unit surface area to a maximum of 2 about 2m (2 by 1 meter), and to design the stacks to comprise a number of relatively small sub-units to facilitate handling. The largest cell in commercial use up to 1974 was 150 x 50 cm. (ii) Number of Cell Pairs A cell pair is the repeating unit in an electrodialysis stack. It consists of a diluting and a concentrating compartment together with a cation- and an anion-permeable membrane. The number of cells in a stack is mainly limited by engineering considerations such as: 17 (a) the total voltage that can be safely applied, (b) the size of the manifold that can distribute flow evenly into each flow channel, (c) the structural stability of the stack, (d) the ease of assembly and repair. Since the failure of a single membrane can impair stack performance, the number of membranes in a stack is limited by the life or reliability of the membranes and the anticipated frequency of other service requirements. The requirements for staging also make it desirable in some cases to have several small stacks rather than one large one. Usually several small subassemblies or "packs" containing about 50 cell pairs (100 membranes) are. used. These packs are then used as the building blocks for a plant of the. required size. As many as 10 of these packs can be placed into a single press. A single set of electrodes may be used for the entire assembly, or several electrodes may be used to provide electrical staging. (iii) Stack Capacity The desired product salinity is achieved by passing the feed liquid through several stacks in series, while desired plant throughput is obtained by operating several electrodialysis paths in parallel. The largest stacks in operation in 1970 handled dilute flows of about 250,000 gal/day. For larger production parallel arrangement of these stacks was planned, rather than scale-up of single stacks. The largest electrodialysis desalting plant in the world is in Benghazi, Libya, con structed by William Boby and Company, England after 1972. It has a production capacity of 5 x 10^ gal/day as shown in Table IV. The plant has 16 parallel trains each of 2 stacks in series, each stack with a capacity of about 310,000 gal/day. 18 Table IV Technical details of Benghazi (Libya) and Siesta Key (Florida) Electrodialysis Plants* Benghazi Siesta Key Stage 1 Stage 2 3 Rated output, m /h net 800 188 310 Waste water, % of output 8 17 Raw water, ppm total dissolved solids 2,000 1,300 Number of parallel trains 16 7 12 Stacks/train 2 2 Total number of cell pairs 9,600 4,200 7,200 2 Total membrane area, m 15,000 3,900 6,700 * From Solt, Chap. 12 in Kuhn (ed.), "Industrial Electrochemical Processes" 19 2.4. Membrane Technology An Ion-exchange membrane is an ion exchanger in sheet form and its physical chemistry is to a large extent also the physical chemistry of ion exchange resins. Ion exchange resins consist of two principal parts: a structural portion or a backbone (a polymer matrix) and a functional portion or an ion-active group. The synthesis of an organic ion-exchanger involves the chemical substitution of an ion-active group and a polymerization reaction. The substitution may precede the polymerization or vice-versa. Most ion exchangers currently in large scale use are based on synthetic resins, usually polystyrene [RO - (CH^ - CH)n ~ 0R] copolymerized with divinylbenzene [C^H^ (Cl^Cl^^] to provide the requisite amount of cross linking. The functional group may be acidic or basic with different degree of strength of acidity or basicity. Strongly-acid (cationic) resins generally contain bound sulfonic acid groups (-SO^OH), while strongly basic resins (anionic) contain quaternary ammonium groups fixed to a polystyrene-divinylbenzene matrix (Pepper, et al,, 1953). Some ion-exchange membranes are made by mixing ion-exchange resins with a polymeric binder and casting or extruding a sheet from the mixture, while others are manufactured by methods that exactly parallel the production of ion-exchange resins - i.e. styrene and divinylbenzene are copolymerized in sheet form, and the resulting structure is then chemically treated to give the sheet ion-exchange properties. The details of methods for making ion-exchange membranes have been reviewed by Wilson (1960), Friedlander and 20 Rickles (1966), Lacey (1972), Chiolle, et al. (1973) and Laskorin, et al, (1973). An excellent summary of preparative methods found in the U.S. Patent literature is given by McDermott (1972). An industrially useful membrane should have the following properties: 1. High ion selectivity - cation-permeable membranes should exclude the passage of anions, and vice-versa. 2. Low electrical resistance - permitting a free flow of counter-ions through the membranes at low energy requirements. 3. High mechanical strength - toughness, flexibility, and crack resistance are important, not only to the service life of the membrane, but also to construction, servicing and, therefore, the cost of electrodialysis plants. 4. High chemical stability - resists hydrolytic, oxidative, and other forms of degradation. 5. Resistance toward fouling by scale deposits and plugging by large polyvalent organic ions present in the solutions to be treated. The properties of a number of commercially available ion-exchange membranes have been tabulated by Shaffer and Mintz (1966) and Lacey and Loeb (1972). A bibliography on membrane technology, pertaining to saline water desalination and ranging from 1908 to 1962 has been compiled by the Office of Saline Water (Mangan, et al., 1963). A comprehensive review of the physical chemistry of ion-selective membranes has been given by Malherbe and Mandersloot (1960). 21 2.4.1. Membrane Selectivity One of the basic characteristics of an ion-exchange membrane is the selectivity, which is defined as the ability of the membrane to distinguish between oppositely charged species leading to the preferential uptake of counter-ions and exclusion of co-ions. Counter-ions and co-ions are the mobile ions possessing charges opposite and similar in sign respectively to the membrane fixed ions. When a cation-selective membrane is immersed in an electrolyte solution the cations in solution will enter into the resin matrix and replace the cations present, but anions are prevented from entering the matrix by the repulsion of the anions affixed to the resin. The opposite phenomena takes place when an anion selective membrane is immersed in an electrolyte solution; the fixed cationic groups permit intrusion and exchange of anions from an external source, but exclude cations. This type of exclusion is called Donnan exclusion. (i) Permselectivity Selectivity is usually reported in terms of permselectivity, P, which is the increase in transport number over the value in free solution due to the presence of the membrane and it is given by: where: t, t = transport numbers of counter-ions in membrane and in free solution respectively (t-t) = increase in transport number over the value in free solution P ~ t -1 -J: t (1) 22 (1-t) = the maximum possible increase or the increase that would be observed in the case of an ideally selective membrane, Both p and t are functions of concentration. They decrease as the external electrolyte concentration increases as shown in Figure 4. (ii) Donnan Exclusion According to the Donnan principle the chemical potential of the salt in the solution external to the membrane must be equal to the chemical potential of the salt inside the membrane, i.e. 2 - -2 RT In a+ = vAp + RT In a^ (2) where: a+, a+ are the ionic activities in free solution and in membrane phases respectively v is the partial molar volume, cm /mole Ap is the difference in internal pressure between the mem brane and the solution phase called the "swelling pressure" of the membrane The pressure-volume term arises from the free energy change due to the difference between the osmotic pressure of the solutions inside and outside the membrane (Wilson, 1960). In the absence of large pressure differences between the interior and the external phase, the Donnan principle requires that: (a+) . (a_) = (a+) . (a_) (3) where: FIGURE 4 Dependence of counterion transport numbers and permselectivity upon external concentration. (Wilson , I960 ). 24 a+ are the ionic activities v's are the stoichiometric coefficients for electrolyte M ,X v+ v-and the barred symbols refer to the membrane phase. For uni-univalent electrolyte, v+ = v- = 1.0, and Eq.(3) reduces to: where y+ is the mean ionic activity coefficient, defined generally as Y+ - Y++ • Y^ • (5) where v = v+ + v-; subscripts j and k refer to co-ion and counter-ion res pectively. Since both the solution and the membrane must be electrically neutral, this requires that: In membrane; C, = C. + C (6) k j x In solution; C = C = C (7k J where C is the fixed ion concentration in the membrane, x Substitute Eqs.(6) and (7) into (4) and replace activities by concentrations: C. C. = C. (C. + C ) (8) J k 3 3 x Assume C. + C = C then 3 x x f2 c - r (9) J x Eq.(9) shows how the selectivity of a membrane is affected in opposite directions by the external salt concentration, C, and the fixed-ions con centration in the membrane, C . The higher the concentration of fixed ions, x the greater the selectivity (C\. -> o as C*x ->• ») while (C. C as C ->• C^) . 25 In a typical electrodialysis system, the concentration outside the membrane may range from 0.001 to 0.1 m, while it is usually possible to make the molality inside the membrane fall in the range 1 to 5m. Accord--7 - -2 ingly Eq.(9) guarantees that 2 x 10 < C.. < 10 (Shaffer and Mintz, 1966). From Eq.(9) it is clear that the current carried by some ions in the system can be made very small. In the extreme case of ideally selective membrane, the co-ions are completely excluded and the whole current is carried by the counter-ions alone through the membrane. Figure 5a shows a negative membrane (cation-exchanger) in sodium chloride solution and it illustrates the basic operating principle involved in all electrodialysis processes i.e. on the left side the electric current carries sodium ions to the membrane at the rate t + i/F and these ions disappear across the membrane at the rate t + i/F where F is Faradays constant and i is the current density. The net result of the passage of 1 Faraday is the removal of t+ - t = 0.6 mole of salt from the solution immediately adjacent to the lefthand face of the membrane and the appearance of a like quantity (t - t =0.6) in the solution adjacent to the righthand face. (For sodium chloride, t - 0.4 and t = 0.6). 2.4.2. Membrane Polarization Concentration polarization at the surfaces of the ion-exchange mem branes limits the current density and the production rate in an electro dialysis unit. Polarization is a natural result of the separation mechanism and it increases as the selectivity of the membrane increases; there is no way to prevent concentration polarization other than by stopping the current flow. Due to the differences in the transport numbers of ions in the solutions and in the ion-exchange membranes two boundary layers with Ha CI it+=l*0 it-=0-6l it+=0-39 £> =-L-0 it-=0® it-=06l FIGURE 5a Ion transport across a permselective membrane , showing current i and transport number t. • rwv,cm c m FIGURE 5b Concentration profile across a permselective membrane in an electrodialysis stack . 27 opposite concentration gradients are formed at the opposite sides of each membrane (Figure 5b). In a well-stirred system the film model (Nernst layer model) can be adopted and.the concentration gradient on the dilute side approximated by i C — C D m where 6 C_, C* are the concentration of the bulk solution and the D m concentration at the membrane surface respectively 6 is the Nernst film thickness In a steady state operation, the rate of arrival of salt at the membrane-solution interface must equal the rate of removal of salt i.e. at a cation-permeable membrane we have: - »f . <»> where D = lateral diffusion coefficient across boundary layer AC = C - c' D m z = valence In the limiting case when C^ -> 0, AC -> C^; the corresponding limiting current density, i^^f is given by i = ZFDCD 1 him = 2— j (11) Polarization is a result of mass transfer limitations adjacent to the membrane-solution interfaces. It occurs when Ion depletion by electro dialysis exceeds the rate of ion diffusion into the boundary layer from the bulk solution, and it becomes appreciable when the bulk solution concentration Cp, is low and the diffusion layer is thick so that the concentration gradient is low. 28 (i) Consequences of Polarization In practice a considerably lower current density than i,. is used. l.im t As Cm approaches zero the resistance increases and efficiency drops tremendously. The concentration of H+ and OH ions in an aqueous solution is about 10 ^ mole/liter, and the mobilities of these ions are 3 to 5 times greater than the mobilities of the other common ions. As soon as c' m approaches 5 x 10 mole/liter, an appreciable amount of current will be carried by hydrogen and hydroxyl ions. This results in the following effects: (1) An enormous increase in the power consumption due to: (a) More current flowing per unit of salt removed e.g., if (u^a+) (C) = (^jj"1") 10 ^ where u is the ionic mobility then Na+ and H+ ions will transfer at equal rates. In this case even an ideal membrane would function with an effective current efficiency, n^., of only 50 per cent, because H transfer does not contribute to desalting. (b) More energy dissipation in the boundary layer resulting from the poor conductivity of nearly pure water (kf^o ~ —8 —1 -1 4 x 10 ohm cm ). (c) The energy required to ionize the water molecules (dissociation energy of water splitting). (d) An increase of the back emf's due to polarization layers. (2) Deviation from neutrality in the polarized layer or the alteration of the pH's of the process streams. Acidity can develop on the cathode side of cation-permeable membrane and alkalinity on the anode side of anion-permeable membrane. As most brackish waters are nearly saturated 29 with scale-forming materials, any transfer of H' or OH into or out of a local region will generally cause serious scale and precipitation problems -4 e.g. Mg(OH)9 precipitation may be expected at pH > 10 (i.e. C_. - - 10 ). ^ OH (3) Polarization changes the electrochemical properties of the mem branes and may result in membrane deterioration if they are not stable to wide pH variation. (Wilson, 1960). Anion-permeable membranes are most affected by this. In practice, polarization is held to reasonable values by controlling the ratio of current density to the normality of the dilute stream, i/CD» and by designing the system to make 6 as small as possible. It should be noted that the polarization limitation rather than the results of economic optimization generally controls the operating current density in practical electrodialysis installations. In any practical apparatus, the picture is far more complex than this. Where there are cells fed in parallel from a manifold, it is impossible to have exactly the same liquid velocity in each cell. Cooke (1967) and Solt (1967) have drawn attention to the fact that, even within an individual cell in the most ideal situation, the local conditions of mass transfer are not uniform over the whole area through which current is passing. (ii) Polarization Control Polarization can not be avoided completely, but it can be held to reasonable values by controlling the ratio of current density to the normality of the dilute stream, i/C^ and by making the thickness of the diffusion layer, 6, as small as possible. There is little that can be done about the bulk concentration when the diluted stream is the required product. However, 6 can be reduced by high 30 solution flow velocity and the introduction of turbulence promoters such as spacers or screens that cause local eddying or turbulence (Hoek, 1956). Both of these measures add to the power consumed in circulating the process fluids, but they reduce the stack power consumption and allow operation at higher current densities with an acceptable level of polarization. An alternative method of reducing polarization was reported by Spiegler (1963) who reversed the current for a fraction of a second after each several seconds of operation. Partial confirmation of the efficacy of this technique was obtained in the Webster, South Dakota, demonstrative plant (OSW, 1964 a). 2.4.3. Scaling and Fouling of Membranes Concentration polarization is often linked with other problems in practice such as membranes scaling and fouling. An increase in the pH of the solution due to polarization promotes the formation of alkaline precipitates, such as calcium carbonate and magnesium hydroxide on the membrane surface. On the dilute-stream side of the anion-permeable membrane the depletion of the more mobile anions encourages the deposition of large polyanions onto the membrane surface. Polyanions commonly found in brackish waters are humic acids, silic acids, phenols, proteins and polyphosphates (OSW, 1963). Scaling of membranes causes additional electrical and flow resistance, a decrease in electrodialysis efficiency and an increase in pumping power requirements. Scale deposits can be found within the membrane gel structure, which is known as fouling and results in rapid embrittlement and physical deterioration of membranes. Several methods have been attempted to control membrane scaling and fouling and can be summarized in the following: 31 (i) Current Density reduction Scale formation is particularly pronounced at high current densities. Reducing the current density may reduce scaling. (ii) Pre-treatment for cation removal Pre-treatment by cation-exchange requires all the feed to be passed through a cation-exchange bed, in order to remove calcium and magnesium. Cations may be partially removed by a preliminary lime or lime-soda treat ment followed by filteration. Such pre-treatments add considerably to operating costs and would be unjustifiable economically except for specific applications. (iii) Acid Treatment of Concentrate Acidification to a pH level low enough to prevent precipitation is commonly practised, but even this method may not completely prevent scale formation at the surfaces of or within the membranes. The addition of sulphuric acid to keep pH below 5.0 for prevention of Ca C0^ scaling was reported by Watanabe, et al. (1972) and Asawa, et al. (1973). Although acidification adds to the direct cost of desalting, the added cost was considered to be partly offset by savings in energy consump tion due to a lower overall electrical resistance. (Furukawa, 1968). (iv) Reversed Polarity Periodic reversal of electrode polarity has been proposed to dissolve scale and control membrane fouling (Matz, 1965). wherever the membranes were suspected of producing a sieve or filter ing effect, rather than acting as a pure ion-transfer medium, current reversal was practiced on a periodic basis to discharge electrochemically entrapped colloids and/or macromolecules so as to restore the original 32 membrane properties. Although the effectiveness of this procedure depends on the type of membrane and the nature of the contaminants that foul it, the reversal of hydrogen and hydroxyl ion transfer and the accompanying inter change of pH effects at the membrane surface is probably the significant defouling factor. (v) Pulsating Current Pulsating current is sometimes used when reversed polarity is not able to prevent rapid accumulation of scale. In this method very brief pulses of reverse current are applied to produce current reversal or current interruption (Matz, et al., 1962). This technique tends to alleviate scaling problems and also apparently improves the efficiency of an operating electrodialysis stack (Israel, 1961). 2.5. Process Efficiency 2.5.1. Principal Energy Sinks The actual energy required to operate an electrodialysis process exceeds that theoretically required for the following reasons: (i) Power losses attributable to resistance i.e. the power that will be dissipated by the Joule heating of the membranes and the electrolyte solution. (ii) Power losses attributable to concentration polarization i.e. the power required to overcome the overpotentials that exist at the membrane-solution interfaces. (iii) Power losses attributable to electrode reaction and the IR drop in the rinse solution streams in the electrodes compartments. 33 (iv) Low current efficiency. The overall efficiency of an electrodialysis stack, n, can be ex pressed as a product of four principal efficiencies: (a) Three voltage terms: n associated with the total resistance, T) associated with the concentration polarization effects and n associated c e with the electrode reactions. (b) The current efficiency, n^ i.e. n = n n n nT (12) Reel where n is primarily a function of the stack design (e.g. number of cell pairs), nc depends mainly on the operating conditions (e.g. current density), while n depends on both design factors such as cell spacing, membrane type R and thickness and on operating conditions, (a) Voltage Terms The major inefficiency in stack operation is associated with the first and second terms in Eq. (12) , Tl^nc« These terms are considered in Chapter 3. In multiple-membrane stacks used in electrodialysis, the energy con sumed in electrode processes, ne» does not contribute to the desired separation and hence the relative effect of this energy consumption can be reduced considerably by increasing the number of membrane cell pairs used in series with a given pair of electrodes. The electrode reactions and the polarization effects are considered briefly in Appendix A. The total external voltage, E^,, that is needed to operate a practical electrodialysis stack is the sum of 3 principal potential drops: ET = Ee+ER+Ec (13) 34 where Eg = potential drops associated with the electrodes and electrode streams (including electrode potential and overpotentials) = the IR drops in the solutions and membranes Ec = concentration potential across the membranes and at the mem brane-solution interfaces. A voltage efficiency term associated with the electrode reactions, n , can be defined for the stack as a whole by e E E + E„ (e„ + e ) . e x T J ET where e^, e£ are defined in a same way as E^ and Ec but they refer to one cell pair instead of the whole stack. A cell pair consists of two membranes and their two associated solution passages. From Eq.(14), it is obvious that whatever the individual values of e^ and e£ for the design selected, will approach 1.0 as the number of cell pairs, j, is increased. Usually the energy consumed at an electrode is of the same order as that consumed by one cell pair. Belfort, et al. (1968) showed in their studies of two electrodialysis plants: Webster, South Dakota and Buckeye, Ariz, that the electrode polarization is a minor factor, making up less than half per cent of the total potential drop, (b) Current Efficiency, n^ In any practical electrodialysis system, it is generally found that the amount of current required to produce a given amount of desalting exceeds the theoretical amount calculated on the basis of current flow through ideal membranes. 35 The current efficiency, n , is defined as I F "w (15) where r\„ is the Faraday efficiency, which is defined as the ratio of the r salt transferred to the theoretical current requirement _ (equivalent of salt transported)  ^F (Faraday of electricity passed)(number of membrane pairs employed) (16) n is the result of water transport through the membranes. When the w feed is of low salinity, as with brackish water, the effect of water transfer is usually small and the water transfer term, riw» can be assumed to be unity. A more detailed discussion of the current efficiency is considered in Appendix B. 2.6. Variants of Electrodialysis Several variants of the electrodialysis process have been developed to overcome some of the problems that have been encountered with conventional electrodialysis. For instance, the anion-selective membranes used in conventional systems are particularly troublesome because of vulnerability to fouling and scaling, so attempts have been made to replace them by either neutral (nonselective) membranes (in transport depletion) or by cation-exchange membranes (in electrogravitational demineralization). 2.6.1. Transport Depletion The transport depletion process is a variant of electrodialysis in which an array of alternate cation exchange and nonselective membranes is used as shown in Figure 6. This concept was first suggested by Deming and 36 Concentrated Demineralized Stream Stream A A N N Na -•Na ->Na+ h^Na"* + VLSU 1 A •ci" — a •«-U i CI A i Anode Rinse Feed ( Na CI ) . Cathode Rinse FIGURE 6 The cation_neutral transport depletion process-, C, cation - selective membrane N, neutral membrane-37 Kollsman (1959) and developed by Lacey (1963). When direct electric current is passed, depleted and concentrated boundary layers form at the two sides of the cation exchange membranes, but not at the nonselective neutral membranes. The latter serve only to separate the depleted and concentrated boundary layers from each other and, in doing so, create alternate diluting and concentrating compartments. Neutral membranes have little tendency to polarize or foul, thus their use trades off the chemical and mechanical disadvantages of anion-exchange membranes for higher power costs, e.g. for solutions of K CI (t = 0.5 = t_), passage of one Faraday shifts 1 mole of salt from diluate to concentrate, when alternating ideally selective cation- and anion-exchange membranes are used in conventional electrodialysis, while only % mole is shifted in transport depletion. Therefore, to achieve the same production rate in the transport depletion stacks as in the basic electrodialysis stack, twice the current is needed. The voltage is then also nearly twice, hence the power costs almost quadruple. However, by eliminating the anion membranes the capital cost drops. It appears that the power consumption is not the decisive factor in electrodialysis since the major desalination costs do not reside in the energy requirements but in the investment costs for equipment or the replacement costs for the membranes (Shaffer and Mintz, 1966). The economics of the transport depletion process have been studied by Huffman (1969) and Redman (1971). Lacey estimated a cost reduction of 8% compared with the normal electrodialysis. The process development continues in the belief that the simplicity of the plant and its freedom from trouble in the field will out-balance the increased power cost(Solt,1971). 38 2.6.2. Electrogravitational Demineralization The term "electrogravitation" was first suggested by Murphy (1950). Electrogravitational demineralization may be achieved in a cell in which only cation exchange membranes are used, as shown in Figure 7. When a direct electric current is passed depleted and concentrated boundary layers form at each side of the membrane, but the solution in the depleted boundary layer rises and collects at the top of the depleted compartment because its density is lower than that of the bulk of the solution. Similarly the solution in the concentrated boundary layer slides downward and collects at the bottom of the enriched compartment. Additional density differences are obtained because the depleted solution has higher electrical resistance than the bulk, and gets hotter. The process is extremely simple to construct and operate. The mem branes may be placed loosely or simply hung in a tank fitted with electrodes; edge seals on the compartments are not necessary; imperfections in the membranes, even holes, will not seriously affect performance. Current leakage through holes or around edges may waste power, but will not interfere with the operation of the system. Very high concentration gradients can be achieved in the process. Mintz and Lang (1965) have shown that concentration gradients of greater than 100 to 1 can be obtained in cells only 6 in. high. Studies by Lang and Huffman (1969) showed that electrogravitation is not competetive with other processes for demineralizing saline water but may be of interest for some industrial separations. 39 Demineralized Product Water .CI* 1 : ^ i Li 1 » ! ^ 1 fort H Repeating) •Mi ! s T n 1 1 cr Brine Feed (Na CI typical) * Concentrated Brine FIGURE 7 Bectrogravitation with cation-selective membranes. 40 2.7. Cyclic Processes 2.7.1. Electrosorption Electrosorption is a modification of electrodialysis which was first conceived by Lacey and Lang (1964, 1968). It is a one-cycle process without reflux. An electrosorption demineralizer consists of many electrosorption membranes arranged between a pair of electrodes, so that solution compart ments are formed between the parallel membrane surfaces as shown in Figure 8, An electrosorption membrane, which is the fundamental desalting unit, is a three-layer membrane comprising a neutral inner layer (which may be a spacer or merely solution) sandwiched between a cation- and an anion-exchange membrane. When a direct current is passed through the system cations and anions are transported (in opposite) directions from the external solution into the electrosorption membranes. The external solution is depleted while that within the membranes becomes highly concentrated. After 20-50 minutes of sorption the direction of the current is reversed and the trapped ions accumulated inside the membranes are driven back to the external solution to regenerate the membranes. The external solution is sent to waste during this step. 2.7.2. Cyclic Electrodialysis Cyclic electrodialysis is a novel cyclic separation process, which uses periodic flow reversal applied to an electrically driven electro sorption stack. The process has been studied and described by Bass (1972) , Bass and Thompson (1973). In this process cyclic times ranging between 30 seconds and 2 minutes were used with the voltage and flow direction Demineralized Product Water t +1-A n Na1 CI + s 1 A Ncf •f?Na+ jM Na* •CI fop- •CI Brine Feed (NaCI Typical) FIGURE 8 Electrosorption Process 42 reversed every half cycle. A concentration difference between the ends of the apparatus is built up with repeated cycling. Separation factors of several hundreds were reported for most of the experiments with aqueous sodium chloride solutions in a closed system. The present work is an extension of cyclic electrodialysis to an open system. Cyclic electrodialysis usually requires more electrical energy per unit of product water than conventional electrodialysis, due to the regeneration step. The cost of this additional energy must be balanced against savings in capital and operating costs resulting from: (i) Extreme simplicity of the manifolding and distributing systems. Lower cost of the stack is possible because only one stream of solution is withdrawn at any one time. (ii) The "sealed-envelope" or "membrane sack" character of electrosorption membranes simplifies the stack construction and results in a better membrane utilization factor. Since the membranes are not used to separate brine and dialystate flow channels, they may be as small as the active interior of the stack. A membrane utilization factor of about 95% is obtained, whereas the factor is only about 70% to 75% in conventional electrodialysis stacks (Lacey, 1968). This results in a lower membrane replacement cost and a lower stack capital cost. (iii) With electrosorption, no pretreatment was needed to remove iron or manganese from feed waters. With feeds containing either CaSO^ or Ca(HC0,j)2> precipitates within membranes did form at high pH values, but these were easily and quickly removed by reversed current flow during desorp-tion without causing any cell blockage or damage to the membranes (Lacey, 1967). It is expected that this would also be true for cyclic electrodialysis. 43 (iv) Increased throughputs are possible because current densities more closely approaching the limiting current density can be used without experiencing permanent damage to the membranes or stack due to precipitates. (v) A high degree of desalination can be obtained in a single stack (Bass, 1972). (vi) The periodic reversed polarity technique provides a repeated rejuvenation of the membranes. So far no problems with membrane deterioration have been encountered. (vii) In cyclic electrodialysis only cheap graphite electrodes need to be used. Such electrodes proved to be satisfactory in a long-term operation. Cyclic electrodialysis has some similarities to thermal parametric pumping. In both processes the flow of a mobile phase is periodically reversed and in both processes the origin of separation lies in the ability of the system to store solute temporarily in the fixed phase, with drawing it from the lean end and subsequently adding it to the rich end of the processing stream. 2.7.3. Parametric Pumping The. term parametric pumping was first introduced by Wilhelm, et al. in 1966 (Wilhelm, et al., 1966 a, 1966 b). It refers to a dynamic principle of separation based on periodic synchronous coupling of two cyclic fields or two transport steps (Wilhelm and Sweed, 1968 a; Wilhelm, et al., 1968 b). Parametric pumping has been reviewed in details by Sweed (1971, 1972) and Wankat (1974).. 44 The system of a direct thermal parametric pumping consists mainly of a jacketed column packed with an adsorbent bed as shown in Figure 9a, a constant-rate, positive displacement dual-syringe infusion-withdrawal pump, sources of hot and cold water for the jacket (not shown in the figure), and a programmed cycle timer. The timer is adjusted to reverse periodically the direction of the fluid stream; also to cycle the jacket temperature by connection to hot or cold sources. Both alterations have the same frequency (i.e. every half cycle) and are in phase. The fluid is heated during the upward stroke and cooled during the downward stroke. The adsorbent holds more solute when the fluid is cool, Thus the solute is held by the adsorbent on the cold half cycle and released to the fluid on the hot half cycle. A multiple succession of these adsorption-desorption actions tends to cause accumulation of solute at: one end of the column and depletion at the other end. Eventually, under ideal conditions, all of the solute will be "pumped" to the upper reservoir and the lower reservoir will contain no solute. In the present case the "pump" is identified as the oscillatory thermal field; the flow displacements between fluid and solid phases simply keep the system in a state of disequilibrium. The four basic requirements for implementing the principle of para metric pumping (according to Sabadell and Sweed, 1970) are: 1. The existence of a two-phase system. 2. An equilibrium distribution of the component being separated between the phases. 3. An alternating relative velocity between the phases. 4. An alternating interphase mass flux obtained by periodically Driven Piston Packed Bed Of Adsorbent Particles Heating And Cooling Jacket Driving Piston Q Q f*-Q ft-Q Q Heating half-Cycle Cooling Half-Cycle FIGURE 9 a Diagram of column for direct mode RR . Thot Tcold Vo o -Vo J mean L Desorptlon Adsorption 0 0-2 0-4 0-6 0-8 10 Fraction Of Cycle FIGURE 9 b Velocity and temperature at a point in the bed as a function of time • 46 changing one or more of the intensive thermodynamic variables that affect equilibrium e.g. temperature. Although thermal parametric pumping results in a large separation in the system toluene-n-heptane-silica gel, with a separation factor of 10"* in batch operation (Wilhelm, et al., 1968 b) and of over 600 in an open system (Chen, et al., 1972 a), it gives only a modest separation in the system Na CI - 1^0 - ion resin with a separation factor of 10 in a closed system (Sweed and Gregory, 1971) and a separation factor of 2.0 in an open system (Wilhelm et al., 1966 a; Sweed and Gregory, 1972). 2.7.4. Cyclic electrodialysis and Parametric Pumping Despite the prementioned similarities between cyclic electrodialysis and parametric pumping, the two processes are different with regard to the nature of the driving force and process design, limitations and applications, In parametric pumping separation is achieved at the expense of thermal energy. By changing the temperature and reversing the fluid flow every half cycle the system is kept in a state of disequilibrium, thus molecules diffuse from one phase into another. In cyclic electrodialysis an external electric field is applied and bodily forces are exerted on the ions that are transferred from one region into another across the stack. A parametric pumping process consists essentially of a column packed with a suitable adsorbent bed while cyclic electrodialysis stack comprises well-defined parallel flow channels between membrane sheets. While parametric pumping operation is controlled by equilibrium con siderations, electrically driven separation process such as cyclic electro dialysis is governed by finite rates of mass transfer and usually operate at concentrations far from equilibrium. The rate of mass transfer is 47 approximately proportional to the current flowing and is thus to some extent under the direct control of the experimenter. Finally cyclic electrodialysis deals only with ionic solutions whereas parametric pumping is not limited to these solutions. However, within the specific field of separation of ionic solutions, cyclic electro dialysis looks more promising since it is not constrained by the chemical nature of the system. In parametric pumping a large separation is only expected when the shift of equilibrium with temperature of the particular system is large. CHAPTER 3 System Models 3.1. Stack Resistance Models The apparent resistance of an electrodialysis stack is determined by multiplying the apparent resistance of one cell pair by the number of the cell pairs and making some allowance for the electrode system*(Generally ignoring the electrode system contribution towards the total stack resis tance will result in only minor error). A cell pair consists of two ion-exchange membranes and their associated flow channels. The apparent resistance comprises the electrical resistance of the solutions and the membranes together with the back emf's caused by polarization, These back emf's oppose the applied voltage and thus represent an apparent resistance. In the development of these analyses two approaches can be dis tinguished which are designated as "non-ohmic" and "ohmic". The non-ohmic analysis is an analytical approach which takes into account the variation of the apparent resistance with current density. This approach breaks down the total resistance into several resistive elements, evaluates the con tribution of each element independently and sums them to get the total value. The ohmic analysis is an empirical approach which assumes proportion ality between current and voltage in the electrodialysis stack. 3.1.1. Non-ohmic Analysis When a voltage is applied across an electrodialysis stack, the initial current is roughly proportional to the voltage, but as the current flows 48 49 through the apparatus concentration gradients and discontinuities are established and the apparent resistance of the stack increases. Apparent resistance comprises the electrical resistances of the solutions and the membranes, and the back electromotive forces (membrane potentials and diffusion potentials) caused by concentration polarization. Figure 10 shows schematically the concentration profiles in an electro dialysis cell pair. The cell pair contains the concentrated and depleted bulk solutions, the two membranes, and the four boundary layers in which the concentrations of salts in the solution near the membrane vary con siderably. The electrical circuit in Figure 10 is an analog of the electro dialysis cell pair. The battery symbols represent the concentration potentials, and the resistor symbols represent the resistances of membranes and segments of solution. This analog can be used to develop an equation for the total potential across a cell pair. (i) Diffusion layer resistance The voltage from 1 to 2 in the depleted diffusion layer is the algebraic sum of the diffusion potential and the IR drop from point 1 to point 2 ji (^ " ^ El-2 I '¥ f <t" - t+)d ln(TC)g + i " 1 p dx (17) r x,z where R is the gas law constant, T is the absolute temperature, F is Faraday's constant; t , t+ are the transport numbers of anion and cation respectively 3 in solution, C is the solute concentration in eq./cm , y is the activity coefficient, p is the resistivity of the solution at the coordinate point X f z x,z, n-cm, where x is the distance from the membrane surface and z is the distance from the inlet along the flow path. The subscript d refers to the depleting solution. 50 Cell Pair L ' Depleting Solution . 13 5 i Enriching Solution I 8 3 .4 .5 6 7 .8 9 - h/VWvH (AiK/VHtvV^rA/H^ FIGURE 10 Simplified concentration profiles in an electrodialysis cell pair and the analogous electrical circuit. 51 The equivalent resistance of the diffusion potential (first term on R.H.S. of equation (17)) is given by (18) Integration of Equation (18) along the flow path (z coordinate) results in (refer to Figure 11) Fi %,d " m RT <cd" " td) „m (Ylci) In ,——vz dz (Y2C2)_ (19) J z=0 where ^ is the equivalent resistance of the "diffusion potential per unit area of the depleted layer. The diffusion layer resistance that the dialyzing current must pass through (the second term on the R.H.S. of equation (17)) is calculated by performing a double integration across the diffusion layer (x coordinate) as well as along the flow path (z coordinate) as indicated in Figure 11. L6,d i r m m z=0 Px,z dx x=0 -1 dz (20) where p is obtained from the basic definition of resistivity: x,z J 1000 x.z (AvVc Cx,z (21) (hv)+or is the equivalent solution conductance at average concentration of salts and t°C. It can be evaluated from the Onsager equation at various temperatures and concentrations (Av)t°c ° (Aoo)toc - [A + B (Aoo)toc]C (Aoo)toc = (A~)25°C [1 + 0,023 (t " 25)1 (22) (23) where 52 Ion-Exchange Diffusion Bulk Membrane Layer Solution FIGURE II Diagram of the concentration profile and the diffusion layer on the dialysate side of an electrodialysis ion exchange membrane. 53 (Aoo) oP is the equivalent conductance at infinite dilution and t°c. After p from Eqs. (21), (22) and (23) is substituted in Eq. (20), C X 9 Z X j z as a function of x and z has to be evaluated from the boundary conditions. To relate the concentration at the membrane surface C(0,Z) with the diffusion layer-bulk Interface concentration, C(6,Z), the Nernst idealized equation will be used (this model is considered in Appendix C): dc = C(6,Z) - C(0,Z) (2A) dx 6 From the Nernst equation and realizing that at the limiting current density, i^^* surface concentration C(0,Z) approaches zero, C(0,Z) = (1 - k) C(6,Z) (25) where k is the ratio of the operating to limiting current density i.e. k = (26) lira At any point (x,z) within the boundary layer C(x,z) is given in terms of bulk solution concentration C(6,Z), diffusion layer thickness, 6, and the current density ratio, k by the following relation (using equations (24) and (25)): C(x,z) = C(0,Z) +XtC(6'Z> - C<°»Z" = [(1-k) + ^ ] C(6,Z) (27) The diffusion layer thickness, 6, the limiting current density, i^ the operating current density, i0per» an<* the bulk solution concentration, C(6,Z) must be evaluated before equation (27) can be used. 54 The diffusion layer thickness The diffusion layer thickness, 6, is obtained from Equation (11) in terms of limiting current density as; . _ C(6,m) FD (28) lim in- (t - t) Limiting current density, i^^* will occur when the exit concentration of the dilute stream C(0,m) shown in Figure 11 reaches zero. The limiting current density can be determined experimentally as shown by Rosenberg and Tirrel (1957), Cowan and Brown (1959) and Cooke (1961). Once i is obtained, 6 can be calculated. The current density ratio, k Using Faraday's Law and a material balance, the capacity is defined as, Cap - ijj^ - Fd n C4± f (29) where capacity is in g-equiv. transferred/sec., n is current efficiency, Ap is the active membrane area [i.e. area available for demineralization] (cm ), n is the number of membrane pairs, F is Faraday No. (coulombs/g-equiv), Fd is dilute stream exit flow rate (lit/(sec)( channel)), Cdi is dialysate inlet bulk concentration (g-equiv/lit), and f is fraction desalted. From Eq. (29) we have F Fd Cd± f 2 i = t amps/cm (30) oper n Ap r From the limiting current value and Equation (30), the current density ratio, k, can be obtained. FIGURE 12 a The concentration profiles (exponential) of both the the dialysate and brine streams-FIGURE 12 b The material balances of both the dialysate and brine streams. 56 Bulk solution concentration, C(6,Z) Based on the traditional treatment of electrodialysis the dialysate bulk stream concentration can be assumed to decay exponentially with the distance Z from the feed point as shown in Figure 12a. On evaluating each bulk solution as a function of path distance Z we get for the dialysate -aZ Cd (Z) = Cd (0) e (31) and from a material balance on the salt at a distance Z along the path length and the top of the unit (at Z = m) we get for the brine (refer to Figure 12b): Cb (Z) = [Cb(m) + ( || ) Cd(m)] - [( || ) Cd(0)]e"aZ (32) On substituting equation (31) into (27) a general expression for the local concentration, C(X,Z), can be obtained: (33) C(x,Z) = [(1-k) + ~] C(6,0) . e~aZ By substituting values from equations (21), (22) , (23) , (25), (26), (28), (30) and (33); equations (19) and (20) can be integrated. From equations (19) and (20) the apparent resistance per unit area of the depleted diffusion layer is given by: Rd " %,d + R6,d m RT (£d - V Fi .m (V-^) In ,—dz -1 (Y2C2)_ L J z=0 + m - z=0 p dx x,z dz -1 (34) 57 A combined expression for the apparent resistances of the two depleted diffusion layers is given by (refer to Figure 10) R6(l-2) + R6(3-4) m RT (td - td) Fi .m (Y1C1} In ——s z dz n Wz z=0-1 + 2m .m z=0 L J x=0 p dx x,z -1 dz -1 (35) The combined apparent resistance of the two enriched diffusion layers can be obtained in a similar way: R R6(5-6) + R6(7-8) m RT (t - t ) e e Fi L J z=0 8 8 z J + 2m m L J z=0 r r 6 -i-l p dx x.z ^ x=0 dz -1 (36) where p is the resistivity at any point (x,z) within the enriched X f z diffusion layer. (ii) The bulk solution resistance The electrical resistance of a solution-filled compartment A cm thick is sol CA ohm - cm (37) The resistances of the bulk depleting and enriching solutions are given by 58 *b = Vd+Rb. = m(A-26) <' -i -1 L J z=0 (C,A ) dz ^ ^ z .m (C6A6) dz L_J z=0 -1 M38) (iii) The membrane resistance and potential terms The resistance of a membrane cannot be calculated by a simple method but it can be measured or obtained from the manufacturer. Although direct current is used in electromembrane processes, alternating currents are usually used to measure the electrical resistance of membranes because con centration gradients that are present with direct current systems are not formed with alternating current and the resistance of the membrane itself can be more easily determined. However, the resistance of a membrane to alternating current is usually lower than the resistance to direct current (Spiegler, 1966). If precise values are needed the resistance to direct current should be determined under conditions of membrane use. There are concentration discontinuities at the membrane-liquid inter face in an ion-exchange membrane as a result of the Donnan equilibrium. Figure 13a shows the concentration distribution in a cation exchange membrane. The concentrations of the anions and cations are equal in the outside solution but deviate from each other within the membrane. The upper line is cation concentration, C+, and the lower line is anion concentration. The total membrane potential, Em, is the sum of three potential m' differences as shown in Figure 13b. E = E, m dl + *h + Ed2 (39) where E<j^, E^ are the two potential jumps occurring at the membrane faces, which form the Donnan potential. 59 I Electrolyte Membrane Electrolyte FIGURE 13 a X Concentration distribution in a cation .exchange membrane ZpCp Is the concentration of fixed charge in membrane. FIGURE 13 b Schematic potential distribution through a cation .exchange membrane. 60 is the Henderson term which is the diffusion potential existing in the interior of the membrane. The detailed expressions of the Donnan terms and Henderson term are given by Vetter (1967). A simplified expression for the electrical potential difference across a membrane in contact with uni-univalent electrolyte solutions of activities am and am on the opposite sides is given by m tt —(t - t ) In ,—T\z F c c' (a') m z (40) where t^, t are the cation and anion transport numbers in a cation-exchange membrane. The membrane potentials oppose the applied electrodialysis potentials when ions are transferred from lower to higher concentrations. The resistance per unit area due to potentials of a cation and an anion membrane is given by R=R +R +p+p m ma mc a c , mRT . p + p + rrr- S pa Fc Fi S r rm + (Y5C5} t ) ln,-~v z i a * (yfJz J -1 dz -1 m L- z=0 (t - t ) In ;•] -l -i -l dz > (41) where subscripts a and c refer to anion- and cation-exchange membrane res pectively p , p are the anion and cation membrane resistance per unit area Si c R . R „ are the equivalent resistance per unit area due to anion and ma mc cation membrane potential. 61 The apparent resistance of a cell pair The apparent resistance per unit area of a cell pair, R , is given by = R, + R + (42) \j i xv • R, "4" R IT d e D m where Rd> Rg, R^ and Rm are defined by equations (35), (36), (38) and (41) respectively. The apparent resistance per unit area of a cell pair can be evaluated by considering a local resistance at any level Z together with the average bulk concentrations of the solutions. In this case equation (42) reduces to (refer to Figure 10) R 7 = <5 TT,Z In C,A.,/C0A0 In C0A0/C.A. In C-A^/C^A, 1 1 2 2 3 3 4 4 5 5 6 6 <C1A1 " C2V (C3A3 " W <C5A5 ~ C6V In C7A7/C8A8 (C7A? - CgAg) + (A-26)(cfc+CiA7)+Pa + Pc RT Fi '22 "6 6 5~5 - 4- - 4- YqCq + (t - t ) In - + (t - t ) In —-a ay y4C4 c c' Y«C5 f8"8 (43) The subscripts d and e refer to the depleting and enriching solutions and a and c refer to the anion- and cation-exchange membranes. The numerical subscripts refer to the corresponding numbers in Figure 10. Eq. (43) is based on the following assumptions: (i) Validity of Nernst idealized model (refer to appendix C) (ii) A uni-univalent electrolyte system (iii) Solution-filled compartments without spacers; each of the same 62 thickness A and with two diffusion layers each of the thick ness 6 (iv) Constant transport numbers of the membranes and solutions over the range of concentrations of interest (v) Single-ion activities can be replaced by molalities and mean activity coefficients. Simplifying Assumptions Even the simplified equation of the apparent resistance of a differ ential area of a cell pair i.e. Eq. (43) is cumbersome and time-consuming, It can be simplified by making several assumptions, most of which can be approached in practice. The first simplifying assumption that can be made is that the two diffusion layers in each of the flow channels are identical and the boundary layer thickness on the two membrane faces is the same. With this assumption the concentration profiles become symmetrical i.e. C. = C. and Cc = CQ and the two junction potentials (the concentration 14 5 o potentials in the boundary layers) cancel out as shown in Figure 14. The assumption implies that: (a) (t - t)a = (t - t)c where t, t are the transport numbers of counterion in membrane and solution phase respectively and subscripts a, c refer to anion- and cation-selective membrane. (b) Same hydrodynamic conditions prevail in the boundary layers in the flow channels i.e. 51,2 = 53,4 = 65,6 = 67,8 = 6 63 T 1 J, | 0) o c o o .o 1 Cone. Dilute E, =-|rn4 "26" C' Cone. to Dilute -4 2rn<p ~|3mc£ c o o o 0-3 C a> o c o o FIGURE 14 Back emf due to concentration and polarization (neglecting IR effects) when current is flowing as marked (Spiegler,l966). Dashed lines , concentration j solid lines potential A,anion .permeable membrane C , cation, permeable membrane. 64 According to this assumption Eq. (43) reduces to YeC In C.A-/C1A1 In CJV,/CJV_ Rl-9 = 2(t - tc) § In f 26( ACACArA 19 c Fi y4C4 C2A2 - C1A]_ C6A6 -+ (A-26)(ctAT + ^A7)+Pa + Pc <44) 2 2 6 6 where t, t£ are the transport numbers of counterions and co-ions in the membrane phase. Eq. (28) can be used to estimate the boundary layer thickness, 6. Other terms which are not accessible to direct measurement in Eq, (44) are the interfacial concentrations, and C^. These can be eliminated as follows: Eq. (10) can be written as i£ = °2 " Cl = i • (45) dx & B ^ ; where the constant B, which depends only on the nature of the dissolved electrolyte and of the membrane, is defined as B == (46) (t - t) substitute Eq. (11) into Eq. (46) B C-6 = -v-^ (47) Him Therefore we get C± = C2 (1 - ~— ) = C2 (1 - k) (48) lim Similarly by assuming the same concentration in both diffusion layers we get 65 C5 " C6+f " C6 <49> where ns is the separation factor defined by C C The following further simplifying assumptions can be made. The equivalent conductance is independent of concentration over the limited range of interest i.e. Al = A2 = = A The activities are equal to the concentrations, y± = Y2 = ' = i-o With these assumptions together with Eqs. (48) and (49) Eq. (44) reduces to where k and ns are defined by Eqs. (26) and (50) respectively and t, t are the transport numbers of the counterion and co-ion respectively in the membrane. For ideally selective membranes (t - tc) = 1.0 Instead of integrating over the whole flow path, a considerable simplification is achieved by using logarithmic^ mean values of the bulk con centrations, C2 and Cg together with Eq. (44) or (51) to evaluate the apparent resistance of a complete cell pair. A 66 Finally it should be noted that all these expressions for the apparent resistance of a cell pair, namely Eqs. (42), (43), (44) and (51) have to be modified to take into account the effects due to: (a) Presence of spacers in spacer filled configurations (b) Ohmic resistance due to scale. Scales, such as CaSO^, CaCO^, Mg(0H)2 etc., can precipitate out of solution and deposit on the membrane surfaces at points of low velocity. 3.1.2. Ohmic Analysis This analysis assumes proportionality between current and voltage in the electrodialysis stack. It is an empirical approach to evaluate stack resistance. For a cell of given design and membrane type, it is a relatively simple matter to use a laboratory model to obtain an empirical set of resistance values as a function of typical operating conditions. These values may then be used to design a full-scale plant. This data may be 2 2 expressed as the resistance of 1 cm of one cell pair in ohm-cm , as a function of external solution concentrations. Although the actual correlation of cell-pair resistance, R^, with solution concentration may take the form of a polynomial power series such 2 B as R = a + bC + cC etc, or an exponential form R = a C as shown by P P Tye (1963), Mason and Kirkham (1959) have suggested the following expression for the local resistance per unit area of a cell pair: Kl R = — + K_ - L C (52) P C 2 3 where K^, ^ and are constants for a given spacer geometry, ionic com position, membrane type and temperature. C is the local "average" con centration calculated from 67 _1_ = 1 C" 1 + r v C. T C Q C (~+~) (53) Here C. and C are the local diluate and concentrate concentrations, and d c ' r is the ratio of spacer thicknesses in the concentrate and in the dilute compartment (frequently r is unity). At low values of C (i.e. in dilute solutions), the term becomes negligible and Eq. (52) reduces to the form Kl R = ^ + K9 (54) P C 2 In dilute solutions the electrical resistance of strong electrolytes is approximately inversely proportional to concentration, and the electrical resistances of commercial ion exchange membranes are relatively independent of changes in electrolyte concentration. This is true up to about 0.1 N (Mason, 1959). Thus Eq. (54) can be considered to consist of a solution resistance term, , plus a membrane resistance term, K0. The K„ term in C Eq. (52) allows for non-linearity between solution concentration and con ductance, and for decrease in membrane resistances with increasing solution concentration. At electrolyte concentrations higher than 0.1 N the membrane resistance begins to decrease with increasing electrolyte concentration because of the increased conductivity of the electrolyte in the resin. Allowances for membrane potentials which oppose the applied voltage and thus represent an apparent resistance, and for resistance increases due to concentration gradients in the diffusion layers is made in choosing the numerical values of K^, and K^. The K's can be estimated from tabulated values of solution and membrane resistance. The stack resistance is calculated from the solution concentration by either using the logarithmic mean concentration or by integrating over the 68 whole flow path. Integration Procedure The local value, at any level z along the flow path, of the resistance per unit area of a cell pair (R ")^ can be integrated over the membrane area (pa) available for desalination to obtain the total resistance of a cell pair, R . P pa 1_ R da o p z cell pair/ft (55) where a, is the actual membrane cross-sectional area, cm (a = m x n); and p is the fraction of membrane area available for desalination. 2 pa = pnz cm pda = pndz cm2 where n is the membrane width (cm) and z is the coordinate system along a membrane surface (refer to Fig. 11) transposing variables, .m R = pn z=0 dz p z (56) From Eqs. (52), (53) P z Kl cjiy + K2 K3 Ca(z) (57) and Ca(z) 1 + r 1 + r Cd(z) Cb(z) (58) Variations of C, (z) and C, (z) with z, will make C (z) a function of a D a 69 Ca(Z) = f(z) K, (59) (60) Substituting Eq. (60) into Eq. (56), R = pn = pn r m o m Kl -1 [ + K2 - K3 f (z)] dz { K± + K2 f(z) - K3[f(z)]2 } 1 f(z) dz (61) f(z) is obtained by substituting values of the bulk solutions from Eqs. (31) and (32) into Eq. (58) f(z) = C (z) = dH-r)(Cd(0)e-aZ){[Cb(m) - (F^F^ (m) ] + [ (F^C^Oe""*]} 3 1 ... ...i . ~ • - - — ...... {[Cb(m) - (Fd/Fb) Cd(m)] + Cd(0)e_CtZ [(F^) + r]} -az. t •««o • u • • i (62) Thus, substituting into Eq. (61) for f(z) or C (z), the cell pair resistance, Si Rp, can be evaluated. Small intervals (Az) can be chosen to evaluate the integral as a summation R = pn Ca(z) Az 2_ + K, Ca(z) -z=0 K3 Ca(z)2 (63) 3.2. Mass Transfer Models The differential equation of material conservation for a component in the flow system* shown in Figure 15 is: FIGURE 15 Differential section of column. 71 s = 0 (64) (a) (b) (c) (d) where and Cg are the concentrations of the component transferred in the mobile and stationary phases respectively, v is the displacement velocity, D is solute diffusivity, e is void fraction. Equation (64) is sometimes called the chromatography equation. The terms in this equation express mass conservation contributions attributable to the following mechanisms: (a) = interstitial, fluid phase transient (b) = axial convection (c) = axial fluid-phase diffusion (d) = adsorptive phase transient Together with an equation relating local values of Cg to C^, and appropriate boundary conditions, Equation (64) applies during every sub-interval of a cyclic flow process. 3.2.1. Equilibrium Model Pigford et al. (1969) used Equation (64) to develop a simple "equilibrium model" for thermal parametric pumping. The basic assumption in this model is that the solid and fluid are locally in equilibrium. This assumption greatly simplifies the equations since rate information is not needed. Tn addition, axial dispersion was neglected and the equilibrium relationship was assumed to be linear. With these assumptions the resulting equation is a hyperbolic partial differential equation which can be solved analytically by the method of characteristics developed by Acrivos (1956).- The characteristic lines can be used to show graphically the development of the separation, and to show 72 when separation will not occur; thus the model offers algebraic solutions that can be used for a rapid calculation of parapump separation. The equilibrium theory was generalized by Aris (1969) and extended to an open system by Gregory and Sweed (1970), Chen and Hill (1971) and it was further extended by Thompson and Bowen (1972) to predict separation in a two-column arrangement where the two columns are operated back-to-back to minimize mixing. Although the equilibrium model is compact and easy to apply it ignores dispersive effects which limit separation in a real system, hence it can not predict the ultimate steady-state separation (Rice, 1973). Gupta and Sweed (1972) have extended the equilibrium model to take into account axial mixing. Foo and Rice (1975, 1976) used a more general temperature dependence in the linear isotherm along with the dissipative forces associated with axial dispersion, film resistance and pore diffusion to predict the ultimate separation in closed parapumps. Mass transfer between the moving phase and the stationary phase is assumed to take place instantaneously in the equi librium model and hence the cycle durations do not enter into the solutions predicted by the model. Since the cycle duration may be assigned any arbitrary value, the equilibrium model solutions are not functions of real time and the model can only serve as in idealization that predicts the best possible separation. Electrically driven separation processes such as electrodialysis are governed by finite rates of mass transfer and usually operate at concen trations far from equilibrium. The rate of mass transfer is proportional to the current flowing (within a certain range of concentration) and is thus to some extent under the direct control of the experimenter. Cyclic 73 operation of such systems may therefore be better represented by a rate model than by equilibrium theory. 3.2.2. Rate Models Two rate models will be considered here: (a) constant rate model (b) concentration-dependent rate model The basic assumption in each of these models is that the equilibrium condition may be disregarded altogether, i.e. if the two phases were left in stationary contact for a sufficiently long period of time, the adsorbate would be transferred completely into one of the phases. These models also assume that the capacity of the storage layers is large enough that it does not impose a limit on mass transfer during the cycle. Axial dispersion is neglected and the fluid is assumed to be incompressible and have constant density. The complete operating cycle is divided into a number of sub-intervals; whenever the fluid velocity changes at the end of these periods it is assumed that it changes in a stepwise manner, while it remains constant during each of these sub-intervals. Furthermore, a system in which one void volume is displaced every half cycle is considered. Concentration changes predicted by the rate models are functions of time, in contrast to the equilibrium model solutions which are functions of the number of cycle but not of real time, (a) Constant rate model A constant rate of Interphase mass transfer, uniform everywhere within the cell, requires a constant, uniform, distribution of electric current. Uniformity can be approximated by connecting a number of short stacks together in series both electrically and hydraulically, as shown in Figure 16. 74 Dialysate Production Br'me Production FIGURE 16 Series connection of ED modules to approximate constant-rate operation. 75 Constant current can be maintained by a suitable power supply. This will ensure constant mass transfer until the solute concentration drops low enough at some point in the apparatus that water splitting occurs and solvent ions start to carry a significant portion of the current. While constant-rate operation is not very practical, an examination of some of the con sequences of this model is of interest since it illustrates limiting conditions. If the rate of mass transfer is held constant, and axial diffusion is neglected, Equation (64) simplifies to dC 9C. .. ac •*r + vTT- = - < ^T^- > TT- = K (constant) (65) dt dZ £ dt during any sub-interval of the cycle. (i) Synchronous (in-phase) operation If the total cycle period T is composed of two equal sub-intervals, with simultaneous reversal of both the flow direction and the direction of mass transfer, then the constant in Equation (65) can be written K = -during the demineralizing half-cycle and K = K2 during enrichment i.e. dCc dC £ s dt"~ = ~ P = ~ ^1 » ^or demineralization (66) dC£ dC t s -j-jT- = - p = K2 ; for enrichment (67) 1 - e where p = e T If we consider K2 > and demineralization takes place for time y ; then to maintain the material balance of the system the enrichment period should be At where 76 T K At - ^ (68) T Kl during the rest of enrichment half cycle i.e. — (1 - — ) the voltage can 2 be switched off to save power. The graphical solution of the model Equations (66, 67, 68) gives the following result (refer to Appendix D): C T K T K K o o o 2 - 1+tf(1-k:^ (70) o o 2 where C„, are the top (demineralized) product and the bottom (enriched) 1 a product respectively C is the initial concentration; CN, N. = C . rtN = C o ' f(t=0) s(t=0) o n is the number of cycles From Equations (69, 70) it is clear that maximum separation occurs when Kl K_ >> K. or when — -»• 0. In this case the separation factor, ns is given £• J. K2 by TK-n ns - TT^ -T,n TK1n 1 -4 C o It is also obvious that when = 1^, no separation occurs after the first cycle. The concentration of solute stored within the membranes returns to its initial value at the end of each cycle and the average top and bottom con centrations (Equations 69, 70) do not change after the first cycle. Figure 17 illustrates successive concentration profiles in the stack 4 Ac Plug Flow Co Plug Flow Plug Flow Btm. Resvr. E.D. Stack Top Resvr. Axial Position a t = 0 b(i ) Well Mixed Plug Flow Well Mixed b(ii) t =0 Ot=T/2 c(i) c(ii) t = T/2 E> t = T d(i) d(ii) t= T Ot=3T/2 FIGURE 17 Concentration profiles predicted by constant.rate model with equal rates-continuous cyclic displacement of fluid and mass transfer. Case (i),the top row, assumes no mixing in the end reservois , while case(ii) assumes well mixed end reservoirs. 78 and in the end reservoirs when = K2» For simplicity it is assumed that the end reservoirs have the same volume and the same L/D ratio as the cell interior. The initial concentration profile is shown in (a), Figure 17, After the first half-cycle the conditions are either as shown in (bi) (if no mixing takes place in the end reservoir) or in (bii) (if the end reservoir is well mixed). The fluid in the top reservoir is displaced back through the column to produce the profiles shown in (ci) or (cii) at the end of the first complete cycle, when the mean concentration in the bottom reservoir has returned to the value it had in (c). Figure 17(d) shows conditions at the end of the 3rd half cycle, which are identical with (b) . In order to obtain separation we must either: (i) make K2 > , or (ii) modify the cycles by periodically interrupting the electric current, or (iii) modify the cycles by periodically interrupting the fluid flow, (iv) introduce lag between current and flow cycles i.e. use out-of-phase operation Case (i) has already been considered. Thompson et al. (1974) has dis cussed the other three cases as shown in the following sections. (ii) Interrupted Current operation This is a more general and more useful type of operation than case (i) Here the current is turned off during a part of every half cycle. Figure 18 shows the flow and current cycles for this kind of operation. During the first half-cycle both flow and mass transfer take place for period T^, at which point the current is turned off and flow continues for period T0. A similar sequence, and T^, follow during the second half-cycle. From the material balance on the salt Vi - K2T3 (72) and from the material balance on the solvent Tl+T2 = T3+T4 (73) If 3 is the fraction of the first half-cycle during which the current is on (3 = T^/, then the successive intervals are; r± = 3(f) T2 = (1 - 3)( | ) t3 - > *1 T and T4 = (1 - ^ 3) ( \ ) (74) Figure 18 shows concentration profiles at consecutive intervals in a batch separation, for simplicity a system in which the end reservoirs remain unmixed is illustrated. The dotted lines represent the concentration at the beginning of each period and the solid lines show the profile at the end of each period. Subsequent cycles result in a progressive build up of the concentration wave. The average top product concentration after n cycles is given by C TK TK K =l--^M2-6)-^M2-Ml+^)] (n - 1) (75) o o o 2 and the average concentration of the bottom (enriched) product is FIGURE 18 Concentration profiles-interrupted current cycle. 81 C TK K = 1 + j± 3 [2 - 3 (1 + ^ )] n (76) o o 2 If = K2 and 3=1 separation ceases after 1 cycle. It is possible to choose a value of 6 that gives continuing separation for any specified value of K^/K,,. Differentiation of equation (75) or (76) shows that the most rapid increase in separation will be obtained when K2 Under these conditions the separation factor is given by TK 1 + 4cTe n ns = - ^ (78) 1 - -~ 3 (n - 3 + 1) o Thus, if K^ = K2> best separation is obtained by setting 3 = h, so that = T_ = x_ = T, and the separation factor is 2 3 4 TK 1 + 8cTn ns - _2 (79) 1 - -ggi (n + W o 8C n = (™ h). If n > n , then n must be used. max TK^ max' max If K2 >> K^, 3=1 and the separation factor is TK 1 + 4cTn ns = ^ (80) 1 " 4C-n o 4C provided that n < —-TK1 82 Since the current is only on for fraction 3 of each cycle, the amount of separation obtained for a given amount of current consumed is approximately the same in equations (79) and (80). If a real system is operated with > K^, but with no externally controlled interruption of the current, as in case (i), the concentration in the storage layers must continually decrease in successive cycles. After a number of cycles the concentration will drop to near zero part way through a depletion half cycle, causing the electrical resistance to become very large. If the voltage is controlled at a constant value the current must then become very small, so that, from this cycle onward, the system will behave as if the current were interrupted part way through each depletion cycle. (iii) Interrupted flow operation A third type of operating cycle is shown in Figure 19. Here the fluid displacement, rather than the current, is periodically interrupted. The current is turned on at the beginning of the cycle, to demineralize the solution, but flow does not start until the end of pause time x^. The fluid is displaced upward during period while the current remains on and further demineralization takes place. The polarity is reversed at the start of period x^ and a similar sequence of flow pause followed by downward displacement completes the cycle. The complete cycle time T consists of the two pause periods x^ and x^ and the displacement periods and x^. In the subsequent work based on this operating cycle the displacement periods are kept constant and the cycle time T varies with the pause time used. From the material balance on the salt Kl (t1 + T2) = K2 (T3 + T4) (81) 83 and from the material balance on the solvent T2 = T4 (82) If pause lasts for a fraction of the total cycle time T, then the successive intervals are: Tl = a(f) TK2 T T2 = Kx + K2 " a( 2 } Kl ~ K2 T and T4 - x2 (83) Figure 19 illustrates the way in which the concentration profile develops in a closed system with no mixing in the. end compartments. The average top-compartment concentration after the nth cycle is given by C TK 2K TK K K -K o o 1 2 o 2 12 (84) and the bottom concentration is C = 1 + 77^ Ul + ^ ) a + 2 ( 1 2 )} n (85) CQ 4CQ K2 KX + K2 If K^ = K2 the separation factor is given by CURRENT FLOW 23 <n c m o _ o o 3 O Deplete Enrich Down Up O o o | <o i 5" CD C » Q-O o >< o CO ro OJ -I* 178 85 1 + a n ns = — 2 (86) , 1 , , l-ots 1 - _ a (n + —) o 2Co 1_a Provided that o < a < 1 and n = ( — -z— ) . max TK^a 2a If n > n , then n must be used, max max Obviously, best separation is obtained as a + 1, giving an operating cycle with relatively long flow-pauses and rapid displacement. This special case may be referred to as instantaneous displacement operation or pure-pause operation in comparison with continuous displacement operation of Case (i). As a 1, the separation is given by TK 1+2C^n ns = (87) TK 1 - 2Tn o which is double the value predicted by case (i) in its best operating con ditions (Equation 71). (iv) Out-of-phase operation Figure 20 illustrates the concentration profiles at successive quarter cycles after the start for a constant rate process operating with the current cycle 90° out-of-phase with the displacement. It is assumed that the rate constants K^ and are equal and that the effluent remains unmixed in the end reservoirs. In contrast to in-phase operation, out-of-phase operation leads to a continuing build-up of the concentration wave. 2T If the current switching leads the flow switching by time T, and y = —» the average top and bottom concentration transients after the nth cycle are FIGURE 20 Concentration profiles predicted by constant-rate modeLcontinuous cyclic displacement of fluid and mass transfer.The mass transfer cycle is 90° out-of .phase with the displacement cycle. 87 given by: C TK TK = 1 - •— [1 - 2 Y2] - -^(1 - Y) (Y) (n - 1) (88) o o o C TK = 1 + (1 - Y) (Y) n (89) o o in the interval o 4 y < h* The concentrations change linearly with the number of cycles and the greatest rate of change occurs when y = h. This is in marked contrast to the results of the equilibrium model of parametric pumping, which predicts best separation when transfer and displacement cycles are in phase and no separation when they are 90° out of phase (Pigford et al., 1969 a). The separation factor when Y = 0 is given by ns = i=- - (90) x 4C o i.e. separation ceases after 1 cycle. When y = h the separation factor is TK-1 + 4cTn ns = ^ (91) 1 " 4CT <n - ^ o 4C n = ( ——I- %). When n > n , then n must be used. . max TK^ max max Figure 21 shows concentration profiles in a possible arrangement of two units operated together, with the top of one cell connected directly to the top of the other and the bottoms of the cells connected together through a reversible pump. With this configuration no end reservoirs are needed and the concentration wave builds up twice as rapidly as with a single unit. Flow J I I I I I I I I J I O-H/4 T/4-H/2 T/2 4 3T/4 3T/4->T FIGURE 21 Back_to_back operation of two units. Case (a) , the top row , operates with cyclic displacement of fluid , 90° out_of_phase mass transfer. Case (b),operates with no flow reversal , cyclic mass transfer. 89 Note that the concentration profile in Figure 21(a) is symmetrical at the end of each half cycle. Because of this symmetry either periodic flow reversal or continuous flow, Figure 21(b), lead to similar separation. In the first method of operation an oscillating concentration wave is generated, which grows with time, while in the second method a rotating wave is produced which grows at the same rate. A third possibility would be to operate a number of units in series to generate a travelling wave, growing as it moves along. Operation of equilibrium systems in this manner has been discussed by Pigford et al. (1969 b). Comments on various operations of the constant-rate model By comparing the separation obtained in the four cases discussed previously, it can be noticed that the concentrations change faster in case (iii) than with either of the other cases considered. Since mass trans fer during displacement contributes little to the final separation in pause operation (case (iii)), some economy in electric power consumption might be obtained by turning the current off during all or part of the displacement periods. (b) Concentration-dependent rate model" While it is possible to operate the process in a constant current/con stant rate mode, it is more convenient to apply a constant potential to the electrodes. The local current density is then a function of the concen trations along the current path and of the effective voltage. If the applied voltage is A<j>, and the voltage available to the stack is At))' (after ohmic losses and overpotentials in the electrode compartment are allowed for), then the current through the stack is given by 90 1 - ^R-^ (92) where A<J>^~XT is the Donnan potential across the membranes of the stack. The DON r resistance is the sum of three terms, R - the resistance of the membranes, m Rf - the integral resistance of the fluid in the flow channels, and R - the integral resistance of the fluid stored in the core layers within each membrane pair. The fluid resistance terms comprise the bulk fluid resistance together with the associated boundary layers resistances. Under the operating conditions for most experiments the Donnan potential was small compared to the applied potential, so that the current density was mainly controlled by the largest resistance in the current path. Low con centrations, and hence high resistances, occurred in the flow channels during most of the depletion part of an operating cycle, and in the membrane cores during enrichment. Accordingly the 'following rate laws were assumed 9C g p -rr— = &i C^. (during depletion) (93) a t JL t ac -r—- = - a„ C (during enrichment) (94) o t 2 s Substituting these equations into equation (64), and neglecting axial diffusion, leads to a set of equations that can be solved analytically for some boundary conditions. Solutions have been obtained (Bass, 1972) for the interrupted-flow operating cycle previously described provided mass transfer is restricted to the flow-pause periods and the displaced fluid volume is equal to the void volume. Under these conditions, the average dialystate and brine concentrations after n cycles are ^ - Pn (95) Co 91 4=n-l i» o 2 + p _ pn _ pqn _ qpn-l (1 _ p) j- { ± ]4 (gg) where alT p = exp ( — ) a2T q = exp ( 2~ ) 1 - e p = —-— An alternative semi-empirical approach can be developed by assuming a concentration-dependent mass transfer rate similar to Equations (93, 94) 9C p = \ CF (during depletion) (97) By considering the overall material balance for the solute and the limiting separation a general solution of the system is obtained in which the average dialystate and brine concentrations after n cycles are given by C -k Tn -k Tn = exp( -j— ) + k2 [1 - exp( -f-)] (98) o C -k.. Tn _k/.Tn = 2 - exp( -|— ) - k2 [1 - exp( -f- )] (99) o This solution can be simplified by assuming that k^ = k^ = k^ in this case Equations (98, 99) reduce to C -k Tn -k Tn o exp( ) + k2 [1 - exp( -|— )] o -k Tn = k2 + (1 - k2) exp ( -1— ) (100) C -k Tn = 2 + (k2 - 1) exp ( -±— ) - k2 (101) 92 where k^, k^ are constants which are functions of system and operating parameters. If we assume flow channel and storage compartment are of the same capacity and dimensions (as is the usual case) then p =1.0 and Equations (95, 96) will be a special case of Equations (98, 99) where the constants are given by kn = a1, k„ = -1, k. = 0 and k. = a. 3.2.3. Comment on Constant-Rate Model Although the constant-rate model is compact and easy to apply it ignores dispersive and current-limiting effects which limit separation in a real system; hence it can not predict the ultimate steady-state separation. However, the model offers simple algebraic solutions to a complicated system which can be utilized to show graphically the development of the concentration profiles and to indicate when separation will not occur. The model has been used extensively in the present work to compare various operating cycles and modes of operation. CHAPTER 4 The Cyclic Electrodialysis Process -Objectives, Techniques and Apparatus 4.1. Objectives of the Program The primary objectives of this experimental program were; to explore the possible regions of application of cyclic operation in an open electrodialysis system, to screen system parameters and to determine their relative importance. Previous work in a batch system (Bass, 1972) showed that the most important operating parameters were the displacement cycle, the applied volt age and the initial concentration. These were further investigated here together with the effect of production rate. An open system offers a high degree of freedom with regard to introduction of feed and withdrawal of products, and a variety of different operating modes were considered. The modular construction of the ED cell allowed crude measurements to be made of the axial distribution of current and probe voltage during the cycle and also permitted the effect of channel length to be investigated. The constant-rate model discussed in Chapter 3 predicted that the interrupted flow operation would result in the best separation compared to the other cycles studied (synchronous, out-of-phase and interrupted current 93 94 cycles). The experimental part of the work was based mainly on this interrupted flow cycle. The cycle is most conveniently described with reference to a single electrodialysis stack, however two stacks close-coupled in a back-to-back configuration were used in most of the experimental work. 4.2. Single Stack Operation Figure 22 illustrates the sequence of events that make up a complete operating cycle. The electrodialysis cell (ED cell) is shown schematically as a rectangular box with an internal shaded area symbolizing the sorption membrane stack. Two well mixed reservoirs (circles in Figure 22) are connected to the ends of the ED cell. Partial shading of the circles indicates the liquid content of these reservoirs at different times during the cycle. Figure 22 shows batch operation but it can be modified to allow for feed addition and product removal in various ways during the cycle. The interior of the cell is divided by many parallel ion-selective membranes into two regions; a set of flow channels connecting the inlet and outlet ports, and an interleaved set of closed "capacity cells" or membrane stack. Depending on the direction of the electric current, ions are either transferred from the solution in the flow channels to that in the capacity cells or vice-versa. During the first half cycle the applied electric potential is controlled to produce a positive square wave. The membranes 95 MOIJ pe||ddv 96 are positioned in such a way that positive polarity is equivalent to solute uptake (i.e. the cationic membranes face the anode). The intrachannel solution is, therefore, depleted during the entire first half-cycle which consists of two parts: a "pause" or no-flow interval (T^) followed by a "displacement" interval (x2) during which the fluid flows with constant rate (Q) from the lower to the upper reservoir. Displacing fluid entering the bottom of the cell may be fresh feed or "reflux" returning after a previous downward displacement, or a mixture of these. The second half-cycle begins with a polarity reversal (- n) and a simultaneous flow stoppage for another "pause" interval (T^). The intrachannel solution receives solute from the membrane stack during the whole period of this second half-cycle, which is concluded by a "displacement" interval (T^) during which the solution is returned from the upper to the lower reservoir with flow rate (- Q). The displacing fluid entering at the top of the cell may be fresh feed, or a reflux stream of depleted solution obtained during period (T^) or a com bination of these. In an open system partial reflux must be used to achieve cyclic operation while in a closed system the operation, in some ways, is analogous to total reflux operation of a distillation column. Initially the solute concentrations in the system are in equilibrium across the membranes and equal everywhere. Each cycle produces depletion of the solution in the upper reservoir and enrichment of the solution in the lower one, and an axial concentration gradient continues to develop in the ED cell until limiting steady-periodic conditions are reached. In most of the experiments reported here symmetric half cycles with regard to time intervals have been used i.e. x.. = x and x„ = x.. 97 A.3. Back-to-Back Stack Configuration Since some, or all, of the fluid leaving the cell during upward displacement is subsequently to be returned as reflux, it is convenient to connect two cells together as shown in Figure 23. This direct coupled-back-to-back configuration avoids the necessity of intermediate reflux storage tanks. Also experiments in a batch operation showed that mixing in the end reservoirs lowers separation and a reduction of mixing in the solution external to the stack helps to reduce the effects of internal mixing by reducing the gradients of the travelling fronts. The average separation factor was increased by 30 - 100% when an end reservoir (well mixed) was replaced by a coil tubing (Bass, 1972). The two cells so connected (Figure 23) are operated electically out-of-phase with each other and, of course, upward displacement in one cell implies downward displacement in the other (with the possible exception of periods when the feed is being introduced or products removed). This type of configuration can be used in either closed or open system operations. Figure 24 shows how the concentration profiles are predicted to develop during the first few cycles of operation in a closed mode, based on the constant rate model. The model neglects axial diffusion, but quali tatively it is apparent that axial mixing will tend to smooth out the square-wave profile into a shape more nearly resembling a sine wave. 4.3.1. Open System Operation of a back-to-back configuration If feed is to be introduced, and products withdrawn, connections must be provided with valves that are timed to open at appropriate moments during the cycle. Since the total volume of the system remains constant, feed must 98 Cell I Cell I (—) Reversing Pump FIGURE 23 Back _to-back operation of two cells. I I Top Bottom Top Co Displace Pause t! Pause '2 Displace Displace FIGURE 24 Developing concentration profile _ two cells operating back_to_bock in a closed system. Pouse f3 Pause VO 100 be introduced whenever product is withdrawn. For best separation it would seem desirable to take products whenever maxima or minima in the concentration profiles pass the appropriate ports, and to introduce feed at a position where the circulating fluid is close to the feed composition. If the concentration profile around the loop comprising the two cells and their interconnections is approximately sinusoidal then feed introduction ports must be located 90° away from product removal ports. Regarding the feed location and the feed timing, an open system can be run under either symmetric, semi-symmetric or asymmetric type of operation. In symmetric operation feed is introduced and products removed every half cycle with the feed being introduced to the top and bottom of each cell. In semi-symmetric operation feed is introduced every half cycle, but to one side only of each cell; while in the third mode of operation neither the feed location nor the feed timing is symmetrical, and the feed is introduced only once to one side of each cell every cycle. Figure 25 represents a symmetric operation with product removal from the mid-points of each cell. It shows the required connections and the valve timing. In symmetric operation each cycle is subdivided into eight intervals t^ (i = 1,2, ... 8). The activity takes place at each time interval as shown in the table of Figure 25 which also shows the polarity of the of the electric field, the condition of the pump (i.e. whether idle or operating and in which direction), it also indicates the state of the various solenoid valves and which of them is energized (open) and which of them is closed during the specific time interval concerned. The developing concentration profile for this mode of operation is shown in Figure 26. Here the amount of feed introduced/cycle is -r- of the total circulating volume. 101 V2 I Xh V4 -X-V5 V3 n V6 -tXr-V7 -{XI-F Time Interval ^v^^ltem Operation\^ VI V2 V3 V4 V5 V6 V7 V8 V9 Pump P Vol_ tage A <j) f| Pause 0 0 0 0 0 0 0 0 0 0 + f2 B from I 0 0 0 y 0 0 0 y 0 0 + f3 D from II / 0 y 0 0 y 0 0 0 0 + !4 Circulation 0 y y 0 0 0 0 0 0 - + *5 Pause 0 0 0 0 0 0 0 0 0 0 -f6 B from IE 0 0 0 0 0 0 y 0 y 0 _ 7 D from I / y 0 0 y 0 0 0 0 0 -f8 Circulation 0 y y 0 0 0 0 0 0 -v -/= Valve open i, n = Cell 1 8 cell 1 1 B = Brine 0= Item idle D =Dialysate or top product FIGURE 25 Flow connections and valve timing sequence for symmetric operation, Top Bottom tTop I I Pause Co-I 1 J '5 Pause 1 B4^ u: •e-V Production FIGURE 26 F- I Production 1 I '4 Circulation 1 *8 Circulation 1 Pause Top Bottom Top Co" r-^T^B 2 3 Production n f 4 Circulation FIGURE 26 _ Continued (I) n t 5 Pause t\t' 6 7 Production o ) Bottom 1 I II r li I Circulation FIGURE 26 _ Continued (2) FIGURE 26 Developing concentration profile , symmetric operation of an open system 105 Figure 26 as well as Figure 28 and 30 ignore axial mixing effects, and concentration changes during feed admission and displacement have been omitted for clarity of presentation. The product will undergo „ total circulating volume - . , , .. . , -2 x :;—- ; : a cycles of enrichment or depletion before total feed volume emerging under this mode of operation. In these Figures vertical axis' indicates concentration level, a horizontal arrow shows circulation of solution from one cell into another, and the letters F, D, B indicate the concentration as well as the location in the cell where the feed, F is introduced or the depleted and enriched products D and B are withdrawn. Figure 27 represents a semi-symmetric operation with its connections and valve timing sequence. Here the products are removed alternately from the top of cell II and the bottom of cell I, while feed is supplied to the top of cell I and the bottom of cell II. The waveform generated in Figure 28 is of sawtooth shape, and the efficiency of this operating cycle will depend on how well this waveform can be maintained under the influence of axial mixing processes. It would be expected that this method of operation would be more sensitive to axial mixing than the scheme shown in Figure 25. In the absence of mixing, both cycles are predicted to give equal separation (compare Figures 26 and 28). Figure 29 shows an asymmetric operation. An operating cycle here consists of six time intervals t^ (i = 1,2 ... 6) that constitute two non-symmetric half cycles and it needs only 4 valves as indicated in Figure 29. An asymmetric operation presents a further simplification of the system with out affecting its separating capability and results in the same separation as that predicted by the previous modes of operation (compare Figures 26, 28 and 30). 106 V4 V3 -txj-V6 -tXr->B V5 V7 B n f2 Time Interval ^vjtem Operation^. VI V2 V3 V4 V5 V6 V7 Pump p Vol tage A(j) * 1 Pause 0 0 0 0 0 0 0 0 f2 B from 1 y 0 0 0 0 0 y 0 *3 D from II 0 y 0 y 0 0 0 0 + f4 Circulation 0 0 y 0 0 0 0 + f5 Pause 0 0 0 0 0 0 0 0 -f6 B from II 0 y 0 0 0 y 0 0 -D from 1 J 0 0 0 y 0 0 0 -*8 Circulation 0 0 y 0 0 0 0 - -y = Valve open 0 = Item idle FIGURE 27 Flow connections and valve timing sequence for semi_symmetric operation. Top Bottom Top I •0 'I Pause '1 J '4 Circulation 1 r5 Pause FIGURE 28 "1 J B Production Production f6 Production Top Bottom Top Co- r '8 Circulation I Pause FIGURE 28 _ Continued (I) Top Bottom Top I o Circulation Pause FIGURE 28 _ Continued (2) Production Production Top Bottom Top Co-I f8 Circulation FIGURE 28 _ Continued (3). FIGURE 28 Developing concentration profile, semLsymmetric operation of an open system. Ill VI V3 V4\ :v2 Time Interval Item Operatiorr-^ VI V2 V3 V4 Pump P Voltage *| Pause 0 0 0 0 0 f2 B from I J 0 0 • 0 + f3 D from H 0 / / 0 0 + f4 Circulation 0 0 0 0 f'5 Pause 0 0 0 0 0 -!6 Circulation 0 0 0 0 -/ = Valve open 0= Item idle FIGURE 29 Flow connections and valve timing sequence for asymmetric operation. Top Bottom Top IE "0 Pause B Production Circulation FIGURE 30 '2 Circulation Pause 'i Pause Circulation Top Bottom Top I I F_ F_ <— J) Pause Production Circulation FIGURE 30 - Continued (I) FIGURE 30 -Developing concentration profile ,asymmetric operation of an open system. 114 It can be concluded that when axial mixing is ignored all the three modes of operation considered here lead to the same separation. However, as can be seen from Figures 25, 27 and 29 the degree of complexity of the system and the valve economy and timing sequence decreases as the cycle becomes less symmetric. 4.4> Apparatus and Operation A photograph of the completed unit is shown in Figure 31 which shows the control panel board with its timer, cycle counter, DC motor speed con troller, DC power supply, conductivity meters, 4-pen recorder and switches. The separating unit consists of two columns or cells which are depicted in Figure 32 and are represented by the boxes ED I and ED II in Figure 36 where they are shown connected to the process line, rinse loop, and the electric power supply. An asymmetric cyclic operation was used here in which the system was open during the first half-cycle and was closed during the second half-cycle (Figure 29). During the first half-cycle the solution in cell II was depleted while that in cell I was enriched. The cycle started with a pause period t^. This was followed by production periods; t^, t^ when the feed was introduced and an enriched product was removed from cell I for the time t2 and a depleted product was removed from cell II for a period t^. The first half-cycle was terminated by circulation of the solution from one cell into another. The second half-cycle consists only of a pause period t followed by a circulation period t when the solution was circulated in 5 6 opposite direction. 115 Figure 31 Electrodialysis Unit and Control Equipment 116 117 A block diagram of the experimental test stand is shown in Figure 36. The figure illustrates the way in which feed solution flows through the stack and the auxiliary equipment and it indicates the points at which the conductivities of the effluent streams, the voltage, the amperage were measured and recorded. The feed solution was introduced into the ED cells from a pressurized tank through the process line, which was an open ended line that terminated in the top and bottom products tanks. Four normally closed Dri-solenoid valves [VALCOR, series 51] were included in this line together with a reversible peristatic pump Pi [COLE-PARMER Model 7017] driven by a variable speed DC motor [CENTURY motor type DN, 0.25 HP and BOSTON motor speed controller Ratiotrol model E 25]. The circulating rate of the process solution was set by the motor controller of pump PI; and the flow direction was controlled by the reversing switch SW II. A separate rinse solution was continually recirculated through the electrode compartments of the ED cells via distributing manifolds by the centrifugal pump P2 (COLE-PARMER model MDX-3, No. 7004-10). The circulating rinse stream served to remove products of electrolysis and any gases evolved at the electrodes were swept out and vented. The electrode wash liquor used was 2000-4000 ppm aqueous solution of sodium chloride and the flow rate was about 0.47 [litre/min] per compartment. Regulated DC power was supplied to the ED cells from S0RENSEN DCR40-10A power supply through the reversing switch SW I. A solid state timer was used to control the sequence of operation, energize the solenoid valves, switch and reverse the polarity of the motor armature, control the polarity of the electric field and give an impulse to an electromechanical counter by the end of each cycle. 118 4.3.1. Details of an ED Cell Design A modular construction was used for the ED cells ED I and ED II. Each cell consists of up to eight separate stacks or stages connected together in series hydraulically and in parallel electrically (Figures 23, 32). Each stage as depicted by Figure 33 was built up from eight multilayer sorption membrane assemblies, clamped between plexiglas end-frames in a filter-press type of construction. The end frames held the graphite electrodes and incorporated flow connections for the process stream and the electrode rinse streams (Figure 33). Each assembled stage had an active 3 3 void volume for the process fluid of 50 cm plus a dead volume of about 5 cm . The construction of one of the individual membrane assemblies is shown in Figures 34, 35. Each unit consisted of the following three components permanently bonded together: (i) An outer low density polyethylene sealing frame (22.54 cm x 7.62 cm x 0.189 cm) with two key-shaped liquid distribution slots cut into each end. (ii) A triple-membrane (capacity cell) 16.19 cm x 4.44 cm, composed of a cation selective membrane (AMF C-100 or IONAC MC-3142) and an anion selective membrane (AMF A-100 or IONAC MA-3148) enclosing a core of Whatman No.l filter paper (15.56 cm x 4.13 cm). (iii) A flow channel of polypropylene spacer screen (17.00 cm x 4.60 cm x 0.098 cm) Vexar TP 23, 10 x 10 strands per inch, cut diagonally. Half of the ion exchange membranes were purchased from American Machine and Foundry Corp., while the rest were obtained from Ionac Chemical Co. and the spacer material was kindly supplied by Du Pont of Canada. 119 FIGURE 33 A single stage with its two endframes. FIGURE 34 A triple membrane _frame _spacer assembly. 120 Section at A_A' Elevation FIGURE 35 Construction of single membrane_spacer assembly for an ED cell Each stack consisted of eight such assemblies,clamped between end frames containing electrodes and flow connectors. .D HXr-VI ©—*^V3 p----( Recorder £2 Probes EDI CI V4 B Rinse • r--i 4 - Pen » i 1  Rinse Tank P2 I—J ED n Q V2 SWI PI swn J L Timer Motor Control FIGURE 36 Schematic diagram showing solution flows and instrumentation.(Asymmetric'operation.) 122 The membranes were heat sealed along both short sides. The long sides remained open to insert and to remove the filter paper. The poly propylene spacer screen was pressed into the frame by means of a heated jig. Then the triple membrane was tacked at three corners to the frame using a heated bar. A detailed construction procedure is given by Bass (Bass, 1972). The manufacturer's specifications of the membranes used are given in Table V. Detailed definitions of the parameters and methods for their measurement are found in "Ion Exchange" by Helfferich (1962) and "Test Manual for Permselective Membranes, Research and Development Progress Report #77, Office of Saline Water, U.S. Department of Interior (1964 b). 4.5. Measuring and Recording 4.5.1. Concentrations, Current, Voltage and pH Measurements (i) Concentrations The concentrations of the process solution at two points indicated by positions CI, C2 in Figure 33 were continuously measured using epoxy flow-type conductivity cells [BECKMAN, CEL-VDJ] with automatic temperature com pensators and direct-reading conductivity meters [BECKMAN, Solu-Meter RA5]. A 0 to 10 (mV) D.C. output signal from the Solu-Meter allowed potentiometric recordering of the concentration in the ranges shown in Table VI. Accuracy of the type RA5 Solu-Meter indication is within 2% of the scale span. However the accuracy of the electrical output is within 1% of span. Table V Reported Properties of Ion-Exchange Membranes " -^Type, Manufacturer and Cation-Exchange Anion-Exchange — D e s igna t ion Property ~ AMF C-100 IONAC MC-3142 AMF A-100 IONAC MA-3142 Backing Polyethylene Polyethylene Active Group Sulfonic Acid Quaternized ammonium 2 Area Resistance (ohm-cm ) 7 (0.6N KC1) 9.1 (0.1N NaCl) 3.4 (l.ON NaCl) 8 (0.6N KC1) 10.1 (0.1N NaCl) 1.7 (l.ON NaCl) (a) Transference number of counterion (selectivity) : (0.5/1.ON KC1 or NaCl) 0.90 0.94 0.90 0.90 (0.2/0.IN NaCl) 0.990 0.999 Ion Exchange Capacity (meq/g) 1.3 1.06 1.5 0.96 Approximate thickness (mm) 0.015 0.015 0.018 0.018 Mullen Burst strength (psi) 60 185 50 190 Dimensional Changes on wetting and drying (%) 10-13 < 3 12-15 < 3 Size available 44 in. wide rolls 40 x 120 in. 44 in. wide rolls 40 x 120 in. (a) Reported from concentration potentials measured between solutions of the two normalities listed. 124 Table VI Conductivity and Na CI Concentration Ranges of BECKMAN conductivity Cells CEL-VDJ corresponding to a 0-10 [mV] D.C. Signal from a BECKMAN Solu-Meter RA5. Cell Constant K [cm-1] Conductivity [micromhos/cm] Na CI Solution Concentration [PPM] 20 0-10,000 0-5,500 50 0-25,000 0-14,800 100 0-50,000 0-30,800 125 After every run samples of the depleted and enriched products were taken and their concentrations were measured using an epoxy dip Cell [BECKMAN, CEL-VH1-10] together with a conductivity bridge [BECKMAN, Model RC 16B2] -2 +3 with scale multiplier 10 - 10 . (ii) Current The current input was measured as a potential drop across a Nichrome resistance wire (14 gauge), shunt A in Figure 36. The shunts were integrated into the electrical manifold which distributed the D.C. power from switch box SW I to the stages. The wiring is shown in Figure 37. The shunt resistances were 50.0 [m^] ± 1.5% for the currents to the individual stages and 25.0 [mft] for the total current. (iii) Voltage Probe electrodes were prepared from silver wire cable which was hammered into strips approximately 3 mm wide and 0.12 mm thick. The strips were dip coated with contact cement (Weldwood of Canada Limited) and the coating was removed from one side of the tip which was located inside the stack. The probes were inserted between the separating membranes and the stack pack and sealed with silicon grease (Dow Corning). A second selector switch was connected to the probes and to one recorder pen. The circuit was analogous to the one shown in Figure 37; but without shunts. (iv) £H Samples for pH-checks were taken for some runs just prior to the experiment and immediately thereafter from the two process products and rinse stream and measured in the usual way (using CORNING digital electrometer model 101). 126 FIGURE 37 Current monitoring circuit. 127 4.5.2. Recording A four-channel recorder (WATANABE Multicorder, Model MC6-11 S4H) was used to continuously monitor the current input to the cells, the potential drop across the membrane stack, and the solute concentrations in the bottom and top conductivity cells Cl and C2 (Figure 36). The stack voltage and the current consumption are measured individually for each stage. However, because of the limited number of pens only one voltage and one current signal are recorded at,a time using two selector switches. The current signal was integrated during several experiments, using a CORNING Recorder 840, to determine the average current consumption. CHAPTER 5 Experimental Results and Discussion The primary objectives of the experimental program have been outlined before (Chapter 4). In the present work altogether 252 runs were made. These are compiled in the main survey tables (Tables IX-XVI), which show the operating conditions, production rates and the separation achieved in each run. These survey tables are followed by group tables and diagrams that illustrate the effect of single variables under otherwise fixed conditions. 5.1. Data Collection The collection of raw data during the course of a complete run consisted of the following consecutive steps: 1. Fill rinse tank with 7.5 liters of fresh rinse liquor (NaCl in distilled water, with the same concentration as the process stream but not less than 1000 ppm NaCl). 2. Fill the feed tank with solution of desired concentration (NaCl in distilled water) and adjust the pressure in the feed tank to about 8 psig. 3. Fill system with the process solution from the pressurized feed tank. 4. Start rinse pump. 5. Set the timer and the peristaltic pump speed and run the system with power off for few cycles to equilibrate sorption membrane with process solution. 6. Adjust check point of conductivity meters. 7. Select recorder pen ranges and chart speed. 8. Take concentration and pH samples of process and rinse solutions, 9. Set the timer off to bring the equilibrated process solution to a pause before starting the run. 128 129 10. Turn cycle counter back to zero. 11. Set operating conditions (final adjustment of the timer and the applied D.C. voltage). 12. Note down date, operating conditions, variable recorded by each pen and appropriate range, chart speed. 13. Set the timer on and close electric power circuit simultaneously to start the first pause interval in the first cycle. 14. When the system approaches its periodic steady state as indicated by the recorded values of concentrations. Empty the product tanks, measure the volumes and note the cycle number. Discard products obtained in this transition period. 15. Record current and voltage signals at different stations by manipulating selector switches, and mark pen traces accordingly. 16. Write down any observation related to experiment. 17. Terminate run when sufficient products are produced and all information regarding current and voltage signals at the various stations have been obtained. 18. Measure the total amount of products produced and read the total number of cycles to find and record the production rates. 19. Take samples of process and rinse streams to measure pH and con centrations. 20. Record the measured values. 5.2. Experimental Designation The experiments reported here fall into two main categories: (i) Category R which refer to the first set of experiments conducted in two columns each consisted of 4 cells or stages connected together in series hydraulically and in parallel electrically (Tables IX-XI). (ii) Category M which refers to the second set of experiments performed 130 in columns with double the length of those used in Category R (Tables XII-XIV), Each experiment in these categories is designated by either Rna or Mna where n is a number which refers to a specific combination of a feed concentration (CQ) and a production rate (P.R.). Three feed concentrations (CQ = 500, 2000 and 4000 ppm NaCl) and four production rates (P.R. = 0.0, 25, 50 and 100 c.c./cycle) have been used which result in 12 combinations and n assumes the values 1,2 12 as shown in Table VII. a is a letter which represents a specific combination of applied voltage (A<J>) and the pause time (T). Three voltages (A<(> = 10, 20 and 30 volt) and three pause times (T = 15, 30 and 45 sec.) have been investigated which lead to 9 combinations and a is symbolized by any of the letters A, B I as shown in Table VIII. 5.3. Main Survey Tables The columns of the main survey tables are (see Tables IX-XVI): 1. EXP Group: This shows the experiment category R or M and the n-value (n = 1, 2, .... 12). 2. Production Rate: of each product (demineralized and concentrated) in c.c./cycle. 3. Feed Concentration: in parts per million NaCl in distilled water. 4. EXP Symbol: the symbol of a in the experimental designation Rna or Mna. 5. Applied Voltage: the constant voltage supplied by the regulated D.C. power source in volts. 6. Pause Time: in each half cycle in seconds. 7. Brine Concentration: 9. Dialysate Concentration: both measured conductometrically and converted by means of calibration curves into concentrations in parts per million NaCl. 131 Table VII Values of n in Experimental Designations Rna and Mna ^v^Op er a t ing TT .. ^^-v. Parameters Value ^^v. of n Feed Cone. Cq (ppm) Production Rate p.p. (c.c./cycle) 1 25 2 2000 0 3 50 4 100 5 25 6 500 0 7 50 8 100 9 25 10 4000 0 11 50 12 100 Table VIII Values of a in Experimental Designations Rna and Mna ^v^Operating ^^Parameters a APPLIED VOLTAGE, A* (volt) PAUSE TIME, x (sec) A 30 B 20 45 C 15 D 15 E 30 30 F 45 G 45 H 10 30 I 15 133 8. Brine Volume: 10. Dialysate Volume: These are the production rates of the two product streams expressed in c.c. per cycle. 11. Separation Factor (ns): Defined as the ratio of brine (bottom product) to dialysate (top product) concentrations ns = The main survey tables of all successful experiments in category R and M are presented on the following pages. Successful means not inter rupted by mechanical, electrical or human failure. 5.4. Parameters and Modes of Operation Investigated (a) Parameters The parameters which are studied are: 1. Demineralizing path length. 2. Production rate. 3. Pause time, x. The total cycle time T is the summation of pause time, x which is variable, the circulation time t£ which is kept constant and production time tp which varies between 1.5-6.0 sec depending on the amount of product. 4. Applied voltage, A<j) 5. Initial concentration, C . o (b) Modes of Operation The following modes of operation were considered: 6. No-pause operation. 7. No-power during circulation operation. 8. Semi-symmetric operation. Each of these parameters or modes of operation is analysed separately by forming groups of experiments in which the other parameters are constant. Table IX Compilation of Experiments with Initial Concentration (Co) of 2000 Two Columns.Each consists of 4 Cells in Series 1 2 3 4 5 6 7 8 9 10 11 PRODUCTION RATE (C.C./CYCLE) FEED CONC. (PPM) APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP-CROUP EXP-SYMBOL VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 3730 212 17.59 1950 B 20 45 4310 135 31.93 C 15 3320 415 8.00 11 15 3450 239 14.44 R2 0.0 1950 E 30 30 4435 133 33.35 F 45 4800 101 47.52 G 45 3380 470 7.19 1950 H 10 30 3020 550 5.49 I 15 2800 880 3.18 A 30 3560 18.80 400 19.83 8.90 1950 B 20 45 3770 18.19 290 19.80 13.00 C 15 3310 17.90 580 18.30 5.71 D 15 3410 17.94 455 18.11 7.49 Rl 20 1950 E 30 30 3900 17.20 280 19.80 13.93 F | 45 4025 17.73 195 19.80 20.64 1 C 45 3300 17.55 735 18.16 4.49 1 i 1950 H 10 30 3010 18.10 820 18.20 3.67 I ! 1 I ! 15 i 2795 18.00 1020 18.13 2.74 Table IX (Continued) 1 2 34567 8 9 10 11 EXP. GROUP PRODUCTION RATE (C.C./CYCLE) FEED CONC. (PPM) EXP» SYMBOL i APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) BRINE DIALYSATE SEPARATION FACTOR ns CONC. (PPM) VOLUME (C.C/CYCLE) CONC (PPM) VOLUME (C.C./CYCLE) R3 50 1950 A 30 3200 47.38 640 48.30 5.00 B 20 45 3460 47.41 480 48.62 7.21 c 15 2850 47.88 990 48.25 2.88 1950 D 15 3180 47.15 830 49.85 3.83 E 30 30 3500 47.34 450 49.69 7.78 F 45 3720 46.46 310 49.83 12.00 1950 G 45 2780 47.14 1130 48.33 2.46 H 10 30 2615 47.64 1290 48.14 2.03 I 15 2370 46.54 1550 48.08 1.53 R4 100 2055 A 30 3050 96.20 1115 98.90 2.74 B 20 45 3270 96.54 870 98.75 3.76 c 15 2580 96.23 1545 97.87 1.67 2055 D 15 2910 96.94 1190 97.11 2.45 E 30 30 3300 97.83 790 98.10 4.18 F 45 3615 97.89 515 98.21 7.02 2055 G 45 2620 97.22 1465 98.50 1.79 H 10 30 2500 97.15 1590 98.43 1.57 I 15 2400 96. S8 1725 98.13 1.39 Table X Compilation of Experiments with Initial Concentration (Co) of 500 PPM Two Columns/Each Consists of 4 Cells in Series 1 2 34567 8 9 10 11 PRODUCTION FEED EXP« SYMBOL APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP. GROUP RATE (C.C./CYCLE) CONC. (PPM) VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 1447 24.5 59.06 530 B 20 45 1915 23.7 30.80 C 15 1300 28.2 46.10 D 15 1790 24.4 73.36 R6 0.0 530 E 30 30 1833 19.2 95.47 F 45 G 45 1332 86.0 15.49 530 H 10 30 1160 101,0 11.49 I 15 1042 157.0 6.64 A 30 1070 17.91 31.5 19.14 33.97 530 B 20 45 1110 17.19 24.0 19.38 46.25 C 15 1040 . 17.94 41.0 19.11 25.37 D 15 1070 17.75 25.0 19.80 42.80 20 530 E • 30 30 1125 17.15 20.4 19.79 55.15 F 45 1150 17.14 16.8 19.82 68.45 G 45 970 17.97 95.0 19.16 10.21 530 H 10 30 940 17.95 123.0 19.03 7.64 I 15 850 17.94 214.0 19.00 3.97 Table X (Continued) 1 2 3 4 5 6 7 8 9 10 11 PRODUCTION RATE (C.C/CYCLE) FEED EXP-SYMBOL APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP. GROUP CONC. (PPM) VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. I (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 980 47.43 38 49.14 25.79 510 B 20 45 1020 46.15 30 48.30 34.00 C 15 960 47.87 48 48.10 20.00 D 15 1016 46.17 40 49.63 25.40 R7 50 510 E 30 30 1044 46.14 32 49.89 32.63 F 45 1055 46.13 27 49.87 39.07 G 45 928 46.96 103 48.04 9.01 510 H 10 30 900 47.85 130 49.13 6.92 I 15 796 47.89 221 48.11 3.60 A 30 935 96.94 66 97.14 14.17 500 B 20 45 950 96.72 57 97.80 16.67 C 15 915 96.16 103 97.84 8.88 D 15 920 97.80 76 98.28 12.11 R8 100 500 E 30 30 948 96.30 57 96.87 16.63 F 45 960 96.15 52 93.31 18.46 G 45 852 96.26 153 97.59 5.57 500 H 10 30 800 97.40 200 97.72 4.00 I 15 706 96.03 298 98.17 2.37 Table XI Compilation of Experiments with Initial Concentration (Co) of 4000 PPM Two Columns^Each consists of 4 Cells in Series 1 2 3 4 5 6 7 8 9 10 U EXP. GROUP PRODUCTION RATE ' (C.C./CYCLE) FEED CONC. (PPM) EXP« SYMBOL APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) BRINE DIALYSATE SEPARATION FACTOR ns CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) RIO 0.0 3670 A 20 30 4980 2080 2.39 B 20 45 5500 1645 3.34 V 30 30 5535 1250 4.43 F 30 45 6210 900 6.90 R9 20 3670 A 20 30 4900 17.73 2475 19.18 1.98 B 20 45 5400 17.80 2020 19.20 2.67 E 30 30 5420 18.61 1750 18.72 3.10 F 30 45 6150 18.13 1350 18.96 4.56 Rll 50 3670 A 20 30 4700 47.50 2645 48.75 1.78 B 20 45 5020 47.24 2280 48.34 2.20 E 30 30 5300 47.45 2120 48.25 2.50 F 30 45 5700 46.85 1655 47.95 3.44 R12 100 3720 A 20 30 4520 96.25 2970 98.35 1.52 B 20 45 4700 96.10 2660 98.35 1.77 E 30 30 4850 96.74 2540 98.00 1.91 F 30 45 5330 96.92 2150 98.85 2.48 Table XII Compilation of Experiments with Initial Concentration (Co) of 2000 PPM Two Columns^Each Consists of 8 Cells in Series 1 2 3 4 5 6 7 8 9 10 11 EXP. GROUP PRODUCTION RATE (C.C./CYCLE) FEED CONC. (PPM) EXP. SYMBOL APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) BRINE DIALYSATE SEPARATION FACTOR ns CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) M2 0.0 2130 A 30 4225 120 35.21 B 20 45 4300 102 42.16 C 15 4025 177 22.74 2120 . D 15 4400 85 51.76 E 30 30 4525 70 64.64 F 45 4675 57 82.02 2120 G 45 3900 280 13.93 H 10 30 3825 380 10.07 I 15 3650 610 5.98 Ml 25 2160 A 30 4000 25.37 196 24.17 20.41 B 20 45 4075 25.52 143 24.48 27.53 C 15 3875 25.87 330 24.13 11.74 2170 D 15 4125 24.67 140 24.50 29.46 E 30 30 4250 25.00 118 25.00 36.02 F 45 4350 24.57 94 25.71 46.28 2170 G 45 3825 25.79 410 24.21 9.33 H 10 30 36.75 25.88 570 24.13 6.45 I 15 3375 25.45 840 24.66 4.02 Table XII (Continued) 1 2 3 4 5 6 7 8 ? 10 11 EXP. GROUP PRODUCTION RATE (C.C./CYCLE) FEED CONC. (PPM) EXP. SYMBOL APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) BRINE DIALYSATE SEPARATION FACTOR ns CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) M3 50 2130 A 30 3950 52.14 232 50.48 17.03 B 20 45 4025 52.55 163 51.76 24.69 C 15 3775 51.43 470 50.30 8.03 2120 D , 15 4050 50.09 154 50.87 26.30 E 30 30 4175 50.27 127 52.69 32.87 F 45 4300 49.12 105 51.68 40.95 2120 G 45 3725 50.52 550 50.70 6.77 H 10 30 3400 52.73 810 52.05 4.20 I 15 3050 50.13 1270 52.39 2.40 M4 100 2100 A 30 3900 101.11 267 99.83 14.61 B 20 45 4000 98.85 192 96.75 20.83 C 15 3675' 99.09 575 98.86 6.39 2160 n 15 4025 101.17 180 98.25 22.36 E 30 30 4125 98.88 145 96.25 28.45 F 45 4200 99.35 125 98.15 33.60 2140 G 45 3625 100.00 640 101.18 5.66 H 10 30 3300 98.17 1100 100.00 3.00 I 15 2880 98.44 1440 99.88 2.00 Table XIII Compilation of Experiments with Initial Concentration (Co) of 500 PPM Two ColumnsjEach Consists of 8 Cells in Series 2 34567 8 9 10 11 EXP* GROUP PRODUCTION FEED EXP. SYMBOL APPLIED PAUSE BRINE DIALYSATE SEPARATION RATE (C.C./CYCLE) CONC. (PPM) VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 1130 16.5 68.48 550 B 20 45 1200 13.6 88.24 C 15 1090 20.2 53.96 D 15 1150 15.1 76.16 M6 0.0 550 E 30 30 1280 12.0 106.67 F 45 G 45 1030 33.0 31.21 530 H 10 30 1010 44.0 22.95 I 15 970 75.0 12.93 A 30 1080 24.20 21.1 25.39 51.18 540 B 20 45 1120 24.14 17.1 25.84 65.50 C 15 1050. 24.38 26.3 25.30 39.92 D 15 1090 24.25 19.7 25.25 55.33 M5 25 560 E • 30 30 1140 23.84 15.7 25.66 72.61 F 45 1160 24.13 14.9 25.95 77.85 G 45 1010 25.34 40.0 25.11 25.25 530 H 10 30 1000 25.07 53.0 24.78 18.87 I 15 960 25.62 90.0 24.84 10.67 Table XIII (Continued) J. T>T?nmTrTTfiM FEED CONC. (PPM) APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP. GROUP RATE (C.C./CYCLE) EXP' SYMBOL VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. 1 (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 1050 51.82 26.3 49.24 39.92 550 B 20 45 1090 50.17 20.2 51.50 53.96 C 15 1030 51.91 33.0 49.03 31.21 D 15 1070 50.09 24.2 51.00 44.21 M7 50 550 E 30 30 1100 50.77 18.1 51.49 60.77 F 45 1110 50.50 17.6 51.57 63.07 G 45 1010 50.25 44.0 51.25 22.95 530 H 10 30 990 50.94 61.0 49.50 16.23 I 15 950 50.77 104 .0 49.67 9.13 A 30 1020 99.72 36.0 98.12 28.33 540 B 20 45 1050 99.09 26 .0 98.18 40.38 C 15 1010 99.45 48 .0 98.79 21.04 D 15 1030 98.50 32 .0 99.65 32.19 M8 100 540 E 30 30 1070 97.32 23 .0 99.92 46.52 F 45 1080 97.69 22.3 99.82 48.43 G 45 1000 98.73 55.0 98.55 18.18 520 H 10 30 970 98.15 80.0 98.50 12.13 I 15 890 97.65 139.0 99.15 6.40 Table XIV Compilation of Experiments with Initial Concentration (Co) of 4000 PPM Two Columns#Each consists of 8 Cells in Series 1 2 3 4 5 6 7 8 9 10 PRODUCTION FEED EXP-SYMBOL APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP« GROUP RATE (C.C./CYCLE) CONC. (PPM) VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) VOLUME (C.C./CYCLE) FACTOR ns A 30 7450 550 13.55 4100 B 20 45 7850 360 21.81 C 15 7125 820 8.69 D 15 8100 271 29.89 M10 0.0 4175 E 30 30 8175 194 42.14 F 45 8300 141 58.87 G 45 6825 1290 5.29 4200 H 10 30 6600 1760 3.75 I 15 6025 2460 2.45 A 30 7150 26.28 810 25.47 8.83 4050 B 20 45 7450 26.00 565 25.00 13.19 C 15 6800 26.34 1310 25.29 5.19 D 15 7600 26.50 450 25.82 16.89 M9 25 4100 E 30 30 8100 25.17 288 26.48 28.13 t F 45 8150 26.78 218 26.85 37.39 G 45 6625 25.87 1700 26.65 3.90 4175 H 10 30 6375 25.09 2240 26.86 2.85 I 15 5325 25.39 2650 25.84 2.20 Table XIV (Continued) 1 2 3 4 5 6 7 8 9 10 11 PRODUCTION FEED EXP-SYMBOL APPLIED PAUSE BRINE DIALYSATE SEPARATION EXP • GROUP RATE (C.C./CYCLE) CONC. (PPM) VOLTAGE (VOLT) TIME (SEC) CONC. (PPM) VOLUME (C.C./CYCLE) CONC. (PPM) ! VOLUME (C.C./CYCLE) FACTOR ns A 30 7050 51.23 940 48.84 7.50 4100 B 20 45 7375 51.39 625 49.61 11.80 C 15 6775 51.20 1470 49.93 4.61 D 15 7500 51.86 490 49.14 15.31 Mil 50 4175 E 30 30 8075 50.15 310 50.15 26.05 F 45 8125 49.21 239 50.86 34.00 G 45 6450 50.14 2010 50.64 3.21 4200 H 10 30 5975 49.70 2490 50.97 2.40 •I 15 5300 49.52 3125 50.85 1.70 A 30 6900 101.33 1190 101.50 5.80 4050 B 20 45 7250 99.75 725 99.50 10.00 C 15 6650. 99.15 1670 101.75 3.98 D 15 7400 101.75 590 99.15 12.54 M12 100 4125 F. ' 30 30 7925 99.11 350 99.11 22.64 F 45 8100 99.25 283 100.81 28.62 G 45 6400 99.11 2210 101.58 2.90 4200 H 10 30 5600 99.41 2800 101.91 2.00 I 15 5000 99.18 3575 101.73 1.40 Table XV Duplicate Experiments to Test Reproducibility - Group R Two Columns,Each Consists of 4 Cells in Series 1 2 3 4 5 6 7 8 9 10 FEED PRODUCTION APPLIED PAUSE BRINE DIALYSATE SEPARATION CONC. EXP. RATE VOLTAGE TIME CONC. VOLUME CONC. VOLUME FACTOR (PPM) (C.C./CYCLE) (VOLT) (SEC) (PPM) (C.C./CYCLE) (PPM) (C.C./CYCLE) ns RRlA 20 20 30 3650 19.72 350 19.52 10.43 RR1D 20 30 15 3540 19.33 415 19.13 8.53 RR1E 20 30 30 3850 18.50 233 19.33 16.52 1980. RR1F 20 30 45 3900 19.60 207 19.70 18.84 RR3B 50 20 45 3350 49.81 550 48.62 6.09 RR4F 100 30 45 3325 99.75 555 99.19 5.99 RR5A 20 20 30 1050 18.29 28.0 19.11 37.50 RR5C 20 20 15 995 19.29 35.0 19.18 28.43 RR5F 20 30 45 1450 17.19 23.4 19.84 61.97 520 RR7A 50 20 30 980 49.26 44.0 48.83 22.27 RR7B 50 20 45 1000 48.88 34.0 49.17 29.41 RR7C 50 20 15 960 49.66 55.0 49.14 17.45 RR8F 100 30 45 970 98.29 46.0 98.10 21.09 RR9E 20 30 30 5600 19.35 1650 19.13 3.39 3725 RR9F 20 30 45 5900 19.95 1440 18.47 4.10 RR11F 50 30 45 5750 49.86 1530 49.14 3.76 Table XVI Duplicate Experiments to Test Reproducibility - Group M Two Columns,Each Consists of 8 Cells in Series 1 2 3 4 5 6 7 8 9 10 FEED PRODUCTION APPLIED PAUSE BRINE DIALYSATE SEPARATION CONC. EXP. RATE VOLTAGE TIME CONC. VOLUME CONC. VOLUME FACTOR (PPM) (C.C./CYCLE) (VOLT) (SEC) (PPM) (C.C./CYCLE) (PPM) (C.C./CYCLE) ns MM1B 25 20 45 4150 25.18 133 24.84 31.20 99nn MM1D 25 30 15 4100 26.86 144 24.66 28.47 ^zuu MM1F 25 30 45 4375 25.59 106 24.84 41.27 MM3C 50 20 15 3950 49.60 415 48.84 9.52 9040 MM4A 100 20 30 3800 102.32 267 99.23 14.23 MM4E 100 30 30 4150 98.13 129 99.57 32.17 MM5C 25 20 15 1040 25.83 28.8 24.64 36.11 MM7C 50 20 15 1020 51.27 36.0 50.17 28.33 540 MM7D 50 30 15 1070 52.78 22.7 50.25 47.14 MM8B 100 20 45 1040 102.41 27.4 99.86 37.96 MM8F 100 30 45 1080 102.89 20.3 99.17 53.20 MM9A 25 20 30 7400 25.13 940 24.87 7.87 4150 MM9E 25 30 30 8350 25.86 271 24.93 30.81 MM11B 50 20 45 7750 50.21 600 50.82 12.92 MM12C 100 20 15 6600 97.30 1820 99.04 3.63 4200 MM12D 100 30 15 7600 97.13 650 101.27 11.69 MM12F 100 30 45 8350 98.17 267 101.48 31.27 147 Appendix E shows the computer program and calculations for separation factors, amount of salt shifted and a check on material balance for each run and lists tables of printout. 5.4.1. Effect of Demineralizing Path Length Since the process generates a concentration difference between the solutions at the two ends of the ED cell, the amount of axial dispersion in the stack has a very great effect on the final separation. In all of the runs the concentrations of the two product streams approached limiting values as the dispersive effects of axial mixing and other irreversible processes became equal to the separation produced by cycling. Increasing the channel length by increasing the number of stages connected in series tends to reduce dispersion. Figures 38, 39 and 40 and Tables XVII, XVIII and XIX show runs in 4-stage columns while Figures 41, 42 and 43 together with Tables XX, XXI and XXII show similar experiments per formed in 8-stage columns. By comparing these figures it will be clear that the separation factor reached higher values with increasing channel length in all sets of experiments. Figures 44-49 and Tables XXIII-XXVIII compare the performance, under the same operating conditions, of a single column consists of 8 stages with that of two short columns each consists of 4 stages which operate in parallel and have the same production rates as the single column. This comparison was made by plotting CQ/Cn versus the reciprocal of the throughput ratio; where C is the feed concentration and C_. is the demineralized product con-o D r centration. In all runs studied .the single column results in a better separation than the two short parallel columns; however, the improvement in separation with the column-length was more pronounced at high feed 148 Table XVII Effect of Production Rate on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co = 500 PPM Exp. Group # R5, R6, R7 and R8 EXP. GRAPH. SYMBOL PI RATE \^ PER ^\ SEPARATION FACTOR ns VOLTAGE (VOLT) CYCLE PAUSE\^ (SEC) \w 0.0 (C.C.) 20 (C.C.) 50 (C.C.) 100 (C.C.) A 30 59.06 33.97 37.50 25.79 22.27 14.17 B y 20 45 80.80 46.25 34.00 29.41 16.67 C 15 46.10 25.37 28.43 20.00 17.45 8.88 D • 15 73.36 42.80 25.40 12.11 E • 30 30 95.47 55.15 32.63 16.63 F • 45 68.45 61.97 39.07 18.46 21.09 G • 45 15.49 10.21 9.01 5.57 H A 10 30 11.49 7.64 6.92 4.00 I O 15 6.64 3.97 3.60 2.37 120 149 FIGURE 38 Effect of production rate on separation. 4-Cell column ;initial cone. Ccf^SOOPPM. 150 Table XVIII Effect of Production Rate on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co * 2000 PPM Exp. Group # Rl, R2, R3 and R4 EXP. GRAPH. SYMBOL PF .OD. RATE "\ PER ^\ SEPARATION FACTOR ns VOLTAGE (VOLT) CYCLE PAUSE\. (SEC) 0.0 (C.C.) 20 (C.C.) 50 (C.C.) 100 (C.C.) A 30 17.59 8.90 10.43 5.00 2.74 B U 20 45 31.93 13.00 7.21 6.09 3.76 C 15 8.00 5.71 2.88 1.67 D • 15 14.44 7.49 8.53 3.83 2.45 E • 30 30 33.35 13.93 16.52 7.78 4.18 F • 45 47.52 20.64 18.84 12.00 7.02 5.99 G • 45 7.19 4.49 2.46 1.79 H A 10 30 5.49 3.67 2.03 1.57 I o 15 3.18 2.74 1.53 1.39 151 FIGURE 39 Effect of production rote on separation. 4-Cell column ^initial cone. CjpSOOOPPM. 152 Table XIX Effect of Production Rate on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co - 4000 PPM Exp. Group # R9, RIO, Rll and R12 EXP. GRAPH. SYMBOL P] VOLTAGE (VOLT) *0D. RATE \. PER ^\ CYCLE PAUSlN^ (SEC) SEPARATION FACTOR ns 0.0 (C.C.) 20 (C.C.) 50 (C.C.) 100 (C.C.) A B u 20 30 45 2.39 3.34 1.98 2.67 1.78 2.20 1.52 1.77 E F • • 30 30 45 4.43 6.90 3.10 3.39 4.56 4.10 2.50 3.44 3.76 1.91 2.48 153 APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) 15 30 45 10 20 U 30 • B FIGURE 40 Effect of production rote on separation. 4-Cell column; initial cone. CQ — 4000 PPM. 154 Table XX Effect of Production Rate on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 500 PPM Exp. Group # M5, M6, M7 and M8 EXP. GRAPH. SYMBOL IOD. RATE \. PER SEPARATION FACTOR ns VOLTAGE (VOLT) CYCLE PAUSED. (SEC) 0.0 (C.C.) 25 (C.C.) 50 (C.C.) 100 (C.C.) A 30 68.48 51.18 39.92 28.33 B y 20 45 88.24 65.50 53.96 40.38 37.96 C 15 53.96 39.92 36.11 31.21 28.33 21.04 D • 15 76.16 55.33 44.21 47.14 32.19 E • 30 30 106.67 72.61 60.77 46.52 F • 45 77.85 63.07 48.43 53.20 G • 45 31.21 25.25 22.95 18.18 H A 10 30 22.95 18.87 16.23 12.13 I O 15 12.93 10.67 9.13 6.40 120 155 FIGURE 41 Effect of production rate on separation. 8-Cell cell column ; initial cone. (^500 PPM. 156 Table XXI Effect of Production Rate on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co - 2000 PPM Exp. Group # Ml, M2, M3 and M4 EXP. GRAPH. SYMBOL PI 10D. RATE \ PER \V SEPARATION FACTOR ns VOLTAGE (VOLT) \w CYCLE PAUSEX. (SEC) 0.0 (c.c.) 25 (C.C.) 50 (C.C.) 100 (C.C.) A 30 35.21 20.41 17.03 14.61 14.23 B a 20 45 42.16 27.53 31.20 24.69 20.83 C 15 22.74 11.74 8.03 9.52 6.39 D • 15 51.76 29.46 28.47 26.30 22.36 E • 30 30 64.64 36.02 32.87 28.45 32.17 F • 45 82.02 46.28 41.27 40.95 33.60 G • 45 13.93 9.33 6.77 5.66 H A 10 30 10.07 6.45 4.20 3.00 I O 15 5.98 4.02 2.40 2.00 157 FIGURE 42 Effect of production rate on separation. 8-Cell column initial cone. CQ—2000PPM. 158 Table XXII Effect of Production Rate on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 4000 PPM Exp. Group # M9, M10, Mil and M12 EXP. GRAPH. SYMBOL P] 10D. RATE \. PER SEPARATION FACTOR ns VOLTAGE (VOLT) CYCLE PAUSE\^ (SEC) 0.0 (C.C.) 25 (C.C.) 50 (C.C.) 100 (C.C.) A 30 13.55 8.83 7.87 7.50 5.80 B U 20 45 21.81 13.19 11.80 12.92 10.00 C 15 8.69 5.19 4.61 3.98 3.63 D • 15 29.89 16.89 15.31 12.54 11.69 E • 30 30 42.14 28.13 30.81 26.05 22.64 F • 45 58.87 37.39 34.00 28.62 31.27 G • 45 5.29 3.90 3.21 2.90 H A 10 30 3.75 2.85 2.40 2.00 I O 15 2.45 2.20 1.70 1.40 159 FIGURE 43 Effect of production rate on separation .8-Cel I column; initial cone- CQ—4000PPM. 160 Table XXIII Effect of Demineralizing Path Length on Separation C = 500 ppm; A<}> = 20 V GRAPHICAL SYMBOL PAUSE 4-CELL COLUMN 8-CELL COLUMN EXP. TIME (SEC) 1 1 THROUGHPUT RATIO CD THROUGHPUT RATIO CD 8 C 2 4.85 4 11.25 7 C o • 15 4 10.64 8 16.67 5 C 10 12.93 16 20.53 8 A 2 7.58 4 15.00 7 A A • 30 4 13.42 8 20.91 5 A 10 16.83 16 25.59 8 B 2 8.77 4 20.77 7 B • • 45 4 17.00 8 27.23 5 B 10 22.08 16 31.58 161 Pause Time 4- Cell 8- Cell ( Sec ) Column Column 15 o c 30 A A 45 • 8 o I  I I I I I I 2 4 6 8 12 16 Reciprocal Throughput Ratio FIGURE 44 Effect of demineralizing path Jength on separation, Co =«= 500 PPM , A(J) = 20V. 162 Table XXIV Effect of Demineralizing Path Length on Separation C - 500 ppm; A<f> = 30 V EXP. GRAPHICAL PAUSE TIME (SEC) 4-CELL COLUMN 8-CELL COLUMN SYMBOL 1 1 THROUGHPUT RATIO cD THROUGHPUT RATIO CD 8 D 2 6.58 4 16.88 7 D o • 15 4 12.75 8 22.73 5 D 10 21.20 16 28.43 8 E 2 8.77 4 23.48 7 E A A 30 4 15.94 8 30.39 5 E 10 25.98 16 35.69 8 F 2 9.62 4 24.22 7 F • • 45 4 18.89 8 31.25 .5 F 10 31.55 16 37.58 163 Pause Time 4 - Cell 8- Cell (Sec ) Column Column 15 o • 30 A • 45 • a FIGURE 45 Effect of demineralizing path length on separation. C0^=500 PPM, A<{)=30V. 164 Table XXV Effect of Demineralizing Path Length on Separation CQ - 2000 ppm; A<j> = 20 V GRAPHICAL PAUSE 4-CELL COLUMN 8-CELL COLUMN EXP. SYMBOL TIME (SEC) 1 1 THROUGHPUT RATIO CD THROUGHPUT RATIO cD 4 C 2 1.33 4 3.65 3 C o • 15 4 1.97 8 4.53 1 C 10 3.36 16 6.55 4 A 2 1.84 4 7.87 3 A A A 30 4 3.05 8 9.18 1 A 10 4.88 16 11.02 4 B 2 2.36 4 10.94 3 B • • 45 4 4.06 8 13.07 1 B 10 6.72 16 14.59 165 Pause Time 4- Cell 8 - Cell ( Sec) Column Column 15 O • 30 A 45 • m J 1 1 1 1 1 2 4 6 8 12 16 Reciprocal Throughput Ratio FIGURE 46 Effect of demineralizing path length on separation. CQ 2000 PPM , A (J) = 20 V. 166 Table XXVI Effect of Demineralizing Path Length on Separation C - 2000 ppm; A<)> = 30 V PAUSE 4-CELL COLUMN 8-CELL COLUMN GRAPHICAL SYMBOL EXP. TIME (SEC) 1 1 THROUGHPUT RATIO cD THROUGHPUT RATIO cD 4 D 2 1.73 4 12.00 3 D o • 15 4 2.35 8 13.77 1 D 10 4.29 16 15.50 4 E 2 2.60 4 14.90 3 E A • 30 4 4.33 8 16.69 1 E 10 6.96 16 18.39 4 F 2 3.99 4 17.28 3 F • • 45 4 6.29 8 20.19 1 F 10 10.00 16 23.09 167 FIGURE 47 Effect of demineralizing path length on separation. CQ^t2000 PPM , = 30V. 168 Table XXVII Effect of Demineralizing Path Length on Separation CO - 4000 ppm; A<j> = 20 V PAUSE TIME (SEC) 4-CELL COLUMN 8-CELL COLUMN EXP. GRAPHICAL SYMBOL 1 1 THROUGHPUT RATIO cD THROUGHPUT RATIO CD 12 A 2 1.25 4 3.40 11 A A • 30 4 1.39 8 4.36 9 A 10 1.48 16 5.00 12 B 2 1.40 4 5.59 11 B • II 45 4 1.61 8 6.56 9 B 10 1.82 16 7.17 169 o o o 3 0>-Pause Time 4- Cell 8- Cell ( Sec. ) Column Column 30 A • 45 • • —o~ . A---a — —A J I 2 4 6 8 Reciprocal Throughput Ratio 12 16 FIGURE 48 Effect of demineralizing path length on separation. CQ =^4000PPM , A(j) = 20V 170 Table XXVIII Effect of Demineralizing Path Length on Separation CQ - 4000 ppm; A(J> = 30 V PAUSE 4-CELL COLUMN 8-CELL COLUMN GRAPHICAL SYMBOL EXP. TIME (SEC) 1 1 Ca THROUGHPUT RATIO cD THROUGHPUT RATIO CD 12 E 2 1.46 4 11.79 11 E A A 30 4 1.73 8 13.47 9 E 10 2.10 16 14.24 12 F 2 1.73 . 4 14.58 11 F a m 45 4 2.22 8 17.47 9 F 10 2.72 16 18.81 171 Pause Time 4 - Cell 8 - Cell (Sec. ) Column Column 30 A A 45 • • a c_> 10 8 0 J L 2 4 6 8 12 16 Reciprocal Throughput Ratio FIGURE 49 Effect of demineralizing path length on separation, CQr«=4000 PPM, A(J)=30V 172 concentration (compare Figures 44, 45 with Figures 48,49). Figures 44 and 45 indicate that for a feed concentration Cq = 500 ppm NaCl an optimum demineralizing path length may lie in the vicinity of 8 stages in series while Figures 46-49 call for longer demineralizing path lengths with the increasing feed concentration. 5.4.2. Effect of Production Rate As the production rate increases the feed undergoes less cycles in the ED cell before it emerges as products. Thus the amount of separation is reduced as the production rate increases. Figures 38, 41 and Tables XVII, XX show the effect of production rate on the separation factor (ns = ) CD for a series of experiments at a feed concentration (CQ) of about 500 ppm NaCl. The parameters studied were the pause time, T (at levels of 15, 30 and 45 sec.) and the applied voltage A<|> (at levels of 10, 20 and 30 volt). Figures 39, 42 and Tables XVIII, XXI show similar experiments at feed con centration CQ - 2000 ppm NaCl; while Figures 40, 43 together with Tables XIX and XXII indicate experiments with feed concentration Cq - 4000 ppm. All these figures referred to show that there is a strong trade-off between production rate and separation factor. However, useful separation can be obtained at all production rates (provided that higher voltages and/ or longer pause times and demineralizing paths are used with high feed concentration). Figures 41, 42 and 43 show that at an applied voltage (A<}>.) of 30 V, a pause time (T) of 45 sec. and a throughput ratio of (i.e. production rate of 100 c.c./cycle), the separation factors for various feed concentrations range between 30 to 50. To fix ideas, most of the commercial ED plants available at present operate with a 2:1 desalination ratio, which means that a feed of 1000 ppm would be desalinated to 500 ppm per path. A mark III stack (Ionics Inc.) which is used in Buckeye ED plant, Ariz., 173 has a maximum desalination ratio of slightly better than 2:1. Two stacks are used in series to reduce a brackish water of 2100 ppm total dissolved solids down to 500 ppm. (also refer to Table IV). Most of the health standards (e.g. the United States Public Health Service Standards) require that the total dissolved solids (TDS) content of potable water to be 500 ppm or less; hence with a feed at 2000 ppm NaCl and an equal split of brine and dialysate a separation factor of 7 would be necessary and a separation factor of 15 is required with a feed at 4000 ppm. 5.4.3. Effect of Pause Time The influence of a pause time (T) at levels of 15, 30 and 45 sec. was studied under various operating conditions. In all cases, a displacement period of 36 sec. and an average production period of 1.5 sec, 3.0 sec. and 6.0 sec. for production rates of 25 c.c, 50 c.c and 100 c.c./cycle respectively were used. Tables XXIX, XXX and XXXI summarize the operating parameters and the final separation factors reached in these experiments, and Figures 50, 51 and 52 directly display the effect of the pause time on separation factor for several groups of experiments performed in 4-stage columns with feed concentrations between 500 ppm and 4000 ppm NaCl. Tables XXXII, XXXIII and XXXIV together with Figures 53, 54 and 55 exhibit results of similar experiments conducted in 8-stage columns. All these figures show that the separation is improved with a prolonged pause time. However, the effect of pause time can best be examined by considering separation per unit real time obtained with various pause times as shown in Tables XXXV, XXXVI and XXXVII and Figures 56, 57 and 58. In these figures ns/T is plotted vs. pause time (x), where ns is the separation factor and T is the complete cycle duration in minutes. The results are Table XXIX Effect of Pause Time on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co = 500 PPM Exp. Group # R5, R7 and R8 EXP. GROUP and PAUSE^^^ •v. TIME (SEO^v, SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL V0LT>\^ (VOLT) 15 30 45 • 30 42.80 55.15 68.45 61.97 R5 20 (C.C./cycle) 20 25.37 28.43 33.97 37.50 46.25 O 10 3.97 7.64 10.21 • 30 25.40 32.63 39.07 R7 50 (C.C./cycle) 20 20.00 17.45 25.79 22.27 34.00 29.41 A 10 3.60 6.92 9.01 • 30 12.11 16.63 18.46 21.09 R8 100 (C.C./cycle) y 20 8.88 14.17 16.67 • 10 2.37 4.00 5.57 175 80 APPLIED VOLTAGE PRODUCTION RATE (C.C./CYCLE) (VOLT) 20 50 100 10 O A • 20 Q 30 m • • 60 0 0 15 30 45 PAUSE TIME (SEC) FIGURE 50 Effect of pause time on separation • 4- Cell column ; initial conc*C0— 500 PPM. Table XXX Effect of Pause Time on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co - 2000 PPM Exp. Group # Rl, R3 and R4 EXP. GROUP and PAUSE^\^ v. TIME (SEC) ^\ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL V0LT>v. (VOLT) 15 30 45 • 30 7.49 8.53 13.93 16.52 20.64 18.84 Rl 20 (C.C./cycle) 20 5.71 8.90 10.43 13.00 O 10 2.74 3.67 4.49 • 30 3.83 7.78 12.00 R3 50 (C.C./cycle) 20 2.88 5.00 7.21 6.09 A 10 1.53 2.03 2.46 • 30 2.45 4.18 7.02 5.99 R4 100 (C.C./cycle) a 20 1.67 2.74 3.76 • 10 1.39 1.57 1.79 FIGUR 51 Effect of pause time on separation. 4- Cell column ; initial cone C0— 2000 PPM. Table XXXI Effect of Pause Time on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co - 4000 PPM Exp. Group # R9, Rll and R12 ^•s. PAUSE SEPARATION FACTOR EXP. GROUP TIME ns and (SEC)^\ PRODUCTION RATE GRAPH. V0LT>\^ SYMBOL (VOLT) 30 45 • 30 3.10 4.56 R9 3.39 4.10 20 (C.C./cycle) 20 1.98 2.67 • 30 2.50 3.44 Rll 3.76 50 (C.C./cycle) 20 1.78 2.20 R12 m 30 1.91 2.48 100 (C.C./cycle) B 20 1.52 1.77 179 APPLIED VOLTAGE (VOLT) PRODUCTION RATE (C.C./CYCLE) 20 50 100 20 a 30 • • 1) or o i-o < 5.0 < or hi CO 2.5 ± PAUSE TIME 30 (SEC) 45 FIGURE 52 Effect of pause time on separation.4-Cell column ; initial cone.C0 —4000 PPM, 180 Table XXXII Effect of Pause Time on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co - 500 PPM Exp. Group # M5, M7 and M8 EXP. GROUP and PAUSE^\^ TIME (SEC) \S SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL VOLT>^ (VOLT) 15 30 45 • 30 55.33 72.61 77.85 M5 25 (C.C./cycle) 20 39.92 36.11 51.18 65.50 o 10 10.67 18.87 25.25 30 44.21 47.14 60.77 63.07 M7 50 (C.C./cycle) 20 31.21 28.33 39.92 53.96 A 10 9.13 16.23 22.95 • 30 32.19 46.52 48.43 53.20 M8 100 (C.C./cycle) a 20 21.04 28.33 40.38 37.96 • 10 6.40 12.13 18.18 80 APPLIED VOLTAGE (VOLT) PRODUCTION RATE (CJC./CYCLE) 25 50 100 10 O A • 20 A y 30 • A • 60 ac o o < li. z o < or < o_ UJ to 40 20 15 PAUSE TIME 30 (SEC) 45 FIGURE 53 Effect of pause time on separation. 8-Cell column; initial cone.C0— 500PPM 182 Table XXXIII Effect of Pause Time on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 2000 PPM Exp. Group # Ml, M3 and M4 EXP. GROUP and PAUSE^\^ iv. TIME (SEC) SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL VOLTV**^ (VOLT) 15 30 45 • 30 29.46 28.47 36.02 46.28 41.27 Ml 25 (C.C./cycle) 20 11.74 20.41 27.53 31.20 O 10 4.02 6.45 9.33 • 30 26.30 32.87 40.95 M3 50 (C.C./cycle) 20 8.03 9.52 17.03 24.69 10 2.40 4.20 6.77 • 30 22.36 28.45 32.17 33.60 M4 100 (C.C./cycle) y 20 6.39 14.61 14.23 20.83 • 10 2.00 3.00 5.66 183 45, APPLIED VOLTAGE (VOLT) PRODUCTION RATE (C.C./CYCLE) 25 50 100 10 O A D 20 A y 30 • A • ac o I-o 2 z o ac < 0_ UJ CO 30 20 3 30 45 PAUSE TIME (SEC) FIGURE ,54 Effect of pause time on separation. 8-Cell column initial cone. 2000PPM. Table XXXIV Effect of Pause Time on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 4000 PPM Exp. Group # M9, Mil and M12 EXP. GROUP and PAUSE^\^ TV. TIME (SEC)^N. SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL V0LTV\^ (VOLT) 15 30 45 • 30 16.89 28.13 30.81 37.39 M9 25 (C.C./cycle) Q 20 5.19 8.83 7.87 13.19 O 10 2.20 2.85 3.90 • 30 15.31 26.05 34.00 Mil 50 (C.C./cycle) 20 4.61 7.50 11.80 12.92 10 1.70 2.40 3.21 Ml 2 100 (C.C./cycle) • B 30 20 12.54 11.69 3.98 3.63 22.64 5.80 28.62 31.27 10.00 • 10 1.40 2.00 2.90 185 40 30 o o ul 20 z o < < UJ CO 10 APPLIED VOLTAGE (VOLT) PRODUCTION RATE (C.C./CYCLE) PAUSE TIME FIGURE 55 Effect of pause time on separation. 8-Cell column j initial cone. CQ — 4000 PPM. 186 Table XXXV Effect of Pause Time on Separation C = 500 ppm; Group M7 GRAPHICAL SYMBOL PAUSE APPLIED CYCLE SEPARATION ns EXP. TIME, x (SEC) VOLTAGE (VOLT) TIME, T (MIN) FACTOR ns T (MIN-1) M7 I o 10 9.13 5.07 M7 C 15 20 1.8 31.21 17.34 M7 D • 30 44.21 24.56 M7 H A 10 16.23 7.06 M7 A 30 20 2.3 39.92 17.36 M7 E • 30 60.77 26.42 M7 G • 10 22.95 8.20 M7 B y 45 20 2.8 53.96 19.27 M7 F • 30 63.07 22.53 187 Applied Voltage (Volt) Pause Time (Sec. ) 15 30 45 10 O A • 20 A y 30 • • B 28 r 24 -16 -z CO c 8 -0 I 1 1 1 0 5 30 45 Pause Time (Sec) FIGURE 56 Effect of pause time on separation • C0=ft:500 PPM Group M7. 188 Table XXXVI Effect of Pause Time on Separation C = 2000 ppm; Group M3 GRAPHICAL SYMBOL PAUSE APPLIED CYCLE SEPARATION ns EXP. TIME, T (SEC) VOLTAGE (VOLT) TIME, T (MIN) FACTOR ns T (MIN-1) M3 I o 10 2.40 1.33 M3 C 15 20 1.8 8.03 4.46 M3 D • 30 26.30 14.61 M3 H A 10 4.20 1.83 M3 A 30 20 2.3 17.03 7.40 M3 E • 30 32.87 14.29 M3 G • 10 6.77 2.42 M3 B y 45 20 2.8 24.69 8.82 M3 F • 30 40.95 14.63 FIGURE 57 Effect of pause time -on separation. C0^ir2000 PPM Group M3 190 Table XXXVII Effect of Pause Time on Separation C = 4000 ppm; Group Mil EXP. ' GRAPHICAL SYMBOL PAUSE TIME, x (SEC) APPLIED VOLTAGE (VOLT) CYCLE TIME, T (MIN) SEPARATION FACTOR ns ns T (MIN-1) Mil I o 10 1.70 0.94 Mil C © 15 20 1.8 4.61 2.56 Mil D • 30 15.31 8.51 Mil H A 10 2.40 1.04 Mil A 30 20 2.3 7.50 3.26 Mil E • 30 26.05 11.33 Mil G • 10 3.21 1.15 Mil B y 45 20 2.8 11.80 4.21 Mil F • 30 34.00 12.14 FIGURE 58 Effect of pause time-on separation. CQ^4000 •, Group Mil, 192 summarized as follows: 1. At low voltage (A<f>) the separation factor per unit time ns/T varies almost linearly with the pause time T. 2. As the voltage increases the effect of pause time beyond a certain value becomes less significant and the curve tends to level off. 3. At a further increased voltage the ns/T vs. x curve goes through a maximum. 4. The maximum pause time that can be utilized without suffering an adverse effect on separation depends on both the applied voltage (A4>) and the feed concentration (C ). At an applied voltage Ad> = 30 V, x o max is about 30 sec for C - 500 ppm NaCl (Figure 56) and x is about 45 sec o rr max for Cq = 2000 ppm (Figure 57) and a longer pause time can be used for the feed concentration of 4000 ppm NaCl (Figure 58). 5.4.4. Effect of Applied Voltage The effect of the applied voltage A(() was investigated in six groups of experiments, each including runs at 10, 20 and 30 V. The other system parameter values are listed in Tables XXXVIII-XLIII which show experiments with feed concentrations of 500, 2000 and 4000 ppm NaCl in 4-stage and 8-stage columns. Figures 59-64 illustrate directly the influence of the applied potential (AcJ>) on the separation factor (ns). Increasing the applied voltage improves the separation. The magnitude of this improvement was affected by both the pause time (x) and the feed concentration (Cq) as shown in Figures 62, 63 and 64. The results are: 1. In experiments with feed concentration CQ - 500 ppm NaCl the separation factor (ns) increases almost linearly with the applied voltage; but it levels off at high voltage and long pause time (Figure 62). Table XXXVIII Effect of Applied Voltage on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co - 500 PPM Exp. Group # R5, R7 and R8 EXP. GROUP and ^vAPI 'LIFJJN. VOLTAGE^s. Atf) (VOLT)^^ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL PAUSE\ (SEC) 10 20 30 • 45 10.21 46.25 68.45 61.97 R5 20 (C.C./cycle) 30 7.64 33.97 37.50 55.15 O 15 3.97 25.37 28.43 42.80 U 45 9.01 34.00 29.41 39.07 R7 50 (C.C./cycle) 30 6.92 25.79 22.27 32.63 15 3.60 20.00 17.45 25.40 • 45 5.57 16.67 18.46 21.09 R8 100 (C.C./cycle) • 30 4.00 14.17 16.63 • 15 2.37 8.88 12.11 194 75 i-w c 50 ct o o < u_ z o < or < 0-w 25 to PRODUCTION RATE PAUSE TIME (SEC) (C.C. / CYCLE) 15 30 45 20 O A • 50 Q A 100 • A • 0 10 20 APPLIED VOLTAGE (VOLT) FIGURE 59 Effect of applied voltage on separation. 4-Cell column initial cone CQ— 500 PPM. 195 Table XXXIX Effect of Applied Voltage on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co = 2000 PPM Exp. Group # Rl, R3 and R4 ^\APPLIED\ VOLTAGE SEPARATION FACTOR EXP. GROUP \. A<j> ns and (VOLT) PRODUCTION RATE GRAPH. PAUSE^n. SYMBOL (SEC) \. 10 20 30 • 45 4.49 13.00 20.64 18.84 Rl A 30 3.67 8.90 13.93 20 (C.C./cycle) 10.43 16.52 O 15 2.74 5.71 7.49 8.53 a 45 2.46 7.21 12.00 6.09 R3 30 2.03 5.00 7.78 50 (C.C./cycle) - 15 1.53 2.88 3.83 • 45 1.79 3.76 7.02 5.99 R4 30 1.57 2.74 4.18 100 (C.C./cycle) • 15 1.39 1.67 2.45 196 225 r-CO c or o \-o < z o on < a. CO 15.0 7.5 PRODUCTION RATE (C.C./CYCLE) PAUSE TIME (SEC) 15 30 45 2Q O A • 50 Q A B 100 • A • J 0 10 20 30 APPLIED VOLTAGE (VOLT) FIGURE 60 Effect of applied voltage on separation.4-Cell column -.initial conc.C0— 2000 PPM. Table XL Effect of Applied Voltage on Separation Two Columns Each Consists of 4 Cells in Series Initial Concentration Co - 4000 PPM Exp. Group # R9, Rll and R12 EXP. GROUP and PRODUCTION RATE GRAPH. SYMBOL 'LIEDN. VOLTAGE^*. A<|> ^\(V0LT) ^s. PAUSE (SEC) SEPARATION FACTOR ns 10 20 30 R9 20 (C.C./cycle) • A 45 30 2.67 1.98 4.56 4.10 3.10 3.39 Rll 50 (C.C./cycle) B 45 30 2.20 1.78 3.44 3.76 2.50 R12 100 (C.C./cycle) • • 45 30 1.77 1.52 2.48 1.91 198 FIGURE 61 Effect of applied voltage on separation . 4-Cell column-, initial cone. CQ— 4000 PPM. Table XLI Effect of Applied Voltage on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 500 PPM Exp. Group # M5, M7 and M8 EXP. GROUP and ^\API 'LIED^s. VOLTAGE^. \ A<() (V0LT)\ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL PAUSE (SEC) 10 20 30 • 45 25.25 65.50 77.85 M5 25 (C.C./cycle) 30 18.87 - 51.18 72.61 o 15 10.67 39.92 36.11 55.33 B 45 22.95 53.96 63.07 M7 50 (C.C./cycle) 30 16.23 39.92 60.77 15 9.13 31.21 28.33 44.21 47.14 M8 100 (C.C./cycle) • • 45 30 18.18 12.13 40.38 37.96 28.33 48.43 53.20 46.52 • 15 6.40 21.04 32.19 200 APPLIED VOLTAGE (VOLT) FIGURE 62 Effect of applied voltage on separation. 8-Cell column ;hitial cone. CQ—500PPM. 201 Table XLII Effect of Applied Voltage on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co = 2000 PPM Exp. Group # Ml, M3 and M4 EXP. GROUP and ^\AP PLIED^v. VOLTAGE^v A<|> \w ^\(V0LT)^\ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL PAUSEX (SEC) 10 20 30 • 45 9.33 27.53 31.20 46.28 41.27 Ml 25 (C.C./cycle) A 30 6.45 20.41 36.02 O 15 4.02 11.74 29.46 28.47 y 45 6.77 24.69 40.95 M3 50 (C.C./cycle) Q 30 15 4.20 2.40 17.03 8.03 9.52 32.87 26.30 • 45 5.66 20.83 33.60 M4 100 (C.C./cycle) • 30 3.00 14.61 14.23 28.45 32.17 • 15 2.00 6.39 22.36 202 PRODUCTION RATE (C.C./CYCLE) PAUSE TIME (SEC) 15 30 45 25 O A • 50 a 100 • • B or o f— o < < or < a. UJ CO FIGURE 63 APPLIED VOLTAGE (VOLT) Effect of applied voltage on separation. 8-Cell column Initial conc.Cg—2000 PPM. 203 Table XLIII Effect of Applied Voltage on Separation Two Columns Each Consists of 8 Cells in Series Initial Concentration Co - 4000 PPM Exp. Group # M9, Mil and M12 ^\APPLIEI)N. VOLTAGE SEPARATION FACTOR EXP. GROUP \ A<j> \. ns and \v(V0LT) \v PRODUCTION RATE GRAPH. PAUSE^s. SYMBOL (SEC) 10 20 30 • 45 3.90 13.19 37.39 M9 A 30 2.85 8.83 28.13 25 (C.C./cycle) • 7.87 30.81 O 15 2.20 5.19 16.89 a 45 3.21 11.80 34.00 12.92 Mil 50 (C.C./cycle) A 30 2.40 7.50 26.05 Q 15 1.70 4.61 15.31 • 45 2.90 10.00 28.62 M12 • 30 2.00 5.80 22.64 100 (C.C./cycle) • 15 1.40 3.98 12.54 3.63 11.69 204 40r-30 or g 20 o < u. z o or & 10 PRODUCTION RATE (C.C./CYCLE) PAUSE TIME (SEC) 15 30 45 25 O A • 50 A a 100 • • B 10 20 APPLIED VOLTAGE (VOLT) 30 FIGURE 64 Effect of applied voltage on separation. 8- Cell column-,initial conc.C0— 4000 PPM. 205 2. With feed concentrations of 2000 ppm and 4000 ppm NaCl the separation factor is. seen to rise more than proportional to the applied voltage. 3. The effect of applied voltage is more pronounced when the feed concentration is high (compare Figures 62 and 64) and/or the pause time is short (refer to Figure 63). The analysis of the influence of the applied voltage (A<j>) is not as straightforward as that of the pause time (T). Operating at high voltage always results in a higher energy consumption per unit product at a fixed product quality, but at the same time increasing voltage increases the current density and accelerates production rate. Using the method of ohmic analysis, the d.c. power dissipation in a given stack of constant average resistance 2 R at current I is RI . The amount of salt shifted, and hence the amount of fresh water produced, are proportional to I. Therefore, the d.c. power dissipation per unit volume of diluate produced is proportional to I. Fixed costs per unit volume of diluate produced, on the other hand, are inversely proportional to I and the optimum current density and the applied voltage can only be determined by the economical evaluation of the plant. The individual items contributing to the total operating cost of an ED process may be placed in three categories: (a) costs that vary directly with current density such as the electric energy costs (b) costs that vary inversely with current density (the fixed charges) such as membrane replacement and amortization of capital investment costs. Less membrane area and lower capital costs are required at high current densities 206 (c) costs that are invariant with current density such as those for operating and maintenance labor and the cost of pretreatment chemicals. Figure 65 shows typical variations of these cost items with current density. The cost-optimization method developed by Cowan (1960) expresses the total cost of processing (y) as the sum of three terms: y = al + Y + c (102) where a, b and c are taken as constants for a given stack if ohmic analysis applies. This simplified method has been modified by Lacey et al. (1963) and Mattson et al. (1965). By differentiation of Eq. (102) to find minimum product cost, the optimum current is seen to be I _ = ( 7 )h (103) opt a Substituting this value in the equation for the total cost y, it is found that for most economical operation the first two terms are to be equal (power costs = fixed costs). This optimum condition can almost never be met in conventional electro dialysis, however, because polarization phenomena set an upper limit to the permissible current densities; and the fixed costs contribute more towards the total cost than they should do under the optimum conditions. Thus the polarization limitation, rather than the results of economic optimization, frequently controls the operating current density and the applied voltage in practical electrodialysis installations. It can be concluded that when no excessive polarization takes place the high voltage is beneficial and generally results in a more efficient and economical operation of an ED plant. 207 FIGURE 65 Variation of individual cost items making up the total processing cost. 208 5.4.5. Effect of Initial Concentration Three groups of experiments were made at initial concentrations Cq of 500, 2000 and 4000 ppm NaCl/R^O. With these experiments the concentration of the rinse solution was 1000, 2000 and 4000 ppm respectively. Tables XLIV, XLV and XLVI summarize the operating conditions of short columns (4 stages in series) at the three feed concentrations and Figures 66, 67 and 68 display the variation of the separation factor with the feed con centration. Tables XLVII, XLVIII and XLIX together with Figures 69, 70 and 71 represent similar groups of experiments performed in longer columns each consisting of 8 stages in series. The results are summarized as follows: 1. In all cases the higher feed concentration had a retarding effect on separation and resulted in a lower separation factor. This is because the higher concentration requires proportionally larger mass transfer rates to achieve the same separation. 2. The effect of the feed concentration C on separation factor ns is o less pronounced with the longer columns than with the short ones (Compare Figures 66-68 with Figures 69-71). At the same separation factor ns the concentration difference AC (AC = C„ - C^) is higher with the higher feed concentration and longer columns are required to diminish the concentration AC gradient — between the column ends and thus to suppress the undesirable axial mixing that developed with the high feed concentration. 5.4.6. No-Pause Operation The pause time x was dropped to zero in 7 runs at various feed con centrations to check findings from the previous work in a batch system (Bass, 1972). Table L summarizes the operating conditions and final results and Figure 72 contrasts the separation factors of no-pause operation (x = 0) Table XLIV Effect of Feed Concentration;(Co) on Separation Two Columns Each Consists of 4 Cells in Series Production Rate - 20 C.C./cycle Exp. Group # Rl, R5 and R9 ^^INITLAL^v^ SEPARATION FACTOR EXP. GRAPH. APPLIED "\C0NC. ns SYMBOL VOLTAGE (VOLT) PAUSE^^ (PPM) (SEC) 500 2000 4000 A 30 33.97 37.50 8.90 10.43 1.98 B a 20 45 46.25 13.00 2.67 C 15 25.37 28.43 5.71 D • 15 42.80 7.49 8.53 E • 30 30 55.15 13.93 16.52 3.10 3.39 F • 45 68.45 61.97 20.64 18.84 4.56 4.10 210 80r-APPLIED PAUSE TIME (SEC) VOLTAGE (VOLT) 15 30 45 20 © A a 30 • • • 1000 2000 3000 FEED CONCENTRATION (PPM) 4000 FIGURE 66 Effect of feed concentration (C0) on separation. 4-Cell column-production rate— 20 C.C/cycle . Table XLV Effect of Feed Concentration (Co) on Separation Two Columns Each Consists of 4 Cells in Series Production Rate = 50 C.C./cycle Exp. Group # R3, R7 and Rll INITIAL SEPARATION FACTOR EXP. GRAPH. APPLIED •^^CONC. ns SYMBOL VOLTAGE (VOLT) PAUSF>v. (PPM) (SEC) 500 2000 4000 A 30 25.79 22.27 5.00 1.78 B y 20 45 34.00 29.41 7.21 6.09 2.20 C 15 20.00 17.45 2.88 D • 15 25.40 3.83 E • 30 30 32.63 7.78 2.50 F m 45 39.07 12.00 3.44 3.76 212 FEED CONCENTRATION (PPM) FIGURE 67 Effect of feed concentration (C0) on separation. 4-Cell column _ production rate — 50 CC./cycle . 213 Table XLVI Effect of Feed Concentration (Co) on Separation Two Columns Each Consists of 4 Cells in Series Production Rate = 100 C.C./cycle Exp. Group # R4, R8 and R12 APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) 15 30 45 20 Q A B 30 • • G c FEED CONCENTRATION (PPM) FIGURE 68 Effect of feed concentration (Co ) on separation. 4 — Cell column— production rate— 100 C.C./cycle . 215 Table XLVII Effect of Feed Concentration (Co) on Separation Two Columns Each Consists of 8 Cells in Series Production Rate - 25 C.C./cycle Exp. Group # Ml, M5 and M9 EXP. GRAPH. APPLIED NITIAL\. ^\C0NC. ^"^^ SEPARATION FACTOR ns SYMBOL VOLTAGE (VOLT) PAUSF>\(PPM) (SEC) 500 2000 4000 A A 30 51.18 20.41 - 8.83 7.87 B y 20 45 65.50 27.53 31.20 13.19 C 15 39.92 36.11 11.74 5.19 D • 15 55.33 29.46 28.47 16.89 E • 30 30 72.61 36.02 28.13 30.81 F • 45 77.85 46.28 41.28 37.39 G • 45 25.25 9.33 3.90 H A 10 30 18.87 6.45 2.85 I O 15 10.67 4.02 2.20 216 m c or o O < u. z o $ or < OL Id CO APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) 15 30 45 10 O A • 20 Q A y 30 • A • 2000 3000 4000 FEED CONCENTRATION ( PPM) FIGURE 69 Effect of feed concentration (Co) on separation . 8-Cell column-Production rate 25 C.C./cycle 217 Table XLVIII Effect of Feed Concentration (Co) on Separation Two Columns Each Consists of 8 Cells in Series Production Rate - 50 C.C./cycle Exp. Group # M3, M7 and Mil ^^^INITIAL^V. SEPARATION FACTOR EXP. GRAPH. APPLIED CONC. ns SYMBOL VOLTAGE (VOLT) PAUSE\. (PPM) (SEC) 500 2000 4000 A 30 39.92 17.03 7.50 B a 20 45 53.96 24.69 11.80 12.92 C 15 31.21 28.33 8.03 9.52 4.61 D • 15 44.21 47.14 26.30 15.31 E • 30 30 60.77 32.87 26.05 F • 45 63.07 40.95 34.00 G • 45 22.95 6.77 3.21 H A 10 30 16.23 4.20 2.40 I O 15 9.13 2.40 1.70 218 APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) 15 30 45 10 O A • 20 y 30 • • B 1000 2000 3000 FEED CONCENTRATION (PPM) 4000 FIGURE 70 Effect of feed concentration (C0) on separation. 8 - Cell column _ production rate — 50 C.C/cycle. 219 Table XLIX Effect of Feed Concentration (Co) on Separation Two Columns Each Consists of 8 Cells in Series Production Rate - 100 C.C./cycle Exp. Group # M4, M8 and Ml2 INITIAL^. SEPARATION FACTOR EXP. GRAPH. APPLIED CONC. ns SYMBOL VOLTAGE (VOLT) PAUS^^ (PPM) (SEC) ^"V. 500 2000 4000 A 30 28.33 14.61 14.23 5.80 B y 20 45 40.38 37.96 20.83 10.00 C 15 21.04 6.39 3.98 3.63 D • 15 32.19 22.36 12.54 11.69 E • 30 30 46.52 28.45 32.17 22.64 F • 45 48.43 53.20 33.60 28.62 31.27 G • 45 18.18 5.66 2.90 H A 10 30 12.13 3.00 2.00 I O 15 6.40 2.00 1.40 220 co c or o i-o < u. or < a. bJ CO APPLIED VOLTAGE (VOLT) PAUSE TIME (SEC) 15 30 45 10 O A • 20 Q A y 30 • A 1000 2000 FEED CONCENTRATION 4000 FIGURE 71 Effect of feed concentration (CQ) on separation. 8_ Cell column _ production rate — 100 C/Vcycle . 221 Table L Comparison of Pause and No-Pause Operations 8-Cell Column Production Rate = 50 C.C./cycle SEPARATION FACTOR ns GRAPH. SYMBOL FEED APPLIED EXP. CONC. VOLTAGE (PPM) (VOLT) PAUSE OPERATION NO-PAUSE OPERATION 45 SEC 30 SEC 15 SEC M7D • 30 63.07 60.77 47.14 44.21 15.77 M7C 500 20 53.96 39.92 28.33 31.21 11.91 M3D • 30 40.95 32.87 26.30 7.56 M3C 2000 20 24.69 17.03 9.52 8.03 3.56 M3I A 10 6.77 4.20 2.40 1.60 Ml ID • 30 34.00 26.05 15.31 3.13 M11C a 4000 20 12.92 11.80 7.50 4.61 2.16 222 80 APPLIED VOLTAGE (VOLT) FEED CONCENTRATION (PPM) 500 2000 4000 10 A 20 Q y 30 • • m 0 15 30 PAUSE TIME (SEC) FIGURE 72 Comparison of pause and no_ pause operations . 8 —Cell column_ production rate — 50 C.C./cycle . 223 with the normal or pause-operation (x = 15, 30 and 45 sec.) under otherwise identical conditions. One can see that reducing the pause time to zero in all cases studied resulted in a considerably decreased separation. This confirmed the previous findings that flow pauses at the beginning of each half cycle represent important features of the cyclic ED operation. 5.4.7. Pure-Pause Operation In pure-pause operation the electric power is off during circulation and interphase mass transfer takes place only during pause periods in each cycle. This mode of operation seemed attractive since it could result in large power savings. Table LI lists 12 runs; half of them were conducted with power on during circulation while the other half were performed with pure-pause operation under otherwise identical conditions. Figure 73 displays the separation factor ns achieved by the two modes of operation. The results are: 1. Pure-pause operation saves electric power, but results in poor separation. 2. This effect is more pronounced with short pause time. 5.4.8. Semi-Symmetric Operation In semi-symmetric operation feed is introduced and products withdrawn every half cycle while in asymmetric operation the system is closed during the first half cycle (refer to Chapter 4). Six experiments were performed under various operating conditions using semi-symmetric operation. Table LII lists the operating conditions and the final separation achieved. These experiments were compared with similar runs under asymmetric operation as 224 Table LI Comparison of Pure Pause with Mixed Mode Operations 8-Cell Columns - PRODUCTION Rate - 50 C.C./cycle Initial Concentration (Co) - 2000 PPM GRAPH. SYMBOL APPLIED PAUSE SEPARATION FACTOR ns EXP. • VOLTAGE (VOLT) TIME (SEC) POWER ON DURING CIRCULATION POWER OFF DURINC CIRCULATION M3A 30 17.03 4.34 M3B B © 20 45 24.69 7.32 M3C 15 8.03 9.52 2.45 M3D 15 26.30 3.37 M3E • • 30 30 32.87 7.02 M3F 45 40.95 11.49 225 4 Or-APPLIED VOLTAGE POWER DURING CIRCULATION ON OFF 20 a 30 • • 30 U o O < z o < OL UJ CO 20 10 15 30 45 PAUSE TIME (SEC) FIGURE 73 Pure pause operation (No. power during circulation). 8-Cell column — production rate — 50 C.C./cycle . Initial concentration CQ=^ 2000 PPM . Table LII Semi-symmetric Operation Feed Concentration Co - 2000 ppm Production rate = 100 C.C./Cycle of each product FEED CONC. • (PPM) PRODUCTION RATE (C.C./CYCLE) APPLIED VOLTAGE • (VOLT) PAUSE TIME (SEC) BRINE DIALYSATE SEPARATION FACTOR ns EXP. CONC. (PPM) VOLUME • (C.C./CYCLE) CONC. (PPM) • VOLUME (C.C./CYCLE) SS-M4A 30 3825 98.57 355 101.71 10.77 2080 SS-M4B 100 20 45 3950 100.54 248 99.29 15.93 SS-M4C 15 3600 99.80 650 99.50 5.54 SS-M4D 15 3925 97.20 261 103.48 15.04 2110 SS-M4E 100 30 30 4100 98.60 204 101.67 20.10 SS-M4F 45 4150 99.40 186 102.08 22.31 227 shown in Table LIII. Figure 74 contrasts the performance'of these two modes. In all cases the semi-symmetric operation results in a lower separation factor. Figures 75 and 76 show the ideal developing concentration profiles predicted for asymmetric and semi-symmetric operation respectively when the mass transfer takes place during both pause and displacement periods. The dotted lines in these figures show separately the previous concentration profile and the change in this profile due to the mass transfer during circulation. Solid line is the summation of the two dotted lines using the feed concentration as the zero level. These figures show that when steady state is reached the two modes of operation should result in the same separation. Table LIV summarizes Figures 75 and 76 and lists the average product concentrations, expressed in arbitrary units, which would be expected during the transient periods and at the periodic steady state. The low separation achieved with semi-symmetric operation in practice may be attributed to external mixing outside the active ED region, since a single port was used to withdraw the depleted and the enriched products successively during the two half-cycles. Any material from the previous half-cycle that mixed with the new product would impair separation. 5.5. Comment on pH-Changes Checks on the pH of both the process and rinse streams showed no significant changes for most runs. Typical results are listed in Table LV. The rinse stream remains almost unchanged and only shows a slight fluctuation in its pH-value while the process solution tends to be a slightly acidic with a drop in the pH-value of about 0.3 from its initial average value of 5.9. A noticeable exception to this are the experiments with low feed concentration (CQ = 500 ppm) which involve relatively long pause time (T = 45 sec.) and/or high voltage (A(j> = 30 V) as exemplified by experiments M7 F, 228 Table LIII Comparison of Semi-Symmetric and Asymmetric Operations 8-Cell Column - Production Rate - 100 C.C./Cycle Feed Concentration Co - 2000 ppm SEPARATION FACTOR ns APPLIED VOLTAGE PAUSE TIME EXP. GRAPHICAL SYMBOL (VOLT) (SEC) SEMI-SYMMETRIC OPERATION ASYMMETRIC OPERATION M4 A 30 10.77 14.61 14.23 M4 B Q a 20 45 15.93 20.83 M4 C 15 5.54 6.39 M4 D 15 15.04 22.36 M4 E • m 30 30 20.10 28.45 32.17 M4 F 45 22.31 33.60 229 40 r-30 CO c or o S 20 z o or < o_ UJ CO 10 APPLIED MODE OF OPERATION VOLTAGE (VOLT) SEML SYMMETRIC ASYMMETRIC 20 Q a 30 • • 30 _J 45 PAUSE TIME (SEC) FIGURE 74 Comparison of semi symmetric and asymmetric operations. 8- Cell column- production rate 100 C.C./cycle. Feed concentration C0 2000 PPM . Bottom Top t '4' f5 Production I? Pause • sr. cycle A • '6 Circulation 4 Circulation t A »3 Pause Pause 2 cycle FIGURE 75 «3 Pause II yi FIGURE 75 - Continued I N3 t N •J- • H Pause 3 cycle Pause FIGURE 75 — Continued 2 t N N N 1/1 N N N H Pause 4^ cycle FIGURE 75 - Continued 3 B D .iv Pause FIGURE 75 T4'T5 FIGURE 75-Continued 4 Developing concentration profile-,asymmetric operation of an open system with mass transfer during both pause and displacement periods. Dialysate product = brine product = 1/3 cell volume / cycle. CO FIGURE 76 FIGURE 76 — Continued I FIGURE 76 — Continued 2 00 Developing concentration profile •, semi_symmetric operation of an open system with mass transfer during both pause and displacement periods. Dialysate product = brine product = 1/3 cell volume/cycle. Table LIV Average products concentrations in arbitrary units obtained under semi-symmetric and asymmetric operations CYCLE NUMBER FIRST HALF-CYCLE SECOND HALF-CYCLE SEMI-SYMMETRIC OPERATION ASYMMETRIC OPERATION ENRICHED PRODUCT CB DEPLETED PRODUCT CD ENRICHED PRODUCT CB DEPLETED PRODUCT CD 1 1 / / Co + 3 Co + 8.5 Co - 3 Co - 8.5 Co + 8 Co - 8 2 2 / / Co + 13 Co + 16.5 Co - 13 Co - 16.5 Co + 12 Co - 12 3 3 / / . Co + 19 Co + 20.5 Co - 19 Co - 20.5 Co + 16 Co - 16 4 4 / / Co + 18 Co + 18 Co - 18 Co - 18 Co + 18 Co - 18 5 5 / / Repeat Repeat Repeat Repeat 242 Table LV pH-Changes for Some ED Runs at various feed concentrations and operating conditions FEED PROCESS pH RINSE pH EXP. CONC. Co (ppm) Initial Final Initial Final M3 A 5.7 5.4 5.7 5.4 M3 F 2000 5.6 5.0 5.6 5.7 M3 E 5.8 5.3 • 5.8 5.6 M3 H 5.6 5.4 5.6 5.7 M7 A 5.7 5.3 6.1 5.9' M7 B 6.2 5.0 5.8 5.6 M7 E 5.6 4.6 6.0 5.8 M7 F 500 5.8 4.2 5.7 5.8 M7 G 6.1 5.6 5.8 6.0 M7 H 6.2 6.0 6.1 6.1 Mil A 5.9 5.7 5.9 5.6 Mil B 4000 6.2 6.0 6.2 5.9 Mil F 5.7 5.3 5.7 5.8 Mil I 6.1 6.0 6.1 6.2 243 M7 B and M7 E (refer to Table LV). 5.6. Temperature Measurements The initial and final temperatures of the process stream for several runs under various operating conditions were measured using an inserted mercury thermometer. An average temperature rise of 3-5°C from its initial value of 23-25°C was observed in most cases. 5.7. Pressure Drop Measurements The pressure drop across an 8-stage ED column was measured at various flow rates using a mercury manometer. Measured values are listed in Table LVI and a plot of AP (mm Hg) vs. flow rate (c.c./sec) is displayed in Figure 77. Most of the runs in the present work involve a flow rate of about 16.7 c.c./sec. The mean hydraulic radius of the flow channel was about 2.76 -2 x 10 cm which gives rise to a Reynolds number of about 760. 5.8. Probe Voltage, Apparent Resistance and Current Consumption In all experiments described here the applied voltage supplied by the D.C. power source was held constant during each half cycle. The voltage drop across the stack (as measured by probe electrodes) was primarily a function of this applied potential, but it is generally below the applied voltage due to resistance in the connectors, rinse solution and electric overpotentials as shown in Table LVII and Figure 78. Both the stack voltage (probe voltage) and the current consumption vary systematically during the cycle and along the demineralization path. Typical examples of these fluctuations are shown in Figures 79 and 80 for the voltage Table LVI Pressure Drop Measurements 8-Stage ED Stack Time Period t, = 63.5 sec MANOMETER VOLUME FLOW RATE READING (C.C.) (C.C./SEC) (mm Hg) 8 84 1.32 20 169 2.66 35 266 '4.19 51 355 5.59 69 495 7.80 89 577 9.09 102 658 10.36 129 760 11.97 198 940 14.80 247 1107 17.43 296 1210 19.06 331 1328 20.91 Flow Rate (CC./Sea) FIGURE 77 Pressure drop vs. flow rate. 8-Stage ED stack. 246 Table LVII Average Probe Voltage (Stack Voltage) over a complete cycle for various feed concentration and applied voltages. Pause time T = 45 sec Exp. Group # M3, M7 and Mil EXP. GRAPH. FEED ^APPLIED VOLTAGE (VOLT) AVERAGE PROBE VOLTAGE (VOLT) GROUP SYMBOL CONC. (ppm) '10 20 30 M7 • 500 8.95 18.00 27.25 M3 • 2000 8.60 17.15 25.50 Mil • 4000 8.25 16,65 24.85 247 FIGURE 78 Average stack voltage (probe voltage) vs. applied voltage for various feed concentrations. Pause time ^= 45 sec , EXFJ group M3, M7 QM II. FIGURE 79 Traces of probe voltage recording during a cycle at four points along the demineralizing path. EXP. M7F . FIGURE 80 Traces of current recording during a cycle at different points along the demineralizing path. EXP M7F. 250 Traces of probe voltage recording during a cycle at four points along the demineralizing path EXP. M IIF. 251 252 and current respectively at the feed concentration Cq - 500 ppm. Figures 81 and 82 display similar variations of stack voltage and current consumption during the cycle and along the demineralization path for the feed con centration Cq - 4000 ppm. Average values of these variations along the demineralization path are indicated in Table LVIII and Figure 83 for the stack voltage and in Tables LIX and LX and Figures 84 and 85 for the current consumption. The current consumption decreases with increasing separation, thus it drops along the demineralization path as we move from the feed end towards the product end (refer to Figure 84) and it increases with increasing feed concentration (refer to Figure 85). The main influence causing the wide variations in the current was the depletion of solute in either the flow channels or the capacity cells towards the'end of each half cycle. The stack voltage, as shown in Figure 83, approaches the applied voltage as the current consumption drops due to either a high separation or a low feed concentration. Tables LXI, LXII and LXIII show variations of probe voltage, current, apparent resistance and power consumption along the demineralization path for various runs with the applied voltage at level of 10, 20 and 30 volt and feed concentrations Cq of 500, 2000 and 4000 ppm NaCl. Table LXIV and Figure 86 show the variation of average stack resistance with feed concentration. The average stack resistance decreases with increasing feed concentration and with decreasing applied voltage. Table LXV and Figure 87 show the variation of stack resistance along the de mineralization path during the depletion half cycle. The resistance increases as the process stream becomes more depleted towards the product end. 253 Table LVIII Variation of probe voltage along the demineralization path during the depletion half cycle for various feed concentrations. A<j> = 30 V Exp. M7F and MlIF EXP. GRAPH. SYMBOL FEED CONC. (PPM) STAGE NUMBER APPLIED VOLTAGE (VOLT) PROBE VOLTAGE/APPL. VOLT. 4 FEED END 3 2 1 PROD. END M7 F Mil F • • 500 4000 30 30 0.883 0.787 0.917 0.850 0.943 0.883 0.960 0.917 254 Symbol Feed Cone-C0 ( PPM.) • 500 • 4000 LOO 0-751 I I I 1 4 3 2Feed Stage Number Product End End FIGURE 83 Variation of stack voltage (probe voltage) alonge the demineralizing path for various feed concentrations. EXP. M7F8i MIIF. 255 Table LIX Variation of current consumption along the demineralization path during the depletion half cycle at various applied voltages. Co - 2000 ppm Exp. M3 B, M3 F and M3 G. EXP. GRAPH. SYMBOL >v STAGE >v NUMBER APPLIED \. VOLTAGE >v (VOLT) CURRENT CONSUMPTION (mA) 4 FEED-END •3 2 1 PROD-END M3 G A 10 167 161 150 109 M3 B • 20 323 273 192 126 M3 F • 30 463 347 232 153 256 Variation of current consumption along the demineralization path at various applied voJtages. CQ=^ 2000 PPM , EXP. M3 B , M3F 8M3G 257 Table LX Variation of current consumption along the demineralization path during the depletion half cycle at various feed concentrations. A<j> = 30 V Exp. M3 F, M7F and Mil F 1—— —1 EXP. GRAPH. SYMBOL >v STAGE \v NUMBER FEED CONC. >v (PPM) \. CURRENT CONSUMPTION (mA) 4 FEED-END '3 2 1 PROD-END M7 F A 500 225 105 55 29 M3 F • 2000 463 347 232 153 Mil F • 4000 1050 640 409 288 258 Variation of current consumption along the demineralization path at various feed concentrations. AO" = 30V, EXP M3F.M7F 8MIIF. Table LXI Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 500 ppm, Exp. M7 B, M7 F and M7 G EXP. APPLIED VOLTAGE (VOLT) STAGE NUMBER VARIABLE ENRICHMENT HALF CYCLE DEPLETION HALF CYCLE 1 2 •3 4 AVERAGE VALUES 1 2 3 4 AVERAGE VALUES M7 B 20 Probe Voltage (Volt) 18.5 17.9 17.3 16.8 17.6 19.1 18.8 18.1 17.5 18.4 Current (mA) 31 56 97 167 88 21 40 76 158 74 Apparent Resistance (f!) 596.8 319.6 178.4 100.6 298.9 909.5 470.0 238.1 110.8 432.1 Power (Watt) 0.57 1,00 1.68 2.81 1.52 0.40 0.75 1.38 2.77 1.33 M7 F 30 Probe Voltage (Volt) 28.3 .27.3 26.0 25.0 26.7 28.8 28.3 27.5 26.5 27.8 Current (mA) 43 77 132 232 121 29 55 105 225 104 Apparent Resistance (fl) 658.1 354.5 197.0 107.8 329.4 993.1 514.5 261.9 117.8 471.8 Power (Watt) 1,22 2.10 3.43 5.80 3.14 0.84 1.56 2,89 5.96 2.81 M7 G 10 Probe Voltage (Volt) 9.1 8.9 8.6 8.4 8.8 9.5 9.3 9.0 8.7 9.1 Current (mA) 25 47 74 84 58 18 37 57 81 48 Apparent Resistance (fl) 364.0 189.4 116.2 100.0 192.4 527.8 251.4 157.9 107.4 261.1 Power (Watt) 0.23. 0.42 0.64 0.71 0.50 0,17 0.34 0.51 0.70 0.43 IS) Table LXII Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 2000 ppm, Exp. M3 B, M3 F and M3 G EXP. APPLIED VOLTAGE (VOLT) STAGE \^ NUMBER VARIABLE ENRICHMENT HALF CYCLE DEPLETION HALF CYCLE 1 2 3 4 AVERACE VALUES 1 2 3 4 AVERAGE VALUES M3 B 20 Probe Voltage (Volt) 18.0 17.3 16.3 15.4 16.8 18.7 18.0 17.1 16.3 17.5 Current (mA) 167 228 324 352 268 126 192 273 323 229 Apparent Resistance (£!) 107.8 75.9 50.3 43.7 69.4 148.4 93.8 62.6 50.4 88.8 Power (Watt) 3.01 3.94 5.28 5.42 4.41 2.36 3.46 4.67 5.26 3.94 M3 F 30 Probe Voltage (Volt) 27.0 25.8 24.4 22.4 24.9 28.0 27.0 25.5 24.0 26.1 Current (mA) 197 278 371 510 339 153 232 347 463 299 Apparent Resistance (£2) 137.1 92.8 65.8 43.9 84.9 183.0 116.4 73.5 51.8 106.2 Power (Watt) 5.32 7.17 9'. 05 11.42 8.24 4.28 6.26 8.85 11.11 7.63 M3 G 10 Probe Voltage (Volt) 9.0 8.6 8.2 7.8 8.4 9.3 9.0 8.6 8.2 8.8 Current (mA) 139 192 210 220 190 109 150 161 167 147 Apparent Resistance (fl) 64.7 44.8 39.0 35.5 46.0 85.3 60.0 53.4 49.1 62.0 Power (Watt) 1.25 1.65 1.72 1.72 1.59 1.01 1.35 1.38 1.37 1.28 Table LXIII Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 4000 ppm, Exp. Mil B, Mil F and Mil G EXP. APPLIED VOLTAGE (VOLT) N. STAGE NUMBER VARIABLE ENRICHMENT HALF CYCLE DEPLETION HALF CYCLE 1 2 3 4 AVERAGE VALUES 1 2 3 4 AVERAGE VALUES Mil B 20 Probe Voltage (Volt) 17.3 16.3 15.6 15.0 16.1 18.3 17.6 16.7 16.0 17.2 Current (mA) 517 639 759 880 699 393 500 685 833 603 Apparent Resistance (£2) 33.5 25.5 20.6 17.0 24.2 46.6 35.2 24.4 19.2 31.4 Power (Watt) 8.94 10.42 11.84 13.20 11.10 7.19 8.80 11.44 13.33 10.19 Mil F 30 Probe Voltage (Volt) 26.0 24.5 23.2 21.7 23.9 27.5 26.5 25.5 23.6 25.8 Current (mA) 391 540 711 1097 685 288 409 640 1050 597 Apparent Resistance (fi) 66.5 45.4 32.6 19.8 41.1 95.5 64.8 39.8 22.48 55.6 Power (Watt) 10.17 13.23 16.50 23.80 15.93 7.92 10.84 16.32 24.78 14.97 Mil G 10 Probe Voltage (Volt) 8,5 8.1 7.7 7.5 8.0 8.9 8.6 8.4 8.1 8.5 Current (mA) •347 443 460 469 430 323 383 403 460 392 Apparent Resistance (fi) 24.5 18.3 16.7 16.0 18.9 27.6 22.5 20.8 17.6 22.1 Power (Watt) 2.95 3.59 3.54 3.52 3.40 2.87 3.29 3.39 3.73 3.32 Table LXIV Effect of Initial Concentration on the equivalent resistance of ED stack Exp. Group M7, M3 and Mil EXP. GRAPH. APPLIED VOLTAGE (VOLT) FEED CONC. (ppm) EQUIVALENT STACK RESISTANCE (ohm) SYMBOL 500 2000 4000 Mn G o 10 46.48 14.82 5.39 Mn B • 20 60.78 18.79 7.00 Mn F • 30 65.54 21.29 10.47 263 FIGURE 86 Effect of initial concentration on equivalent resistance of ED stack Table LXV Variation of ED Stack Resistance along the de mineralization path during the depletion half cycle at various applied voltages. Co - 500 ppm Exp. M7 B, M7 F and M7 G >v STAGE >v NUMBER RESISTANCE, R = A<j>/I (ft) EXP. GRAPH. SYMBOL APPLIED X. VOLTAGE \ (VOLT) X. 4 FEED-END 3 2 1 PROD-END M7 G • 10 107.4 157.9 251.4 527.8 M7 B • 20 110.8 238.1 470.0 909^5 M7 F • 30 117.8 261.9 514.5 993.1 265 1000 1 o 800 600 0> o c o tn or 400 c <u o a. o. < 200 Symbol Applied Volt AO (Volt ) • 30 • 10 Feed End 3 Stage Number I Product End FIGURE 87 Variation of stack resistance along the demineralizing path during the depletion half cycle . CQ^ 500 PPM ; EXP M7F & M7G 266 Figure 88 displays the plot of the stage apparent resistance (R = A<j>/I) on logarithmic scale vs. the stage position along the deminerali zation path during the depletion half cycle. The plots are fitted by straight lines which suggest that the apparent resistance of an ED stack may be expressed by an empirical relation of the form: In R£ = C± + C2Z (104) where R^ is the local resistance at distance I from the feed inlet and and C2 are constants. If we are concerned only with the average value of the stage resistance then we have I = nV (105) where £' is a single stage length and n is the stage number (n = 1 at feed end). Substitute Eq. (105) into Eq. (104): In R = C. + C„n (106) n 1 J where RN is the average resistance of stage number n. Figure 89 shows the variation of the average stage resistance with the stage position on a semi-logarithmic scale when the feed concentration Cq - 2000 ppm and applied voltage was at levels of 10, 20 and 30 V. Various points under the same operating conditions are fitted by straight lines. The slope of these lines increases with increasing applied voltage and when these lines are extrapolated they tend to merge into a single point (a pole). For feed concentration Cq = 2000 ppm the pole lies at the point P (0.70, 45 ) (refer to Figure 89). For this case Eq. (106) can be written as In R = In 45 +'CQ (n - 0.70) (107) n 3 The value of can be obtained from the slope of the lines in Figure 89 267 1000 800 Initial Cone. Symbol ( PPM) • 500 O 2000 A 4000 600 400 101 4 3 2 I Feed Stage Number Product End End FIGURE 88 Variation of apparent ED stack resistance along the demineralizing path during the depletion half cycle using a semiJog scale . AO" =30V; EXP. M3F.M7F a Mil F (refer to Tables LXI-LXIU.) 268 FIGURE 89 Variation of apparent ED stack resistance along the demineralization path using a semi-log-scale. 2000 PPMSEXP.M3B ,M3F 6 M3G . (refer to Table LXll) 269 as follows: C3 * 0.43 C3 = 0.34 and C3 - 0.17 for A<j> = 30 V for Atj) = 20 V for A<j> = 10 V Similarly the parameters and in the expirical Eq. (106) can be determined for the other feed concentrations under various operating conditions. 5.9. Voltage Efficiency Voltage efficiency may be defined as the fraction of the applied voltage that is utilized in separation (probe voltage). A<t> " A(f,con " A<{,el r, = — •* 100 (108) v A<j> where A<j> = applied voltage Acb = voltage drop in the connectors con ° r A<|>g£ = voltage drop due to the rinse solution and electrode overpotentials Table LXVI lists voltage efficiency for several runs under various operating conditions. The voltage efficiency ranges between 82.50 and 90.83%. 5.10. Current density and efficiency In the present work the current density, i, varies between 1.00 and 2 10.82 mA/cm . Low current density corresponds to operation with a low feed concentration and a small applied voltage. The true current efficiency, n , is defined by Eq. B.7 as Table LXVI Voltage Efficiency APPLIED UTILIZED VOLTAGE EXP. VOLTAGE VOLTAGE EFFICIENCY (VOLT) (VOLT) % M3 B 20 17.15 85.75 M3 F 30 25.50 85.00 M3 G 10 8.30 83.00 M7 B 20 18.00 90.00 M7 F 30 27.25 90.83 M7 G 10 8.95 89.50 Mil B 20 16.65 83.25 Mil F 30 24.85 82.83 Mil G 10 8.25 82.50 271 nT = n„ n n (B.7.) I s m w When the selectivity of the membrane is 0.90 the true current efficiency, n is usually about 80%. The current utilization factor or the overall current efficiency, n^ can be defined as actual amount of salt transported A (109) I theoretical amount of salt transported where the theoretical amount of salt transported in g-equivalent is given by ,6 VAC = 1 ' Z ' 10 • M (110> ZF where V = the volume of fluid demineralized during time t in a flow channel (c.c.) AC = change in fluid concentration (ppm) I = current passed (amp) t = duration of the current passage (sec) Z = valence (g-equiv./g-mole) F = Faraday's constant = 96500 (coulomb/g-equiv.) M = Molecular weight of solute = 58.44 (g/g-mole) The overall current efficiency as defined above includes the true current efficiency, together with any inefficiencies in the process such as dispersive effects, diffusion under concentration gradient and internal and external leakage if any exist. The overall current efficiency, n-j-, was evaluated for several runs under various operating conditions as shown in Table LXVII. The overall current efficiency ranges between 26 and 32% in most cases; runs with high feed concentration resulted in lower values. Previous work in the closed Table LXVII Overall Current Efficiency APPROX. OVERALL EXP. FEED CONC (ppm) CURRENT (Amp) CURRENT EFFICIENCY % M4 A 2000 3.98 26.26 M4 D 2000 5.10 27.19 M4 G 2000 2.70 26.35 M8 C 500 1.30 26.63 M8 I 500 0.85 31.57 M12 E 4000 10.26 20.98 M12 G 4000 6.58 15.16 273 system indicated an overall current efficiency between 20 and 40 for the first cycle, decreasing rapidly for subsequent cycles, and tending to zero as the separation approached steady periodic state. The overall current efficiency could be improved by utilizing a more efficient unsymmetric power wave with a short regeneration step compared with the demineralizing step and by using a longer demineralizing path. Also as most of the useful separation takes place during pause periods decreasing circulation time may result in an increased current efficiency. 5.11. Comments on Stack Resistance Models Four experiments under various operating conditions have been used to test the non-ohmic model. The following simplified equation (Eq. 51) was used to predict the apparent resistance of an ED stage at the product end. 2RT rN . ns + k , RP = FT [(t " V ln—T ] 2FD 1 + k/ns (t - t)Ai 1 - k , A - 26 . A - 26 . , + _ + _ + p + p (51) D D UCAC a C where 2 R is the resistance per unit area (ohm-cm ) P R is the gas law constant = 8.3144 (Joule-gmole-1 - °K_1) .T = the absolute temperature (°K) F = Faraday's constant (Coulomb/g.equiv) 2 i = current density (A/cm ) t,t = transport numbers of counter-ions in membrane and solution respectively 274 D k ns A t c = transport number of co-ions in the membrane 2 = equivalent solution conductance (mho.cm /gmole) 2 = diffusivity (cm /sec) = separation factor = —— CD = ratio of the operating to limiting current density A = flow channel thickness (cm) 6 = diffusion layer thickness (cm) = the anion and cation membrane resistance per unit area (ohm - cm^) System Data and Assumptions Room temperature = 25°C = 298°K Molecular weight of NaCl = 58.44 Equivalent conductance of aqueous sodium chloride solution, A, is given by Table LXVIII and Figure 90. Diffusivity of aqueous sodium chloride, D, is given by Table LXVIII and Figure 91. A - 26 - A 2 Electrode area = 61.23 cm Spacer thickness = 0.098 cm Exposed area of spacer = 0.50 Membrane selectivity = 90% (t - tc) = 0.90 (t - t) av = 0.45 = 19.2 ft-cm 2 k = 0.80 275 Table LXVIII Equivalent Conductance and Diffusivity of aqueous sodium chloride solutions* CONC. of NaCl (ppm) EQUIVALENT CONDUCTANCE, A (mho - cm^/gmole) DIFFUSIVITY D x 10^ cm^/sec 0 126.45 100 125.60 1.599 500 122.89 1.585 2000 117.57 1.535 4000 113.47 1.494 8000 108.96 1.481 * Saline Water Conversion Engineering Data Book, Second Edition, U.S. Office of Saline Water, November, 1971. 276 0 1000 2000 3000 4000 5000 6000 7000 8000 Concentration , PPM FIGURE 90 Equivalent conductance of aqueous sodium chloride solutions at 25° c . • 1.47 ;l I I J 1 I I I. 1 0 1000 2000 3000 4000 5000 6000 70C0 8000 Concentration , PPM FIGURE 91 Diffusivity of aqueous sodium chloride solutions at 25° c. 278 Sample of Calculations EXP M3F ; Cq = 2120 ppm 2 Cp = 105 ppm ; = 125.6 mho. cm /gmole D = 1.599 x 10"5 cm2/sec 2 C„ = 4300 ppm ; A„ = 113 mho. cm /gmole ns =40.95 ; i = 2.858 mA/cm2 av 1st term (membrane potential term) = (2)(8.3144)(298)(0.9) ln 40.95 + 0.8 = 86>37 , _ cm2 <t>,m (96500) (2.858)10 J U'Z 2nd term (diffusion layer resistance term) p - (2)(96500)(1.599) 10"5 . 1 + 0.0195 _ o, 19 0 2 R6 - (2.858) (0.45) (125.6)10-3 ln O 31'1Z " " Cm 3rd term (membrane resistance term) 2 R = 38.40 n - cm m 4th term (depleted solution resistance term) (0.098)(58.44)106 = 868.58'n - cm2 d (0.5)(105)(125.6) 5th term (enriched solution resistance term) R = (11.45) 106 c, n 2 (4300)(113) = 23'57 ° " Cm The apparent resistance per unit area of a cell pair, R^ is given by R=RX+R. +R+R, +R = 1048.04 fi - cm2 p cj>,m o m d e The predicted stage resistance is given by 279 Measured stage resistance = 160.05 ft ... «. 136.93 - 160.05 .._ the percentage error = 1(.Q ^ = - 14.44% Table LXIX lists values of predicted and measured resistances for several experiments and breaks down the total predicted resistance into its main resistive elements and it also indicates the contribution of each element towards the overall value. Figure 92 displays the discrepancy between predicted and measured values of an ED stage resistance. The discrepancy may be attributed to the assumed values used in the calculation or to the simplifying assumptions involved in the model or to both of them. From Table LXIX it can be seen that the membrane potential term together with the diffusion layer resistance contribute about 20% while the bulk solutions contribute about 80% towards the overall resistance value. These findings also indicate that ohmic model can be used satisfactorily to predict the stack resistance. The basic equation of ohmic analysis is given as Ki ll = — + Ko - KoC (52) PC where K^, and are constants for a given system and C is the local average concentration. Measured stage resistances in several runs were plotted vs. the reciprocal of the average concentration as shown in Figure 93 and Table LXX. The plot was fitted by a straight line. The model constants were determined from the slope and intercept of the graph as follows: * 216484 K2 * 191.34 and K3 - 0.0 Table LXIX Distribution of the predicted resistance of an ED stage, R , between its resistive elements RESISTIVE ELEMENT M3 F 2000 ppm M3 B 2000 ppm M7 G 500 ppm Mil F 4000 ppm VALUE a % age of Rs VALUE n % age of Rs VALUE a % age of Rs VALUE n % age of Rs Membrane Potential 11.29 8.24 12.23 12.37 82.18 20.41 5.62 8.67 Membrane Resistance 5.02 3.66 5.02 5.07 5.02 1.25 5.02 7.75 Diffusion Layer Resistance 4.07 2.97 4.91 4.97 33.30 8.27 2.11 3.26 Depleted Bulk Sol. Resistance 113.48 82.88 73.45 74.27 269.96 67.02 50.34 77.71 Enriched Bulk Sol. Resistance 3.08 2.25 3.28 3.32 12.29 3.05 1.69 2.61 Predicted total Resistance Value 136.93 100 98.90 100 402.74 100 64.78 100 Measured Resistance Value 160.05 128.1 445.90 81.00 Discrepancy as % Age - 14.44 - 22.80 i - 9.68 - 20.03 520 i 480 400 320 240 160 80 7T Initial Cone. (PPM) Voltage (Volt) 10 20 30 500 O 2000 • 4000 B o /A V / / / / 4-80 160 240 320 400 480 520 Measured Value of ED Stage Resistance (ohm ) FIGURE 92 Discrepency between predicted and measured value d an ED stage . Table LXX Values of local average concentration, C and measured stage resistance EXP. PRODUCT CONC (ppm) LOCAL AVERAGE CONC. (ppm) STAGE RESISTANCE («) CB CD M3 B 4025 163 313 128 M3 F 4300 105 205 160 M3 G 3725 550 958 75 M7 B 1090 20.2 40 753 M7 F 1110 17.6 35 826 Mil B 7375 625 1152 40 Mil F 8125 239 464 81 Mil G 6450 2010 3065 26 283 900 FIGURE 93 Variation of apparent resistance of an ED stage with the reciprocal of Ihe average product concentrations. 284 5.12 Comparison with Previous Work in Closed System (i) Separation Bass (1972) reported some experiments performed in a batch-recirculacion mode of operation in which a 90% demineralized product was intermittently replaced by fresh feed every eight cycles. Experiments under this mode of operation resulted in a separation factor of 16 with a feed concentration Cq = 1250 ppm, applied voltage A<}> = 10 V, pause time x = 10 sec, displaced volume 6 = 2/3 the active volume and a throughput ratio of about 0.075. In the present work experiments with A<j> = 20 V, x = 15 sec result in a separation factor of 20 at a throughput ratio of 0.25 which is the same magnitude of separation per unit power consumption as in the previous case. However, the previous work does not show any consistent effect of initial concentration, Cq on the final separation. (ii) Resistance and Current Consumption The initial resistance and current consumption in the closed system were generally of the same magnitude as in the present work and they exhibit the same trend of variation along the demineralizing path. (iii) Analysis of Axial Dispersion The axial dispersion in the ED cells has been determined previously using the step response method. The resulting F-diagrams did not suggest excessive channelling or by-passing. From the slope of response curve it was estimated that the system corresponds to about 50 effective mixing stages. In the spacer used in both works there are 10 x 10 strands per inch and there are about 55 holes along the flowpath in the ED cell. 285 (iv) Effect of Pause Time The previous work in the batch operation showed that flow pauses at the beginning of each half cycle represent important features of the cyclic process operation. This is in line with the findings in the present work. 5.13 Reproducibility Several of the runs under different operating conditions were repeated to test the reproducibility of the results. Table LXXI lists the duplicate experiments and compares them with the initial ones conducted in 4-stage columns. Table LXXII makes the same comparison for experiments performed in 8-stage columns. In both cases the reproducibility of the results are considered as quite satisfactory. Table LXXI Reproducibility - GROUP R Two Columns Each Consists of 4 Cells in Series EXP. SEPARATION FACTOR ns DISCREPANCY OLD NEW AS PERCENTAGE OF (ns) Av, Rl A 8.90 10.43 + 15.83 Rl D 7.49 8.53 + 12.98 Rl E 13.93 16.52 + 17.01 Rl F 20.64. 18.84 - 9.12 R3 B 7.21 6.09 - 16.84 R4 F 7.02 5.99 - 15.83 R5 A 33.97 37.50 + 9.88 R5 C 25.37 28.43 + 11.38 R5 F 68.45 61.97 - 9.94 R7 A 25.79 22.27 - 14.65 R7 B 34.00 29.41 - 14.48 R7 C 20.00 17.45 - 13.62 R8 F 18.46 21.09 + 13.30 R9 E 3.10 3.39 + 8.94 R9 F 4.56 4.10 - 10.62 Rll F 3.44 3.76 + 8.89 287 Table LXXII Reproducibility - Group M Two Columns Each Consists of 8 Cells in Series SEPARATION FACTOR ns DISCREPANCY EXP. OLD NEW AS PERCENTAGE OF (ns) Av. Ml B 27.53 31.20 + 12.50 Ml D 29.46 28.47 - 3.42 Ml F 46.28 41.27 - 11.44 M3 C 8.03 9.52 + 16.98 M4 A 14.61 14.23 - 2.64 M4 E 28.45 32.17 + 12.27 M5 C 39.92 36.11 - 10.02 M7 C 31.21 28.33 - 9.67 M7 D 44.21 47.14 + 6.41 M8 B 40.38 37.96 - 6.18 M8 F 48.43 53.20 + 9.39 M9 A 8.83 7.87 - 11.50 M9 E 28.13 30.81 + 9.09 Mil B 11.80 12.92 + 9.06 M12 C 3.98 3.63 - 9.20 Ml 2 D 12.54 11.69 - 7.02 M12 F 28.62 31.27 + 8.85 CHAPTER 6 Conclusions and Recommendations The present work has proven the feasibility of continuous cyclic electrodialysis for desalination of brackish waters. The conventional electrodialysis demineralizing process competes mainly with distillation and it appears to be more attractive economically than distillation for low salinity waters (with concentrations of up to about 10,000 ppm dissolved salt). However, conventional electrodialysis is subject to excessive, polarization, fouling and scale formation on ion-exchange membranes, an<-l generally requires expensive materials for electrodes. Cyclic electrodialysis promises to overcome these problems by the reversed polarity technique. In the present work no excessive polarization was noticed in most of the runs (up to the maximum voltage applied of 30 volts) and inexpensive graphite electrodes proved to be satisfactory over a reasonably long period of time. The process resulted in a separation factor. ' (ns = C-./C ) up to 50 at a throughput ratio of 0.25 which is equivalent i.< B D a desalination ratio (defined as C /C_) of about 25 compared with the o D desalination ratio per path of about 2 in most commercial plants currently in operation. The primary objectives of the experimental program undertaken were to explore the possible region of application of cyclic operation in an open electrodialysis system, to screen system parameters, and to determine. 288 289 their relative importance. The following design and operating parameters have been investigated: a) Design Parameters (i) Demineralization path length (ii) Semi-symmetric and asymmetric modes of operation (iii) Pause and no-pause operations (iv) Pure-pause operation with power off during circulation b) Operating Parameters (v) Production rate with throughput ratio varying from 0.0625 to 0.50. (vi) Applied voltage A<|) at levels of 10, 20 and 30 volt, (vii) Pause time x at levels of 15, 30 and 45 sec. (viii) Feed concentration Cq at levels of 500, 2000 and 4000 ppm The results of the study can be summarized in the following: 1. Despite the strong trade-off between production rate and separation, the separation factor ranged from 30 (for 4000 ppm feed) to 50 (for 500 ppm feed) at the highest production rate used (100 c.c./cycle). 2. The pause time proved to be an important operating parameter. Decreasing the pause time below 15 sec. resulted in considerably lower separation. 3. The maximum pause time that can be utilized without an adverse effect on separation depends on both the applied voltage Acj> and the feed con centration C . At an applied voltage A<}> = 30 V; x was about 30 sec. for o max Cq - 500 ppm and it was about 45 sec. for Cq - 2000 ppm. 4. In all cases increasing the applied voltage improves the separation. The separation factor increases at least proportionally with the applied 290 voltage. The effect of applied voltage was more pronounced when the feed concentration was high and/or the pause time was short. 5. With the feed concentration CQ - 500 ppm the optimum conditions are thought to be: a demineralizing path length in the vicinity of 8 stages in series, an applied voltage in the range 20-30 volt and a pause time of about 30 sec. An increase of pause time above 30 sec. had a deleterious effect on separation, presumably because of polarization. 6. As the feed concentration Cq increases the separation decreases. Higher feed concentration calls for a longer demineralizing path, higher voltage and longer pause time. 7. Pure-pause operation saves electric power at the expense of poor separation. 8. Variations in the methods of feed introduction and product with drawal, such as symmetric, semi-symmetric and asymmetric operations, were investigated theoretically (Chapter 4). When axial mixing is ignored all these modes predict the same final separation as shown by the graphical solutions. However, the degree of complexity of the system, the number of valves and the number of subdivisions in the timing sequence, decrease as the operation becomes less symmetric. 9. When semi-symmetric and asymmetric operations were compared experimentally under otherwise identical conditions the former resulted in lower separation. This may be attributed mainly to the external mixing outside the active demineralizing area. 10. The experimental results are generally highly reproducible. 11. Cyclic electrodialysis in an open system has been fully demon strated. The process looks promising and it deserves further study along the 291 following lines: a) The present work has been limited by the following design parameters: (i) A demineralizing path of maximum length of 8 stages in series (ii) A D.C. power supply of 400 watts (a maximum applied voltage of about 30 volts) (iii) A maximum time interval of about 50 sec. To explore fully the whole operating domain at feed concentration CQ higher than 500 ppm all these parameters need to be relaxed by modifying the process design. b) The feed concentration should be extended to the range CQ = 10,000 - 15,000 ppm. c) Other operating procedures should be investigated. In particular it is proposed to disconnect the electric power from the ED stacks during part of the displacement. Also, the system may be run in semi-batch operation with feed introduction and product withdrawal once every several cycles. Different voltage waves other than the present rectangular wave can be applied such as triangular wave and unsymmetric wave with different magnitude and duration in the two half cycles. This may result in a better power economy. d) The proposed stack resistance model predicts quite accurately the resistance of the experimental stacks under the operating conditions used here. An extension of the constant-rate model based on the stack resistance could form a basis for a more refined representation. 292 e) A scale-up and an optimization study of the system are essential for evaluation of the process economics and its comparison on a commercial scale with other competitive processes. f) Other solutes should be investigated, both in binary and in multicomponent mixtures. g) By using cation and anion exchange membranes selectively permeable for univalent ions only, the system can be used to separate monovalent ions from divalent and other ions. NOMENCLATURE membrane area ionic activity of cation (+) or anion (-) rate constant during dilution half cycle rate constant during enrichment half cycle membrane area solute concentration constant diffusion coefficient potential drop per cell pair potential drop the fraction desalted Faraday's constant or flow rate of process stream current density current ionic flux vector electrical conductivity or the ratio between operating and limiting current density Typical Unit 2 cm g-mole litre sec -1 sec cm -1 g-mole litre or ppm cm /sec volt volt A.sec/g-equiv. litre/sec. mA/cm^ A 2 (g-mole)/(cm )(sec) mho/cm 293 294 constant Typical Unit rate constant or cell constant constant channel length a single stage length phenomenological coefficient length of the membrane or the demineralizing path number of cycles or number of membrane pairs or width of membrane separation factor normality of solution exp (- a]L — ) or permselectivity of ion exchange membrane or membrane area utilizing factor exp (- a2 ) flow rate heat flow vector dimensionless ratio of spacer thickness in the concentrate and the diluate compartments areal resistance or the gas law constant transport number or temperature cycle time or absolute temperature ionic mobility total chemical potential cm -1 cm cm cm cm g-equiv.litre cm / sec ohm cm (joules) /(°K) (mole) sec °K (cm )/(volt)(sec) 295 Typical Unit v . = displacement velocity cm/sec v = velocity vector cm/se3 V = volume cm w = water transport number x = distance co-ordinate cm y = lateral distance co-ordinate cz = valence of charged species (g-equiv)/(g-mole) or direction of flow Greek Symbols a = fraction of half cycle g = fraction of half cycle Y = phase lag Y+ = the mean ionic activity coefficient 6 = thickness of Nernst layer or diffusion cm layer A = compartment thickness cm e ." = fractional void volume of packing n = efficiency ri = electric field vector volt/cm 2 A" = equivalent conductance (mho) (cm )/(g-equiv) 3 v = partial molar volume cm /mole v+ = stoichiometric coefficients for electrolyte Mv+ p = electrical resistivity ohm-cm p = (1 - E)/E = ratio of volume of packing to void volume x = pause time sec or tranference number of water 296 Typical Unit A<|> = applied electric potential volt Acb = Donnan potential volDon V = divergence operator or gradient operator Subscripts 1,2 ... refer to positions across a cell pair or to the number of time interval during a cycle; (T1,T2) + for positively charged species; (t+) - for negatively charged species; (t_) a for anion-exchange membrane; (fca) or an average value; (C ) cL b brine product; (C, ) b B brine (enriched) product; (CB) c cation-exchange membrane; (t£) or concentrate product; (C ) or concentration polarization; d dialysate (depleted) product; (C^) d^,d2 Donnan terms; (EQ^E^) D dialysate (depleted) product; (C^) e enriched product; (C ) or electrode; (1 ) ' e f fluid or mobile phase; (C^) F Faraday; (n^,) H Henderson term; (E^) i refers to inlet; (C^) I current ; (y j co-ion; (C^) 297 k counter-ion; (C^) ^ or species k; (J^) SL refers to local value at distance I from the feed inlet; (R^) m manifold; (nm) or membrane; (F^) or membrane solution interface; (Cm) n stage number; (^n) o refers to initial state; (C ) o p cell pair; (R^) R resistance; (n^) S solid or stationary phase; (C ) or permselectively; (ng) T total; (ET) or top (demineralized) product; (Cj) or temperature; (V^U) w water transport; (nw) IT unit area per cell pair; (R^) v refers to the average concentration of salt; (^v) °° refers to infinite dilution; (Ara) Superscripts = refers to property in membrane; (C,,C.) k 3 or to negatively charged species; (t~) .+ = refers to positively charged species; (t^) REFERENCES Acrivos, A., Ind. Eng. Chem., 48,703 (1956). Aris, R. , Ind. Eng. Chem. Fund am., 8, 603 (1969). Asawa, T., et al., "Proc. 4th Intern. Symp. Fresh Water Sea", Vol. 3, p. 143, Heidelberg, 1973. Bass, D., "A Cyclic Electrodialysis Process - Investigation of Closed Systems", Ph.D. Thesis, University of British Columbia, 1972. Bass, D. and D.W. Thompson, "Proc. 4th Intern. Symp. Fresh Water Sea", Vol. 3, p. 269. Heidelberg, 1973. Belfort, G. and G.A. Guter, "U.S. Off. Saline Water Res. Dev. Rep. 459 (1968)". Belfort, G. and G.A. Guter, Desalination, 10, 221 (1972). Bell, W.E., et al., "U.S. Off. Saline Water Res. Dev. Rep. 536 (1970)". Bockris, J. O'M. and A.K.N. Reddy, Ed., "Modern Electrochemistry," Plenum Press, New York, 4th ed., 1973. Bradley, C.C, Science [2] 138, 489 (1962). Bradley, P.H. , et al. , "U.S. Off. Saline Water Res. Dev. Rep. 597. (1970)". Calvit, B.W. and J.J. Sloan, "Proc. First Intern. Symp. on Water Desalination", Vol. 2, p. 11, Washington, D.C., Oct. 3-9, 1965. Chapman, T.W. , "Lectures in Transport Phenomena", A.I.Ch.E. Continuing Education Series 4_, 90 (1969). Chen, H.T. and F.B. Hill, Separ. Sci., 6, 411 (1971). Chen, H.T., J.L. Rak, J.D. Stokes and F.B. Hill, Amer. Instit. Chem. Eng. J., 18, 356 (1972). Chiolle, A., L. Credali and P. Parrini, "Proc. 4th Intern. Symp. Fresh Water Sea", Vol. 3, p. 81, Heidelberg, 1973. Cooke, B.A., Electrochem. Acta, 3, 307; 4_, 179; 5_, 216 (1961). 298 299 Cooke, B.A., "Proc. First Intern. Symp. on Water Desalination", Vol. 1, p. 219, Washington, D.C., Oct. 3-9, 1965. Cowan, D.A. and J.G. Brown, Ind. Eng. Chem., 51, 1445 (1959). Cowan, D.A., Advances in Chem. Ser., Z7_, 224, American Chemical Society, Washington, D.C., 1960. Craig, L.C., and D. Craig, "Technique of organic Chemistry", Vol. 3, A. Weissberger, Ed., Wiley-Intersci., New York, 1956. Davis, T.A. and G.F. Brockman, "Physiochemical Aspects of Electromembrane Processes", in "Industrial Processing with membranes", R.E. Lacey and S. Loeb, Eds., Wiley-Intersci., New York, 1972. Deming and P. Kollsman, U.S. Pat. 2, 872, 407 (1959). Foo, S.C. and R.G. Rice, A.I.Ch.E.J., _21 (6), 1149 (1975). Foo, S.C. and R.G. Rice, A.I.Ch.E.J., to be published. Friedlander, H.Z. and R.N. Rickles, Anal. Chem., 37.' 27A (1966). Furukawa, D.H., "U.S. Off. Saline Water Res. Dev. Rep. 285 (1968)". Gregory, R.A. and N.H. Sweed, Chem. Eng. J., 1, 207 (1970). Gregory, R.A. and N.H. Sweed, Chem. Eng. J., 4_, 139 (1972). Gupta, R. and N.H. Sweed, "Nonequilibrium Theory of Parametric Pumping", A.I.Ch.E. National Meeting, Minneapolis, Aug. 24 (1972). Helfferich, F., Ed., "Ion-Exchange", Chapter 8, McGraw-Hill Book Co., New York, 1962. Hills, G.J., et al., Proc. Roy. Soc. (London), A 262, 246 (1961). Hoek, van C, U.S. Pat. 2, 735, 812 (1956). •Huffman, E.L., "U.S. Off. Saline Water Res. Dev. Rep. 439 (1969)". Hwang, Sun-Tank and Kammermeyer, K., "Membranes in Separation", Wiley-Intersci, New York, 1975. Israel Patent 13, 242, Mar. 23, 1961. Kellogg, M.W. Company, "Saline Water Conversion Engineering Data Book", Washington, D.C., 1965, Supplement 1, 1966. Kobus, E.J.M. and P.M. Heertjes, Desalination, 10, 383 (1972). Korngold, E., et al., Desalination, 8_, 195 (1970). 300 Kuhn, A.T., Ed., "Industrial Electrochemical Processes", Elsevier Publishing Co., Amsterdam, 1971. Lacey, R.E., "U.S. Off. Saline Water Res. Dev. Rep. 80 (1963)". Lacey, R.E., "U.S. Off. Saline Water Res. Dev. Rep. 135 (1965)". Lacey, R.E., Ed., "Membrane Processes for Industry", Southern Research Instit., Birmingham, Ala., 1966. Lacey, R.E., Desalination, _2, 387 (1967). Lacey, R.E., "U.S. Off. Saline Water Res. Dev. Rep. 398 (1968)". Lacey, R.E., E.W. Lang and E.L. Huffman, Advances in Chem. Ser., _3j8, 168, American Chemical Society, Washington, D.C, 1963. Lacey, R.E. and E.W. Lang, "U.S. Off. Saline Water Res. Dev. Rep. 106 (1964)". Lang, E.W. and F.L. Huffman, "U.S. Off. Saline Water Res. Dev. Rep. 439 (1969)". Laskorin, B.N., et al., "Proc. 4th Intern. Symp. Fresh Water Sea", Vol. 3, p. 99, Heidelberg, 1973. Lynch, M.A. and M.S. Mintz, J. Am. Water, _64, 711 (1972). McDermott, J., Ed., "Industrial Membranes Design and Applications", Noyes Data Cor., New Jersey, 1972. Malherbe P. Le. and W.G.B. Mandersloot in "Demineralization by Electrodialysis", Chapter 2, J.R. Wilson, Ed., Butterworth, London, 1960. Mandersloot, W.G.B. and R.E. Hicks, Ind. Eng. Chem. Proc. Des. Dev., 4^, 304 (1966). Mangan, G.F., J.M. Shackelford and K.A. Kase, "U.S. Off. Saline Water Res. Dev. Rep. 83 (1963)". Mason, E.A. and T.A. Kirkham, Chem. Eng. Progr. Symp. Series, 55_ (24), 173 (1959). Mattson, M.E., L.L. Snedden and J.E. Gugeler, "Proc. First Intern. Symp. on Water Desalination", Vol. 3, p. 265, Washington, D.C, Oct. 3-9, 1965. Matz, R.C, C. Forgacs and S. Perlmutter, U.S. Pat. 3, 029, 196 (1962). Matz, R.C, "Proc. Interregional Seminar Economic Appl. Water Desal.," New York, 22 Sept., 1965. 301 Mintz, M.S. and E.W. Lang, "Study of Electrogravitational Separation", Southern Research Instit. Rep. 7374-1650-1 (1965). Murphy, G.W. , Electrochem. Soc, _97, 405 (1950). Nernst, W. , Z. Physik Chem. (Leipzig), 47, 52 (1904). O'Shaughnessy, F., "Desalting Plant Inventory Rep. 4_ (1973)", ed. by the U.S. Off. Saline Water. OSW (1963), "Saline Water Conversion Report for 1962", U.S. Off. Saline Water, Washington, D.C. OSW (1964 a), "Saline Water Conversion Report for 1963", U.S. Off. Saline Water, Washington, D.C. OSW (1964 b), "Test Manual for Permselective Membranes", U.S. Off. Saline Water Res. Dev. Rep. 77 (1964). OSW (1968), "U.S. Off. Saline Water Res. Dev. Rep. 325 (1968)". Patrick, R.R., J.T. Schrodt and R.I. Kermode, Separ. Sci., _7, 331 (1972). Pepper, K.W. , H.M. Paisley and M.A. Young, J. Chem. Soc, 4097 (1953). Pigford, R.L., B. Baker III and D.E. Blum, Ind. Eng. Chem. Fundam., J3, 144 (1969 a). Pigford, R.L. , B. Baker III and D.E. Blum, Ind. Eng. Chem. Fundam., 8^, 848 (1969 b). Popkin, R., Ed., "Desalination Water for the World's Future", Frederick A. Praeger Publishers, New York, 1968. Redman, R., "U.S. Off. Saline Water Res. Dev. Rep. 683 (1971)". Rhee, H.K. and N.R. Amundson, Ind. Eng. Chem., _9_, 303 (1970). .Rice, R.G., Ind. Eng. Chem. Fundam., _12 (4), 406 (1973). Rickles, R.N., Ed., "Membranes Technology and Economics", Noyes Develop. Corp., New Jersey, 1967. Roberts, E.J., U.S. Pat. 2, 799, 638 (1957). Rosenberg, N.W. and C.E. Tirrel, Ind. Eng. Chem., 4_9, 780 (1957). Sabadell, J.E. and N.H. Sweed, Separ. Sci., J5 (3), 171 (1970). Shaffer, L.H. and M.S. Mintz, "Electrodialysis", in "Principles of desalination", K.E. Spiegler, Ed., Acad. Press, New York, 1966. 302 Smith, J.D. and J.L. Eisenman, Eds., "Electrodialysis in Advanced Waste Treatment", U.S. Dept. of the Interior, 1967. Solan, A. and Y. Winograd, Phys. Fluids, 12, 1372 (1969). Solt, G.S., "Proc. First Intern. Symp. on Water Desalination", Vol 1, p. 13, Washington, D.C, Oct. 3-9, 1965. Solt, G.S., "Electrodialysis" in: "Industrial Electrochemical Processes", A. Kuhn, Ed., Elsevier Publ. Co., Amsterdam, 1971. Sonin, A.A. and R.F. Probstein, Desalination, 5>, 293 (1968). Sonin, A.A. and R.F. Probstein, "U.S. Off. Saline Water Res. Dev. Rep. 375 (1968)". Spiegler, K.S., Ed., "Salt-Water Purification", John Wiley and Sons, New York, 1962. Spiegler, K.S., Advanc. Chem. Ser. , 3j8, 179 (1963). Spiegler, K.S., Ed., "Principles of Desalination", Acad. Press, New York, 1966 a. Spiegler, K.S., Interim Rept. 4-, U.S. Off. Saline Water, 13 (1966). Spiegler, K.S., Desalination, j), 367 (1971). Sporn, P., Ed., "Fresh Water from Saline Waters", Pergamon Press, Oxford, 1966. Sweed, N.H., in: "Progress in Separation and Purification", Vol. 4, pp. 171-240, Wiley-Intersci, New York, 1971. Sweed, N.H. and R.A. Gregory, A.I.Ch.E. J. , 17_, 171 (1971). Sweed, N.H., in: "Recent Developments in Separation Science", Vol. 1, Chemical Rubber Co., Cleveland, 1972. Thangappan, et al., Ind. Eng. Chem. Prod. Res. Dev., 9_ (4), 563 (1970). Thompson, D.W. and B.D. Bowen, Ind. Eng. Chem., 11, 415 (1972). Thompson, D.W. , D. Bass and M.E. Abu-Goukh, Can. J. Chem. Eng., 52, 479 (1974). Tuwiner, S.B., Ed., "Diffusion and Membrane Technology", Reinhold, New York, 1962. Tye, F.L., Trans. Inst. Chem. Eng. (London), 41 (1963). 303 United Nations, "First Desalination Plant Operation Survey Rept. No. E.69.11. B. 17 (1969); Second Rept. No. E.73.11. A. 10 (1973). U.S. Bureau of Reclamation and Office of Saline Water, "Desalting Handbook for Planners", 1st. ed. May 1972, 2nd ed. Nov. 1972. Vetter, K.J., Ed., "Electrochemical Kinetics, Theory and Experimental Aspects", translated by Bruckenstein, S. and Howard, B., Acad. Press. New York, 1967. Wankat, P.C., Separ. Sci., 9 (2), 85 (1974). Watanabe, T. , et al., Nippon Kaisui Gakkai-Shi, _26, 83 (1972); C.A. 7_8 (1973), No. 163, 886. Weiner, S.A., P.M. Rapier and W.K. Baker, Ind. Eng. Chem. Proc. Design Dev., _3 (2), 126 (1964). Wiechers, S.G., U.S. Pat. 2, 676, 144 (1954). Wilhelm, R.H., A.W. Rice and A.R. Bendelius, Ind. Eng. Chem. Fundam., J>, 141 (1966 a). Wilhelm, R.H., in: "Interacellular Transport, Symp. of the International Society for Cell Biology", Vol. 5, p. 199, K.B. Warren, Ed., Acad. Press, New York, 1966 b. Wilhelm, R.H. and N.H. Sweed, Science, 159, 522 (1968 a). Wilhelm, R.H., A.W. Rice, R.W. Rolke and N.H. Sweed, Ind. Eng. Chem. Fundam., 2, 337 (1968 b). Wilson, J.R., Ed., "Demineralization by Electrodialysis", Butterworth, London, 1960. Zajic, J.E., "Water Pollution Disposal and Reuse", Vol. 2, Marcel Dekker, Inc., New York, 1971. Appendix A Electrode System A.l. Electrode Materials Various materials for electrodes are in use, for example, graphite and stainless steel, which are gradually attacked in oxidizing conditions and must be replaced. Platinum-coated metals (e.g. titanium, tantalum, or zirconium), with a high level of corrosion resistance and a life of several years, are now frequently used, especially as anodes. Oxides of some metals such as lead and ruthenium have proven to be sufficiently conductive and insoluble in acids to be used as coating for anodes (Thangappan, et al., 1970). Magnetite electrodes have been used for anodes in electrodialysis, but this material is very fragile (Davis and Brockman, 1972). A.2. Electrode Reactions Throughout the diluting and concentrating cells of an electrodialysis stack, and in the intervening membranes, electrical conduction is ionic. At the electrodes, however, the mechanism of electrical conduction changes abruptly from ionic to electronic. The technology of electrode reactions is highly developed in many respects, but there is still considerable con troversy concerning mechanisms and the relative importance of competing reactions that occur at the electrodes (Davis and Brockman, 1972). 304 305 The cathode or negatively changed electrode is the source of electrons, and at the cathode, the electrons must be transferred from the external circuit to ions in the solution. The following are typical reactions by which this transfer of charge may be accomplished: -> M° metal deposition (A.l.) -* 40H reduction of gaseous oxygen (A. 2.) -> H2 (acidic solution) evolution of gaseous (A.3.) -> H2 + 20H (basic solution) hydrogen (A.4.) Metal-deposition reactions are useful in processes such as electro plating and the recovery of spent pickle liquor. Reactions in which gaseous oxygen is reduced are important in fuel cells. The principal cations present in typical brine are much less readily discharged than hydrogen ion, and the net result of this is that the cathode reaction is almost invariably the cathodic half of the water electrolysis reaction: 2H„0 + 2e~ -> H„ + 20H~ E = 0 (A. 5.) 2 2 O There is usually almost no deterioration of the cathode, and almost any conductor that is compatible with the rest of the system can be used as a cathode. Carbon steel is a commonly used cathode material. Heavy metal ions such as copper and iron may plate out on the cathode, and, in addition, the shift in pH caused by the cathode reaction may cause the precipitation of a variety of substances that may foul the system. The principal problems are apt to be due to CaCO^, Mg(0H)2, and Fe(0H).j. Depending on the composition of the solution, pH, anode composition, and current density, one or more of the following reactions may occur at the anode: M" + xe 02 + 2H20 + 4e' 2H+ + 2e' 2H20 + 2e" 306 +x — M° ->• M + xe ; metal dissolution (A. 6.) M° + xOH~ -> M(0H)x + xe" oxidation of electrode (A.7.) 2M° + 2xOH~ -> M20x + xH20 + 2xe~ (A. 8.) H2 -»• 2H+ + 2e~ oxidation of gaseous hydrogen (A.9.) 2H20 02 + 4H+ + 4e~ (acidic solutions) evolution of (A. 10.) 40H~ •*• . Q2 + 2H20 + 4e~ (basic solutions) gaseous oxygen (A. 11). 2C1~ -> Cl2 + 2e , evolution of gaseous chlorine (A.12). Oxidation of gaseous hydrogen is an important reaction in fuel-cell operation. Metal dissolution results in destruction of the electrode. When the anode is oxidized, hydroxyl ions are consumed. Unless provision is made for removing the companion hydrogen ions or supplying hydroxyl ions, the electrode solution will become acidic. Most metal oxides and hydroxides are soluble in acidic solutions. M20x + 2xH+ -> 2M+X + xH20 (A. 13.) or M(0H)x + xH+ -»• M4^ + xH20 (A.14.) The net result is the dissolution of electrode metal. Reactions in which gaseous oxygen or chlorine is evolved are commonly encountered in electrodialysis when noble metal anodes are used. In a • typical naturally occurring brine such as seawater chloride ions may be oxidized at the anode to produce hypochlorite: Cl~ + 20H~ - 2e~ •* 0C1~ + Ho0 E =0.94 volt (A.15.) 2 o Or, in acidic media chlorine gas will be released, Cl~ - e" -> h Cl2 (g) Eq = 1.35 volt (A. 16.) 307 A portion of the chloride oxidized at the anode will be carried out of the cell in the anode rinse stream (anolyte), and a portion may escape as chlorine gas. Chlorine remaining in the solution will eventually form an equilibrium mixture according to Cl2 + H20 = HCl + HOCl (A.17.) In many situations, and most particularly in a high-sulfate, low-chloride water, we will find that the anode reaction discharges oxygen from the water with the simultaneous production of hydrogen ions: Ho0 - 2e~ -> h0* + 2H+ E =1.23 volts (A. 18.) Z £ O Typical brackish water contains significant amounts of both chloride and sulfate, and frequently both chlorine and oxygen are evolved simul taneously. We cannot predict the relative amounts of each with any degree of success because the reactions are principally controlled by electrode kinetics rather than by any considerations of electrode potential. Any or all of the reactions listed above, or further reactions that produce even more highly oxidized products, such as C10^, may occur, depending on local current densities and the nature of the electrode surface. If noble metal electrodes are not used, the anode reaction will also include the oxidative products of the electrodes. Iron or steel anodes, for example, will produce iron oxides in various degrees, and carbon anodes will produce carbon dioxide. The electrode reactions necessarily associated with electrodialysis operation introduce two problems: first, added power must be supplied to provide the electrode reaction energy; second, the products of the electrode reactions may be harmful to the electrodialysis stack or may interfere with 308 the continued operation of the system. The first of these may be minimized easily by increasing the number of cells per electrode pairs as will be discussed in process efficiency section; the second is more complicated and there is no single simple solution. We can expect that the chlorine or other oxidizing materials formed at the anode may cause rapid deterioration of the stack components; and the alkaline cathode material, if allowed to enter the stack, is obviously likely to produce precipitation. Because of this it is usual to provide for hydraulic isolation of the two electrode stream compartments at the ends of the dialysis stacks. Frequently isolation of these streams plus a high rate of flushing with feed water is all that is attempted by way of controlling the possible harmful effects of the electrode reaction products. The use of sodium bisulfite in the anode rinse stream, to avoid the formation of chlorine, has been described by Wiechers (1954). The catholyte basicity can be controlled by the addition of inorganic acids to the cathode stream. Several more nearly closed systems have also been tried or proposed. In principle we could circulate sodium sulfate or sulfuric acid in the anolyte-catholyte system and limit the reactions to oxygen and hydrogen generation. If this were all that happened, electrolyte volume could be maintained by adding very small quantities of pure water froi time to time or by reacting the two gases. An even more subtle approach has been suggested by Roberts (1957), who has patented the circulation of a redox solution between the two. compartments. The oxidation at the anode and the reduction at the cathode theoretically balance each other in this case. Unfortunately, none of these "closed" schemes work too well in practice 309 because it is difficult to confine a given ion to a particular stream. Either the materials in the electrode stream tend to diffuse into the remainder of the cell or vice versa, and in either case problems of oxidation, pH shift, and fouling inevitably arise. A.3. Electrode Polarization Effect on power Consumption The energy consumed by the processes occurring at the electrodes depends upon a number of factors, including the electrode materials, the reactions involved, the concentrations of the ions, the applied current density and the solution velocity. A detailed discussion of electrode polarization is given by Vetter (1967) and by Bockris and Reddy (1973). The passage of current through each of the electrode compartments involve three steps: (1) The transfer of ions from the bulk of the solution to the surface of the electrode. (2) The electrochemical reaction at the electrode. (3) The formation of the final products of the reaction and their removal from the electrode surface. Three overpotentials are involved: (i) Concentration overpotential When the current is flowing, the ions that discharge migrate towards the electrode and cause a concentration gradient across the thin diffusion layer at the electrode surface. This phenomenon is exactly analogous to the concentration gradient that occurs at the ion exchange membranes. The concentration gradient leads to a change in electrode potential of _ RT Sulk , . \on " T±n C I (A-19*) surface 310 (ii) Chemical overpotential The chemical overpotential, » is defined to be that potential in excess of the discharge potential for the given reaction which must be applied to the cell in order to maintain a finite rate of discharge. Chemical overpotential occurs as a result of steps (2) and (3) above. The value of n , for the electrode reaction is given by Tafel's Formula: chem ° J n , = a + —r=r In i (A. 20.) chem a F where a' = h. and a = constant (depends on nature of cathode), (iii) Ohmic overpotential The ohmic overpotential, n consists of two parts, namely the voltage drop which occurs in the bulk solution of constant concentration plus the voltage drop across the diffusion layer where the concentration gradient varies linearly with the current density n , = n , + ru ohm sol 6 = i R , (A.21.) ohm where R , consists of two series resistances, ohm R . = R . + RX (A. 22.) ohm sol o R , can be evaluated in terms of the mean resistivity of the bulk sol solution, R = P meany (A. 23.) sol Ap where-311 p = the mean restivity of the electrode solution, ft - cm Kmean y = bulk solution thickness,. cm 2 Ap = active membrane area, cm may be evaluated by specifying the resistivity at any point within the diffusion layer as a function p(x,z) and by computing the double integral of this function as discussed in Section 3.1.1. -1 dz (A.24.) Thus, the electrode polarization potential, Ee> can be evaluated by summing these separate components. A. 4. Electrode Flow System The two electrode compartments present in each multimembrane stack are usually supplied with rinse solution from a separate recirculating hydraulic system. In passing through the cell catholyte becomes basic and anolyte becomes acidic, when these are mixed they partially neutralize one another. Provision should be made in electrode system for discharge of the electrode gases, and a small discharge of electrode solution is required to prevent buildup of ions produced by electrode reactions. A feed-and-bleed system as shown in Figure A.l, is frequently employed. 1_ R, 1 J z-0 p(x,z)dx x=0 Gases ± Rinse]" Tank Liquid Discharge €5" Make. Up Water Stacks 1x FIGURE A_| Electrode system flow sheet Appendix B The Current Efficiency The total current efficiency, n^., is related to the Faraday efficiency, rip by the relation n = n n (B.l.) I F* w where n is the water transfer term, w The Faraday efficiency, n , is defined as the ratio of the salt shifted r to the theoretical current requirement (equivalent of salt transported) F (Faradays of electricity passed)(number of membrane pairs employed) = I^OE (B.2.In where F = Faraday's constant, 96500 A/(sec)(equivalent) AN = change in product stream normality, equiv/liter Fp = flow rate of the product stream, liter/sec I = total current passed through the stack, A n = number of membrane pairs used Faraday efficiency, n_, as defined by Eq.(B.2.) depends on both the r actual membrane used and the amount of leakage current that a particular stack design may permit and it expresses the performance of the process w.r.t. the current. It is often determined by an inexact method (apparent values) for brine and dialy'state streams independently: 313 314 VDi - VF , nD - s (B.3.) ^B = nl (B'4>where TV.*1^ = apparent Faraday efficiencies based on the dialystate and brine streams respectively F ,F = dialystate and brine efflux rates respectively, ml/sec. D B D^,B^ = dialystate and brine influent concentrations respectively equiv/ml ^>2'^2 ~ dialystate an(* Drine effluent concentrations respectively The influent and effluent flow rates of a single stream are not identical because of: (a) water transfer by osmosis and electro-osmosis (b) a minor volume change resulting from the salt displacement The true Faraday efficiency, rip, is defined by: nD = nF (1 - 18 w Dx) (B.5.) nB = nF (1 - 18 w B1) (B.6.where w = moles of water transported per equivalent of salt transfer; w = w3 + wC, where w3, wC are water transport numbers (- hydration 3. C number of ions) e.g. for NaCl, w = 4, w =8. Determination of n ancj n enable both r\„ and w to be calculated D D r (Wilson, 1960). The factors that may contribute towards low current efficiency in an electrodialysis stack are mechanical and electrochemical ones: 315 (1) Imperfect selectivity of membranes or deterioration of membranes. The fact that the membranes are not perfectly selective means that more than the theoretical current must be passed. (2) Electrical leakage by stray current and parallel current paths through the stack manifold. (3) Short-circuiting of membrane packs. (4) Internal and external water leakage. A large water transfer may accompany the current flow across the membrane due to osmosis and electro-osmosis, which results in loss of product water. Also there may be hydraulic leakages between cells and/or external leakages. (5) Back diffusion of electrolytes. (6) Severe polarization effects or unwanted ion transfer. At sufficiently high current densities or low salt concentrations, the H+ and OH ions normally present in water will begin to participate in the current-carrying process. Assuming that obvious problems, such as external parallel current paths through bolts and containers, gross leaks between the product and waste compartments, and water splitting, have been properly taken care of, we can express an over all current efficiency, n^., as the product of these efficiencies: nT = n n n = run (B.7. I s m w F w where ris: takes care of effects due to the permselectivity of the individual membranes n : accounts for the effects of current leakage through the m manifold 316 ri : is the result of water transport through the membranes, w The quantities ris, n.m and are all defined in such a way that ideally they approach 1.0. (i) Permselectivity efficiency, n^ The permselectivity efficiency, rt^, is defined as nt-Pc+nt+Pa 's n t + n t, c - a + where n ,n c a are numbers of cation and anion-permeable membranes t+,t are transport numbers in solution of cation and anion respectively Pc,Pa are permselectivity of cation and anion-permeable membranes respectively Pc = = 1 " fc+ t - t t - t Pa = — - = ~- 11 (B.9.) 1 " C-where t+, t refer to transport numbers of counter-ions in membranes. Mien n = n , Eq.(B.8.) reduces to: c a ^ n = t Pc + t, Pa s - + = (t+ + t_) - 1 = 1 - (t^ + t*) (B.10.) where t = anion transport number in the cation-permeable membrane t_^ = cation transport number in the anion-permeable membrane 317 - (tC + t*) is imperfect selectivity factor or penetration of co-ions into a membrane. If t = t = 0.5, then ns will be equal to the average permselectivity = (Zl + ii) (B.H.) s I (ii) Electrical Leakage and Short-circuiting term, nm The partial short-circuiting of a membrane stack by conduction through manifolds and stray parallel current paths consume power without producing any useful results, thus reduce the effective current efficiency. Because of the inherent engineering design of electrodialysis units, each concentration stream within the stack is connected, via conduits, to all other concentration streams. The same applies for the dilution streams. Since the concentration stream is more conductive to electricity than the dilute stream, it would be expected that a high fraction of non-productive-leakage current would flow through the concentration stream. Leakage current calculations have been developed by Wilson (1960) and Mandersloot and Hicks (1966) and presented by Belfort and Guter (1968). Usually the effect of current leakage through the manifold is a reduction in efficiency of less than 5%, Belfort and Guter (1968) in their study of Webster and Buckeye electrodialysis plants showed that current leakage has only minor effect. The leakage current for a given design can be estimated by assembling a sample stack with insulating sheets of plastic in place of the membranes, thereby interrupting the electrical field, but not the liquid flow. The normal operating voltage is then applied and the current measured is regarded as being that due to leakage through the entire 318 internal and external liquid flow path of the stack. (iii) Water transfer term, n. w Some water is transported through the membranes along with the electrolytes due to electro-osmosis. The amount of electro-osmotic water transport varies with membrane type, ionic species, and concentration of solution. When the feed is of low salinity or when moderate quantities of salt are removed from brackish water, transport is seldom a problem. However, in more concentrated solutions or in systems involving a high degree of desalination, water transfer can have important effects on the current utilization in the process. A large transfer of water will: product quality specifications, (b) reduce the quality of product obtainable from a given amount of feed to the dilute stream. The effect of water transport on the current efficiency is given by: (a) require the use of additional current to meet the desalted-1 -nx (0.018) m. w 1 (B.12.) n. w where m. x the molality of the feed water T transference number of water defined as the number of w moles water transferred per Faraday n number of membrane pairs. Appendix C Nernst Idealized Model of Wall Layers C.l. The Flow Field in an Electrodialysis Cell In almost all electromembrane processes the solutions to be treated flow between parallel planar ion-exchange membranes. The flow channels are filled with spacer materials that cause complex flow patterns. The velocity of the solutions past the membranes and through the spacer materials results in relatively good mixing of the solution in the center portions of the flow channels, but the mixing is less near the surfaces of the membranes, where the solution is almost static. C.2. Nernst Model The complex hydraulic pattern in an electrodialysis cell is approxi mated by the simplified Nernst model. This is an idealized model (Nernst, 1904) based on the following assumptions: - there are layers adjacent to the membranes in which the solutions are completely static or in laminar flow. - the solution in the bulk (i.e. between the wall layers) is thoroughly mixed so that the concentration of electrolyte at any point in this zone is the same as that at any other point. - there is no change of either the thickness of the wall layers or the concentration gradients along the flow channel. 319 320 Despite the complexity in a real system, Nernst model affords a simplified mathematical approach which results in expressions that are easy to use and that predict performance adequately for use in the design of electromembrane processes. C.3. Some derivations of the Model Since frequent use is made of the assumption that the concentration gradient in the wall layer of an electrodialysis cell is linear, a justi fication of this assumption with the other main assumptions involved is in order. ' C.3.1. General theory of coupled processes When an ion moves in an electrolyte solution it does not do so in the complete absence of other effects. Its motion is accompanied by a flow of electric current, and there may also be a flow of heat and a flow of solvent. We are faced with the problem of describing simultaneously a minimum of four fluxes: salt, electricity, solvent and heat. In analyzing systems in which several forces and fluxes are coupled, it is sometimes convenient to make use of the theory of the thermodynamics of irreversible processes. Although an analysis made in these terms cannot deal with the underlying causes of the phenomena that may be observed, it is of great value in clearly defining certain relationships that must necessarily hold between the various forces and flows when the system is ir the steady state. The general equations for flow may be written (Hills et al., 1961) as: 321 -y Jl = -L11VTU1 " L12VTU2 " L13VTU3 " L14Vln T -> J2 = -L12VTU1 " L22VTU2 - L23VTU3 - L24Vln T \ = -L13VTU1 " L23VTU2 " L33VTU3 - L-.Vln 34 T -> Q = "L14VTU1 " L24VTU2 " L34VTU3 - L-.Vln 44 T (CI.) where are phenomenological coefficients and the subscripts 1,2,3,and 4 refer to the positive ions, negative ions, water and heat respectively. V^U is the gradient of total chemical potential, taken at constant temperature, and Q is the flow of heat. If we consider an isothermal process in which both non-electrostatic interaction between the ions together with electro-osmosis are neglected, then all the terms except the first will drop out and the ionic flux, J is given by Jk = " LkkVk = - VkVk (c-2-} 2 where is the flux of an ionic species in g-mole/(cm )(sec), is the ionic mobility which is defined as the average velocity imparted to the species under the action of a unit generalized force (per mole), and is the concentration in g-moles/cu.cm. The total chemical potential, U, is meant to include effects due to electricity, as well as temperature, pressure, concentration and gravitational field, if any. Assume that gravitational fields are unimportant, then V U = Z F VE + —• Vp + |£ VC (C.3.) T dp dC where VE is the electric field in volts/cm F is the Faraday constant in coulombs/g.equiv. Z is the valence 322 In real electrodialysis systems the modest differences in temperature and pressure have no significant effect on the current flowing as long as HJ 3U even very small potential differences exist. Therefore — Vp term is negligible. For ideal solution, U = U + RT ln a (C4.) o where Uo is the standard chemical potential and a is the activity. For dilute solutions concentration can be used instead of activity (a = yC ^ C). From Eq.(C.4.) we get {2. •? vc (C.5., A term including the derivative of the activity coefficient could be included (see for example, Hills, et al., 1961), but this does not affect the general principle; and, in practice, omission of the term that would arise from differentiation of the activity coefficient is no worse than some of the other assumptions that are needed to facilitate the integration of these equations when they are used to describe real systems. Substitute Eq.(C.5.) into Eq.(C.3.) and drop the pressure term RT Jk = "ukck (zkF VE + c7vck> (c'6-) k The ionic mobility, u^ (g-moles)(sq.cm)/(joule)(sec), can be related to the ionic-diffusion coefficient, (sq.cm/sec) through the Nernst-Einstein relation: uk = VRT (c-7-) where T is the absolute temperature, °K., and R is the gas constant, 8.3143 joules/(°K)(mole). Eq.(C.7.) is true only when the activity coefficient 323 is unity, that is, at infinite dilution (Chapman, 1969). From Eqs.(C.6.) and (C.7.) Jk = - Vk F ck VE - Vck (c-8-> Eq.(C.8.) is the well-known Nernst-Planck equation of ionic flux with negligible convection (i.e. C^y = 0, where v is the stream velocity). Although the Nernst-Planck equation has a number of shortcomings which limit its rigorous applications to dilute solutions, we will use it because it accomplishes a great simplification of a complex problem. To do this however, we must assume the validity of the Nernst-Einstein relation and neglect any gradients in the solvent concentration as well as interactions between the fluxes of the charged species. For a more thorough analysis of ionic transport e.g. concentrated multicomponent solutions, it is necessary to use a more complete flux expression (Chapman, 1969). C.3.2. Ionic Fluxes For a uni-directional flow of a 1-1 electrolyte Eqs.(C7.) and (C.8.) can be written as J+ - - D+ t( fj ) C ( |f ) + ( £ )] Because of electroneutrality in the solution phase C+ = C_ = C (CIO.) and for mono-monovalent electrolyte Z+ = - Z_ = 1.0 (C.ll.) 324 In the membrane, the numerical value of the flux ratio, —- , is equal to the transport number ratio ^ . Since by definition of the steady state the fluxes are independent of position x (perpendicular to membrane face), the same flux ratio prevails also in the solution: i± = |± = _|± = 1±__ (C.12.) J_ J_ t_ (1 - t+) The negative sign is introduced because the J's are vectors. In the membrane J+ and J_ have opposite signs, while t+ and t_ are always taken as positive. It should be noted that the ion flux ratio is equal to the ratio of the ion transport numbers in the membrane only when ion transport in membranes takes place entirely by electromigration. Unless the membrane is ideally permselective, there exist additional ion fluxes due to diffusion across the membrane caused by the salt concentration difference in the solutions at the two membrane faces. This back diffusion of the salt will be neglected here, however, because almost ideally permselective membranes are used in most electrodialysis installations, and since in practice.the electrical driving forces are in general much larger than the diffusion driving forces, even when membranes are used which are not fully perm selective. From Eqs.(C9.) and (C.12.): = - t- J+ FC dE dc t+ D_ RT dx ~ dx OR 325 substitute Eq.(C.13.) into (C.9.) and + + dx t+ D_ dx . _ 2D4. + lZ J+ °+ + dx t+ D_ - 2D+ dc j = _ ~~Z dx" (C.14.) J+ 1 - (D+ t_/D_ t+) flX 2D" dG (C.15.) 1 - (D_ t+/D+ t_) dX Since fluxes, ionic diffusion coefficients and membrane transport dc numbers are constant, it follows that — is constant also. In other words, ' dx the application of the Nernst-Planck equation with the above assumptions leads to a linear concentration gradient in the boundary layer. It is often more convenient to express the fluxes in terms of the diffusion coefficient of the electrolyte, D, rather than the ionic diffusion coefficients, D+ and D_. Noting that in free solution D+ = t+ = t+ (C.16.) D_ t_ (1 - t+) and using the Nernst expression for the diffusion coefficient of 1-1 electro lyte in dilute solution !-!(!+!) D 2 D+ D_ OR 326 From Eq.(C.16.) D_ = t_ = (1 - t+) (C.18.) D+ + D_ t_ + t+ Substitute Eq.(C18.) into Eq. (C.17.) D = 2D+ (1 - t ) = 2D_ (1 - t_) (C.19.) From Eqs.(C.14.) and (C.16.) J = ®± %L = - 2D+ (l-t+) l+ dc (Ci2(J<) 1 - (t+ t_/t_ t+) dX (t_ t+ - t+ t_) dX But t_ t+ - t+ t_ = (1 - t+) t+ - t+ (1 - t+) = t+ - t+ (C.21.) Substitute Eqs.(C.19.) and (C.21.) into Eq.(C.20.) •j-.—Sk-^ (c.22.) (t+ - t+) dx Similarly J •- Di- £ = Dt- 4S. (C.23.) Ct. - t_) dx (t+ - t+) dx For ideally, selective cation exchange membranes, t+ = 1.0. Hence from Eqs, (C.22.) and (C.23.): J+ = -D [iot]; J- = 0 (c-240 and for ideally selective anion exchange membrane t_= 1.0 J, = 0; J =-D[~4£] (C.25.) + - t+ dx Note that both Eqs.(C.24.) and (C.25.) are of the type of Fick's law, but the 327 ratio ^ replaces the ionic coefficient D± (i.e. the flux is higher because the electric field provides additional driving force). The current density, i, is given by Faraday's law i = F (J+ - J_) (C.26.) Substitute for J+ and J_ from Eqs.(C.22.) and (C.23.) i = 2L— dc = FD dc ? Ct+ " V dX (t_ - t_) dx If i, D and the transport numbers are constant, Eq.(C.27.) then, within the range of applicability of the Nernst-Planck equations, the concentration gradient in the wall layer is linear. C.4. Wall layer thickness The wall layer thickness, 6, depends on distance from solution inlet and it varys along the flow path. In the Nernst model it is assumed that a steady state has been reached. It is also assumed that the hydraulic flow conditions of the solutions are chosen such that variation along the membrane can be neglected. In this case, the solution concentration profile in the wall layer is time-invariant and also does not vary along the membrane. According to the Nernst model an approximate average value (or a critical value) of 6 is used and the problem can be solved without integration over the whole flow path. Studies which stress the hydrodynamic aspects of the problem and the influence of non-uniform diffusion layers have been published (Sonin and Probstein, 1968; Solan and Winograd, 1969). It is of interest that the hydrodynamic analysis leads to justification of Nernst's polarization layer concept [replacement of the actual mass-transfer boundary layer (diffusion layer) by a diffusion layer of uniform thickness] as a fairly good approximation for certain flow situations (Spiegler, 1971). 328 C.5. Conclusion It can be concluded that the Nernst idealized model is in effect equivalent to the application of the Nernst-Planck equations and the use of an average thickness of the diffusion layer. Appendix D Graphical Solution of Constant-Rate Model Graphical solution for synchronous (in-phase) operation [case (i) -chapter (3)] will be considered here. Graphical solutions for the other cases can be developed in a similar manner. The system consists of a separator (ED stack) and two end reservoirs as shown in Figure D-l(a). Initially the separator and the bottom reservoir are full of solution of concentration Cq, top reservoir is empty. The abseissa in Figure D-l(b), which represents the vertical coordinate in Figure D-l(a), is divided into three sections: Section I : -I -4 z ^ o , the bottom reservoir Section II : o 4 z 4 I , the separator Section III: I 4 z 4 2H , the top reservoir Operation starts with up-stroke (demineralization half cycle). During this period solute is transferred from the mobile phase into the storage compartments of the separator. By the end of the first half cycle the concentration profiles of solution in the separator and the top reservoir are indicated by the lines abc, cde respectively in Figure D-2. The amount of solute stored in the separator during this half cycle is given by the rectangle afgh (Figure D-2) which has the same area as the two triangles acf and cef (i.e. cf = fg). The stored material is returned to the mobile phase during the second half cycle and it distributes itself between 329 330 c c <D U c o o I Bottom Reservoir E Separator n Top Resrvoir ii Axial Position ,z (b) Figure D_l (a) Separator (EDStack) and two end reservoirs, (b ) Initial concentration profile. 331 FIGURE D_2 Concentration profile abcde and amount of material stored afgh at the end of the first half cycle. 332 regions II and III in different proportions depending on the ratio of the Kl mass transfer rates in the two half-cycles, — where K2 dCf = - K, : for demineralization (D.l.) dt 1 ' dC f = K2 ; for enrichment (D.2.) dt T If K2 £ K^ and demineralization is assumed to take place for time , then to maintain the material balance of the solute, the enrichment period should be At, where TK At = ^ (D.3.) Kl Graphical solutions of three different cases of .the ratio — will be 2 considered. Kl (a) -i = 1.0 K2 In this case La = Z.3 as shown in Figure D-3(a) where a = tan K^ and g = tan ^ K2; and the stored material is distributed equally between regions II and III during the second half cycle. Each point along the lines abc, cde will gain a concentration shift given by the length of the corresponding arrow vertically above it (concentrations at points a and e remain constant while that at point c shows the maximum jump). Figure D-3(b) shows that by the end of the first cycle all points along the concentration profiles return to their initial values and no separation is obtained in this case. FIGURE D_3(a) Mass transfer during the second half cycle (enrichment half cycle) K2=K, FIGURE D_3(b) Concentration profile at the beginning (dotted line) and at the end (solid line)of the second half cycle. 334 (b) K2 » Kx Kl In this case — -> 0. From Equation (D.3.) At -*• 0, which means K2 that all the stored material is transferred instantaneously to region II (i.e. Z,B 90°). Figure D-4(a) shows the mass transfer during this half cycle, where the vertical arrows indicate the concentration shifts at various points along abC^, while Figure D-4(b) shows the concentration profiles at the beginning and at the end of the second (enrichment) half cycle. Due to the instantaneous mass transfer there is a concentration discontinuity at the boundary of the two regions (points C.^ and CJ-J-J) • Every cycle the depleted product suffers a loss of material represented by the triangle e ^ (Figure D-4(a)) while the enriched product gains a net increase of similar amount. The average top and bottom concentrations after the nth cycle are given by: C N K Tn -iS - 1-^- (D.4.) o o and C_ K. Tn o o (c) K2 > Kx K2 is assumed to be larger than K^, but both are of the same order of magnitude e.g. K2 = 2K^. In this case Equation (D.3.) gives that At = r (D.6.) 4 The mass transfer during the second half cycle is shown in Figure D-5(a) where L 3 = 2 La. /K A A A A /N Cm Ui S FIGURE D_4(a) Mass transfer during the second half cycle (enrichment half cycle), K2>KI FIGURE D_4(b) Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle-K2>KI FIGURE D_5(a) Mass transfe during the second half cycle (enrichment half cycle). K2 = 2K, FIGURE D_5(b) Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle. K2=2K, 337 After the first half cycle the material lost by the top (demineralized) product is given by A ceo (Figure D-5(a)) where 1 T TK1 A ceo = ( \ )( -j=- ) (D.7.) and the average concentration of the top product is given by TK CT,1 = Co-— (D-8') Then every cycle the top product will lose a material given by 1 K T ' K T A ceo - Ac'od' = ±(-J_)(i)-A(_±_) (At) T K T At K • i ("i ri) (D-90 and the average concentration change will be given by * • n -. K.T K^T material loss _ _1 1 (T/2) " 4 K24 (D.10.) The average top concentration after the nth cycle is given by C_, TK TK K = i-^-^-KT 0).ll.) o o o 2 Similarly every cycle the bottom product gains the material given by trapezium ab'c'o - triangle aoc 1 K1T T T 1 KT1 T T K1T Kl = I ( "T" )(1 " Kj } - (D.12.) The average bottom concentration after the nth cycle is given by CB,n TKi K! ~t- - 1 +ir (1 - F >n (D-13-) o ^0 K2 APPENDIX E COMPUTER PROGRAMS 338 Appendix E Symbols used in Computer Program i) DATA CB = Brine Concentration (ppm) CD = Dialysate Concentration (ppm) VB = Volume of Brine product (c.c./cycle) VD = Volume of dialysate product (c.c./cycle) CF = Initial (Feed) Concentration (ppm) Numbers 1, 2, .... 9 stand for Exp. letters A, B, .... I. ii) RESULTS (A) This first part of the program computes: a) Separation factor NS = CB/CD b) Material balance and % error ERR % = ( ?PFp FF ) 100 where PP = BB + DD (Salt in product streams) BB = CB * VB (Salt in brine) DD = CD * VD (Salt in dialysate) FF = CF * (VB + VD) (Salt in feed) iii) RESULTS (B) This second part of the program computes the amount of salt shifted during separation, AS where AS = (CB - CF) * VB + (CF - CD) * VD 339 $r *watflv scards=exp 5=ml •EXECUTION BEGINS 2 3 1* 5 6 7 8 9 10 11 12 13 li» 15 16 17 18 19 20 21 22 23 21* 25 26 27 28 29 30 31 32 33 31* 35 36 37 15 6 60 26 36 $COMPILE DIMENSION X(12,5) ,BB(12),DD(12),PPC12),VF( 12),FFU2), 1ERRC12),CBF(12),CDFC12),BFC12),DF(12),ASC12) REAL MBC12),NS(12) N = 9 READ(5,15)((XCI,J),J-1,5>,I»1,N) FORMAT( 5F10.2) WRITE(6,6) FORMAT(IX,1DATA'//1X;12X,,C8,,9X,'VB,,8X,,CD'/ 18X,1VD',8X,1CF') DO 60 1=1,N WR!TECG,26)l,XCI,l>,XCl,2),XCI,3),X(l,l»),XCI,5) F0RMATC1X, I7,5F10.2) WRITEC6,36) F0RMATC//1X,'RESULTSCA)'/IX,'MATERIAL BALANCE & SEPARATION FACTOR' 1//1X/1!*X/,BB',11X/'DD,,11X/ 1'PP',11X, 'FF' , 10X, 'MB'^X, 'ERRS',7X, 'NS*) DO 80 1=1,N BBCI)=X(1,1)*X(I,2 ) DD( I ) =X ( I , 3 ) *X ( I , 1*) PP(I)=BB(I)+DD( I ) VF( I )=X( I , 2 ) +X ( I , 1*) FF(I)=VF(I)*X(I,5) MB(I)=PP(I )-FF( I ) ERR(I)=MB(I)*100.0/FF( I ) NS(I)=X(I,1)/X(I,3) CBF(l)=X(l/l)-X(l/5) CDF(I)=X(I,5)-X(I,3) BF(I)=CBF(I)*X(I,2) DF( I ) = CDF( I )*X( I ,i*> AS(I) = 8F(I ) + DF( I ) WRITE (6,1*6) I ,BB( I ),DD( I ),PP( I ),FF(I ),MB( I ),ERR( I ) , N S ( I ) FORMAT(IX, I7,I»F13.2,F11.2,2F10.3) WRITE(6,66) WRI TEC 6,86) DO 90 1=1,N WRI TEC 6,76)I,C3F(I),BFCI),CDF(I),DF(I),ASCI) FORMAT(//IX,'RESULTS(B)'/IX,'AMOUNT OF SEPARATION1) FORMATC//IX,13X,1CB-CF',7X,'BF1,10X,'CF-CD',8X,»DF1,12X,'AS') FORMAT C 1X,I7,I»F12.2,F11*.2) STO? END 80 1*5 90 66 86 '76 2 3 i« 5 6 7 8 9 10 il 12 13 11* 15 16 17 18 19 20 21 22 23 21* 25 26 27 28 29 30 31 32 33 31* 35 36 37 38 39 1*0 1*1 1*2 CO •p-o $DATA DATA GROUP Ml C3 VB cn VD CF 1 U 000 .00 25.37 196.00 21*.17 2160.00 2 U 07 5 .00 25 .52 11*8.00 21* .1*8 2160.00 3 3875 .00 25 .87 330.00 21*. 13 2160.00 i* 1(125 .00 214.67" 11*0.00 21*. 50 2170.00 5 1*250 .00 25.00 118.00 25.00 2170.00 6 1*350 .00 21*.57 91*. 00 25*7} 2170.00 7 3825 .00 25.79 1*10.00 21*.21 2170.00 8 3675 .00 25 .88 570.00 21*.13 2170.00 9 3375 .00 2S.U5 81*0.00 21*.66 2170.00 RESULTS(A) MATERIAL 8ALANCE & SEPARATION FACTOR BB 1011*79.90 103991*.00 10021(5.10 101763.60 106250.00 106879.50 986U6.69 95109.00 85893.69 DD 1*737.32 3623 . 01* 7962.90 31*30.00 2950.00 21*16.71* 9926.10 13751*.10 20711*.1*0 PP 106217.20 107617.00 103209.00 105193.60 109200.00 109296.10 108572.70 108863.00 106608.00 FF 107006.30 108000.00 108000.00 106698.80 108500.00 109107.60 108500.00 108521.60 108738.60 MB -789.13 -3C3.00 209.06 -1505.19 700.00 188.56 72.75 31*1.38 -2130.63 ERR% •0.737 -0.355 0.194 •1.1*11 0.645 0.173 0.067 0.315 •1.959 NS 20.1*03 27 .531* 11.71*2 29.1*61* 36.017 1*6.277 9.329 6.1*1*7 I*.018 RESULTS(8) AMOUNT OF SEPARATION CB- CF BF CF- CD DF 1 181*0 .00 1*6680 .79 1961* .00 1*71*69. 88 2 1915 .00 438 70 .80 2012 .00 1*9253 . 75 3 1715 .00 1*1*367 .01* 1830 .00 1*1*157. 91 I* 1955 .00 1+8229 .81* 203 0 .00 1*9735 . 00 5 2080 .00 52000 .00 2052 .00 51300. 00 6 2180 .00 53562 .61 2076 .00 53373. 97 7 1655 .00 1*2682 .1*1* 1760 .00 1*2609. 61 8 1505 .00 3891*9 .1*1 1600 .00 38608. 01 9 1205 .00 30667 .25 1330 .00 32797. 80 AS 91*150.63 98121*.50 88521*.91* 97961*.81 103300.00 106936.50 85292.00 77557.38 631*65.05 CORE USAGE OBJECT CODE" 2608 BYTES,ARRAY AREA" 861* BYTES,TOTAL AREA AVAILABLE- 1021*00 BYTES DIAGNOSTICS NUMBER OF ERRORS" 0, NUMBER OF WARNINGS" 0, NUMBER OF EXTENSIONS- 0 COMPILE TIME" 0.15 .SEC,EXECUTION TIME" 0.15 SEC, WATFIV - JUL 1973 V1L4 16:45:00 FRIDAY 21 NOV 75 $STOP #EXECUTION TERMINATED # •*> *-> $r *watfiv scards-exp 5-m4 par-nollst •EXECUTION BEGINS $COMPILE $DATA DATA CB VB CD VD 1 3900.00 101.11 267.00 99.83 2 4000.00 98 .85 192.00 96.75 3 3675.00 99.09 575.00 98 .86 4 4025.00 101.17 180.00 98.25 5 4125.00 98 .88 145.00 96.25 6 4200.00 99.35 125.00 98.15 7 3625.00 100.00 640.00 101.18 8 3300.00 93.17 1100.00 100.00 9 2880.00 98.44 1440.00 99.88 RESULTS(A) MATERIAL 8ALANCE & SEPARATION FACTOR BB no PP 1 394329. 00 26654 .61 420983 .50 2 395400. 00 18576 .00 413976 .00 3 364155. 60 56344 .50 421000 .10 4 407209. 10 17685 .00 424894 .10 5 407880. 00 13956 .25 421836 .20 6 417270. 00 12268 .75 429533 .60 7 362500. 00 64755 .20 427255 .10 8 323960. 90 110000 .00 433960 .90 9 283507. 10 143827 .10 427334 .30 CF 2100.00 2100.00 2100.00 2160.00 2160.00 2160.00 2140.00 2140.00 2140.00 FF MB ERR% NS 421974 .00 -990 .44 -0.235 14.607 410760 .00 3216 .00 0.783 20.833 415694 .90 5305 .25 1.276 6.391 430747 .10 -5853 .00 -1.359 22.361 421480 .70 355 .50 0.084 28 . 448 426600 .00 2938 .69 0.689 33.600 430525 .10- -3269.94 -0.760 5.664 424083 .70 9877 .19 2.329 3.000 424404.80 2929 .56 0.690 2.000 RESULTS(B} AMOUNT OF SEPARATION CORE USAGE AS 364986.30 372414.OC 306828.10 383217.00 383242.90 402409.10 300269.90 217877.10 142761.50 03JECT COOE= 2608 BYTES,ARRAY ARF.A= 864 BYTES,TOTAL AREA AVAILABLE" 102400 NVM'JER OF ERRORS" 0, nUMSER OF WARNINGS* 0, TJM3ER OF EXTENSIONS-CB-CF 3F CF-cn OF 1 1800 .00 181998 .00 1833 . 00 13 2 9 3 8 .30 2 1900 .00 1S7815 .00 1908 . 00 184599 .00 3 1575 .00 156066 .60 1525 . 00 150761 .50 4 1865 .CO 133632 . 00 1980. 00 194535 .00 5 1SG5 .0 0 194299 .10 2015 . 0 0 193943 .70 6 2 04 0 .00 202674 .00 2035 . 00 199735 .10 7 14SS .00 143500 . oo 1500. 00 151769 .90 8 1160 .00 113S77 .10 1040. 00 104000 .00 9 740 .00 72845 .56 700. 00 69916 .00 jr *watflv scards-exp 5*m5 par-nollst •EXECUTION BEGINS DATA $C0MPILE $DATA CB VB 1 1080.00 2U.20 2 1120.00 2«*. 11* 3 1050.00 2U .38 it 1090.00 24.25 5 11U0.0O 23.8lt C 1160.00 2U.13 7 1010.00 25.3U 8 1000.00 25.07 9 960.00 25.62 CD VD CF 21.10 25 .39 5U0.00 17.10 25.31) 51)0.00 26.30 25.30 51)0.00 19.70 25.25 560.00 15.70 25 .65 560.00 11). 90 25.95 560.00 1)0.00 25.11 530.00 53.00 21).78 530.00 90.00 21).81) 530.00 RESULTSCA) MATERIAL BALANCE ti SEPARATION FACTOR BB DD PP FF MB ERR* NS 1 26136. ,00 535. ,73 26671.72 26778.60 -106. ,88 -0.399 51.185 2 27035, .80 i»i)l. ,86 271)78 . 66 . 26989.20 1)89, .1.6 1.811) 65 .1)97 3 25599, ,00 665. ,39 26251).39 26827.20 -5 62. .81 -2.098 39.921) ii 26U32, .50 U97. ,1)2 2G929.92 27720.00 -790, .08 -2.850 55.330 5 27177, .59 1*02, .35 27580.U5 27720.00 -139, .55 -0.503 72.611 6 27990, .80 386, ,65 28377.U6 28 0i)U.80 332, .66 1.136 77 . 352 7 25533, .39 1001). .1)0 ' • 26597 .79 26738.50 -mo, .70 -0.526 25.250 o 25070, .00 1313, ,31) 26383.31) 261)20.50 -37 , .16 -0.1U1 13.868 9 21)595, .20 2235, .60 26830.79 2671)3 .79 87, .00 0.325 10.667 RESULTSCB) AMOUNT OF SEPARATION CB-CF BF CF-CD DF AS 1 51)0.00 13068 .00 518.90 13171). 87 2521)2 .86 2 580.00 H001 .20 522.90 13511.73 27512.93 3 510.00 121)33 .80 513.70 12996.61 251)30.1)1 1* 530.00 12852 .50 5i)C30 1361)2.57 261*95 . 07 5 580.00 13827 .20 51)1).30 13966.73 27793.93 6 600.00 11)1*78 .00 51)5.10 11)11)5.31) 28523.3U 7 1*80.00 12163 .20 U9O.00 12303.90 21)1)67.09 8 1*70.00 11782 .90 1)77.00 11320.06 23602.95 9 1*30.00 11016 .60 1*1)0.00 10929.60 2131)6.20 USAGE OBJECT ' CODE1 2608 BYTES, ARRAY AREA* 861* 8YTES DIAGNOSTICS COMPILE TIME-NUMBER OF ERRORS" 0.03 SEC,EXECUTION TIME" 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS-0.15 SEC, WATFIV - JUL 1973 V1LU. 16:11:U5 FRIDAY 21 NOV 75 CO CO tr *watfiv scards-exp 5-m7 par-nollst #EXECUTION BEGINS $C0MPILE $DATA DATA CB VB 1 1050.00 51. 82 2 1090.00 50. 17 3 1030.00 51. 91 U 1070.00• 50. 09 5 1100.00 50. 77 6 1110.00 50. 50 7 1010.00 50. 25 8 990 . 00 50. 94 9 950.00 50. 77 CD VD CF 26.30 49. 24 550. 00 20.20 51. 50 550. 00 33.00 49. 03 550. 00 24.20 51. 00 550. 00 18.10 51. 49 550. 00 17.60 51. 57 55 0. 00 UU.OO 51. 25 530. 00 61.00 49. 5C 530. 00 104.00 U9. 67 530. 00 RESULTS(A) MATERIAL BALANCE & SEPARATION FACTOR BB DD PP 1 5UU11 .00 1295.01 55706 .02 2 34G35 .30 10U0.30 55725 .59 3 53U67 .30 1617.99 55085 .29 U 53596 .29 123U.20 5U830 .U9 5 55 8 U7 .00 931.97 56778 .97 6 56055 .00 907.63 56962 .63 7 50752 .50 2255.00 53007 .50 8 50430 .60 3019.50 53450 .10 9 U8231 .50 5165.68 53397 .18 FF MB ERRS NS S55S3. ,00 123.01 0.221 39.92U 55918, ,50 -192.90 -0.345 53.960 55517. ,00 -431.71 -0.778 31.212 555 99, .50' -769.00 -1.383 4U.215 56243, ,00 535.97 0.953 GO* 71 56138. .50 82U.13 1.46S 63.068 53795, .00 -737.50 -1.U6U 22.955 53233, .20 216.90 0.U07 16.230 53233, .20 163.98 0.308 9.135 RESULTS(B) AMOUNT OF SEPARATION CB-CF BF CF-CO DF AS 1 500.00 25910.00 5 23 J TJ 25736. ,99 51596.99 2 540.00 27091.80 529.80 27284, ,69 54376.48 3 U80.00 24916.80 517.00 25348. ,51 50265.31 U 520.00 26045.80 525.80 - 26315. .79 52362.59 5 550.00 27923.50 531.90 27387. .53 53311.03 6 560.00 28280.00 532.40 27U55, ,86 55735 . 86 7 480.00 24120.00 480.00 24907, .50 U9027.50 8 460.00 23432.40 U63.00 23 215 .50 46647.90 9 420.00 21323.40 U26.00 21159 .42 42482.82 USAGE 03JECT CODE- 2608 3YTES, ARRAY AREA" ' 864 3YTES DIAGNOSTICS COMPILE TIM5 NUMBER OF ERRORS- 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 0.03 SEC,EXECUTION TIME- 0.15 SEC, WATFIV - JUL 1973 V1L4 16:16:11 FRIDAY 21 NOV 75 $r *watfiv scards"exp'5»m8 par-nollst 'EXECUTION BEGINS DATA JCOMPILE $OATA CB V8 1 1020.00 99. 72 2 1050.00 99. 09 3 1010.00 99. U5 (* 1030.00 98. 50 5 1070.00 97. 32 6 -1080.00 97. 69 7 1000.00 98. 73 8 970.00 98. 15 9 890.00 97. 65 cn vn CF 36.00 98.12 5U0. 00 26.00 98.18 540. 00 1*8.00 98.79 540. 00 32.00 99.65 SUO. 00 23.00 99.92 5tt0. 00 2^.30 99.82 51)0. 00 55.00 98.55 520. 00 80.00 98.50 520 . 00 139.00 99.15 5 20. 00 RESULTS(A) MATERIAL BALANCE ft SEPARATION FACTOR BB DD PP FF K3 ERR? NS 1 10171'*.30 3532. 32 10521*6.60 106833 .50 -1586 .88 -1. .1*35 28.333 2 10UOUU.UO 2552. 68 106597. .00 1065 25 j TJ 71 .31 0. .067 1*0.385 3 1001*!* I*.1*0 1*71*1. 92 105186 .3C 10701*9 .50 -1853 .25 -1. .71*1 21.01*2 k 1C11*55 .00 3188. 80 101*61*3 .70 107000 .90 -2357 .19 -2, ,203 32.188 5 101*132.30 2298 . 16 1061*30 .50 105509 .50 -79 .06 -0, .071* 1*6.522 6 105505.10 2325 . 81 107830 .90 106655 .30 1175 .56 • 1, ,102 itS.SiO 7 98729.9U 51*20. 25 10U150 .10 102585 .50 1561* .63 1, .525 • 18.182 8 95205 .1*1* 7880. 00 103085 .1*0 102257 .90 827 .50 0, .809 12.125 9 86908 .1*1* 13781. 85 100690 .20 102335 .90 -161*5 .69 -1, .608 6.403 RESULTS(B) OF SEPARATION C3-CF BF 1 1*80.00 1*7865 . 60 2 510.00 50535 .89 3 U7O.00 1*671*1.50 i» 1*90.00 1*8265 . 00 5 530.00 51579.60 C 51*0.00 52752.60 7 1*80.00 1*7390. 39 8 1*50.00 1*1*167.50 9 370.00 36130.50 CF-CD DF AS 501* .00 1*91*52.1*8 97318 .06 5]l* .00 501*61*. 52 101000 .30 1*92 .00 l*850i*.68 9531*5 .13 503 .00 50622.20 98887 .19 517 .00 51658 . 61* 10323S .10 515 .70 51576.99 101*329 .50 1*65 .00 1*5825 .75 93215 .13 1*1*0 .00 1*331*0.00 87507 .1*1* 381 .00 37776. 11* 73906 .63 CORE USAGE OBJECT CODE- 2608 BYTES,ARRAY AREA- " 86U BYTES,TOTAL AREA AVAILABLE- 102U0O BYTES DIAGNOSTICS ' NUMBER OF ERRORS- 0, NUMBER OF WARMINGS- 0, NUMBER OF EXTENSIONS- 0 COMPILE TIME- 0.03 SEC,EXECUTION TIME- 0.15 SEC, WATFIV - JUL 1973 V1L1* 16:20:1.5 FRIDAY 21 NOV 75 .*>-Ln tr *watf!v scards-exp 5-m9 par«noltst #EXECUTION BEGINS $COMPILE JDATA DATA C3 1 7150. ,00 2 7450. ,00 3 6800. ,00 it 7600. .00 5 8100, .00 S 3150, .00 7 6625 .00 8 6375 .00 9 5825 .00 VB CD 26.28 810.00 26.00 565.00 26.34 1310.00 26.50 450.00 25.17 288.00 26.78 218.00 25.37 1700.00 25.09 2240.00 25.39 2650.00 VD CF 25.47 4050.00 25 .00 1(050. 00 25 .29 405 0:00 25.82 4100.00 26.48 4100.00 26.85 4100.00 26.65 4175.00 26.86 " 4175.00 25.84 4175.00 RESULTS(A) MATERIAL BALANCE S SEPARATION FACTOR 1 2 3 4 5 6 7 8 9 BB 187301.90 193700.00 173111.30 201"(00.00 203876.90 218256.30 171388.60 159948.60 11(7896 .60 DD 20630.70 14125.00 33129.33 11619.00 7626.24 5853.30 45304.99 60166.40 63475.94 PP 208532.60 207825.00 212241.80 213019.00 211503.10 224110.10 216693.60 220115.00 216372.60 FF 209587.50 206550.00 200101.40 214512.00 211764.90 219883.00 219270.90 2168 91 .1 0 213835.10 MS -1054.88 1275.00 3140.38 -1493.00 -261.31 4227 .19 -2577.31 3223.88 2487.44 ERR* -0.503 0.617 1.502 -0.696 -0.124 1.922 -1.175 1.486 1.163 NS 8.827 13.136 5.191 16.889 23.125 37 3 2 2 .385 897 ,346 .198 RESULTS(B) AMOUNT OF SEPARATION 1 2 3 4 5 6 7 8 9 CB-CF BF CF-CD 3100. 00 81467.94 3240. 00 3400. 00 88400.00 3485. .00 2750. ,00 72434.94 2740. .00 3500. ,00 92750.00 3650. .00 4000, ,00 100679.90 3812, ,00 4050, .00 108458.90 3332, .00 2450, .00 63331.48 2475 .00 2200 .00 55197.99 1935 .00 1650 .00 41893.50 1525 .00 DF 825 22 j 5 87125 .00 69234.56 94243.00 100941.60 104231.60 65958.69 51974.10 39405 .99 AS 163930.60 175525.00 141723.50. 136393.00 201621.60 212630.60 123340.10 107172.00 81299.44 CORE USAGE OBJECT CODE- 2608 8YTES,ARRAY AREA" 864 BYTES,TOTAL AREA AVAILABLE" 102400 DIAGNOSTICS NUMBER OF ERRORS- 0. NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 COMPILE TIME- 0.03 SEC,EXECUTI ON TIME- 0.15 SEC, WATFIV - JUL 1973 V1L4 16: 25 :07 FRIDAY 21 NOV 75 ON Jr *watflv scards»exp' #EXECUTION BEGINS 5=mll par»nollst JCOMPILE $DATA DATA C8 VB CD VD CF 1 7 050. 00 51.23 91*0. 00 1*8.81* 1*100. 00 2 7375 . 00 51.39 625 . 00 1*9.61 1*100. 00 3 6775. 00 51.20 1£*70. 00 1*9.93 1*100. 00 It 7500. 00 51.86 1*90. 00 !*9.1l* 1*175. 00 5 8 075. 00 50.15 310. 00 50.15 1*175. 00 6 8125. 00 1*9.21 259 . 00 50.86 1*175. 00 7 6IJ50. 00 50.11* 2010. 00 50.61* 1*200. 00 8 5975 . 00 1*9.70 21*90. 00 50.97 1*200. 00 9 5300. 00 1*9.52 3125. 00 50.85 1*200. 00 RESULTS(A) MATERIAL BALANCE & SEPARATION FACTOR B3 DD PP 1 361171.1*0 1*5909. ,59 1*07031. .00 2 379001, ,10 31005, .25 1*10007. ,1*0 3 31*6879, ,90 73397, .06 1*20277. .00 i» 388 950, .00 21*078 , .60 U1302S. .50 5 1*01*961, .10 1551*6, .50 1*20507, .60 6 399331, .20 12155, .51* 1*11935, .70 7 3231*02, .90 101786, .30 1*25189. ,30 8 295957, .1*0 126915.20 1*23872, .60 9 2621*56, .00 158906.20 1*21362, .20 RESULTS(B) AMOUNT OF SEPARATION FF MB ERR? NS 1*10286.90 -3205 .94 -0,721 7.500 1*11*100.00 -1*092 .56 -0.988 11.800 1*11*632.90 561*1* .06 1.361 i*.G09 1*21575 .00 -85l<6 .1*1* -2.050 15.306 413752 .<»0 1755 .19 0.1*19 26.01*8 1*17792 .20 -5805 .50 -1.390 33.996 1*23275 .90 1913 .38 0.1*52 3.209 1*22813 .90 . 1058 j 3 0.250 2.1*00 1*21551*.00 -191 .75 -0.01*5 1.696 CB-CF BF CF-CO OF AS 1 2950, .00 151128 .1*0 3160, .00 151*331* .30 3051*62 .80 2 3275, .00 163302 .10 31*75. .00 172391* .70 31*0696 .90 3 2675 .00 136959 .90 2630.00 131315 .80 268275 .80 (* 3325 .00 1721*31* .50 3685, .00 181080 .80 353515 .30 5 3900 .00 195581* .90 3865 .00 193329 .60 3891*11* .60 6 3950 .00 191*379.5 0 3936 .00 200181* .90 391*561* .1*0 7 2250 .00 1128H* .90 2190 .00 110901 .50 223716 .50 8 1775 .00 88217 .1*1* 1710 .00 87158 .69 175376 .10 9 1100.00 51*1*72 .00 1075 .00 51*663 j 3 109135 ; TJ CORE USAGE OBJECT CODE- 2608 BYTES,ARRAY AREA- 86U BYTES,TOTAL AREA AVAILABLE- 1021*00 3YTES DIAGNOSTICS COMPILE TIME-NUMBER OF ERRORS- 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 0.03 SEC,EXECUTION TIME- 0.15 SEC, WATFIV - JUL 1973 V1LU 16:29:27 FRIDAY 21 NOV 75 Co %r *watfiv scards-exp'5»ml2 par-nollst IEXECUTION BEGINS SCOMPILE SDATA DATA C3 1 6900 . 00 2 7250. ,00 3 665 0. ,00 4 7400. ,00 5 7925. .00 6 8100, .00 7 6400 .00 8 5600 .00 9 5000 .00 V3 CD 101.33 1190.00 93.75 725.00 99.15 1670.00 101.75 590.00 99.11 350.00 99.25 283.00 99.11 2210.00 99 .1.1 2800.00 93.18 3575.00 VD Cr 101.50 4050.00 33.50 4050.00 101.75 4050.00 39.15 4125.00 99.11 4125.00 100.81 4125.00 101.58 4200.00 101.31 4200.00 101.73 4200.00 MATERULABALANCE S SEPARATION FACTOR 1 2 3 4 5 6 7 8 9 8B 699177.00 723187.50 659347.40 752950.00 785446.70 803925 . 634304. 556696.00 495899.90 .00 .00 DO 120785.00 72137.50 169922.50 53498.50 34633.50 23529.23 224491.70 235348.00 363684.60 PR 819962.00 795325.00 829269.03 811448.40 820135.20 832454.10 85S795 .70 842044.00 859584.60 FF 821451.50 806962.50 813644.90 823712.40 8 17 657 .5 0 825247.40 842893.00 845544.00 843821.30 MB -1439.50 -11637.50 15625.00 -17264.SO 2477.75 7206.75 15337.75 -3500.00 15762.69 ERRS -0.183 -1.442 1.920 -2.033 0.303 0.S73 1.8S5 -0.414 1.868 NS 5.798 10.000 3.982 12.542 22 .643 28 .622 .S95 ,000 ,399 RESUITS(S) AMOUNT OF SEPARATION 1 2 3 4 5 6 7 8 9 C3-CF 2850.00 3200.00 2600.00 3275 . 00 3800.00 3975 . 00 2200.00 1400.00 800.00 BF 288790.50 319200.00 257789.90 335231.20 376618.00 394518.70 218042.00 139174.00 79343.94 CF-CO 2860.00 3325.00 2380.00 3535.00 3775.00 3842 . 00 1990.00 1400.00 625.00 DF 290290.00 330837.50 242165.00 350495.10 374140.20 387312.00 202144.10 142674.00 63581.25 AS 579080.50 650037 .50 499954.90 683726.40 750758.20 781830.70 4201S6.10 28184S.00 142925.10 CORE USAGE OBJECT CODE- 2608 BYTES,ARRAY AREA- 864 BYTES,TOTAL AREA 102400 BYTES D.AGNOSTICS NUMBER OF ERRORS- 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 COVP.LE T.Mr- 0.03 SEC,EXECUTI ON TI ME- 0.15 SEC, WATF.V - JUL 1973 V1L4 16:33:51 FRIDAY 21 NOV 75 OJ •O-00 —$ i—*w atf! v-s card s - co rt-5 •- r-1-#EXECUTION BEGINS $C0MPILE -1 — UMrMLt DIMENSION X(12/4)/BB(12)vDD(12),PP(12)/VF(12)/FF(12->v-1ERR(12),CBF(12),CDF(12),BF(12),DF(12),AS(12) 2 REAL MB(12),NSU2) —3 N»9 4 READ(5,5)CF 5 5 FORMAKF10.2) _5 READ(5,15)((X(l>-J)>J»l>l»)/ -l-l-,N> 7 15 FORMAT(4F10.2) 8 WRITE(6,6) -9 6—FORMAKIX/' DATA V71X>-12Xv-'CB ^^X>—VB-V8X^—C^'— 18X,'VD') 10 DO 60 1=1,N 11 60- WRITE(6,26)I,X(I,1),X(I,2)>X(I>3),X(l>4) 12 26 FORMAT (IX, I 7,4F10.2) 13 WRITE(6,36) -lit 36—FORM AT ( //1X> 1 RESULTS (A) /lXv—MAT-ER-l AL--BALANCE—&—SE-PARAT-4-ON—F-AGTOR 1//1X,14X,'BB',11X,'DD'^IX, 1'PPMIX, 'FF',10X, 'MB'^X/ERRS'^X/NS') 15 DO 80 1 = 1,N 16 BBO)=X(I,1)»X(I,2) 17 DD(I)=XCI,3)*X(I,4) -18 PP( I )°BB( I )+DD( I) 19 VF(I)=X(I,2)+X(I,4) 20 FF(I)=VF(I)*CF 21 MB( I ) = PP( I )-FF( I ) 22 ERR(I)=MB(I)*100.0/FF(I) 23 NS(I)=X(I,1)/X(I,3) -24 CBF( I )=X( l,l)-CF 25 CDF(I) = CF-X( I ,3) 26 BF(I)=CBF(I)*X(1,2) 27 DF( !)=CDF( I )*X( 1,4) 28 AS(I) = RF(I)+DF( I )  ASlI)  BF(IJ+DFlI ; 29 80 WRITE(6,46)I,BB(I),DD(I),PP(I),FF(I),MB(I),ERR(I),NS(I) -30 4 6—FORMATC 1X> I 7> 4F13 . 2, Fll. 2 , 2F10.3 ) 31 WRITE(6,66) 32 WR!TE(6,86.33 DO 90 l=l,N - - — 34 90 WRITE(6,76)I,CBF(I),BF(I),CDF(I),DF(I),AS(I) 35 66 FORMAT(//lX,'RESULTS(B)'/IX,'AMOUNT OF SEPARATION') -36 8 6--FORMAT(//lX>13X,J CB-CF',-7X^ 37 76 FORMATCIX,I7,4F12.2,F14.2) 38 STOP 39 END $DATA CS VB CD VD -1 3560.-00 18-.80 40 0.00 19.83-2 3770.00 18.19 290.00 19.80 3 3310.00 17.90 580.00 18.30 ~~k~ 341 Or 0 0 17-. 9 4 4 5 5vO 0 18 -.--11 -5 3900.00 17.20 280.00 19.80 6 4025.00 17.73 195.00 19.86 7 3300.00 17.55 735.00 18.16 8 3010.00 18.10 820.00 18.20 9 2795.00 18.00 1020.00 18.15 RESULTS(A) MATERIAL BALANCE ft SEPARATION FACTOR 2 3 ...»+_.. 5 6 -7— 8 •9 BB -66928.-00-68576.25 59248.98 -61175.41-67079.94 71363.19 -57915.01-54481.02 50310.00 DD 7932.00-5742.00 10614.00 8240.05 5544.00 3872.70 13347.50-14924.00 18492.60 PP -74860.00 74318.25 69862.94 -69415 .44 — 72623.94 75235.88 -7126 2.-5 6— 69405.00 68802.56 FF -75328-r50-74080.50 70589.94 -70297.50-72150.00 73300.44 -69634.5 0-70785.00 70453.50 M3 4 68r50-237.75 • -727.00 -•—88 2.06-473.94 1935.44 —162 8.0 6--1380.00 -1650.94 ERR? -0.622-0.321 •1.030 -1.255 -0.657 2.640 -2.-338 -1.950 -2.343 NS —S-r900-13.000 5.707 -7.495 13.929 20.641 —4v490-3.671 2.740 RESULTS(B) -AMOUNT—OF—SEPARATION--CB-CF— 1610.00 1820.00 -1360.0 0 -1460.00 1950.00 2075.00 1350.00 1060.00 845.00-— BF -30268 33105 -24343 26192 33539 36789 23692 19186 -15210 ,00 ,80 ,99-.40 .99 .74 .50 .00 ,00--CF-CD — 1550.00 1660.00 -1370.00-1495.00 1670.00 -1755 .00 1215.00 1130.00 — 930.00--DF-30736.50 32868.00 -2 5071-. 00-27074.45 33066.00 -34854.30 22064.40 20566.00 -16860.90--—- AS 61004.50 65973.75 -49414.99-53266.85 66605.94 71644.00-45756.91 39752.00 -32070.90-CORE USAGE DIAGNOSTICS -COMP1LE-TIME* OBJECT CODE= 2600 BYTES,ARRAY AREA- 816 BYTES,TOTAL AREA^AVAILABLE- 102400 BYTES  NUMBER OF ERRORS" 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS" 0 —0-.18-SEC, EXECUTION -TIME--: 0.13-SEC—-WATFIV — VERS ION-1 LEVE L:-3 MARCH—1971 DATE"—07-30-74-$STOP -•EXECUTION TERMINATED # CO O DATA $COMPILE 4 DATA CB __ _VB CD VD 1 3200.00 47.38 61*0.00 1*8.30 2 3it60.00 i»7.t*l 480.00 48.62 3 2850.00 4 7.88 990.00 1*8.25-U 3180. 00 1*7.15 830.00 1*9.85 5 3500.00 1*7.31* 1*50.00 1*9. 69 -6 37 20.00 1*6.-1*6 310.00 i»9;83-7 2780. 00 1*7. 11* 1130.00 1*8. 33 8 2615.00 l»7.6t* 1290.00 i*8.H» -9—2370. 00 1*6.51* —155 0,00 — 1*8.08 RESULTS(A) MATERIAL BALANCE h SEPARATION FACTOR BB 1 2 -3-U 5 -6 7 8 -9-151616.00 161*038.50 -1361*58.00- — 11*9936.90 165689.90 172831.10 — 13101*9.10 121*578 .50 -110299 .70— — DD 30912.00 23337.60 -1*7767.50-1*1375 .50 22360.50 -151*1*7.30 51*612.90 62100.60 -71+52U .00 pp -182528. 187376. -181*225; 191312, 188050, -188278, 185662, 186679. -181*823, FF- -MB 00 10 50-t»0 1*0 1*0-00 10 70-186576.00 187258. 1*0 -1871*53.50-189150.00 189208 .1*0 187765.50 186165.50 186770.90 -181*508 ;90--1*01*8.00 117.69 —322 8.00-2162.t»i* -1158.00 -512.91* -501*.Ui* -91.81 — 311*. 81-—ERR%— -2.170 0.063 — 1.722-1.11*3 -0.612 - 0.273--0.271 -0.01*9 -0.171-—NS 5.000 7.208 -2T879-831 778 -12.000 1*60 027 529-RESULTSCB)-AMOUNT OF SEPARATION CB-CF 1250.00 1510.00 900.00 1230.00 -15 5 0 1770 00-00 830.00 665.00 1*20.00 BF 59225, -71589. 1*3092. 57991*, -7 33 76, 82231*. 39126, -31680, 1951*6, 00 0r. -00 1*9 9i*-19 20 60-80 CF-CD 1310.00 -11*70.00-960.00 1120.00 -1500.00-161*0.00 820.00 - 660.00 1*00.00 DF 63273.00 •711*71.38-1*6320.00 55832.00 -71*535 .00-81721.19 39630.60 31772.UO 19232.00 AS 1221*98.00 -11*3060.1*0-891*12.00 113826.1*0 -11*7911.90-163955.30 78755.75 — 631*53.00 38778.80 —CORE-USAGE OBJECT-CODE- 2600- BYTES,-ARRAY AREA- 816 BYTES,-TOTAt—AREA~A-VA-|-tABtE-—102!r00—BYTES DIAGNOSTICS NUMBER OF ERRORS'- 0, NUMBER OF WARN INGS= 0, NUMBER OF EXTENSIONS* 0 COMPILE TIME- 0.03 SEC,EXECUT1 ON TIME- 0.12 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 DATE- 07-30-7U u> $STOP • #EXECUTION TERMINATED $ COM PI LE DATA -$DATA--CB-1 3050. 00 2 3270. 00 -3— 2580. 00 i» 2910. 00 5 3500. 00 -6 -3615. 00 7 2620. 00 8 2500. 00 9 2400. 00 V3 96.20 96.54 —96.23-96.94 97.83 — 97.89-97.22 97.15 -96.88 CD 1115.00 870.00 -1545.00-1190.00 790.00 -515.00-1465.00 1590.00 -1725.00 —VD 98.90 98.75 -97.87 97.11 98.10 -98.21-98.50 98.43 98.13 -RESULTS (A) MATERIAL BALANCE & SEPARATION FACTOR BB -1 293409. 2 315685. -3 2482 73-. 282095. 322839, - 353872 254716 242874 —232512 DD 90 110273 70 85912 -30 151209 30 115560 00 30 — 30 90 00— 77499 -50578 144302 156503 -169274 PP ,40 403683.30 ,50 401598.20 r-10 399482:50-,80 397656.20 ,00 400338.00 ,15 404450.40 ,50 399018.80 ,60 399378.60 r20 401786v20-FF-400930.40 401320.80 -3S8875-.40-398772.70 402636.10 402935.50-402204.50 401916.80 -400745.-50-MB 2752.94 277.38 6 07.06--1116.50 -2298.13 -- 1464.94 -3185.69 -2538.19 — 1040.-69-—ERR%— 0.687 0.069 —0:15 2--0.280 -0.571 -0.364 -0.792 -0.632 —0.260--NS 2.735 3.759 -1.67 0-2.445 4.177 .019 ,788 .572 .391-RESULTS(B) -AMOUNT OF SEPARATION CB-CF 995.00 -1215.00-525.00 855.00 -1245.00-1560.00 565.00 - 445.00 345.00 BF 95718.94 -117296 00-50520.75 82383.69 -12 17 98". 3 0-152708.30 54929.30 - 43231.75 33423.60 CORE-USAGE DIAGNOSTICS COMPILE TIME= OBJECT-CODE=-CF-CD 940.00 1185 .00-510.00 865.00 -12'55.00 1540.00 590.00 -465.00 330.00 DF 92965.94 — 117018.70 49913.70 84000.13 —124096.50-151243.30 58115.00 --45769.95 32382.90 AS 188684.80 -234314.80 — 100434.40 166883.80 -245894.80 — 303951.70 113044.20 - 89001.69 -65806.50 -2600- BYTESyARRAY-AREA= -816 - BYTES7TOTAL-—AREA—AVAItAB LE"=—102400—BYTES-NUMBER OF ERRORS* 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 0.03 SEC,EXECUTION TIME- 0.13 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 DATE- 07-30-74 u> $STOP. •EXECUTION TERMINATED t $COMPf LE- •GKOUP K5 DATA-$DATA CB •1070:00-1110.00 1040.00 -1070.00-1125.00 1150.00 -• 970.00 940.00 850.00 VB 7.91-7.19 7.94 7-v75-15 14 97-95 94 CD —31.-5 0-24.00 41.00 —2 5-. 0 0 20.40 16.80 -95.00 123.00 214.00 VD 19.-14-19.38 19.11 19.8 0-19.79 19.82 —- 19.16-19.03 19.00 RESULTS(A) MATERIAL- BALANCE &-SEPARATION-FACTOR BB -19163; 19080. 18657, - 18992, 19293, 19711, -17430, 16873, 15249, 70-90 60 50-74 00 90-00 00 DD -60 2:91-465.12 783.51 -495.00-403.72 332.98 -18 20.20-2340.69 4066.00 PP -19766r61-19546.02 19441.11 19487.50-19697.46 20043.97 19251.10-19213.68 1931?.00 FF —19636v50-19382.10 19636.50 — 19901.50 19578.19 19588.80 —19678.90-19599.39 19578.20 MB -130.-11-163.92 •195.39 -414.00-119.27 455.17 •427.80 -385.71 -263.20 ERR? —0.663-0.846 -0.995 -2.080 0.609 2.324 -2rl74--1.968 -1.344 NS —33:968-46.250 25.366 - 42.800-55.147 68.452 —10.211-7.642 3.972 RESULTS(B) — AMOUNT-OF—SEPARATI ON -CB-CF— 540.00 580.00 -510.00 540.00 595.00 620.00 440.00 410.00 -320.00-—BF 9671.40 9970.20 —91I-1.40-9585.00 10204.25 10626.80 7906.80 7359.50 —5 74 0.80-CF-CD— 498.50 506.00 -489.00-505.00 509.60 513.20-435.00 407.00 -316.00-DF AS-9541.29 9806.28 —9344:79-9999.00 10084.98 10171.63 8334.60 7745.21 -6004.00-19212.69 19776.48 -18 494.19-19584.00 20289.22 20798.42 16241.40 15104.70 11744.80-CORE USAGE 03JECT CODE- 2600 BYTES,ARRAY AREA- 816 BYTES,TOTAL AREA AVAILABLE- 102400 BYTES DIAGNOSTICS NUMBER OF ERRORS- 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS- 0 -COMPILE TIME- 0:03-SEC;EXECUT ION "TIME- 0.-12-SEC;—WATFIV VERS I ON-!" LEVEL"-3 "MARCH 1971 DATE-—07-30-74-$STOP •EXECUTION TERMINATED Co Cn Co $C0MP1LE GROUP R7 •DATA -$DATA • CB VB CD ; VD 1 980.00 47.43 38 .00 ' 49.14 2 1020.00 46.15 30.00 48.30 -3 960.0 0 47.8 7 48.00 48.10-4 1016.00 46.17 40.00 49.63 5 1044.00 46.14 32.00 49.89 -6 1055 .00 46;-13 27.00 49.87-7 928.00 46.96 103.00 48.04 8 900.00 47.85 130.00 49.13 -9 796.00 47.89 2 21.00 48 .11-—RESUtTS (A) ——— MATERIAL BALANCE ft SEPARATION FACTOR - BB 46481. 47072. -45955; 46908. 48170. -48667. 43578. 43065. -38120. 39 99 20-71 16 15-88 00 44--DO — 1867. 1449. -2 308; 1985, 1596, -1346. 4948, 6386, 32 00 80-20 48 49 12 90 -10632.31-— pp 48348.71 48521.99 -482 63799 48393.91 49766.63 -50013.64 48527.00 49451.90 -48752.75 — FF 49250.70 48169.50 -48944770-48853.00 48975.30 -48960.00-48450.00 49459.80 -48960.00-—MB -901.99 352.50 --63 0.-71-35.91 791.34 -105 3.64-77.00 -7.90 -207.25-—ERR?— -1.831 0.732 -17-391-0.074 1.616 -2.152-0.159 -0.016 -0.423-— NS 25.789 34.000 -2 0.-000-25.400 32.625 -39.074-,010 ,923 -3.602-RESULTS(B) AMOUNT OF SEPARATION 8 9 CORE-tlSAGE" CB-CF 470.00 -510.00" 450.00 506.00 -534:00-545.00 418.00 -390.00 286.00 BF 22292.09 -23536. 50-21541.50 23362.02 -24638.76"-25140.85 19629.28 -18 661.50--13696.54 CF-CD 472.00 -480.00-462.00 470.00 "478.00 483.00 407.00 380.00 289.00 DF 23194.08 -2 318 4.00-22222.20 23326.10 -2 3847.42-24087.21 19552.27 " 18669.40 13903.79 AS 45486.17 46720.50" 43763.70 46688.12 -48486.18-49228.06 39131.55 37330.90 27600.33 OBJECT-CODE= —2&OO-BYTES7ARRAY AREA3 DIAGNOSTICS COMPILE TIME= NUMBER OF ERRORS-0.03 SEC,EXECUTION TIME" —816 BYTES7TOTAL—AREA-AVAttABtE"—102400—BYTES" 0, NUMBER OF WARNINGS" 0, NUMBER OF EXTENSIONS" 0 0.12 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 DATE" 07-30-74 $STOP •EXECUTION TERMINATED • $COMPILE $DATA DATA CB VB CD VD 1 935.00 96.94 66.00 97.14 2 950.00 96.72 57.00 97.80 -3 915.00 96.-16 103.00 97.84-4 920.00 97.80 76.00 98.28 5 948.00 96.30 57.00 96.87 -6 96 0.0 0 9 6.15 5 2:0 0 9 8v31~ 7 852.00 96.26 153.00 97.59 8 800.00 97.40 200.00 97.72 9— -706.0 0— 96.03 298.0 0 98 .17' RESULTS ("AO MATERIAL BALANCE & SEPARATION FACTOR BB— 90638. 91884. -8798 6. 89976. 91292. 92303. 82013. 77919. 67797. DO 88 00 -3 8-00 38 94" 50 94 -1-3-6411.24 5574.60 -10077.52-7469.28 5521.59 -5112.12 14931.27 19544.00 -29254.66-pp 97050.06 97458.56 -98 063r8 8-97445.25 96813.94 -97416.00-96944.75 97463.94 -97051.75--FF- -MB-97040.00 97260.00 -97000.-0C-98040.00 96584.94 -97229.94-96924.94 97559.94 -97099.94-10.06 198.56 -1063.8 8--594.75 229.00 - 186.06-19.81 -96.00 —-48.19-ERR%-0.010 0.204 -NS-097-607 237 ,191" ,020 ,098 14.167 16.667 —8~. 88 3-12.105 16.632 -18.462 569 000 '0.050- "2.369--RESULTS(B) AMOUNT OF SEPARATION CORE-USAGE-CB-CF 435.00 450.00 — 415.00 420.00 -448 .00 — 460.00 352.00 -300.00 — 206.00 BF 42168.90 -435 2 4.00 39906.40 41076.00 -43142-.40-44229.00 33883.52 29220.00-19782.18 CF-CD 434.00 443.00-397.00 424.00 -443.00-448.00 347.00 300.00 202.00 DF 42158.76 43325.-40-38842.48 41670.72 -42913.41-44042.88 33863.73 29316.00-19830.34 AS 84327.63 86849.38-78748.88 82746.69 -86055.75-88271.88 67747.19 58536.00 39612.52 OBJECTCODE= 2600 BYTES",i\RRAY AREA= 816" BYTES/TOTAL—AREA-AVAILABLE"—l-02Wt>—BYTES-DIAGNOSTICS NUMBER OF ERRORS" 0, NUMBER OF WARNINGS" 0, NUMBER OF EXTENSIONS" 0 COMPILE TIME" 0.03 SEC,EXECUTION TIME" 0.12 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 DATE- 07-30-74 $STOP •EXECUTION TERMINATED # $r »watftv scardsBcon 5ar9 par>»noltst •EXECUTION BEGINS $COMPILE $DATA DATA CB VB CD VD . I 4900.00 17.73 21*75.00 19.18 2 51*00.00 17 ".SO- 2020.00 19.20 3 51*20.00 lS. 61 1750.00 18.72 k 6150.00 18.13 1350.00 18.96 RESULTS(A) "MATER I AL~"B ALAN CE ' &~SEPARAT I ON'FACTOR' BB ~ 86876T9T 96120.00 100866.10 -1111*99.50-DD -i»7t*7 o-i* r 38783.99 32760.00 25596.01" PP "1:31*31*7730-131*903. ZO 133626.10 "137095.50" FF -1-35U59T61T 135790.00 137001.00 "136120.30-MB -1T12T25--886.06 -3371*.88 - 975.19-ERR* ^07821--0.653 -2.1*63 0.716" NS -1T980-2.673 3.097 -U.556-"RESULTStBT AMOUNT OF SEPARATION CB-CF BF CF-CD DF AS 1 1230.00 21807.39 1195.00 22920.09 1*1*727.98 2 173070 0 30791*70 0 r6 5 0T0 0 316 797^ 9 621* 71* 70 0 3 1750.00 32567.50 1920.00 3591*2.1*0 68509.88 1* 21*80.00 1*1*962.1*1 2320.00 1*3987.21 8891*9.63 CORE USAGE OBJECT CODE= 2592 BYTES,ARRAY AREA" 816 BYTES,TOTAL AREA AVAILABLE- 1021*00 BYTES TjrAGNOSTTCS NUMBERS TERRORS- 07-NUMBER-OF-WARNTNGS- Or-NUMBER—OF-EXTENSIONS3 0~ COMPILE TIME- 0.03 SEC,EXECUTION TIME- 0.08 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 DATE- 07-30-71* $STOP # EXECUTION TERM INATED" # CO Cn jr *watriv scardS"con i°ril par=noiist "EXECUTION BEGINS $COMPILE $DATA DATA CB VB CD VD 1 4700.00 47.50 2645.00 48.75 "2 5 0 2 0'.- 0 0 4-772 4 2 28 0.0 0 48 .3 4' 3 5300.00 47.45 2120.00 48.25 4 5700.00 46.85 1655.00 47.95 RESULTS(A) "MATER rAL"~B A L AN C E "S^STPAR AT 10 N~ F A CTO R" BB "7232507&MT 237144.80 251484.90 ""2670 45700" DO T2 8943770" 110215.10 102290.00 "79357.19" PP -352T9-377ir 347360.00 353774.90 "346402710" FF r377T0-350778.50 351218.90 "34791670 0-MB —1043775" -3418.56 2556.00 -=1513.81" ERR? ~=Tj7295" -0.975 0.728 -=0:435-NS "T7777-2.202 2.500 "37444" RESULTS(B) AMOUNT OF SEPARATION CB-CF 1030.00 "135070 0" 1630.00 2030.00 BF 48925.00 "6377470X'" 77343.44 95105.50 CORE USAGE -DTAGNOSTrCS COMPILE TIME" OBJECT CODE' CF-CD 1025.00 T390700" 1550.00 2015.00 DF 49968.75 "67192755" 74787.50 96619.19 2592 BYTES,ARRAY AREA= AS 98893.75 "T30956750" 152130.90 191724.60 816 BYTES,TOTAL AREA AVAILABLE" 102400 BYTES TCUMBER"OF~ERR"ORS= 07"NUMBER""aF"WAWrNGS=^ LT7 NUMBERTTJF-TXTENSTTWS" 0.03 SEC,EXECUTION TIME" 0.08 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971 —0 DATE- 07-30-74 $STOP ?EXECUnON"TERmiTATED i r *watflv scards-con 5-rl2 par-nollst „5r_*watfI  scard "EXECUTION BEGINS DATA "$ COMPILE" SDATA CB VB CD VD 1 1*520.00 96:25 "2970.00 98.35 2 4700.00 96.10 2660.00 98.35 3 1*850.00 96.71* 251*0.00 98.00 (* 533070TT 96.62 _ 2150.00 98.85 "RESULTS ("A3 MATERIAL BALANCE & SEPARATION FACTOR BB 1*35050.00 1*51670. 00 _ I* 69189700" 511*981*.50 DT) 292099.50 261611.00 "71*8920.00" 212527.50 PP 72711*9.50 713281.00 "718109700" 727512.00 FF MB 723912.00 3237.50 723351*.00 -10073.00 "721*1*32.80 "-6323.81" 72711*8.30 363.69 "ERR? 0.1*1*7 •1.393. •0.873" 0.050 NS 1.522 1.767 "17909" 2.1*79 RESULTS(B) AMOUNT OF SEPARATION 2 3 "I*-CB-CF "~ 800701 980.00 1130.00 "161070 0" BF rO'DTJTDTT 91*178.00 109316.lu ""155558710-CF-CD —750-70 TJ" 1060.00 1180.00 "15 70.0 0" 101*251.00 11561*0.00 ""155191+ .50" AS T5D7UZT3TT 1981*29.00 221*956.10 "310752.60" CORE USAGE OBJECT CODE= 2592 BYTES,ARRAY AREA= DIAGNOSTICS NUMBER OF ERRORS- 0, NUMBER OF WARNINGS- 0, NUMBER OF EXTENSIONS--COMPUT-TiMF- 0T03-SEC7EXECUTrON"TIME- 07 09 "SECT-WATFI V — "VERSHOITTTEVEL~3~HAR-CH"~I"97I 816 BYTES,TOTAL AREA AVAILABLE- 1021*00 BYTES  0 DATE" 07-30-71*" "$STOPr_ * EXECUTION TERMINATED # Co Cn 00 APPENDIX F Theoretical and Practical Energy Requirements for a Desalting Process F.l. Minimum Work of Separation The mixing of two substances always results in an increase in entropy, due to the increase in "randomness" of the system. This increase is accompanied by a corresponding decrease in free energy, so that the separation of the resulting mixture under thermodynamically reversible conditions requires the supply of an equal amount of energy to counteract nature's tendency to mix rather than unmix spontaneously. In general, heat and work both depend on the particular path, and one cannot calculate the minimum requirement of either without considering the process in detail. There is however, one particular process - the isothermal reversible process - for which the work is measured by the change in the Helmholtz free energy (the work function), A. The term "minimum work of separation" is usually used to mean the thermodynamic reversible work of separation for an isothermal process and hence it is independent of the process mechanism and dependent only on the initial and final states. The minimum work to separate one mole of a feed solution of composition x^ into two product solutions of compositions and x^ respectively is given by (Dodge, 1944)* * Dodge, B.F., Ed., "Chemical Engineering Thermodynamics", McGraw Hill Co., New York, 1944. 359 360 v2 ~ XJ PA? W. . . = - AA = - RT I —  ln — + ideal L x2 - x3 PAl fx. (1 - x2)(Xl - x3) pB2 x3 (x2 - xL) pA3 _ ln 1 - ln  X2 X3 PB1 X2 x3 PA1 1 (1 - x„)(x0 - x ) p + 3 1 1 in-B3| (F.l.) X2 - X3 PB1 where p Is the partial pressure and subscripts 1, 2 and 3 refer to feed, first product, and second product, respectively, and subscripts A and B to the components. Spiegler (1966 a) developed a general equation for the minimum theoretical energy requirement to separate salt from a saline. For any desalting process in which a 1-1 electrolyte solution of cone. Cf is converted into two product solutions of cones. Cd and C£ at 25°C, the minimum energy is given by U = 1.377 x AN ( - ) (F.2.) p — J. ot — J-3 where U is the energy in kwh/m AN = the normality difference between feed and product solution N = the normality (g-equiv/lit) Nf Nf = N~~ ; a = NT c d subscripts f, d, c identify feed, product (diluate) and concentrate respectively. 361 F.2. Practical Energy Requirements The theoretical energy requirements for a desalting process usually represents merely a small portion of the actual energy requirement. When the minimum work requirement for demineralization is compared with the actual requirement of operating process, it is found that this latter • have an energy efficiency of the order of only 2 to 5% (Dodge and Eshaya, I960)*. These low efficiencies are, of course, attributable to the driving forces which are necessary in any practical process, as contrasted with the reversible process that assumes zero driving forces. These driving forces are the finite temperature differences, pressure differences, concentration differences, e.m.f. differences, etc., which are necessary for equipment of practical size. Any reduction in the driving force always entails an increase in size and hence cost of equipment and because the total costs of a desalting process are about equally divided between costs of energy and fixed costs on equipment, one reaches a cost minimum at an efficiency which is generally less than 20%. The main irreversible effects that make the actual process differs from the ideal reversible one are: i) Pressure drop in lines and equipment due to fluid friction, ii) Throttling processes. iii) Finite temperature difference between fluids exchanging heat. iv) Heat conduction along solids. v) Heat leak into the system from the surroundings. * Dodge, B.F. and A.M. Eshaya, in: "Saline Water Conversion" Number 27 in Advances in Chemistry Series, American Chemical Society, Washington, D.C., 1960. 362 vi) Fluid mixing when there is a difference in temperature or concentration. vii) Mass transfer with finite concentration gradient, viii) Joule heating in electric current flow, ix) Polarization effects at electrodes, x) Mechanical friction, as in pumps and compressors. These effects can never be completely eliminated and frequently must remain of considerable magnitude, if the size of the equipment is to be kept within reasonable bounds [Dodge B.F. and A.M. Eshaya, I960]. 

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