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A Cyclic electrodialysis process : investigation of closed systems 1976

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A CYCLIC ELECTRODIALYSIS PROCESS I n v e s t i g a t i o n of Open Systems by MOHAMMED ELAMIEN ABU-GOUKH B.Sc. (Hons.), U n i v e r s i t y of Khartoum, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of Chemical E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1976 c \ Mohammed Elamlen Abu-Goukh, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f< an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag ree tha the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f CK^AYU^AX IMtoLyw^ The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date ABSTRACT C y c l i c e l e c t r o d i a l y s i s i s a novel s e p a r a t i o n process i n which a modified membrane stack i s operated i n a p e r i o d i c unsteady-state manner. Repeated r e v e r s a l s of p o l a r i t y could avoid the main problems encountered i n c o n v e n t i o n a l e l e c t r o d i a l y s i s ; f o u l i n g and s c a l e formation on the membranes. In c y c l i c e l e c t r o d i a l y s i s the standard e l e c t r o d i a l y s i s stack i s converted i n t o an a d s o r p t i o n - d e s o r p t i o n stack w i t h only one set of flow channels, the other set being r e p l a c e d by storage compartments. Thesr compartments are i n the form of t h r e e - l a y e r membranes c o n s i s t i n g of an anion and a c a t i o n s e l e c t i v e membrane e n c l o s i n g a core of non- s e l e c t i v e m a t e r i a l . The depleted and enriched products are produced s u c c e s s i v e l y i n the s i n g l e set of channels i n s t e a d of simultaneously i n adjacent channels. The process i s p o t e n t i a l l y a p p l i c a b l e f o r commercial d e s a l i n a t i o n of b r a c k i s h water to make i t p o t a b l e , to remove harmful ions from discharge waters, or to concentrate i o n i c s o l u t i o n s f o r recovery of v a l u a b l e m a t e r i a l s . P r e v i o u s l y reported experiments w i t h aqueous NaCl s o l u t i o n s i n a c l o s e d (batch) system showed th a t a l a r g e s e p a r a t i o n f a c t o r could be obtained i n c y c l i c e l e c t r o d i a l y s i s . Batch o p e r a t i o n i s somewhat analogous to t o t a l r e f l u x i n d i s t i l l a t i o n . The present work extends the e a r l i e r work to p o t e n t i a l l y more u s e f u l o p e r a t i n g c o n d i t i o n s i n which feed i s s u p p l i e d and product removed. A c o n s t a n t - r a t e model has been developed f o r the process and used e x t e n s i v e l y throughout the work as a simple and e f f i c i e n t t o o l to compare i i v a r i o u s o p e r a t i n g c y c l e s and modes of o p e r a t i o n . Scattered a r t i c l e s i n the l i t e r a t u r e on the r e s i s t a n c e of an e l e c t r o d i a l y s i s stack have been compiled to develop a stack r e s i s t a n c e model. Good agreement was obtained between the model p r e d i c t i o n s and measured val u e s of r e s i s t a n c e . Experimental apparatus i s described and the e f f e c t s of the f o l l o w i n g e i g h t system parameters are r e p o r t e d : ( i ) D e m i n e r a l i z i n g path l e n g t h ( i i ) P r o d u c t i o n r a t e ( i i i ) Pause time ( i v ) A p p l i e d v o l t a g e (v) I n i t i a l c o n c e n t r a t i o n ( v i ) No-pause o p e r a t i o n ( v i i ) Pure-pause o p e r a t i o n ( v i i ) Semi-symmetric o p e r a t i o n Large separations were achieved f o r asymmetrical paused o p e r a t i o n w i t h long d e m i n e r a l i z i n g path, long pause time, h i g h a p p l i e d v o l t a g e , low feed c o n c e n t r a t i o n and s m a l l p r o d u c t i o n r a t e . D e s p i t e the strong t r a d e - o f f between p r o d u c t i o n r a t e and s e p a r a t i o n , a s e p a r a t i o n f a c t o r as high as 50 was obtained a t the highest p r o d u c t i o n r a t e used. This v a l u e i s higher than that obtained i n commercial p l a n t s c u r r e n t l y i n use. The process looks promising and i s worth f u r t h e r c o n s i d e r a t i o n . i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i i i LIST OF FIGURES x i i i ACKNOWLEDGEMENTS xx Chapter 1 INTRODUCTION AND GENERAL . . . . . . . . 1 2 THEORY AND REVIEW 5 2.1 D e s a l t i n g Processes . . . . 5 2.2 Some Economic Aspects of S e l e c t i v e and S t a t e - Change Processes 7 2.3 E l e c t r o d i a l y s i s 10 2.3.1 E l e c t r o d i a l y s i s Stack 14 2.3.2 Stack S i z e and Capacity . . . . . 16 2.4 Membrane Technology 19 2.4.1 Membrane S e l e c t i v i t y 21 2.4.2 Membrane P o l a r i z a t i o n 25 2.4.3 S c a l i n g and F o u l i n g of Membranes 30 2.5 Process E f f i c i e n c y 32 2.5.1 P r i n c i p a l Energy Sinks 32 2.6 V a r i a n t s of E l e c t r o d i a l y s i s 35 2.6.1 Transport D e p l e t i o n 35 2.6.2 E l e c t r o g r a v i t a t i o n a l D e m i n e r a l i z a t i o n . . . . 38 i v Chapter Page 2.7 C y c l i c Processes . 40 2.7.1 E l e c t r o s o r p t i o n . . . 40 2.7.2 C y c l i c E l e c t r o d i a l y s i s 40 2.7.3 Parametric Pumping 43 2.7.4 C y c l i c E l e c t r o d i a l y s i s and Parametric Pumping . 46 3 SYSTEM MODELS 48 3.1 Stack Resistance Models 48 3.1.1 Non-ohmic A n a l y s i s . . 48 3.1.2 Ohmic A n a l y s i s 66 3.2 Mass Transfer Models 69 3.2.1 E q u i l i b r i u m 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 O b j e c t i v e s of the Program . . . . . 93 4.2 S i n g l e Stack Operation . . . . 94 4.3 Back-to-Back Stack C o n f i g u r a t i o n . . . . . 97 4.3.1 Open System Operation of a back-to-back c o n f i g u r a t i o n 97 4.4 Apparatus and Operation 114 4.4.1 D e t a i l s of an ED C e l l Design 118 4.5 Measuring and Recording 122 4.5.1 Concentrations, Current, Voltage and pH measurements 122 4.5.2 Recording 127 5 EXPERIMENTAL RESULTS and DISCUSSION 128 v Chapter Page 5.1 D a t a - C o l l e c t i o n 128 5.2 Experimental D e s i g n a t i o n 129 5.3 Main Survey Tables 130 5.4 Parameters and Modes of Operation I n v e s t i g a t e d . . . . 133 5.4.1 E f f e c t of D e m i n e r a l i z i n g Path Length 147 5.4.2 E f f e c t of P r o d u c t i o n Rate 172 5.4.3 E f f e c t of Pause Time 173 5.4.4 E f f e c t of A p p l i e d Voltage 192 5.4.5 E f f e c t of I n i t i a l C o ncentration 208 5.4.6 No-Pause Operation , . . . . 208 5.4.7 Pure-Pause Operation . 223 5.4.8 Semi-Symmetric Operation 223 5.5 Comment on pH-Changes 227 5.6 Temperature Measurements » . . . . 243 5.7 Pressure Drop Measurements , . . . , 243 5.8 Probe V o l t a g e , Apparent Resistance and Current Consumption 243 5.9 Voltage E f f i c i e n c y 269 5.10 Current Density and E f f i c i e n c y 269 5.11 Comments on Stack Resistance Models . 273 5.12 Comparison w i t h Previous Work i n Closed System . . . . 284 5.13 R e p r o d u c i b i l i t y . . . . . . . . . 285 6 CONCLUSIONS and RECOMMENDATIONS . . . . . 288 NOMENCLATURE . . . . . 293 REFERENCES . . . . . 298 APPENDICES 304 v i Appendix Page A ELECTRODE SYSTEM . . . . . 304 A . l E l e c t r o d e s M a t e r i a l s . , 304 A.2 E l e c t r o d e s Reactions 304 A.3 E l e c t r o d e P o l a r i z a t i o n E f f e c t on Power Consumption , . , 309 A. 4 E l e c t r o d e Flow System . . , , 311 B THE CURRENT EFFICIENCY . 313 C NERNST IDEALIZED MODEL OF WALL LAYERS 319 C . l The Flow F i e l d i n an E l e c t r o d i a l y s i s C e l l 319 C.2 Nernst Model 319 C.3 Some D e r i v a t i o n s of the Model 320 C.3.1 Generalized Theory of Coupled Processes . . . . . . . . . 320 C.3.2 I o n i c Fluxes 323 C.4 W a l l 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 P r a c t i c a l Energy Requirements . . . . . . 361 v i i LIST OF TABLES Table Page I C l a s s i f i c a t i o n of Main D e s a l t i n g Processes . . . . . . . 6 I I T o t a l Number and Capacity of D e s a l t i n g P l a n t s exceeding 95 nrVday 8 I I I Large E l e c t r o d i a l y s i s P l a n t s - Over 100,000 gpd . . . . 9 IV T e c h n i c a l D e t a i l s of Benghazi (Libya) and S i e s t a Key ( F l o r i d a ) E l e c t r o d i a l y s i s P l a n t s 18 V Reported P r o p e r t i e s of Ion-Exchange Membranes . . . . . . J.22 VI C o n d u c t i v i t y and NaCl Concentration Ranges of BECKMAN C o n d u c t i v i t y C e l l s (EL-VDJ) 323 V I I Values of n i n Experimental Designations Rna and Mna . , . . 131 V I I I Values of a i n Experimental Designations Rna and Mna . . . . . . . . > 3 2 IX Compilation of Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 2000 ppm; 4 - c e l l columns 134 X C o m p i l a t i o n of Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 500 ppm; 4 - c e l l columns 136 XI Compilation of Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 4000 ppm; 4 - c e l l columns 138 X I I Compilation of Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 2000 ppm; 8 - c e l l columns 139 X I I I C o m p i l a t i o n of Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 500 ppm; 8 - c e l l columns 141 XIV Compilation of. Experiments w i t h i n i t i a l c o n c e n t r a t i o n ( C q ) of 4000 ppm; 8 - c e l l columns 143 XV D u p l i c a t e Experiments to Test R e p r o d u c i b i l i t y - Group R 145 v i i i Table Page XVI D u p l i c a t e Experiments to Test R e p r o d u c i b i l i t y - Group M 146 X V I I E f f e c t of Pr o d u c t i o n Rate on Separation; 4 - c e l l columns; C Q - 500 ppm 148 X V I I I E f f e c t of Pr o d u c t i o n Rate on Separation; 4 - c e l l columns; C q - 2000 ppm 150 XIX E f f e c t of Pro d u c t i o n Rate on Separation; 4 - c e l l columns; C q - 4000 ppm 152 XX E f f e c t of Pro d u c t i o n Rate on Separation; 8 - c e l l columns; C - 500 ppm „ . 154 o XXI E f f e c t of Pr o d u c t i o n Rate on Separation; 8 - c e l l columns; C q - 2000 ppm 156 X X I I E f f e c t of Pr o d u c t i o n Rate on Separation; 8 - c e l l columns; C q = 4000 ppm 158 X X I I I E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C Q = 500 ppm; A<J> = 20 V 160 XXIV E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C q = 500 ppm; A<|> = 30 V 162 XXV E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C q = 2000 ppm; A<j> = 20 V 164 XXVI E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C q = 2000 ppm; A<|> = 30 V 166 XXVII E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C q = 4000 ppm; A<j> = 20 V 168 X X V I I I E f f e c t of D e m i n e r a l i z i n g Path Length on Separation; C Q = 4000 ppm; A<|> = 30 V 170 XXIX E f f e c t of Pause Time on Separation; 4 - c e l l columns; C = 500 ppm 174 o XXX E f f e c t of Pause Time on Separation; 4 - c e l l columns; C Q = 2000 ppm 176 XXXI E f f e c t of Pause Time on Separation; 4 - c e l l columns; C Q - 4000 ppm 178 i x Table Page XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI X L I I X L I I I XLIV XLV XLVI XLVII E f f e c t of Pause Time on Separation; 8 - c e l l columns; C q = 500 ppm 180 E f f e c t of Pause Time on Separation; 8 - c e l l columns; C q = 2000 ppm 182 E f f e c t of Pause Time on Sep a r a t i o n ; 8 - c e l l columns; C q = 4000 ppm 184 E f f e c t of Pause Time on Separation; C = 500 ppm; Group M7 ° 186 E f f e c t of Pause Time on Sep a r a t i o n ; C = 2000 ppm; Group M3 ° 188 E f f e c t of Pause Time on Separation; C =; 4000 ppm; Group M i l ° 190 E f f e c t of A p p l i e d V o l t a g e on Sep a r a t i o n ; 4 - c e l l columns; C q = 500 ppm 193 E f f e c t of A p p l i e d Voltage on Separation; 4 - c e l l columns; C q = 2000 ppm 195 E f f e c t of A p p l i e d V o l t a g e on Sep a r a t i o n ; 4 - c e l l columns; C q = 4000 ppm 197 E f f e c t of A p p l i e d Voltage on Separation; 8 - c e l l columns; C q = 500 ppm 199 E f f e c t of A p p l i e d V o l t a g e on Separation; 8 - c e l l columns; C q = 2000 ppm 201 E f f e c t of A p p l i e d Voltage on Separation; 8 - c e l l columns; C q - 4000 ppm 203 E f f e c t of Feed Concentration on Separation; 4 - c e l l columns; P.R. = 20 c . c . / c y c l e 209 E f f e c t of Feed Concentration on Separation; 4 - c e l l columns; P.R. - 50 c . c . / c y c l e 211 E f f e c t of Feed Concentration on Separation; 4 - c e l l columns; P.R. = 100 c . c . / c y c l e 213 E f f e c t of Feed Concentration on Separation; 8 - c e l l columns; P.R. = 25 c . c . / c y c l e 215 Table Page XLVIII E f f e c t of Feed Concentration on Separation; 8 - c e l l columns; P.R. ~ 50 c . c . / c y c l e 217 XLIX E f f e c t of Feed Concentration on Separation; 8 - c e l l columns; P.R. = 100 c . c . / c y c l e 219 L Comparison of Pause and No-Pause Operations 221 L I Comparison of Pure Pause w i t h Mixed Mode Operations; C q = 2000 ppm 224 L I I Semi-Symmetric Operation; C q = 2000 ppm . 226 L I I I Comparison of Semi-Symmetric and Asymmetric Operations 228 LIV Average Product Concentrations i n A r b i t r a r y U n i t s obtained under Semi-Symmetric and Asymmetric Operations 241 LV pH - Changes f o r some ED runs at v a r i o u s feed c o n c e n t r a t i o n s and operating c o n d i t i o n s . . . 242 LVI Pressure Drop Measurements 244 LVI I Average Probe Voltage (Stack Voltage) over a complete c y c l e f o r v a r i o u s feed c o n c e n t r a t i o n and A p p l i e d Voltages 246 L V I I I V a r i a t i o n of Probe Voltage along the D e m i n e r a l i z a t i o n path during the d e p l e t i o n h a l f c y c l e f o r v a r i o u s feed c o n c e n t r a t i o n s ; A<|> = 30 V 253 LIX V a r i a t i o n of Current Consumption along the D e m i n e r a l i z a t i o n Path during the d e p l e t i o n h a l f c y c l e at v a r i o u s a p p l i e d v o l t a g e s ; C q - 2000 ppm 255 LX V a r i a t i o n of Current Consumption along the D e m i n e r a l i z a t i o n Path during the d e p l e t i o n h a l f c y c l e at v a r i o u s feed c o n c e n t r a t i o n s ; A<j> = 30 V . 257 LXI V a r i a t i o n of Probe V o l t a g e , Current, R e s i s t a n c e and Power Consumption along the d e m i n e r a l i z i n g path; C Q - 500 ppm 259 L X I I V a r i a t i o n of Probe V o l t a g e , Current, R e s i s t a n c e and Power Consumption along the d e m i n e r a l i z i n g path; C q - 2000 ppm 260 x i Table Page L X I I I V a r i a t i o n of Probe V o l t a g e , Current, R e s i s t a n c e and Power Consumption along the d e m i n e r a l i z i n g path; C q = 4000 ppm 261 LXIV E f f e c t of I n i t i a l C oncentration on the Eq u i v a l e n t Resistance of ED Stack 262 LXV V a r i a t i o n of ED Stack r e s i s t a n c e along the d e m i n e r a l i z i n g path during the d e p l e t i o n h a l f c y c l e at v a r i o u s a p p l i e d v o l t a g e s ; C Q - 500 ppm 264 LXVI Voltage E f f i c i e n c y 270 LXVII O v e r a l l Current E f f i c i e n c y 272 LXVIII E q u i v a l e n t Conductance and D i f f u s i v i t y of aqueous sodium c h l o r i d e s o l u t i o n s 275 LXIX D i s t r i b u t i o n of the p r e d i c t e d r e s i s t a n c e of an ED stage between i t s r e s i s t i v e elements 280 LXX Values of L o c a l Average C o n c e n t r a t i o n , C and Measured Stage Resistance 282 LXXI R e p r o d u c i b i l i t y - Group R; 4 - c e l l columns 286 LXXII R e p r o d u c i b i l i t y - Group M; 8 - c e l l columns . . . . . . . 287 x i i LIST OF FIGURES F i g u r e Page 1 Comparison of energy c o s t s f o r d i s t i l l a t i o n and e l e c t r o d i a l y s i s 11 2 Multiple-chamber a l t e r n a t e membrane e l e c t r o d i a l y s i s c e l l 13 3 Exploded view of components i n an e l e c t r o - membrane st a c k 15 4 Dependence of c o u n t e r i o n t r a n s p o r t numbers and p e r m s e l e c t i v i t y upon e x t e r n a l c o n c e n t r a t i o n 23 5a Ion t r a n s p o r t across a p e r m s e l e c t i v e membrane 26 5b C o n c e n t r a t i o n p r o f i l e a c r o s s a p e r m s e l e c t i v e membrane i n an e l e c t r o d i a l y s i s s t a ck . . . . 26 6 The c a t i o n - n e u t r a l t r a n s p o r t d e p l e t i o n process . . . . . 36 7 E l e c t r o g r a v i t a t i o n w i t h c a t i o n - s e l e c t i v e membranes 39 8 E l e c t r o s o r p t i o n Process . . 41 9a Diagram of column f o r d i r e c t mode P.P 45 9b V e l o c i t y and temperature a t a p o i n t i n the bed 45 as a f u n c t i o n of time 10 S i m p l i f i e d c o n c e n t r a t i o n p r o f i l e s i n an e l e c t r o d i a l y s i s c e l l p a i r and the analogous e l e c t r i c a l c i r c u i t . . . . 50 11 Diagram of the c o n c e n t r a t i o n p r o f i l e and the d i f f u s i o n l a y e r on the d i a l y s a t e s i d e of an e l e c t r o d i a l y s i s i o n exchange membrane . . . . . 52 12a The c o n c e n t r a t i o n p r o f i l e s ( e x p o n e n t i a l ) of both the d i a l y s a t e and b r i n e streams 55 12b The m a t e r i a l balances of both the d i a l y s a t e and b r i n e streams 55 x i i i F i g u r e • Page 13a C o n c e n t r a t i o n d i s t r i b u t i o n i n a cation-exchange membrane. Z r C r i s the c o n c e n t r a t i o n of f i x e d J charge i n membrane 59 13b Schematic p o t e n t i a l d i s t r i b u t i o n through a cation-exchange membrane 59 14 Back emf due to c o n c e n t r a t i o n and p o l a r i z a t i o n 63 15 D i f f e r e n t i a l s e c t i o n of column , . . 70 16 S e r i e s connection of ED modules to approximate c o n s t a n t - r a t e o p e r a t i o n , . , . , 74 17 Co n c e n t r a t i o n p r o f i l e s p r e d i c t e d by c o n s t a n t - r a t e model w i t h equal r a t e s j continuous c y c l i c displacement of f l u i d and mass t r a n s f e r . . . . . . . . 77 18 Co n c e n t r a t i o n p r o f i l e s - i n t e r r u p t e d c u r r e n t c y c l e . . . '. 80 19 C o n c e n t r a t i o n p r o f i l e s - i n t e r r u p t e d f l o w c y c l e . 84 20 . C o n c e n t r a t i o n p r o f i l e s p r e d i c t e d by c o n s t a n t - r a t e model-continuous c y c l i c displacement of f l u i d and mass t r a n s f e r . The mass t r a n s f e r c y c l e i s 90° out- of-phase w i t h the displacement c y c l e 36 21 Back-to-back o p e r a t i o n of two u n i t s 88 22 Batch o p e r a t i o n of c y c l i c e l e c t r o d i a l y s i s process 94 23 Back-to-back o p e r a t i o n of two c e l l s 97 24 Developing c o n c e n t r a t i o n p r o f i l e - two c e l l s o p e r a t i n g back-to-back i n a c l o s e d system 98 25 Flow connections and v a l v e t i m i n g sequence f o r symmetric o p e r a t i o n . . . . . 100 26 Developing c o n c e n t r a t i o n p r o f i l e , symmetric o p e r a t i o n of an open system 103 27 Flow connections and v a l v e t i m i n g sequence f o r semi-symmetric o p e r a t i o n . . 105 28 Developing c o n c e n t r a t i o n p r o f i l e , semi-symmetric o p e r a t i o n of an open system 109 x i v F i g u r e Page 29 Flow connections and v a l v e t i m i n g sequence f o r asymmetric o p e r a t i o n 110 30 Developing c o n c e n t r a t i o n p r o f i l e , asymmetric o p e r a t i o n of an open system 112 31 E l e c t r o d i a l y s i s U n i t and C o n t r o l Equipment . 114 32 E l e c t r o d i a l y s i s C e l l s i n Back-to-Back Operation . . , . 115 33 A s i n g l e stage w i t h i t s two end-frames 118 34 A t r i p l e membrane-frame-spacer assembly , , . 118 35 C o n s t r u c t i o n of s i n g l e membrane-spacer assembly f o r an ED c e l l 119 36 Schematic diagram showing s o l u t i o n flows and in s t r u m e n t a t i o n (Asymmetric operation) » 120 37 Current monitoring c i r c u i t . , . 125 38 E f f e c t of pro d u c t i o n r a t e on s e p a r a t i o n . 4 - c e l l column; i n i t i a l cone. C Q - 500 ppm ' 149 39 E f f e c t of pro d u c t i o n r a t e on s e p a r a t i o n . 4 - c e l l column; i n i t i a l cone. C Q = 2000 ppm 151 40 E f f e c t of pr o d u c t i o n r a t e on s e p a r a t i o n . 4 - c e l l column; i n i t i a l cone. C Q = 4000 ppm , . 153 41 E f f e c t of pr o d u c t i o n r a t e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q = 500 ppm 155 42 E f f e c t of pro d u c t i o n r a t e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q = 2000 ppm 157 43 E f f e c t of pro d u c t i o n r a t e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q = 4000 ppm . 159 44 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . C Q * 500 ppm, Acfi = 20 V 161 45 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . C Q = 500 ppm, A<j> = 30 V 163 46 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . C Q = 2000 ppm, A<() = 20 V 165 47 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . Cn = 2000 ppm, A<j> = 30 V 167 xv F i g u r e Page 48 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . C Q a 4000 ppm, A<j> = 20 V '. 169, 49 E f f e c t of d e m i n e r a l i z i n g path l e n g t h on s e p a r a t i o n . C q = 4000 ppm, A<|> = 30 V 171 50 E f f e c t of pause time on s e p a r a t i o n ; 4 - c e l l column; i n i t i a l cone. C Q - 500 ppm 175 51 E f f e c t of pause time on s e p a r a t i o n ; 4 - c e l l column; i n i t i a l cone. C q = 2000 ppm 177 52 E f f e c t of pause time on s e p a r a t i o n ; 4 - c e l l column; i n i t i a l cone. C q * 4000 ppm 179 53 E f f e c t of pause time on s e p a r a t i o n ; 8 - c e l l column; i n i t i a l cone. C q = 500 ppm 181 54 E f f e c t of pause time on s e p a r a t i o n ; 8 - c e l l column; i n i t i a l cone. C Q - 2000 ppm . . . . . . . . . . . 183 55 E f f e c t of pause time on s e p a r a t i o n ; 8 - c e l l column; i n i t i a l cone. C q - 4000 ppm . . . . 185 56 E f f e c t of pause time on s e p a r a t i o n . C = 500 ppm. Group M7 ° » 87 57 E f f e c t of pause time on s e p a r a t i o n . C = 2000 ppm; Group M3 ° . 189 58 E f f e c t of pause time on s e p a r a t i o n . C = 4000 ppm. Group M i l ° 191 59 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n . 4 - c e l l column; i n i t i a l cone. C q - 500 ppm 194 60 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n . 4 - c e l l column; i n i t i a l cone. C q = 2000 ppm . . . . . . . . . 196 61 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n ; 4 - c e l l column; i n i t i a l cone. C q = 4000 ppm - 198 62 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q = 500 ppm 200 63 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q - 2000 ppm 202 64 E f f e c t of a p p l i e d v o l t a g e on s e p a r a t i o n . 8 - c e l l column; i n i t i a l cone. C Q - 4000 ppm 204 x v i F i g u r e 65 V a r i a t i o n of i n d i v i d u a l c o s t items making up the t o t a l p r o c e s s i n g c o s t Pace 207 66 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on s e p a r a t i o n . 4 - c e l l column; p r o d u c t i o n r a t e - 20 c . c . / c y c l e 210 67 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on s e p a r a t i o n . 4 - c e l l column; p r o d u c t i o n r a t e - 50 c . c . / c y c l e . 212 68 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on s e p a r a t i o n . 4 - c e l l column; p r o d u c t i o n r a t e = 100 c . c . / c y c l e 214 69 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on s e p a r a t i o n . 8 - c e l l column; p r o d u c t i o n r a t e = 25 c . c . / c y c l e , . . > 216 70 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on s e p a r a t i o n . 8 - c e l l column; p r o d u c t i o n r a t e = 50 c . c . / c y c l e . . . 218 71 E f f e c t of feed c o n c e n t r a t i o n ( C Q ) on- s e p a r a t i o n . 8 - c e l l column; p r o d u c t i o n r a t e ~ 100 c . c . / c y c l e . . , . 220 72 Comparison of pause and no-pause o p e r a t i o n s . 8 - c e l l column; p r o d u c t i o n r a t e - 50 c . c . / c y c l e . . . . . 222 73 Pure pause o p e r a t i o n (no power d u r i n g c i r c u l a t i o n ) . 8 - c e l l column; p r o d u c t i o n r a t e - 50 c . c . c y c l e . I n i t i a l c o n c e n t r a t i o n C Q - 2000 ppm . . . . . . . . . . 225 74 Comparison of semi-symmetric and asymmetric o p e r a t i o n s , 8 - c e l l column; p r o d u c t i o n r a t e - 100 c . c . / c y c l e . Feed c o n c e n t r a t i o n C q - 2000 ppm 229 75 Developing c o n c e n t r a t i o n p r o f i l e ; asymmetric o p e r a t i o n of an open system w i t h mass t r a n s f e r d u r i n g both pause and displacement p e r i o d s . D i a l y s a t e product = b r i n e product = 1/3 c e l l volume/cycle . . . . 234 76 Developing c o n c e n t r a t i o n p r o f i l e ; semi-symmetric o p e r a t i o n of an open system w i t h mass t r a n s f e r d u r i n g both pause and displacement p e r i o d s . D i a l y s a t e product = b r i n e product = 1/3 c e l l volume/cycle . . . . 240 77 Pressure drop v s . f l o w r a t e . 8-Stage ED s t a c k . . . . . . 245 x v i i F i g u r e 78 79 80 81 82 83 84 85 86 87 88 89 Page Average stack v o l t a g e (probe v o l t a g e ) v s . a p p l i e d v o l t a g e f o r v a r i o u s feed c o n c e n t r a t i o n s . Pause time T = 45 sec. Exp. group M3, H7 and M i l . . . . 247 Traces of probe v o l t a g e r e c o r d i n g d u r i n g a c y c l e a t four p o i n t s along the d e m i n e r a l i z i n g path. Exp. M7F 248 Traces of c u r r e n t r e c o r d i n g d u r i n g a c y c l e a t d i f f e r e n t p o i n t s along the d e m i n e r a l i z i n g path. Exp. M7F 249 Traces of probe v o l t a g e r e c o r d i n g d u r i n g a c y c l e at four p o i n t s along the d e m i n e r a l i z i n g path. Exp. M11F 250 Traces of c u r r e n t r e c o r d i n g d u r i n g a c y c l e a t fo u r p o i n t s along the d e m i n e r a l i z i n g path. Exp. M11F 251 V a r i a t i o n of s t a c k v o l t a g e (probe v o l t a g e ) along the d e m i n e r a l i z i n g path f o r v a r i o u s feed c o n c e n t r a t i o n s . Exp. M7F and M11F 254 V a r i a t i o n of c u r r e n t consumption along the d e m i n e r a l i z a t i o n path at v a r i o u s a p p l i e d v o l t a g e s C q = 2000 ppm, Exp. M3B, M3F and M3G 256 V a r i a t i o n of c u r r e n t consumption along the d e m i n e r a l i z a t i o n path a t v a r i o u s feed c o n c e n t r a t i o n s . A* = 30 V; Exp. M3F, M7F and M11F 258 E f f e c t of I n i t i a l C oncentration on e q u i v a l e n t r e s i s t a n c e of ED stack 263 V a r i a t i o n of stack r e s i s t a n c e along the d e m i n e r a l i z a t i o n path d u r i n g the d e p l e t i o n h a l f c y c l e a t v a r i o u s a p p l i e d v o l t a g e s . C Q - 500 ppm; Exp. M7F and M7G . V a r i a t i o n of apparent ED s t a c k r e s i s t a n c e along the d e m i n e r a l i z a t i o n path d u r i n g the d e p l e t i o n h a l f c y c l e u s i n g semi-log s c a l e . A(J> = 30 V; Exp. M3F, M7F and M11F 265 267 V a r i a t i o n of apparent ED s t a c k r e s i s t a n c e along the d e m i n e r a l i z a t i o n path u s i n g semi-log s c a l e C Q = 2000 ppm, Exp. M3B, M3F and M3G 268 x v i i i F i g u r e Page 90 Equivalent conductance of aqueous sodium c h l o r i d e s o l u t i o n s at 25°C 276 91 D i f f u s i v i t y of aqueous sodium c h l o r i d e s o l u t i o n s at 25°C 277 92 Discrepancy between p r e d i c t e d and measured valu e of an ED stage , , . 281 93 V a r i a t i o n of apparent r e s i s t a n c e of an ED stage w i t h the r e c i p r o c a l of the average product c o n c e n t r a t i o n . . 283 x i x ACKNOWLEDGEMENT I wish to thank Dr. D.W. Thompson, under whose d i r e c t i o n t h i s i n v e s t i g a t i o n was undertaken, f o r h i s u n f a i l i n g h e l p , i n v a l u a b l e ideas and encouragement i n a l l stages of t h i s work. A l s o thanks are due to the f a c u l t y and s t a f f of Chemical Engineering Department of the U n i v e r s i t y of B r i t i s h Columbia f o r t h e i r w i l l i n g a s s i s t a n c e and co-operation throughout these years. H i g h l y appreciated i s the a s s i s t a n c e o f f e r e d and the work performed by the personnel of the Workshop and the Stores of the same department . Al s o I am indebted to the s t a f f of the U.B.C. Main L i b r a r y and the I n t e r - l i b r a r y Loan s e c t i o n f o r t h e i r e f f i c i e n t s e r v i c e i n p r o v i d i n g and borrowing u s e f u l m a t e r i a l s from other l i b r a r i e s . I am most g r a t e f u l to Ms. Jane Winn f o r her expert t y p i n g of co u n t l e s s pages of strange symbols. Further thanks are due to the N a t i o n a l Research C o u n c i l and Environment Canada f o r t h e i r f i n a n c i a l support. F i n a l l y , I must express my g r a t i t u d e to my w i f e , Soad, f o r her s a c r i f i c e s and c o n t i n u a l support throughout t h i s work. XX CHAPTER 1 I n t r o d u c t i o n and General Water i s the most important chemical compound on E a r t h , When men s e t t l e d down to a g r i c u l t u r e and farming, they b u i l t t h e i r houses near potable water resources, such as r i v e r s and l a k e s . I n c r e a s i n g the s i z e of settlements augmented the needs of f r e s h water supply. The t h e o r e t i c a l minimum water requirements, i n c l u d i n g a g r i c u l t u r e , to s u s t a i n human l i f e 3 are about 1.1 m per person per day, assuming t h a t man can l i v e on broad alone. The i n t r o d u c t i o n of 0.5 kg of animal f a t and p r o t e i n to the ciief 3 i n c r e a s e s the water requirement f o r subsistence to about 9.5 m pet person per day (Bradley, 1962). I n c r e a s i n g demand f o r water caused by the r i s i n g standard of l i v i n g and by the i n c r e a s e i n p o p u l a t i o n , i r r e s p o n s i b l e wasting of water i n many l a r g e c i t i e s , and above a l l p o l l u t i o n of n a t u r a l water reserves w i t h i n d u s t r i a l waste and sewage, have brought many regions i n v a r i o u s c o u n t r i e s c l o s e to the c r i t i c a l p o i n t where e x i s t i n g resources can no longer s a t i s f y the growing demand. The s i t u a t i o n w i l l become worse i f adequate means are not adopted i n time. Although the annual p r e c i p i t a t i o n on Earth's surface might be s u f f i c i e n t , the uneven d i s t r i b u t i o n of r a i n f a l l does not meet the human needs i n a l l regions of the world. In s e v e r a l a r i d areas, e x i s t i n g water resources are s a l i n e , exceeding, the l i m i t of p o t a b l e water which i s set as 1 2 500 mg/1 f o r t o t a l d i s s o l v e d s o l i d s . A c t u a l l y there are many communities i n v a r i o u s c o u n t r i e s which are s t i l l s u p p l i e d w i t h water c o n t a i n i n g over 1000 mg/1 t o t a l d i s s o l v e d s o l i d s and sometimes up to 3000 mg/1. For such b r a c k i s h and s i m i l a r p o l l u t e d waters treatment by d i s t i l l a t i o n i s not economically f e a s i b l e and e f f o r t s have been made to r e s o r t to other processes such as e l e c t r o d i a l y s i s . However, co n v e n t i o n a l e l e c t r o d i a l y s i s has achieved only p a r t i a l success i n b r a c k i s h water d e m i n e r a l i z a t i o n d e s p i t e many theo- r e t i c a l advantages i t o f f e r s over other processes. Under steady s t a t e o p e r a t i o n , c o n v e n t i o n a l e l e c t r o d i a l y s i s i s subject to mud and s c a l e b u i l d - u p on the membrane surfaces which may hinder the t r a n s f e r of ions through the membranes, thus decreasing the c a p a c i t y of the u n i t . The d e p o s i t may p a r t i a l l y b l o c k f l o w channels, i n c r e a s i n g pumping c o s t , and may r e a c t w i t h and damage the membranes, reducing the s e l e c t i v i t y and e f f i c i e n c y of the s e p a r a t i o n (Matz, 1965 and Korngold, 1970). P e r i o d i c c u r r e n t i n t e r r u p t i o n s and/or r e v e r s a l s have been employed i n standard e l e c t r o d i a l y s i s p l a n t s to reduce p o l a r i z a t i o n e f f e c t s and d e p o s i t i o n of p a r t i c u l a t e s on the membranes (Matz, et a l . , 1962; C a l v i t and Sloan, 1965). Based on c u r r e n t r e v e r s a l technique, Lacey (1965, 1968) invented an e l e c t r o s o r p t i o n stack of much simpler c o n s t r u c t i o n than con- v e n t i o n a l e l e c t r o d i a l y s i s s t a c k s . E l e c t r o s o r p t i o n can be considered as a one-cycle process without r e f l u x . This idea was f u r t h e r m o d i f i e d and developed i n t o c y c l i c e l e c t r o d i a l y s i s by Thompson and Bass (1972, 1974). C y c l i c e l e c t r o d i a l y s i s i s a c y c l i c s e p a r a t i o n process which a p p l i e s the p e r i o d i c f l o w - r e v e r s a l technique to an e l e c t r i c a l l y d r i v e n e l e c t r o s o r p t i o n stack. The process has a wide f i e l d of p o t e n t i a l a p p l i c a t i o n s such as: i ) B r a c k i s h water d e m i n e r a l i z a t i o n i i ) B r i n e p r o d u c t i o n from sea water i i i ) R a d i o a c t i v e waste decontamination i v ) S e l e c t i v e s e p a r a t i o n of monovalent s a l t from d i v a l e n t and other p o l y v a l e n t s a l t s v) I n the food i n d u s t r i e s i t may be used f o r d e s a l i n a t i o n of cheese whey and d e - a c i d i f i c a t i o n of orange j u i c e and treatment (mainly de-ashing) of sugars and syrups and r e l a t e d compounds v i ) Other p o t e n t i a l a p p l i c a t i o n s o u t s i d e the food i n d u s t r y concern the treatment of l e a c h s o l u t i o n s in- m e t a l l u r g y , waste p i c k l e - l i q u o r recovery and waste s u l f i t e - l i q u o r recovery. Although c y c l i c e l e c t r o d i a l y s i s may be most economical f o r the c o n v e r s i o n of b r a c k i s h waters (up to 10,000 ppm) to p o t a b l e water of 500 ppm, n e v e r t h e l e s s s p e c i f i c c o n d i t i o n s can c r e a t e other s i t u a t i o n s when the process could become unexpectedly economical. For example, there seems to be a 3 l a r g e p o t e n t i a l demand f o r sea water c o n v e r s i o n on the 2-5 m /h s c a l e f o r t o u r i s t r e s o r t s . In these cases, the a m o r t i s a t i o n and i n t e r e s t charges tend to be very h i g h and the u t i l i s a t i o n f a c t o r i s o f t e n as low as 33% per annum, C a p i t a l c o s t i s t h e r e f o r e overwhelmingly the most important f a c t o r , and i t appears that the process may provide the cheapest c a p i t a l p l a n t f o r meeting these requirements, although, a t t h i s s a l i n i t y l e v e l , the power cost of c y c l i c e l e c t r o d i a l y s i s would be higher than the other c o m p e t i t i v e processes. C y c l i c e l e c t r o d i a l y s i s has been i n v e s t i g a t e d i n a c l o s e d system and s e p a r a t i o n f a c t o r s of s e v e r a l hundreds were reported f o r most of the runs w i t h aqueous sodium c h l o r i d e s o l u t i o n s (Bass, 1972). The present work i s an e x t e n s i o n of the previous work to an open system which r e p r e s e n t s a more u s e f u l mode of o p e r a t i o n . The main o b j e c t i v e s are to analyze the p o t e n t i a l of the c y c l i c process on a continuous b a s i s and to i n v e s t i g a t e s y s t e m a t i c a l l y 4 the e f f e c t of the v a r i o u s design and operating parameters on the performance of the process. The present program makes a r a t h e r extensive study and e x p l o r a t i o n of the system w i t h i n the design parameters and i t provides i n f o r m a t i o n that should be u s e f u l i n f u r t h e r study and i n o p t i m i z i n g the system. CHAPTER 2 Theory and Review 2.1. D e s a l t i n g Processes D e s a l t i n g techniques p o t e n t i a l l y u s e f u l as commercial s e p a r a t i o n pro- cesses may be c l a s s i f i e d i n t o two general c a t e g o r i e s , as shown i n Table I;; a) Processes that remove pure water from s o l u t i o n b) Processes that remove s a l t s from s o l u t i o n The most developed process i n category (a) i s d i s t i l l a t i o n . F r e e z i n g i s a process c u r r e n t l y being developed, w h i l e hydrate formation i s s t i l l , i n the experimental stage. Reverse osmosis, a f t e r a long p e r i o d of membrane development, i s e n t e r i n g the f i e l d of commercial o p e r a t i o n . The l a t e n t heat f o r changing phase i s an important f a c t o r i n the o v e r a l l economics of d i s t i l l a t i o n processes w h i l e the degree of s a l i n i t y of the raw water i s of l i t t l e importance. This process i s t h e r e f o r e e q u a l l y s u i t a b l e f o r d e s a l t i n g seawater or b r a c k i s h water. The same a p p l i e s f or f r e e z i n g . However, the feed c o n c e n t r a t i o n i s important i n revers e osmosis, as the r e q u i r e d counterpressure depends g r e a t l y upon the s a l t content of the raw water. The most developed process i n category (b) i s e l e c t r o d i a l y s i s , and work has been done w i t h i o n exchange. The economics of these processes depends c l o s e l y on the s a l t content of the raw water, which determines the amount of e l e c t r i c power r e q u i r e d , or the consumption of chemicals needed 5 6 Table I C l a s s i f i c a t i o n of Main D e s a l i n a t i o n Processes Processes that Separate Water from S o l u t i o n S a l t s from S o l u t i o n 1. D i s t i l l a t i o n V e r t i c a l tube evaporator H o r i z o n t a l tube evaporator M u l t i - s t a g e f l a s h evaporator Vapor compression Solar evaporation 2. Reverse osmosis 3. C r y s t a l l i z a t i o n 1. I o n i c processes Ion exchange E l e c t r o d i a l y s i s Transport d e p l e t i o n Osmionic P i e z o d i a l y s i s E l e c t r o c h e m i c a l B i o l o g i c a l Systems 2. Other processes L i q u i d - l i q u i d e x t r a c t i o n F r e e z i n g Hydrate formation 7 f o r the r e g e n e r a t i o n of the r e s i n s . Hence, these processes are more s u i t a b l e f o r the p u r i f i c a t i o n of b r a c k i s h waters. Table I I shows the number and c a p a c i t y of p l a n t s by process and by geographic l o c a t i o n . (0 1Shaughnessy, 1973). M u l t i - s t a g e f l a s h evaporation accounts f o r 65% of the t o t a l c a p a c i t y of the d i s t i l l a t i o n p l a n t s . Two regions which represent l a r g e centres of d e s a l t i n g are the i s l a n d s i n the Caribbean Sea, and the Middle E a s t , i n c l u d i n g c o u n t r i e s around the P e r s i a n G u l f . A l i s t i n g of most e l e c t r o d i a l y s i s p l a n t s having a c a p a c i t y of 100,000 gpd or more i s given i n Table I I I . I t has a l s o been reported that a p p r o x i - mately 300 e l e c t r o d i a l y s i s p l a n t s have been constructed and i n s t a l l e d i n the U.S.S.R. (Lynch and M i n t z , 1972). 0 2.2. Some Economic Aspects of S e l e c t i v e and State-Change Processes S e l e c t i v e processes such as e l e c t r o d i a l y s i s achieve s e p a r a t i o n without a change of phase of any component i n the system. Such processes have economical advantages over state-change processes such as d i s t i l l a t i o n and f r e e z i n g . The methods of s e p a r a t i o n that r e l y on a change of s t a t e i n v o l v e a high r a t e of energy c i r c u l a t i o n i n the system, because the heat of f u s i o n or v a p o r i z a t i o n of the solvent must be s u p p l i e d . In g e n e r a l , t h i s energy i s many times l a r g e r than the energy t h e o r e t i c a l l y needed to separate the s a l t from the s o l v e n t ; and the energy r e q u i r e d f o r v a p o r i z a t i o n or f u s i o n must be recovered and reused to make such processes p r a c t i c a l . The l o s s e s and i n e f f i c i e n c i e s i n any system tend to be p r o p o r t i o n a l to the energy Table II Total number and capacity of desalting plants exceeding 25000 gpd (95 m /day)* P = plants number; a = data i n 1000 m3/day; b = data i n Mgd. Geographic Total E l e c t r o d i a l s i s Reverse Freezing Total desalination Location d i s t i l l a t i o n 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. T e r r i t o r i e s 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 I I I Large E l e c t r o d i a l y s i s P l a n t s - Over 100,000 gpd* P l a n t L o c a t i o n A c t u a l or Planned Year of Start-up Feedwater S a l i n i t y ppm Manufacturer Capacity B r i n d i s i , I t a l y 1971 2,000 Ion i c s 1,300,000 Buckeye, A r i z . 1962 2,200 Ion i c s 650,000 P a n t e l l e r i a , I t a l y 1971 4,500 Ion i c s 265,000 S i e s t a Key, F l a . 1969 1,300 Ion i c s 1,500,000 Aramco, Dhahran, Saudi A r a b i a 1961 2,700 Ion i c s 115,000 Bahrain Petroleum Co., Bahrain, P e r s i a n Gulf 1964 3,150 Io n i c s 100,000 Anaconda Copper Co., C h i l e 1970 2,200 Ionics 265,000 I n d u s t r i a l Co., Tex. 1969 2,500 Ion i c s 880,000 Automobile F a c t o r y , B a r i , I t a l y 1970 2,000 Ion i c s 530,000 U.S. Army N.M. 1970 3,100 Io n i c s 100,000 A l Saudi Co., A l Khobar, Saudi A r a b i a 1967 2,800 Io n i c s 100,000 G i l l e t t e , Wyo. 1971 2,500 Io n i c s 1,500,000 Por t M a n s f i e l d , Tex. 1965 2,400 Ion i c s 265,000 Ras Gharib, Egypt 1971 Io n i c s 113,000 E l Adem, L i b y a 1971 Io n i c s 170,000 Bahrain H o s p i t a , Bahrain 1971 Io n i c s 105,000 Benghazi, L i b y a Under c o n s t r u c t i o n 2,000 Wm. Boby Co. 5,000,000 Moshabei, Sadeh, I s r a e l 1971 2,300 Tahal Co n s u l t i n g 1,250,000 Engineers Heinekens Brewery, Rotterdam, Netherlands 1968 1,100 Wm. Boby Co. 177,000 Z l i t e n , L i b y a 1968 4,400 Wm. Boby Co. 105,000 Kazakstan, U.S.S.R. Under c o n s t r u c t i o n Unknown 500,000 * From Lynch and M i n t z , J . Am. Water, 64̂ , 711 (1972) 10 c i r c u l a t i o n ; and, to a f i r s t approximation at l e a s t , the energy needed to operate a d i s t i l l a t i o n system w i l l be a d e f i n i t e f r a c t i o n of the heat of v a p o r i z a t i o n of the s olvent and independent of the amount of s o l u t e present (Shaffer & M i n t z , 1966). On the other hand, processes that are based, on s e l e c t i v e t r a n s p o r t r e q u i r e energy at a r a t e that v a r i e s w i t h the t h e o r e t i c a l minimum energy (Helmholtz f r e e energy) needed to produce a d e s a l t e d and concentrated stream from a s a l i n e feed water i . e . w h i l e the s a l i n i t y does not a f f e c t the p r a c t i c a l energy requirements f o r a process such as d i s t i l l a t i o n , i t does make a great d e a l of d i f f e r e n c e to a process such as e l e c t r o d i a l y s i s . For f u r t h e r d i s c u s s i o n on t h e o r e t i c a l and a c t u a l energy requirements f o r a d e s a l t i n g process r e f e r to Appendix F. The energy l o s s e s i n the s e l e c t i v e t r a n s p o r t systems a r i s e p r i m a r i l y as a r e s u l t of the d e s i r e to m a i n t a i n p r a c t i c a l p r o d u c t i o n r a t e s ; thus n e c e s s i t a t e s the use of s u b s t a n t i a l d r i v i n g f o r c e s i n s t e a d of i n f i n i t e s i m a l f o r c e s , which would cause the processes to take p l a c e s l o w l y and r e v e r r . i b l y . The net r e s u l t of these c o n s i d e r a t i o n s can best be seen by examining F i g u r e 1, ( Shaffer & M i n r z , 1966) which compares the energies a c t u a l l y r e q u i r e d f o r d i s t i l l a t i o n and e l e c t r o d i a l y s i s w i t h the t h e o r e t i c a l r e q u i r e - ments at v a r i o u s s a l i n i t i e s and f i x e d blowdown and product s p e c i f i c a t i o n s . According to t h i s graph d i s t i l l a t i o n i s more economical f o r de- m i n e r a l i z i n g h i g h - s a l i n i t y waters w h i l e e l e c t r o d i a l y s i s i s more a t t r a c t i v e f o r b r a c k i s h waters up to about 10,000 ppm. 2.3. E l e c t r o d i a l y s i s E l e c t r o d i a l y s i s i s a s e l e c t i v e t r a n s p o r t process, i n which the p a r t i a l s e p a r a t i o n of the components of an i o n i c s o l u t i o n i s induced by an e l e c t r i c c u r r e n t . The s e p a r a t i o n i s accomplished by p l a c i n g i o n s e l e c t i v e 11 2,000 4,000 10,000 20,000 40,000 F E E D PPM FIGURE I Comparison of energy costs for distillation and electrodialysis of salt water. Basis : Average equivalent weight of sait =60 ;btowdown concentration £ = t w o times feed concentration ^distillation to produce pure water; and electrodialysis to produce 0-005-N ( 3 0 0 - p p m ) 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 cu r r e n t flow. The process takes advantage of the a b i l i t y of the membranes to d i s c r i m i n a t e between d i f f e r e n t l y charged ions and the o r i g i n of s e p a r a t i o n l i e s i n t h i s membrane's s e l e c t i v i t y . I f n o n - s e l e c t i v e membranes that are permeable to ions (e.g. cellophane) are used i n e l e c t r o d i a l y s i s processes, e l e c t r o l y t e s can be separated from n o n - e l e c t r o l y t e s . On the other hand, w i t h membranes that are more permeable to u n i v a l e n t ions than to m u l t i v a l e n t i o n s , e l e c t r o d i a l y s i s can be used to simultaneously separate and concentrate u n i v a l e n t ions from s o l u t i o n s c o n t a i n i n g mixtures of u n i - and m u l t i v a l e n t e l e c t r o l y t e s . E l e c t r o d i a l y s i s d i f f e r s fundamentally from the great m a j o r i t y of e l e c t r o c h e m i c a l processes i n that i t does not u t i l i z e the e l e c t r o d e r e a c t i o n s . E l e c t r o d e s do, of course, have to be inc o r p o r a t e d i n an e l e c t r o - d i a l y s i s p l a n t , but they serve the p u r e l y a n c i l l a r y purpose of a p p l y i n g the EMF. They are i n f a c t a necessary e v i l , s i n c e they i n v o l v e a great d e a l of e x t r a c o m p l i c a t i o n i n the design and o p e r a t i o n of the p l a n t . A pioneer book on e l e c t r o d i a l y s i s , e d i t e d by Wilson (1960), d e s c r i b e s the process and the use of i o n exchange membranes i n water d e s a l t i n g . Chapters i n books by Tuwiner (1962), S p i e g l e r (1962, 1966 a ) , Sporn (1966), Popkin (1968) and Kuhn (1971) a l s o d e s c r i b e e l e c t r o d i a l y s i s mainly as a d e s a l i n a t i o n process. Lacey and Loeb (1972) consider v a r i o u s a p p l i c a t i o n s of the process such as c o n c e n t r a t i o n of e l e c t r o l y t e s i n d i l u t e s o l u t i o n s , processing of cheese whey and recovery of c o n s t i t u e n t s from p u l p i n g l i q u o r s . Recently Hwang and Kammermeyer (1975) have reviewed the process. The e l e c t r o d i a l y s i s process uses c e l l s c o n s i s t i n g of many (at l e a s t three) compartments formed a l t e r n a t i v e l y by an anion exchange membrane and a c a t i o n exchange membrane placed between an anode and a cathode as shown i n F i g u r e 2. Demineralized Water Electrode Reaction .•MA A j 1 Cone * t * ? ? ? Raw Water — Feed H 2 O O O Cathode r\ o o c $ 0 centrate Brine Electrode ^ Reaction .9 Products ° 0 2 , c i 2 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 s a l i n e water feed i s pumped through the compartments of the membrane stack and, when a d i r e c t c u r r e n t p o t e n t i a l i s a p p l i e d , c a t i o n s . migrate toward the cathode and anions migrate toward the anode. Cations pass e a s i l y through the cation-permeable membrane and are blocked from f u r t h e r t r a n s f e r by the anion-permeable membrane. S i m i l a r l y , anions have f r e e passage through the anion-permeable membrane and are stopped a t the c a t i o n permeable membrane. As a r e s u l t the adjacent c e l l s become a l t e r - n a t e l y d i l u t i n g and c o n c e n t r a t i n g compartments. 2.3.1. E l e c t r o d i a l y s i s Stack The e s s e n t i a l elements of a membrane stack a r e : (a) a l a r g e number of ion-permeable membranes arranged i n the c o r r e c t order. (b) gaskets and spacers to provide s e a l i n g between compartments and to m a i n t a i n proper d i s t a n c e s between membranes. (c) m a n i fold systems to d i r e c t f e e d , product and waste streams i n t o and out of the compartments without leakage. (d) e l e c t r o d e s and conductors. (e) a p a i r of strong presses to hold the above-mentioned p a r t s i n p l a c e . The m u l t i c e l l e l e c t r o d i a l y s i s stacks are normally assembled i n the same f a s h i o n as a plate-and-frame f i l t e r press (Fi g u r e 3 ) . In a d d i t i o n to the sta c k , which i s the a c t u a l p a r t t h a t e f f e c t s the d e s a l i n a t i o n , e l e c t r o d i a l y s i s p l a n t s c o n s i s t o f : I H y d r a u l i c equipment and a u x i l a r i e s such as p i p e s , pumps, v a l v e s , f i l t e r s , raw water supply, concentrate d i s p o s a l . FIGURE 3 Exploded view of components In an electromembrane stack. 16 I I A power supply w i t h transformers and r e c t i f i e r s and a s s o c i a t e d e l e c t r i c a l and c o n t r o l i n s t r u m e n t a t i o n . 2.3.2. Stack S i z e and Capacity ( i ) C e l l s i z e E l e c t r o d i a l y s i s c e l l dimensions are l i m i t e d o n ly by the a v a i l a b i l i t y of s u i t a b l y s i z e d membrane sheets and the p r a c t i c a b i l i t y of han d l i n g the gaskets and membrane m a t e r i a l s , Weiner and co-workers a t the U n i v e r s i t y of C a l i f o r n i a have developed a 10-foot-long stack to study p o l a r i z a t i o n e f f e c t s (Weiner, et a l . , 1964). I n order to i n c r e a s e d e s a l i n a t i o n and to reduce o p e r a t i n g c o s t s , the area of each c e l l - p a i r should be as l a r g e as p r a c t i c a b l e . One of the s i z e l i m i t a t i o n s i s the f a c t that membrane stacks need, at p e r i o d i c i n t e r v a l s , to be dismantled i n order to remove s o l i d d e p o s i t s formed d u r i n g o p e r a t i o n . I t i s necessary that the stack should be r e l a t i v e l y small i n order to be co n v e n i e n t l y handled. I n a d d i t i o n , l a r g e s i z e membranes which are g e n e r a l l y mechanically weak, tend to t e a r and break more r e a d i l y d u r ing h a n d l i n g . The p r a c t i c e today i s to l i m i t the u n i t s u r f a c e area to a maximum of 2 about 2m (2 by 1 meter), and to design the stacks to comprise a number of r e l a t i v e l y s m a l l sub-units to f a c i l i t a t e h a n d l i n g . The l a r g e s t c e l l i n commercial use up to 1974 was 150 x 50 cm. ( i i ) Number of C e l l P a i r s A c e l l p a i r i s the r e p e a t i n g u n i t i n an e l e c t r o d i a l y s i s stack. I t c o n s i s t s of a d i l u t i n g and a c o n c e n t r a t i n g compartment together w i t h a c a t i o n - and an anion-permeable membrane. The number of c e l l s i n a stack i s mainly l i m i t e d by engineering c o n s i d e r a t i o n s such as: 17 (a) the t o t a l v o l t a g e that can be s a f e l y a p p l i e d , (b) the s i z e of the manifold that can d i s t r i b u t e f l o w evenly i n t o each fl o w channel, (c) the s t r u c t u r a l s t a b i l i t y of the sta c k , (d) the ease of assembly and r e p a i r . Since the f a i l u r e of a s i n g l e membrane can impair stack performance, the number of membranes i n a stack i s l i m i t e d by the l i f e or r e l i a b i l i t y of the membranes and the a n t i c i p a t e d frequency of other s e r v i c e requirements. The requirements f o r st a g i n g a l s o make i t d e s i r a b l e i n some cases to have s e v e r a l s m a l l s t a c k s r a t h e r than one l a r g e one. U s u a l l y s e v e r a l small subassemblies or "packs" c o n t a i n i n g about 50 c e l l p a i r s (100 membranes) are. used. These packs are then used as the b u i l d i n g b l o c k s f o r a p l a n t of the. re q u i r e d s i z e . As many as 10 of these packs can be placed i n t o a s i n g l e press. A s i n g l e s et of e l e c t r o d e s may be used f o r the e n t i r e assembly, or s e v e r a l e l e c t r o d e s may be used to provide e l e c t r i c a l s t a g i n g . ( i i i ) Stack Capacity The d e s i r e d product s a l i n i t y i s achieved by passing the feed l i q u i d through s e v e r a l stacks i n s e r i e s , w h i l e d e s i r e d p l a n t throughput i s obtained by op e r a t i n g s e v e r a l e l e c t r o d i a l y s i s paths i n p a r a l l e l . The l a r g e s t stacks i n o p e r a t i o n i n 1970 handled d i l u t e flows of about 250,000 gal/day. For l a r g e r p r o d u c t i o n p a r a l l e l arrangement of these s t a c k s was planned, r a t h e r than scale-up of s i n g l e s t a c k s . The l a r g e s t e l e c t r o d i a l y s i s d e s a l t i n g p l a n t i n the world i s i n Benghazi, L i b y a , con- s t r u c t e d by W i l l i a m Boby and Company, England a f t e r 1972. I t has a prod u c t i o n c a p a c i t y of 5 x 10^ gal/day as shown i n Table IV. The p l a n t has 16 p a r a l l e l t r a i n s each of 2 stacks i n s e r i e s , each stack w i t h a c a p a c i t y of about 310,000 gal/day. 18 Table IV T e c h n i c a l d e t a i l s of Benghazi (Libya) and S i e s t a Key ( F l o r i d a ) E l e c t r o d i a l y s i s P l a n t s * Benghazi S i e s t a Key Stage 1 Stage 2 3 Rated output, m /h net 800 188 310 Waste water, % of output 8 17 Raw water, ppm t o t a l d i s s o l v e d s o l i d s 2,000 1,300 Number of p a r a l l e l t r a i n s 16 7 12 S t a c k s / t r a i n 2 2 T o t a l number of c e l l p a i r s 9,600 4,200 7,200 2 T o t a l membrane area, m 15,000 3,900 6,700 * From S o l t , Chap. 12 i n Kuhn (ed.), " I n d u s t r i a l E l e c t r o c h e m i c a l Processes" 19 2.4. Membrane Technology An Ion-exchange membrane i s an i o n exchanger i n sheet form and i t s p h y s i c a l chemistry i s to a l a r g e extent a l s o the p h y s i c a l chemistry of i o n exchange r e s i n s . Ion exchange r e s i n s c o n s i s t of two p r i n c i p a l p a r t s : a s t r u c t u r a l p o r t i o n or a backbone (a polymer matrix) and a f u n c t i o n a l p o r t i o n or an i o n - a c t i v e group. The s y n t h e s i s of an organic ion-exchanger i n v o l v e s the chemical s u b s t i t u t i o n of an i o n - a c t i v e group and a p o l y m e r i z a t i o n r e a c t i o n . The s u b s t i t u t i o n may precede the p o l y m e r i z a t i o n or v i c e - v e r s a . Most i o n exchangers c u r r e n t l y i n l a r g e s c a l e use are based on s y n t h e t i c r e s i n s , u s u a l l y p o l y s t y r e n e [RO - (CH^ - C H ) n ~ 0 R ] copolymerized w i t h d i v i n y l b e n z e n e [C^H^ ( C l ^ C l ^ ^ ] t o provide the r e q u i s i t e amount of cross l i n k i n g . The f u n c t i o n a l group may be a c i d i c or b a s i c w i t h d i f f e r e n t degree of s t r e n g t h of a c i d i t y or b a s i c i t y . S t r o n g l y - a c i d ( c a t i o n i c ) r e s i n s g e n e r a l l y c o n t a i n bound s u l f o n i c a c i d groups (-SO^OH), w h i l e s t r o n g l y b a s i c r e s i n s ( a n i o n i c ) c o n t a i n quaternary ammonium groups f i x e d to a p o l y s t y r e n e - d i v i n y l b e n z e n e m a t r i x (Pepper, et a l , , 1953). Some ion-exchange membranes are made by mixing ion-exchange r e s i n s w i t h a polymeric binder and c a s t i n g or ex t r u d i n g a sheet from the mixture, w h i l e others are manufactured by methods th a t e x a c t l y p a r a l l e l the pro d u c t i o n of ion-exchange r e s i n s - i . e . styrene and di v i n y l b e n z e n e are copolymerized i n sheet form, and the r e s u l t i n g s t r u c t u r e i s then c h e m i c a l l y t r e a t e d to giv e the sheet ion-exchange p r o p e r t i e s . The d e t a i l s of methods f o r making ion-exchange membranes have been reviewed by Wilson (1960), F r i e d l a n d e r and 20 R i c k l e s (1966), Lacey (1972), C h i o l l e , et a l . (1973) and L a s k o r i n , et a l , (1973). An e x c e l l e n t summary of p r e p a r a t i v e methods found i n the U.S. Patent l i t e r a t u r e i s given by McDermott (1972). An i n d u s t r i a l l y u s e f u l membrane should have the f o l l o w i n g p r o p e r t i e s : 1. High i o n s e l e c t i v i t y - cation-permeable membranes should exclude the passage of anions, and v i c e - v e r s a . 2. Low e l e c t r i c a l r e s i s t a n c e - p e r m i t t i n g a f r e e f l o w of counter- ions through the membranes at low energy requirements. 3. High mechanical s t r e n g t h - toughness, f l e x i b i l i t y , and crack r e s i s t a n c e are important, not only to the s e r v i c e l i f e of the membrane, but a l s o to c o n s t r u c t i o n , s e r v i c i n g and, t h e r e f o r e , the c o s t of e l e c t r o d i a l y s i s p l a n t s . 4. High chemical s t a b i l i t y - r e s i s t s h y d r o l y t i c , o x i d a t i v e , and other forms of degradation. 5. Re s i s t a n c e toward f o u l i n g by s c a l e d e p o s i t s and plugging by l a r g e p o l y v a l e n t organic ions present i n the s o l u t i o n s to be t r e a t e d . The p r o p e r t i e s of a number of commercially a v a i l a b l e ion-exchange membranes have been tabulated by Shaffer and Mintz (1966) and Lacey and Loeb (1972). A b i b l i o g r a p h y on membrane technology, p e r t a i n i n g to s a l i n e water d e s a l i n a t i o n and ranging from 1908 to 1962 has been compiled by the O f f i c e of S a l i n e Water (Mangan, et a l . , 1963). A comprehensive review of the p h y s i c a l chemistry of i o n - s e l e c t i v e membranes has been given by Malherbe and Mandersloot (1960). 21 2.4.1. Membrane S e l e c t i v i t y One of the b a s i c c h a r a c t e r i s t i c s of an ion-exchange membrane i s the s e l e c t i v i t y , which i s def i n e d as the a b i l i t y of the membrane to d i s t i n g u i s h between o p p o s i t e l y charged species l e a d i n g to the p r e f e r e n t i a l uptake of counter-ions and e x c l u s i o n of co-ions. Counter-ions and co-ions are the mobile ions possessing charges opposite and s i m i l a r i n s i g n r e s p e c t i v e l y to the membrane f i x e d i o n s . When a c a t i o n - s e l e c t i v e membrane i s immersed i n an e l e c t r o l y t e s o l u t i o n the c a t i o n s i n s o l u t i o n w i l l enter i n t o the r e s i n m a t r i x and re p l a c e the c a t i o n s present, but anions are prevented from e n t e r i n g the mat r i x by the r e p u l s i o n of the anions a f f i x e d to the r e s i n . The opposite phenomena takes p l a c e when an anion s e l e c t i v e membrane i s immersed i n an e l e c t r o l y t e s o l u t i o n ; the f i x e d c a t i o n i c groups permit i n t r u s i o n and exchange of anions from an e x t e r n a l source, but exclude c a t i o n s . This type of e x c l u s i o n i s c a l l e d Donnan e x c l u s i o n . ( i ) P e r m s e l e c t i v i t y S e l e c t i v i t y i s u s u a l l y r e p o r t e d i n terms of p e r m s e l e c t i v i t y , P, which i s the i n c r e a s e i n t r a n s p o r t number over the v a l u e i n f r e e s o l u t i o n due to the presence of the membrane and i t i s given by: where: t , t = t r a n s p o r t numbers of counter-ions i n membrane and i n f r e e s o l u t i o n r e s p e c t i v e l y ( t - t ) = i n c r e a s e i n t r a n s p o r t number over the v a l u e i n f r e e s o l u t i o n P ~ t - 1 - J: t (1) 22 (1-t) = the maximum p o s s i b l e i n c r e a s e or the in c r e a s e that would be observed i n the case of an i d e a l l y s e l e c t i v e membrane, Both p and t are f u n c t i o n s of c o n c e n t r a t i o n . They decrease as the e x t e r n a l e l e c t r o l y t e c o n c e n t r a t i o n i n c r e a s e s as shown i n F i g u r e 4. ( i i ) Donnan E x c l u s i o n According to the Donnan p r i n c i p l e the chemical p o t e n t i a l of the s a l t i n the s o l u t i o n e x t e r n a l to the membrane must be equal to the chemical p o t e n t i a l of the s a l t i n s i d e the membrane, i . e . 2 - -2 RT I n a + = vAp + RT I n a^ (2) where: a + , a + are the i o n i c a c t i v i t i e s i n f r e e s o l u t i o n and i n membrane phases r e s p e c t i v e l y v i s the p a r t i a l molar volume, cm /mole Ap i s the d i f f e r e n c e i n i n t e r n a l pressure between the mem- brane and the s o l u t i o n phase c a l l e d the " s w e l l i n g pressure" of the membrane The pressure-volume term a r i s e s from the f r e e energy change due to the d i f f e r e n c e between the osmotic pressure of the s o l u t i o n s i n s i d e and o u t s i d e the membrane (Wilson, 1960). I n the absence of l a r g e pressure d i f f e r e n c e s between the i n t e r i o r and the e x t e r n a l phase, the Donnan p r i n c i p l e r e q u i r e s t h a t : ( a + ) . (a_) = ( a + ) . (a_) (3) where: FIGURE 4 Dependence of counterion transport numbers and permselectivity upon external concentration. (Wilson , I960 ). 24 a + are the i o n i c a c t i v i t i e s v's are the s t o i c h i o m e t r i c c o e f f i c i e n t s f o r e l e c t r o l y t e M ,X v+ v- and the barred symbols r e f e r to the membrane phase. For u n i - u n i v a l e n t e l e c t r o l y t e , v+ = v- = 1.0, and Eq.(3) reduces t o : where y + i s the mean i o n i c a c t i v i t y c o e f f i c i e n t , d efined g e n e r a l l y as Y+ - Y+ + • Y^ • (5) where v = v + + v-; s u b s c r i p t s j and k r e f e r to c o - i o n and co u n t e r - i o n r e s - p e c t i v e l y . Since both the s o l u t i o n and the membrane must be e l e c t r i c a l l y n e u t r a l , t h i s r e q u i r e s t h a t : I n membrane; C, = C. + C (6) k j x In s o l u t i o n ; C = C = C (7) k J where C i s the f i x e d i o n c o n c e n t r a t i o n i n the membrane, x S u b s t i t u t e Eqs.(6) and (7) i n t o (4) and r e p l a c e a c t i v i t i e s by co n c e n t r a t i o n s : C. C. = C. (C. + C ) (8) J k 3 3 x Assume C. + C = C then 3 x x f 2 c - r ( 9 ) J x Eq.(9) shows how the s e l e c t i v i t y of a membrane i s a f f e c t e d i n opposite d i r e c t i o n s by the e x t e r n a l s a l t c o n c e n t r a t i o n , C, and the f i x e d - i o n s con- c e n t r a t i o n i n the membrane, C . The higher the c o n c e n t r a t i o n of f i x e d i o n s , x the greater the s e l e c t i v i t y (C\. -> o as C*x ->• ») w h i l e (C. C as C ->• C^) . 25 In a t y p i c a l e l e c t r o d i a l y s i s system, the c o n c e n t r a t i o n o u t s i d e the membrane may range from 0.001 to 0.1 m, w h i l e i t i s u s u a l l y p o s s i b l e to make the m o l a l i t y i n s i d e the membrane f a l l i n the range 1 to 5m. Accord- -7 - -2 i n g l y Eq.(9) guarantees that 2 x 10 < C.. < 10 (Shaffer and M i n t z , 1966). From Eq.(9) i t i s c l e a r t h a t the cur r e n t c a r r i e d by some ions i n the system can be made very s m a l l . I n the extreme case of i d e a l l y s e l e c t i v e membrane, the co-ions are completely excluded and the whole c u r r e n t i s c a r r i e d by the counter-ions alone through the membrane. F i g u r e 5a shows a negative membrane (cation-exchanger) i n sodium c h l o r i d e s o l u t i o n and i t i l l u s t r a t e s the b a s i c o p e r a t i n g p r i n c i p l e i n v o l v e d i n a l l e l e c t r o d i a l y s i s processes i . e . on the l e f t s i d e the e l e c t r i c current c a r r i e s sodium ions to the membrane at the r a t e t + i / F and these ions disappear across the membrane a t the r a t e t + i / F where F i s Faradays constant and i i s the curr e n t d e n s i t y . The net r e s u l t of the passage of 1 Faraday i s the removal of t + - t = 0.6 mole of s a l t from the s o l u t i o n immediately adjacent to the l e f t h a n d face of the membrane and the appearance of a l i k e q u a n t i t y ( t - t =0.6) i n the s o l u t i o n adjacent to the righthand face. (For sodium c h l o r i d e , t - 0.4 and t = 0.6). 2.4.2. Membrane P o l a r i z a t i o n C oncentration p o l a r i z a t i o n a t the surfaces of the ion-exchange mem- branes l i m i t s the cu r r e n t d e n s i t y and the pr o d u c t i o n r a t e i n an e l e c t r o - d i a l y s i s u n i t . P o l a r i z a t i o n i s a n a t u r a l r e s u l t of the s e p a r a t i o n mechanism and i t i n c r e a s e s as the s e l e c t i v i t y of the membrane i n c r e a s e s ; there i s no way to prevent c o n c e n t r a t i o n p o l a r i z a t i o n other than by stopping the cur r e n t f l o w . Due to the d i f f e r e n c e s i n the t r a n s p o r t numbers of ions i n the s o l u t i o n s and i n the ion-exchange membranes two boundary l a y e r s w i t h Ha CI it+=l*0 it-=0-6l it+=0-39 £ > = - L - 0 i t -=0® it-=06l FIGURE 5a Ion transport across a permselective membrane , showing current i and transport number t. • r w v , c m c m FIGURE 5b Concentration profile across a permselective membrane in an electrodialysis stack . 27 opposite c o n c e n t r a t i o n g r a d i e n t s are formed a t the opposite s i d e s of each membrane (Figure 5b). In a w e l l - s t i r r e d system the f i l m model (Nernst l a y e r model) can be adopted and.the c o n c e n t r a t i o n gradient on the d i l u t e s i d e approximated by i C — C D m where 6 C_, C* are the c o n c e n t r a t i o n of the b u l k s o l u t i o n and the D m co n c e n t r a t i o n a t the membrane surface r e s p e c t i v e l y 6 i s the Nernst f i l m t h i c k n e s s I n a steady s t a t e o p e r a t i o n , the r a t e of a r r i v a l of s a l t a t the membrane-solution i n t e r f a c e must equal the r a t e of removal of s a l t i . e . a t a cation-permeable membrane we have: - » f . <»> where D = l a t e r a l d i f f u s i o n c o e f f i c i e n t across boundary l a y e r AC = C - c' D m z = valence In the l i m i t i n g case when C^ -> 0, AC -> C^; the corresponding l i m i t i n g c u r r e n t d e n s i t y , i ^ ^ f i s given by i = Z F D C D 1 him = 2 — j (11) P o l a r i z a t i o n i s a r e s u l t of mass t r a n s f e r l i m i t a t i o n s adjacent to the membrane-solution i n t e r f a c e s . I t occurs when Ion d e p l e t i o n by e l e c t r o - d i a l y s i s exceeds the r a t e of i o n d i f f u s i o n i n t o the boundary l a y e r from the bulk s o l u t i o n , and i t becomes a p p r e c i a b l e when the b u l k s o l u t i o n c o n c e n t r a t i o n Cp, i s low and the d i f f u s i o n l a y e r i s t h i c k so th a t the c o n c e n t r a t i o n gradient i s low. 28 ( i ) Consequences of P o l a r i z a t i o n In p r a c t i c e a c o n s i d e r a b l y lower cu r r e n t d e n s i t y than i , . i s used. l.im t As C m approaches zero the r e s i s t a n c e i n c r e a s e s and e f f i c i e n c y drops tremendously. The c o n c e n t r a t i o n of H + and OH ions i n an aqueous s o l u t i o n i s about 10 ^ m o l e / l i t e r , and the m o b i l i t i e s of these ions are 3 to 5 times greater than the m o b i l i t i e s of the other common i o n s . As soon as c' m approaches 5 x 10 m o l e / l i t e r , an a p p r e c i a b l e amount of curr e n t w i l l be c a r r i e d by hydrogen and hydroxyl i o n s . This r e s u l t s i n the f o l l o w i n g e f f e c t s : (1) An enormous i n c r e a s e i n the power consumption due t o : (a) More c u r r e n t f l o w i n g per u n i t of s a l t removed e.g., i f (u^ a+) (C) = (̂ jj"1") 10 ^ where u i s the i o n i c m o b i l i t y then N a + and H + ions w i l l t r a n s f e r a t equal r a t e s . In t h i s case even an i d e a l membrane would f u n c t i o n w i t h an e f f e c t i v e c u r r e n t e f f i c i e n c y , n̂ ., of only 50 per cent, because H t r a n s f e r does not c o n t r i b u t e to d e s a l t i n g . (b) More energy d i s s i p a t i o n i n the boundary l a y e r r e s u l t i n g from the poor c o n d u c t i v i t y of n e a r l y pure water (kf^o ~ —8 —1 -1 4 x 10 ohm cm ) . (c) The energy r e q u i r e d to i o n i z e the water molecules ( d i s s o c i a t i o n energy of water s p l i t t i n g ) . (d) An in c r e a s e of the back emf's due to p o l a r i z a t i o n l a y e r s . (2) D e v i a t i o n from n e u t r a l i t y i n the p o l a r i z e d l a y e r or the a l t e r a t i o n of the pH's of the process streams. A c i d i t y can develop on the cathode s i d e of cation-permeable membrane and a l k a l i n i t y on the anode s i d e of anion-permeable membrane. As most b r a c k i s h waters are n e a r l y s a t u r a t e d 29 w i t h scale-forming m a t e r i a l s , any t r a n s f e r of H' or OH i n t o or out of a l o c a l r e g i o n w i l l g e n e r a l l y cause s e r i o u s s c a l e and p r e c i p i t a t i o n problems -4 e.g. Mg(OH) 9 p r e c i p i t a t i o n may be expected at pH > 10 ( i . e . C_. - - 10 ). ^ OH (3) P o l a r i z a t i o n changes the e l e c t r o c h e m i c a l p r o p e r t i e s of the mem- branes and may r e s u l t i n membrane d e t e r i o r a t i o n i f they are not s t a b l e to wide pH v a r i a t i o n . (Wilson, 1960). Anion-permeable membranes are most a f f e c t e d by t h i s . I n p r a c t i c e , p o l a r i z a t i o n i s h e l d to reasonable v a l u e s by c o n t r o l l i n g the r a t i o of c u r r e n t d e n s i t y to the n o r m a l i t y of the d i l u t e stream, i/CD» and by designing the system to make 6 as s m a l l as p o s s i b l e . I t should be noted that the p o l a r i z a t i o n l i m i t a t i o n r a t h e r than the r e s u l t s of economic o p t i m i z a t i o n g e n e r a l l y c o n t r o l s the o p e r a t i n g c u r r e n t d e n s i t y i n p r a c t i c a l e l e c t r o d i a l y s i s i n s t a l l a t i o n s . I n any p r a c t i c a l apparatus, the p i c t u r e i s f a r more complex than t h i s . Where there are c e l l s fed i n p a r a l l e l from a m a n i f o l d , i t i s impossible to have e x a c t l y the same l i q u i d v e l o c i t y i n each c e l l . Cooke (1967) and S o l t (1967) have drawn a t t e n t i o n to the f a c t t h a t , even w i t h i n an i n d i v i d u a l c e l l i n the most i d e a l s i t u a t i o n , the l o c a l c o n d i t i o n s of mass t r a n s f e r are not uniform over the whole area through which c u r r e n t i s passing. ( i i ) P o l a r i z a t i o n C o n t r o l P o l a r i z a t i o n can not be avoided completely, but i t can be held to reasonable v a l u e s by c o n t r o l l i n g the r a t i o of c u r r e n t d e n s i t y to the n o r m a l i t y of the d i l u t e stream, i / C ^ and by making the t h i c k n e s s of the d i f f u s i o n l a y e r , 6, as s m a l l as p o s s i b l e . There i s l i t t l e that can be done about the bulk c o n c e n t r a t i o n when the d i l u t e d stream i s the r e q u i r e d product. However, 6 can be reduced by high 30 s o l u t i o n f l o w v e l o c i t y and the i n t r o d u c t i o n of turbulence promoters such as spacers or screens that cause l o c a l eddying or turbulence (Hoek, 1956). Both of these measures add to the power consumed i n c i r c u l a t i n g the process f l u i d s , but they reduce the stack power consumption and a l l o w o p e r a t i o n at higher c u r r e n t d e n s i t i e s w i t h an acceptable l e v e l of p o l a r i z a t i o n . An a l t e r n a t i v e method of reducing p o l a r i z a t i o n was reported by S p i e g l e r (1963) who reversed the c u r r e n t f o r a f r a c t i o n of a second a f t e r each s e v e r a l seconds of o p e r a t i o n . P a r t i a l c o n f i r m a t i o n of the e f f i c a c y of t h i s technique was obtained i n the Webster, South Dakota, demonstrative p l a n t (OSW, 1964 a ) . 2.4.3. S c a l i n g and F o u l i n g of Membranes Concentration p o l a r i z a t i o n i s o f t e n l i n k e d w i t h other problems i n p r a c t i c e such as membranes s c a l i n g and f o u l i n g . An i n c r e a s e i n the pH of the s o l u t i o n due to p o l a r i z a t i o n promotes the formation of a l k a l i n e p r e c i p i t a t e s , such as c a l c i u m carbonate and magnesium hydroxide on the membrane s u r f a c e . On the d i l u t e - s t r e a m s i d e of the anion-permeable membrane the d e p l e t i o n of the more mobile anions encourages the d e p o s i t i o n of l a r g e polyanions onto the membrane s u r f a c e . Polyanions commonly found i n b r a c k i s h waters are humic a c i d s , s i l i c a c i d s , phenols, p r o t e i n s and polyphosphates (OSW, 1963). S c a l i n g of membranes causes a d d i t i o n a l e l e c t r i c a l and f l o w r e s i s t a n c e , a decrease i n e l e c t r o d i a l y s i s e f f i c i e n c y and an i n c r e a s e i n pumping power requirements. Scale d e p o s i t s can be found w i t h i n the membrane g e l s t r u c t u r e , which i s known as f o u l i n g and r e s u l t s i n r a p i d embrittlement and p h y s i c a l d e t e r i o r a t i o n of membranes. Several methods have been attempted to c o n t r o l membrane s c a l i n g and f o u l i n g and can be summarized i n the f o l l o w i n g : 31 ( i ) Current Density r e d u c t i o n Scale formation i s p a r t i c u l a r l y pronounced at h i g h current d e n s i t i e s . Reducing the c u r r e n t d e n s i t y may reduce s c a l i n g . ( i i ) Pre-treatment f o r c a t i o n removal Pre-treatment by cation-exchange r e q u i r e s a l l the feed to be passed through a cation-exchange bed, i n order to remove calcium and magnesium. Cations may be p a r t i a l l y removed by a p r e l i m i n a r y lime or lime-soda t r e a t - ment f o l l o w e d by f i l t e r a t i o n . Such pre-treatments add c o n s i d e r a b l y to o p e r a t i n g c o s t s and would be u n j u s t i f i a b l e economically except f o r s p e c i f i c a p p l i c a t i o n s . ( i i i ) A c i d Treatment of Concentrate A c i d i f i c a t i o n to a pH l e v e l low enough to prevent p r e c i p i t a t i o n i s commonly p r a c t i s e d , but even t h i s method may not completely prevent s c a l e formation at the surfaces of or w i t h i n the membranes. The a d d i t i o n of s u l p h u r i c a c i d to keep pH below 5.0 f o r p r e v e n t i o n of Ca C0^ s c a l i n g was reported by Watanabe, et a l . (1972) and Asawa, et a l . (1973). Although a c i d i f i c a t i o n adds to the d i r e c t cost of d e s a l t i n g , the added cost was considered to be p a r t l y o f f s e t by savings i n energy consump- t i o n due to a lower o v e r a l l e l e c t r i c a l r e s i s t a n c e . (Furukawa, 1968). ( i v ) Reversed P o l a r i t y P e r i o d i c r e v e r s a l of e l e c t r o d e p o l a r i t y has been proposed to d i s s o l v e s c a l e and c o n t r o l membrane f o u l i n g (Matz, 1965). wherever the membranes were suspected of producing a s i e v e or f i l t e r - i n g e f f e c t , r a t h e r than a c t i n g as a pure i o n - t r a n s f e r medium, cur r e n t r e v e r s a l was p r a c t i c e d on a p e r i o d i c b a s i s to discharge e l e c t r o c h e m i c a l l y entrapped c o l l o i d s and/or macromolecules so as to r e s t o r e the o r i g i n a l 32 membrane p r o p e r t i e s . Although the e f f e c t i v e n e s s of t h i s procedure depends on the type of membrane and the nature of the contaminants that f o u l i t , the r e v e r s a l of hydrogen and hydroxyl i o n t r a n s f e r and the accompanying i n t e r - change of pH e f f e c t s a t the membrane sur f a c e i s probably the s i g n i f i c a n t d e f o u l i n g f a c t o r . (v) P u l s a t i n g Current P u l s a t i n g c u r r e n t i s sometimes used when reversed p o l a r i t y i s not able to prevent r a p i d accumulation of s c a l e . I n t h i s method very b r i e f pulses of re v e r s e c u r r e n t are a p p l i e d to produce c u r r e n t r e v e r s a l or curre n t i n t e r r u p t i o n (Matz, et a l . , 1962). T h i s technique tends to a l l e v i a t e s c a l i n g problems and a l s o apparently improves the e f f i c i e n c y of an ope r a t i n g e l e c t r o d i a l y s i s stack ( I s r a e l , 1961). 2.5. Process E f f i c i e n c y 2.5.1. P r i n c i p a l Energy Sinks The a c t u a l energy r e q u i r e d to operate an e l e c t r o d i a l y s i s process exceeds that t h e o r e t i c a l l y r e q u i r e d f o r the f o l l o w i n g reasons: ( i ) Power l o s s e s a t t r i b u t a b l e to r e s i s t a n c e i . e . the power t h a t w i l l be d i s s i p a t e d by the J o u l e heating of the membranes and the e l e c t r o l y t e s o l u t i o n . ( i i ) Power l o s s e s a t t r i b u t a b l e to c o n c e n t r a t i o n p o l a r i z a t i o n i . e . the power r e q u i r e d to overcome the o v e r p o t e n t i a l s t h a t e x i s t at the membrane-solution i n t e r f a c e s . ( i i i ) Power l o s s e s a t t r i b u t a b l e to e l e c t r o d e r e a c t i o n and the IR drop i n the r i n s e s o l u t i o n streams i n the e l e c t r o d e s compartments. 33 ( i v ) Low c u r r e n t e f f i c i e n c y . The o v e r a l l e f f i c i e n c y of an e l e c t r o d i a l y s i s s t a c k , n, can be ex- pressed as a product of four p r i n c i p a l e f f i c i e n c i e s : (a) Three v o l t a g e terms: n a s s o c i a t e d w i t h the t o t a l r e s i s t a n c e , T) a s s o c i a t e d w i t h the c o n c e n t r a t i o n p o l a r i z a t i o n e f f e c t s and n a s s o c i a t e d c e w i t h the e l e c t r o d e r e a c t i o n s . (b) The cur r e n t e f f i c i e n c y , n^ i . e . n = n n n n T (12) R e e l where n i s p r i m a r i l y a f u n c t i o n of the stack design (e.g. number of c e l l p a i r s ) , n c depends mainly on the ope r a t i n g c o n d i t i o n s (e.g. cur r e n t d e n s i t y ) , w h i l e n depends on both design f a c t o r s such as c e l l spacing, membrane type R and t h i c k n e s s and on ope r a t i n g c o n d i t i o n s , (a) Voltage Terms The major i n e f f i c i e n c y i n stack o p e r a t i o n i s a s s o c i a t e d w i t h the f i r s t and second terms i n Eq. (12) , Tl^ n c« These terms are considered i n Chapter 3. In multiple-membrane stacks used i n e l e c t r o d i a l y s i s , the energy con- sumed i n e l e c t r o d e processes, n e» does not c o n t r i b u t e to the d e s i r e d s e p a r a t i o n and hence the r e l a t i v e e f f e c t of t h i s energy consumption can be reduced c o n s i d e r a b l y by i n c r e a s i n g the number of membrane c e l l p a i r s used i n s e r i e s w i t h a given p a i r of e l e c t r o d e s . The e l e c t r o d e r e a c t i o n s and the p o l a r i z a t i o n e f f e c t s are considered b r i e f l y i n Appendix A. The t o t a l e x t e r n a l v o l t a g e , Ê ,, that i s needed to operate a p r a c t i c a l e l e c t r o d i a l y s i s stack i s the sum of 3 p r i n c i p a l p o t e n t i a l drops: E T = E e + E R + E c (13) 34 where E g = p o t e n t i a l drops a s s o c i a t e d w i t h the e l e c t r o d e s and e l e c t r o d e streams ( i n c l u d i n g e l e c t r o d e p o t e n t i a l and o v e r p o t e n t i a l s ) = the IR drops i n the s o l u t i o n s and membranes E c = c o n c e n t r a t i o n p o t e n t i a l across the membranes and at the mem- br a n e - s o l u t i o n i n t e r f a c e s . A v o l t a g e e f f i c i e n c y term a s s o c i a t e d w i t h the e l e c t r o d e r e a c t i o n s , n , can be defined f o r the stack as a whole by e E E + E„ (e„ + e ) . e x T J E T where e^, e £ are d e f i n e d i n a same way as E^ and E c but they r e f e r to one c e l l p a i r i n s t e a d of the whole stack. A c e l l p a i r c o n s i s t s of two membranes and t h e i r two a s s o c i a t e d s o l u t i o n passages. From Eq.(14), i t i s obvious that whatever the i n d i v i d u a l v a l u e s of e^ and e £ f o r the design s e l e c t e d , w i l l approach 1.0 as the number of c e l l p a i r s , j , i s i n c r e a s e d . U s u a l l y the energy consumed a t an e l e c t r o d e i s of the same order as that consumed by one c e l l p a i r . B e l f o r t , et a l . (1968) showed i n t h e i r s t u d i e s of two e l e c t r o d i a l y s i s p l a n t s : Webster, South Dakota and Buckeye, A r i z , that the e l e c t r o d e p o l a r i z a t i o n i s a minor f a c t o r , making up l e s s than h a l f per cent of the t o t a l p o t e n t i a l drop, (b) Current E f f i c i e n c y , n^ In any p r a c t i c a l e l e c t r o d i a l y s i s system, i t i s g e n e r a l l y found that the amount of c u r r e n t r e q u i r e d to produce a given amount of d e s a l t i n g exceeds the t h e o r e t i c a l amount c a l c u l a t e d on the b a s i s of c u r r e n t flow through i d e a l membranes. 35 The cu r r e n t e f f i c i e n c y , n , i s defined as I F "w (15) where r\„ i s the Faraday e f f i c i e n c y , which i s defined as the r a t i o of the r s a l t t r a n s f e r r e d to the t h e o r e t i c a l current requirement _ (equivalent of s a l t transported) ^F (Faraday of e l e c t r i c i t y passed)(number of membrane p a i r s employed) (16) n i s the r e s u l t of water t r a n s p o r t through the membranes. When the w feed i s of low s a l i n i t y , as w i t h b r a c k i s h water, the e f f e c t of water t r a n s f e r i s u s u a l l y s m a l l and the water t r a n s f e r term, riw» can be assumed to be u n i t y . A more d e t a i l e d d i s c u s s i o n of the current e f f i c i e n c y i s considered i n Appendix B. 2.6. V a r i a n t s of E l e c t r o d i a l y s i s S everal v a r i a n t s of the e l e c t r o d i a l y s i s process have been developed to overcome some of the problems t h a t have been encountered w i t h c o n v e n t i o n a l e l e c t r o d i a l y s i s . For i n s t a n c e , the a n i o n - s e l e c t i v e membranes used i n conventional systems are p a r t i c u l a r l y troublesome because of v u l n e r a b i l i t y to f o u l i n g and s c a l i n g , so attempts have been made to r e p l a c e them by e i t h e r n e u t r a l ( n o n s e l e c t i v e ) membranes ( i n t r a n s p o r t d e p l e t i o n ) or by cation-exchange membranes ( i n e l e c t r o g r a v i t a t i o n a l d e m i n e r a l i z a t i o n ) . 2.6.1. Transport D e p l e t i o n The t r a n s p o r t d e p l e t i o n process i s a v a r i a n t of e l e c t r o d i a l y s i s i n which an a r r a y of a l t e r n a t e c a t i o n exchange and n o n s e l e c t i v e membranes i s used as shown i n Fi g u r e 6. This concept was f i r s t suggested by Deming and 36 Concentrated Demineralized Stream Stream A A N N Na - • N a ->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 d i r e c t e l e c t r i c c urrent i s passed, depleted and concentrated boundary l a y e r s form at the two s i d e s of the c a t i o n exchange membranes, but not at the n o n s e l e c t i v e n e u t r a l membranes. The l a t t e r serve only to separate the depleted and concentrated boundary l a y e r s from each other and, i n doing so, create a l t e r n a t e d i l u t i n g and c o n c e n t r a t i n g compartments. N e u t r a l membranes have l i t t l e tendency to p o l a r i z e or f o u l , thus t h e i r use trades o f f the chemical and mechanical disadvantages of anion-exchange membranes f o r higher power c o s t s , e.g. f o r s o l u t i o n s of K CI (t = 0.5 = t _ ) , passage of one Faraday s h i f t s 1 mole of s a l t from d i l u a t e to concentrate, when a l t e r n a t i n g i d e a l l y s e l e c t i v e c a t i o n - and anion-exchange membranes are used i n c o n v e n t i o n a l e l e c t r o d i a l y s i s , w h i l e only % mole i s s h i f t e d i n t r a n s p o r t d e p l e t i o n . Therefore, to achieve the same pr o d u c t i o n r a t e i n the t r a n s p o r t d e p l e t i o n stacks as i n the b a s i c e l e c t r o d i a l y s i s s t a c k , twice the c u r r e n t i s needed. The v o l t a g e i s then a l s o n e a r l y t w i c e , hence the power c o s t s almost quadruple. However, by e l i m i n a t i n g the anion membranes the c a p i t a l c ost drops. I t appears that the power consumption i s not the d e c i s i v e f a c t o r i n e l e c t r o d i a l y s i s s i n c e the major d e s a l i n a t i o n c o s t s do not r e s i d e i n the energy requirements but i n the investment co s t s f o r equipment or the replacement co s t s f o r the membranes (Shaffer and M i n t z , 1966). The economics of the t r a n s p o r t d e p l e t i o n process have been s t u d i e d by Huffman (1969) and Redman (1971). Lacey estimated a cost r e d u c t i o n of 8% compared w i t h the normal e l e c t r o d i a l y s i s . The process development continues i n the b e l i e f that the s i m p l i c i t y of the p l a n t and i t s freedom from t r o u b l e i n the f i e l d w i l l out-balance the increased power c o s t ( S o l t , 1 9 7 1 ) . 38 2.6.2. E l e c t r o g r a v i t a t i o n a l D e m i n e r a l i z a t i o n The term " e l e c t r o g r a v i t a t i o n " was f i r s t suggested by Murphy (1950). E l e c t r o g r a v i t a t i o n a l d e m i n e r a l i z a t i o n may be achieved i n a c e l l i n which o n l y c a t i o n exchange membranes are used, as shown i n F i g u r e 7. When a d i r e c t e l e c t r i c c urrent i s passed depleted and concentrated boundary l a y e r s form at each s i d e of the membrane, but the s o l u t i o n i n the depleted boundary l a y e r r i s e s and c o l l e c t s a t the top of the depleted compartment because i t s d e n s i t y i s lower than that of the b u l k of the s o l u t i o n . S i m i l a r l y the s o l u t i o n i n the concentrated boundary l a y e r s l i d e s downward and c o l l e c t s at the bottom of the enriched compartment. A d d i t i o n a l d e n s i t y d i f f e r e n c e s are obtained because the depleted s o l u t i o n has higher e l e c t r i c a l r e s i s t a n c e than the b u l k , and gets h o t t e r . The process i s extremely simple to c o n s t r u c t and operate. The mem- branes may be placed l o o s e l y or simply hung i n a tank f i t t e d w i t h e l e c t r o d e s ; edge s e a l s on the compartments are not necessary; i m p e r f e c t i o n s i n the membranes, even h o l e s , w i l l not s e r i o u s l y a f f e c t performance. Current leakage through holes or around edges may waste power, but w i l l not i n t e r f e r e w i t h the o p e r a t i o n of the system. Very high c o n c e n t r a t i o n g r a d i e n t s can be achieved i n the process. Mintz and Lang (1965) have shown that c o n c e n t r a t i o n g r a d i e n t s of greater than 100 to 1 can be obtained i n c e l l s o n l y 6 i n . high. Studies by Lang and Huffman (1969) showed th a t e l e c t r o g r a v i t a t i o n i s not competetive w i t h other processes f o r d e m i n e r a l i z i n g s a l i n e water but may be of i n t e r e s t f o r some i n d u s t r i a l s e p a r a t i o n s . 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. C y c l i c Processes 2.7.1. E l e c t r o s o r p t i o n E l e c t r o s o r p t i o n i s a m o d i f i c a t i o n of e l e c t r o d i a l y s i s which was f i r s t conceived by Lacey and Lang (1964, 1968). I t i s a one-cycle process without r e f l u x . An e l e c t r o s o r p t i o n d e m i n e r a l i z e r c o n s i s t s of many e l e c t r o s o r p t i o n membranes arranged between a p a i r of e l e c t r o d e s , so that s o l u t i o n compart- ments are formed between the p a r a l l e l membrane surfaces as shown i n Fi g u r e 8, An e l e c t r o s o r p t i o n membrane, which i s the fundamental d e s a l t i n g u n i t , i s a t h r e e - l a y e r membrane comprising a n e u t r a l inner l a y e r (which may be a spacer or merely s o l u t i o n ) sandwiched between a c a t i o n - and an anion-exchange membrane. When a d i r e c t current i s passed through the system c a t i o n s and anions are tra n s p o r t e d ( i n opposite) d i r e c t i o n s from the e x t e r n a l s o l u t i o n i n t o the e l e c t r o s o r p t i o n membranes. The e x t e r n a l s o l u t i o n i s depleted w h i l e that w i t h i n the membranes becomes h i g h l y concentrated. A f t e r 20-50 minutes of s o r p t i o n the d i r e c t i o n of the cur r e n t i s reversed and the trapped ions accumulated i n s i d e the membranes are d r i v e n back to the e x t e r n a l s o l u t i o n to regenerate the membranes. The e x t e r n a l s o l u t i o n i s sent to waste during t h i s step. 2.7.2. C y c l i c E l e c t r o d i a l y s i s C y c l i c e l e c t r o d i a l y s i s i s a novel c y c l i c s e p a r a t i o n process, which uses p e r i o d i c f l o w r e v e r s a l a p p l i e d to an e l e c t r i c a l l y d r i v e n e l e c t r o - s o r p t i o n s t a c k . The process has been s t u d i e d and de s c r i b e d by Bass (1972) , Bass and Thompson (1973). I n t h i s process c y c l i c times ranging between 30 seconds and 2 minutes were used w i t h the v o l t a g e and flo w d i r e c t i o n 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 h a l f c y c l e . A c o n c e n t r a t i o n d i f f e r e n c e between the ends of the apparatus i s b u i l t up w i t h repeated c y c l i n g . Separation f a c t o r s of s e v e r a l hundreds were reported f o r most of the experiments with aqueous sodium c h l o r i d e s o l u t i o n s i n a c l o s e d system. The present work i s an extension of c y c l i c e l e c t r o d i a l y s i s to an open system. C y c l i c e l e c t r o d i a l y s i s u s u a l l y r e q u i r e s more e l e c t r i c a l energy per u n i t of product water than co n v e n t i o n a l e l e c t r o d i a l y s i s , due to the r e g e n e r a t i o n s t e p . The c o s t of t h i s a d d i t i o n a l energy must be balanced against savings i n c a p i t a l and o p e r a t i n g c o s t s r e s u l t i n g from: ( i ) Extreme s i m p l i c i t y of the m a n i f o l d i n g and d i s t r i b u t i n g systems. Lower cost of the stack i s p o s s i b l e because only one stream of s o l u t i o n i s withdrawn at any one time. ( i i ) The "sealed-envelope" or "membrane sack" c h a r a c t e r of e l e c t r o s o r p t i o n membranes s i m p l i f i e s the stack c o n s t r u c t i o n and r e s u l t s i n a b e t t e r membrane u t i l i z a t i o n f a c t o r . Since the membranes are not used to separate b r i n e and d i a l y s t a t e flow channels, they may be as small as the a c t i v e i n t e r i o r of the stack. A membrane u t i l i z a t i o n f a c t o r of about 95% i s o btained, whereas the f a c t o r i s only about 70% to 75% i n c o n v e n t i o n a l e l e c t r o d i a l y s i s s t a c k s (Lacey, 1968). T h i s r e s u l t s i n a lower membrane replacement cost and a lower stack c a p i t a l c o s t . ( i i i ) With e l e c t r o s o r p t i o n , no pretreatment was needed to remove i r o n or manganese from feed waters. With feeds c o n t a i n i n g e i t h e r CaSO^ or Ca(HC0,j)2> p r e c i p i t a t e s w i t h i n membranes d i d form at h i g h pH v a l u e s , but these were e a s i l y and q u i c k l y removed by reversed c u r r e n t f l o w during desorp- t i o n without causing any c e l l blockage or damage to the membranes (Lacey, 1967). I t i s expected t h a t t h i s would a l s o be t r u e f o r c y c l i c e l e c t r o d i a l y s i s . 43 ( i v ) Increased throughputs are p o s s i b l e because cu r r e n t d e n s i t i e s more c l o s e l y approaching the l i m i t i n g c u r r e n t d e n s i t y can be used without e x p e r i e n c i n g permanent damage to the membranes or stack due to p r e c i p i t a t e s . (v) A h i g h degree of d e s a l i n a t i o n can be obtained i n a s i n g l e stack (Bass, 1972). ( v i ) The p e r i o d i c reversed p o l a r i t y technique provides a repeated r e j u v e n a t i o n of the membranes. So f a r no problems w i t h membrane d e t e r i o r a t i o n have been encountered. ( v i i ) In c y c l i c e l e c t r o d i a l y s i s o n ly cheap g r a p h i t e e l e c t r o d e s need to be used. Such e l e c t r o d e s proved to be s a t i s f a c t o r y i n a long-term o p e r a t i o n . C y c l i c e l e c t r o d i a l y s i s has some s i m i l a r i t i e s to thermal parametric pumping. In both processes the flo w of a mobile phase i s p e r i o d i c a l l y reversed and i n both processes the o r i g i n of s e p a r a t i o n l i e s i n the a b i l i t y of the system to s t o r e s o l u t e t e m p o r a r i l y i n the f i x e d phase, w i t h - drawing i t from the l e a n end and subsequently adding i t to the r i c h end of the processing stream. 2.7.3. Parametric Pumping The. term parametric pumping was f i r s t introduced by Wilhelm, et a l . i n 1966 (Wilhelm, e t a l . , 1966 a, 1966 b ) . I t r e f e r s to a dynamic p r i n c i p l e of s e p a r a t i o n based on p e r i o d i c synchronous c o u p l i n g of two c y c l i c f i e l d s or two t r a n s p o r t steps (Wilhelm and Sweed, 1968 a; Wilhelm, et a l . , 1968 b ) . Parametric pumping has been reviewed i n d e t a i l s by Sweed (1971, 1972) and Wankat (1974).. 44 The system of a d i r e c t thermal parametric pumping c o n s i s t s mainly of a j a c k e t e d column packed w i t h an adsorbent bed as shown i n F i g u r e 9a, a c o n s t a n t - r a t e , p o s i t i v e displacement d u a l - s y r i n g e i n f u s i o n - w i t h d r a w a l pump, sources of hot and c o l d water f o r the j a c k e t (not shown i n the f i g u r e ) , and a programmed c y c l e timer. The timer i s adjusted to r e v e r s e p e r i o d i c a l l y the d i r e c t i o n of the f l u i d stream; a l s o to c y c l e the j a c k e t temperature by connection to hot or c o l d sources. Both a l t e r a t i o n s have the same frequency ( i . e . every h a l f c y c l e ) and are i n phase. The f l u i d i s heated during the upward s t r o k e and cooled during the downward s t r o k e . The adsorbent holds more s o l u t e when the f l u i d i s c o o l , Thus the s o l u t e i s h e l d by the adsorbent on the c o l d h a l f c y c l e and r e l e a s e d to the f l u i d on the hot h a l f c y c l e . A m u l t i p l e succession of these a d s o r p t i o n - d e s o r p t i o n a c t i o n s tends to cause accumulation of s o l u t e at: one end of the column and d e p l e t i o n at the other end. E v e n t u a l l y , under i d e a l c o n d i t i o n s , a l l of the s o l u t e w i l l be "pumped" to the upper r e s e r v o i r and the lower r e s e r v o i r w i l l c o n t a i n no s o l u t e . I n the present case the "pump" i s i d e n t i f i e d as the o s c i l l a t o r y thermal f i e l d ; the f l o w displacements between f l u i d and s o l i d phases simply keep the system i n a s t a t e of d i s e q u i l i b r i u m . The f o u r b a s i c requirements f o r implementing the p r i n c i p l e of para- m e t r i c pumping (according to Sabadell and Sweed, 1970) a r e : 1. The e x i s t e n c e of a two-phase system. 2. An e q u i l i b r i u m d i s t r i b u t i o n of the component being separated between the phases. 3. An a l t e r n a t i n g r e l a t i v e v e l o c i t y between the phases. 4. An a l t e r n a t i n g interphase mass f l u x obtained by p e r i o d i c a l l y Driven Piston Packed Bed Of Adsorbent Particles Heating And Cooling Jacket Driving Piston Q Q f * - Q f t - 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 i n t e n s i v e thermodynamic v a r i a b l e s t h a t a f f e c t e q u i l i b r i u m e.g. temperature. Although thermal parametric pumping r e s u l t s i n a l a r g e s e p a r a t i o n i n the system t o l u e n e - n - h e p t a n e - s i l i c a g e l , w i t h a s e p a r a t i o n f a c t o r of 10"* i n batch o p e r a t i o n (Wilhelm, et a l . , 1968 b) and of over 600 i n an open system (Chen, et a l . , 1972 a ) , i t g i v e s only a modest s e p a r a t i o n i n the system Na CI - 1^0 - i o n r e s i n w i t h a s e p a r a t i o n f a c t o r of 10 i n a c l o s e d system (Sweed and Gregory, 1971) and a s e p a r a t i o n f a c t o r of 2.0 i n an open system (Wilhelm et a l . , 1966 a; Sweed and Gregory, 1972). 2.7.4. C y c l i c e l e c t r o d i a l y s i s and Parametric Pumping De s p i t e the prementioned s i m i l a r i t i e s between c y c l i c e l e c t r o d i a l y s i s and parametric pumping, the two processes are d i f f e r e n t w i t h regard to the nature of the d r i v i n g f o r c e and process d e s i g n , l i m i t a t i o n s and a p p l i c a t i o n s , I n parametric pumping s e p a r a t i o n i s achieved a t the expense of thermal energy. By changing the temperature and r e v e r s i n g the f l u i d f l o w every h a l f c y c l e the system i s kept i n a s t a t e of d i s e q u i l i b r i u m , thus molecules d i f f u s e from one phase i n t o another. I n c y c l i c e l e c t r o d i a l y s i s an e x t e r n a l e l e c t r i c f i e l d i s a p p l i e d and b o d i l y f o r c e s a r e exerted on the ions t h a t are t r a n s f e r r e d from one r e g i o n i n t o another across the stack. A parametric pumping process c o n s i s t s e s s e n t i a l l y of a column packed w i t h a s u i t a b l e adsorbent bed w h i l e c y c l i c e l e c t r o d i a l y s i s s t a ck comprises w e l l - d e f i n e d p a r a l l e l f l o w channels between membrane sheets. While parametric pumping o p e r a t i o n i s c o n t r o l l e d by e q u i l i b r i u m con- s i d e r a t i o n s , e l e c t r i c a l l y d r i v e n s e p a r a t i o n process such as c y c l i c e l e c t r o - d i a l y s i s i s governed by f i n i t e r a t e s of mass t r a n s f e r and u s u a l l y operate at c o n c e n t r a t i o n s f a r from e q u i l i b r i u m . The r a t e of mass t r a n s f e r i s 47 approximately p r o p o r t i o n a l to the cu r r e n t f l o w i n g and i s thus to some extent under the d i r e c t c o n t r o l of the experimenter. F i n a l l y c y c l i c e l e c t r o d i a l y s i s d e a l s only w i t h i o n i c s o l u t i o n s whereas parametric pumping i s not l i m i t e d to these s o l u t i o n s . However, w i t h i n the s p e c i f i c f i e l d of s e p a r a t i o n of i o n i c s o l u t i o n s , c y c l i c e l e c t r o - d i a l y s i s l o o k s more promising s i n c e i t i s not co n s t r a i n e d by the chemical nature of the system. In parametric pumping a l a r g e s e p a r a t i o n i s only expected when the s h i f t of e q u i l i b r i u m w i t h temperature of the p a r t i c u l a r system i s l a r g e . CHAPTER 3 System Models 3.1. Stack Resistance Models The apparent r e s i s t a n c e of an e l e c t r o d i a l y s i s stack i s determined by m u l t i p l y i n g the apparent r e s i s t a n c e of one c e l l p a i r by the number of the c e l l p a i r s and making some allowance f o r the e l e c t r o d e system*(Generally i g n o r i n g the e l e c t r o d e system c o n t r i b u t i o n towards the t o t a l stack r e s i s - tance w i l l r e s u l t i n only minor e r r o r ) . A c e l l p a i r c o n s i s t s of two i o n - exchange membranes and t h e i r a s s o c i a t e d f l o w channels. The apparent r e s i s t a n c e comprises the e l e c t r i c a l r e s i s t a n c e of the s o l u t i o n s and the membranes together w i t h the back emf's caused by p o l a r i z a t i o n , These back emf's oppose the a p p l i e d v o l t a g e and thus represent an apparent r e s i s t a n c e . In the development of these analyses two approaches can be d i s - t i n g u i s h e d which are designated as "non-ohmic" and "ohmic". The non-ohmic a n a l y s i s i s an a n a l y t i c a l approach which takes i n t o account the v a r i a t i o n of the apparent r e s i s t a n c e w i t h c u r r e n t d e n s i t y . T h i s approach breaks down the t o t a l r e s i s t a n c e i n t o s e v e r a l r e s i s t i v e elements, evaluates the con- t r i b u t i o n of each element independently and sums them to get the t o t a l v a l u e . The ohmic a n a l y s i s i s an e m p i r i c a l approach which assumes p r o p o r t i o n - a l i t y between cur r e n t and v o l t a g e i n the e l e c t r o d i a l y s i s stack. 3.1.1. Non-ohmic A n a l y s i s When a v o l t a g e i s a p p l i e d a c r o s s an e l e c t r o d i a l y s i s stack, the i n i t i a l c u r r e n t i s roughly p r o p o r t i o n a l to the v o l t a g e , but as the cu r r e n t flows 48 49 through the apparatus c o n c e n t r a t i o n g r a d i e n t s and d i s c o n t i n u i t i e s are e s t a b l i s h e d and the apparent r e s i s t a n c e of the stack i n c r e a s e s . Apparent r e s i s t a n c e comprises the e l e c t r i c a l r e s i s t a n c e s of the s o l u t i o n s and the membranes, and the back e l e c t r o m o t i v e f o r c e s (membrane p o t e n t i a l s and d i f f u s i o n p o t e n t i a l s ) caused by c o n c e n t r a t i o n p o l a r i z a t i o n . F i g u r e 10 shows s c h e m a t i c a l l y the c o n c e n t r a t i o n p r o f i l e s i n an e l e c t r o - d i a l y s i s c e l l p a i r . The c e l l p a i r c o n t a i n s the concentrated and depleted bulk s o l u t i o n s , the two membranes, and the four boundary l a y e r s i n which the c o n c e n t r a t i o n s of s a l t s i n the s o l u t i o n near the membrane vary con- s i d e r a b l y . The e l e c t r i c a l c i r c u i t i n F i g u r e 10 i s an analog of the e l e c t r o - d i a l y s i s c e l l p a i r . The b a t t e r y symbols represent the c o n c e n t r a t i o n p o t e n t i a l s , and the r e s i s t o r symbols represent the r e s i s t a n c e s of membranes and segments of s o l u t i o n . This analog can be used to develop an equation f o r the t o t a l p o t e n t i a l across a c e l l p a i r . ( i ) D i f f u s i o n l a y e r r e s i s t a n c e The v o l t a g e from 1 to 2 i n the depleted d i f f u s i o n l a y e r i s the a l g e b r a i c sum of the d i f f u s i o n p o t e n t i a l and the IR drop from p o i n t 1 to p o i n t 2 j i ( ^ " ^ E l - 2 I '¥ f <t" - t+)d l n ( T C ) g + i " 1 p dx (17) r x,z where R i s the gas law constant, T i s the abs o l u t e temperature, F i s Faraday's constant; t , t + are the t r a n s p o r t numbers of anion and c a t i o n r e s p e c t i v e l y 3 i n s o l u t i o n , C i s the s o l u t e c o n c e n t r a t i o n i n eq./cm , y i s the a c t i v i t y c o e f f i c i e n t , p i s the r e s i s t i v i t y of the s o l u t i o n a t the coordinate p o i n t X f z x,z, n-cm, where x i s the d i s t a n c e from the membrane sur f a c e and z i s the d i s t a n c e from the i n l e t a l ong the f l o w path. The s u b s c r i p t d r e f e r s to the d e p l e t i n g s o l u t i o n . 50 Cell Pair L ' Depleting Solution . 13 5 i Enriching Solution I 8 3 .4 .5 6 7 .8 9 - h/VWvH ( A i K / V H t v V ^ r A / H ^ FIGURE 10 Simplified concentration profiles in an electrodialysis cell pair and the analogous electrical circuit. 51 The eq u i v a l e n t r e s i s t a n c e of the d i f f u s i o n p o t e n t i a l ( f i r s t term on R.H.S. of equation (17)) i s given by (18) I n t e g r a t i o n of Equation (18) along the f l o w path (z coordinate) r e s u l t s i n ( r e f e r to F i g u r e 11) F i % , d " m R T <cd" " t d ) „m ( Y l c i ) I n , — — v z dz (Y 2C 2)_ (19) J z=0 where ^ i s the eq u i v a l e n t r e s i s t a n c e of the " d i f f u s i o n p o t e n t i a l per u n i t area of the depleted l a y e r . The d i f f u s i o n l a y e r r e s i s t a n c e t h a t the d i a l y z i n g c u r r e n t must pass through (the second term on the R.H.S. of equation (17)) i s c a l c u l a t e d by performing a double i n t e g r a t i o n across the d i f f u s i o n l a y e r (x coordinate) as w e l l as along the f l o w path (z coordinate) as i n d i c a t e d i n F i g u r e 11. L6 , d i r m m z=0 Px,z dx x=0 -1 dz (20) where p i s obtained from the b a s i c d e f i n i t i o n of r e s i s t i v i t y : x,z J 1000 x.z ( A v V c C x , z (21) (hv)+or i s the equ i v a l e n t s o l u t i o n conductance at average c o n c e n t r a t i o n of s a l t s and t°C. I t can be evaluated from the Onsager equation a t v a r i o u s temperatures and c o n c e n t r a t i o n s ( A v ) t ° c ° (Aoo) to c - [A + B (Aoo) to c]C (Aoo) to c = ( A~) 25° C [ 1 + 0 , 0 2 3 ( t " 2 5 ) 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) o P i s the equ i v a l e n t conductance at i n f i n i t e d i l u t i o n and t °c . A f t e r p from Eqs. (21), (22) and (23) i s s u b s t i t u t e d i n Eq. (20), C X 9 Z X j z as a f u n c t i o n of x and z has to be evaluated from the boundary c o n d i t i o n s . To r e l a t e the c o n c e n t r a t i o n a t the membrane surface C(0,Z) w i t h the d i f f u s i o n l a y e r - b u l k I n t e r f a c e c o n c e n t r a t i o n , C(6,Z), the Nernst i d e a l i z e d equation w i l l be used ( t h i s model i s considered i n Appendix C): dc = C(6,Z) - C(0,Z) ( 2 A ) dx 6 From the Nernst equation and r e a l i z i n g t h a t a t the l i m i t i n g c u r r e n t d e n s i t y , i^^* surface c o n c e n t r a t i o n C(0,Z) approaches zero, C(0,Z) = (1 - k) C(6,Z) (25) where k i s the r a t i o of the ope r a t i n g to l i m i t i n g c u r r e n t d e n s i t y i . e . k = (26) l i r a At any p o i n t (x,z) w i t h i n the boundary l a y e r C(x,z) i s given i n terms of bulk s o l u t i o n c o n c e n t r a t i o n C(6,Z), d i f f u s i o n l a y e r t h i c k n e s s , 6, and the c u r r e n t d e n s i t y r a t i o , k by the f o l l o w i n g r e l a t i o n (using equations (24) and ( 2 5 ) ) : C(x,z) = C(0, Z) + X t C ( 6 ' Z > - C < ° » Z " = [(1-k) + ^ ] C(6,Z) (27) The d i f f u s i o n l a y e r t h i c k n e s s , 6, the l i m i t i n g c u r r e n t d e n s i t y , i ^ the o p e r a t i n g c u r r e n t d e n s i t y , i 0p e r» a n <* the b u l k s o l u t i o n c o n c e n t r a t i o n , C(6,Z) must be evaluated before equation (27) can be used. 54 The d i f f u s i o n l a y e r t h i c k n e s s The d i f f u s i o n l a y e r t h i c k n e s s , 6, i s obtained from Equation (11) i n terms of l i m i t i n g c u r r e n t d e n s i t y as; . _ C(6,m) FD (28) l i m i n - (t - t) L i m i t i n g c u r r e n t d e n s i t y , i ^ ^ * w i l l occur when the e x i t c o n c e n t r a t i o n of the d i l u t e stream C(0,m) shown i n F i g u r e 11 reaches zero. The l i m i t i n g c urrent d e n s i t y can be determined e x p e r i m e n t a l l y as shown by Rosenberg and T i r r e l (1957), Cowan and Brown (1959) and Cooke (1961). Once i i s obtained, 6 can be c a l c u l a t e d . The c u r r e n t d e n s i t y r a t i o , k Using Faraday's Law and a m a t e r i a l balance, the c a p a c i t y i s defined as, Cap - i j j ^ - F d n C 4 ± f (29) where c a p a c i t y i s i n g-equiv. t r a n s f e r r e d / s e c . , n i s cu r r e n t e f f i c i e n c y , Ap i s the a c t i v e membrane area [ i . e . area a v a i l a b l e f o r d e m i n e r a l i z a t i o n ] (cm ) , n i s the number of membrane p a i r s , F i s Faraday No. (coulombs/g-equiv), F d i s d i l u t e stream e x i t f l o w r a t e ( l i t / ( s e c ) ( c h a n n e l ) ) , C d i i s d i a l y s a t e i n l e t b u l k c o n c e n t r a t i o n ( g - e q u i v / l i t ) , and f i s f r a c t i o n d e s a l t e d . From Eq. (29) we have F F d C d ± f 2 i = t amps/cm (30) oper n Ap r From the l i m i t i n g c u r r e n t v a l u e and Equation (30), the c u r r e n t d e n s i t y r a t i o , 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 s o l u t i o n c o n c e n t r a t i o n , C(6,Z) Based on the t r a d i t i o n a l treatment of e l e c t r o d i a l y s i s the d i a l y s a t e b u l k stream c o n c e n t r a t i o n can be assumed to decay e x p o n e n t i a l l y w i t h the d i s t a n c e Z from the feed p o i n t as shown i n F i g u r e 12a. On e v a l u a t i n g each bulk s o l u t i o n as a f u n c t i o n of path d i s t a n c e Z we get f o r the d i a l y s a t e -aZ C d ( Z ) = C d ( 0 ) e (31) and from a m a t e r i a l balance on the s a l t at a d i s t a n c e Z along the path l e n g t h and the top of the u n i t (at Z = m) we get f o r the b r i n e ( r e f e r to F i g u r e 12b): C b (Z) = [C b(m) + ( | | ) C d(m)] - [( | | ) C d ( 0 ) ] e " a Z (32) On s u b s t i t u t i n g equation (31) i n t o (27) a g e n e r a l expression f o r the l o c a l c o n c e n t r a t i o n , C(X,Z), can be obtained: (33) C(x,Z) = [(1-k) + ~ ] C(6,0) . e ~ a Z By s u b s t i t u t i n g values from equations (21), (22) , (23) , (25), (26), (28), (30) and (33); equations (19) and (20) can be i n t e g r a t e d . From equations (19) and (20) the apparent r e s i s t a n c e per u n i t area of the depleted d i f f u s i o n l a y e r i s given by: R d " % , d + R 6 , d m R T ( £ d - V F i .m ( V - ^ ) I n , — d z -1 (Y 2C 2)_ L J z=0 + m - z=0 p dx x,z dz -1 (34) 57 A combined expr e s s i o n f o r the apparent r e s i s t a n c e s of the two depleted d i f f u s i o n l a y e r s i s given by ( r e f e r to F i g u r e 10) R 6 ( l - 2 ) + R6(3-4) m RT ( t d - t d ) F i .m ( Y 1 C 1 } I n — — s z dz n W z z=0 z -1 + 2m .m z=0 L J x=0 p dx x,z -1 dz -1 (35) The combined apparent r e s i s t a n c e of the two enriched d i f f u s i o n l a y e r s can be obtained i n a s i m i l a r way: R R6(5-6) + R6(7-8) m RT (t - t ) e e F i 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 i s the r e s i s t i v i t y at any p o i n t (x,z) w i t h i n the enriched X f z d i f f u s i o n l a y e r . ( i i ) The bulk s o l u t i o n r e s i s t a n c e The e l e c t r i c a l r e s i s t a n c e of a s o l u t i o n - f i l l e d compartment A cm t h i c k i s s o l CA ohm - cm (37) The r e s i s t a n c e s of the bulk d e p l e t i n g and e n r i c h i n g s o l u t i o n s are given by 58 *b = V d + R b . = m(A-26) <' - i -1 L J z=0 (C,A ) dz ^ ^ z .m (C 6 A 6 ) dz L_ J z=0 -1 M38) ( i i i ) The membrane r e s i s t a n c e and p o t e n t i a l terms The r e s i s t a n c e of a membrane cannot be c a l c u l a t e d by a simple method but i t can be measured or obtained from the manufacturer. Although d i r e c t c urrent i s used i n electromembrane processes, a l t e r n a t i n g c u r r e n t s are u s u a l l y used to measure the e l e c t r i c a l r e s i s t a n c e of membranes because con- c e n t r a t i o n g r a d i e n t s t h a t are present w i t h d i r e c t c u r r e n t systems are not formed w i t h a l t e r n a t i n g c u r r e n t and the r e s i s t a n c e of the membrane i t s e l f can be more e a s i l y determined. However, the r e s i s t a n c e of a membrane t o a l t e r n a t i n g c u r r e n t i s u s u a l l y lower than the r e s i s t a n c e to d i r e c t c u r r e n t ( S p i e g l e r , 1966). I f p r e c i s e v a l u e s are needed the r e s i s t a n c e to d i r e c t c u r r e n t should be determined under c o n d i t i o n s of membrane use. There are c o n c e n t r a t i o n d i s c o n t i n u i t i e s a t the membrane-liquid i n t e r - f ace i n an ion-exchange membrane as a r e s u l t of the Donnan e q u i l i b r i u m . F i g u r e 13a shows the c o n c e n t r a t i o n d i s t r i b u t i o n i n a c a t i o n exchange membrane. The c o n c e n t r a t i o n s of the anions and c a t i o n s are equal i n the o u t s i d e s o l u t i o n but d e v i a t e from each other w i t h i n the membrane. The upper l i n e i s c a t i o n c o n c e n t r a t i o n , C +, and the lower l i n e i s anion c o n c e n t r a t i o n . The t o t a l membrane p o t e n t i a l , E m , i s the sum of three p o t e n t i a l m' d i f f e r e n c e s as shown i n F i g u r e 13b. E = E, m d l + *h + E d 2 (39) where E<j^, E ^ a r e the two p o t e n t i a l jumps o c c u r r i n g at the membrane f a c e s , which form the Donnan p o t e n t i a l . 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 i s the Henderson term which i s the d i f f u s i o n p o t e n t i a l e x i s t i n g i n the i n t e r i o r of the membrane. The d e t a i l e d expressions of the Donnan terms and Henderson term are given by V e t t e r (1967). A s i m p l i f i e d e x p r e s s i o n f o r the e l e c t r i c a l p o t e n t i a l d i f f e r e n c e across a membrane i n contact w i t h u n i - u n i v a l e n t e l e c t r o l y t e s o l u t i o n s of a c t i v i t i e s a m and a m on the opposite s i d e s i s given by m tt — ( t - t ) I n ,—T\z F c c' (a') m z (40) where t ^ , t are the c a t i o n and anion t r a n s p o r t numbers i n a cation-exchange membrane. The membrane p o t e n t i a l s oppose the a p p l i e d e l e c t r o d i a l y s i s p o t e n t i a l s when ions are t r a n s f e r r e d from lower to higher c o n c e n t r a t i o n s . The r e s i s t a n c e per u n i t area due to p o t e n t i a l s of a c a t i o n and an anion membrane i s given by R = R + R + p + p m ma mc a c , mRT . p + p + r r r - S p a F c F i S r rm + ( Y 5 C 5 } t ) l n , - ~ v z i a * ( y f J z J -1 dz -1 m L- z=0 ( t - t ) I n ;•] - l - i - l dz > (41) where s u b s c r i p t s a and c r e f e r to anion- and cation-exchange membrane r e s - p e c t i v e l y p , p are the anion and c a t i o n membrane r e s i s t a n c e per u n i t area Si c R . R „ are the equi v a l e n t r e s i s t a n c e per u n i t area due to anion and ma mc c a t i o n membrane p o t e n t i a l . 61 The apparent r e s i s t a n c e of a c e l l p a i r The apparent r e s i s t a n c e per u n i t area of a c e l l p a i r , R , i s given by = R, + R + (42) \ j i xv • R, "4" R IT d e D m where R d > R g, R^ and R m are def i n e d by equations (35), (36), (38) and (41) r e s p e c t i v e l y . The apparent r e s i s t a n c e per u n i t area of a c e l l p a i r can be evaluated by c o n s i d e r i n g a l o c a l r e s i s t a n c e a t any l e v e l Z together w i t h the average bulk c o n c e n t r a t i o n s of the s o l u t i o n s . In t h i s case equation (42) reduces to ( r e f e r to F i g u r e 10) R 7 = <5 TT,Z I n C,A.,/C0A0 I n C 0A 0/C.A. I n C-A^/C^A, 1 1 2 2 3 3 4 4 5 5 6 6 < C1 A1 " C 2 V ( C 3 A 3 " W < C5 A5 ~ C 6 V In C 7A 7/C 8A 8 ( C 7 A ? - CgAg) + ( A - 2 6 ) ( c f c + C i A 7 ) + P a + Pc RT F i '22 "6 6 5~5 - 4- - 4- YqCq + ( t - t ) I n - + ( t - t ) I n — -a a y y 4 C 4 c c' Y«C 5 f8"8 (43) The s u b s c r i p t s d and e r e f e r to the d e p l e t i n g and e n r i c h i n g s o l u t i o n s and a and c r e f e r to the anio n - and cation-exchange membranes. The numerical s u b s c r i p t s r e f e r to the corresponding numbers i n F i g u r e 10. Eq. (43) i s based on the f o l l o w i n g assumptions: ( i ) V a l i d i t y of Nernst i d e a l i z e d model ( r e f e r to appendix C) ( i i ) A u n i - u n i v a l e n t e l e c t r o l y t e system ( i i i ) S o l u t i o n - f i l l e d compartments without spacers; each of the same 62 th i c k n e s s A and w i t h two d i f f u s i o n l a y e r s each of the t h i c k - ness 6 ( i v ) Constant t r a n s p o r t numbers of the membranes and s o l u t i o n s over the range of co n c e n t r a t i o n s of i n t e r e s t (v) S i n g l e - i o n a c t i v i t i e s can be repl a c e d by m o l a l i t i e s and mean a c t i v i t y c o e f f i c i e n t s . S i m p l i f y i n g Assumptions Even the s i m p l i f i e d equation of the apparent r e s i s t a n c e of a d i f f e r - e n t i a l area of a c e l l p a i r i . e . Eq. (43) i s cumbersome and time-consuming, I t can be s i m p l i f i e d by making s e v e r a l assumptions, most of which can be approached i n p r a c t i c e . The f i r s t s i m p l i f y i n g assumption that can be made i s t h a t the two d i f f u s i o n l a y e r s i n each of the f l o w channels are i d e n t i c a l and the boundary l a y e r t h i c k n e s s on the two membrane faces i s the same. With t h i s assumption the c o n c e n t r a t i o n p r o f i l e s become symmetrical i . e . C. = C. and C c = C Q and the two j u n c t i o n p o t e n t i a l s (the c o n c e n t r a t i o n 1 4 5 o p o t e n t i a l s i n the boundary l a y e r s ) c a n c e l out as shown i n F i g u r e 14. The assumption i m p l i e s t h a t : (a) ( t - t ) a = ( t - t ) c where t , t are the t r a n s p o r t numbers of c o u n t e r i o n i n membrane and s o l u t i o n phase r e s p e c t i v e l y and s u b s c r i p t s a, c r e f e r to anion- and c a t i o n - s e l e c t i v e membrane. (b) Same hydrodynamic c o n d i t i o n s p r e v a i l i n the boundary l a y e r s i n the f l o w 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 t h i s assumption Eq. (43) reduces to YeC I n C.A-/C1A1 In CJV,/CJV_ R l - 9 = 2 ( t - t c ) § I n f 26( A C A C A r A 1 9  F i y 4 C 4 C 2 A 2 - C1A]_ C 6A 6 - + ( A - 2 6 ) ( c t A T + ^ A 7 ) + P a + Pc < 4 4 ) 2 2 6 6 where t , t £ are the t r a n s p o r t numbers of counterions and co-ions i n the membrane phase. Eq. (28) can be used to estimate the boundary l a y e r t h i c k n e s s , 6. Other terms which are not a c c e s s i b l e to d i r e c t measurement i n Eq, (44) are the i n t e r f a c i a l c o n c e n t r a t i o n s , and C^. These can be e l i m i n a t e d as f o l l o w s : Eq. (10) can be w r i t t e n as i£ = °2 " C l = i • ( 4 5 ) dx & B ^ ; where the constant B, which depends o n l y on the nature of the d i s s o l v e d e l e c t r o l y t e and of the membrane, i s defined as B == (46) (t - t ) s u b s t i t u t e Eq. (11) i n t o Eq. (46) B C- 6 = - v - ^ (47) H i m Therefore we get C± = C 2 (1 - ~— ) = C 2 (1 - k) (48) l i m S i m i l a r l y by assuming the same c o n c e n t r a t i o n i n both d i f f u s i o n l a y e r s we get 65 C 5 "  C 6 + f " C 6 <49> where ns i s the s e p a r a t i o n f a c t o r d e f i n e d by C C The f o l l o w i n g f u r t h e r s i m p l i f y i n g assumptions can be made. The equ i v a l e n t conductance i s independent of c o n c e n t r a t i o n over the l i m i t e d range of i n t e r e s t i . e . A l = A 2 = = A The a c t i v i t i e s are equal to the c o n c e n t r a t i o n s , y± = Y 2 = ' = i - o With these assumptions together w i t h Eqs. (48) and (49) Eq. (44) reduces to where k and ns are defined by Eqs. (26) and (50) r e s p e c t i v e l y and t , t are the t r a n s p o r t numbers of the cou n t e r i o n and c o - i o n r e s p e c t i v e l y i n the membrane. For i d e a l l y s e l e c t i v e membranes (t - t c ) = 1.0 Instead of i n t e g r a t i n g over the whole flo w path, a c o n s i d e r a b l e s i m p l i f i c a t i o n i s achieved by u s i n g l o g a r i t h m i c ^ mean values of the bulk con- c e n t r a t i o n s , C 2 and Cg together w i t h Eq. (44) or (51) to evaluate the apparent r e s i s t a n c e of a complete c e l l p a i r . A 66 F i n a l l y i t should be noted that a l l these expressions f o r the apparent r e s i s t a n c e of a c e l l p a i r , namely Eqs. (42), (43), (44) and (51) have to be modified to take i n t o account the e f f e c t s due t o : (a) Presence of spacers i n spacer f i l l e d c o n f i g u r a t i o n s (b) Ohmic r e s i s t a n c e due to s c a l e . S c a l e s , such as CaSO^, CaCO^, Mg(0H)2 e t c . , can p r e c i p i t a t e out of s o l u t i o n and de p o s i t on the membrane surfaces at p o i n t s of low v e l o c i t y . 3.1.2. Ohmic A n a l y s i s T h i s a n a l y s i s assumes p r o p o r t i o n a l i t y between c u r r e n t and v o l t a g e i n the e l e c t r o d i a l y s i s stack. I t i s an e m p i r i c a l approach to evaluate stack r e s i s t a n c e . For a c e l l of given design and membrane type, i t i s a r e l a t i v e l y simple matter to use a l a b o r a t o r y model to o b t a i n an e m p i r i c a l set of r e s i s t a n c e v a l u e s as a f u n c t i o n of t y p i c a l o p e r a t i n g c o n d i t i o n s . These val u e s may then be used to design a f u l l - s c a l e p l a n t . This data may be 2 2 expressed as the r e s i s t a n c e of 1 cm of one c e l l p a i r i n ohm-cm , as a f u n c t i o n of e x t e r n a l s o l u t i o n c o n c e n t r a t i o n s . Although the a c t u a l c o r r e l a t i o n of c e l l - p a i r r e s i s t a n c e , R^, w i t h s o l u t i o n c o n c e n t r a t i o n may take the form of a polynomial power s e r i e s such 2 B as R = a + bC + cC e t c , or an e x p o n e n t i a l form R = a C as shown by P P Tye (1963), Mason and Kirkham (1959) have suggested the f o l l o w i n g e x p r e s s i o n f o r the l o c a l r e s i s t a n c e per u n i t area of a c e l l p a i r : K l R = — + K_ - L C (52) P C 2 3 where K^, ^ and are constants f o r a given spacer geometry, i o n i c com- p o s i t i o n , membrane type and temperature. C i s the l o c a l "average" con- c e n t r a t i o n c a l c u l a t e d from 67 _1_ = 1 C" 1 + r v C. T C Q C ( ~ + ~ ) (53) Here C. and C are the l o c a l d i l u a t e and concentrate c o n c e n t r a t i o n s , and d c ' r i s the r a t i o of spacer thicknesses i n the concentrate and i n the d i l u t e compartment ( f r e q u e n t l y r i s u n i t y ) . At low values of C ( i . e . i n d i l u t e s o l u t i o n s ) , the term becomes n e g l i g i b l e and Eq. (52) reduces to the form K l R = ^ + K 9 (54) P C 2 I n d i l u t e s o l u t i o n s the e l e c t r i c a l r e s i s t a n c e of strong e l e c t r o l y t e s i s approximately i n v e r s e l y p r o p o r t i o n a l to c o n c e n t r a t i o n , and the e l e c t r i c a l r e s i s t a n c e s of commercial i o n exchange membranes are r e l a t i v e l y independent of changes i n e l e c t r o l y t e c o n c e n t r a t i o n . This i s tr u e up to about 0.1 N (Mason, 1959). Thus Eq. (54) can be considered to c o n s i s t of a s o l u t i o n r e s i s t a n c e term, , plu s a membrane r e s i s t a n c e term, K 0. The K„ term i n C Eq. (52) al l o w s f o r n o n - l i n e a r i t y between s o l u t i o n c o n c e n t r a t i o n and con- ductance, and f o r decrease i n membrane r e s i s t a n c e s w i t h i n c r e a s i n g s o l u t i o n c o n c e n t r a t i o n . At e l e c t r o l y t e c o n c e n t r a t i o n s higher than 0.1 N the membrane r e s i s t a n c e begins to decrease w i t h i n c r e a s i n g e l e c t r o l y t e c o n c e n t r a t i o n because of the increased c o n d u c t i v i t y of the e l e c t r o l y t e i n the r e s i n . Allowances f o r membrane p o t e n t i a l s which oppose the a p p l i e d v o l t a g e and thus represent an apparent r e s i s t a n c e , and f o r r e s i s t a n c e i n c r e a s e s due to c o n c e n t r a t i o n g r a d i e n t s i n the d i f f u s i o n l a y e r s i s made i n choosing the numerical v a l u e s of K^, and K^. The K's can be estimated from ta b u l a t e d values of s o l u t i o n and membrane r e s i s t a n c e . The stack r e s i s t a n c e i s c a l c u l a t e d from the s o l u t i o n c o n c e n t r a t i o n by e i t h e r u s i n g the l o g a r i t h m i c mean c o n c e n t r a t i o n o r by i n t e g r a t i n g over the 68 whole f l o w path. I n t e g r a t i o n Procedure The l o c a l v a l u e , at any l e v e l z along the f l o w path, of the r e s i s t a n c e per u n i t area of a c e l l p a i r (R ")^ can be i n t e g r a t e d over the membrane area (pa) a v a i l a b l e f o r d e s a l i n a t i o n to o b t a i n the t o t a l r e s i s t a n c e of a c e l l p a i r , R . P pa 1_ R da o p z c e l l p a i r / f t (55) where a, i s the a c t u a l membrane c r o s s - s e c t i o n a l area, cm (a = m x n ) ; and p i s the f r a c t i o n of membrane area a v a i l a b l e f o r d e s a l i n a t i o n . 2 pa = pnz cm pda = pndz cm 2 where n i s the membrane width (cm) and z i s the coordinate system along a membrane sur f a c e ( r e f e r to F i g . 11) transposing v a r i a b l e s , .m R = pn z=0 dz p z (56) From Eqs. (52), (53) P z K l c j i y + K 2 K 3 C a ( z ) (57) and C a ( z ) 1 + r 1 + r C d ( z ) C b ( z ) (58) V a r i a t i o n s of C, (z) and C, (z) w i t h z, w i l l make C (z) a f u n c t i o n of a D a 69 C a ( Z ) = f ( z ) K, (59) (60) S u b s t i t u t i n g Eq. (60) i n t o Eq. (56), R = pn = pn r m o m K l -1 [ + K 2 - K 3 f (z)] dz { K± + K 2 f ( z ) - K 3 [ f ( z ) ] 2 } 1 f ( z ) dz (61) f ( z ) i s obtained by s u b s t i t u t i n g v a l u e s of the b u l k s o l u t i o n s from Eqs. (31) and (32) i n t o Eq. (58) f ( z ) = C (z) = d H - r ) ( C d ( 0 ) e - a Z ) { [ C b ( m ) - ( F ^ F ^ (m) ] + [ ( F ^ C ^ O e " " * ] } 3 1 . . . . . . i . ~ • - - — . . . . . . {[C b(m) - ( F d / F b ) C d(m)] + C d ( 0 ) e _ C t Z [ ( F ^ ) + r ] } -az. t • « « o • u • • i (62) Thus, s u b s t i t u t i n g i n t o Eq. (61) f o r f ( z ) or C ( z ) , the c e l l p a i r r e s i s t a n c e , Si Rp, can be evaluated. Small i n t e r v a l s (Az) can be chosen to evaluate the i n t e g r a l as a summation R = pn C a ( z ) Az 2 _ + K, C a ( z ) - z=0 K 3 C a ( z ) 2 (63) 3.2. Mass Transfer Models The d i f f e r e n t i a l equation of m a t e r i a l c o n s e r v a t i o n f o r a component i n the f l o w system* shown i n F i g u r e 15 i s : FIGURE 15 Differential section of column. 71 s = 0 (64) (a) (b) (c) (d) where and C g are the c o n c e n t r a t i o n s of the component t r a n s f e r r e d i n the mobile and s t a t i o n a r y phases r e s p e c t i v e l y , v i s the displacement v e l o c i t y , D i s s o l u t e d i f f u s i v i t y , e i s v o i d f r a c t i o n . Equation (64) i s sometimes c a l l e d the chromatography equation. The terms i n t h i s equation express mass co n s e r v a t i o n c o n t r i b u t i o n s a t t r i b u t a b l e to the f o l l o w i n g mechanisms: (a) = i n t e r s t i t i a l , f l u i d phase t r a n s i e n t (b) = a x i a l convection (c) = a x i a l f l u i d - p h a s e d i f f u s i o n (d) = a d s o r p t i v e phase t r a n s i e n t Together w i t h an equation r e l a t i n g l o c a l v a l u e s of C g to C^, and a p p r o p r i a t e boundary c o n d i t i o n s , Equation (64) a p p l i e s during every sub- i n t e r v a l of a c y c l i c f l o w process. 3.2.1. E q u i l i b r i u m Model P i g f o r d et a l . (1969) used Equation (64) to develop a simple " e q u i l i b r i u m model" f o r thermal parametric pumping. The b a s i c assumption i n t h i s model i s that the s o l i d and f l u i d are l o c a l l y i n e q u i l i b r i u m . This assumption g r e a t l y s i m p l i f i e s the equations s i n c e r a t e i n f o r m a t i o n i s not needed. Tn a d d i t i o n , a x i a l d i s p e r s i o n was neglected and the e q u i l i b r i u m r e l a t i o n s h i p was assumed to be l i n e a r . With these assumptions the r e s u l t i n g equation i s a h y p e r b o l i c p a r t i a l d i f f e r e n t i a l equation which can be solved a n a l y t i c a l l y by the method of c h a r a c t e r i s t i c s developed by A c r i v o s (1956).- The c h a r a c t e r i s t i c l i n e s can be used to show g r a p h i c a l l y the development of the s e p a r a t i o n , and to show 72 when s e p a r a t i o n w i l l not occur; thus the model o f f e r s a l g e b r a i c s o l u t i o n s that can be used f o r a r a p i d c a l c u l a t i o n of parapump s e p a r a t i o n . The e q u i l i b r i u m theory was g e n e r a l i z e d by A r i s (1969) and extended to an open system by Gregory and Sweed (1970), Chen and H i l l (1971) and i t was f u r t h e r extended by Thompson and Bowen (1972) to p r e d i c t s e p a r a t i o n i n a two-column arrangement where the two columns are operated back-to-back to minimize mixing. Although the e q u i l i b r i u m model i s compact and easy to apply i t ignores d i s p e r s i v e e f f e c t s which l i m i t s e p a r a t i o n i n a r e a l system, hence i t can not p r e d i c t the u l t i m a t e s t e a d y - s t a t e s e p a r a t i o n ( R i c e , 1973). Gupta and Sweed (1972) have extended the e q u i l i b r i u m model to take i n t o account a x i a l mixing. Foo and R i c e (1975, 1976) used a more general temperature dependence i n the l i n e a r isotherm along w i t h the d i s s i p a t i v e f o r c e s a s s o c i a t e d w i t h a x i a l d i s p e r s i o n , f i l m r e s i s t a n c e and pore d i f f u s i o n to p r e d i c t the u l t i m a t e s e p a r a t i o n i n c l o s e d parapumps. Mass t r a n s f e r between the moving phase and the s t a t i o n a r y phase i s assumed to take p l a c e i n s t a n t a n e o u s l y i n the e q u i - l i b r i u m model and hence the c y c l e d u r a t i o n s do not enter i n t o the s o l u t i o n s p r e d i c t e d by the model. Since the c y c l e d u r a t i o n may be assigned any a r b i t r a r y v a l u e , the e q u i l i b r i u m model s o l u t i o n s are not f u n c t i o n s of r e a l time and the model can only serve as i n i d e a l i z a t i o n that p r e d i c t s the best p o s s i b l e s e p a r a t i o n . E l e c t r i c a l l y d r i v e n s e p a r a t i o n processes such as e l e c t r o d i a l y s i s are governed by f i n i t e r a t e s of mass t r a n s f e r and u s u a l l y operate at concen- t r a t i o n s f a r from e q u i l i b r i u m . The r a t e of mass t r a n s f e r i s p r o p o r t i o n a l to the current f l o w i n g ( w i t h i n a c e r t a i n range of c o n c e n t r a t i o n ) and i s thus to some extent under the d i r e c t c o n t r o l of the experimenter. C y c l i c 73 o p e r a t i o n of such systems may t h e r e f o r e be b e t t e r represented by a r a t e model than by e q u i l i b r i u m theory. 3.2.2. Rate Models Two r a t e models w i l l be considered here: (a) constant r a t e model (b) concentration-dependent r a t e model The b a s i c assumption i n each of these models i s t h a t the e q u i l i b r i u m c o n d i t i o n may be disregarded a l t o g e t h e r , i . e . i f the two phases were l e f t i n s t a t i o n a r y contact f o r a s u f f i c i e n t l y long p e r i o d of time, the adsorbate would be t r a n s f e r r e d completely i n t o one of the phases. These models a l s o assume that the c a p a c i t y of the storage l a y e r s i s l a r g e enough th a t i t does not impose a l i m i t on mass t r a n s f e r during the c y c l e . A x i a l d i s p e r s i o n i s neglected and the f l u i d i s assumed to be incompressible and have constant d e n s i t y . The complete op e r a t i n g c y c l e i s d i v i d e d i n t o a number of sub- i n t e r v a l s ; whenever the f l u i d v e l o c i t y changes a t the end of these per i o d s i t i s assumed that i t changes i n a stepwise manner, w h i l e i t remains constant during each of these s u b - i n t e r v a l s . Furthermore, a system i n which one v o i d volume i s d i s p l a c e d every h a l f c y c l e i s considered. Concentration changes p r e d i c t e d by the r a t e models are f u n c t i o n s of time, i n c o n t r a s t to the e q u i l i b r i u m model s o l u t i o n s which are f u n c t i o n s of the number of c y c l e but not of r e a l time, (a) Constant r a t e model A constant r a t e of Interphase mass t r a n s f e r , uniform everywhere w i t h i n the c e l l , r e q u i r e s a constant, uniform, d i s t r i b u t i o n of e l e c t r i c c u r r e n t . U n i f o r m i t y can be approximated by connecting a number of short s t a c k s together i n s e r i e s both e l e c t r i c a l l y and h y d r a u l i c a l l y , as shown i n F i g u r e 16. 74 Dialysate Production Br'me Production FIGURE 16 Series connection of ED modules to approximate constant-rate operation. 75 Constant c u r r e n t can be maintained by a s u i t a b l e power supply. This w i l l ensure constant mass t r a n s f e r u n t i l the s o l u t e c o n c e n t r a t i o n drops low enough at some p o i n t i n the apparatus t h a t water s p l i t t i n g occurs and sol v e n t ions s t a r t to c a r r y a s i g n i f i c a n t p o r t i o n of the c u r r e n t . While constant- r a t e o p e r a t i o n i s not very p r a c t i c a l , an examination of some of the con- sequences of t h i s model i s of i n t e r e s t s i n c e i t i l l u s t r a t e s l i m i t i n g c o n d i t i o n s . I f the r a t e of mass t r a n s f e r i s h e l d constant, and a x i a l d i f f u s i o n i s negle c t e d , Equation (64) s i m p l i f i e s to dC 9C. .. ac •*r + vTT- = - < ̂ T^- > TT- = K (constant) (65) dt dZ £ dt during any s u b - i n t e r v a l of the c y c l e . ( i ) Synchronous (in-phase) o p e r a t i o n I f the t o t a l c y c l e p e r i o d T i s composed of two equal s u b - i n t e r v a l s , w i t h simultaneous r e v e r s a l of both the f l o w d i r e c t i o n and the d i r e c t i o n of mass t r a n s f e r , then the constant i n Equation (65) can be w r i t t e n K = - during the d e m i n e r a l i z i n g h a l f - c y c l e and K = K 2 during enrichment i . e . dC c dC £ s dt"~ = ~ P = ~ ^1 » ^ o r d e m i n e r a l i z a t i o n (66) dC £ dC t s -j-jT- = - p = K 2 ; f o r enrichment (67) 1 - e where p = e T I f we consider K 2 > and d e m i n e r a l i z a t i o n takes p l a c e f o r time y ; then to ma i n t a i n the m a t e r i a l balance of the system the enrichment p e r i o d should be At where 76 T K At - ^ (68) T K l during the r e s t of enrichment h a l f c y c l e i . e . — (1 - — ) the v o l t a g e can 2 be switched o f f to save power. The g r a p h i c a l s o l u t i o n of the model Equations (66, 67, 68) g i v e s the f o l l o w i n g r e s u l t ( r e f e r to Appendix D): C T K T K K o o o 2 - 1 + t f ( 1 - k : ^ ( 7 0 ) o o 2 where C„, are the top (demineralized) product and the bottom (enriched) 1 a product r e s p e c t i v e l y C i s the i n i t i a l c o n c e n t r a t i o n ; CN, N. = C . rtN = C o ' f(t=0) s(t=0) o n i s the number of c y c l e s From Equations (69, 70) i t i s c l e a r that maximum s e p a r a t i o n occurs when K l K_ >> K. or when — -»• 0. I n t h i s case the s e p a r a t i o n f a c t o r , ns i s given £• J. K 2 by TK-n n s - T T ^ - T,n TK 1n 1 - 4 C o I t i s a l s o obvious that when = 1^, no s e p a r a t i o n occurs a f t e r the f i r s t c y c l e . The c o n c e n t r a t i o n of s o l u t e stored w i t h i n the membranes r e t u r n s to i t s i n i t i a l v a l u e a t the end of each c y c l e and the average top and bottom con- c e n t r a t i o n s (Equations 69, 70) do not change a f t e r the f i r s t c y c l e . F i g u r e 17 i l l u s t r a t e s s u ccessive c o n c e n t r a t i o n p r o f i l e s i n 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(i i ) t =0 O t = T / 2 c ( i ) c( i i ) t = T /2 E> t = T d ( i ) d(ii) t= T O t = 3 T / 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 i n the end r e s e r v o i r s when = K 2» For s i m p l i c i t y i t i s assumed that the end r e s e r v o i r s have the same volume and the same L/D r a t i o as the c e l l i n t e r i o r . The i n i t i a l c o n c e n t r a t i o n p r o f i l e i s shown i n ( a ) , F i g u r e 17, A f t e r the f i r s t h a l f - c y c l e the c o n d i t i o n s are e i t h e r as shown i n ( b i ) ( i f no mixing takes p l a c e i n the end r e s e r v o i r ) or i n ( b i i ) ( i f the end r e s e r v o i r i s w e l l mixed). The f l u i d i n the top r e s e r v o i r i s d i s p l a c e d back through the column to produce the p r o f i l e s shown i n ( c i ) or ( c i i ) at the end of the f i r s t complete c y c l e , when the mean c o n c e n t r a t i o n i n the bottom r e s e r v o i r has returned to the v a l u e i t had i n ( c ) . F i g u r e 17(d) shows c o n d i t i o n s at the end of the 3rd h a l f c y c l e , which are i d e n t i c a l w i t h (b) . I n order to o b t a i n s e p a r a t i o n we must e i t h e r : ( i ) make K 2 > , or ( i i ) modify the c y c l e s by p e r i o d i c a l l y i n t e r r u p t i n g the e l e c t r i c c u r r e n t , or ( i i i ) modify the c y c l e s by p e r i o d i c a l l y i n t e r r u p t i n g the f l u i d f l o w , ( i v ) i n t r o d u c e l a g between c u r r e n t and f l o w c y c l e s i . e . use out-of- phase o p e r a t i o n Case ( i ) has a l r e a d y been considered. Thompson et a l . (1974) has d i s - cussed the other three cases as shown i n the f o l l o w i n g s e c t i o n s . ( i i ) I n t e r r u p t e d Current o p e r a t i o n This i s a more general and more u s e f u l type of o p e r a t i o n than case ( i ) Here the c u r r e n t i s turned o f f during a p a r t of every h a l f c y c l e . F i g u r e 18 shows the f l o w and c u r r e n t c y c l e s f o r t h i s k i n d of o p e r a t i o n . During the f i r s t h a l f - c y c l e both f l o w and mass t r a n s f e r take p l a c e f o r p e r i o d T^, at which p o i n t the c u r r e n t i s turned o f f and f l o w continues f o r p e r i o d T 0 . A s i m i l a r sequence, and T^, f o l l o w d u r ing the second h a l f - c y c l e . From the m a t e r i a l balance on the s a l t V i - K 2 T 3 ( 7 2 ) and from the m a t e r i a l balance on the solvent T l + T 2 = T 3 + T 4 ( 7 3 ) I f 3 i s the f r a c t i o n of the f i r s t h a l f - c y c l e during which the c u r r e n t i s on (3 = T ^ / , then the suc c e s s i v e i n t e r v a l s a r e ; r± = 3 ( f ) T 2 = (1 - 3)( | ) t 3 - > *1 T and T 4 = (1 - ^ 3) ( \ ) (74) F i g u r e 18 shows c o n c e n t r a t i o n p r o f i l e s a t consecutive i n t e r v a l s i n a batch s e p a r a t i o n , f o r s i m p l i c i t y a system i n which the end r e s e r v o i r s remain unmixed i s i l l u s t r a t e d . The dotted l i n e s represent the c o n c e n t r a t i o n at the beginning of each p e r i o d and the s o l i d l i n e s show the p r o f i l e a t the end of each p e r i o d . Subsequent c y c l e s r e s u l t i n a p r o g r e s s i v e b u i l d up of the c o n c e n t r a t i o n wave. The average top product c o n c e n t r a t i o n a f t e r n c y c l e s i s given by C TK TK K = l - - ^ M 2 - 6 ) - ^ M 2 - M l + ^ ) ] (n - 1) (75) o o o 2 and the average c o n c e n t r a t i o n of the bottom (enriched) product i s FIGURE 18 Concentration profiles-interrupted current cycle. 81 C TK K = 1 + j± 3 [2 - 3 (1 + ^ )] n (76) o o 2 I f = K 2 and 3 = 1 s e p a r a t i o n ceases a f t e r 1 c y c l e . I t i s p o s s i b l e to choose a valu e of 6 that g i v e s c o n t i n u i n g s e p a r a t i o n f o r any s p e c i f i e d v a l u e of K̂ /K,,. D i f f e r e n t i a t i o n of equation (75) or (76) shows th a t the most r a p i d i n c r e a s e i n s e p a r a t i o n w i l l be obtained when K 2 Under these c o n d i t i o n s the s e p a r a t i o n f a c t o r i s given by TK 1 + 4 c T e n ns = - ^ (78) 1 - - ~ 3 (n - 3 + 1) o Thus, i f K^ = K 2 > best s e p a r a t i o n i s obtained by s e t t i n g 3 = h, so that = T_ = x_ = T, and the s e p a r a t i o n f a c t o r i s 2 3 4 TK 1 + 8 c T n ns - _ 2 (79) 1 - -ggi (n + W o 8C n = ( ™ h). I f n > n , then n must be used. max TK^ max' max I f K 2 >> K^, 3 = 1 and the s e p a r a t i o n f a c t o r i s TK 1 + 4 c T n ns = ^ (80) 1 " 4 C - n o 4C provided t h a t n < — - T K 1 82 Since the c u r r e n t i s o n l y on f o r f r a c t i o n 3 of each c y c l e , the amount of s e p a r a t i o n obtained f o r a given amount of c u r r e n t consumed i s approximately the same i n equations (79) and (80). I f a r e a l system i s operated w i t h > K^, but w i t h no e x t e r n a l l y c o n t r o l l e d i n t e r r u p t i o n of the c u r r e n t , as i n case ( i ) , the c o n c e n t r a t i o n i n the storage l a y e r s must c o n t i n u a l l y decrease i n s u c c e s s i v e c y c l e s . A f t e r a number of c y c l e s the c o n c e n t r a t i o n w i l l drop to near zero part way through a d e p l e t i o n h a l f c y c l e , causing the e l e c t r i c a l r e s i s t a n c e to become very l a r g e . I f the v o l t a g e i s c o n t r o l l e d at a constant v a l u e the c u r r e n t must then become very s m a l l , so t h a t , from t h i s c y c l e onward, the system w i l l behave as i f the c u r r e n t were i n t e r r u p t e d p a r t way through each d e p l e t i o n c y c l e . ( i i i ) I n t e r r u p t e d f l o w o p e r a t i o n A t h i r d type of o p e r a t i n g c y c l e i s shown i n F i g u r e 19. Here the f l u i d displacement, r a t h e r than the c u r r e n t , i s p e r i o d i c a l l y i n t e r r u p t e d . The c u r r e n t i s turned on at the beginning of the c y c l e , to d e m i n e r a l i z e the s o l u t i o n , but f l o w does not s t a r t u n t i l the end of pause time x^. The f l u i d i s d i s p l a c e d upward during p e r i o d w h i l e the c u r r e n t remains on and f u r t h e r d e m i n e r a l i z a t i o n takes p l a c e . The p o l a r i t y i s reversed at the s t a r t of p e r i o d x^ and a s i m i l a r sequence of f l o w pause f o l l o w e d by downward displacement completes the c y c l e . The complete c y c l e time T c o n s i s t s of the two pause peri o d s x^ and x^ and the displacement p e r i o d s and x^. In the subsequent work based on t h i s o p e r a t i n g c y c l e the displacement p e r i o d s are kept constant and the c y c l e time T v a r i e s w i t h the pause time used. From the m a t e r i a l balance on the s a l t K l ( t 1 + T 2 ) = K 2 ( T 3 + T 4 ) ( 8 1 ) 83 and from the m a t e r i a l balance on the s o l v e n t T 2 = T 4 (82) I f pause l a s t s f o r a f r a c t i o n of the t o t a l c y c l e time T, then the successive i n t e r v a l s are: T l =  a(f) T K 2 T T 2 = K x + K 2 " a ( 2 } K l ~ K 2 T and T 4 - x 2 (83) F i g u r e 19 i l l u s t r a t e s the way i n which the c o n c e n t r a t i o n p r o f i l e develops i n a c l o s e d system w i t h no mixing i n the. end compartments. The average top-compartment c o n c e n t r a t i o n a f t e r the nth c y c l e i s given by C TK 2K TK K K -K o o 1 2 o 2 1 2 (84) and the bottom c o n c e n t r a t i o n i s C = 1 + 7 7 ^ U l + ^ ) a + 2 ( 1 2 )} n (85) C Q 4C Q K 2 K X + K 2 I f K^ = K 2 the s e p a r a t i o n f a c t o r i s 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 ( 8 6 ) , 1 , , l-ot s 1 - _ a (n + — ) o 2C o 1 _ a Provided that o < a < 1 and n = ( — -z— ) . max TK^a 2a I f n > n , then n must be used, max max Obviously, best s e p a r a t i o n i s obtained as a + 1, g i v i n g an op e r a t i n g c y c l e w i t h r e l a t i v e l y long flow-pauses and r a p i d displacement. This s p e c i a l case may be r e f e r r e d to as instantaneous displacement o p e r a t i o n or pure- pause o p e r a t i o n i n comparison w i t h continuous displacement o p e r a t i o n of Case ( i ) . As a 1, the s e p a r a t i o n i s given by TK 1 + 2 C ^ n ns = (87) TK 1 - 2 T n o which i s double the valu e p r e d i c t e d by case ( i ) i n i t s best o p e r a t i n g con- d i t i o n s (Equation 71). ( i v ) Out-of-phase o p e r a t i o n F i g u r e 20 i l l u s t r a t e s the c o n c e n t r a t i o n p r o f i l e s a t s u c c e s s i v e quarter c y c l e s a f t e r the s t a r t f o r a constant r a t e process o p e r a t i n g w i t h the cur r e n t c y c l e 90° out-of-phase w i t h the displacement. I t i s assumed that the r a t e constants K^ and are equal and th a t the e f f l u e n t remains unmixed i n the end r e s e r v o i r s . I n c o n t r a s t to in-phase o p e r a t i o n , out-of-phase o p e r a t i o n leads to a c o n t i n u i n g b u i l d - u p of the c o n c e n t r a t i o n wave. 2T I f the c u r r e n t s w i t c h i n g leads the flo w s w i t c h i n g by time T, and y = —» the average top and bottom c o n c e n t r a t i o n t r a n s i e n t s a f t e r the nth c y c l e are FIGURE 20 Concentration profiles predicted by constant-rate modeLcontinuous cyclic displacement of fluid and mass transfer.The mass transfer cycle is 9 0 ° out-of .phase with the displacement cycle. 87 given by: C TK TK = 1 - • — [1 - 2 Y 2 ] - - ^ ( 1 - Y) (Y) (n - 1) (88) o o o C TK = 1 + (1 - Y) (Y) n (89) o o i n the i n t e r v a l o 4 y < h* The conce n t r a t i o n s change l i n e a r l y with the number of c y c l e s and the gr e a t e s t r a t e of change occurs when y = h. This i s i n marked c o n t r a s t to the r e s u l t s of the e q u i l i b r i u m model of parametric pumping, which p r e d i c t s best s e p a r a t i o n when t r a n s f e r and displacement c y c l e s are i n phase and no s e p a r a t i o n when they are 90° out of phase ( P i g f o r d et a l . , 1969 a ) . The s e p a r a t i o n f a c t o r when Y = 0 i s given by ns = i = - - (90) x 4C o i . e . s e p a r a t i o n ceases a f t e r 1 c y c l e . When y = h the s e p a r a t i o n f a c t o r i s TK- 1 + 4 c T n ns = ^ (91) 1 " 4CT < n - ^ o 4C n = ( — — I - % ) . When n > n , then n must be used. . max TK^ max max Figure 21 shows c o n c e n t r a t i o n p r o f i l e s i n a p o s s i b l e arrangement of two u n i t s operated together, w i t h the top of one c e l l connected d i r e c t l y to the top of the other and the bottoms of the c e l l s connected together through a r e v e r s i b l e pump. With t h i s c o n f i g u r a t i o n no end r e s e r v o i r s are needed and the c o n c e n t r a t i o n wave b u i l d s up twice as r a p i d l y as w i t h a s i n g l e u n i t . Flow J I I I I I I I I J I O - H / 4 T / 4 - H / 2 T / 2 4 3T/4 3 T / 4 - > T FIGURE 21 Back_to_back operation of two units. Case (a) , the top row , operates with cyclic displacement of fluid , 9 0 ° out_of_phase mass transfer. Case (b),operates with no flow reversal , cyclic mass transfer. 89 Note that the c o n c e n t r a t i o n p r o f i l e i n F i g u r e 21(a) i s symmetrical at the end of each h a l f c y c l e . Because of t h i s symmetry e i t h e r p e r i o d i c f l o w r e v e r s a l or continuous f l o w , F i g u r e 21(b), l e a d to s i m i l a r s e p a r a t i o n . In the f i r s t method of o p e r a t i o n an o s c i l l a t i n g c o n c e n t r a t i o n wave i s generated, which grows with time, w h i l e i n the second method a r o t a t i n g wave i s produced which grows at the same r a t e . A t h i r d p o s s i b i l i t y would be to operate a number of u n i t s i n s e r i e s to generate a t r a v e l l i n g wave, growing as i t moves along. Operation of e q u i l i b r i u m systems i n t h i s manner has been discussed by P i g f o r d et a l . (1969 b ) . Comments on v a r i o u s operations of the c o n s t a n t - r a t e model By comparing the s e p a r a t i o n obtained i n the f o u r cases d i s c u s s e d p r e v i o u s l y , i t can be n o t i c e d t h a t the c o n c e n t r a t i o n s change f a s t e r i n case ( i i i ) than w i t h e i t h e r of the other cases considered. Since mass t r a n s - f e r d u r ing displacement c o n t r i b u t e s l i t t l e to the f i n a l s e p a r a t i o n i n pause ope r a t i o n (case ( i i i ) ) , some economy i n e l e c t r i c power consumption might be obtained by t u r n i n g the current o f f during a l l or p a r t of the displacement p e r i o d s . (b) Concentration-dependent r a t e model" While i t i s p o s s i b l e to operate the process i n a constant c u r r e n t / c o n - s t a n t r a t e mode, i t i s more convenient to apply a constant p o t e n t i a l to the e l e c t r o d e s . The l o c a l c u r r e n t d e n s i t y i s then a f u n c t i o n of the concen- t r a t i o n s along the current path and of the e f f e c t i v e v o l t a g e . I f the a p p l i e d v o l t a g e i s A<j>, and the v o l t a g e a v a i l a b l e to the stack i s At))' ( a f t e r ohmic l o s s e s and o v e r p o t e n t i a l s i n the e l e c t r o d e compartment are allowed f o r ) , then the c u r r e n t through the stack i s given by 90 1 - ^ R - ^ ( 9 2 ) where A<J>̂ ~XT i s the Donnan p o t e n t i a l across the membranes of the stack. The DON r r e s i s t a n c e i s the sum of three terms, R - the r e s i s t a n c e of the membranes, m R f - the i n t e g r a l r e s i s t a n c e of the f l u i d i n the f l o w channels, and R - the i n t e g r a l r e s i s t a n c e of the f l u i d s t o r e d i n the core l a y e r s w i t h i n each membrane p a i r . The f l u i d r e s i s t a n c e terms comprise the b u l k f l u i d r e s i s t a n c e together w i t h the a s s o c i a t e d boundary l a y e r s r e s i s t a n c e s . Under the operating c o n d i t i o n s f o r most experiments the Donnan p o t e n t i a l was s m a l l compared to the a p p l i e d p o t e n t i a l , so t h a t the c u r r e n t d e n s i t y was mainly c o n t r o l l e d by the l a r g e s t r e s i s t a n c e i n the c u r r e n t path. Low con- c e n t r a t i o n s , and hence high r e s i s t a n c e s , occurred i n the f l o w channels during most of the d e p l e t i o n p a r t of an o p e r a t i n g c y c l e , and i n the membrane cores during enrichment. A c c o r d i n g l y the 'following r a t e laws were assumed 9C g p - r r — = &i Ĉ . (during d e p l e t i o n ) (93) a t JL t ac - r — - = - a„ C (during enrichment) (94) o t 2 s S u b s t i t u t i n g these equations i n t o equation (64), and n e g l e c t i n g a x i a l d i f f u s i o n , leads to a set of equations t h a t can be solved a n a l y t i c a l l y f o r some boundary c o n d i t i o n s . S o l u t i o n s have been obtained (Bass, 1972) f o r the i n t e r r u p t e d - f l o w operating c y c l e p r e v i o u s l y described provided mass t r a n s f e r i s r e s t r i c t e d to the flow-pause periods and the d i s p l a c e d f l u i d volume i s equal to the v o i d volume. Under these c o n d i t i o n s , the average d i a l y s t a t e and b r i n e c o n c e n t r a t i o n s a f t e r n c y c l e s are ^ - P n (95) C o 91 4=n-l i » o 2 + p _ p n _ p q n _ q p n - l ( 1 _ p ) j- { ± ] 4 ( g g ) where a l T p = exp ( — ) a 2 T q = exp ( 2~ ) 1 - e p = — - — An a l t e r n a t i v e s e m i - e m p i r i c a l approach can be developed by assuming a concentration-dependent mass t r a n s f e r r a t e s i m i l a r to Equations (93, 94) 9C p = \ CF (during d e p l e t i o n ) (97) By c o n s i d e r i n g the o v e r a l l m a t e r i a l balance f o r the s o l u t e and the l i m i t i n g s e p a r a t i o n a general s o l u t i o n of the system i s obtained i n which the average d i a l y s t a t e and b r i n e c o n c e n t r a t i o n s a f t e r n c y c l e s are given by C -k Tn -k Tn = exp( -j— ) + k 2 [1 - exp( -f-)] (98) o C -k.. Tn _ k/. T n = 2 - exp( - | — ) - k 2 [1 - exp( -f- )] (99) o This s o l u t i o n can be s i m p l i f i e d by assuming that k^ = k^ = k^ i n t h i s case Equations (98, 99) reduce to C -k Tn -k Tn o exp( ) + k 2 [1 - exp( - | — )] o -k Tn = k 2 + (1 - k 2 ) exp ( - 1 — ) (100) C -k Tn = 2 + ( k 2 - 1) exp ( - ± — ) - k 2 (101) 92 where k^, k^ are constants which are f u n c t i o n s of system and o p e r a t i n g parameters. I f we assume f l o w channel and storage compartment are of the same c a p a c i t y and dimensions (as i s the u s u a l case) then p =1.0 and Equations (95, 96) w i l l be a s p e c i a l case of Equations (98, 99) where the constants are given by k n = a 1 , k„ = - 1 , k. = 0 and k. = a. 3.2.3. Comment on Constant-Rate Model Although the c o n s t a n t - r a t e model i s compact and easy to apply i t ignores d i s p e r s i v e and c u r r e n t - l i m i t i n g e f f e c t s which l i m i t s e p a r a t i o n i n a r e a l system; hence i t can not p r e d i c t the u l t i m a t e s t e a d y - s t a t e s e p a r a t i o n . However, the model o f f e r s simple a l g e b r a i c s o l u t i o n s to a complicated system which can be u t i l i z e d to show g r a p h i c a l l y the development of the c o n c e n t r a t i o n p r o f i l e s and to i n d i c a t e when s e p a r a t i o n w i l l not occur. The model has been used e x t e n s i v e l y i n the present work to compare v a r i o u s o p e r a t i n g c y c l e s and modes of o p e r a t i o n . CHAPTER 4 The C y c l i c E l e c t r o d i a l y s i s Process - O b j e c t i v e s , Techniques and Apparatus 4.1. O b j e c t i v e s of the Program The primary o b j e c t i v e s of t h i s experimental program were; to explore the p o s s i b l e regions of a p p l i c a t i o n of c y c l i c o p e r a t i o n i n an open e l e c t r o d i a l y s i s system, to screen system parameters and to determine t h e i r r e l a t i v e importance. Previous work i n a batch system (Bass, 1972) showed that the most important o p e r a t i n g parameters were the displacement c y c l e , the a p p l i e d v o l t - age and the i n i t i a l c o n c e n t r a t i o n . These were f u r t h e r i n v e s t i g a t e d here together w i t h the e f f e c t of pro d u c t i o n r a t e . An open system o f f e r s a h i g h degree of freedom w i t h regard to i n t r o d u c t i o n of feed and withdrawal of products, and a v a r i e t y of d i f f e r e n t o p e r a t i n g modes were considered. The modular c o n s t r u c t i o n of the ED c e l l allowed crude measurements to be made of the a x i a l d i s t r i b u t i o n of c u r r e n t and probe v o l t a g e during the c y c l e and a l s o permitted the e f f e c t of channel l e n g t h to be i n v e s t i g a t e d . The c o n s t a n t - r a t e model discussed i n Chapter 3 p r e d i c t e d that the i n t e r r u p t e d f l o w o p e r a t i o n would r e s u l t i n the best s e p a r a t i o n compared to the other c y c l e s s t u d i e d (synchronous, out-of-phase and i n t e r r u p t e d c u r r e n t 93 94 c y c l e s ) . The experimental p a r t of the work was based mainly on t h i s i n t e r r u p t e d f l o w c y c l e . The c y c l e i s most c o n v e n i e n t l y described w i t h r e f e r e n c e to a s i n g l e e l e c t r o d i a l y s i s s t a c k , however two stacks c l o s e - coupled i n a back-to-back c o n f i g u r a t i o n were used i n most of the experimental work. 4.2. S i n g l e Stack Operation F i g u r e 22 i l l u s t r a t e s the sequence of events t h a t make up a complete o p e r a t i n g c y c l e . The e l e c t r o d i a l y s i s c e l l (ED c e l l ) i s shown s c h e m a t i c a l l y as a r e c t a n g u l a r box w i t h an i n t e r n a l shaded area symbolizing the s o r p t i o n membrane stack. Two w e l l mixed r e s e r v o i r s ( c i r c l e s i n F i g u r e 22) are connected to the ends of the ED c e l l . P a r t i a l shading of the c i r c l e s i n d i c a t e s the l i q u i d content of these r e s e r v o i r s a t d i f f e r e n t times during the c y c l e . F i g u r e 22 shows batch o p e r a t i o n but i t can be mo d i f i e d to a l l o w f o r feed a d d i t i o n and product removal i n v a r i o u s ways during the c y c l e . The i n t e r i o r of the c e l l i s d i v i d e d by many p a r a l l e l i o n - s e l e c t i v e membranes i n t o two r e g i o n s ; a set of f l o w channels connecting the i n l e t and o u t l e t p o r t s , and an i n t e r l e a v e d set of c l o s e d " c a p a c i t y c e l l s " or membrane stack. Depending on the d i r e c t i o n of the e l e c t r i c c u r r e n t , ions are e i t h e r t r a n s f e r r e d from the s o l u t i o n i n the f l o w channels to that i n the c a p a c i t y c e l l s or v i c e - v e r s a . During the f i r s t h a l f c y c l e the a p p l i e d e l e c t r i c p o t e n t i a l i s c o n t r o l l e d to produce a p o s i t i v e square wave. The membranes 95 MOIJ pe||ddv 96 are p o s i t i o n e d i n such a way that p o s i t i v e p o l a r i t y i s e q u i v a l e n t to s o l u t e uptake ( i . e . the c a t i o n i c membranes face the anode). The i n t r a c h a n n e l s o l u t i o n i s , t h e r e f o r e , depleted during the e n t i r e f i r s t h a l f - c y c l e which c o n s i s t s of two p a r t s : a "pause" or no-flow i n t e r v a l (T^) f o l l o w e d by a "displacement" i n t e r v a l ( x 2 ) during which the f l u i d flows w i t h constant r a t e (Q) from the lower to the upper r e s e r v o i r . D i s p l a c i n g f l u i d e n t e r i n g the bottom of the c e l l may be f r e s h feed or " r e f l u x " r e t u r n i n g a f t e r a previous downward displacement, or a mixture of these. The second h a l f - c y c l e begins w i t h a p o l a r i t y r e v e r s a l (- n) and a simultaneous f l o w stoppage f o r another "pause" i n t e r v a l (T^). The i n t r a c h a n n e l s o l u t i o n r e c e i v e s s o l u t e from the membrane stack during the whole p e r i o d of t h i s second h a l f - c y c l e , which i s concluded by a "displacement" i n t e r v a l (T^) d u r i n g which the s o l u t i o n i s returned from the upper to the lower r e s e r v o i r w i t h f l o w r a t e (- Q). The d i s p l a c i n g f l u i d e n t e r i n g at the top of the c e l l may be f r e s h f e e d , or a r e f l u x stream of depleted s o l u t i o n obtained during p e r i o d (T^) or a com- b i n a t i o n of these. In an open system p a r t i a l r e f l u x must be used to achieve c y c l i c o p e r a t i o n w h i l e i n a c l o s e d system the o p e r a t i o n , i n some ways, i s analogous to t o t a l r e f l u x o p e r a t i o n of a d i s t i l l a t i o n column. I n i t i a l l y the s o l u t e c o n c e n t r a t i o n s i n the system are i n e q u i l i b r i u m across the membranes and equal everywhere. Each c y c l e produces d e p l e t i o n of the s o l u t i o n i n the upper r e s e r v o i r and enrichment of the s o l u t i o n i n the lower one, and an a x i a l c o n c e n t r a t i o n g r a d i e n t continues to develop i n the ED c e l l u n t i l l i m i t i n g s t e a d y - p e r i o d i c c o n d i t i o n s are reached. In most of the experiments report e d here symmetric h a l f c y c l e s w i t h regard to time i n t e r v a l s have been used i . e . x.. = x and x„ = x.. 97 A.3. Back-to-Back Stack C o n f i g u r a t i o n Since some, or a l l , of the f l u i d l e a v i n g the c e l l d u r i n g upward displacement i s subsequently to be returned as r e f l u x , i t i s convenient to connect two c e l l s together as shown i n F i g u r e 23. This d i r e c t coupled- back-to-back c o n f i g u r a t i o n avoids the n e c e s s i t y of i n t e r m e d i a t e r e f l u x storage tanks. A l s o experiments i n a batch o p e r a t i o n showed th a t mixing i n the end r e s e r v o i r s lowers s e p a r a t i o n and a r e d u c t i o n of mixing i n the s o l u t i o n e x t e r n a l to the stack helps to reduce the e f f e c t s of i n t e r n a l mixing by reducing the g r a d i e n t s of the t r a v e l l i n g f r o n t s . The average s e p a r a t i o n f a c t o r was increased by 30 - 100% when an end r e s e r v o i r ( w e l l mixed) was replaced by a c o i l t ubing (Bass, 1972). The two c e l l s so connected (Fi g u r e 23) are operated e l e c t i c a l l y out- of-phase w i t h each other and, of course, upward displacement i n one c e l l i m p l i e s downward displacement i n the other (with the p o s s i b l e exception of periods when the feed i s being introduced or products removed). This type of c o n f i g u r a t i o n can be used i n e i t h e r c l o s e d or open system o p e r a t i o n s . F i g u r e 24 shows how the c o n c e n t r a t i o n p r o f i l e s are p r e d i c t e d to develop during the f i r s t few c y c l e s of o p e r a t i o n i n a c l o s e d mode, based on the constant r a t e model. The model n e g l e c t s a x i a l d i f f u s i o n , but q u a l i - t a t i v e l y i t i s apparent that a x i a l mixing w i l l tend to smooth out the square- wave p r o f i l e i n t o a shape more n e a r l y resembling a s i n e wave. 4.3.1. Open System Operation of a back-to-back c o n f i g u r a t i o n I f feed i s to be i n t r o d u c e d , and products withdrawn, connections must be provided w i t h v a l v e s that are timed to open at a p p r o p r i a t e moments during the c y c l e . Since the t o t a l volume of the system remains cons t a n t , 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 f 3 Pause VO 100 be introduced whenever product i s withdrawn. For best s e p a r a t i o n i t would seem d e s i r a b l e to take products whenever maxima or minima i n the c o n c e n t r a t i o n p r o f i l e s pass the ap p r o p r i a t e p o r t s , and to intr o d u c e feed at a p o s i t i o n where the c i r c u l a t i n g f l u i d i s c l o s e to the feed composition. I f the c o n c e n t r a t i o n p r o f i l e around the loop comprising the two c e l l s and t h e i r i n t e r c o n n e c t i o n s i s approximately s i n u s o i d a l then feed i n t r o d u c t i o n p o r t s must be l o c a t e d 90° away from product removal p o r t s . Regarding the feed l o c a t i o n and the feed t i m i n g , an open system can be run under e i t h e r symmetric, semi-symmetric or asymmetric type of o p e r a t i o n . In symmetric o p e r a t i o n feed i s introduced and products removed every h a l f c y c l e w i t h the feed being introduced to the top and bottom of each c e l l . I n semi-symmetric o p e r a t i o n feed i s introduced every h a l f c y c l e , but to one s i d e only of each c e l l ; w h i l e i n the t h i r d mode of o p e r a t i o n n e i t h e r the feed l o c a t i o n nor the feed t i m i n g i s symmetrical, and the feed i s introduced only once to one s i d e of each c e l l every c y c l e . F i g u r e 25 represents a symmetric o p e r a t i o n w i t h product removal from the mid-points of each c e l l . I t shows the r e q u i r e d connections and the v a l v e t i m i n g . I n symmetric o p e r a t i o n each c y c l e i s subdivided i n t o e i g h t i n t e r v a l s t ^ ( i = 1,2, ... 8) . The a c t i v i t y takes p l a c e at each time i n t e r v a l as shown i n the t a b l e of F i g u r e 25 which a l s o shows the p o l a r i t y of the of the e l e c t r i c f i e l d , the c o n d i t i o n of the pump ( i . e . whether i d l e or ope r a t i n g and i n which d i r e c t i o n ) , i t a l s o i n d i c a t e s the s t a t e of the v a r i o u s s o l e n o i d v a l v e s and which of them i s energized (open) and which of them i s c l o s e d during the s p e c i f i c time i n t e r v a l concerned. The developing c o n c e n t r a t i o n p r o f i l e f o r t h i s mode of o p e r a t i o n i s shown i n F i g u r e 26. Here the amount of feed i n t r o d u c e d / c y c l e i s -r- of the t o t a l c i r c u l a t i n g volume. 101 V2 I X h V4 -X- V5 V3 n V6 -tXr- V7 -{XI- F Time Interval ^ v ^ ^ l t e m Opera t ion \^ 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 + f 2 B from I 0 0 0 y 0 0 0 y 0 0 + f 3 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 - f 6 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 - f 8 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 B 4 ^ 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 l i I Circulation FIGURE 26 _ Continued (2) FIGURE 26 Developing concentration profile , symmetric operation of an open system 105 F i g u r e 26 as w e l l as F i g u r e 28 and 30 ignore a x i a l mixing e f f e c t s , and c o n c e n t r a t i o n changes d u r i n g feed admission and displacement have been omitted f o r c l a r i t y of p r e s e n t a t i o n . The product w i l l undergo „ t o t a l c i r c u l a t i n g volume - . , , .. . , -2 x :;—- ; : a c y c l e s of enrichment or d e p l e t i o n before t o t a l feed volume emerging under t h i s mode of o p e r a t i o n . In these F i g u r e s v e r t i c a l axis' i n d i c a t e s c o n c e n t r a t i o n l e v e l , a h o r i z o n t a l arrow shows c i r c u l a t i o n of s o l u t i o n from one c e l l i n t o another, and the l e t t e r s F, D, B i n d i c a t e the c o n c e n t r a t i o n as w e l l as the l o c a t i o n i n the c e l l where the feed, F i s introduced or the depleted and enriched products D and B are withdrawn. F i g u r e 27 represents a semi-symmetric o p e r a t i o n w i t h i t s connections and v a l v e timing sequence. Here the products are removed a l t e r n a t e l y from the top of c e l l I I and the bottom of c e l l I , w h i l e feed i s s u p p l i e d to the top of c e l l I and the bottom of c e l l I I . The waveform generated i n F i g u r e 28 i s of sawtooth shape, and the e f f i c i e n c y of t h i s o p e r a t i n g c y c l e w i l l depend on how w e l l t h i s waveform can be maintained under the i n f l u e n c e of a x i a l mixing processes. I t would be expected that t h i s method of o p e r a t i o n would be more s e n s i t i v e to a x i a l mixing than the scheme shown i n F i g u r e 25. In the absence of mixing, both c y c l e s are p r e d i c t e d to g i v e equal s e p a r a t i o n (compare F i g u r e s 26 and 28). F i g u r e 29 shows an asymmetric o p e r a t i o n . An operating c y c l e here c o n s i s t s of s i x time i n t e r v a l s t ^ ( i = 1,2 ... 6) that c o n s t i t u t e two non- symmetric h a l f c y c l e s and i t needs o n l y 4 v a l v e s as i n d i c a t e d i n F i g u r e 29. An asymmetric o p e r a t i o n presents a f u r t h e r s i m p l i f i c a t i o n of the system w i t h - out a f f e c t i n g i t s s e p a r a t i n g c a p a b i l i t y and r e s u l t s i n the same s e p a r a t i o n as t h a t p r e d i c t e d by the previous modes of o p e r a t i o n (compare F i g u r e s 26, 28 and 30). 106 V4 V3 -txj- V6 - t X r - > B V5 V7 B n f2 Time Interval ^ v j t e m Operation^. VI V2 V3 V4 V5 V6 V7 Pump p Vol- tage A(j) * 1 Pause 0 0 0 0 0 0 0 0 f 2 B from 1 y 0 0 0 0 0 y 0 *3 D from II 0 y 0 y 0 0 0 0 + f 4 Circulation 0 0 y 0 0 0 0 + f 5 Pause 0 0 0 0 0 0 0 0 - f 6 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 r 5 Pause FIGURE 28 "1 J B Production Production f 6 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 C o - I f 8 Circulation FIGURE 28 _ Continued (3). FIGURE 28 Developing concentration profile, semLsymmetric operation of an open system. I l l VI V3 V4\ :v2 Time Interval Item Operatiorr-^ VI V2 V3 V4 Pump P Voltage *| Pause 0 0 0 0 0 f 2 B from I J 0 0 • 0 + f 3 D from H 0 / / 0 0 + f 4 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 I t can be concluded that when a x i a l mixing i s ignored a l l the three modes of o p e r a t i o n considered here le a d to the same s e p a r a t i o n . However, as can be seen from F i g u r e s 25, 27 and 29 the degree of complexity of the system and the v a l v e economy and t i m i n g sequence decreases as the c y c l e becomes l e s s symmetric. 4.4> Apparatus and Operation A photograph of the completed u n i t i s shown i n F i g u r e 31 which shows the c o n t r o l panel board w i t h i t s t i m e r , c y c l e counter, DC motor speed con- t r o l l e r , DC power supply, c o n d u c t i v i t y meters, 4-pen recorder and switches. The s e p a r a t i n g u n i t c o n s i s t s of two columns or c e l l s which are d e p i c t e d i n F i g u r e 32 and are represented by the boxes ED I and ED I I i n F i g u r e 36 where they are shown connected to the process l i n e , r i n s e l o o p , and the e l e c t r i c power supply. An asymmetric c y c l i c o p e r a t i o n was used here i n which the system was open d u r i n g the f i r s t h a l f - c y c l e and was c l o s e d d u r i n g the second h a l f - c y c l e ( F i g u r e 29). During the f i r s t h a l f - c y c l e the s o l u t i o n i n c e l l I I was depleted w h i l e that i n c e l l I was enriched. The c y c l e s t a r t e d w i t h a pause p e r i o d t ^ . T h i s was f o l l o w e d by p r o d u c t i o n p e r i o d s ; t ^ , t ^ when the feed was introduced and an enriched product was removed from c e l l I f o r the time t 2 and a depleted product was removed from c e l l I I f o r a p e r i o d t ^ . The f i r s t h a l f - c y c l e was terminated by c i r c u l a t i o n of the s o l u t i o n from one c e l l i n t o another. The second h a l f - c y c l e c o n s i s t s o n l y of a pause p e r i o d t f o l l o w e d by a c i r c u l a t i o n p e r i o d t when the s o l u t i o n was c i r c u l a t e d i n 5 6 opposite d i r e c t i o n . 115 F i g u r e 31 E l e c t r o d i a l y s i s U n i t and C o n t r o l Equipment 116 117 A b l o c k diagram of the experimental t e s t stand i s shown i n F i g u r e 36. The f i g u r e i l l u s t r a t e s the way i n which feed s o l u t i o n flows through the stack and the a u x i l i a r y equipment and i t i n d i c a t e s the p o i n t s a t which the c o n d u c t i v i t i e s of the e f f l u e n t streams, the v o l t a g e , the amperage were measured and recorded. The feed s o l u t i o n was introduced i n t o the ED c e l l s from a p r e s s u r i z e d tank through the process l i n e , which was an open ended l i n e that terminated i n the top and bottom products tanks. Four normally c l o s e d D r i - s o l e n o i d v a l v e s [VALCOR, s e r i e s 51] were in c l u d e d i n t h i s l i n e together w i t h a r e v e r s i b l e p e r i s t a t i c pump P i [COLE-PARMER Model 7017] d r i v e n by a v a r i a b l e speed DC motor [CENTURY motor type DN, 0.25 HP and BOSTON motor speed c o n t r o l l e r R a t i o t r o l model E 25]. The c i r c u l a t i n g r a t e of the process s o l u t i o n was set by the motor c o n t r o l l e r of pump P I ; and the f l o w d i r e c t i o n was c o n t r o l l e d by the r e v e r s i n g switch SW I I . A separate r i n s e s o l u t i o n was c o n t i n u a l l y r e c i r c u l a t e d through the e l e c t r o d e compartments of the ED c e l l s v i a d i s t r i b u t i n g manifolds by the c e n t r i f u g a l pump P2 (COLE-PARMER model MDX-3, No. 7004-10). The c i r c u l a t i n g r i n s e stream served to remove products of e l e c t r o l y s i s and any gases evolved at the e l e c t r o d e s were swept out and vented. The e l e c t r o d e wash l i q u o r used was 2000-4000 ppm aqueous s o l u t i o n of sodium c h l o r i d e and the f l o w r a t e was about 0.47 [ l i t r e / m i n ] per compartment. Regulated DC power was sup p l i e d to the ED c e l l s from S0RENSEN DCR40-10A power supply through the r e v e r s i n g switch SW I . A s o l i d s t a t e timer was used to c o n t r o l the sequence of o p e r a t i o n , energize the so l e n o i d v a l v e s , s w i t c h and r e v e r s e the p o l a r i t y of the motor armature, c o n t r o l the p o l a r i t y of the e l e c t r i c f i e l d and g i v e an impulse to an ele c t r o m e c h a n i c a l counter by the end of each c y c l e . 118 4.3.1. D e t a i l s of an ED C e l l Design A modular c o n s t r u c t i o n was used f o r the ED c e l l s ED I and ED I I . Each c e l l c o n s i s t s of up to eigh t separate stacks or stages connected together i n s e r i e s h y d r a u l i c a l l y and i n p a r a l l e l e l e c t r i c a l l y ( Figures 23, 32). Each stage as depicted by F i g u r e 33 was b u i l t up from e i g h t m u l t i l a y e r s o r p t i o n membrane assemblies, clamped between p l e x i g l a s end-frames i n a f i l t e r - p r e s s type of c o n s t r u c t i o n . The end frames he l d the g r a p h i t e e l e c t r o d e s and inc o r p o r a t e d f l o w connections f o r the process stream and the e l e c t r o d e r i n s e streams (Figure 33). Each assembled stage had an a c t i v e 3 3 v o i d volume f o r the process f l u i d of 50 cm p l u s a dead volume of about 5 cm . The c o n s t r u c t i o n of one of the i n d i v i d u a l membrane assemblies i s shown i n F i g u r e s 34, 35. Each u n i t c o n s i s t e d of the f o l l o w i n g three components permanently bonded together: ( i ) An outer low d e n s i t y p o l y e t h y l e n e s e a l i n g frame (22.54 cm x 7.62 cm x 0.189 cm) w i t h two key-shaped l i q u i d d i s t r i b u t i o n s l o t s cut i n t o each end. ( i i ) A triple-membrane ( c a p a c i t y c e l l ) 16.19 cm x 4.44 cm, composed of a c a t i o n s e l e c t i v e membrane (AMF C-100 or IONAC MC-3142) and an anion s e l e c t i v e membrane (AMF A-100 or IONAC MA-3148) e n c l o s i n g a core of Whatman No.l f i l t e r paper (15.56 cm x 4.13 cm). ( i i i ) A fl o w channel of polypropylene spacer screen (17.00 cm x 4.60 cm x 0.098 cm) Vexar TP 23, 10 x 10 strands per i n c h , cut d i a g o n a l l y . H a l f of the i o n exchange membranes were purchased from American Machine and Foundry Corp., w h i l e the r e s t were obtained from Ionac Chemical Co. and the spacer m a t e r i a l was k i n d l y s u p p l i e d 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 © — * ^ V 3 p - - - - ( Recorder £2 Probes EDI CI V4 B Rinse • r - - i 4 - Pen » i 1 Rinse Tank P2 I—J ED n Q V2 S W I 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 s i d e s . The long sides remained open to i n s e r t and to remove the f i l t e r paper. The p o l y - propylene spacer screen was pressed i n t o the frame by means of a heated j i g . Then the t r i p l e membrane was tacked at three corners to the frame u s i n g a heated bar. A d e t a i l e d c o n s t r u c t i o n procedure i s given by Bass (Bass, 1972). The manufacturer's s p e c i f i c a t i o n s of the membranes used are given i n Table V. D e t a i l e d d e f i n i t i o n s of the parameters and methods f o r t h e i r measurement are found i n "Ion Exchange" by H e l f f e r i c h (1962) and "Test Manual f o r P e r m s e l e c t i v e Membranes, Research and Development Progress Report #77, O f f i c e of S a l i n e Water, U.S. Department of I n t e r i o r (1964 b ) . 4.5. Measuring and Recording 4.5.1. Concentrations, Current, Voltage and pH Measurements ( i ) Concentrations The c o n c e n t r a t i o n s of the process s o l u t i o n a t two p o i n t s i n d i c a t e d by p o s i t i o n s C I , C2 i n F i g u r e 33 were c o n t i n u o u s l y measured u s i n g epoxy f l o w - type c o n d u c t i v i t y c e l l s [BECKMAN, CEL-VDJ] w i t h automatic temperature com- pensators and d i r e c t - r e a d i n g c o n d u c t i v i t y meters [BECKMAN, Solu-Meter RA5]. A 0 to 10 (mV) D.C. output s i g n a l from the Solu-Meter allowed p o t e n t i o m e t r i c r e c o r d e r i n g of the c o n c e n t r a t i o n i n the ranges shown i n Table VI. Accuracy of the type RA5 Solu-Meter i n d i c a t i o n i s w i t h i n 2% of the s c a l e span. However the accuracy of the e l e c t r i c a l output i s w i t h i n 1% of span. Table V Reported P r o p e r t i e s of Ion-Exchange Membranes " - ^ T y p e , Manufacturer and Cation-Exchange Anion-Exchange — D e s igna t i o n Property ~ AMF C-100 IONAC MC-3142 AMF A-100 IONAC MA-3142 Backing Polyethylene Polyethylene A c t i v e Group S u l f o n i c A c i d 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 ( s e l e c t i v i t y ) : (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 t h i c k n e s s (mm) 0.015 0.015 0.018 0.018 Mullen Burst s t r e n g t h ( p s i ) 60 185 50 190 Dimensional Changes on we t t i n g and d r y i n g (%) 10-13 < 3 12-15 < 3 Size a v a i l a b l e 44 i n . wide r o l l s 40 x 120 i n . 44 i n . wide r o l l s 40 x 120 i n . (a) Reported from c o n c e n t r a t i o n p o t e n t i a l s measured between s o l u t i o n s of the two n o r m a l i t i e s l i s t e d . 124 Table VI C o n d u c t i v i t y and Na CI Concentration Ranges of BECKMAN c o n d u c t i v i t y C e l l s CEL-VDJ corresponding to a 0-10 [mV] D.C. S i g n a l from a BECKMAN Solu-Meter RA5. C e l l Constant K [cm-1] C o n d u c t i v i t y [micromhos/cm] Na CI S o l u t i o n Concentration [PPM] 20 0-10,000 0-5,500 50 0-25,000 0-14,800 100 0-50,000 0-30,800 125 A f t e r every run samples of the depleted and enriched products were taken and t h e i r c o n c e n t r a t i o n s were measured u s i n g an epoxy d i p C e l l [BECKMAN, CEL-VH1-10] together w i t h a c o n d u c t i v i t y b r i d g e [BECKMAN, Model RC 16B2] -2 +3 w i t h s c a l e m u l t i p l i e r 10 - 10 . ( i i ) Current The c u r r e n t input was measured as a p o t e n t i a l drop across a Nichrome r e s i s t a n c e w i r e (14 gauge), shunt A i n F i g u r e 36. The shunts were i n t e g r a t e d i n t o the e l e c t r i c a l manifold which d i s t r i b u t e d the D.C. power from s w i t c h box SW I to the stages. The w i r i n g i s shown i n F i g u r e 37. The shunt r e s i s t a n c e s were 50.0 [m^] ± 1.5% f o r the c u r r e n t s to the i n d i v i d u a l stages and 25.0 [mft] f o r the t o t a l c u r r e n t . ( i i i ) V o ltage Probe e l e c t r o d e s were prepared from s i l v e r w i r e cable which was hammered i n t o s t r i p s approximately 3 mm wide and 0.12 mm t h i c k . The s t r i p s were d i p coated w i t h contact cement (Weldwood of Canada Lim i t e d ) and the c o a t i n g was removed from one s i d e of the t i p which was l o c a t e d i n s i d e the stack. The probes were i n s e r t e d between the s e p a r a t i n g membranes and the stack pack and sealed w i t h s i l i c o n grease (Dow Corning). A second s e l e c t o r s w i t c h was connected to the probes and to one recorder pen. The c i r c u i t was analogous to the one shown i n F i g u r e 37; but without shunts. ( i v ) £H Samples f o r pH-checks were taken f o r some runs j u s t p r i o r to the experiment and immediately t h e r e a f t e r from the two process products and r i n s e stream and measured i n the u s u a l way (using CORNING d i g i t a l electrometer model 101). 126 FIGURE 37 Current monitoring circuit. 127 4.5.2. Recording A four-channel recorder (WATANABE M u l t i c o r d e r , Model MC6-11 S4H) was used to c o n t i n u o u s l y monitor the c u r r e n t input to the c e l l s , the p o t e n t i a l drop across the membrane stack, and the s o l u t e c o n c e n t r a t i o n s i n the bottom and top c o n d u c t i v i t y c e l l s C l and C2 (Figure 36). The stack v o l t a g e and the current consumption are measured i n d i v i d u a l l y f o r each stage. However, because of the l i m i t e d number of pens o n l y one v o l t a g e and one current s i g n a l are recorded a t , a time u s i n g two s e l e c t o r switches. The c u r r e n t s i g n a l was i n t e g r a t e d d u r i n g s e v e r a l experiments, u s i n g a CORNING Recorder 840, to determine the average cu r r e n t consumption. CHAPTER 5 Experimental R e s u l t s and D i s c u s s i o n The primary o b j e c t i v e s of the experimental program have been o u t l i n e d before (Chapter 4 ) . In the present work a l t o g e t h e r 252 runs were made. These are compiled i n the main survey t a b l e s (Tables IX-XVI), which show the oper a t i n g c o n d i t i o n s , production r a t e s and the s e p a r a t i o n achieved i n each run. These survey t a b l e s are fo l l o w e d by group t a b l e s and diagrams that i l l u s t r a t e the e f f e c t of s i n g l e v a r i a b l e s under otherwise f i x e d c o n d i t i o n s . 5.1. Data C o l l e c t i o n The c o l l e c t i o n of raw data during the course of a complete run c o n s i s t e d of the f o l l o w i n g consecutive steps: 1. F i l l r i n s e tank w i t h 7.5 l i t e r s of f r e s h r i n s e l i q u o r (NaCl i n d i s t i l l e d water, w i t h the same c o n c e n t r a t i o n as the process stream but not l e s s than 1000 ppm NaCl). 2. F i l l the feed tank w i t h s o l u t i o n of d e s i r e d c o n c e n t r a t i o n (NaCl i n d i s t i l l e d water) and ad j u s t the pressure i n the feed tank to about 8 p s i g . 3. F i l l system w i t h the process s o l u t i o n from the p r e s s u r i z e d feed tank. 4. S t a r t r i n s e pump. 5. Set the timer and the p e r i s t a l t i c pump speed and run the system w i t h power o f f f o r few c y c l e s to e q u i l i b r a t e s o r p t i o n membrane w i t h process s o l u t i o n . 6. Adjust check p o i n t of c o n d u c t i v i t y meters. 7. S e l e c t recorder pen ranges and c h a r t speed. 8. Take c o n c e n t r a t i o n and pH samples of process and r i n s e s o l u t i o n s , 9. Set the timer o f f to b r i n g the e q u i l i b r a t e d process s o l u t i o n to a pause before s t a r t i n g the run. 128 129 10. Turn c y c l e counter back to zero. 11. Set operating c o n d i t i o n s ( f i n a l adjustment of the timer and the a p p l i e d D.C. v o l t a g e ) . 12. Note down date, o p e r a t i n g c o n d i t i o n s , v a r i a b l e recorded by each pen and a p p r o p r i a t e range, chart speed. 13. Set the timer on and c l o s e e l e c t r i c power c i r c u i t simultaneously to s t a r t the f i r s t pause i n t e r v a l i n the f i r s t c y c l e . 14. When the system approaches i t s p e r i o d i c steady s t a t e as i n d i c a t e d by the recorded v a l u e s of c o n c e n t r a t i o n s . Empty the product tanks, measure the volumes and note the c y c l e number. D i s c a r d products obtained i n t h i s t r a n s i t i o n p e r i o d . 15. Record c u r r e n t and v o l t a g e s i g n a l s a t d i f f e r e n t s t a t i o n s by m a n i p u l a t i n g s e l e c t o r switches, and mark pen t r a c e s a c c o r d i n g l y . 16. Write down any o b s e r v a t i o n r e l a t e d to experiment. 17. Terminate run when s u f f i c i e n t products are produced and a l l i n f o r m a t i o n regarding current and v o l t a g e s i g n a l s at the v a r i o u s s t a t i o n s have been obtained. 18. Measure the t o t a l amount of products produced and read the t o t a l number of c y c l e s to f i n d and r e c o r d the p r o d u c t i o n r a t e s . 19. Take samples of process and r i n s e streams to measure pH and con- c e n t r a t i o n s . 20. Record the measured v a l u e s . 5.2. Experimental D e s i g n a t i o n The experiments reported here f a l l i n t o two main c a t e g o r i e s : ( i ) Category R which r e f e r to the f i r s t set of experiments conducted i n two columns each c o n s i s t e d of 4 c e l l s or stages connected together i n s e r i e s h y d r a u l i c a l l y and i n p a r a l l e l e l e c t r i c a l l y (Tables I X - X I ) . ( i i ) Category M which r e f e r s to the second set of experiments performed 130 i n columns w i t h double the l e n g t h of those used i n Category R (Tables X I I - X I V ) , Each experiment i n these c a t e g o r i e s i s designated by e i t h e r Rna or Mna where n i s a number which r e f e r s to a s p e c i f i c combination of a feed c o n c e n t r a t i o n (C Q) and a pr o d u c t i o n r a t e (P.R.). Three feed c o n c e n t r a t i o n s ( C Q = 500, 2000 and 4000 ppm NaCl) and four p r o d u c t i o n r a t e s (P.R. = 0.0, 25, 50 and 100 c . c . / c y c l e ) have been used which r e s u l t i n 12 combinations and n assumes the valu e s 1,2 12 as shown i n Table V I I . a i s a l e t t e r which represents a s p e c i f i c combination of a p p l i e d v o l t a g e (A<J>) and the pause time ( T ) . Three v o l t a g e s (A<(> = 10, 20 and 30 v o l t ) and th r e e pause times (T = 15, 30 and 45 sec.) have been i n v e s t i g a t e d which l e a d to 9 combinations and a i s symbolized by any of the l e t t e r s A, B I as shown i n Table V I I I . 5.3. Main Survey Tables The columns of the main survey t a b l e s are (see Tables IX-XVI): 1. EXP Group: T h i s shows the experiment category R or M and the n-value (n = 1, 2, .... 1 2 ) . 2. P r o d u c t i o n Rate: of each product (demineralized and concentrated) i n c . c . / c y c l e . 3. Feed Concentration: i n p a r t s per m i l l i o n NaCl i n d i s t i l l e d water. 4. EXP Symbol: the symbol of a i n the experimental d e s i g n a t i o n Rna or Mna. 5. A p p l i e d V o l t a g e : the constant v o l t a g e s u p p l i e d by the reg u l a t e d D.C. power source i n v o l t s . 6. Pause Time: i n each h a l f c y c l e i n seconds. 7. B r i n e C o n c e n t r a t i o n : 9 . D i a l y s a t e Concentration: both measured c o n d u c t o m e t r i c a l l y and converted by means of c a l i b r a t i o n curves i n t o c o n c e n t r a t i o n s i n p a r t s per m i l l i o n NaCl. 131 Table V I I Values of n i n Experimental Designations Rna and Mna ^ v ^ O p er a t i n g T T .. ^^-v. Parameters Value ^^v. of n Feed Cone. C q (ppm) Pr o d u c t i o n Rate p.p. ( c . c . / c y c l e ) 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 V I I I Values of a i n Experimental D e s i g n a t i o n s Rna and Mna ^ v ^ O p e r a t i n g ^ ^ P a r a m e t e r s a APPLIED VOLTAGE, A* ( v o l t ) 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. B r i n e Volume: 10. D i a l y s a t e Volume: These are the pro d u c t i o n r a t e s of the two product streams expressed i n c.c. per c y c l e . 11. Separation F a c t o r ( n s ) : Defined as the r a t i o of b r i n e (bottom product) to d i a l y s a t e (top product) c o n c e n t r a t i o n s ns = The main survey t a b l e s of a l l s u c c e s s f u l experiments i n category R and M are presented on the f o l l o w i n g pages. S u c c e s s f u l means not i n t e r - rupted by mechanical, e l e c t r i c a l or human f a i l u r e . 5.4. Parameters and Modes of Operation I n v e s t i g a t e d (a) Parameters The parameters which are s t u d i e d a r e : 1. D e m i n e r a l i z i n g path l e n g t h . 2. P r o d u c t i o n r a t e . 3. Pause time, x. The t o t a l c y c l e time T i s the summation of pause time, x which i s v a r i a b l e , the c i r c u l a t i o n time t £ which i s kept constant and p r o d u c t i o n time t p which v a r i e s between 1.5-6.0 sec depending on the amount of product. 4. A p p l i e d v o l t a g e , A<j) 5. I n i t i a l c o n c e n t r a t i o n , C . o (b) Modes of Operation The f o l l o w i n g modes of o p e r a t i o n were considered: 6. No-pause o p e r a t i o n . 7. No-power du r i n g c i r c u l a t i o n o p e r a t i o n . 8. Semi-symmetric o p e r a t i o n . Each of these parameters or modes of o p e r a t i o n i s analysed s e p a r a t e l y by forming groups of experiments i n which the other parameters are constant. Table IX Compilation of Experiments with In i t i a l 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 3 4 5 6 7 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 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 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 R l l 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 3 4 5 6 7 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 In i t i a l 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 D u p l i c a t e Experiments to Test R e p r o d u c i b i l i t y - Group R Two Columns,Each Co n s i s t s of 4 C e l l s i n Se r i e s 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 D u p l i c a t e Experiments to Test R e p r o d u c i b i l i t y - Group M Two Columns,Each Consists of 8 C e l l s i n 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 c a l c u l a t i o n s f o r s e p a r a t i o n f a c t o r s , amount of s a l t s h i f t e d and a check on m a t e r i a l balance f o r each run and l i s t s t a b l e s of p r i n t o u t . 5.4.1. E f f e c t of D e m i n e r a l i z i n g Path Length Since the process generates a c o n c e n t r a t i o n d i f f e r e n c e between the s o l u t i o n s at the two ends of the ED c e l l , the amount of a x i a l d i s p e r s i o n i n the stack has a ve r y great e f f e c t on the f i n a l s e p a r a t i o n . I n a l l of the runs the co n c e n t r a t i o n s of the two product streams approached l i m i t i n g v a l u e s as the d i s p e r s i v e e f f e c t s of a x i a l mixing and other i r r e v e r s i b l e processes became equal to the s e p a r a t i o n produced by c y c l i n g . I n c r e a s i n g the channel l e n g t h by i n c r e a s i n g the number of stages connected i n s e r i e s tends to reduce d i s p e r s i o n . F i g u r e s 38, 39 and 40 and Tables X V I I , X V I I I and XIX show runs i n 4-stage columns w h i l e F i g u r e s 41, 42 and 43 together w i t h Tables XX, XXI and XXII show s i m i l a r experiments per- formed i n 8-stage columns. By comparing these f i g u r e s i t w i l l be c l e a r that the s e p a r a t i o n f a c t o r reached higher v a l u e s w i t h i n c r e a s i n g channel l e n g t h i n a l l s e t s of experiments. F i g u r e s 44-49 and Tables X X I I I - X X V I I I compare the performance, under the same op e r a t i n g c o n d i t i o n s , of a s i n g l e column c o n s i s t s of 8 stages w i t h t h a t of two short columns each c o n s i s t s of 4 stages which operate i n p a r a l l e l and have the same production r a t e s as the s i n g l e column. This comparison was made by p l o t t i n g C Q/C n versus the r e c i p r o c a l of the throughput r a t i o ; where C i s the feed c o n c e n t r a t i o n and C_. i s the demine r a l i z e d product con-o D r c e n t r a t i o n . In a l l runs stu d i e d .the s i n g l e column r e s u l t s i n a b e t t e r s e p a r a t i o n than the two short p a r a l l e l columns; however, the improvement i n se p a r a t i o n w i t h the column-length was more pronounced a t h i g h feed 148 Table XVII E f f e c t of Pr o d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 500 PPM Exp. Group # R5, R6, R7 and R8 E X P . G R A P H . S Y M B O L PI R A T E \ ^ P E R ^ \ S E P A R A T I O N F A C T O R ns V O L T A G E ( V O L T ) C Y C L E P A U S E \ ^ ( S E C ) \ 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 X V I I I E f f e c t of Pro d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co * 2000 PPM Exp. Group # R l , 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 E f f e c t of P r o d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 4000 PPM Exp. Group # R9, RIO, R l l and R12 EXP. GRAPH. SYMBOL P] VOLTAGE (VOLT) *0D. RATE \ . PER ^ \ CYCLE P A U S l N ^ (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. C Q — 4000 PPM. 154 Table XX E f f e c t of Pro d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration 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 - C e l l cell column ; initial cone. ( ^ 5 0 0 PPM. 156 Table XXI E f f e c t of Pro d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 2000 PPM Exp. Group # M l , M2, M3 and M4 E X P . G R A P H . S Y M B O L PI 10D. R A T E \ P E R \ V S E P A R A T I O N F A C T O R ns V O L T A G E ( V O L T ) \ w C Y C L E P A U S E X . ( S E C ) 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-Cel l column initial cone. C Q —2000PPM. 158 Table XXII E f f e c t of Pro d u c t i o n Rate on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 4000 PPM Exp. Group # M9, M10, M i l and M12 EXP. GRAPH. SYMBOL P] 10D. RATE \ . PER SEPARATION FACTOR ns VOLTAGE (VOLT) CYCLE P A U S E \ ^ (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 - C e l I column; initial cone- C Q — 4 0 0 0 P P M . 160 Table X X I I I E f f e c t of D e m i n e r a l i z i n g 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 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 E f f e c t of D e m i n e r a l i z i n g 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 c D 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. C 0^=500 PPM, A<{)=30V. 164 Table XXV E f f e c t of D e m i n e r a l i z i n g Path Length on Separation C Q - 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 E f f e c t of De m i n e r a l i z i n g 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 c D THROUGHPUT RATIO c D 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. C Q ^ t 2 0 0 0 PPM , = 30V. 168 Table XXVII E f f e c t of D e m i n e r a l i z i n g Path Length on Separation C O - 4000 ppm; A<j> = 20 V PAUSE TIME (SEC) 4-CELL COLUMN 8-CELL COLUMN EXP. GRAPHICAL SYMBOL 1 1 THROUGHPUT RATIO c D 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 • I I 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 = ^ 4 0 0 0 P P M , A(j) = 2 0 V 170 Table XXVIII E f f e c t of D e m i n e r a l i z i n g Path Length on Separation C Q - 4 0 0 0 ppm; A(J> = 3 0 V PAUSE 4-CELL COLUMN 8-CELL COLUMN GRAPHICAL SYMBOL EXP. TIME (SEC) 1 1 Ca THROUGHPUT RATIO c D THROUGHPUT RATIO CD 1 2 E 2 1 . 4 6 4 1 1 . 7 9 1 1 E A A 3 0 4 1 . 7 3 8 1 3 . 4 7 9 E 1 0 2 . 1 0 1 6 1 4 . 2 4 1 2 F 2 1 . 7 3 . 4 1 4 . 5 8 1 1 F a m 4 5 4 2 . 2 2 8 1 7 . 4 7 9 F 1 0 2 . 7 2 1 6 1 8 . 8 1 171 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, C Q r « = 4 0 0 0 PPM, A(J)=30V 172 c o n c e n t r a t i o n (compare F i g u r e s 44, 45 w i t h F i g u r e s 48,49). F i g u r e s 44 and 45 i n d i c a t e that f o r a feed c o n c e n t r a t i o n C q = 500 ppm NaCl an optimum d e m i n e r a l i z i n g path l e n g t h may l i e i n the v i c i n i t y of 8 stages i n s e r i e s w h i l e F i g u r e s 46-49 c a l l f o r longer d e m i n e r a l i z i n g path lengths w i t h the i n c r e a s i n g feed c o n c e n t r a t i o n . 5.4.2. E f f e c t of P r o d u c t i o n Rate As the p r o d u c t i o n r a t e i n c r e a s e s the feed undergoes l e s s c y c l e s i n the ED c e l l before i t emerges as products. Thus the amount of s e p a r a t i o n i s reduced as the production r a t e i n c r e a s e s . F i g u r e s 38, 41 and Tables X V I I , XX show the e f f e c t of p r o d u c t i o n r a t e on the s e p a r a t i o n f a c t o r (ns = ) CD f o r a s e r i e s of experiments at a feed c o n c e n t r a t i o n (C Q) of about 500 ppm NaCl. The parameters stu d i e d were the pause time, T (at l e v e l s of 15, 30 and 45 sec.) and the a p p l i e d v o l t a g e A<|> (at l e v e l s of 10, 20 and 30 v o l t ) . F i g u r e s 39, 42 and Tables X V I I I , XXI show s i m i l a r experiments at feed con- c e n t r a t i o n C Q - 2000 ppm NaCl; w h i l e F i g u r e s 40, 43 together w i t h Tables XIX and XXII i n d i c a t e experiments w i t h feed c o n c e n t r a t i o n C q - 4000 ppm. A l l these f i g u r e s r e f e r r e d to show th a t there i s a strong t r a d e - o f f between pr o d u c t i o n r a t e and s e p a r a t i o n f a c t o r . However, u s e f u l s e p a r a t i o n can be obtained at a l l p r o d u c t i o n r a t e s (provided that higher v o l t a g e s and/ or longer pause times and d e m i n e r a l i z i n g paths are used w i t h h i g h feed c o n c e n t r a t i o n ) . F i g u r e s 41, 42 and 43 show that at an a p p l i e d v o l t a g e (A<}>.) of 30 V, a pause time (T) of 45 sec. and a throughput r a t i o of ( i . e . p r o d u c t i o n r a t e of 100 c . c . / c y c l e ) , the s e p a r a t i o n f a c t o r s f o r v a r i o u s feed c o n c e n t r a t i o n s range between 30 to 50. To f i x i d e a s , most of the commercial ED p l a n t s a v a i l a b l e at present operate w i t h a 2:1 d e s a l i n a t i o n r a t i o , which means that a feed of 1000 ppm would be d e s a l i n a t e d to 500 ppm per path. A mark I I I stack ( I o n i c s Inc.) which i s used i n Buckeye ED p l a n t , A r i z . , 173 has a maximum d e s a l i n a t i o n r a t i o of s l i g h t l y b e t t e r than 2:1. Two stacks are used i n s e r i e s to reduce a b r a c k i s h water of 2100 ppm t o t a l d i s s o l v e d s o l i d s down to 500 ppm. ( a l s o r e f e r to Table I V ) . Most of the h e a l t h standards (e.g. the United States P u b l i c Health S e r v i c e Standards) r e q u i r e that the t o t a l d i s s o l v e d s o l i d s (TDS) content of potable water to be 500 ppm or l e s s ; hence w i t h a feed at 2000 ppm NaCl and an equal s p l i t of b r i n e and d i a l y s a t e a s e p a r a t i o n f a c t o r of 7 would be necessary and a s e p a r a t i o n f a c t o r of 15 i s r e q u i r e d w i t h a feed at 4000 ppm. 5.4.3. E f f e c t of Pause Time The i n f l u e n c e of a pause time (T) at l e v e l s of 15, 30 and 45 sec. was s t u d i e d under v a r i o u s o p e r a t i n g c o n d i t i o n s . In a l l cases, a displacement p e r i o d of 36 sec. and an average p r o d u c t i o n p e r i o d of 1.5 s e c , 3.0 sec. and 6.0 sec. f o r p r o d u c t i o n r a t e s of 25 c . c , 50 c . c and 100 c . c . / c y c l e r e s p e c t i v e l y were used. Tables XXIX, XXX and XXXI summarize the o p e r a t i n g parameters and the f i n a l s e p a r a t i o n f a c t o r s reached i n these experiments, and F i g u r e s 50, 51 and 52 d i r e c t l y d i s p l a y the e f f e c t of the pause time on s e p a r a t i o n f a c t o r f o r s e v e r a l groups of experiments performed i n 4-stage columns w i t h feed c o n c e n t r a t i o n s between 500 ppm and 4000 ppm NaCl. Tables XXXII, XXXIII and XXXIV together w i t h F i g u r e s 53, 54 and 55 e x h i b i t r e s u l t s of s i m i l a r experiments conducted i n 8-stage columns. A l l these f i g u r e s show that the s e p a r a t i o n i s improved w i t h a prolonged pause time. However, the e f f e c t of pause time can best be examined by c o n s i d e r i n g s e p a r a t i o n per u n i t r e a l time obtained w i t h v a r i o u s pause times as shown i n Tables XXXV, XXXVI and XXXVII and F i g u r e s 56, 57 and 58. In these f i g u r e s ns/T i s p l o t t e d v s . pause time ( x ) , where ns i s the s e p a r a t i o n f a c t o r and T i s the complete c y c l e d u r a t i o n i n minutes. The r e s u l t s are Table XXIX E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 500 PPM Exp. Group # R5, R7 and R8 EXP. GROUP and P A U S E ^ ^ ^ •v. TIME ( S E O ^ v , SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL V 0 L T > \ ^ (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 • • 6 0 0 0 15 30 45 PAUSE TIME (SEC) FIGURE 5 0 Effect of pause time on separation • 4 - Cell column ; initial c o n c * C 0 — 5 0 0 P P M . Table XXX E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C o ncentration Co - 2000 PPM Exp. Group # R l , R3 and R4 EXP. GROUP and P A U S E ^ \ ^ 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 R l 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 C 0 — 2000 PPM. Table XXXI E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 4000 PPM Exp. Group # R9, R l l and R12 ^ • s . PAUSE SEPARATION FACTOR EXP. GROUP TIME ns and ( S E C ) ^ \ PRODUCTION RATE GRAPH. V 0 L T > \ ^ 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 R l l 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.C 0 — 4 0 0 0 PPM, 1 8 0 Table XXXII E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 500 PPM Exp. Group # M5, M7 and M8 E X P . G R O U P and P A U S E ^ \ ^ T I M E ( S E C ) \ S S E P A R A T I O N F A C T O R ns P R O D U C T I O N R A T E G R A P H . S Y M B O L V O L T > ^ ( V O L T ) 1 5 3 0 4 5 • 3 0 5 5 . 3 3 7 2 . 6 1 7 7 . 8 5 M 5 2 5 ( C . C . / c y c l e ) 2 0 3 9 . 9 2 3 6 . 1 1 5 1 . 1 8 6 5 . 5 0 o 1 0 1 0 . 6 7 1 8 . 8 7 2 5 . 2 5 3 0 4 4 . 2 1 4 7 . 1 4 6 0 . 7 7 6 3 . 0 7 M7 5 0 ( C . C . / c y c l e ) 2 0 3 1 . 2 1 2 8 . 3 3 3 9 . 9 2 5 3 . 9 6 A 1 0 9 . 1 3 1 6 . 2 3 2 2 . 9 5 • 3 0 3 2 . 1 9 4 6 . 5 2 4 8 . 4 3 5 3 . 2 0 M 8 1 0 0 ( C . C . / c y c l e ) a 2 0 2 1 . 0 4 2 8 . 3 3 4 0 . 3 8 3 7 . 9 6 • 1 0 6 . 4 0 1 2 . 1 3 1 8 . 1 8 8 0 APPLIED VOLTAGE (VOLT) PRODUCTION RATE (CJC./CYCLE) 2 5 5 0 100 10 O A • 2 0 A y 3 0 • A • 6 0 ac o o < li. z o < or < o_ UJ to 4 0 2 0 15 PAUSE TIME 3 0 ( S E C ) 4 5 FIGURE 53 Effect of pause time on separation. 8-Cell column; initial c o n e . C 0 — 500PPM 182 Table XXXIII E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 2000 PPM Exp. Group # M l , M3 and M4 EXP. GROUP and P A U S E ^ \ ^ 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. 2000P P M . Table XXXIV E f f e c t of Pause Time on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 4000 PPM Exp. Group # M9, M i l and M12 EXP. GROUP and P A U S E ^ \ ^ TV. TIME ( S E C ) ^ N . SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL V 0 L T V \ ^ (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 M i l 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 4 0 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 -Cel l column j initial cone. CQ — 4000 PPM. 186 Table XXXV E f f e c t 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 15 30 45 Pause Time (Sec) FIGURE 56 Effect of pause time on separation • C0=ft:500 PPM Group M7. 188 Table XXXVI E f f e c t 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. C 0 ^ i r 2 0 0 0 PPM Group M3 190 Table XXXVII E f f e c t of Pause Time on Separation C = 4000 ppm; Group M i l EXP. ' GRAPHICAL SYMBOL PAUSE TIME, x (SEC) APPLIED VOLTAGE (VOLT) CYCLE TIME, T (MIN) SEPARATION FACTOR ns ns T (MIN - 1) M i l I o 10 1.70 0.94 M i l C © 15 20 1.8 4.61 2.56 M i l D • 30 15.31 8.51 M i l H A 10 2.40 1.04 M i l A 30 20 2.3 7.50 3.26 M i l E • 30 26.05 11.33 M i l G • 10 3.21 1.15 M i l B y 45 20 2.8 11.80 4.21 M i l F • 30 34.00 12.14 FIGURE 58 Effect of pause time-on separation. C Q ^4000 •, Group M i l , 192 summarized as f o l l o w s : 1. At low v o l t a g e (A<f>) the s e p a r a t i o n f a c t o r per u n i t time ns/T v a r i e s almost l i n e a r l y w i t h the pause time T. 2. As the v o l t a g e i n c r e a s e s the e f f e c t of pause time beyond a c e r t a i n v a l u e becomes l e s s s i g n i f i c a n t and the curve tends to l e v e l o f f . 3. At a f u r t h e r increased v o l t a g e the ns/T v s . x curve goes through a maximum. 4. The maximum pause time that can be u t i l i z e d without s u f f e r i n g an adverse e f f e c t on s e p a r a t i o n depends on both the a p p l i e d v o l t a g e (A4>) and the feed c o n c e n t r a t i o n (C ) . At an a p p l i e d v o l t a g e Ad> = 30 V, x o max i s about 30 sec f o r C - 500 ppm NaCl ( F i g u r e 56) and x i s about 45 sec o r r max f o r C q = 2000 ppm (Figure 57) and a longer pause time can be used f o r the feed c o n c e n t r a t i o n of 4000 ppm NaCl (Figure 58). 5.4.4. E f f e c t of A p p l i e d Voltage The e f f e c t of the a p p l i e d v o l t a g e A(() was i n v e s t i g a t e d i n s i x groups of experiments, each i n c l u d i n g runs at 10, 20 and 30 V. The other system parameter v a l u e s are l i s t e d i n Tables XXXVIII-XLIII which show experiments w i t h feed c o n c e n t r a t i o n s of 500, 2000 and 4000 ppm NaCl i n 4-stage and 8-stage columns. F i g u r e s 59-64 i l l u s t r a t e d i r e c t l y the i n f l u e n c e of the a p p l i e d p o t e n t i a l (AcJ>) on the s e p a r a t i o n f a c t o r ( n s ) . In c r e a s i n g the a p p l i e d v o l t a g e improves the s e p a r a t i o n . The magnitude of t h i s improvement was a f f e c t e d by both the pause time (x) and the feed c o n c e n t r a t i o n (C q) as shown i n F i g u r e s 62, 63 and 64. The r e s u l t s a re: 1. In experiments w i t h feed c o n c e n t r a t i o n C Q - 500 ppm NaCl the se p a r a t i o n f a c t o r (ns) in c r e a s e s almost l i n e a r l y w i t h the a p p l i e d v o l t a g e ; but i t l e v e l s o f f at h i g h v o l t a g e and long pause time (Fi g u r e 62). Table XXXVIII E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C o n c entration Co - 500 PPM Exp. Group # R5, R7 and R8 EXP. GROUP and ^ v A P I 'LIFJJN. VOLTAGE^s. Atf) ( V O L T ) ^ ^ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL P A U S E \ (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 C Q — 500 PPM. 195 Table XXXIX E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 2000 PPM Exp. Group # R l , R3 and R4 ^ \ A P P L I E D \ VOLTAGE SEPARATION FACTOR EXP. GROUP \ . A<j> ns and (VOLT) PRODUCTION RATE GRAPH. P A U S E ^ n . SYMBOL (SEC) \ . 10 20 30 • 45 4.49 13.00 20.64 18.84 R l 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 c o n c . C 0 — 2000 PPM. Table XL E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 4000 PPM Exp. Group # R9, R l l and R12 EXP. GROUP and PRODUCTION RATE GRAPH. SYMBOL 'LIEDN. VOLTAGE^*. A<|> ^ \ ( V 0 L T ) ^ 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 R l l 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. C Q — 4000 PPM. Table XLI E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co = 500 PPM Exp. Group # M5, M7 and M8 EXP. GROUP and ^ \ A P I 'LIED^s. VOLTAGE^. \ A<() ( V 0 L T ) \ 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 V O L T A G E ( V O L T ) FIGURE 62 Effect of applied voltage on separation. 8-Cell column ;hitial cone. C Q —500PPM. 201 Table X L I I E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C o ncentration Co = 2000 PPM Exp. Group # M l , M3 and M4 EXP. GROUP and ^ \ A P PLIED^v. VOLTAGE^v A<|> \w ^ \ ( V 0 L T ) ^ \ SEPARATION FACTOR ns PRODUCTION RATE GRAPH. SYMBOL P A U S E X (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 R A T E ( C . C . / C Y C L E ) PAUSE TIME (SEC) 15 3 0 4 5 2 5 O A • 5 0 a 100 • • B or o f— o < < or < a. UJ CO FIGURE 63 APPLIED V O L T A G E ( V O L T ) Effect of applied voltage on separation. 8-Cell column Initial conc.Cg—2000 PPM. 203 Table X L I I I E f f e c t of A p p l i e d Voltage on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s I n i t i a l C oncentration Co - 4000 PPM Exp. Group # M9, M i l and M12 ^ \ A P P L I E I ) N . VOLTAGE SEPARATION FACTOR EXP. GROUP \ A<j> \ . ns and \ v ( V 0 L T ) \ 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 M i l 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.C 0 — 4000 PPM. 205 2. With feed c o n c e n t r a t i o n s of 2000 ppm and 4000 ppm NaCl the s e p a r a t i o n f a c t o r i s . seen to r i s e more than p r o p o r t i o n a l to the a p p l i e d v o l t a g e . 3. The e f f e c t of a p p l i e d v o l t a g e i s more pronounced when the feed c o n c e n t r a t i o n i s h i g h (compare F i g u r e s 62 and 64) and/or the pause time i s short ( r e f e r to F i g u r e 63). The a n a l y s i s of the i n f l u e n c e of the a p p l i e d v o l t a g e (A<j>) i s not as s t r a i g h t f o r w a r d as that of the pause time (T). Operating at h i g h v o l t a g e always r e s u l t s i n a higher energy consumption per u n i t product at a f i x e d product q u a l i t y , but at the same time i n c r e a s i n g v o l t a g e i n c r e a s e s the c u r r e n t d e n s i t y and a c c e l e r a t e s production r a t e . Using the method of ohmic a n a l y s i s , the d.c. power d i s s i p a t i o n i n a given stack of constant average r e s i s t a n c e 2 R at c u r r e n t I i s RI . The amount of s a l t s h i f t e d , and hence the amount of f r e s h water produced, are p r o p o r t i o n a l to I . Therefore, the d.c. power d i s s i p a t i o n per u n i t volume of d i l u a t e produced i s p r o p o r t i o n a l to I . F i x e d c o s t s per u n i t volume of d i l u a t e produced, on the other hand, are i n v e r s e l y p r o p o r t i o n a l to I and the optimum c u r r e n t d e n s i t y and the a p p l i e d v o l t a g e can only be determined by the economical e v a l u a t i o n of the p l a n t . The i n d i v i d u a l items c o n t r i b u t i n g to the t o t a l o p e r a t i n g c o s t of an ED process may be placed i n three c a t e g o r i e s : (a) c o s t s that vary d i r e c t l y w i t h c u r r e n t d e n s i t y such as the e l e c t r i c energy c o s t s (b) c o s t s that vary i n v e r s e l y w i t h current d e n s i t y (the f i x e d charges) such as membrane replacement and a m o r t i z a t i o n of c a p i t a l investment c o s t s . Less membrane area and lower c a p i t a l c o s t s are r e q u i r e d at h i g h c u r r e n t d e n s i t i e s 206 (c) c o s t s that are i n v a r i a n t w i t h c u r r e n t d e n s i t y such as those f o r operating and maintenance l a b o r and the cost of pretreatment chemicals. F i g u r e 65 shows t y p i c a l v a r i a t i o n s of these cost items w i t h current d e n s i t y . The c o s t - o p t i m i z a t i o n method developed by Cowan (1960) expresses the t o t a l cost of processing (y) as the sum of three terms: y = a l + Y + c (102) where a, b and c are taken as constants f o r a given stack i f ohmic a n a l y s i s a p p l i e s . This s i m p l i f i e d method has been modified by Lacey et a l . (1963) and Mattson et a l . (1965). By d i f f e r e n t i a t i o n of Eq. (102) to f i n d minimum product c o s t , the optimum c u r r e n t i s seen to be I _ = ( 7 )h (103) opt a S u b s t i t u t i n g t h i s v a l u e i n the equation f o r the t o t a l c ost y, i t i s found that f o r most economical o p e r a t i o n the f i r s t two terms are to be equal (power c o s t s = f i x e d c o s t s ) . This optimum c o n d i t i o n can almost never be met i n c o n v e n t i o n a l e l e c t r o - d i a l y s i s , however, because p o l a r i z a t i o n phenomena set an upper l i m i t to the p e r m i s s i b l e c u r r e n t d e n s i t i e s ; and the f i x e d c o s t s c o n t r i b u t e more towards the t o t a l cost than they should do under the optimum c o n d i t i o n s . Thus the p o l a r i z a t i o n l i m i t a t i o n , r a t h e r than the r e s u l t s of economic o p t i m i z a t i o n , f r e q u e n t l y c o n t r o l s the operating c u r r e n t d e n s i t y and the a p p l i e d v o l t a g e i n p r a c t i c a l e l e c t r o d i a l y s i s i n s t a l l a t i o n s . I t can be concluded that when no excessive p o l a r i z a t i o n takes place the high v o l t a g e i s b e n e f i c i a l and g e n e r a l l y r e s u l t s i n a more e f f i c i e n t and economical o p e r a t i o n of an ED p l a n t . 207 FIGURE 65 Variation of individual cost items making up the total processing cost. 208 5.4.5. E f f e c t of I n i t i a l C oncentration Three groups of experiments were made at i n i t i a l c o n c e n t r a t i o n s C q of 500, 2000 and 4000 ppm NaCl/R^O. With these experiments the c o n c e n t r a t i o n of the r i n s e s o l u t i o n was 1000, 2000 and 4000 ppm r e s p e c t i v e l y . Tables XLIV, XLV and XLVI summarize the o p e r a t i n g c o n d i t i o n s of short columns (4 stages i n s e r i e s ) at the three feed c o n c e n t r a t i o n s and F i g u r e s 66, 67 and 68 d i s p l a y the v a r i a t i o n of the s e p a r a t i o n f a c t o r w i t h the feed con- c e n t r a t i o n . Tables XLVII, XLVIII and XLIX together w i t h F i g u r e s 69, 70 and 71 represent s i m i l a r groups of experiments performed i n longer columns each c o n s i s t i n g of 8 stages i n s e r i e s . The r e s u l t s are summarized as f o l l o w s : 1. In a l l cases the higher feed c o n c e n t r a t i o n had a r e t a r d i n g e f f e c t on s e p a r a t i o n and r e s u l t e d i n a lower s e p a r a t i o n f a c t o r . T h i s i s because the higher c o n c e n t r a t i o n r e q u i r e s p r o p o r t i o n a l l y l a r g e r mass t r a n s f e r r a t e s to achieve the same s e p a r a t i o n . 2. The e f f e c t of the feed c o n c e n t r a t i o n C on s e p a r a t i o n f a c t o r ns i s o l e s s pronounced w i t h the longer columns than w i t h the short ones (Compare Fi g u r e s 66-68 w i t h F i g u r e s 69-71). At the same s e p a r a t i o n f a c t o r ns the c o n c e n t r a t i o n d i f f e r e n c e AC (AC = C„ - C^) i s higher w i t h the higher feed c o n c e n t r a t i o n and longer columns are r e q u i r e d to d i m i n i s h the c o n c e n t r a t i o n AC gradient — between the column ends and thus to suppress the u n d e s i r a b l e a x i a l mixing that developed w i t h the h i g h feed c o n c e n t r a t i o n . 5.4.6. No-Pause Operation The pause time x was dropped to zero i n 7 runs at v a r i o u s feed con- c e n t r a t i o n s to check f i n d i n g s from the previous work i n a batch system (Bass, 1972). Table L summarizes the operating c o n d i t i o n s and f i n a l r e s u l t s and F i g u r e 72 c o n t r a s t s the s e p a r a t i o n f a c t o r s of no-pause o p e r a t i o n (x = 0) Table XLIV E f f e c t of Feed Concentration;(Co) on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s P r o d u c t i o n Rate - 20 C.C./cycle Exp. Group # R l , R5 and R9 ^ ^ I N I T L A L ^ v ^ SEPARATION FACTOR EXP. GRAPH. APPLIED " \ C 0 N C . ns SYMBOL VOLTAGE (VOLT) P A U S E ^ ^ (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 8 0 r - APPLIED PAUSE TIME (SEC) VOLTAGE (VOLT) 15 30 45 2 0 © A a 30 • • • 1000 2000 3000 FEED CONCENTRATION (PPM) 4000 FIGURE 66 Effect of feed concentration (C 0 ) on separation. 4 -Ce l l column-production rate— 20 C.C/cycle . Table XLV E f f e c t of Feed Concentration (Co) on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s P r o d u c t i o n Rate = 50 C.C./cycle Exp. Group # R3, R7 and R l l 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 F E E D CONCENTRATION (PPM) FIGURE 67 Effect of feed concentration (C 0 ) on separation. 4-Cell column _ production rate — 50 CC./cycle . 213 Table XLVI E f f e c t of Feed Concentration (Co) on Separation Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s Production Rate = 100 C.C./cycle Exp. Group # R4, R8 and R12 APPLIED V O L T A G E ( V O L T ) PAUSE TIME ( S E C ) 15 3 0 4 5 2 0 Q A B 3 0 • • G c F E E D CONCENTRATION (PPM) FIGURE 68 Effect of feed concentration (Co ) on separation. 4 — Cell column— production rate— 100 C.C./cycle . 215 Table XLVII E f f e c t of Feed Concentration (Co) on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s P r oduction Rate - 25 C.C./cycle Exp. Group # M l , M5 and M9 EXP. GRAPH. APPLIED N I T I A L \ . ^ \ C 0 N C . ^ " ^ ^ SEPARATION FACTOR ns SYMBOL VOLTAGE (VOLT) P A U SF>\(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 V O L T A G E ( V O L T ) P A U S E TIME (SEC) 15 3 0 4 5 10 O A • 2 0 Q A y 3 0 • A • 2 0 0 0 3 0 0 0 4 0 0 0 F E E D C O N C E N T R A T I O N ( P P M ) FIGURE 69 Effect of feed concentration (Co) on separation . 8 - C e l l column-Production rate 25 C.C./cycle 217 Table X L V I I I E f f e c t of Feed Concentration (Co) on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s P r o d u c t i o n Rate - 50 C.C./cycle Exp. Group # M3, M7 and M i l ^ ^ ^ I N I T I A L ^ 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 ( S E C ) 15 3 0 4 5 10 O A • 2 0 y 3 0 • • B 1000 2 0 0 0 3 0 0 0 F E E D C O N C E N T R A T I O N ( P P M ) 4 0 0 0 FIGURE 70 Effect of feed concentration (C 0 ) on separation. 8 - Cell column _ production rate — 50 C.C/cycle. 219 Table XLIX E f f e c t of Feed Concentration (Co) on Separation Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s P r o d u c t i o n Rate - 100 C.C./cycle Exp. Group # M4, M8 and Ml2 I N I T I A L ^ . SEPARATION FACTOR EXP. GRAPH. APPLIED CONC. ns SYMBOL VOLTAGE (VOLT) P A U S ^ ^ (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 V O L T A G E ( V O L T ) PAUSE TIME ( S E C ) 15 3 0 4 5 10 O A • 20 Q A y 30 • A 1000 2 0 0 0 F E E D C O N C E N T R A T I O N 4 0 0 0 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 - C e l l 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 8 0 APPLIED V O L T A G E ( V O L T ) F E E D CONCENTRATION ( P P M ) 5 0 0 2 0 0 0 4 0 0 0 10 A 2 0 Q y 3 0 • • m 0 15 3 0 PAUSE TIME ( S E C ) FIGURE 72 Comparison of pause and no_ pause operations . 8 —Cell column_ production rate — 50 C.C./cycle . 223 w i t h the normal or pause-operation (x = 15, 30 and 45 sec.) under otherwise i d e n t i c a l c o n d i t i o n s . One can see that reducing the pause time to zero i n a l l cases stu d i e d r e s u l t e d i n a c o n s i d e r a b l y decreased s e p a r a t i o n . This confirmed the previous f i n d i n g s t h a t f l o w pauses at the beginning of each h a l f c y c l e represent important f e a t u r e s of the c y c l i c ED o p e r a t i o n . 5.4.7. Pure-Pause Operation In pure-pause o p e r a t i o n the e l e c t r i c power i s o f f during c i r c u l a t i o n and interphase mass t r a n s f e r takes p l a c e only during pause p e r i o d s i n each c y c l e . This mode of o p e r a t i o n seemed a t t r a c t i v e s i n c e i t could r e s u l t i n l a r g e power savings. Table L I l i s t s 12 runs; h a l f of them were conducted w i t h power on during c i r c u l a t i o n w h i l e the other h a l f were performed w i t h pure-pause o p e r a t i o n under otherwise i d e n t i c a l c o n d i t i o n s . F i g u r e 73 d i s p l a y s the s e p a r a t i o n f a c t o r ns achieved by the two modes of o p e r a t i o n . The r e s u l t s a r e : 1. Pure-pause o p e r a t i o n saves e l e c t r i c power, but r e s u l t s i n poor se p a r a t i o n . 2. This e f f e c t i s more pronounced w i t h short pause time. 5.4.8. Semi-Symmetric Operation In semi-symmetric o p e r a t i o n feed i s introduced and products withdrawn every h a l f c y c l e w h i l e i n asymmetric o p e r a t i o n the system i s c l o s e d during the f i r s t h a l f c y c l e ( r e f e r to Chapter 4 ) . S i x experiments were performed under v a r i o u s operating c o n d i t i o n s u s i n g semi-symmetric o p e r a t i o n . Table L I I l i s t s the o p e r a t i n g c o n d i t i o n s and the f i n a l s e p a r a t i o n achieved. These experiments were compared w i t h s i m i l a r runs under asymmetric o p e r a t i o n as 224 Table LI Comparison of Pure Pause with Mixed Mode Operations 8-Cell Columns - PRODUCTION Rate - 50 C.C./cycle I n i t i a l 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 O r - APPLIED V O L T A G E POWER DURING CIRCULATION ON OFF 2 0 a 3 0 • • 30 U o O < z o < OL UJ CO 2 0 10 15 3 0 4 5 P A U S E TIME ( S E C ) FIGURE 73 Pure pause operation (No. power during circulation). 8 - C e l l column — production rate — 5 0 C.C./cycle . Initial concentration CQ=^ 2 0 0 0 PPM . Table L I I Semi-symmetric Operation Feed Concentration Co - 2000 ppm Production r a t e = 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 i n Table L I I I . F i g u r e 74 c o n t r a s t s the performance'of these two modes. In a l l cases the semi-symmetric o p e r a t i o n r e s u l t s i n a lower s e p a r a t i o n f a c t o r . F i g u r e s 75 and 76 show the i d e a l developing c o n c e n t r a t i o n p r o f i l e s p r e d i c t e d f o r asymmetric and semi-symmetric o p e r a t i o n r e s p e c t i v e l y when the mass t r a n s f e r takes place during both pause and displacement p e r i o d s . The dotted l i n e s i n these f i g u r e s show s e p a r a t e l y the previous c o n c e n t r a t i o n p r o f i l e and the change i n t h i s p r o f i l e due to the mass t r a n s f e r d u r i n g c i r c u l a t i o n . S o l i d l i n e i s the summation of the two dotted l i n e s u s i n g the feed c o n c e n t r a t i o n as the zero l e v e l . These f i g u r e s show that when steady s t a t e i s reached the two modes of o p e r a t i o n should r e s u l t i n the same s e p a r a t i o n . Table LIV summarizes F i g u r e s 75 and 76 and l i s t s the average product c o n c e n t r a t i o n s , expressed i n a r b i t r a r y u n i t s , which would be expected during the t r a n s i e n t p e r i o d s and at the p e r i o d i c steady s t a t e . The low s e p a r a t i o n achieved w i t h semi-symmetric o p e r a t i o n i n p r a c t i c e may be a t t r i b u t e d to e x t e r n a l mixing o u t s i d e the a c t i v e ED r e g i o n , s i n c e a s i n g l e p o r t was used to withdraw the depleted and the enriched products s u c c e s s i v e l y d uring the two h a l f - c y c l e s . Any m a t e r i a l from the previous h a l f - c y c l e that mixed w i t h the new product would impair s e p a r a t i o n . 5.5. Comment on pH-Changes Checks on the pH of both the process and r i n s e streams showed no s i g n i f i c a n t changes f o r most runs. T y p i c a l r e s u l t s are l i s t e d i n Table LV. The r i n s e stream remains almost unchanged and o n l y shows a s l i g h t f l u c t u a t i o n i n i t s pH-value w h i l e the process s o l u t i o n tends to be a s l i g h t l y a c i d i c w i t h a drop i n the pH-value of about 0.3 from i t s i n i t i a l average v a l u e of 5.9. A n o t i c e a b l e exception to t h i s are the experiments w i t h low feed c o n c e n t r a t i o n ( C Q = 500 ppm) which i n v o l v e r e l a t i v e l y long pause time (T = 45 sec.) and/or high v o l t a g e (A(j> = 30 V) as e x e m p l i f i e d by experiments M7 F, 228 Table L I I I Comparison of Semi-Symmetric and Asymmetric Operations 8 - C e l l Column - Pro d u c t i o n 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 C 0 2 0 0 0 PPM . Bottom Top t '4' f 5 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 i n a r b i t r a r y u n i t s 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 C B 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 f o r Some ED Runs a t v a r i o u s feed c o n c e n t r a t i o n s and op e r a t i n g c o n d i t i o n s FEED PROCESS pH RINSE pH EXP. CONC. Co (ppm) I n i t i a l F i n a l I n i t i a l F i n a l 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 M i l A 5.9 5.7 5.9 5.6 M i l B 4000 6.2 6.0 6.2 5.9 M i l F 5.7 5.3 5.7 5.8 M i l I 6.1 6.0 6.1 6.2 243 M7 B and M7 E ( r e f e r to Table LV). 5.6. Temperature Measurements The i n i t i a l and f i n a l temperatures of the process stream f o r s e v e r a l runs under v a r i o u s o p e r a t i n g c o n d i t i o n s were measured using an i n s e r t e d mercury thermometer. An average temperature r i s e of 3-5°C from i t s i n i t i a l v a lue of 23-25°C was observed i n most cases. 5.7. Pressure Drop Measurements The pressure drop across an 8-stage ED column was measured at v a r i o u s f l o w r a t e s u s i n g a mercury manometer. Measured val u e s are l i s t e d i n Table LVI and a p l o t of AP (mm Hg) v s . f l o w r a t e (c.c./sec) i s d i s p l a y e d i n F i g u r e 77. Most of the runs i n the present work i n v o l v e a f l o w r a t e of about 16.7 c.c./sec. The mean h y d r a u l i c r a d i u s of the f l o w channel was about 2.76 -2 x 10 cm which give s r i s e to a Reynolds number of about 760. 5.8. Probe V o l t a g e , Apparent Resistance and Current Consumption I n a l l experiments described here the a p p l i e d v o l t a g e s u p p l i e d by the D.C. power source was held constant during each h a l f c y c l e . The v o l t a g e drop across the stack (as measured by probe e l e c t r o d e s ) was p r i m a r i l y a f u n c t i o n of t h i s a p p l i e d p o t e n t i a l , but i t i s g e n e r a l l y below the a p p l i e d v o l t a g e due to r e s i s t a n c e i n the connectors, r i n s e s o l u t i o n and e l e c t r i c o v e r p o t e n t i a l s as shown i n Table L V I I and F i g u r e 78. Both the stack v o l t a g e (probe v o l t a g e ) and the c u r r e n t consumption vary s y s t e m a t i c a l l y d u ring the c y c l e and along the d e m i n e r a l i z a t i o n path. T y p i c a l examples of these f l u c t u a t i o n s are shown i n F i g u r e s 79 and 80 f o r the v o l t a g e Table LVI Pressure Drop Measurements 8-Stage ED Stack Time P e r i o d 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 L V I I Average Probe Voltage (Stack Voltage) over a complete c y c l e f o r v a r i o u s feed c o n c e n t r a t i o n and a p p l i e d v o l t a g e s . Pause time T = 45 sec Exp. Group # M3, M7 and M i l 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 M i l • 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 M 3 , M7 QM II. FIGURE 79 Traces of probe voltage recording during a cycle at four points along the demineralizing path. EXP. M7F . FIGURE 8 0 Traces of current recording during a cycle at different points along the demineralizing path. E X P M 7 F . 250 Traces of probe voltage recording during a cycle at four points along the demineralizing path EXP. M IIF. 251 252 and c u r r e n t r e s p e c t i v e l y a t the feed c o n c e n t r a t i o n C q - 500 ppm. F i g u r e s 81 and 82 d i s p l a y s i m i l a r v a r i a t i o n s of stack v o l t a g e and c u r r e n t consumption during the c y c l e and along the d e m i n e r a l i z a t i o n path f o r the feed con- c e n t r a t i o n C q - 4000 ppm. Average va l u e s of these v a r i a t i o n s along the d e m i n e r a l i z a t i o n path are i n d i c a t e d i n Table L V I I I and F i g u r e 83 f o r the stack v o l t a g e and i n Tables LIX and LX and F i g u r e s 84 and 85 f o r the c u r r e n t consumption. The c u r r e n t consumption decreases w i t h i n c r e a s i n g s e p a r a t i o n , thus i t drops along the d e m i n e r a l i z a t i o n path as we move from the feed end towards the product end ( r e f e r to F i g u r e 84) and i t i n c r e a s e s w i t h i n c r e a s i n g feed c o n c e n t r a t i o n ( r e f e r to F i g u r e 85). The main i n f l u e n c e causing the wide v a r i a t i o n s i n the cur r e n t was the d e p l e t i o n of s o l u t e i n e i t h e r the flow channels or the c a p a c i t y c e l l s towards the'end of each h a l f c y c l e . The stack v o l t a g e , as shown i n F i g u r e 83, approaches the a p p l i e d v o l t a g e as the cur r e n t consumption drops due to e i t h e r a h i g h s e p a r a t i o n or a low feed c o n c e n t r a t i o n . Tables L X I , L X I I and L X I I I show v a r i a t i o n s of probe v o l t a g e , c u r r e n t , apparent r e s i s t a n c e and power consumption along the d e m i n e r a l i z a t i o n path f o r v a r i o u s runs w i t h the a p p l i e d v o l t a g e a t l e v e l of 10, 20 and 30 v o l t and feed c o n c e n t r a t i o n s C q of 500, 2000 and 4000 ppm NaCl. Table LXIV and F i g u r e 86 show the v a r i a t i o n of average stack r e s i s t a n c e w i t h feed c o n c e n t r a t i o n . The average stack r e s i s t a n c e decreases w i t h i n c r e a s i n g feed c o n c e n t r a t i o n and w i t h decreasing a p p l i e d v o l t a g e . Table LXV and F i g u r e 87 show the v a r i a t i o n of stack r e s i s t a n c e along the de- m i n e r a l i z a t i o n path during the d e p l e t i o n h a l f c y c l e . The r e s i s t a n c e i n c r e a s e s as the process stream becomes more depleted towards the product end. 253 Table L V I I I V a r i a t i o n of probe v o l t a g e along the d e m i n e r a l i z a t i o n path during the d e p l e t i o n h a l f c y c l e f o r v a r i o u s feed c o n c e n t r a t i o n s . 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 M i l 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- C 0 ( PPM.) • 5 0 0 • 4 0 0 0 LOO 0-751 I I I 1 4 3 2 1 Feed S tage N u m b e r 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 V a r i a t i o n of cu r r e n t consumption along the d e m i n e r a l i z a t i o n path during the d e p l e t i o n h a l f c y c l e a t v a r i o u s a p p l i e d v o l t a g e s . 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 , E X P . M3 B , M 3 F 8 M 3 G 257 Table LX V a r i a t i o n of curr e n t consumption along the d e m i n e r a l i z a t i o n path during the d e p l e t i o n h a l f c y c l e a t v a r i o u s feed c o n c e n t r a t i o n s . A<j> = 30 V Exp. M3 F, M7F and M i l 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 M i l F • 4000 1050 640 409 288 258 Variation of current consumption along the demineralization path at various feed concentrations. AO" = 3 0 V , E X P M 3 F . M 7 F 8 M I I F . 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 E f f e c t of I n i t i a l C oncentration on the e q u i v a l e n t r e s i s t a n c e of ED stack Exp. Group M7, M3 and M i l 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 V a r i a t i o n of ED Stack R e s i s t a n c e along the de- m i n e r a l i z a t i o n path d u r i n g the d e p l e t i o n h a l f c y c l e a t v a r i o u s a p p l i e d v o l t a g e s . 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 6 0 0 0> o c o tn or 4 0 0 c <u o a. o. < 200 Symbol Applied Volt A O (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 . C Q ^ 5 0 0 PPM ; EXP M7F & M7G 266 F i g u r e 88 d i s p l a y s the p l o t of the stage apparent r e s i s t a n c e ( R = A<j>/I) on l o g a r i t h m i c s c a l e v s . the stage p o s i t i o n along the d e m i n e r a l i - z a t i o n path during the d e p l e t i o n h a l f c y c l e . The p l o t s are f i t t e d by s t r a i g h t l i n e s which suggest that the apparent r e s i s t a n c e of an ED stack may be expressed by an e m p i r i c a l r e l a t i o n of the form: I n R £ = C± + C2Z (104) where R^ i s the l o c a l r e s i s t a n c e at d i s t a n c e I from the feed i n l e t and and C2 are constants. I f we are concerned only w i t h the average v a l u e of the stage r e s i s t a n c e then we have I = nV (105) where £' i s a s i n g l e stage l e n g t h and n i s the stage number (n = 1 a t feed end). S u b s t i t u t e Eq. (105) i n t o Eq. (104): I n R = C . + C„n (106) n 1 J where R N i s the average r e s i s t a n c e of stage number n. Fi g u r e 89 shows the v a r i a t i o n of the average stage r e s i s t a n c e w i t h the stage p o s i t i o n on a semi-logarithmic s c a l e when the feed c o n c e n t r a t i o n C q - 2000 ppm and a p p l i e d v o l t a g e was at l e v e l s of 10, 20 and 30 V. Various p o i n t s under the same operating c o n d i t i o n s are f i t t e d by s t r a i g h t l i n e s . The slope of these l i n e s i n c r e a s e s w i t h i n c r e a s i n g a p p l i e d v o l t a g e and when these l i n e s are e x t r a p o l a t e d they tend to merge i n t o a s i n g l e p o i n t (a p o l e ) . For feed c o n c e n t r a t i o n C q = 2000 ppm the pole l i e s a t the p o i n t P (0.70, 45 ) ( r e f e r to F i g u r e 89). For t h i s case Eq. (106) can be w r i t t e n as In R = I n 45 +'C Q (n - 0.70) (107) n 3 The value of can be obtained from the slope of the l i n e s i n F i g u r e 89 267 1000 8 0 0 Initial Cone. Symbol ( PPM) • 5 0 0 O 2000 A 4 0 0 0 600 4 0 0 1 0 1 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" = 3 0 V ; E X P . M 3 F . M 7 F 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 L X l l ) 269 as f o l l o w s : C 3 * 0.43 C 3 = 0.34 and C 3 - 0.17 f o r A<j> = 30 V f o r Atj) = 20 V f o r A<j> = 10 V S i m i l a r l y the parameters and i n the e x p i r i c a l Eq. (106) can be determined f o r the other feed c o n c e n t r a t i o n s under v a r i o u s o p e r a t i n g c o n d i t i o n s . 5.9. V o l t a g e E f f i c i e n c y V oltage e f f i c i e n c y may be defined as the f r a c t i o n of the a p p l i e d v o l t a g e t h a t i s u t i l i z e d i n s e p a r a t i o n (probe v o l t a g e ) . A < t > " A ( f ,con " A < { , e l r, = — •* 100 (108) v A<j> where A<j> = a p p l i e d v o l t a g e Acb = v o l t a g e drop i n the connectors con ° r A<|>g£ = v o l t a g e drop due to the r i n s e s o l u t i o n and e l e c t r o d e o v e r p o t e n t i a l s Table LXVI l i s t s v o l t a g e e f f i c i e n c y f o r s e v e r a l runs under v a r i o u s o p e r a t i n g c o n d i t i o n s . The v o l t a g e e f f i c i e n c y ranges between 82.50 and 90.83%. 5.10. Current d e n s i t y and e f f i c i e n c y I n the present work the c u r r e n t d e n s i t y , i , v a r i e s between 1.00 and 2 10.82 mA/cm . Low c u r r e n t d e n s i t y corresponds to o p e r a t i o n w i t h a low feed c o n c e n t r a t i o n and a small a p p l i e d v o l t a g e . The t r u e c u r r e n t e f f i c i e n c y , n , i s d e f i n e d by Eq. B.7 as Table LXVI Voltage E f f i c i e n c y 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 M i l B 20 16.65 83.25 M i l F 30 24.85 82.83 M i l G 10 8.25 82.50 271 nT = n„ n n (B.7.) I s m w When the s e l e c t i v i t y of the membrane i s 0.90 the true c u r r e n t e f f i c i e n c y , n i s u s u a l l y about 80%. The curr e n t u t i l i z a t i o n f a c t o r or the o v e r a l l c u r r e n t e f f i c i e n c y , n^ can be de f i n e d as a c t u a l amount of s a l t t r a n s p o r t e d A (109) I t h e o r e t i c a l amount of s a l t t ransported where the t h e o r e t i c a l amount of s a l t t r a n s p o r t e d i n g-equivalent i s given by ,6 VAC =  1 ' Z ' 1 0 • M ( 1 1 0> ZF where V = the volume of f l u i d demineralized during time t i n a f l o w channel (c.c.) AC = change i n f l u i d c o n c e n t r a t i o n (ppm) I = curr e n t passed (amp) t = d u r a t i o n of the c u r r e n t passage (sec) Z = valence (g-equiv./g-mole) F = Faraday's constant = 96500 (coulomb/g-equiv.) M = Molecular weight of s o l u t e = 58.44 (g/g-mole) The o v e r a l l c u r r e n t e f f i c i e n c y as def i n e d above i n c l u d e s the tru e current e f f i c i e n c y , together w i t h any i n e f f i c i e n c i e s i n the process such as d i s p e r s i v e e f f e c t s , d i f f u s i o n under c o n c e n t r a t i o n g r a d i e n t and i n t e r n a l and e x t e r n a l leakage i f any e x i s t . The o v e r a l l c u r r e n t e f f i c i e n c y , n-j-, was evaluated f o r s e v e r a l runs under v a r i o u s o p e r a t i n g c o n d i t i o n s as shown i n Table LXVII. The o v e r a l l c u r r e n t e f f i c i e n c y ranges between 26 and 32% i n most cases; runs w i t h h i g h feed c o n c e n t r a t i o n r e s u l t e d i n lower v a l u e s . Previous work i n the c l o s e d Table LXVII O v e r a l l Current E f f i c i e n c y 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 i n d i c a t e d an o v e r a l l c u r r e n t e f f i c i e n c y between 20 and 40 f o r the f i r s t c y c l e , decreasing r a p i d l y f o r subsequent c y c l e s , and tending to zero as the s e p a r a t i o n approached steady p e r i o d i c s t a t e . The o v e r a l l c u r r e n t e f f i c i e n c y could be improved by u t i l i z i n g a more e f f i c i e n t unsymmetric power wave w i t h a short r e g e n e r a t i o n step compared w i t h the d e m i n e r a l i z i n g step and by usin g a longer d e m i n e r a l i z i n g path. A l s o as most of the u s e f u l s e p a r a t i o n takes place during pause peri o d s decreasing c i r c u l a t i o n time may r e s u l t i n an increased c u r r e n t e f f i c i e n c y . 5.11. Comments on Stack Resistance Models Four experiments under v a r i o u s o p e r a t i n g c o n d i t i o n s have been used to t e s t the non-ohmic model. The f o l l o w i n g s i m p l i f i e d equation (Eq. 51) was used to p r e d i c t the apparent r e s i s t a n c e of an ED stage at the product end. 2RT r N . ns + k , R P  = F T [ ( t " V l n — T ] 2FD 1 + k/ns ( t - t ) A i 1 - k , A - 26 . A - 26 . , + _ + _ + p + p (51) D D UC AC a C where 2 R i s the r e s i s t a n c e per u n i t area (ohm-cm ) P R i s the gas law constant = 8.3144 ( J o u l e - g m o l e - 1 - °K _ 1) .T = the absolute temperature (°K) F = Faraday's constant (Coulomb/g.equiv) 2 i = cur r e n t d e n s i t y (A/cm ) t , t = t r a n s p o r t numbers of counter-ions i n membrane and s o l u t i o n r e s p e c t i v e l y 274 D k ns A t c = t r a n s p o r t number of co-ions i n the membrane 2 = e q u i v a l e n t s o l u t i o n conductance (mho.cm /gmole) 2 = d i f f u s i v i t y (cm /sec) = s e p a r a t i o n f a c t o r = —— CD = r a t i o of the operating to l i m i t i n g c u r r e n t d e n s i t y A = f l o w channel t h i c k n e s s (cm) 6 = d i f f u s i o n l a y e r t h i c k n e s s (cm) = the anion and c a t i o n membrane r e s i s t a n c e per u n i t area (ohm - cm^) System Data and Assumptions Room temperature = 25°C = 298°K Molecular weight of NaCl = 58.44 Eq u i v a l e n t conductance of aqueous sodium c h l o r i d e s o l u t i o n , A, i s given by Table LXVIII and F i g u r e 90. D i f f u s i v i t y of aqueous sodium c h l o r i d e , D, i s given by Table LXVIII and F i g u r e 91. A - 26 - A 2 E l e c t r o d e area = 61.23 cm Spacer t h i c k n e s s = 0.098 cm Exposed area of spacer = 0.50 Membrane s e l e c t i v i t y = 90% (t - t c ) = 0.90 (t - t ) av = 0.45 = 19.2 ft-cm 2 k = 0.80 275 Table LXVIII E q u i v a l e n t Conductance and D i f f u s i v i t y of aqueous sodium c h l o r i d e s o l u t i o n s * 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 * S a l i n e Water Conversion Engineering Data Book, Second E d i t i o n , U.S. O f f i c e of S a l i n e 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 C a l c u l a t i o n s EXP M3F ; C q = 2120 ppm 2 Cp = 105 ppm ; = 125.6 mho. cm /gmole D = 1.599 x 10" 5 cm 2/sec 2 C„ = 4300 ppm ; A„ = 113 mho. cm /gmole ns =40.95 ; i = 2.858 mA/cm2 av 1st term (membrane p o t e n t i a l term) = (2)(8.3144)(298)(0.9) l n 40.95 + 0.8 = 8 6 > 3 7 , _ c m 2 < t > , m (96500) (2.858)10 J U ' Z 2nd term ( d i f f u s i o n l a y e r r e s i s t a n c e term) p - (2)(96500)(1.599) 10" 5 . 1 + 0.0195 _ o, 1 9 0 2 R 6 - (2.858) (0.45) (125.6)10-3 l n O 3 1 ' 1 Z " " C m 3rd term (membrane r e s i s t a n c e term) 2 R = 38.40 n - cm m 4th term (depleted s o l u t i o n r e s i s t a n c e term) (0.098)(58.44)10 6 = 868.58'n - cm 2 d (0.5)(105)(125.6) 5th term (enriched s o l u t i o n r e s i s t a n c e term) R = (11.45) 1 0 6 c, n 2 (4300)(113) = 2 3 ' 5 7 ° " C m The apparent r e s i s t a n c e per u n i t area of a c e l l p a i r , R^ i s given by R = R X + R . + R + R , + R = 1048.04 fi - cm 2 p cj>,m o m d e The p r e d i c t e d stage r e s i s t a n c e i s given by 279 Measured stage r e s i s t a n c e = 160.05 ft ... «. 136.93 - 160.05 .._ the percentage e r r o r = 1 (. Q ^ = - 14.44% Table LXIX l i s t s v a l u e s of p r e d i c t e d and measured r e s i s t a n c e s f o r s e v e r a l experiments and breaks down the t o t a l p r e d i c t e d r e s i s t a n c e i n t o i t s main r e s i s t i v e elements and i t a l s o i n d i c a t e s the c o n t r i b u t i o n of each element towards the o v e r a l l v a l u e . F i g u r e 92 d i s p l a y s the discrepancy between p r e d i c t e d and measured values of an ED stage r e s i s t a n c e . The discrepancy may be a t t r i b u t e d to the assumed val u e s used i n the c a l c u l a t i o n or to the s i m p l i f y i n g assumptions i n v o l v e d i n the model or to both of them. From Table LXIX i t can be seen that the membrane p o t e n t i a l term together w i t h the d i f f u s i o n l a y e r r e s i s t a n c e c o n t r i b u t e about 20% while the b u l k s o l u t i o n s c o n t r i b u t e about 80% towards the o v e r a l l r e s i s t a n c e v a l u e . These f i n d i n g s a l s o i n d i c a t e t h a t ohmic model can be used s a t i s f a c t o r i l y to p r e d i c t the stack r e s i s t a n c e . The b a s i c equation of ohmic a n a l y s i s i s given as K i -l l = — + Ko - KoC (52) P C where K^, and are constants f o r a given system and C i s the l o c a l average c o n c e n t r a t i o n . Measured stage r e s i s t a n c e s i n s e v e r a l runs were p l o t t e d v s . the r e c i p r o c a l of the average c o n c e n t r a t i o n as shown i n F i g u r e 93 and Table LXX. The p l o t was f i t t e d by a s t r a i g h t l i n e . The model constants were determined from the slope and i n t e r c e p t of the graph as f o l l o w s : * 216484 K 2 * 191.34 and K 3 - 0.0 Table LXIX Distribution of the predicted resistance of an ED stage, R , between i t s resistive elements RESISTIVE ELEMENT M3 F 2000 ppm M3 B 2000 ppm M7 G 500 ppm Mil F 4000 ppm VALUE a % age of R s VALUE n % age of R s VALUE a % age of R s VALUE n % age of R s 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 4 0 0 320 240 160 8 0 7T Initial Cone. (PPM) Voltage (Volt) 10 20 30 500 O 2000 • 4 0 0 0 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 l o c a l average c o n c e n t r a t i o n , C and measured stage r e s i s t a n c e EXP. PRODUCT CONC (ppm) LOCAL AVERAGE CONC. (ppm) STAGE RESISTANCE («) C B 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 M i l B 7375 625 1152 40 M i l F 8125 239 464 81 M i l G 6450 2010 3065 26 283 9 0 0 FIGURE 93 Variation of apparent resistance of an ED stage with the reciprocal of Ihe average product concentrations. 284 5.12 Comparison w i t h P r e v i o u s Work i n Closed System ( i ) Separation Bass (1972) reported some experiments performed i n a b a t c h - r e c i r c u l a c i o n mode of o p e r a t i o n i n which a 90% demineralized product was i n t e r m i t t e n t l y r eplaced by f r e s h feed every e i g h t c y c l e s . Experiments under t h i s mode of op e r a t i o n r e s u l t e d i n a s e p a r a t i o n f a c t o r of 16 w i t h a feed c o n c e n t r a t i o n C q = 1250 ppm, a p p l i e d v o l t a g e A<}> = 10 V, pause time x = 10 sec, d i s p l a c e d volume 6 = 2/3 the a c t i v e volume and a throughput r a t i o of about 0.075. In the present work experiments w i t h A<j> = 20 V, x = 15 sec r e s u l t i n a se p a r a t i o n f a c t o r of 20 a t a throughput r a t i o of 0.25 which i s the same magnitude of s e p a r a t i o n per u n i t power consumption as i n the previous case. However, the previous work does not show any c o n s i s t e n t e f f e c t of i n i t i a l c o n c e n t r a t i o n , C q on the f i n a l s e p a r a t i o n . ( i i ) R e s i s t a n c e and Current Consumption The i n i t i a l r e s i s t a n c e and cu r r e n t consumption i n the closed system were g e n e r a l l y of the same magnitude as i n the present work and they e x h i b i t the same trend of v a r i a t i o n along the d e m i n e r a l i z i n g path. ( i i i ) A n a l y s i s of A x i a l D i s p e r s i o n The a x i a l d i s p e r s i o n i n the ED c e l l s has been determined p r e v i o u s l y u s i n g the step response method. The r e s u l t i n g F-diagrams d i d not suggest excessive c h a n n e l l i n g or by-passing. From the slope of response curve i t was estimated t h a t the system corresponds to about 50 e f f e c t i v e mixing stages. In the spacer used i n both works there are 10 x 10 strands per inch and there are about 55 holes along the flowpath i n the ED c e l l . 285 ( i v ) E f f e c t of Pause Time The previous work i n the batch o p e r a t i o n showed that f l o w pauses at the beginning of each h a l f c y c l e represent important f e a t u r e s of the c y c l i c process o p e r a t i o n . This i s i n l i n e w i t h the f i n d i n g s i n the present work. 5.13 R e p r o d u c i b i l i t y S e v e r a l of the runs under d i f f e r e n t o p e r a t i n g c o n d i t i o n s were repeated to t e s t the r e p r o d u c i b i l i t y of the r e s u l t s . Table LXXI l i s t s the d u p l i c a t e experiments and compares them w i t h the i n i t i a l ones conducted i n 4-stage columns. Table LXXII makes the same comparison f o r experiments performed i n 8-stage columns. I n both cases the r e p r o d u c i b i l i t y of the r e s u l t s are considered as q u i t e s a t i s f a c t o r y . Table LXXI R e p r o d u c i b i l i t y - GROUP R Two Columns Each C o n s i s t s of 4 C e l l s i n S e r i e s EXP. SEPARATION FACTOR ns DISCREPANCY OLD NEW AS PERCENTAGE OF (ns) Av, R l A 8.90 10.43 + 15.83 R l D 7.49 8.53 + 12.98 R l E 13.93 16.52 + 17.01 R l 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 R l l F 3.44 3.76 + 8.89 287 Table LXXII R e p r o d u c i b i l i t y - Group M Two Columns Each C o n s i s t s of 8 C e l l s i n S e r i e s 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 M i l 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 f e a s i b i l i t y of continuous c y c l i c e l e c t r o d i a l y s i s f o r d e s a l i n a t i o n of b r a c k i s h waters. The conventional e l e c t r o d i a l y s i s d e m i n e r a l i z i n g process competes mainly w i t h d i s t i l l a t i o n and i t appears to be more a t t r a c t i v e economically than d i s t i l l a t i o n f o r low s a l i n i t y waters (with c o n c e n t r a t i o n s of up to about 10,000 ppm d i s s o l v e d s a l t ) . However, con v e n t i o n a l e l e c t r o d i a l y s i s i s subject to excessive, p o l a r i z a t i o n , f o u l i n g and s c a l e formation on ion-exchange membranes, an<-l g e n e r a l l y r e q u i r e s expensive m a t e r i a l s f o r e l e c t r o d e s . C y c l i c e l e c t r o d i a l y s i s promises to overcome these problems by the reversed p o l a r i t y technique. In the present work no excessive p o l a r i z a t i o n was n o t i c e d i n most of the runs (up to the maximum v o l t a g e a p p l i e d of 30 v o l t s ) and inexpensive g r a p h i t e e l e c t r o d e s proved to be s a t i s f a c t o r y over a reasonably long p e r i o d of time. The process r e s u l t e d i n a s e p a r a t i o n factor. ' (ns = C-./C ) up to 50 at a throughput r a t i o of 0.25 which i s eq u i v a l e n t i.< B D a d e s a l i n a t i o n r a t i o (defined as C /C_) of about 25 compared w i t h the o D d e s a l i n a t i o n r a t i o per path of about 2 i n most commercial p l a n t s c u r r e n t l y i n o p e r a t i o n . The primary o b j e c t i v e s of the experimental program undertaken were to e xplore the p o s s i b l e r e g i o n of a p p l i c a t i o n of c y c l i c o p e r a t i o n i n an open e l e c t r o d i a l y s i s system, to screen system parameters, and to determine. 288 289 t h e i r r e l a t i v e importance. The f o l l o w i n g design and op e r a t i n g parameters have been i n v e s t i g a t e d : a) Design Parameters ( i ) D e m i n e r a l i z a t i o n path l e n g t h ( i i ) Semi-symmetric and asymmetric modes of o p e r a t i o n ( i i i ) Pause and no-pause operations ( i v ) Pure-pause o p e r a t i o n w i t h power o f f du r i n g c i r c u l a t i o n b) Operating Parameters (v) P r o d u c t i o n r a t e w i t h throughput r a t i o v a r y i n g from 0.0625 to 0.50. ( v i ) A p p l i e d v o l t a g e A<|) at l e v e l s of 10, 20 and 30 v o l t , ( v i i ) Pause time x at l e v e l s of 15, 30 and 45 sec. ( v i i i ) Feed c o n c e n t r a t i o n C q a t l e v e l s of 500, 2000 and 4000 ppm The r e s u l t s of the study can be summarized i n the f o l l o w i n g : 1. D e s p i t e the strong t r a d e - o f f between p r o d u c t i o n r a t e and s e p a r a t i o n , the s e p a r a t i o n f a c t o r ranged from 30 ( f o r 4000 ppm feed) to 50 ( f o r 500 ppm feed) at the highest p r o d u c t i o n r a t e used (100 c . c . / c y c l e ) . 2. The pause time proved to be an important o p e r a t i n g parameter. Decreasing the pause time below 15 sec. r e s u l t e d i n c o n s i d e r a b l y lower s e p a r a t i o n . 3. The maximum pause time that can be u t i l i z e d without an adverse e f f e c t on s e p a r a t i o n depends on both the a p p l i e d v o l t a g e Acj> and the feed con- c e n t r a t i o n C . At an a p p l i e d v o l t a g e A<}> = 30 V; x was about 30 sec. f o r o max C q - 500 ppm and i t was about 45 sec. f o r C q - 2000 ppm. 4. In a l l cases i n c r e a s i n g the a p p l i e d v o l t a g e improves the s e p a r a t i o n . The s e p a r a t i o n f a c t o r i n c r e a s e s at l e a s t p r o p o r t i o n a l l y w i t h the a p p l i e d 290 v o l t a g e . The e f f e c t of a p p l i e d v o l t a g e was more pronounced when the feed c o n c e n t r a t i o n was high and/or the pause time was sh o r t . 5. With the feed c o n c e n t r a t i o n C Q - 500 ppm the optimum c o n d i t i o n s are thought to be: a d e m i n e r a l i z i n g path l e n g t h i n the v i c i n i t y of 8 stages i n s e r i e s , an a p p l i e d v o l t a g e i n the range 20-30 v o l t and a pause time of about 30 sec. An i n c r e a s e of pause time above 30 sec. had a d e l e t e r i o u s e f f e c t on s e p a r a t i o n , presumably because of p o l a r i z a t i o n . 6. As the feed c o n c e n t r a t i o n C q i n c r e a s e s the s e p a r a t i o n decreases. Higher feed c o n c e n t r a t i o n c a l l s f o r a longer d e m i n e r a l i z i n g path, higher v o l t a g e and longer pause time. 7. Pure-pause o p e r a t i o n saves e l e c t r i c power a t the expense of poor s e p a r a t i o n . 8. V a r i a t i o n s i n the methods of feed i n t r o d u c t i o n and product with- drawal, such as symmetric, semi-symmetric and asymmetric o p e r a t i o n s , were i n v e s t i g a t e d t h e o r e t i c a l l y (Chapter 4). When a x i a l mixing i s ignored a l l these modes p r e d i c t the same f i n a l s e p a r a t i o n as shown by the g r a p h i c a l s o l u t i o n s . However, the degree of complexity of the system, the number of v a l v e s and the number of s u b d i v i s i o n s i n the t i m i n g sequence, decrease as the op e r a t i o n becomes l e s s symmetric. 9. When semi-symmetric and asymmetric operations were compared e x p e r i m e n t a l l y under otherwise i d e n t i c a l c o n d i t i o n s the former r e s u l t e d i n lower s e p a r a t i o n . This may be a t t r i b u t e d mainly to the e x t e r n a l mixing o u t s i d e the a c t i v e d e m i n e r a l i z i n g area. 10. The experimental r e s u l t s are g e n e r a l l y h i g h l y r e p r o d u c i b l e . 11. C y c l i c e l e c t r o d i a l y s i s i n an open system has been f u l l y demon- s t r a t e d . The process looks promising and i t deserves f u r t h e r study along the 291 f o l l o w i n g l i n e s : a) The present work has been l i m i t e d by the f o l l o w i n g design parameters: ( i ) A d e m i n e r a l i z i n g path of maximum l e n g t h of 8 stages i n s e r i e s ( i i ) A D.C. power supply of 400 watts (a maximum a p p l i e d v o l t a g e of about 30 v o l t s ) ( i i i ) A maximum time i n t e r v a l of about 50 sec. To explore f u l l y the whole op e r a t i n g domain at feed c o n c e n t r a t i o n C Q higher than 500 ppm a l l these parameters need to be r e l a x e d by modifying the process design. b) The feed c o n c e n t r a t i o n should be extended to the range C Q = 10,000 - 15,000 ppm. c) Other o p e r a t i n g procedures should be i n v e s t i g a t e d . In p a r t i c u l a r i t i s proposed to disconnect the e l e c t r i c power from the ED stacks during p a r t of the displacement. A l s o , the system may be run i n semi-batch o p e r a t i o n w i t h feed i n t r o d u c t i o n and product withdrawal once every s e v e r a l c y c l e s . D i f f e r e n t v o l t a g e waves other than the present r e c t a n g u l a r wave can be a p p l i e d such as t r i a n g u l a r wave and unsymmetric wave w i t h d i f f e r e n t magnitude and d u r a t i o n i n the two h a l f c y c l e s . This may r e s u l t i n a b e t t e r power economy. d) The proposed stack r e s i s t a n c e model p r e d i c t s q u i t e a c c u r a t e l y the r e s i s t a n c e of the experimental s t a c k s under the o p e r a t i n g c o n d i t i o n s used here. An e x t e n s i o n of the c o n s t a n t - r a t e model based on the stack r e s i s t a n c e could form a b a s i s f o r a more r e f i n e d r e p r e s e n t a t i o n . 292 e) A scale-up and an o p t i m i z a t i o n study of the system are e s s e n t i a l f o r e v a l u a t i o n of the process economics and i t s comparison on a commercial s c a l e w i t h other c o m p e t i t i v e processes. f ) Other s o l u t e s should be i n v e s t i g a t e d , both i n b i n a r y and i n multicomponent mixtures. g) By u s i n g c a t i o n and anion exchange membranes s e l e c t i v e l y permeable f o r u n i v a l e n t ions o n l y , the system can be used to separate monovalent ions from d i v a l e n t and other i o n s . NOMENCLATURE membrane area i o n i c a c t i v i t y of c a t i o n (+) or anion (-) r a t e constant during d i l u t i o n h a l f c y c l e r a t e constant d u r i n g enrichment h a l f c y c l e membrane area s o l u t e c o n c e n t r a t i o n constant d i f f u s i o n c o e f f i c i e n t p o t e n t i a l drop per c e l l p a i r p o t e n t i a l drop the f r a c t i o n d e s a l t e d Faraday's constant or f l o w r a t e of process stream cur r e n t d e n s i t y c u r r e n t i o n i c f l u x v e c t o r e l e c t r i c a l c o n d u c t i v i t y or the r a t i o between o p e r a t i n g and l i m i t i n g c u r r e n t d e n s i t y T y p i c a l U n i t 2 cm g-mole l i t r e sec -1 sec cm -1 g-mole l i t r e or ppm cm /sec v o l t v o l t A.sec/g-equiv. l i t r e / s e c . mA/cm^ A 2 (g-mole)/(cm ) ( s e c ) mho/cm 293 294 constant T y p i c a l U n i t r a t e constant or c e l l constant constant channel l e n g t h a s i n g l e stage l e n g t h phenomenological c o e f f i c i e n t l e n g t h of the membrane or the d e m i n e r a l i z i n g path number of c y c l e s or number of membrane p a i r s or width of membrane sep a r a t i o n f a c t o r n o r m a l i t y of s o l u t i o n exp (- a ] L — ) or p e r m s e l e c t i v i t y of i o n exchange membrane or membrane area u t i l i z i n g f a c t o r exp (- a 2 ) fl o w r a t e heat f l o w v e c t o r dimensionless r a t i o of spacer t h i c k n e s s i n the concentrate and the d i l u a t e compartments a r e a l r e s i s t a n c e or the gas law constant t r a n s p o r t number or temperature c y c l e time or absolute temperature i o n i c m o b i l i t y t o t a l chemical p o t e n t i a l cm -1 cm cm cm cm g - e q u i v . l i t r e cm / sec ohm cm ( j o u l e s ) /(°K) (mole) sec °K (cm ) / ( v o l t ) ( s e c ) 295 T y p i c a l U n i t v . = displacement v e l o c i t y cm/sec v = v e l o c i t y v e c t o r cm/sec 3 V = volume cm w = water t r a n s p o r t number x = d i s t a n c e co-ordinate cm y = l a t e r a l d i s t a n c e c o - o r d i n a t e cm z = valence of charged species (g-equiv)/(g-mole) or d i r e c t i o n of f l o w Greek Symbols a = f r a c t i o n of h a l f c y c l e g = f r a c t i o n of h a l f c y c l e Y = phase l a g Y + = the mean i o n i c a c t i v i t y c o e f f i c i e n t 6 = t h i c k n e s s of Nernst l a y e r or d i f f u s i o n cm l a y e r A = compartment t h i c k n e s s cm e ." = f r a c t i o n a l v o i d volume of packing n = e f f i c i e n c y ri = e l e c t r i c f i e l d v e c t o r v o l t / c m 2 A" = e q u i v a l e n t conductance (mho) (cm )/(g-equiv) 3 v = p a r t i a l molar volume cm /mole v + = s t o i c h i o m e t r i c c o e f f i c i e n t s f o r e l e c t r o l y t e M v + p = e l e c t r i c a l r e s i s t i v i t y ohm-cm p = (1 - E)/E = r a t i o of volume of packing to v o i d volume x = pause time sec or t r a n f e r e n c e number of water 296 T y p i c a l U n i t A<|> = a p p l i e d e l e c t r i c p o t e n t i a l v o l t Acb = Donnan p o t e n t i a l v o l t Don V = divergence operator or gradient operator S u b s c r i p t s 1,2 ... r e f e r to p o s i t i o n s across a c e l l p a i r or to the number of time i n t e r v a l d u r i n g a c y c l e ; ( T 1 , T 2 ) + f o r p o s i t i v e l y charged s p e c i e s ; ( t + ) - f o r n e g a t i v e l y charged s p e c i e s ; ( t _ ) a f o r anion-exchange membrane; ( f c a) or an average v a l u e ; (C ) cL b b r i n e product; (C, ) b B b r i n e (enriched) product; (C B) c cation-exchange membrane; ( t £ ) or concentrate product; (C ) or c o n c e n t r a t i o n p o l a r i z a t i o n ; d d i a l y s a t e (depleted) product; (C^) d^,d 2 Donnan terms; ( E Q ^ E ^ ) D d i a l y s a t e (depleted) product; (C^) e enriched product; (C ) or e l e c t r o d e ; (1 ) ' e f f l u i d or mobile phase; (C^) F Faraday; (n^,) H Henderson term; (E^) i r e f e r s to i n l e t ; ( C ^ ) I c u r r e n t ; (y j c o - i o n ; (C^) 297 k c o u n t e r - i o n ; (C^) ^ or species k; (J^) SL r e f e r s to l o c a l v a l u e a t d i s t a n c e I from the feed i n l e t ; (R^) m m a n i f o l d ; ( n m) or membrane; (F^) or membrane s o l u t i o n i n t e r f a c e ; (C m) n stage number; (^n) o r e f e r s to i n i t i a l s t a t e ; (C ) o p c e l l p a i r ; (R^) R r e s i s t a n c e ; (n^) S s o l i d or s t a t i o n a r y phase; (C ) or p e r m s e l e c t i v e l y ; ( n g ) T t o t a l ; ( E T) or top (demineralized) product; (Cj) or temperature; (V^U) w water t r a n s p o r t ; ( n w ) IT u n i t area per c e l l p a i r ; (R^) v r e f e r s to the average c o n c e n t r a t i o n of s a l t ; (^v) °° r e f e r s to i n f i n i t e d i l u t i o n ; (A r a) S u p e r s c r i p t s = r e f e r s to property i n membrane; (C,,C.) k 3 or to n e g a t i v e l y charged s p e c i e s ; ( t ~ ) .+ = r e f e r s to p o s i t i v e l y charged s p e c i e s ; ( t ^ ) REFERENCES A c r i v o s , A., Ind. 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Wilhelm, R.H., i n : " I n t e r a c e l l u l a r Transport, Symp. of the I n t e r n a t i o n a l S o c i e t y f o r C e l l B i o l o g y " , V o l . 5, p. 199, K.B. Warren, Ed., Acad. P r e s s , New York, 1966 b. Wilhelm, R.H. and N.H. Sweed, Science, 159, 522 (1968 a ) . Wilhelm, R.H., A.W. R i c e , R.W. Rolke and N.H. Sweed, Ind. Eng. Chem. Fundam., 2, 337 (1968 b ) . Wil s o n , J.R., Ed., " D e m i n e r a l i z a t i o n by E l e c t r o d i a l y s i s " , B utterworth, London, 1960. Z a j i c , J.E., "Water P o l l u t i o n D i s p o s a l and Reuse", V o l . 2, Marc e l Dekker, In c . , New York, 1971. Appendix A E l e c t r o d e System A . l . E l e c t r o d e M a t e r i a l s V a r i o u s m a t e r i a l s f o r e l e c t r o d e s are i n use, f o r example, g r a p h i t e and s t a i n l e s s s t e e l , which are g r a d u a l l y attacked i n o x i d i z i n g c o n d i t i o n s and must be re p l a c e d . Platinum-coated metals (e.g. t i t a n i u m , tantalum, or zi r c o n i u m ) , w i t h a high l e v e l of c o r r o s i o n r e s i s t a n c e and a l i f e of s e v e r a l y e a r s , are now f r e q u e n t l y used, e s p e c i a l l y as anodes. Oxides of some metals such as lead and ruthenium have proven to be s u f f i c i e n t l y conductive and i n s o l u b l e i n a c i d s to be used as c o a t i n g f o r anodes (Thangappan, et a l . , 1970). Magnetite e l e c t r o d e s have been used f o r anodes i n e l e c t r o d i a l y s i s , but t h i s m a t e r i a l i s very f r a g i l e (Davis and Brockman, 1972). A.2. E l e c t r o d e Reactions Throughout the d i l u t i n g and c o n c e n t r a t i n g c e l l s of an e l e c t r o d i a l y s i s s t a c k , and i n the i n t e r v e n i n g membranes, e l e c t r i c a l conduction i s i o n i c . At the e l e c t r o d e s , however, the mechanism of e l e c t r i c a l conduction changes a b r u p t l y from i o n i c to e l e c t r o n i c . The technology of e l e c t r o d e r e a c t i o n s i s h i g h l y developed i n many r e s p e c t s , but there i s s t i l l c o n s i d e r a b l e con- t r o v e r s y concerning mechanisms and the r e l a t i v e importance of competing r e a c t i o n s that occur a t the e l e c t r o d e s (Davis and Brockman, 1972). 304 305 The cathode or n e g a t i v e l y changed e l e c t r o d e i s the source of e l e c t r o n s , and a t the cathode, the e l e c t r o n s must be t r a n s f e r r e d from the e x t e r n a l c i r c u i t to ions i n the s o l u t i o n . The f o l l o w i n g are t y p i c a l r e a c t i o n s by which t h i s t r a n s f e r of charge may be accomplished: -> M° metal d e p o s i t i o n ( A . l . ) -* 40H r e d u c t i o n of gaseous oxygen (A. 2.) -> H2 ( a c i d i c s o l u t i o n ) e v o l u t i o n of gaseous (A.3.) -> H 2 + 20H ( b a s i c s o l u t i o n ) hydrogen (A.4.) M e t a l - d e p o s i t i o n r e a c t i o n s are u s e f u l i n processes such as e l e c t r o - p l a t i n g and the recovery of spent p i c k l e l i q u o r . Reactions i n which gaseous oxygen i s reduced are important i n f u e l c e l l s . The p r i n c i p a l c a t i o n s present i n t y p i c a l b r i n e are much l e s s r e a d i l y discharged than hydrogen i o n , and the net r e s u l t of t h i s i s th a t the cathode r e a c t i o n i s almost i n v a r i a b l y the c a t h o d i c h a l f of the water e l e c t r o l y s i s r e a c t i o n : 2H„0 + 2e~ -> H„ + 20H~ E = 0 (A. 5.) 2 2 O There i s u s u a l l y almost no d e t e r i o r a t i o n of the cathode, and almost any conductor that i s compatible w i t h the r e s t of the system can be used as a cathode. Carbon s t e e l i s a commonly used cathode m a t e r i a l . Heavy metal ions such as copper and i r o n may p l a t e out on the cathode, and, i n a d d i t i o n , the s h i f t i n pH caused by the cathode r e a c t i o n may cause the p r e c i p i t a t i o n of a v a r i e t y of substances that may f o u l the system. The p r i n c i p a l problems are apt to be due to CaCO^, Mg(0H) 2, and Fe(0H).j. Depending on the composition of the s o l u t i o n , pH, anode composition, and c u r r e n t d e n s i t y , one or more of the f o l l o w i n g r e a c t i o n s may occur a t the anode: M " + xe 0 2 + 2H 20 + 4e' 2H + + 2e' 2H 20 + 2e" 306 +x — M° ->• M + xe ; metal d i s s o l u t i o n (A. 6.) M° + xOH~ -> M(0H) x + xe" o x i d a t i o n of e l e c t r o d e (A.7.) 2M° + 2xOH~ -> M 20 x + xH 20 + 2xe~ (A. 8.) H 2 -»• 2H + + 2e~ o x i d a t i o n of gaseous hydrogen (A.9.) 2H 20 0 2 + 4H + + 4e~ ( a c i d i c s o l u t i o n s ) e v o l u t i o n of (A. 10.) 40H~ •*• . Q 2 + 2H 20 + 4e~ ( b a s i c s o l u t i o n s ) gaseous oxygen (A. 11). 2C1~ -> C l 2 + 2e , e v o l u t i o n of gaseous c h l o r i n e (A.12). O x i d a t i o n of gaseous hydrogen i s an important r e a c t i o n i n f u e l - c e l l o p e r a t i o n . M etal d i s s o l u t i o n r e s u l t s i n d e s t r u c t i o n of the e l e c t r o d e . When the anode i s o x i d i z e d , h y d r o x y l ions are consumed. Unless p r o v i s i o n i s made f o r removing the companion hydrogen ions or supplying h y d r o x y l i o n s , the e l e c t r o d e s o l u t i o n w i l l become a c i d i c . Most metal oxides and hydroxides are s o l u b l e i n a c i d i c s o l u t i o n s . M 2 0 x + 2xH + -> 2M + X + xH 20 (A. 13.) or M(0H) x + x H + -»• M 4^ + xH 20 (A.14.) The net r e s u l t i s the d i s s o l u t i o n of e l e c t r o d e metal. Reactions i n which gaseous oxygen or c h l o r i n e i s evolved are commonly encountered i n e l e c t r o d i a l y s i s when noble metal anodes are used. In a • t y p i c a l n a t u r a l l y o c c u r r i n g b r i n e such as seawater c h l o r i d e ions may be o x i d i z e d a t the anode to produce h y p o c h l o r i t e : C l ~ + 20H~ - 2e~ •* 0C1~ + H o0 E =0.94 v o l t (A.15.) 2 o Or, i n a c i d i c media c h l o r i n e gas w i l l be r e l e a s e d , C l ~ - e" -> h C l 2 (g) E q = 1.35 v o l t (A. 16.) 307 A p o r t i o n of the c h l o r i d e o x i d i z e d at the anode w i l l be c a r r i e d out of the c e l l i n the anode r i n s e stream ( a n o l y t e ) , and a p o r t i o n may escape as c h l o r i n e gas. C h l o r i n e remaining i n the s o l u t i o n w i l l e v e n t u a l l y form an e q u i l i b r i u m mixture according to C l 2 + H 20 = HCl + HOCl (A.17.) I n many s i t u a t i o n s , and most p a r t i c u l a r l y i n a h i g h - s u l f a t e , low- c h l o r i d e water, we w i l l f i n d that the anode r e a c t i o n discharges oxygen from the water w i t h the simultaneous pr o d u c t i o n of hydrogen i o n s : H o0 - 2e~ -> h0* + 2H + E =1.23 v o l t s (A. 18.) Z £ O T y p i c a l b r a c k i s h water contains s i g n i f i c a n t amounts of both c h l o r i d e and s u l f a t e , and f r e q u e n t l y both c h l o r i n e and oxygen are evolved s i m u l - taneously. We cannot p r e d i c t the r e l a t i v e amounts of each w i t h any degree of success because the r e a c t i o n s are p r i n c i p a l l y c o n t r o l l e d by e l e c t r o d e k i n e t i c s r a t h e r than by any c o n s i d e r a t i o n s of e l e c t r o d e p o t e n t i a l . Any or a l l of the r e a c t i o n s l i s t e d above, or f u r t h e r r e a c t i o n s t h a t produce even more h i g h l y o x i d i z e d products, such as C10^, may occur, depending on l o c a l c u r r e n t d e n s i t i e s and the nature of the e l e c t r o d e s u r f a c e . I f noble metal e l e c t r o d e s are not used, the anode r e a c t i o n w i l l a l s o i n c l u d e the o x i d a t i v e products of the e l e c t r o d e s . I r o n or s t e e l anodes, f o r example, w i l l produce i r o n oxides i n v a r i o u s degrees, and carbon anodes w i l l produce carbon d i o x i d e . The e l e c t r o d e r e a c t i o n s n e c e s s a r i l y a s s o c i a t e d w i t h e l e c t r o d i a l y s i s o p e r a t i o n introduce two problems: f i r s t , added power must be s u p p l i e d to provide the e l e c t r o d e r e a c t i o n energy; second, the products of the e l e c t r o d e r e a c t i o n s may be harmful to the e l e c t r o d i a l y s i s stack or may i n t e r f e r e w i t h 308 the continued o p e r a t i o n of the system. The f i r s t of these may be minimized e a s i l y by i n c r e a s i n g the number of c e l l s per e l e c t r o d e p a i r s as w i l l be discussed i n process e f f i c i e n c y s e c t i o n ; the second i s more complicated and there i s no s i n g l e simple s o l u t i o n . We can expect that the c h l o r i n e or other o x i d i z i n g m a t e r i a l s formed a t the anode may cause r a p i d d e t e r i o r a t i o n of the stack components; and the a l k a l i n e cathode m a t e r i a l , i f allowed to enter the s t a c k , i s o b v i o u s l y l i k e l y to produce p r e c i p i t a t i o n . Because of t h i s i t i s u s u a l to provide f o r h y d r a u l i c i s o l a t i o n of the two e l e c t r o d e stream compartments at the ends of the d i a l y s i s s t a c k s . Frequently i s o l a t i o n of these streams p l u s a h i g h r a t e of f l u s h i n g w i t h feed water i s a l l t h a t i s attempted by way of c o n t r o l l i n g the p o s s i b l e harmful e f f e c t s of the e l e c t r o d e r e a c t i o n products. The use of sodium b i s u l f i t e i n the anode r i n s e stream, to a v o i d the formation of c h l o r i n e , has been described by Wiechers (1954). The c a t h o l y t e b a s i c i t y can be c o n t r o l l e d by the a d d i t i o n of i n o r g a n i c a c i d s to the cathode stream. Several more n e a r l y c l o s e d systems have a l s o been t r i e d or proposed. I n p r i n c i p l e we could c i r c u l a t e sodium s u l f a t e or s u l f u r i c a c i d i n the a n o l y t e - c a t h o l y t e system and l i m i t the r e a c t i o n s to oxygen and hydrogen generation. I f t h i s were a l l that happened, e l e c t r o l y t e volume could be maintained by adding very s m a l l q u a n t i t i e s of pure water f r o i time to time or by r e a c t i n g the two gases. An even more s u b t l e approach has been suggested by Roberts (1957), who has patented the c i r c u l a t i o n of a redox s o l u t i o n between the two. compartments. The o x i d a t i o n at the anode and the r e d u c t i o n a t the cathode t h e o r e t i c a l l y balance each other i n t h i s case. U n f o r t u n a t e l y , none of these " c l o s e d " schemes work too w e l l i n p r a c t i c e 309 because i t i s d i f f i c u l t to confine a given i o n to a p a r t i c u l a r stream. E i t h e r the m a t e r i a l s i n the e l e c t r o d e stream tend to d i f f u s e i n t o the remainder of the c e l l or v i c e v e r s a , and i n e i t h e r case problems of o x i d a t i o n , pH s h i f t , and f o u l i n g i n e v i t a b l y a r i s e . A.3. E l e c t r o d e P o l a r i z a t i o n E f f e c t on power Consumption The energy consumed by the processes o c c u r r i n g a t the e l e c t r o d e s depends upon a number of f a c t o r s , i n c l u d i n g the e l e c t r o d e m a t e r i a l s , the r e a c t i o n s i n v o l v e d , the c o n c e n t r a t i o n s of the i o n s , the a p p l i e d c u r r e n t d e n s i t y and the s o l u t i o n v e l o c i t y . A d e t a i l e d d i s c u s s i o n of e l e c t r o d e p o l a r i z a t i o n i s given by V e t t e r (1967) and by B o c k r i s and Reddy (1973). The passage of c u r r e n t through each of the e l e c t r o d e compartments i n v o l v e three s t e p s : (1) The t r a n s f e r of ions from the bulk of the s o l u t i o n to the surface of the e l e c t r o d e . (2) The e l e c t r o c h e m i c a l r e a c t i o n a t the e l e c t r o d e . (3) The formation of the f i n a l products of the r e a c t i o n and t h e i r removal from the e l e c t r o d e s u r f a c e . Three o v e r p o t e n t i a l s are i n v o l v e d : ( i ) Concentration o v e r p o t e n t i a l When the c u r r e n t i s f l o w i n g , the ions t h a t discharge migrate towards the e l e c t r o d e and cause a c o n c e n t r a t i o n gradient across the t h i n d i f f u s i o n l a y e r at the e l e c t r o d e s u r f a c e . This phenomenon i s e x a c t l y analogous to the c o n c e n t r a t i o n g r a d i e n t that occurs a t the i o n exchange membranes. The c o n c e n t r a t i o n g r a d i e n t leads to a change i n e l e c t r o d e p o t e n t i a l of _ R T Sulk , . \ o n " T ± n C I ( A - 1 9 * ) surface 310 ( i i ) Chemical o v e r p o t e n t i a l The chemical o v e r p o t e n t i a l , » i s def i n e d to be that p o t e n t i a l i n excess of the discharge p o t e n t i a l f o r the given r e a c t i o n which must be a p p l i e d to the c e l l i n order to ma i n t a i n a f i n i t e r a t e of disc h a r g e . Chemical o v e r p o t e n t i a l occurs as a r e s u l t of steps (2) and (3) above. The value of n , f o r the e l e c t r o d e r e a c t i o n i s given by T a f e l ' s Formula: chem ° J n , = a + —r=r I n i (A. 20.) chem a F where a' = h. and a = constant (depends on nature of cathode), ( i i i ) Ohmic o v e r p o t e n t i a l The ohmic o v e r p o t e n t i a l , n c o n s i s t s of two p a r t s , namely the vo l t a g e drop which occurs i n the bu l k s o l u t i o n of constant c o n c e n t r a t i o n p l u s the v o l t a g e drop across the d i f f u s i o n l a y e r where the co n c e n t r a t i o n gradient v a r i e s l i n e a r l y w i t h the curr e n t d e n s i t y n , = n , + ru ohm s o l 6 = i R , ( A .21.) ohm where R , c o n s i s t s of two s e r i e s r e s i s t a n c e s , ohm R . = R . + R X (A. 22.) ohm s o l o R , can be evaluated i n terms of the mean r e s i s t i v i t y of the bulk s o l s o l u t i o n , R = P meany (A. 23.) s o l Ap where- 311 p = the mean r e s t i v i t y of the e l e c t r o d e s o l u t i o n , ft - cm Kmean y = b u l k s o l u t i o n t h i c k n e s s , . cm 2 Ap = a c t i v e membrane a r e a , cm may be evaluated by s p e c i f y i n g the r e s i s t i v i t y a t any p o i n t w i t h i n the d i f f u s i o n l a y e r as a f u n c t i o n p(x,z) and by computing the double i n t e g r a l of t h i s f u n c t i o n as discussed i n S e c t i o n 3.1.1. -1 dz (A.24.) Thus, the e l e c t r o d e p o l a r i z a t i o n p o t e n t i a l , E e > can be evaluated by summing these separate components. A. 4. E l e c t r o d e Flow System The two e l e c t r o d e compartments present i n each multimembrane stack are u s u a l l y s u p p l i e d w i t h r i n s e s o l u t i o n from a separate r e c i r c u l a t i n g h y d r a u l i c system. In passing through the c e l l c a t h o l y t e becomes b a s i c and ano l y t e becomes a c i d i c , when these are mixed they p a r t i a l l y n e u t r a l i z e one another. P r o v i s i o n should be made i n e l e c t r o d e system f o r discharge of the e l e c t r o d e gases, and a s m a l l discharge of e l e c t r o d e s o l u t i o n i s r e q u i r e d to prevent b u i l d u p of ions produced by e l e c t r o d e r e a c t i o n s . A feed-and- bleed system as shown i n F i g u r e A . l , i s f r e q u e n t l y 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 E f f i c i e n c y The t o t a l c u r r e n t e f f i c i e n c y , n̂ ., i s r e l a t e d to the Faraday e f f i c i e n c y , rip by the r e l a t i o n n = n n ( B . l . ) I F* w where n i s the water t r a n s f e r term, w The Faraday e f f i c i e n c y , n , i s d e f i n e d as the r a t i o of the s a l t s h i f t e d r to the t h e o r e t i c a l c u r r e n t requirement (e q u i v a l e n t of s a l t transported) F (Faradays of e l e c t r i c i t y passed)(number of membrane p a i r s employed) = I ^ O E (B.2.) In where F = Faraday's constant, 96500 A / ( s e c ) ( e q u i v a l e n t ) AN = change i n product stream n o r m a l i t y , e q u i v / l i t e r Fp = f l o w r a t e of the product stream, l i t e r / s e c I = t o t a l c u r r e n t passed through the s t a c k , A n = number of membrane p a i r s used Faraday e f f i c i e n c y , n_, as d e f i n e d by Eq.(B.2.) depends on both the r a c t u a l membrane used and the amount of leakage c u r r e n t t h a t a p a r t i c u l a r stack design may permit and i t expresses the performance of the process w.r.t. the c u r r e n t . I t i s o f t e n determined by an i n e x a c t method (apparent values) f o r b r i n e and dialy'state streams independently: 313 314 V D i - V F , n D - s ( B . 3 . ) ^B = n l ( B ' 4 > ) where TV.*1^ = apparent Faraday e f f i c i e n c i e s based on the d i a l y s t a t e and b r i n e streams r e s p e c t i v e l y F ,F = d i a l y s t a t e and b r i n e e f f l u x r a t e s r e s p e c t i v e l y , ml/sec. D B D^,B^ = d i a l y s t a t e and b r i n e i n f l u e n t c o n c e n t r a t i o n s r e s p e c t i v e l y equiv/ml ^>2'^2 ~ d i a l y s t a t e a n (* D r i n e e f f l u e n t c o n c e n t r a t i o n s r e s p e c t i v e l y The i n f l u e n t and e f f l u e n t f l o w r a t e s of a s i n g l e stream are not i d e n t i c a l because o f : (a) water t r a n s f e r by osmosis and elec t r o - o s m o s i s (b) a minor volume change r e s u l t i n g from the s a l t displacement The true Faraday e f f i c i e n c y , rip, i s defined by: n D = n F (1 - 18 w D x) (B.5.) n B = n F (1 - 18 w B 1) (B.6.) where w = moles of water transported per e q u i v a l e n t of s a l t t r a n s f e r ; w = w 3 + w C, where w 3, w C are water t r a n s p o r t numbers (- h y d r a t i o n 3. C number of ions) e.g. f o r NaCl, w = 4, w = 8 . Determination of n a n c j n enable both r\„ and w to be c a l c u l a t e d D D r (Wilson, 1960). The f a c t o r s that may c o n t r i b u t e towards low cu r r e n t e f f i c i e n c y i n an e l e c t r o d i a l y s i s stack are mechanical and e l e c t r o c h e m i c a l ones: 315 (1) Imperfect s e l e c t i v i t y of membranes or d e t e r i o r a t i o n of membranes. The f a c t that the membranes are not p e r f e c t l y s e l e c t i v e means that more than the t h e o r e t i c a l c urrent must be passed. (2) E l e c t r i c a l leakage by s t r a y c u r r e n t and p a r a l l e l c u r r e n t paths through the stack m a n i f o l d . (3) S h o r t - c i r c u i t i n g of membrane packs. (4) I n t e r n a l and e x t e r n a l water leakage. A l a r g e water t r a n s f e r may accompany the cur r e n t f l o w across the membrane due to osmosis and e l e c t r o - osmosis, which r e s u l t s i n l o s s of product water. A l s o there may be h y d r a u l i c leakages between c e l l s and/or e x t e r n a l leakages. (5) Back d i f f u s i o n of e l e c t r o l y t e s . (6) Severe p o l a r i z a t i o n e f f e c t s or unwanted i o n t r a n s f e r . A t s u f f i c i e n t l y high c u r r e n t d e n s i t i e s or low s a l t c o n c e n t r a t i o n s , the H + and OH ions normally present i n water w i l l begin to p a r t i c i p a t e i n the c u r r e n t - c a r r y i n g process. Assuming t h a t obvious problems, such as e x t e r n a l p a r a l l e l c u r r e n t paths through b o l t s and c o n t a i n e r s , gross l e a k s between the product and waste compartments, and water s p l i t t i n g , have been p r o p e r l y taken care o f , we can express an over a l l c u r r e n t e f f i c i e n c y , n̂ ., as the product of these e f f i c i e n c i e s : n T = n n n = run (B.7. I s m w F w where r i s : takes care of e f f e c t s due to the p e r m s e l e c t i v i t y of the i n d i v i d u a l membranes n : accounts f o r the e f f e c t s of c u r r e n t leakage through the m manifold 316 ri : i s the r e s u l t of water t r a n s p o r t through the membranes, w The q u a n t i t i e s r i s , n.m and are a l l defined i n such a way that i d e a l l y they approach 1.0. ( i ) P e r m s e l e c t i v i t y e f f i c i e n c y , n^ The p e r m s e l e c t i v i t y e f f i c i e n c y , rt^, i s de f i n e d as n t - P c + n t + P a 's n t + n t , c - a + where n ,n c a are numbers of c a t i o n and anion-permeable membranes t + , t are t r a n s p o r t numbers i n s o l u t i o n of c a t i o n and anion r e s p e c t i v e l y Pc,Pa are p e r m s e l e c t i v i t y of c a t i o n and anion-permeable membranes r e s p e c t i v e l y Pc = = 1 " fc+ t - t t - t Pa = — - = ~- 1 1 (B.9.) 1 " C - where t + , t r e f e r to t r a n s p o r t numbers of counter-ions i n membranes. Mien n = n , Eq.(B.8.) reduces t o : c a ^ n = t Pc + t , Pa s - + = ( t + + t_) - 1 = 1 - ( t ^ + t*) (B.10.) where t = anion t r a n s p o r t number i n the cation-permeable membrane t_^ = c a t i o n t r a n s p o r t number i n the anion-permeable membrane 317 - ( t C + t*) i s imperfect s e l e c t i v i t y f a c t o r or p e n e t r a t i o n of co-ions i n t o a membrane. I f t = t = 0.5, then n s w i l l be equal to the average p e r m s e l e c t i v i t y = ( Z l + i i ) (B.H.) s I ( i i ) E l e c t r i c a l Leakage and S h o r t - c i r c u i t i n g term, n m The p a r t i a l s h o r t - c i r c u i t i n g of a membrane stack by conduction through manifolds and s t r a y p a r a l l e l c u r r e n t paths consume power without producing any u s e f u l r e s u l t s , thus reduce the e f f e c t i v e c u r r e n t e f f i c i e n c y . Because of the inherent engineering design of e l e c t r o d i a l y s i s u n i t s , each c o n c e n t r a t i o n stream w i t h i n the stack i s connected, v i a c o n d u i t s , to a l l other c o n c e n t r a t i o n streams. The same a p p l i e s f o r the d i l u t i o n streams. Since the c o n c e n t r a t i o n stream i s more conductive to e l e c t r i c i t y than the d i l u t e stream, i t would be expected t h a t a high f r a c t i o n of non-productive- leakage c u r r e n t would fl o w through the c o n c e n t r a t i o n stream. Leakage c u r r e n t c a l c u l a t i o n s have been developed by Wilson (1960) and Mandersloot and Hicks (1966) and presented by B e l f o r t and Guter (1968). U s u a l l y the e f f e c t of c u r r e n t leakage through the manifold i s a r e d u c t i o n i n e f f i c i e n c y of l e s s than 5%, B e l f o r t and Guter (1968) i n t h e i r study of Webster and Buckeye e l e c t r o d i a l y s i s p l a n t s showed that c u r r e n t leakage has only minor e f f e c t . The leakage c u r r e n t f o r a given design can be estimated by assembling a sample stack w i t h i n s u l a t i n g sheets of p l a s t i c i n p l a c e of the membranes, thereby i n t e r r u p t i n g the e l e c t r i c a l f i e l d , but not the l i q u i d flow. The normal operating v o l t a g e i s then a p p l i e d and the current measured i s regarded as being t h a t due to leakage through the e n t i r e 318 i n t e r n a l and e x t e r n a l l i q u i d f l o w path of the stack. ( i i i ) Water t r a n s f e r term, n. w Some water i s transported through the membranes along w i t h the e l e c t r o l y t e s due to el e c t r o - o s m o s i s . The amount of e l e c t r o - o s m o t i c water t r a n s p o r t v a r i e s w i t h membrane type, i o n i c s p e c i e s , and c o n c e n t r a t i o n of s o l u t i o n . When the feed i s of low s a l i n i t y or when moderate q u a n t i t i e s of s a l t are removed from b r a c k i s h water, t r a n s p o r t i s seldom a problem. However, i n more concentrated s o l u t i o n s or i n systems i n v o l v i n g a hig h degree of d e s a l i n a t i o n , water t r a n s f e r can have important e f f e c t s on the curr e n t u t i l i z a t i o n i n the process. A l a r g e t r a n s f e r of water w i l l : product q u a l i t y s p e c i f i c a t i o n s , (b) reduce the q u a l i t y of product o b t a i n a b l e from a given amount of feed to the d i l u t e stream. The e f f e c t of water t r a n s p o r t on the cur r e n t e f f i c i e n c y i s given by: (a) r e q u i r e the use of a d d i t i o n a l c u r r e n t to meet the d e s a l t e d - 1 - nx (0.018) m. w 1 (B.12.) n. w where m. x the m o l a l i t y of the feed water T t r a n s f e r e n c e number of water d e f i n e d as the number of w moles water t r a n s f e r r e d per Faraday n number of membrane p a i r s . Appendix C Nernst I d e a l i z e d Model of Wa l l Layers C . l . The Flow F i e l d i n an E l e c t r o d i a l y s i s C e l l In almost a l l electromembrane processes the s o l u t i o n s to be t r e a t e d flow between p a r a l l e l p l anar ion-exchange membranes. The flow channels are f i l l e d w i t h spacer m a t e r i a l s that cause complex fl o w p a t t e r n s . The v e l o c i t y of the s o l u t i o n s past the membranes and through the spacer m a t e r i a l s r e s u l t s i n r e l a t i v e l y good mixing of the s o l u t i o n i n the center p o r t i o n s of the flow channels, but the mixing i s l e s s near the surfaces of the membranes, where the s o l u t i o n i s almost s t a t i c . C.2. Nernst Model The complex h y d r a u l i c p a t t e r n i n an e l e c t r o d i a l y s i s c e l l i s a p p r o x i - mated by the s i m p l i f i e d Nernst model. This i s an i d e a l i z e d model (Nernst, 1904) based on the f o l l o w i n g assumptions: - there are l a y e r s adjacent to the membranes i n which the s o l u t i o n s are completely s t a t i c or i n laminar f l o w . - the s o l u t i o n i n the bulk ( i . e . between the w a l l l a y e r s ) i s thoroughly mixed so that the c o n c e n t r a t i o n of e l e c t r o l y t e at any p o i n t i n t h i s zone i s the same as that at any other p o i n t . - there i s no change of e i t h e r the th i c k n e s s of the w a l l l a y e r s or the c o n c e n t r a t i o n g r a d i e n t s along the flo w channel. 319 320 Despite the complexity i n a r e a l system, Nernst model a f f o r d s a s i m p l i f i e d mathematical approach which r e s u l t s i n expressions that are easy to use and that p r e d i c t performance adequately f o r use i n the design of electromembrane processes. C.3. Some d e r i v a t i o n s of the Model Since frequent use i s made of the assumption that the c o n c e n t r a t i o n gradient i n the w a l l l a y e r of an e l e c t r o d i a l y s i s c e l l i s l i n e a r , a j u s t i - f i c a t i o n of t h i s assumption w i t h the other main assumptions i n v o l v e d i s i n order. ' C.3.1. General theory of coupled processes When an i o n moves i n an e l e c t r o l y t e s o l u t i o n i t does not do so i n the complete absence of other e f f e c t s . I t s motion i s accompanied by a flow of e l e c t r i c c u r r e n t , and there may a l s o be a flo w of heat and a flo w of s o l v e n t . We are faced w i t h the problem of d e s c r i b i n g simultaneously a minimum of four f l u x e s : s a l t , e l e c t r i c i t y , s o l v e n t and heat. In a n a l y z i n g systems i n which s e v e r a l f o r c e s and f l u x e s are coupled, i t i s sometimes convenient to make use of the theory of the thermodynamics of i r r e v e r s i b l e processes. Although an a n a l y s i s made i n these terms cannot de a l w i t h the u n d e r l y i n g causes of the phenomena that may be observed, i t i s of great value i n c l e a r l y d e f i n i n g c e r t a i n r e l a t i o n s h i p s that must n e c e s s a r i l y h o l d between the v a r i o u s f o r c e s and flows when the system i s i r the steady s t a t e . The general equations f o r f l o w may be w r i t t e n ( H i l l s et a l . , 1961) as: 321 -y J l = - L 1 1 V T U 1 " L 1 2 V T U 2 " L 1 3 V T U 3 " L 1 4 V l n T -> J 2 = - L 1 2 V T U 1 " L 2 2 V T U 2 - L 2 3 V T U 3 - L 2 4 V l n T \ = - L 1 3 V T U 1 " L 2 3 V T U 2 " L 3 3 V T U 3 - L-.Vln 34 T -> Q = " L 1 4 V T U 1 " L 2 4 V T U 2 " L 3 4 V T U 3 - L-.Vln 44 T ( C I . ) where are phenomenological c o e f f i c i e n t s and the s u b s c r i p t s 1,2,3,and 4 r e f e r to the p o s i t i v e i o n s , negative i o n s , water and heat r e s p e c t i v e l y . V^U i s the gradient of t o t a l chemical p o t e n t i a l , taken a t constant temperature, and Q i s the f l o w of heat. I f we consider an i s o t h e r m a l process i n which both n o n - e l e c t r o s t a t i c i n t e r a c t i o n between the ions together with electro-osmosis are n e g l e c t e d , then a l l the terms except the f i r s t w i l l drop out and the i o n i c f l u x , J i s given by Jk = " LkkVk = - VkVk (c-2-} 2 where i s the f l u x of an i o n i c species i n g-mole/(cm ) ( s e c ) , i s the i o n i c m o b i l i t y which i s defined as the average v e l o c i t y imparted to the species under the a c t i o n of a u n i t g e n e r a l i z e d f o r c e (per mole), and i s the c o n c e n t r a t i o n i n g-moles/cu.cm. The t o t a l chemical p o t e n t i a l , U, i s meant to i n c l u d e e f f e c t s due to e l e c t r i c i t y , as w e l l as temperature, pressure, c o n c e n t r a t i o n and g r a v i t a t i o n a l f i e l d , i f any. Assume that g r a v i t a t i o n a l f i e l d s are unimportant, then V U = Z F VE + — • Vp + |£ VC (C.3.) T dp dC where VE i s the e l e c t r i c f i e l d i n vo l t s / c m F i s the Faraday constant i n coulombs/g.equiv. Z i s the valence 322 I n r e a l e l e c t r o d i a l y s i s systems the modest d i f f e r e n c e s i n temperature and pressure have no s i g n i f i c a n t e f f e c t on the curr e n t f l o w i n g as long as HJ 3U even very s m a l l p o t e n t i a l d i f f e r e n c e s e x i s t . Therefore — Vp term i s n e g l i g i b l e . For i d e a l s o l u t i o n , U = U + RT l n a ( C 4 . ) o where U o i s the standard chemical p o t e n t i a l and a i s the a c t i v i t y . For d i l u t e s o l u t i o n s c o n c e n t r a t i o n can be used i n s t e a d of a c t i v i t y (a = yC ^ C). From Eq.(C.4.) we get { 2 . •? vc (C.5., A term i n c l u d i n g the d e r i v a t i v e of the a c t i v i t y c o e f f i c i e n t could be in c l u d e d (see f o r example, H i l l s , e t a l . , 1961), but t h i s does not a f f e c t the general p r i n c i p l e ; and, i n p r a c t i c e , omission of the term t h a t would a r i s e from d i f f e r e n t i a t i o n of the a c t i v i t y c o e f f i c i e n t i s no worse than some of the other assumptions t h a t are needed to f a c i l i t a t e the i n t e g r a t i o n of these equations when they are used to d e s c r i b e r e a l systems. S u b s t i t u t e Eq.(C.5.) i n t o Eq.(C.3.) and drop the pressure term RT Jk = " uk ck ( zk F V E + c7vck> (c'6-) k The i o n i c m o b i l i t y , u ^ (g- m o l e s ) ( s q . c m ) / ( j o u l e ) ( s e c ) , can be r e l a t e d to the i o n i c - d i f f u s i o n c o e f f i c i e n t , (sq.cm/sec) through the N e r n s t - E i n s t e i n r e l a t i o n : uk = V R T (c-7-) where T i s the abs o l u t e temperature, °K., and R i s the gas const a n t , 8.3143 joules/(°K)(mole). Eq.(C.7.) i s true only when the a c t i v i t y c o e f f i c i e n t 323 i s u n i t y , that i s , at i n f i n i t e d i l u t i o n (Chapman, 1969). From Eqs.(C.6.) and (C.7.) J k  = - Vk F c k V E - V c k ( c- 8-> Eq.(C.8.) i s the well-known Nernst-Planck equation of i o n i c f l u x w i t h n e g l i g i b l e convection ( i . e . C^y = 0, where v i s the stream v e l o c i t y ) . Although the Nernst-Planck equation has a number of shortcomings which l i m i t i t s r i g o r o u s a p p l i c a t i o n s to d i l u t e s o l u t i o n s , we w i l l use i t because i t accomplishes a great s i m p l i f i c a t i o n of a complex problem. To do t h i s however, we must assume the v a l i d i t y of the N e r n s t - E i n s t e i n r e l a t i o n and n e g l e c t any g r a d i e n t s i n the s olvent c o n c e n t r a t i o n as w e l l as i n t e r a c t i o n s between the f l u x e s of the charged s p e c i e s . For a more thorough a n a l y s i s of i o n i c t r a n s p o r t e.g. concentrated multicomponent s o l u t i o n s , i t i s necessary to use a more complete f l u x e xpression (Chapman, 1969). C.3.2. I o n i c Fluxes For a u n i - d i r e c t i o n a l f l o w of a 1-1 e l e c t r o l y t e E q s .(C7.) and (C.8.) can be w r i t t e n as J + - - D + t ( f j ) C ( | f ) + ( £ ) ] Because of e l e c t r o n e u t r a l i t y i n the s o l u t i o n phase C + = C_ = C ( C I O . ) and f o r mono-monovalent e l e c t r o l y t e Z + = - Z_ = 1.0 ( C . l l . ) 324 I n the membrane, the numerical v a l u e of the f l u x r a t i o , —- , i s equal to the t r a n s p o r t number r a t i o ^ . Since by d e f i n i t i o n of the steady s t a t e the f l u x e s are independent of p o s i t i o n x (perpendicular to membrane f a c e ) , the same f l u x r a t i o p r e v a i l s a l s o i n the s o l u t i o n : i± = |± = _ | ± = 1±__ (C.12.) J _ J _ t _ (1 - t + ) The negative s i g n i s introduced because the J's are v e c t o r s . I n the membrane J+ and J _ have opposite s i g n s , w h i l e t+ and t _ are always taken as p o s i t i v e . I t should be noted t h a t the i o n f l u x r a t i o i s equal to the r a t i o of the i o n t r a n s p o r t numbers i n the membrane only when i o n t r a n s p o r t i n membranes takes p l a c e e n t i r e l y by e l e c t r o m i g r a t i o n . Unless the membrane i s i d e a l l y p e r m s e l e c t i v e , there e x i s t a d d i t i o n a l i o n f l u x e s due to d i f f u s i o n across the membrane caused by the s a l t c o n c e n t r a t i o n d i f f e r e n c e i n the s o l u t i o n s a t the two membrane fac e s . This back d i f f u s i o n of the s a l t w i l l be neglected here, however, because almost i d e a l l y p e r m s e l e c t i v e membranes are used i n most e l e c t r o d i a l y s i s i n s t a l l a t i o n s , and s i n c e i n p r a c t i c e . t h e e l e c t r i c a l d r i v i n g f o r c e s are i n general much l a r g e r than the d i f f u s i o n d r i v i n g f o r c e s , even when membranes are used which are not f u l l y perm- s e l e c t i v e . From Eqs.(C9.) and (C.12.): = - t - J+ FC dE dc t+ D_ R T dx ~ dx OR 325 s u b s t i t u t e Eq.(C.13.) i n t o (C.9.) and + + d x t+ D_ d x . _ 2D4. + lZ J+ °+ + d x t+ D_ - 2D+ dc j = _ ~~Z dx" (C.14.) J+ 1 - (D+ t_/D_ t+) flX 2 D " d G (C.15.) 1 - (D_ t+/D+ t_) d X Since f l u x e s , i o n i c d i f f u s i o n c o e f f i c i e n t s and membrane t r a n s p o r t dc numbers are constant, i t f o l l o w s t h a t — i s constant a l s o . In other words, ' dx the a p p l i c a t i o n of the Nernst-Planck equation w i t h the above assumptions leads to a l i n e a r c o n c e n t r a t i o n gradient i n the boundary l a y e r . I t i s o f t e n more convenient to express the f l u x e s i n terms of the d i f f u s i o n c o e f f i c i e n t of the e l e c t r o l y t e , D, r a t h e r than the i o n i c d i f f u s i o n c o e f f i c i e n t s , D + and D_. Noting that i n f r e e s o l u t i o n D+ = t+ = t+ (C.16.) D_ t _ (1 - t + ) and u s i n g the Nernst expression f o r the d i f f u s i o n c o e f f i c i e n t of 1-1 e l e c t r o - l y t e i n d i l u t e s o l u t i o n ! - ! ( ! + ! ) D 2 D + D_ OR 326 From Eq.(C.16.) D_ = t _ = (1 - t + ) (C.18.) D + + D_ t _ + t+ S u b s t i t u t e Eq.(C18.) i n t o 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 ( C i 2 ( J < ) 1 - (t+ t _ / t _ t+) d X ( t _ t+ - t+ t_) d X But t _ t + - t + t _ = (1 - t + ) t+ - t + (1 - t + ) = t + - t + (C.21.) S u b s t i t u t e Eqs.(C.19.) and (C.21.) i n t o Eq.(C.20.) • j - . — S k - ^ ( c . 2 2 . ) ( t + - t + ) d x S i m i l a r l y J • - D i - £ = D t - 4S. (C.23.) Ct. - t_) d x ( t + - t + ) d x For i d e a l l y , s e l e c t i v e c a t i o n exchange membranes, t + = 1.0. Hence from Eqs, (C.22.) and (C.23.): J+ = - D [ i o t ] ; J - = 0 ( c - 2 4 0 and f o r i d e a l l y s e l e c t i v e 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 F i c k ' s law, but the 327 r a t i o ^ r e p l a c e s the i o n i c c o e f f i c i e n t D± ( i . e . the f l u x i s higher because the e l e c t r i c f i e l d provides a d d i t i o n a l d r i v i n g f o r c e ) . The c u r r e n t d e n s i t y , i , i s given by Faraday's law i = F ( J + - J_) (C.26.) S u b s t i t u t e f o r J + and J _ from Eqs.(C.22.) and (C.23.) i = 2 L — dc = FD dc ? C t + " V d X ( t _ - t_) d x I f i , D and the t r a n s p o r t numbers are constant, Eq.(C.27.) then, w i t h i n the range of a p p l i c a b i l i t y of the Nernst-Planck equations, the c o n c e n t r a t i o n g r a d i e n t i n the w a l l l a y e r i s l i n e a r . C.4. W a l l l a y e r t h i c k n e s s The w a l l l a y e r t h i c k n e s s , 6, depends on d i s t a n c e from s o l u t i o n i n l e t and i t varys along the flo w path. I n the Nernst model i t i s assumed that a steady s t a t e has been reached. I t i s a l s o assumed t h a t the h y d r a u l i c f l o w c o n d i t i o n s of the s o l u t i o n s are chosen such t h a t v a r i a t i o n along the membrane can be neg l e c t e d . I n t h i s case, the s o l u t i o n c o n c e n t r a t i o n p r o f i l e i n the w a l l l a y e r i s t i m e - i n v a r i a n t and a l s o does not vary along the membrane. According to the Nernst model an approximate average v a l u e (or a c r i t i c a l value) of 6 i s used and the problem can be solved without i n t e g r a t i o n over the whole f l o w path. Studies which s t r e s s the hydrodynamic aspects of the problem and the i n f l u e n c e of non-uniform d i f f u s i o n l a y e r s have been published (Sonin and P r o b s t e i n , 1968; Solan and Winograd, 1969). I t i s of i n t e r e s t that the hydrodynamic a n a l y s i s leads to j u s t i f i c a t i o n of Nernst's p o l a r i z a t i o n l a y e r concept [replacement of the a c t u a l mass-transfer boundary l a y e r ( d i f f u s i o n l a y e r ) by a d i f f u s i o n l a y e r of uniform t h i c k n e s s ] as a f a i r l y good approximation f o r c e r t a i n f l o w s i t u a t i o n s ( S p i e g l e r , 1971). 328 C.5. Conclusion I t can be concluded that the Nernst i d e a l i z e d model i s i n e f f e c t e q u i v a l e n t to the a p p l i c a t i o n of the Nernst-Planck equations and the use of an average t h i c k n e s s of the d i f f u s i o n l a y e r . Appendix D G r a p h i c a l S o l u t i o n of Constant-Rate Model G r a p h i c a l s o l u t i o n f o r synchronous (in-phase) o p e r a t i o n [case ( i ) - chapter (3)] w i l l be considered here. G r a p h i c a l s o l u t i o n s f o r the other cases can be developed i n a s i m i l a r manner. The system c o n s i s t s of a separator (ED stack) and two end r e s e r v o i r s as shown i n F i g u r e D - l ( a ) . I n i t i a l l y the separator and the bottom r e s e r v o i r are f u l l of s o l u t i o n of c o n c e n t r a t i o n C q , top r e s e r v o i r i s empty. The ab s e i s s a i n F i g u r e D - l ( b ) , which represents the v e r t i c a l c o o r d i n a t e i n F i g u r e D - l ( a ) , i s d i v i d e d i n t o three s e c t i o n s : S e c t i o n I : -I -4 z ^ o , the bottom r e s e r v o i r S e c t i o n I I : o 4 z 4 I , the separator S e c t i o n I I I : I 4 z 4 2H , the top r e s e r v o i r Operation s t a r t s w i t h up-stroke ( d e m i n e r a l i z a t i o n h a l f c y c l e ) . During t h i s p e r i o d s o l u t e i s t r a n s f e r r e d from the mobile phase i n t o the storage compartments of the separator. By the end of the f i r s t h a l f c y c l e the c o n c e n t r a t i o n p r o f i l e s of s o l u t i o n i n the separator and the top r e s e r v o i r are i n d i c a t e d by the l i n e s abc, cde r e s p e c t i v e l y i n F i g u r e D-2. The amount of s o l u t e stored i n the separator during t h i s h a l f c y c l e i s given by the r e c t a n g l e afgh (Figure D-2) which has the same area as the two t r i a n g l e s acf and cef ( i . e . c f = f g ) . The stored m a t e r i a l i s returned to the mobile phase during the second h a l f c y c l e and i t d i s t r i b u t e s i t s e l f 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 a fgh at the end of the first half cycle. 332 regions I I and I I I i n d i f f e r e n t p r o p o r t i o n s depending on the r a t i o of the K l mass t r a n s f e r r a t e s i n the two h a l f - c y c l e s , — where K 2 dC f = - K, : f o r d e m i n e r a l i z a t i o n (D.l.) dt 1 ' dC f = K 2 ; f o r enrichment (D.2.) dt T I f K 2 £ K^ and d e m i n e r a l i z a t i o n i s assumed to take p l a c e f o r time , then to m a i n t a i n the m a t e r i a l balance of the s o l u t e , the enrichment p e r i o d should be At, where TK At = ^ (D.3.) K l G r a p h i c a l s o l u t i o n s of three d i f f e r e n t cases of .the r a t i o — w i l l be 2 considered. K l (a) - i = 1.0 K 2 I n t h i s case La = Z.3 as shown i n F i g u r e D-3(a) where a = tan K^ and g = tan ^ K 2; and the stored m a t e r i a l i s d i s t r i b u t e d e q u a l l y between regions I I and I I I during the second h a l f c y c l e . Each p o i n t along the l i n e s abc, cde w i l l g a i n a c o n c e n t r a t i o n s h i f t given by the l e n g t h of the corresponding arrow v e r t i c a l l y above i t (co n c e n t r a t i o n s at p o i n t s a and e remain constant w h i l e that a t p o i n t c shows the maximum jump). F i g u r e D-3(b) shows that by the end of the f i r s t c y c l e a l l p o i n t s along the c o n c e n t r a t i o n p r o f i l e s r e t u r n to t h e i r i n i t i a l v a l u e s and no s e p a r a t i o n i s obtained i n t h i s case. FIGURE D_3(a) Mass transfer during the second half cycle (enrichment half cycle) K 2 = 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) K 2 » K x K l I n t h i s case — -> 0. From Equation (D.3.) At -*• 0, which means K 2 that a l l the stored m a t e r i a l i s t r a n s f e r r e d i n s t a n t a n e o u s l y to r e g i o n I I ( i . e . Z,B 90°). F i g u r e D-4(a) shows the mass t r a n s f e r during t h i s h a l f c y c l e , where the v e r t i c a l arrows i n d i c a t e the c o n c e n t r a t i o n s h i f t s a t v a r i o u s p o i n t s along a b C ^ , w h i l e F i g u r e D-4(b) shows the c o n c e n t r a t i o n p r o f i l e s at the beginning and at the end of the second (enrichment) h a l f c y c l e . Due to the instantaneous mass t r a n s f e r there i s a c o n c e n t r a t i o n d i s c o n t i n u i t y at the boundary of the two regions ( p o i n t s C.^ and CJ-J-J) • Every c y c l e the depleted product s u f f e r s a l o s s of m a t e r i a l represented by the t r i a n g l e e ^ (Figure D-4(a)) w h i l e the enriched product gains a net i n c r e a s e of s i m i l a r amount. The average top and bottom c o n c e n t r a t i o n s a f t e r the nth c y c l e are given by: C N K Tn - i S - 1 - ^ - (D.4.) o o and C_ K. Tn o o (c) K 2 > K x K 2 i s assumed to be l a r g e r than K^, but both are of the same order of magnitude e.g. K 2 = 2K^. In t h i s case Equation (D.3.) gives that At = r (D.6.) 4 The mass t r a n s f e r during the second h a l f c y c l e i s shown i n F i g u r e D-5(a) where L 3 = 2 La. /K A A A A /N C m Ui S FIGURE D_4(a) Mass transfer during the second half cycle (enrichment half cycle), K 2 > K I FIGURE D_4(b) Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle- K 2 > K I FIGURE D_5(a) Mass transfe during the second half cycle (enrichment half cycle). K 2 = 2K, FIGURE D_5(b) Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle. K 2 = 2 K , 337 A f t e r the f i r s t h a l f c y c l e the m a t e r i a l l o s t by the top (demineralized) product i s given by A ceo (Figure D-5(a)) where 1 T T K 1 A ceo = ( \ ) ( -j=- ) (D.7.) and the average c o n c e n t r a t i o n of the top product i s given by TK CT,1 = C o - — ( D - 8 ' ) Then every c y c l e the top product w i l l l o s e a m a t e r i a l given by 1 K T ' K T A ceo - Ac'od' = ± ( - J _ ) ( i ) - A ( _ ± _ ) (At) T K T At K • i ( " i r i ) ( D - 9 0 and the average c o n c e n t r a t i o n change w i l l be given by * • n -. K.T K^T m a t e r i a l l o s s _ _1 1 (T/2) " 4 K 24 (D.10.) The average top c o n c e n t r a t i o n a f t e r the nth c y c l e i s given by C_, TK TK K = i - ^ - ^ - K T 0 ) . l l . ) o o o 2 S i m i l a r l y every c y c l e the bottom product gains the m a t e r i a l given by trapezium ab'c'o - t r i a n g l e aoc 1 K 1 T T T 1 K T 1 T T K 1 T K l = I ( "T" ) ( 1 " K j } - (D.12.) The average bottom c o n c e n t r a t i o n a f t e r the nth c y c l e i s given by CB,n T K i K ! ~t- - 1 + i r ( 1 - F > n ( D- 1 3- ) o ^ 0 K 2 APPENDIX E COMPUTER PROGRAMS 338 Appendix E Symbols used i n Computer Program i ) DATA CB = B r i n e Concentration (ppm) CD = D i a l y s a t e Concentration (ppm) VB = Volume of B r i n e product ( c . c . / c y c l e ) VD = Volume of d i a l y s a t e product ( c . c . / c y c l e ) CF = I n i t i a l (Feed) Concentration (ppm) Numbers 1, 2, .... 9 stand f o r Exp. l e t t e r s A, B, .... I . i i ) RESULTS (A) Thi s f i r s t p a r t of the program computes: a) Separation f a c t o r NS = CB/CD b) M a t e r i a l balance and % e r r o r ERR % = ( ? P F p F F ) 100 where PP = BB + DD ( S a l t i n product streams) BB = CB * VB ( S a l t i n b r i n e ) DD = CD * VD ( S a l t i n d i a l y s a t e ) FF = CF * (VB + VD) ( S a l t i n feed) i i i ) RESULTS (B) Thi s second part of the program computes the amount of s a l t s h i f t e d d u r i n g s e p a r a t i o n , 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) C B F ( 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,'BF 1,10X,'CF-CD',8X,»DF 1,12X,'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 i l 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 C 3 VB c n VD C F 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 9 1 * . 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 F F 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 . 5 3 1 * 11.71*2 29.1*61* 36.017 1*6.277 9.329 6.1*1*7 I*.018 RESULTS(8) AMOUNT OF SEPARATION C B - C F B F C F - C D D F 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 . 0 1 * 1830 .00 1*1*157. 91 I* 1955 .00 1+8229 . 8 1 * 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* 9 7 9 6 1 * . 8 1 103300.00 106936.50 85292.00 77557.38 631*65.05 CORE USAGE OBJECT CODE" 2608 BYTES,ARRAY AREA" 8 6 1 * 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 p a r - n o l l s t •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 j r * w a t f l v s c a r d s - e x p 5*m5 p a r - n o l l s t •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 H 0 0 1 .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 5 i ) C 3 0 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 * w a t f i v scards"exp'5»m8 p a r - n o l l s t '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 t r *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 * w a t f l v 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 * w a t f i v scards-exp'5»ml2 p a r - n o l l s t 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 a t f ! 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') 1 5 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 ) - C F 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 )  l )  B ( I J l I ; 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, F l l . 2 , 2F10.3 ) 31 WRITE(6,66) 32 WR!TE(6,86) . 3 3 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 — 1 6 2 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 4 7.38 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 — 2 3 7 0 . 00 1 * 6 . 5 1 * — 1 5 5 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 - 5 1 2 . 9 1 * -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. 5 7 9 9 1 * , -7 33 76, 82231*. 39126, -31680, 1951*6, 00 0r. - 00 1*9 9 i * - 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 0 0 — 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 - 2 r l 7 4 - -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- — B F 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 scards Bcon 5 ar9 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 l S . 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 - 3 3 7 1 * .88 - 9 7 5 . 1 9 - 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 8 8 9 1 * 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 j r *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 $STOP ? E X E C U n O N " T E R m i T A T E D i r *watflv scards-con 5-rl2 par -nol ls t „5 _ I "EXECUTION BEGINS DATA "$ 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 D A T E " 07-30-71*" "$STOPr_ * EXECUTION TERMINATED # Co Cn 00 APPENDIX F T h e o r e t i c a l and P r a c t i c a l Energy Requirements f o r a D e s a l t i n g Process F . l . Minimum Work of Separation The mixing of two substances always r e s u l t s i n an i n c r e a s e i n entropy, due to the i n c r e a s e i n "randomness" of the system. This i n c r e a s e i s accompanied by a corresponding decrease i n f r e e energy, so t h a t the s e p a r a t i o n of the r e s u l t i n g mixture under thermodynamically r e v e r s i b l e c o n d i t i o n s r e q u i r e s the supply of an equal amount of energy to counteract nature's tendency t o mix r a t h e r than unmix spontaneously. In g e n e r a l , heat and work both depend on the p a r t i c u l a r path, and one cannot c a l c u l a t e the minimum requirement of e i t h e r without c o n s i d e r i n g the process i n d e t a i l . There i s however, one p a r t i c u l a r process - the i s o t h e r m a l r e v e r s i b l e process - f o r which the work i s measured by the change i n the Helmholtz f r e e energy (the work f u n c t i o n ) , A. The term "minimum work of s e p a r a t i o n " i s u s u a l l y used to mean the thermodynamic r e v e r s i b l e work of s e p a r a t i o n f o r an i s o t h e r m a l process and hence i t i s independent of the process mechanism and dependent only on the i n i t i a l and f i n a l s t a t e s . The minimum work to separate one mole of a feed s o l u t i o n of composition x^ i n t o two product s o l u t i o n s of compositions and x^ r e s p e c t i v e l y i s given by (Dodge, 1944)* * Dodge, B.F., Ed., "Chemical Engineering Thermodynamics", McGraw H i l l Co., New York, 1944. 359 360 v2 ~ XJ PA? W. . . = - AA = - RT I — — l n — + i d e a l L x 2 - x 3 P A l f x . (1 - x 2 ) ( X l - x 3 ) p B 2 x 3 ( x 2 - x L ) p A 3 _ l n 1 - l n X 2 X 3 PB1 X 2 x 3 PA1 1 (1 - x„)(x 0 - x ) p + 3 1 1 i n - B 3 | ( F . l . ) X 2 - X 3 PB1 where p Is the p a r t i a l pressure and s u b s c r i p t s 1, 2 and 3 r e f e r to feed, f i r s t product, and second product, r e s p e c t i v e l y , and s u b s c r i p t s A and B to the components. S p i e g l e r (1966 a) developed a gen e r a l equation f o r the minimum t h e o r e t i c a l energy requirement to separate s a l t from a s a l i n e . For any d e s a l t i n g process i n which a 1-1 e l e c t r o l y t e s o l u t i o n of cone. Cf i s converted i n t o two product s o l u t i o n s of cones. C d and C £ at 25°C, the minimum energy i s given by U = 1.377 x AN ( - ) (F.2.) p — J. ot — J- 3 where U i s the energy i n kwh/m AN = the n o r m a l i t y d i f f e r e n c e between feed and product s o l u t i o n N = the n o r m a l i t y ( g - e q u i v / l i t ) N f N f = N~~ ; a = NT c d s u b s c r i p t s f , d, c i d e n t i f y feed, product ( d i l u a t e ) and concentrate r e s p e c t i v e l y . 361 F.2. P r a c t i c a l Energy Requirements The t h e o r e t i c a l energy requirements f o r a d e s a l t i n g process u s u a l l y r epresents merely a small p o r t i o n of the a c t u a l energy requirement. When the minimum work requirement f o r d e m i n e r a l i z a t i o n i s compared w i t h the a c t u a l requirement of o p e r a t i n g process, i t i s found that t h i s l a t t e r • have an energy e f f i c i e n c y of the order of only 2 to 5% (Dodge and Eshaya, I960)*. These low e f f i c i e n c i e s a r e , of course, a t t r i b u t a b l e to the d r i v i n g f o r c e s which are necessary i n any p r a c t i c a l process, as c o n t r a s t e d w i t h the r e v e r s i b l e process t h a t assumes zero d r i v i n g f o r c e s . These d r i v i n g f o r c e s are the f i n i t e temperature d i f f e r e n c e s , pressure d i f f e r e n c e s , c o n c e n t r a t i o n d i f f e r e n c e s , e.m.f. d i f f e r e n c e s , e t c . , which are necessary f o r equipment of p r a c t i c a l s i z e . Any r e d u c t i o n i n the d r i v i n g f o r c e always e n t a i l s an i n c r e a s e i n s i z e and hence cost of equipment and because the t o t a l c o s t s of a d e s a l t i n g process are about e q u a l l y d i v i d e d between c o s t s of energy and f i x e d c o s t s on equipment, one reaches a cost minimum at an e f f i c i e n c y which i s g e n e r a l l y l e s s than 20%. The main i r r e v e r s i b l e e f f e c t s that make the a c t u a l process d i f f e r s from the i d e a l r e v e r s i b l e one are: i ) Pressure drop i n l i n e s and equipment due to f l u i d f r i c t i o n , i i ) T h r o t t l i n g processes. i i i ) F i n i t e temperature d i f f e r e n c e between f l u i d s exchanging heat. i v ) Heat conduction along s o l i d s . v) Heat l e a k i n t o the system from the surroundings. * Dodge, B.F. and A.M. Eshaya, i n : " S a l i n e Water Conversion" Number 27 i n Advances i n Chemistry S e r i e s , American Chemical S o c i e t y , Washington, D.C., 1960. 362 v i ) F l u i d mixing when there i s a d i f f e r e n c e i n temperature or co n c e n t r a t i o n . v i i ) Mass t r a n s f e r w i t h f i n i t e c o n c e n t r a t i o n g r a d i e n t , v i i i ) J o u l e h e a t i n g i n e l e c t r i c c u r r e n t f l o w , i x ) P o l a r i z a t i o n e f f e c t s at e l e c t r o d e s , x) Mechanical f r i c t i o n , as i n pumps and compressors. These e f f e c t s can never be completely e l i m i n a t e d and f r e q u e n t l y must remain of co n s i d e r a b l e magnitude, i f the s i z e of the equipment i s to be kept w i t h i n reasonable bounds [Dodge B.F. and A.M. Eshaya, I960].

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