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A Cyclic electrodialysis process : investigation of closed systems Bass, Dieter 1976-12-31

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A CYCLIC ELECTRODIALYSIS PROCESS I n v e s t i g a t i o n o f Open Systems  by  MOHAMMED ELAMIEN ABU-GOUKH B.Sc.  ( H o n s . ) , U n i v e r s i t y o f K h a r t o u m , 1970  A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES Department o f C h e m i c a l E n g i n e e r i n g  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g to the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA November, 1976 c \  Mohammed E l a m l e n Abu-Goukh,  1976  In  presenting  this  an a d v a n c e d d e g r e e the I  Library  further  for  shall  agree  thesis  in p a r t i a l  fulfilment  of  at  University  of  Columbia,  the  make  it  freely  available  that permission for  his  of  this  representatives. thesis  for  It  for  extensive  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  British  by  the  gain  shall  not  The  CK^AYU^AX  of  University  of  British  2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  Date  Columbia  reference  Head o f  IMtoLyw^  I  agree  and this  copying or  tha  study. thesis  my D e p a r t m e n t  be a l l o w e d  written permission.  Department  r e q u i r e m e n t s f<  copying of  i s understood that  financial  the  or  publication  w i t h o u t my  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 separation process m o d i f i e d membrane s t a c k i s o p e r a t e d  i n which a  i n a p e r i o d i c unsteady-state  manner.  Repeated r e v e r s a l s o f p o l a r i t y c o u l d a v o i d the main problems e n c o u n t e r e d i n conventional 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 f o r m a t i o n on the membranes.  I n c y c l i c e l e c t r o d i a l y s i s the standard 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  channels,  e l e c t r o d i a l y s i s stack i s  s t a c k w i t h o n l y one  s e t of  the o t h e r s e t b e i n g r e p l a c e d by s t o r a g e compartments.  flow Thesr  compartments a r e i n the form o f t h r e e - l a y e r membranes c o n s i s t i n g of  an  a n i o n 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 c o r e of non- s e l e c t i v e material.  The d e p l e t e d and e n r i c h e d p r o d u c t s a r e produced s u c c e s s i v e l y  i n the s i n g l e s e t of c h a n n e l s i n s t e a d of s i m u l t a n e o u s l y The p r o c e s s  i n adjacent  channels.  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 c o m m e r c i a l d e s a l i n a t i o n of b r a c k i s h  water t o make i t p o t a b l e , t o remove h a r m f u l or t o c o n c e n t r a t e  i o n s from d i s c h a r g e  waters,  i o n i c s o l u t i o n s f o r r e c o v e r y 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 r e p o r t e d e x p e r i m e n t s w i t h aqueous N a C l s o l u t i o n s i n a c l o s e d ( b a t c h ) system showed t h a t a l a r g e s e p a r a t i o n f a c t o r c o u l d be  obtained  in cyclic electrodialysis.  total  reflux in distillation.  Batch o p e r a t i o n i s somewhat a n a l o g o u s to  The p r e s e n t work e x t e n d s t h e 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 w h i c h f e e d i s s u p p l i e d product  and  removed.  A c o n s t a n t - r a t e model has been d e v e l o p e d f o r the p r o c e s s e x t e n s i v e l y t h r o u g h o u t t h e work as a s i m p l e and ii  and  used  e f f i c i e n t t o o l t o 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 .  Scattered  articles  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 s t a c k have been compiled  t o d e v e l o p a s t a c k 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 v a l u e s of r e s i s t a n c e . Experimental  a p p a r a t u s i s d e s c r i b e d and  e i g h t system p a r a m e t e r s a r e (i) (ii) (iii) (iv) (v) (vi) (vii) (vii)  the e f f e c t s of the f o l l o w i n g  reported:  D e m i n e r a l i z i n g path  length  Production rate Pause t i m e Applied voltage Initial  concentration  No-pause o p e r a t i o n Pure-pause o p e r a t i o n Semi-symmetric o p e r a t i o n  L a r g e s e p a r a t i o n s were a c h i e v e d  f o r asymmetrical  paused o p e r a t i o n w i t h  l o n g d e m i n e r a l i z i n g p a t h , l o n g pause t i m e , h i g h a p p l i e d v o l t a g e , low c o n c e n t r a t i o n and  small production rate.  between p r o d u c t i o n r a t e and was  D e s p i t e the s t r o n g t r a d e - o f f  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 h i g h as  obtained a t the highest p r o d u c t i o n r a t e used.  than that obtained The p r o c e s s  feed  T h i s v a l u e i s higher  i n c o m m e r c i a l p l a n t s c u r r e n t l y i n use. looks promising  and  iii  i s worth f u r t h e r c o n s i d e r a t i o n .  50  TABLE OF CONTENTS  Page ABSTRACT  i i  LIST OF TABLES  viii  LIST OF FIGURES  xiii  ACKNOWLEDGEMENTS  xx  Chapter 1  INTRODUCTION AND GENERAL  2  THEORY AND REVIEW  . . . . . . . .  5  2.1  D e s a l t i n g Processes  2.2  Some Economic A s p e c t s o f S e l e c t i v e and S t a t e Change P r o c e s s e s  2.3  2.4  2.5  2.6  1  . . . .  5 7  Electrodialysis  10  2.3.1  E l e c t r o d i a l y s i s Stack  14  2.3.2  S t a c k S i z e and C a p a c i t y  . . . . .  16  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 o f Membranes  30  Process E f f i c i e n c y  32  2.5.1  32  P r i n c i p a l Energy S i n k s  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 Depletion  35  2.6.2  Electrogravitational iv  Demineralization  . . . .  38  Chapter 2.7  Page C y c l i c Processes  .  40  . . .  40  2.7.1  Electrosorption  2.7.2  Cyclic Electrodialysis  40  2.7.3  P a r a m e t r i c 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 P a r a m e t r i c Pumping  3  48  3.1  48  THE  S t a c k R e s i s t a n c e Models 3.1.1  Non-ohmic A n a l y s i s  3.1.2  Ohmic A n a l y s i s  . .  48 66  Mass T r a n s f e r Models  69  3.2.1  E q u i l i b r i u m Model  71  3.2.2  R a t e Models  .  73  3.2.3  Comment on C o n s t a n t - R a t e Model'  , . .  92  . . , . .  93  CYCLIC ELECTRODIALYSIS PROCESS - OBJECTIVES,  TECHNIQUES AND  APPARATUS  4.1  O b j e c t i v e s of t h e Program  .....  93  4.2 4.3  S i n g l e Stack Operation Back-to-Back S t a c k C o n f i g u r a t i o n  .... .....  94 97  4.3.1  Open System O p e r a t i o n o f a  back-to-back  configuration 4.4  4.5  97  A p p a r a t u s and O p e r a t i o n  114  4.4.1  D e t a i l s o f an ED C e l l D e s i g n  118  M e a s u r i n g and R e c o r d i n g 4.5.1 C o n c e n t r a t i o n s , C u r r e n t , V o l t a g e and measurements  122  4.5.2 5  46  SYSTEM MODELS  3.2  4  .  Recording  pH 122 127  EXPERIMENTAL RESULTS and DISCUSSION v  128  Chapter  Page 5.1  Data-Collection  128  5.2  Experimental Designation  129  5.3  M a i n Survey T a b l e s  130  5.4  P a r a m e t e r s and Modes o f O p e r a t i o n 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 o f Pause Time  173  5.4.4  E f f e c t of A p p l i e d V o l t a g e  192  5.4.5  E f f e c t of I n i t i a l Concentration  208  5.4.6  No-Pause O p e r a t i o n  5.4.7  Pure-Pause O p e r a t i o n .  223  5.4.8  Semi-Symmetric O p e r a t i o n  223  , . . . .  5.5  Comment on pH-Changes  5.6  Temperature Measurements  » . . . .  243  5.7  P r e s s u r e Drop Measurements  , . . . ,  243  5.8  Probe V o l t a g e , A p p a r e n t R e s i s t a n c e and C u r r e n t Consumption  243  Voltage E f f i c i e n c y  269  5.9  227  5.10 C u r r e n t D e n s i t y and E f f i c i e n c y  269  5.11 Comments on S t a c k R e s i s t a n c e Models  .  5.12 Comparison w i t h P r e v i o u s Work i n C l o s e d System 5.13 6  208  Reproducibility  ....  . . . . . . . . .  CONCLUSIONS and RECOMMENDATIONS  273 284 285  . . . . .  288  NOMENCLATURE  . . . . .  293  REFERENCES  . . . . .  298  APPENDICES  304  vi  Appendix A  Page ELECTRODE SYSTEM  . . . . .  A.l  Electrodes Materials .  A.2  Electrodes Reactions  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  ,  304 304  Consumption A. 4  304  E l e c t r o d e F l o w System  , . ,  309  . . , ,  311  .  313  B  THE CURRENT EFFICIENCY  C  NERNST IDEALIZED MODEL OF WALL LAYERS  319  C.l  The F l o w 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 o f t h e Model  320  C.3.1  G e n e r a l i z e d Theory o f Coupled Processes  C.3.2  . . . . . . . . .  320  Ionic Fluxes  C.4  Wall Layer Thickness  C.5  Conclusion  323 . . •. ,  327  . . . . . . .  328  D  GRAPHICAL SOLUTION OF CONSTANT-RATE MODEL . . . . . . . . . .  329  E  COMPUTER PROGRAMS  . . . . .  338  F  THEORETICAL AND PRACTICAL ENERGY REQUIREMENTS FOR . . . . . .  359  A DESALTING PROCESS F.l  Minimum Work o f S e p a r a t i o n  F.2  P r a c t i c a l Energy Requirements  vii  , . . . . . .  359 361  LIST OF TABLES  Table  Page I  II  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  IV  VI VII VIII  IX  95 nrVday  8  L a r g e 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 T e c h n i c a l D e t a i l s of B e n g h a z i ( L i b y a ) and Key  V  ....  (Florida) Electrodialysis Plants  18  R e p o r t e d P r o p e r t i e s of Ion-Exchange Membranes  ......  >32  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 f 2000 ppm; 4 - c e l l columns  concentration 134  Compilation of Experiments w i t h i n i t i a l ( C ) of 500 ppm; 4 - c e l l columns  concentration  C o m p i l a t i o n of E x p e r i m e n t s w i t h i n i t i a l ( C ) of 4000 ppm; 4 - c e l l columns  concentration  C o m p i l a t i o n of E x p e r i m e n t s w i t h i n i t i a l ( C ) of 2000 ppm; 8 - c e l l columns  concentration  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 f 500 ppm; 8 - c e l l columns  concentration  C o m p i l a t i o n of. E x p e r i m e n t s w i t h i n i t i a l ( C ) of 4000 ppm; 8 - c e l l columns  concentration  139  141  q  XIV  q  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 viii  131  138  q  XIII  323  136  q  XII  J.22  C o n d u c t i v i t y and N a C l C o n c e n t r a t i o n Ranges of BECKMAN C o n d u c t i v i t y C e l l s (EL-VDJ) V a l u e s o f n i n E x p e r i m e n t a l D e s i g n a t i o n s Rna and Mna . , . . V a l u e s of a i n E x p e r i m e n t a l D e s i g n a t i o n s Rna and Mna ........  q  XI  9  Siesta  q  X  6  T o t a l Number and C a p a c i t y o f D e s a l t i n g P l a n t s exceeding  III  . . . . . . .  143  145  Table XVI  XVII  Page 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  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C - 500 ppm  4-cell 148  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C - 2000 ppm  4-cell  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C - 4000 ppm  4-cell  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C - 500 ppm o E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C - 2000 ppm  8-cell  Q  XVIII  150  q  XIX  152  q  XX XXI  „ . 8-cell  156  q  XXII  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n ; columns; C = 4000 ppm  8-cell  q  XXIII  =  500 ppm;  A<J> = 20 V  160  q  =  500 ppm;  A<|> = 30  162  V  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C  XXVI  Q  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C  XXV  q  =  2000 ppm; A<j>  = 20 V  164  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C = 2000 ppm; A<|> = 30 V  166  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C = 4000 ppm; A<j> = 20 V  168  q  XXVII  q  XXVIII  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C  XXIX  XXX  Q  =  4000 ppm; A<|>  = 30 V  170  E f f e c t o f Pause Time on S e p a r a t i o n ; C = 500 ppm o E f f e c t o f Pause Time on S e p a r a t i o n ; C = 2000 ppm  4 - c e l l columns;  E f f e c t o f Pause Time on S e p a r a t i o n ; C - 4000 ppm  4 - c e l l columns;  174 4 - c e l l columns; 176  Q  XXXI  158  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n ; C  XXIV  154  Q  ix  178  Table XXXII  Page E f f e c t o f Pause Time on S e p a r a t i o n ; = 500 ppm  8-cell  E f f e c t of Pause Time on S e p a r a t i o n ; C = 2000 ppm  8-cell  E f f e c t o f Pause Time on S e p a r a t i o n ; C = 4000 ppm  8-cell  E f f e c t o f Pause Time on S e p a r a t i o n ; Group M7  C  E f f e c t o f Pause Time on S e p a r a t i o n ; Group M3  C  E f f e c t o f Pause Time on S e p a r a t i o n ; Group M i l  C  C  XXXIII  columns; 180  q  columns; 182  q  XXXIV  columns; 184  q  XXXV  XXXVI XXXVII XXXVIII  = 500 ppm; °  186 = 2000 ppm;  °  188 =; 4000 ppm;  °  190  E f f e c t o f 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 ; columns; C = 500 ppm  4-cell  E f f e c t o f 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 ; columns; C = 2000 ppm  4-cell  E f f e c t of A p p l i e d V o l t a g e on Separation; columns; C = 4000 ppm  4-cell  E f f e c t o f 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 ; columns; C = 500 ppm  8-cell  E f f e c t o f 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 ; columns; C = 2000 ppm  8-cell  E f f e c t o f 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 ; columns; C - 4000 ppm  8-cell  193  q  XXXIX  195  q  XL  197  q  XLI  199  q  XLII  201  q  XLIII  q  XLIV  XLV XLVI  XLVII  203  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 4 - c e l l columns; P.R. = 20 c . c . / c y c l e  209  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 4 - c e l l columns; P.R. - 50 c . c . / c y c l e  211  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 4 - c e l l columns; P.R. = 100 c . c . / c y c l e  213  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 8 - c e l l columns; P.R. = 25 c . c . / c y c l e  215  Page  Table XLVIII  XLIX L LI  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 8 - c e l l columns; P.R. ~ 50 c . c . / c y c l e  217  E f f e c t o f Feed C o n c e n t r a t i o n on S e p a r a t i o n ; 8 - c e l l columns; P.R. = 100 c . c . / c y c l e  219  Comparison o f Pause and No-Pause O p e r a t i o n s  221  Comparison o f P u r e Pause w i t h M i x e d Mode O p e r a t i o n s ; C  LII LIII LIV  LV  q  = 2000 ppm  224  Semi-Symmetric O p e r a t i o n ;  C  q  = 2000 ppm  Comparison o f Semi-Symmetric and Asymmetric Operations Average P r o d u c t C o n c e n t r a t i o n s i n A r b i t r a r y U n i t s o b t a i n e d under Semi-Symmetric and Asymmetric Operations  LVII  LVIII  LIX  228  241  ...  P r e s s u r e Drop Measurements  LXI  A v e r a g e Probe V o l t a g e ( S t a c k V o l t a g e ) over a c o m p l e t e c y c l e f o r v a r i o u s f e e d c o n c e n t r a t i o n and Applied Voltages V a r i a t i o n o f Probe V o l t a g e a l o n g t h e 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  V a r i a t i o n o f C u r r e n t Consumption a l o n g t h e Demineralization 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 ; C - 2000 ppm  255  V a r i a t i o n o f C u r r e n t Consumption a l o n g t h e Demineralization 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 f e e d c o n c e n t r a t i o n s ; A<j> = 30 V .  257  V a r i a t i o n o f Probe V o l t a g e , C u r r e n t , R e s i s t a n c e and Power Consumption a l o n g t h e d e m i n e r a l i z i n g p a t h ; C - 500 ppm  259  V a r i a t i o n o f Probe V o l t a g e , C u r r e n t , R e s i s t a n c e and Power Consumption a l o n g t h e d e m i n e r a l i z i n g p a t h ; C - 2000 ppm  260  Q  LXII  242 244  q  LX  226  pH - Changes f o r some ED r u n s a t v a r i o u s f e e d c o n c e n t r a t i o n s and o p e r a t i n g c o n d i t i o n s  LVI  .  q  xi  246  Table LXIII  Page V a r i a t i o n o f P r o b e V o l t a g e , C u r r e n t , R e s i s t a n c e and Power Consumption a l o n g t h e d e m i n e r a l i z i n g p a t h ; C = 4000 ppm  261  E f f e c t o f I n i t i a l C o n c e n t r a t i o n on t h e E q u i v a l e n t R e s i s t a n c e o f ED S t a c k  262  V a r i a t i o n o f ED S t a c k r e s i s t a n c e a l o n g t h e demineralizing 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 ; C - 500 ppm  264  Voltage E f f i c i e n c y  270  O v e r a l l Current E f f i c i e n c y  272  E q u i v a l e n t Conductance and D i f f u s i v i t y o f aqueous sodium c h l o r i d e s o l u t i o n s  275  D i s t r i b u t i o n o f t h e p r e d i c t e d r e s i s t a n c e o f an ED s t a g e between i t s r e s i s t i v e elements  280  q  LXIV LXV  Q  LXVI LXVII LXVIII LXIX LXX  V a l u e s o f 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  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  LXXII  R e p r o d u c i b i l i t y - Group M;  8 - c e l l columns  xii  286 . . . . . . .  287  L I S T OF FIGURES  Figure 1 2 3  4 5a 5b 6  7  Page Comparison o f energy c o s t s f o r d i s t i l l a t i o n and electrodialysis  11  M u l t i p l e - c h a m b e r a l t e r n a t e membrane electrodialysis cell  13  E x p l o d e d v i e w o f components i n an e l e c t r o membrane s t a c k  15  Dependence o f 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  Ion transport across a permselective membrane  26  Concentration p r o f i l e across a permselective membrane i n an e l e c t r o d i a l y s i s s t a c k . . . .  26  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  . . . . .  Electrogravitation with cation-selective membranes  39  8  E l e c t r o s o r p t i o n Process  9a 9b  Diagram o f column f o r d i r e c t mode P.P V e l o c i t y and t e m p e r a t u r e a t a p o i n t i n t h e bed as a f u n c t i o n o f t i m e  10  11  12a  12b  36  . .  41 45 45  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 t h e a n a l o g o u s e l e c t r i c a l c i r c u i t . . . .  50  Diagram o f t h e c o n c e n t r a t i o n p r o f i l e and t h e d i f f u s i o n l a y e r on t h e d i a l y s a t e s i d e o f an e l e c t r o d i a l y s i s i o n exchange membrane . . . . .  52  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 ) o f b o t h t h e d i a l y s a t e and b r i n e streams  55  The m a t e r i a l b a l a n c e s b r i n e streams  55  o f b o t h t h e d i a l y s a t e and xiii  Figure 13a  13b  •  Page  Concentration d i s t r i b u t i o n i n a cation-exchange membrane. Z r C r i s t h e c o n c e n t r a t i o n o f f i x e d c h a r g e i n membrane  J  59  Schematic p o t e n t i a l d i s t r i b u t i o n t h r o u g h a c a t i o n - e x c h a n g e membrane  59  14  Back emf due t o 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 16  D i f f e r e n t i a l s e c t i o n o f column , . . S e r i e s c o n n e c t i o n o f ED modules t o a p p r o x i m a t e constant-rate operation , . , . ,  70  17  18  19 20  74  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 w i t h e q u a l r a t e s j c o n t i n u o u s c y c l i c d i s p l a c e m e n t o f f l u i d and mass t r a n s f e r . . . . . . . .  77  Concentration p r o f i l e s - interrupted current cycle . . . '.  80  Concentration p r o f i l e s - interrupted flow cycle  .  . 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 m o d e l - c o n t i n u o u s c y c l i c d i s p l a c e m e n t o f 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° o u t of-phase w i t h the displacement c y c l e  21  B a c k - t o - b a c k o p e r a t i o n o f two u n i t s  22  Batch operation of c y c l i c  84  36 88  electrodialysis  process  94  23  B a c k - t o - b a c k o p e r a t i o n o f two c e l l s  97  24  D e v e l o p i n g 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 b a c k - t o - b a c k i n a c l o s e d system F l o w c o n n e c t i o n s 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  Developing concentration p r o f i l e , o p e r a t i o n o f an open system  103  25  26  27  28  symmetric  F l o w c o n n e c t i o n s 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 Developing concentration p r o f i l e , o p e r a t i o n o f an open system xiv  98  . .  105  semi-symmetric 109  Figure 29  30  Page F l o w c o n n e c t i o n s 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  D e v e l o p i n g 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 o f 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  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  33  A s i n g l e s t a g e w i t h i t s two end-frames  34  A t r i p l e membrane-frame-spacer a s s e m b l y  35  C o n s t r u c t i o n o f s i n g l e membrane-spacer a s s e m b l y f o r an ED c e l l Schematic d i a g r a m showing s o l u t i o n f l o w s and i n s t r u m e n t a t i o n (Asymmetric o p e r a t i o n )  36  .  . . , . 115 118 , , . 118  37  Current monitoring c i r c u i t  38  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C - 5 0 0 ppm '  4-cell  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C = 2 0 0 0 ppm  4-cell  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C = 4 0 0 0 ppm  4-cell  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C = 5 0 0 ppm  8-cell  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C = 2 0 0 0 ppm  8-cell  E f f e c t o f p r o d u c t i o n r a t e on s e p a r a t i o n . column; i n i t i a l cone. C = 4 0 0 0 ppm  8-cell  , . 153  155  Q  42  157  Q  43  Q  44  161  E f f e c t o f d e m i n e r a l i z i n g p a t h l e n g t h on s e p a r a t i o n . C = 5 0 0 ppm, A<j> = 3 0 V  163  Q  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  47  . 159  E f f e c t o f d e m i n e r a l i z i n g p a t h l e n g t h on s e p a r a t i o n . C * 5 0 0 ppm, Acfi = 20 V Q  45  120  151  Q  41  »  149  Q  40  119  . , . 125  Q  39  114  Q  = 2 0 0 0 ppm,  A<() = 20 V  165  E f f e c t o f 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  n  = 2000 ppm, A<j> = 3 0 V  xv  167  Figure 48  Page E f f e c t o f d e m i n e r a l i z i n g p a t h l e n g t h on s e p a r a t i o n . C a 4000 ppm, A<j> = 20 V '.  169,  E f f e c t o f d e m i n e r a l i z i n g p a t h l e n g t h on s e p a r a t i o n . C = 4000 ppm, A<|> = 30 V  171  E f f e c t o f pause t i m e on s e p a r a t i o n ; column; i n i t i a l cone. C - 500 ppm  175  Q  49  q  50  4-cell  Q  51  E f f e c t o f pause t i m e on s e p a r a t i o n ; 4-cell column; i n i t i a l cone. C = 2000 ppm  177  E f f e c t o f pause t i m e on s e p a r a t i o n ; 4-cell column; i n i t i a l cone. C * 4000 ppm  179  E f f e c t o f pause time on s e p a r a t i o n ; column; i n i t i a l cone. C = 500 ppm  181  q  52  q  53  8-cell  q  54  E f f e c t o f pause t i m e on s e p a r a t i o n ; 8-cell column; i n i t i a l cone. C - 2000 ppm . . . . . . . . . . .  183  E f f e c t o f pause t i m e on s e p a r a t i o n ; 8-cell column; i n i t i a l cone. C - 4000 ppm  185  Q  55  q  56 57  58  59  E f f e c t o f pause t i m e on s e p a r a t i o n . Group M7  C  E f f e c t o f pause t i m e on s e p a r a t i o n . Group M3  C  E f f e c t o f pause t i m e on s e p a r a t i o n . Group M i l  C  . . . .  = 500 ppm. °  » 87 = 2000 ppm;  °  . 189 = 4000 ppm.  °  E f f e c t o f 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 . column; i n i t i a l cone. C - 500 ppm  191 4-cell 194  q  60  E f f e c t o f 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-cell column; i n i t i a l cone. C = 2000 ppm . . . . . . . . .  196  q  61  E f f e c t o f 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 ; column; i n i t i a l cone. C = 4000 ppm  4-cell  E f f e c t o f 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 . column; i n i t i a l cone. C = 500 ppm  8-cell  E f f e c t o f 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-cell  -  q  62  200  Q  63  column; 64  i n i t i a l cone. C  Q  -  2000 ppm  E f f e c t o f 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 . column; i n i t i a l cone. C - 4000 ppm Q  xvi  198  202 8-cell 204  Pace  Figure 65  66  67  68  69  70  71  V a r i a t i o n o f i n d i v i d u a l c o s t i t e m s making up the t o t a l p r o c e s s i n g c o s t E f f e c t o f f e e d 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 . 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 Q  73  210  E f f e c t of f e e d 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 . 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 Q  .  E f f e c t o f f e e d 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 . 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  E f f e c t o f f e e d 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 . 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  E f f e c t of f e e d 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 . 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  . . , .  220  Q  Q  E f f e c t of f e e d c o n c e n t r a t i o n ( C ) ons 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 ~ Q  Comparison o f 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  P u r e 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 - 2000 ppm . . . . . . . ...  225  C o m p a r i s o n o f semi-symmetric and a s y m m e t r i c 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 - 2000 ppm  229  Developing concentration 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 b o t h pause and d i s p l a c e m e n t p e r i o d s . D i a l y s a t e p r o d u c t = b r i n e p r o d u c t = 1/3 c e l l v o l u m e / c y c l e ....  234  Developing concentration p r o f i l e ; semi-symmetric o p e r a t i o n o f an open system w i t h mass t r a n s f e r d u r i n g b o t h pause and d i s p l a c e m e n t p e r i o d s . D i a l y s a t e p r o d u c t = b r i n e p r o d u c t = 1/3 c e l l v o l u m e / c y c l e ....  240  P r e s s u r e drop v s . f l o w r a t e .  245  Q  74  q  75  76  77  212  Q  100 c . c . / c y c l e 72  207  xvii  8-Stage ED  stack . . . . . .  Figure 78  79  80  81  Page A v e r a g e s t a c k 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 t i m e T = 45 s e c . 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 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. M7F  248  Traces of current recording during 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 o f 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  82  Traces of current 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. M11F 251  83  V a r i a t i o n o f s t a c k v o l t a g e (probe v o l t a g e ) a l o n g 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 t h e 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 a p p l i e d v o l t a g e s C = 2000 ppm, Exp. M3B, M3F and M3G  256  V a r i a t i o n o f 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 o f I n i t i a l C o n c e n t r a t i o n on e q u i v a l e n t r e s i s t a n c e o f ED s t a c k  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 during the d e p l e t i o n h a l f cycle at various applied voltages. C - 500 ppm; Exp. M7F and M7G .  265  V a r i a t i o n of apparent d e m i n e r a l i z a t i o n path c y c l e using semi-log A(J> = 30 V; Exp. M3F,  ED s t a c k r e s i s t a n c e a l o n g t h e during the d e p l e t i o n h a l f scale. M7F and M11F  267  V a r i a t i o n o f a p p a r e n t ED s t a c k r e s i s t a n c e a l o n g t h e d e m i n e r a l i z a t i o n path using semi-log s c a l e C = 2000 ppm, Exp. M3B, M3F and M3G  268  84  q  85  86 87  Q  88  89  Q  xviii  Figure  90  91 92 93  Page  E q u i v a l e n t conductance o f aqueous sodium c h l o r i d e s o l u t i o n s a t 25°C  276  D i f f u s i v i t y o f aqueous sodium c h l o r i d e a t 25°C  277  D i s c r e p a n c y between p r e d i c t e d an ED s t a g e  solutions  and measured v a l u e o f  V a r i a t i o n o f a p p a r e n t r e s i s t a n c e o f an ED s t a g e w i t h the r e c i p r o c a l o f t h e a v e r a g e p r o d u c t c o n c e n t r a t i o n  xix  , , .  281  . .  283  ACKNOWLEDGEMENT  I w i s h t o thank Dr. D.W. investigation  Thompson, under whose d i r e c t i o n  this  was u n d e r t a k e n , 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 i d e a s and  encouragement i n a l l s t a g e s o f t h i s work.  A l s o t h a n k s a r e due t o t h e  f a c u l t y and s t a f f o f C h e m i c a l E n g i n e e r i n g Department o f t h e U n i v e r s i t y o f 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 c o - o p e r a t i o n these  throughout  years. H i g h l y a p p r e c i a t e d i s t h e a s s i s t a n c e o f f e r e d and t h e work performed  by t h e p e r s o n n e l  o f t h e Workshop and t h e S t o r e s o f t h e same department .  A l s o I am i n d e b t e d  t o t h e s t a f f o f t h e U.B.C. M a i n L i b r a r y and t h e 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 b o r r o w i n g u s e f u l m a t e r i a l s from o t h e r l i b r a r i e s . I am most g r a t e f u l pages o f s t r a n g e  t o Ms. Jane Winn f o r h e r e x p e r t t y p i n g o f c o u n t l e s s  symbols.  F u r t h e r t h a n k s a r e due t o t h e N a t i o n a l R e s e a r c h 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 e x p r e s s my g r a t i t u d e t o 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 s u p p o r t  t h r o u g h o u t 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 t h e most i m p o r t a n t c h e m i c a l compound on E a r t h ,  When  men  s e t t l e d down t o a g r i c u l t u r e and f a r m i n g , t h e y b u i l t t h e i r houses near p o t a b l e water r e s o u r c e s , 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  of s e t t l e m e n t s augmented t h e needs o f f r e s h water s u p p l y . minimum water r e q u i r e m e n t s ,  The  size  theoretical  i n c l u d i n g a g r i c u l t u r e , t o s u s t a i n human l i f e  3 a r e about 1.1 m alone.  The  per p e r s o n per day, assuming t h a t man  i n t r o d u c t i o n of 0.5  can l i v e on  broad  kg o f a n i m a l 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 per day  ( B r a d l e y , 1962).  f o r s u b s i s t e n c e t o about 9.5  m  I n c r e a s i n g demand f o r water caused by  pet  person  the r i s i n g  s t a n d a r d of l i v i n g and by t h e 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 r e s e r v e s w i t h i n d u s t r i a l waste and  sewage, have b r o u g h t many r e g i o n s i n  v a r i o u s c o u n t r i e s c l o s e t o t h e c r i t i c a l p o i n t where e x i s t i n g r e s o u r c e s no l o n g e r s a t i s f y t h e growing  demand.  The  can  s i t u a t i o n w i l l become worse i f  adequate means a r e not adopted i n t i m e . A l t h o u g h t h e a n n u a l p r e c i p i t a t i o n on E a r t h ' s s u r f a c e might  be  s u f f i c i e n t , t h e 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 t h e human needs i n a l l r e g i o n s o f the w o r l d .  In s e v e r a l a r i d a r e a s , e x i s t i n g water  r e s o u r c e s a r e s a l i n e , exceeding, t h e l i m i t of p o t a b l e w a t e r w h i c h i s s e t as 1  2  500 mg/1  for total dissolved solids.  A c t u a l l y t h e r e a r e 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 o v e r  1000 mg/1  sometimes up t o 3000 mg/1.  t o t a l d i s s o l v e d s o l i d s and  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  economically  f e a s i b l e and  such as e l e c t r o d i a l y s i s . only p a r t i a l success  For  such  by d i s t i l l a t i o n i s not  e f f o r t s have been made t o r e s o r t to o t h e r  processes  However, 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 has  achieved  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 t h e o -  r e t i c a l advantages i t o f f e r s o v e r o t h e r p r o c e s s e s .  Under s t e a d y  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 s u b j e c t t o mud on t h e membrane s u r f a c e s w h i c h may membranes, t h u s d e c r e a s i n g  The d e p o s i t  i n c r e a s i n g pumping c o s t , and may  and damage t h e membranes, r e d u c i n g s e p a r a t i o n (Matz, 1965  scale build-up  h i n d e r t h e t r a n s f e r of i o n s t h r o u g h t h e  t h e c a p a c i t y of the u n i t .  p a r t i a l l y block flow channels,  and  state  the s e l e c t i v i t y and  and K o r n g o l d ,  may  react with  e f f i c i e n c y of  the  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 t o r e d u c e 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, e t a l . , 1962;  Calvit  S l o a n , 1965).  1968)  Based on c u r r e n t r e v e r s a l t e c h n i q u e , L a c e y (1965,  and  i n v e n t e d an e l e c t r o s o r p t i o n s t a c k of much s i m p l e r c o n s t r u c t i o n t h a n conventional e l e c t r o d i a l y s i s stacks.  E l e c t r o s o r p t i o n can be c o n s i d e r e d as a  one-cycle process without r e f l u x .  T h i s i d e a was  further modified  and  d e v e l o p e d 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 stack.  t o 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  The  p r o c e s s has a wide f i e l d o f p o t e n t i a l a p p l i c a t i o n s such a s :  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  ii)  B r i n e p r o d u c t i o n f r o m sea w a t e r  iii) iv) polyvalent v)  R a d i o a c t i v e waste  decontamination  S e l e c t i v e s e p a r a t i o n o f monovalent s a l t f r o m d i v a l e n t and salts I n t h e f o o d 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 o f orange j u i c e and o f s u g a r s and vi)  other  treatment  (mainly de-ashing)  s y r u p s and r e l a t e d compounds  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 t h e f o o d i n d u s t r y c o n c e r n  the treatment  o f 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 , w a s t e p i c k l e - l i q u o r  and w a s t e s u l f i t e - l i q u o r  recovery  recovery.  A l t h o u g h c y c l i c e l e c t r o d i a l y s i s may conversion of b r a c k i s h waters  be most e c o n o m i c a l  (up t o 10,000 ppm)  f o r the  t o p o t a b l e water o f 500  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 o t h e r s i t u a t i o n s when the c o u l d become u n e x p e c t e d l y  economical.  ppm,  process  F o r example, t h e r e seems t o 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 t h e tourist resorts.  I n t h e s e c a s e s , t h e a m o r t i s a t i o n and  t o be v e r y h i g h and  2-5  m /h s c a l e f o r  i n t e r e s t charges  tend  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 a p p e a r s t h a t the p r o c e s s may  t h e most i m p o r t a n t f a c t o r , and i t  p r o v i d e the cheapest  c a p i t a l p l a n t f o r meeting  t h e s e r e q u i r e m e n t s , a l t h o u g h , a t t h i s s a l i n i t y l e v e l , t h e power c o s t of c y c l i c e l e c t r o d i a l y s i s would be h i g h e r than t h e o t h e r 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 r e p o r t e d f o r most o f t h e w i t h aqueous sodium c h l o r i d e s o l u t i o n s ( B a s s , 1972).  runs  The p r e s e n t work i s  an e x t e n s i o n of the p r e v i o u s work to an open system w h i c h r e p r e s e n t s a more u s e f u l mode o f o p e r a t i o n .  The main o b j e c t i v e s a r e to a n a l y z e t h e  o f t h e c y c l i c p r o c e s s on a c o n t i n u o u s b a s i s and  potential  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  t h e e f f e c t of t h e v a r i o u s d e s i g n and o p e r a t i n g p a r a m e t e r s on the performance of the process.  The p r e s e n t program makes a r a t h e r e x t e n s i v e study  and  e x p l o r a t i o n of t h e system w i t h i n the d e s i g n parameters and i t p r o v i d e s i n f o r m a t i o n t h a t s h o u l d be u s e f u l i n f u r t h e r s t u d y 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 t e c h n i q u e s p o t e n t i a l l y u s e f u l a s commercial  separation pro-  c e s s e s may be c l a s s i f i e d i n t o two g e n e r a l c a t e g o r i e s , a s shown i n T a b l e I;; a)  P r o c e s s e s t h a t remove pure water from  b)  P r o c e s s e s t h a t remove s a l t s from  solution  solution  The most developed p r o c e s s i n c a t e g o r y (a) i s d i s t i l l a t i o n .  Freezing  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.  R e v e r s e o s m o s i s , a f t e r a l o n g p e r i o d o f membrane  development, i s e n t e r i n g t h e f i e l d o f c o m m e r c i a l o p e r a t i o n . The l a t e n t heat f o r c h a n g i n g phase i s an i m p o r t a n t f a c t o r i n t h e o v e r a l l economics o f d i s t i l l a t i o n p r o c e s s e s w h i l e t h e degree o f s a l i n i t y o f t h e raw water i s o f l i t t l e i m p o r t a n c e .  This process i s therefore 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 o r b r a c k i s h w a t e r . freezing.  The same a p p l i e s f o r  However, t h e f e e d c o n c e n t r a t i o n i s i m p o r t a n t i n r e v e r s e o s m o s i s ,  as t h e r e q u i r e d c o u n t e r p r e s s u r e depends g r e a t l y upon t h e s a l t c o n t e n t o f t h e raw w a t e r . The most d e v e l o p e d p r o c e s s i n c a t e g o r y (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 o f t h e s e p r o c e s s e s  depends c l o s e l y on t h e s a l t c o n t e n t o f t h e raw w a t e r , w h i c h d e t e r m i n e s t h e amount o f e l e c t r i c power r e q u i r e d , o r t h e consumption 5  o f c h e m i c a l s needed  6  Table I  C l a s s i f i c a t i o n of M a i n D e s a l i n a t i o n P r o c e s s e s  Processes that Separate Water from S o l u t i o n 1.  Distillation  S a l t s from S o l u t i o n 1.  V e r t i c a l tube e v a p o r a t o r H o r i z o n t a l tube e v a p o r a t o r Multi-stage f l a s h evaporator Vapor c o m p r e s s i o n Solar evaporation  2.  R e v e r s e osmosis  Ionic processes Ion exchange Electrodialysis Transport d e p l e t i o n Osmionic Piezodialysis Electrochemical B i o l o g i c a l Systems  2.  Other p r o c e s s e s Liquid-liquid  3.  Crystallization Freezing Hydrate formation  extraction  7  for  the regeneration of the r e s i n s .  Hence, t h e s e p r o c e s s e s a r e 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. T a b l e I I shows t h e number and c a p a c i t y o f p l a n t s by p r o c e s s and by geographic l o c a t i o n .  (0 Shaughnessy, 1  1973).  Multi-stage f l a s h evaporation  a c c o u n t s f o r 65% o f t h e t o t a l c a p a c i t y o f t h e 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 a r e the i s l a n d s i n the C a r i b b e a n Sea, and t h e M i d d l e E a s t , i n c l u d i n g c o u n t r i e s around  the Persian  Gulf. A l i s t i n g o f most e l e c t r o d i a l y s i s p l a n t s h a v i n g a c a p a c i t y o f 100,000 gpd o r more i s g i v e n i n T a b l e I I I .  I t has a l s o been r e p o r t e d t h a t a p p r o x i -  m a t e l y 300 e l e c t r o d i a l y s i s p l a n t s have been c o n s t r u c t e d and i n s t a l l e d i n t h e U.S.S.R.  2.2.  (Lynch and M i n t z , 1972). 0  Some Economic A s p e c t s o f S e l e c t i v e and State-Change  Processes  S e l e c t i v e p r o c e s s e s such a s e l e c t r o d i a l y s i s a c h i e v e s e p a r a t i o n w i t h o u t a change o f phase o f any component i n t h e system.  Such p r o c e s s e s have  e c o n o m i c a l advantages o v e r s t a t e - c h a n g e p r o c e s s e s such a s d i s t i l l a t i o n and freezing. The methods o f s e p a r a t i o n t h a t r e l y on a change o f s t a t e i n v o l v e a h i g h r a t e o f energy c i r c u l a t i o n i n t h e system, because t h e heat o f f u s i o n or v a p o r i z a t i o n o f t h e s o l v e n t must be s u p p l i e d .  In general, this  energy  i s many t i m e s l a r g e r t h a n t h e energy t h e o r e t i c a l l y needed t o s e p a r a t e t h e s a l t from t h e s o l v e n t ;  and t h e energy r e q u i r e d f o r v a p o r i z a t i o n o r f u s i o n  must be r e c o v e r e d and r e u s e d t o make such p r o c e s s e s 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 t o be p r o p o r t i o n a l t o t h e energy  Table I I T o t a l number and c a p a c i t y of d e s a l t i n g plants exceeding 25000 gpd (95 m /day)* P = p l a n t s number; a = data i n 1000 m /day; b = data i n Mgd. 3  Geographic Location  Total d i s t i l l a t i o n plants P  United States ... U.S. T e r r i t o r i e s N. America except South America ... Caribbean  a  Electrodial s i s ^ P  b  281 16  161.7 47.8  42.7 12.6  13 24  32.5 18.5  a  Reverse Osmosis  b  15  21.6  5.7  8.6 4.9  2  1.9  0.5  P  a  Freezing Processes b  24  9.1 2.4  1  1.1 0.3  37  99.2  26.2  1  0.1  0.1  1  1.1 0.3  Europe C o n t i n e n t a l ... England and  102  174.9  46.3  12  16.3  4.3  2  0.2 0.1  U*S«S*K* ••••••••  63 12 29  59.8 111.7 21.2  15.8 29.5 5.5  1 1  0.1 0.1  77 55 5  405.0 107.0 92.8 24.5 1.2 4.5  18 10 1  Middle East and Persian Gulf ..  Total Plants  714  8.7 22.0 0.1  T o t a l 1000 m /day  2.3 5.8 0  4  3.4 0.9  1  0.1 0  33  93.36 * From O'Shaughnessy, F.' , " D e s a l t i n g Plant Inventory  5.38  %  192.7 48.1  50.9 12.7  14.63 3.65  1  0.4 0.1  14 27  33.6 20.8  8.9 5.5  2.56 1.58  39  100.4  26.6  7.65  117  191.8  50.8  14.60  64 13 33  59.9 111.8 24.6  15.8 29.5 6.4  4.54 8.48 1.84  96 65 6  413.8 109.3 114.8 30.3 4.6 1.2  31.41 8.71 0.34  1  0.4 0.1  812 0.4  347.9 1316.9  0.49 1.15  b  321 17  1.4  4.06  a  0.3 0.1 0.3 0.1  15.0  • 7.51  P  1 1  4.0  70.8  87.93  b  4  18.7  1229.7  a  0 0  61 324.8  3  P  Total desalination plant c a p a c i t y  100.0 0.11  100.0  Kept. No. 4 (1973), ed. by the U.S. O f f i c e of Saline Water.  100.0  T a b l e I I I L a r g e 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*  Plant  Location  Brindisi, Italy Buckeye, A r i z . Pantelleria, Italy S i e s t a Key, F l a . Aramco, Dhahran, S a u d i A r a b i a B a h r a i n P e t r o l e u m Co., B a h r a i n , Persian Gulf Anaconda Copper Co., C h i l e I n d u s t r i a l Co., Tex. Automobile Factory, B a r i , I t a l y U.S. Army N.M. A l S a u d i Co., A l Khobar, S a u d i A r a b i a G i l l e t t e , Wyo. P o r t M a n s f i e l d , Tex. Ras G h a r i b , Egypt E l Adem, L i b y a Bahrain Hospita, Bahrain Benghazi, Libya M o s h a b e i , Sadeh, I s r a e l Heinekens Brewery, Rotterdam, Netherlands Z l i t e n , Libya K a z a k s t a n , U.S.S.R.  Feedwater Salinity ppm  Manufacturer  1971 1962 1971 1969 1961  2,000 2,200 4,500 1,300 2,700  Ionics Ionics Ionics Ionics Ionics  1,300,000 650,000 265,000 1,500,000 115,000  1964 1970 1969 1970 1970 1967 1971 1965 1971 1971 1971 Under c o n s t r u c t i o n 1971  3,150 2,200 2,500 2,000 3,100 2,800 2,500 2,400  Ionics Ionics Ionics Ionics Ionics Ionics Ionics Ionics Ionics Ionics Ionics Wm. Boby Co. Tahal Consulting Engineers  100,000 265,000 880,000 530,000 100,000 100,000 1,500,000 265,000 113,000 170,000 105,000 5,000,000 1,250,000  A c t u a l o r Planned Year o f S t a r t - u p  Under  1968 1968 construction  * From Lynch and M i n t z , J . Am. Water, 64^, 711 (1972)  2,000 2,300  1,100 4,400  Wm. Boby Co. Wm. Boby Co. Unknown  Capacity  177,000 105,000 500,000  10  circulation;  and,  t o a f i r s t a p p r o x i m a t i o n a t l e a s t , the  energy needed  o p e r a t e 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 v a p o r i z a t i o n of the  s o l v e n t and  ( S h a f f e r & M i n t z , 1966). selective  On  the  independent of the amount of  to  of  solute present  o t h e r hand, p r o c e s s e s t h a t a r e based, on  t r a n s p o r t r e q u i r e energy a t a r a t e t h a t v a r i e s  w i t h the  theoretical  minimum energy ( H e l m h o l t z f r e e energy) needed to produce a d e s a l t e d  and  c o n c e n t r a t e d stream from a s a l i n e f e e d water i . e . w h i l e the  does  affect  the p r a c t i c a l energy r e q u i r e m e n t s f o r a p r o c e s s such as  i t does make a g r e a t d e a l of d i f f e r e n c e For  salinity  further  desalting  d i s c u s s i o n on t h e o r e t i c a l and  p r o c e s s r e f e r t o Appendix  The  t o a p r o c e s s such as  energy l o s s e s i n the  actual  distillation,  electrodialysis.  energy r e q u i r e m e n t s f o r  selective  forces,  of s u b s t a n t i a l  w h i c h would cause the The  F i g u r e 1,  net  r e s u l t of  t r a n s p o r t systems a r i s e  d r i v i n g f o r c e s i n s t e a d of  primarily  t h e s e c o n s i d e r a t i o n s can  r e q u i r e d f o r d i s t i l l a t i o n and ments a t v a r i o u s s a l i n i t i e s  b e s t be  w h i c h compares the  and  f i x e d blowdown and  reverr.ibly.  seen by  energies  e l e c t r o d i a l y s i s w i t h the  thus  infinitesimal  p r o c e s s e s to t a k e p l a c e s l o w l y and  ( S h a f f e r & M i n r z , 1966)  theoretical  product  require-  specifications. de-  h i g h - s a l i n i t y w a t e r s 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 w a t e r s up  2.3.  examining  actually  A c c o r d i n g t o t h i s graph d i s t i l l a t i o n i s more e c o n o m i c a l f o r mineralizing  a  F.  as a r e s u l t o f 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 ; n e c e s s i t a t e s the use  not  to about 10,000  ppm.  Electrodialysis  Electrodialysis  i s a selective  p a r t i a l s e p a r a t i o n of the e l e c t r i c current.  The  transport process, i n which  components of an i o n i c s o l u t i o n  the  i s i n d u c e d by  s e p a r a t i o n i s a c c o m p l i s h e d by p l a c i n g  ion  an  selective  11  2,000  4,000 FEED  10,000 PPM  20,000  40,000  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 - 0 0 5 - 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 a c r o s s t h e p a t h o f t h e c u r r e n t f l o w .  The p r o c e s s  t a k e s advantage  of t h e a b i l i t y o f t h e membranes t o 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 i o n s and t h e o r i g i n o f 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 t h a t a r e permeable t o i o n s (e.g. a r e used i n e l e c t r o d i a l y s i s p r o c e s s e s , non-electrolytes.  cellophane)  e l e c t r o l y t e s c a n be s e p a r a t e d  from  On t h e o t h e r hand, w i t h membranes t h a t a r e more permeable  t o u n i v a l e n t i o n s t h a n t o 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 c a n be used to simultaneously  s e p a r a t e and c o n c e n t r a t e u n i v a l e n t i o n s f r o m s o l u t i o n s  c o n t a i n i n g m i x t u r e s o f 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 e l e c t r o c h e m i c a l processes reactions.  from t h e g r e a t m a j o r i t y o f  i n t h a t i t does n o t u t i l i z e t h e e l e c t r o d e  E l e c t r o d e s do, o f c o u r s e , have t o be i n c 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 , b u t they s e r v e t h e p u r e l y a n c i l l a r y purpose o f a p p l y i n g the EMF.  They a r e i n f a c t a n e c e s s a r y  e v i l , s i n c e they i n v o l v e a g r e a t  d e a l o f e x t r a c o m p l i c a t i o n i n t h e d e s i g n and o p e r a t i o n o f t h e p l a n t . A p i o n e e r book on e l e c t r o d i a l y s i s , e d i t e d by W i l s o n  (1960),  describes  t h e p r o c e s s and t h e u s e o f i o n exchange membranes i n water d e s a l t i n g . C h a p t e r s i n books by Tuwiner (1962), S p i e g l e r (1962, 1966 a ) , Sporn Popkin  (1966),  (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 m a i n l y a s a  d e s a l i n a t i o n process. of the process  L a c e y and Loeb (1972) c o n s i d e r v a r i o u s a p p l i c a t i o n s  such a s c o n c e n t r a t i o n o f 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 ,  p r o c e s s i n g o f cheese whey and r e c o v e r y o f c o n s t i t u e n t s f r o m p u l p i n g R e c e n t l y Hwang and Kammermeyer (1975) have r e v i e w e d The  liquors.  the process.  e l e c t r o d i a l y s i s p r o c e s s u s e s c e l l s c o n s i s t i n g o f many ( a t l e a s t  t h r e e ) compartments formed a l t e r n a t i v e l y by an a n i o n exchange membrane and a c a t i o n exchange membrane p l a c e d between a n anode and a c a t h o d e a s shown i n F i g u r e 2.  Demineralized Water  A j  Electrode Reaction  *  .•MA  H  t  1  *  c  ?  ?  ?  O  2  Cathode  Concentrate Brine Cone Electrode ^ Reaction .9 Products ° 0 , ci 2  O  O  O  O  r\  o  $0  I  - Anode ° I +-  o"  o  Raw Water Feed  —  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.  2  14  The s a l i n e water f e e d i s pumped t h r o u g h t h e compartments o f t h e membrane s t a c k a n d , 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 . m i g r a t e toward t h e cathode and a n i o n s m i g r a t e toward t h e anode.  Cations  pass e a s i l y t h r o u g h t h e c a t i o n - p e r m e a b l e membrane and a r e b l o c k e d f r o m f u r t h e r t r a n s f e r by t h e anion-permeable f r e e passage t h r o u g h t h e anion-permeable c a t i o n permeable membrane.  membrane.  S i m i l a r l y , a n i o n s have  membrane and a r e stopped a t t h e  As a r e s u l t t h e a d j a c e n t 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 o f a membrane s t a c k a r e : (a)  a l a r g e number o f i o n - p e r m e a b l e membranes a r r a n g e d i n t h e correct order.  (b)  g a s k e t s and s p a c e r s t o p r o v i d e s e a l i n g between compartments and t o m a i n t a i n p r o p e r d i s t a n c e s between membranes.  (c)  m a n i f o l d systems t o d i r e c t f e e d , p r o d u c t and w a s t e  streams  i n t o and o u t o f t h e compartments w i t h o u t l e a k a g e . (d)  e l e c t r o d e s and c o n d u c t o r s .  (e)  a p a i r o f s t r o n g p r e s s e s t o h o l d t h e above-mentioned  parts i n  place. 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 s t a c k s a r e n o r m a l l y assembled  i n the  same f a s h i o n a s a p l a t e - a n d - f r a m e f i l t e r p r e s s ( F i g u r e 3 ) . In a d d i t i o n t o the s t a c k , which i s the a c t u a l p a r t that e f f e c t s t h e desalination, electrodialysis plants consist of: 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 s u p p l y , c o n c e n t r a t e d i s p o s a l .  FIGURE 3 Exploded view of components In an electromembrane  stack.  16  II  A power s u p p l y w i t h t r a n s f o r m e r s 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.  S t a c k S i z e and C a p a c i t y (i)  Cell  size  E l e c t r o d i a l y s i s c e l l d i m e n s i o n s a r e l i m i t e d o n l y by t h e a v a i l a b i l i t y o f s u i t a b l y s i z e d membrane s h e e t s and t h e p r a c t i c a b i l i t y o f h a n d l i n g t h e g a s k e t s and membrane m a t e r i a l s ,  Weiner and c o - w o r k e r s a t t h e U n i v e r s i t y o f  C a l i f o r n i a have d e v e l o p e d a 1 0 - f o o t - l o n g  stack t o study p o l a r i z a t i o n e f f e c t s  (Weiner, e t a l . , 1964). I n o r d e r t o i n c r e a s e d e s a l i n a t i o n and t o r e d u c e o p e r a t i n g c o s t s , t h e a r e a o f each c e l l - p a i r s h o u l d be a s l a r g e a s p r a c t i c a b l e .  One o f t h e s i z e  l i m i t a t i o n s i s t h e f a c t t h a t membrane s t a c k s n e e d , a t p e r i o d i c i n t e r v a l s , to be d i s m a n t l e d I t i s necessary  i n o r d e r t o 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 . t h a t t h e s t a c k s h o u l d be r e l a t i v e l y s m a l l i n o r d e r t o be  conveniently handled.  I n a d d i t i o n , l a r g e s i z e membranes w h i c h a r e g e n e r a l l y  m e c h a n i c a l l y weak, tend t o t e a r and b r e a k more r e a d i l y d u r i n g  handling.  The p r a c t i c e t o d a y i s t o l i m i t t h e u n i t s u r f a c e a r e a t o a maximum of 2 about 2m  (2 by 1 m e t e r ) , and t o d e s i g n t h e s t a c k s t o c o m p r i s e a number o f  r e l a t i v e l y small sub-units to f a c i l i t a t e handling.  The l a r g e s t c e l l i n  c o m m e r c i a l u s e up t o 1974 was 150 x 50 cm. (ii)  Number o f C e l l P a i r s  A c e l l p a i r i s t h e 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 s t a c k .  It  c o n s i s t s o f 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 t o g e t h e r w i t h a c a t i o n - and an a n i o n - p e r m e a b l e membrane. The number o f c e l l s i n a s t a c k i s m a i n l y l i m i t e d by e n g i n e e r i n g c o n s i d e r a t i o n s such a s :  17  (a)  t h e t o t a l v o l t a g e t h a t c a n be s a f e l y a p p l i e d ,  (b)  t h e s i z e of t h e m a n i f o l d i n t o each f l o w  t h a t can d i s t r i b u t e f l o w  evenly  channel,  (c)  the s t r u c t u r a l s t a b i l i t y of the stack,  (d)  t h e ease o f assembly and r e p a i r .  S i n c e t h e f a i l u r e o f a s i n g l e membrane c a n i m p a i r s t a c k p e r f o r m a n c e , the number o f membranes i n a s t a c k i s l i m i t e d by t h e l i f e o r r e l i a b i l i t y o f the membranes and t h e a n t i c i p a t e d f r e q u e n c y  of o t h e r s e r v i c e  requirements.  The r e q u i r e m e n t s f o r s t a g i n g a l s o make i t d e s i r a b l e i n some c a s e s t o 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 t h a n one l a r g e one.  Usually several small  s u b a s s e m b l i e s o r " p a c k s " 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 a r e then used a s t h e 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.  required size. press.  As many as 10 o f t h e s e p a c k s c a n be p l a c e d i n t o a s i n g l e  A s i n g l e s e t o f e l e c t r o d e s may be used f o r t h e e n t i r e a s s e m b l y ,  or s e v e r a l e l e c t r o d e s may be used t o p r o v i d e e l e c t r i c a l s t a g i n g . (iii)  Stack  Capacity  The d e s i r e d p r o d u c t  s a l i n i t y i s a c h i e v e d by p a s s i n g t h e f e e d  liquid  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 o b t a i n e d by o p 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 p a t h s i n p a r a l l e l . The l a r g e s t s t a c k s i n o p e r a t i o n i n 1970 h a n d l e d d i l u t e f l o w s o f about 250,000 g a l / d a y .  F o r 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 t h e s e  s t a c k s was p l a n n e d , r a t h e r t h a n s c a l e - u p o f 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 t h e world i s i n Benghazi, L i b y a , cons t r u c t e d by W i l l i a m Boby and Company, E n g l a n d a f t e r 1972.  I t has a  p r o d u c t i o n c a p a c i t y o f 5 x 10^ g a l / d a y a s shown i n T a b l e I V .  The p l a n t h a s  16 p a r a l l e l t r a i n s each o f 2 s t a c k s i n s e r i e s , each s t a c k w i t h a c a p a c i t y o f about 310,000 g a l / d a y .  18  T a b l e IV  T e c h n i c a l d e t a i l s o f B e n g h a z i ( L i b y a ) 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  3  800  Rated o u t p u t , m /h n e t Waste w a t e r , % o f o u t p u t Raw w a t e r , ppm t o t a l d i s s o l v e d Number o f p a r a l l e l  trains  188  pairs 2  T o t a l membrane a r e a , m  310  8  17  2,000  1,300  16  12  7 2  2  Stacks/train T o t a l number of c e l l  solids  S i e s t a Key Stage 1 Stage 2  9,600  4,200  7,200  15,000  3,900  6,700  * From S o l t , Chap. 12 i n Kuhn ( e d . ) , " 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 P r o c e s s e s "  19  2.4.  Membrane T e c h n o l o g y  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 . I o n exchange r e s i n s c o n s i s t o f two p r i n c i p a l p a r t s :  a structural  p o r t i o n o r a backbone (a polymer m a t r i x ) and a f u n c t i o n a l p o r t i o n o r an i o n - a c t i v e group.  The s y n t h e s i s o f an o r g a n i c  ion-exchanger i n v o l v e s the  c h e m i c a l s u b s t i t u t i o n o f 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 The  s u b s t i t u t i o n may p r e c e d e t h e p o l y m e r i z a t i o n  reaction.  or vice-versa.  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 u s e a r e based on synthetic r e s i n s , usually polystyrene with divinylbenzene cross l i n k i n g .  [C^H^ ( C l ^ C l ^ ^ ]  [RO - (CH^ -  t o  provide  C  H  )  n  ~  0 R  ] copolymerized  t h e r e q u i s i t e amount o f  The f u n c t i o n a l group may be a c i d i c o r b a s i c w i t h d i f f e r e n t  degree o f s t r e n g t h o f a c i d i t y o r b a s i c i t y . Strongly-acid  ( 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 ammonium groups f i x e d t o 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  matrix  quaternary  (Pepper, e t a l , ,  1953). Some i o n - e x c h a n g e membranes a r e made by m i x i n g i o n - e x c h a n g e r e s i n s with a polymeric binder  and c a s t i n g o r e x t r u d i n g a sheet f r o m t h e m i x t u r e ,  w h i l e o t h e r s a r e manufactured by methods t h a t e x a c t l y p a r a l l e l t h e p r o d u c t i o n of ion-exchange r e s i n s - i . e . s t y r e n e and d i v i n y l b e n z e n e  are copolymerized  i n sheet f o r m , and t h e r e s u l t i n g s t r u c t u r e i s t h e n c h e m i c a l l y g i v e t h e sheet ion-exchange p r o p e r t i e s .  treated to  The d e t a i l s o f methods f o r making  ion-exchange membranes have been r e v i e w e d by W i l s o n ( 1 9 6 0 ) , F r i e d l a n d e r and  20  R i c k l e s (1966), Lacey (1973).  (1972), C h i o l l e , e t a l . (1973) and L a s k o r i n , e t a l ,  An e x c e l l e n t summary o f p r e p a r a t i v e methods found i n t h e U.S.  P a t e n t l i t e r a t u r e i s g i v e n by McDermott (1972). An i n d u s t r i a l l y u s e f u l membrane s h o u l d have t h e f o l l o w i n g 1.  properties:  H i g h i o n s e l e c t i v i t y - c a t i o n - p e r m e a b l e membranes s h o u l d  e x c l u d e t h e passage o f a n i o n s , 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 c o u n t e r -  i o n s t h r o u g h t h e membranes a t l o w energy 3.  requirements.  High mechanical s t r e n g t h - toughness, f l e x i b i l i t y ,  and c r a c k  r e s i s t a n c e a r e i m p o r t a n t , n o t o n l y t o t h e s e r v i c e l i f e o f t h e membrane, b u t 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 plants. 4.  H i g h c h e m i c a l 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  o t h e r forms o f d e g r a d a t i o n . 5.  R e 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 p l u g g i n g by l a r g e  p o l y v a l e n t o r g a n i c i o n s p r e s e n t i n t h e s o l u t i o n s t o be t r e a t e d . The p r o p e r t i e s o f a number o f c o m m e r c i a l l y a v a i l a b l e  ion-exchange  membranes have been t a b u l a t e d by S h a f f e r and M i n t z (1966) and Lacey and Loeb (1972). A b i b l i o g r a p h y on membrane t e c h n o l o g y , p e r t a i n i n g t o s a l i n e  water  d e s a l i n a t i o n and r a n g i n g from 1908 t o 1962 has been c o m p i l e d by t h e O f f i c e of  S a l i n e Water (Mangan, e t a l . , 1963).  A comprehensive  review of the  p h y s i c a l c h e m i s t r y o f i o n - s e l e c t i v e membranes has been g i v e n by Malherbe and M a n d e r s l o o t  (1960).  21  2.4.1.  Membrane S e l e c t i v i t y One o f t h e b a s i c c h a r a c t e r i s t i c s o f an ion-exchange membrane i s t h e  s e l e c t i v i t y , which i s defined  a s t h e a b i l i t y o f t h e membrane t o d i s t i n g u i s h  between o p p o s i t e l y charged s p e c i e s counter-ions  l e a d i n g t o t h e p r e f e r e n t i a l uptake of  and e x c l u s i o n o f c o - i o n s .  mobile ions possessing  C o u n t e r - i o n s and c o - i o n s a r e t h e  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  t o t h e 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 cations i n s o l u t i o n w i l l enter  i n t o t h e r e s i n m a t r i x and  r e p l a c e the c a t i o n s p r e s e n t , but anions a r e prevented from e n t e r i n g the m a t r i x by t h e r e p u l s i o n o f t h e a n i o n s a f f i x e d t o t h e r e s i n .  The  opposite  phenomena t a k e s p l a c e when an a n i o n s e l e c t i v e membrane i s immersed i n an electrolyte solution;  t h e f i x e d c a t i o n i c groups p e r m i t i n t r u s i o n and  exchange o f a n i o n s from an e x t e r n a l s o u r c e , b u t e x c l u d e c a t i o n s .  This  t y p e o f 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)  Permselectivity  S e l e c t i v i t y i s usually reported i s the increase  i n terms o f p e r m s e l e c t i v i t y , P, w h i c h  i n t r a n s p o r t number o v e r t h e v a l u e i n f r e e s o l u t i o n due t o  the p r e s e n c e o f t h e membrane and i t i s g i v e n b y :  P  ~  t - J: 1 - t  (1)  where: t , t = t r a n s p o r t numbers o f c o u n t e r - i o n s  i n membrane and i n f r e e  solution respectively ( t - t ) = i n c r e a s e i n t r a n s p o r t number o v e r t h e v a l u e i n f r e e s o l u t i o n  22  ( 1 - t ) = t h e maximum p o s s i b l e i n c r e a s e o r t h e i n c r e a s e  t h a t would be  o b s e r v e d i n t h e c a s e o f an i d e a l l y s e l e c t i v e membrane, B o t h p and t a r e f u n c t i o n s o f c o n c e n t r a t i o n . external e l e c t r o l y t e concentration (ii)  increases  They d e c r e a s e as t h e  a s shown i n F i g u r e  4.  Donnan E x c l u s i o n  A c c o r d i n g t o t h e Donnan p r i n c i p l e t h e c h e m i c a l p o t e n t i a l o f t h e s a l t i n t h e s o l u t i o n e x t e r n a l t o t h e membrane must be e q u a l t o t h e c h e m i c a l p o t e n t i a l o f t h e s a l t i n s i d e t h e membrane, i . e . RT I n a  2 +  =  -2 vAp + RT I n a ^  (2)  where: a ,  a  +  +  a r e t h e 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 Ap  i s t h e p a r t i a l m o l a r volume, cm /mole i s t h e d i f f e r e n c e i n i n t e r n a l p r e s s u r e between t h e memb r a n e and t h e s o l u t i o n phase c a l l e d t h e " s w e l l i n g  pressure"  o f t h e membrane The  p r e s s u r e - v o l u m e t e r m a r i s e s from t h e f r e e energy change due t o t h e  d i f f e r e n c e between t h e o s m o t i c p r e s s u r e o f t h e s o l u t i o n s i n s i d e and o u t s i d e t h e membrane ( W i l s o n , 1960).  I n t h e absence o f l a r g e p r e s s u r e d i f f e r e n c e s  between t h e i n t e r i o r and t h e e x t e r n a l phase, t h e Donnan p r i n c i p l e r e q u i r e s that: (a ) +  where:  . (a_)  =  (a ) +  . (a_)  (3)  FIGURE 4 Dependence of counterion transport numbers and permselectivity upon external concentration. (Wilson , I960 ).  24  a  are the i o n i c  +  activities  v's a r e t h e 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+ vand t h e b a r r e d symbols r e f e r t o t h e membrane phase. F o r 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) r e d u c e s t o :  where y  +  i s t h e 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 e f i n e d g e n e r a l l y a s Y+  where v = v  -  Y+  + v-;  +  +  • Y^ •  (5)  s u b s c r i p t s j and k r e f e r t o c o - i o n and c o u n t e r - i o n r e s -  pectively. S i n c e b o t h t h e s o l u t i o n and t h e membrane must be e l e c t r i c a l l y n e u t r a l , this requires that: I n membrane;  C, = C. + C k j x  (6)  In solution;  C  (7)  k  = C = C J  where C i s t h e f i x e d i o n c o n c e n t r a t i o n i n t h e membrane, x S u b s t i t u t e E q s . ( 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 concentrations: C. C. J k Assume  C. + C  3  c  J  =  C. (C. + C ) 3 3 x =  x f r  C  x  (8)  then  2  ( 9 )  x  Eq.(9) shows how t h e s e l e c t i v i t y o f a membrane i s a f f e c t e d i n o p p o s i t e d i r e c t i o n s by t h e 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 t h e f i x e d - i o n s conc e n t r a t i o n i n t h e membrane, C . The h i g h e r t h e c o n c e n t r a t i o n o f f i x e d i o n s , x the g r e a t e r t h e s e l e c t i v i t y (C\. -> o a s C* ->• ») w h i l e (C. C as C ->• C^) . x  25  I n a t y p i c a l e l e c t r o d i a l y s i s system, t h e c o n c e n t r a t i o n o u t s i d e t h e membrane may range from 0.001 t o 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 t o make t h e m o l a l i t y i n s i d e t h e membrane f a l l i n t h e r a n g e 1 t o 5 m . -7 i n g l y Eq.(9) g u a r a n t e e s t h a t 2 x 10  < C.. < 10  Accord-  -2 ( S h a f f e r and M i n t z , 1966).  From Eq.(9) i t i s c l e a r t h a t t h e c u r r e n t c a r r i e d by some i o n s i n t h e system can be made v e r y s m a l l .  I n t h e extreme c a s e o f i d e a l l y s e l e c t i v e membrane,  the c o - i o n s a r e c o m p l e t e l y counter-ions  excluded  and t h e whole c u r r e n t i s c a r r i e d by t h e  a l o n e t h r o u g h t h e membrane.  F i g u r e 5a shows a n e g a t i v e membrane ( c a t i o n - e x c h a n g e r )  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 t h e 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 t h e l e f t s i d e t h e e l e c t r i c  c a r r i e s sodium i o n s t o t h e membrane a t t h e r a t e t + i / F and t h e s e disappear  1 Faraday i s t h e removal o f t immediately  adjacent  +  - t  The n e t r e s u l t o f t h e passage o f  = 0.6 mole o f s a l t f r o m t h e s o l u t i o n  t o t h e l e f t h a n d f a c e o f t h e membrane and t h e appearance  of a l i k e q u a n t i t y ( t - t  2.4.2.  ions  a c r o s s t h e membrane a t t h e r a t e t + i / F where F i s F a r a d a y s  c o n s t a n t and i i s t h e c u r r e n t d e n s i t y .  face.  current  =0.6) i n the s o l u t i o n adjacent  ( F o r sodium c h l o r i d e , t  -  0.4 and t  to the righthand  = 0.6).  Membrane P o l a r i z a t i o n 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 a t t h e s u r f a c e s o f t h e ion-exchange mem-  b r a n e s l i m i t s t h e c u r r e n t d e n s i t y and t h e p r o d u c t i o n r a t e i n an e l e c t r o dialysis unit. and  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 o f t h e s e p a r a t i o n mechanism  i t i n c r e a s e s a s t h e s e l e c t i v i t y o f t h e membrane i n c r e a s e s ;  way t o p r e v e n t flow.  t h e r e i s no  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 o t h e r t h a n by s t o p p i n g t h e c u r r e n t  Due t o t h e d i f f e r e n c e s i n t h e t r a n s p o r t numbers o f i o n s i n t h e  s o l u t i o n s and i n t h e ion-exchange membranes two boundary l a y e r s w i t h  Ha CI it+=l*0  it =0-39 £ > +  = it-=0-6l  it-=0®  L  - 0  it-=06l  FIGURE 5a Ion transport across a permselective membrane , showing current i and transport number t . •  rwv,c  m  c  m  FIGURE 5b Concentration profile across a permselective membrane in an electrodialysis stack .  27  o p p o s i t e c o n c e n t r a t i o n g r a d i e n t s a r e formed a t t h e o p p o s i t e s i d e s o f each membrane ( F i g u r e 5 b ) . I n a w e l l - s t i r r e d system t h e f i l m model ( N e r n s t l a y e r model) c a n be adopted and.the c o n c e n t r a t i o n g r a d i e n t on t h e d i l u t e s i d e a p p r o x i m a t e d by i C — C D m where 6 C_, C* a r e t h e c o n c e n t r a t i o n o f t h e b u l k s o l u t i o n and t h e D m c o n c e n t r a t i o n a t t h e membrane s u r f a c e r e s p e c t i v e l y 6 i s the Nernst f i l m  thickness  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 m e m b r a n e - s o l u t i o n i n t e r f a c e must e q u a l t h e r a t e o f r e m o v a l o f s a l t i . e . a t a cation-permeable  membrane we have:  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 a c r o s s boundary l a y e r  AC = z  » f  C - c' D m  =  valence  I n t h e l i m i t i n g c a s e when C^ -> 0, AC -> C^;  the corresponding  limiting  c u r r e n t d e n s i t y , i ^ ^ f i s g i v e n by i  =  him  Z F D C  =  D  1 2—  j  (11)  P o l a r i z a t i o n i s a r e s u l t o f mass t r a n s f e r l i m i t a t i o n s a d j a c e n t membrane-solution i n t e r f a c e s .  to the  I t o c c u r s when I o n 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 t h e r a t e o f i o n d i f f u s i o n i n t o t h e boundary l a y e r f r o m t h e b u l k s o l u t i o n , and i t becomes a p p r e c i a b l e when t h e 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 l o w and t h e d i f f u s i o n l a y e r i s t h i c k so t h a t t h e 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 c u r r e n t d e n s i t y than i , . l.im  i s used.  t As C  m  approaches z e r o t h e 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 d r o p s  tremendously.  The c o n c e n t r a t i o n o f H  +  and OH  i o n s 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 t h e m o b i l i t i e s o f t h e s e i o n s a r e 3 t o 5 t i m e s g r e a t e r t h a n t h e m o b i l i t i e s o f t h e o t h e r common i o n s .  approaches 5 x 10  As soon a s c' m  m o l e / l i t e r , a n a p p r e c i a b l e amount o f c u r r e n t w i l l  c a r r i e d by hydrogen and h y d r o x y l i o n s .  be  This r e s u l t s i n the f o l l o w i n g  effects: (1)  An enormous i n c r e a s e i n t h e power consumption due t o : (a)  More c u r r e n t f l o w i n g p e r u n i t o f s a l t removed e.g., i f (u^ +) (C) = (^jj"") 10 ^ where u i s t h e i o n i c m o b i l i t y t h e n 1  a  Na  +  and H  +  ions w i l l t r a n s f e r a t equal r a t e s .  I n 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 , n^., o f o n l y 50 p e r c e n t , because H t r a n s f e r does n o t c o n t r i b u t e t o 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 t h e boundary  layer resulting  from t h e poor c o n d u c t i v i t y o f n e a r l y p u r e water —8 —1 -1 4 x 10 ohm cm ) . (c)  The energy r e q u i r e d t o i o n i z e t h e w a t e r m o l e c u l e s ( d i s s o c i a t i o n energy o f water  (d) (2)  (kf^o ~  splitting).  An i n c r e a s e o f t h e back emf's due t o p o l a r i z a t i o n l a y e r s .  D e v i a t i o n from n e u t r a l i t y i n t h e p o l a r i z e d l a y e r o r t h e  a l t e r a t i o n o f t h e pH's o f t h e p r o c e s s s t r e a m s .  A c i d i t y c a n d e v e l o p on t h e  c a t h o d e s i d e o f c a t i o n - p e r m e a b l e membrane and a l k a l i n i t y on t h e anode s i d e o f a n i o n - p e r m e a b l e membrane.  A s most b r a c k i s h w a t e r s a r e n e a r l y  saturated  29  w i t h s c a l e - f o r m i n g 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 e.g. Mg(OH) p r e c i p i t a t i o n may ^ 9  (3)  -4  ( i . e . C_. - - 10 OH  ).  P o l a r i z a t i o n changes t h e 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-  b r a n e s 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 t h e y a r e not s t a b l e to  wide pH v a r i a t i o n . a f f e c t e d by  be expected a t pH > 10  ( W i l s o n , 1960).  Anion-permeable membranes a r e most  this.  In p r a c t i c e , p o l a r i z a t i o n i s held to reasonable  v a l u e s by  controlling  the r a t i o of c u r r e n t d e n s i t y t o the n o r m a l i t y of the d i l u t e s t r e a m , i/C » D  and by d e s i g n i n g  the system t o make 6 as s m a l l as p o s s i b l e .  I t should  be  noted t h a t t h e 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 t h a n t h e 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 electrodialysis  installations.  I n any p r a c t i c a l a p p a r a t u s , t h e p i c t u r e i s f a r more complex t h a n t h i s . Where t h e r e a r e c e l l s f e d i n p a r a l l e l f r o m a m a n i f o l d , 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 .  i t i s impossible  Cooke (1967) and  (1967) have drawn a t t e n t i o n t o the f a c t t h a t , even w i t h i n an  to  Solt  individual  c e l l i n t h e most i d e a l s i t u a t i o n , t h e 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 a r e not u n i f o r m o v e r t h e whole a r e a t h r o u g h w h i c h c u r r e n t i s p a s s i n g . (ii)  P o l a r i z a t i o n Control  P o l a r i z a t i o n can not be a v o i d e d reasonable  completely,  but i t can be h e l d  v a l u e s by c o n t r o l l i n g t h e r a t i o of c u r r e n t d e n s i t y to  to  the  n o r m a l i t y of the d i l u t e s t r e a m , 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 t h a t can be done about t h e b u l k 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 r e d u c e d by  high  30  s o l u t i o n f l o w v e l o c i t y and as s p a c e r s o r s c r e e n s  the i n t r o d u c t i o n o f t u r b u l e n c e promoters such  t h a t cause l o c a l e d d y i n g o r t u r b u l e n c e  B o t h of t h e s e measures add  (Hoek, 1956).  to t h e power consumed i n c i r c u l a t i n g the  process  f l u i d s , b u t t h e y r e d u c e t h e s t a c k power consumption and a l l o w o p e r a t i o n a t h i g h e r c u r r e n t d e n s i t i e s w i t h an a c c e p t a b l e 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 o f r e d u c i n g p o l a r i z a t i o n was (1963) who  t e c h n i q u e was  2.4.3.  1964  Spiegler  r e v e r s e d t h e c u r r e n t f o r a f r a c t i o n o f a second a f t e r each  s e v e r a l seconds o f o p e r a t i o n .  (OSW,  r e p o r t e d by  obtained  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  i n t h e Webster, South D a k o t a , d e m o n s t r a t i v e  this  plant  a).  S c a l i n g and F o u l i n g o f Membranes 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 s o f t e n l i n k e d w i t h o t h e r problems i n  p r a c t i c e such as membranes s c a l i n g and s o l u t i o n due  fouling.  An i n c r e a s e i n the pH of  the  t o p o l a r i z a t i o n promotes t h e f o r m a t i o n 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 c a r b o n a t e and magnesium h y d r o x i d e  on the membrane s u r f a c e .  On t h e d i l u t e - s t r e a m s i d e o f the a n i o n - p e r m e a b l e membrane the d e p l e t i o n of t h e more m o b i l e a n i o n s  encourages the d e p o s i t i o n of l a r g e p o l y a n i o n s  t h e membrane s u r f a c e .  P o l y a n i o n s commonly found i n b r a c k i s h w a t e r s a r e  humic a c i d s , s i l i c a c i d s , p h e n o l s ,  p r o t e i n s and p o l y p h o s p h a t e s (OSW,  S c a l i n g o f membranes c a u s e s a d d i t i o n a l e l e c t r i c a l and  onto  1963).  flow resistance,  a d e c r e a s e 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.  S c a l e d e p o s i t s can be found w i t h i n t h e membrane g e l s t r u c t u r e ,  w h i c h 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 e m b r i t t l e m e n t  and p h y s i c a l  d e t e r i o r a t i o n of membranes. S e v e r a l methods have been a t t e m p t e d t o 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  reduction  S c a l e f o r m a t i o n i s p a r t i c u l a r l y pronounced a t h i g h c u r r e n t 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 (ii)  Pre-treatment  Pre-treatment  f o r c a t i o n removal  by c a t i o n - e x c h a n g e r e q u i r e s a l l t h e f e e d t o be passed  t h r o u g h a c a t i o n - e x c h a n g e bed, C a t i o n s may  reduce s c a l i n g .  i n o r d e r t o remove c a l c i u m and magnesium.  be p a r t i a l l y removed by a p r e l i m i n a r y l i m e or l i m e - s o d a  ment f o l l o w e d by f i l t e r a t i o n .  Such p r e - t r e a t m e n t s  treat-  add c o n s i d e r a b l y t o  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 e c o n o m i c a l l y  except f o r s p e c i f i c  applications. (iii)  A c i d Treatment of  Concentrate  A c i d i f i c a t i o n t o a pH l e v e l low enough t o p r e v e n t commonly p r a c t i s e d , but even t h i s method may  not c o m p l e t e l y  f o r m a t i o n a t the s u r f a c e s o f or w i t h i n the membranes. s u l p h u r i c a c i d t o keep pH b e l o w 5.0  precipitation is  The  prevent  scale  a d d i t i o n of  f o r p r e v e n t i o n o f Ca C0^  s c a l i n g was  r e p o r t e d by Watanabe, e t a l . (1972) and Asawa, e t a l . (1973). Although added c o s t was t i o n due  a c i d i f i c a t i o n adds t o t h e d i r e c t c o s t o f d e s a l t i n g , the considered  t o be p a r t l y o f f s e t by s a v i n g s i n energy consump-  t o 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 .  (iv)  (Furukawa, 1968).  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 o f 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 t h e membranes were s u s p e c t e d  of producing  a s i e v e or  filter-  i n g e f f e c t , r a t h e r t h a n a c t i n g as a p u r e i o n - t r a n s f e r medium, c u r 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 t o d i s c h a r g e e l e c t r o c h e m i c a l l y  e n t r a p p e d c o l l o i d s and/or m a c r o m o l e c u l e s so as t o r e s t o r e the  original  32  membrane p r o p e r t i e s .  A l t h o u g h t h e e f f e c t i v e n e s s o f t h i s p r o c e d u r e depends  on t h e t y p e o f membrane and t h e n a t u r e o f t h e c o n t a m i n a n t s t h a t f o u l i t , t h e r e v e r s a l o f hydrogen and h y d r o x y l  i o n t r a n s f e r and t h e accompanying i n t e r -  change o f pH e f f e c t s a t t h e membrane s u r f a c e i s p r o b a b l y t h e s i g n i f i c a n t defouling factor. (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 r e v e r s e d able t o prevent r a p i d accumulation of s c a l e .  p o l a r i t y i s not  I n t h i s method v e r y b r i e f  p u l s e s o f r e v e r s e c u r r e n t a r e a p p l i e d t o produce c u r r e n t r e v e r s a l o r c u r r e n t i n t e r r u p t i o n (Matz, e t a l . , 1962).  T h i s technique tends t o  a l l e v i a t e s c a l i n g problems and a l s o a p p a r e n t l y of an o p e r a t i n g  2.5.  2.5.1.  e l e c t r o d i a l y s i s stack  improves t h e e f f i c i e n c y  ( I s r a e l , 1961).  Process E f f i c i e n c y  P r i n c i p a l Energy The  Sinks  a c t u a l energy r e q u i r e d t o o p e r a t e an e l e c t r o d i a l y s i s p r o c e s s  exceeds t h a t t h e o r e t i c a l l y r e q u i r e d f o r t h e f o l l o w i n g r e a s o n s : (i)  Power l o s s e s a t t r i b u t a b l e t o r e s i s t a n c e i . e . t h e power t h a t  w i l l be d i s s i p a t e d by t h e J o u l e h e a t i n g o f t h e membranes and t h e e l e c t r o l y t e solution. (ii)  Power l o s s e s a t t r i b u t a b l e t o 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 t o overcome t h e o v e r p o t e n t i a l s t h a t e x i s t a t t h e membrane-solution i n t e r f a c e s . (iii)  Power l o s s e s a t t r i b u t a b l e t o e l e c t r o d e r e a c t i o n and t h e IR drop  i n t h e r i n s e s o l u t i o n streams i n t h e e l e c t r o d e s  compartments.  33  (iv)  Low c u r r e n t  efficiency.  The o v e r a l l e f f i c i e n c y o f an e l e c t r o d i a l y s i s s t a c k , n, c a n be e x pressed as a product (a)  of four p r i n c i p a l  Three v o l t a g e terms:  n  efficiencies:  associated 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 t h e 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 with the electrode reactions. (b)  The c u r r e n t e f f i c i e n c y , n^  i.e.  n  =  n R  where n  n  n  e  e  n  (12)  T  l  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 o f c e l l  p a i r s ) , n depends m a i n l y on t h e o p e r a t i n g c o n d i t i o n s ( e . g . c u r r e n t d e n s i t y ) , w h i l e n depends on b o t h d e s i g n f a c t o r s such as c e l l s p a c i n g , membrane t y p e R c  and  t h i c k n e s s and on o p e r a t i n g c o n d i t i o n s , (a)  V o l t a g e Terms  The major i n e f f i c i e n c y i n s t a c k 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 t h e f i r s t and  second terms i n Eq. (12) , l^ « T  n  c  These terms a r e c o n s i d e r e d  i n Chapter 3.  I n multiple-membrane s t a c k s used i n e l e c t r o d i a l y s i s , t h e energy c o n sumed i n e l e c t r o d e p r o c e s s e s ,  n » does n o t c o n t r i b u t e t o t h e d e s i r e d e  s e p a r a t i o n and hence t h e r e l a t i v e e f f e c t o f t h i s energy c o n s u m p t i o n c a n 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 t h e number o f 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 t h e  p o l a r i z a t i o n e f f e c t s a r e c o n s i d e r e d b r i e f l y i n A p p e n d i x A. The t o t a l e x t e r n a l v o l t a g e , E^,, t h a t i s needed t o o p e r a t e 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 s t a c k i s t h e sum o f 3 p r i n c i p a l p o t e n t i a l d r o p s : E  T  =  E  e  + E  R  + E  c  (13)  34  where E  = 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  g  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 = the E  IR  electrode  overpotentials)  d r o p s i n the s o l u t i o n s and membranes  = c o n c e n t r a t i o n p o t e n t i a l a c r o s s the membranes and a t the mem-  c  brane-solution interfaces. 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 t h e e l e c t r o d e r e a c t i o n s , n , can be d e f i n e d f o r t h e s t a c k as a whole by e E e where e^,  e  £  E x  + E„  (e„ + e ) .  T  J  E  a r e d e f i n e d i n a same way  as E^ and E  c e l l p a i r i n s t e a d of t h e whole s t a c k . and  t h e i r two  T c  but t h e y r e f e r t o  A c e l l p a i r c o n s i s t s of two membranes  a s s o c i a t e d s o l u t i o n passages.  From E q . ( 1 4 ) , i t i s o b v i o u s t h a t whatever t h e i n d i v i d u a l v a l u e s e^ and  e  £  one  f o r the design s e l e c t e d ,  w i l l a p p r o a c h 1.0  of  as the number of  cell  p a i r s , j , i s increased. 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 o r d e r t h a t consumed by one s t u d i e s of two  c e l l pair.  as  B e l f o r t , e t a l . (1968) showed i n t h e i r  electrodialysis plants:  Webster, South Dakota and  A r i z , t h a t t h e 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  Buckeye, less  t h a n h a l f per c e n t of t h e t o t a l p o t e n t i a l d r o p , (b)  Current E f f i c i e n c y ,  n^  I n 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 s y s t e m , i t i s g e n e r a l l y found t h a t the amount of c u r r e n t r e q u i r e d to produce a g i v e n 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 t h e b a s i s of c u r r e n t t h r o u g h i d e a l membranes.  flow  35  The 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 as  I  (15)  F "w  where r\„ i s t h e Faraday e f f i c i e n c y , w h i c h i s d e f i n e d as t h e r a t i o o f t h e 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 _ ^F  (equivalent of s a l t transported) (Faraday o f e l e c t r i c i t y passed)(number o f membrane p a i r s employed) n  w  i s t h e r e s u l t o f w a t e r t r a n s p o r t t h r o u g h t h e membranes.  (16)  When t h e  f e e d i s o f l o w s a l i n i t y , as w i t h b r a c k i s h w a t e r , t h e e f f e c t o f water t r a n s f e r i s u s u a l l y s m a l l and t h e water t r a n s f e r t e r m , ri» c a n be assumed t o be u n i t y . w  A more d e t a i l e d d i s c u s s i o n o f t h e c u r r e n t e f f i c i e n c y i s c o n s i d e r e d 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 e v e r a l v a r i a n t s of t h e e l e c t r o d i a l y s i s p r o c e s s have been d e v e l o p e d t o  overcome some o f t h e problems t h a t have been e n c o u n t e r e d w i t h electrodialysis.  conventional  F o r i n s t a n c e , t h e a n i o n - s e l e c t i v e membranes used i n  c o n v e n t i o n a l systems a r e p a r t i c u l a r l y t r o u b l e s o m e because o f v u l n e r a b i l i t y t o f o u l i n g and s c a l i n g , so a t t e m p t s have been made t o 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 ) o r by c a t i o n - e x c h a n g e 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 Depletion The t r a n s p o r t d e p l e t i o n p r o c e s s i s a v a r i a n t o f e l e c t r o d i a l y s i s i n  w h i c h an a r r a y o f 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 F i g u r e 6.  T h i s c o n c e p t was f i r s t s u g g e s t e d by Deming and  36  Concentrated Stream  Demineralized Stream  A  A  N  N  Na  +  VLSU  -•Na  ->Na  h^Na"*  +  1  •ci"  A Anode Rinse  — a •«-  Ui Feed ( Na CI )  FIGURE 6 The cation_neutral transport depletion process-, C , cation - selective membrane N , neutral membrane-  CI  A  i  .  Cathode Rinse  37  K o l l s m a n (1959) and d e v e l o p e d by L a c e y  (1963).  When d i r e c t e l e c t r i c c u r r e n t i s p a s s e d , d e p l e t e d and  concentrated  boundary l a y e r s form a t the two s i d e s o f t h e c a t i o n exchange membranes, but not a t the n o n s e l e c t i v e n e u t r a l membranes. separate  the d e p l e t e d and c o n c e n t r a t e d  The  l a t t e r s e r v e o n l y to  boundary l a y e r s from each o t h e r  and,  i n d o i n g s o , c r e a t e 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 t o p o l a r i z e or f o u l , t h u s t h e i r t r a d e s o f f the c h e m i c a l and m e c h a n i c a l d i s a d v a n t a g e s membranes f o r h i g h e r power c o s t s , e.g.  use  of anion-exchange  f o r s o l u t i o n s of K CI  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 t o  (t  = 0.5  = t_),  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 a r e 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 o n l y % mole i s s h i f t e d i n transport depletion.  Therefore,  to achieve  the same p r 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 s t a c k s 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 , the c u r r e n t i s needed.  The v o l t a g e i s t h e n a l s o n e a r l y t w i c e , hence the  power c o s t s a l m o s t q u a d r u p l e . the c a p i t a l c o s t d r o p s .  twice  However, by e l i m i n a t i n g t h e a n i o n membranes  I t appears t h a t the power consumption i s not  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  the do  not r e s i d e i n the energy r e q u i r e m e n t s b u t i n the i n v e s t m e n t c o s t s f o r equipment or the r e p l a c e m e n t c o s t s f o r the membranes ( S h a f f e r and  Mintz,  1966). The  economics o f the t r a n s p o r t d e p l e t i o n p r o c e s s have been s t u d i e d  by Huffman (1969) and Redman (1971).  L a c e y e s t i m a t e d a c o s t 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 . continues  The p r o c e s s  development  i n the b e l i e f t h a t the s i m p l i c i t y of the p l a n t and  from t r o u b l e i n the f i e l d w i l l o u t - b a l a n c e  i t s freedom  the i n c r e a s e d power c o s t ( S o l t , 1 9 7 1 ) .  38  2.6.2.  Electrogravitational Demineralization 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 s u g g e s t e d by Murphy  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 a c h i e v e d  i n a c e l l i n which only  c a t i o n exchange membranes a r e u s e d , as shown i n F i g u r e 7. e l e c t r i c c u r r e n t i s passed d e p l e t e d and a t each s i d e of the membrane, but  concentrated  (1950).  When a d i r e c t  boundary l a y e r s f o r m  the s o l u t i o n i n the d e p l e t e d boundary  l a y e r r i s e s and c o l l e c t s a t the top o f the d e p l e t e d compartment because i t s d e n s i t y i s lower t h a n t h a t o f the b u l k of t h e s o l u t i o n . s o l u t i o n i n the c o n c e n t r a t e d  Similarly  boundary l a y e r s l i d e s downward and  a t the bottom o f the e n r i c h e d compartment.  the  collects  Additional density differences  a r e o b t a i n e d because the d e p l e t e d s o l u t i o n has h i g h e r e l e c t r i c a l r e s i s t a n c e t h a n t h e b u l k , and g e t s h o t t e r . The b r a n e s may  process i s extremely  s i m p l e t o c o n s t r u c t and o p e r a t e .  be p l a c e d l o o s e l y or s i m p l y hung i n a t a n k 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 a r e not n e c e s s a r y ;  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 n o t s e r i o u s l y a f f e c t p e r f o r m a n c e . leakage  The mem-  t h r o u g h h o l e s or around edges may  waste power, but w i l l  Current not  i n t e r f e r e w i t h t h e o p e r a t i o n of the system. V e r y h i g h c o n c e n t r a t i o n g r a d i e n t s can be a c h i e v e d  i n the  process.  M i n t z and Lang (1965) have shown t h a t c o n c e n t r a t i o n g r a d i e n t s of g r e a t e r t h a n 100  t o 1 can be o b t a i n e d i n c e l l s o n l y 6 i n . h i g h .  S t u d i e s by Lang  and Huffman (1969) showed t h a t e l e c t r o g r a v i t a t i o n i s not c o m p e t e t i v e 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 w a t e r b u t may  some i n d u s t r i a l  separations.  be of i n t e r e s t f o r  39  Demineralized Product Water  1  Li » !  .CI*  !s T  : ^ i 1  ^  1  fort H  cr  Repeating)  1  •Mi  Brine Feed (Na CI typical)  1  * Concentrated Brine  FIGURE 7 Bectrogravitation with cation-selective membranes.  n  40  2.7.  C y c l i c Processes  2.7.1.  Electrosorption 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  c o n c e i v e d b y L a c e y and Lang (1964, 1968).  I t i s a one-cycle process without  reflux. 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 o f many e l e c t r o s o r p t i o n  membranes a r r a n g e d between a p a i r o f e l e c t r o d e s , so t h a t s o l u t i o n compartments a r e formed between t h e p a r a l l e l membrane s u r f a c e s as shown i n F i g u r e  8,  An e l e c t r o s o r p t i o n membrane, w h i c h i s t h e f u n d a m e n t a l 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 c o m p r i s i n g  a n e u t r a l i n n e r l a y e r (which may be a  s p a c e r o r m e r e l y 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 c u r r e n t i s passed through t h e system c a t i o n s and  anions are transported  ( i n opposite)  i n t o t h e e l e c t r o s o r p t i o n membranes.  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 The e x t e r n a l s o l u t i o n i s d e p l e t e d  w h i l e t h a t w i t h i n t h e membranes becomes h i g h l y c o n c e n t r a t e d . m i n u t e s o f s o r p t i o n t h e d i r e c t i o n of t h e c u r r e n t i s r e v e r s e d  A f t e r 20-50 and t h e  t r a p p e d i o n s accumulated i n s i d e t h e membranes a r e d r i v e n back t o t h e e x t e r n a l s o l u t i o n t o r e g e n e r a t e t h e membranes. s e n t t o waste d u r i n g t h i s 2.7.2.  The e x t e r n a l s o l u t i o n i s  step.  CyclicElectrodialysis 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 separation 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 t o 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 sorption stack.  The p r o c e s s has been s t u d i e d and d e s c r i b e d  Bass and Thompson (1973).  by Bass (1972) ,  I n t h i s process c y c l i c times ranging  between  30 seconds and 2 m i n u t e s were used w i t h t h e v o l t a g e and f l o w d i r e c t i o n  Demineralized Product Water  t +1  A  A  n +s  Na  CI  Ncf •f?Na jM  Na*  •CI  •CI  +  1  1  fop-  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 a p p a r a t u s i s b u i l t up w i t h r e p e a t e d  cycling.  Separation f a c t o r s  of s e v e r a l hundreds were r e p o r t e d f o r most of the e x p e r i m e n t s w i t h 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 p r e s e n t work i s an  e x t e n s 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 t o 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 o f p r o d u c t w a t e r t h a 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 , due regeneration step.  to  The c o s t o f t h i s a d d i t i o n a l e n e r g y must be  the balanced  a g a i n s t s a v i n g s 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  Lower c o s t o f the s t a c k i s p o s s i b l e because o n l y one w i t h d r a w n a t any one (ii)  The  systems.  stream of s o l u t i o n i s  time.  "sealed-envelope"  or "membrane s a c k " 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 s t a c k c o n s t r u c t i o n and 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 .  S i n c e the membranes a r e not used t o  s e p a r a t e b r i n e and d i a l y s t a t e f l o w c h a n n e l s , a c t i v e i n t e r i o r of the s t a c k .  results i n  they may  be as s m a l l as  A membrane u t i l i z a t i o n f a c t o r of about  the 95%  i s o b t a i n e d , whereas the f a c t o r i s o n l y about 70% t o 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  r e p l a c e m e n t c o s t and a lower s t a c k c a p i t a l c o s t . (iii)  W i t h e l e c t r o s o r p t i o n , no p r e t r e a t m e n t  i r o n or manganese from f e e d w a t e r s .  was  needed t o remove  W i t h f e e d s 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 a t h i g h pH v a l u e s ,  but  t h e s e were e a s i l y and q u i c k l y removed by r e v e r s e d c u r r e n t f l o w d u r i n g d e s o r p t i o n without 1967).  c a u s i n g any c e l l b l o c k a g e or damage t o the membranes  I t i s e x p e c t e d 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  (Lacey,  electrodialysis.  43  (iv)  Increased  t h r o u g h p u t s a r e p o s s i b l e because c u r r e n t d e n s i t i e s  more c l o s e l y a p p r o a c h i n g t h e 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 t o t h e membranes o r s t a c k due t o precipitates. (v)  A h i g h degree o f d e s a l i n a t i o n can be o b t a i n e d  i n a single  s t a c k ( B a s s , 1972). (vi)  The p e r i o d i c r e v e r s e d p o l a r i t y t e c h n i q u e  r e j u v e n a t i o n o f t h e membranes.  provides a repeated  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 e n c o u n t e r e d . (vii) to be used.  I n c y c l i c e l e c t r o d i a l y s i s o n l y cheap g r a p h i t e e l e c t r o d e s need Such e l e c t r o d e s p r o v e d t o be s a t i s f a c t o r y i n a  long-term  operation. 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 t o t h e r m a l pumping.  I n both processes  parametric  t h e f l o w o f a m o b i l e phase i s p e r i o d i c a l l y  r e v e r s e d and i n b o t h p r o c e s s e s  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 o f t h e system t o s t o r e s o l u t e t e m p o r a r i l y i n t h e f i x e d phase, w i t h drawing i t from t h e l e a n end and s u b s e q u e n t l y the p r o c e s s i n g  2.7.3.  a d d i n g i t t o t h e r i c h end o f  stream.  Parametric  Pumping  The. term p a r a m e t r i c  pumping was f i r s t i n t r o d u c e d by W i l h e l m , e t a l .  i n 1966 ( W i l h e l m , e t a l . , 1966 a, 1966 b ) .  I t r e f e r s t o 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 o f two c y c l i c f i e l d s o r two  transport steps  (Wilhelm and Sweed, 1968 a;  P a r a m e t r i c pumping has been r e v i e w e d Wankat  (1974)..  W i l h e l m , e t a l . , 1968 b ) .  i n d e t a i l s by Sweed (1971, 1972) and  44  The  system o f a d i r e c t t h e r m a l p a r a m e t r i c  pumping c o n s i s t s m a i n l y  of  a j a c k e t e d column packed w i t h an a d s o r b e n t 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,  s o u r c e s o f hot and c o l d w a t e r f o r the j a c k e t (not shown i n the and a programmed c y c l e t i m e r .  The  figure),  timer i s adjusted to reverse  periodically  the d i r e c t i o n of t h e f l u i d s t r e a m ;  a l s o t o c y c l e the j a c k e t t e m p e r a t u r e by  c o n n e c t i o n t o hot o r c o l d s o u r c e s .  B o t h a l t e r a t i o n s have t h e same  ( i . e . e v e r y h a l f c y c l e ) and The  a r e i n phase.  f l u i d i s h e a t e d d u r i n g t h e upward s t r o k e and c o o l e d d u r i n g  downward s t r o k e .  The a d s o r b e n t h o l d s more s o l u t e when the f l u i d  t h e f l u i d on t h e hot h a l f c y c l e .  A m u l t i p l e s u c c e s s i o n of  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 end of t h e column and d e p l e t i o n a t t h e o t h e r end.  the  i s cool,  Thus the s o l u t e i s h e l d by t h e a d s o r b e n t on the c o l d h a l f c y c l e and to  frequency  released  these  of s o l u t e at: one  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 o f the s o l u t e w i l l be "pumped" t o t h e 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  i s i d e n t i f i e d as t h e o s c i l l a t o r y t h e r m a l f i e l d ; between f l u i d and  the f l o w  c a s e the "pump" displacements  s o l i d phases s i m p l y keep the system i n a s t a t e of  disequilibrium. 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  m e t r i c pumping ( a c c o r d i n g t o S a b a d e l l and  Sweed, 1970)  para-  are:  1.  The  e x i s t e n c e o f 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 o f t h e component b e i n g  separated  between t h e 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 i n t e r p h a s e mass f l u x o b t a i n e d by  periodically  Driven Piston Q  Packed Bed Of Adsorbent Particles  Q  f*-Q  Q  ft-Q  Heating And Cooling Jacket  Heating half-Cycle  Driving Piston  Cooling Half-Cycle  FIGURE 9 a Diagram of column for direct mode RR . Thot  J mean  L  Tcold Desorptlon  Adsorption  Vo o -Vo  0  0-2  0-4  0-6  0-8  10  Fraction Of Cycle  FIGURE 9 b Velocity and temperature as a function of time •  at  a  point in the bed  46  c h a n g i n g one  or more of t h e 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. Although  thermal parametric  temperature. 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  t h e 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 o f 10"* i n batch o p e r a t i o n (Wilhelm, system (Chen, e t a l . , 1972 Na CI - 1^0  e t a l . , 1968  b) and of o v e r 600  a ) , i t g i v e s o n l y a modest s e p a r a t i o n i n t h e system  - 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 G r e g o r y , 1971)  and a s e p a r a t i o n f a c t o r o f 2.0  (Wilhelm  Sweed and G r e g o r y , 1972).  2.7.4.  i n an open  e t a l . , 1966  a;  C y c l i c e l e c t r o d i a l y s i s and P a r a m e t r i c  i n an open system  Pumping  D e s p i t e t h e prementioned s i m i l a r i t i e s between c y c l i c and p a r a m e t r i c  pumping, t h e two p r o c e s s e s  electrodialysis  are d i f f e r e n t w i t h regard to  the  n a t u r e o f t h e d r i v i n g f o r c e and p r o c e s s 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 , In parametric energy.  pumping s e p a r a t i o n i s a c h i e v e d  a t t h e expense o f  thermal  By c h a n g i n g t h e t e m p e r a t u r e and r e v e r s i n g t h e f l u i d f l o w e v e r y h a l f  c y c l e t h e system i s k e p t i n a s t a t e of d i s e q u i l i b r i u m , t h u s m o l e c u l e s d i f f u s e f r o m one phase i n t o a n o t h e r .  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 e x e r t e d on t h e i o n s t h a t a r e t r a n s f e r r e d f r o m one r e g i o n i n t o a n o t h e r a c r o s s t h e  stack.  A p a r a m e t r i c pumping p r o c e s s c o n s i s t s e s s e n t i a l l y o f a column packed w i t h a s u i t a b l e a d s o r b e n t 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 c k c o m p r i s e s w e l l - d e f i n e d p a r a l l e l f l o w c h a n n e l s between membrane s h e e t s . W h i l e p a r a m e t r i c 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 c o n 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 separation process  such as c y c l i c  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 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 .  electrooperate  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 t o t h e c u r r e n t f l o w i n g and i s t h u s t o some  e x t e n t under t h e d i r e c t c o n t r o l o f t h e e x p e r i m e n t e r . 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 deals only with ionic solutions whereas p a r a m e t r i c  pumping i s n o t l i m i t e d t o t h e s e 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 separation of i o n i c s o l u t i o n s , c y c l i c d i a l y s i s l o o k s more p r o m i s i n g n a t u r e o f t h e system.  electro-  s i n c e i t i s n o t c o n s t r a i n e d by t h e c h e m i c a l  I n p a r a m e t r i c pumping a l a r g e s e p a r a t i o n i s o n l y  expected when t h e s h i f t o f e q u i l i b r i u m w i t h t e m p e r a t u r e o f t h e 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 The  Models  a p p a r e n t r e s i s t a n c e o f an e l e c t r o d i a l y s i s s t a c k i s d e t e r m i n e d  by m u l t i p l y i n g t h e a p p a r e n t r e s i s t a n c e o f one c e l l p a i r by t h e number o f t h e c e l l p a i r s and making some a l l o w a n c e f o r t h e e l e c t r o d e  system*(Generally  i g n o r i n g t h e e l e c t r o d e system c o n t r i b u t i o n towards t h e t o t a l s t a c k t a n c e w i l l r e s u l t i n o n l y minor e r r o r ) . exchange membranes and t h e i r a s s o c i a t e d  resis-  A c e l l p a i r c o n s i s t s o f two i o n flow channels.  The a p p a r e n t  r e s i s t a n c e c o m p r i s e s t h e e l e c t r i c a l r e s i s t a n c e o f t h e s o l u t i o n s and t h e membranes t o g e t h e r w i t h t h e back emf's caused by p o l a r i z a t i o n ,  These back  emf's oppose t h e a p p l i e d v o l t a g e and t h u s r e p r e s e n t an a p p a r e n t r e s i s t a n c e . I n t h e development o f t h e s e a n a l y s e s two approaches c a n be d i s t i n g u i s h e d w h i c h a r e d e s i g n a t e d a s "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 a p p r o a c h w h i c h t a k e s i n t o a c c o u n t t h e v a r i a t i o n o f the apparent r e s i s t a n c e w i t h current d e n s i t y .  T h i s a p p r o a c h b r e a k s 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 e l e m e n t s , e v a l u a t e s  the con-  t r i b u t i o n o f each element i n d e p e n d e n t l y and sums them t o g e t t h e t o t a l value.  The ohmic a n a l y s i s i s an e m p i r i c a l a p p r o a c h w h i c h assumes  a l i t y between c u r r e n t and v o l t a g e  3.1.1.  proportion-  i n the e l e c t r o d i a l y s i s stack.  Non-ohmic A n a l y s i s When a v o l t a g e  current  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 s t a c k , t h e i n i t i a l  i s roughly p r o p o r t i o n a l t o the v o l t a g e , but as the current 48  flows  49  t h r o u g h t h e a p p a r a t u s 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 a r e e s t a b l i s h e d and t h e a p p a r e n t r e s i s t a n c e o f t h e s t a c k i n c r e a s e s .  Apparent  r e s i s t a n c e c o m p r i s e s t h e e l e c t r i c a l r e s i s t a n c e s o f t h e s o l u t i o n s and t h e membranes, and t h e 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 t h e 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 dialysis c e l l pair.  The c e l l p a i r c o n t a i n s t h e c o n c e n t r a t e d  and d e p l e t e d  b u l k s o l u t i o n s , t h e two membranes, and t h e f o u r boundary l a y e r s i n w h i c h t h e c o n c e n t r a t i o n s o f s a l t s i n t h e s o l u t i o n n e a r t h e membrane v a r y c o n siderably.  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 a n a l o g o f t h e e l e c t r o -  dialysis c e l l pair.  The b a t t e r y symbols r e p r e s e n t  p o t e n t i a l s , and t h e r e s i s t o r symbols r e p r e s e n t and  segments o f s o l u t i o n .  for  the t o t a l p o t e n t i a l across a c e l l (i)  the concentration  t h e r e s i s t a n c e s o f membranes  T h i s a n a l o g c a n be used t o d e v e l o p an e q u a t i o n pair.  Diffusion layer resistance  The v o l t a g e from 1 t o 2 i n t h e d e p l e t e d d i f f u s i o n l a y e r i s t h e a l g e b r a i c sum o f t h e d i f f u s i o n p o t e n t i a l and t h e IR drop f r o m p o i n t 1 t o point 2 E  l-2  I  '¥  f j i  <t" - t + ) d l n ( T C ) (  ^  "  ^  g  p  + i  r  x,z  dx  (17)  "1  where R i s t h e gas l a w c o n s t a n t , T i s t h e a b s o l u t e t e m p e r a t u r e , F i s F a r a d a y ' s constant;  t , t  +  a r e t h e t r a n s p o r t numbers o f a n i o n 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 t h e 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 t h e a c t i v i t y coefficient, 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  point  Xfz  x , z , n-cm, where x i s t h e d i s t a n c e f r o m t h e membrane s u r f a c e and z i s t h e d i s t a n c e from t h e i n l e t a l o n g the f l o w path. depleting  solution.  The s u b s c r i p t d r e f e r s t o t h e  50  Cell Pair  5  L  8  i  '  Depleting Solution .  13  Enriching Solution  I  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 e q u i v a l e n t r e s i s t a n c e o f t h e 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. o f e q u a t i o n ( 1 7 ) ) i s g i v e n by  (18)  Integration of Equation  (18) a l o n g t h e f l o w p a t h ( z c o o r d i n a t e ) r e s u l t s i n  ( r e f e r t o F i g u r e 11) „m  Fi %,d where  "  m  R  c  In  < d" " d  T  (Yl i)  c  t  )  , — — v  z  (Y C )_ 2  (19)  dz  2  J z=0  ^ i s the equivalent 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 o f t h e depleted  layer.  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 t h e d i a l y z i n g c u r r e n t must pass through  ( t h e second term on t h e R.H.S. o f e q u a t i o n ( 1 7 ) ) i s c a l c u l a t e d by  p e r f o r m i n g a d o u b l e i n t e g r a t i o n a c r o s s t h e d i f f u s i o n l a y e r (x c o o r d i n a t e ) a s w e l l a s a l o n g t h e f l o w p a t h (z c o o r d i n a t e ) a s i n d i c a t e d i n F i g u r e 1 1 .  L  rm  i m  6,d  -1  dx  Px,z  (20)  dz  x=0  z=0  where p i s obtained from t h e b a s i c d e f i n i t i o n o f r e s i s t i v i t y : x,z J  1000 x.z (hv)+o  r  (  v V  C c  (21)  x,z  i s the e q u i v a l e n t s o l u t i o n conductance a t average c o n c e n t r a t i o n of  s a l t s and t°C. temperatures  I t c a n be e v a l u a t e d from t h e Onsager e q u a t i o n a t v a r i o u s  and c o n c e n t r a t i o n s (A ) ° v  t  (Aoo) o t  where  A  c  c  °  (Aoo) o  =  ( ~) 5°  t  c  - [A + B (Aoo) o ]C t  A  2  [ 1 C  +  0  ,  0  2  3  ( t  "  2  c  5  )  1  (22) (23)  52  Ion-Exchange Membrane  Diffusion Layer  Bulk Solution  FIGURE II Diagram of the concentration profile and the diffusion layer on the side of an electrodialysis ion exchange membrane.  dialysate  53  (Aoo) o  P  i s t h e e q u i v a l e n t conductance a t i n f i n i t e d i l u t i o n and  t°c. After p  from Eqs.  ( 2 1 ) , (22) and (23) i s s u b s t i t u t e d i n Eq. ( 2 0 ) , C Xjz  X 9Z  as a f u n c t i o n o f x and z has t o be e v a l u a t e d f r o m t h e boundary c o n d i t i o n s . To r e l a t e t h e c o n c e n t r a t i o n a t t h e membrane s u r f a c e C(0,Z) w i t h t h e 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 e q u a t i o n w i l l be used ( t h i s model i s c o n s i d e r e d dc dx  i n Appendix C ) :  C(6,Z) - C(0,Z) 6  =  ( 2 A )  From t h e N e r n s t e q u a t i o n and r e a l i z i n g t h a t a t t h e l i m i t i n g d e n s i t y , i^^*  idealized  current  s u r f a c e c o n c e n t r a t i o n C(0,Z) approaches z e r o ,  C(0,Z)  =  (1 - k ) C(6,Z)  (25)  where k i s t h e r a t i o o f t h e o p e r a t i n g t o 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) lira  A t any p o i n t ( x , z ) w i t h i n t h e boundary l a y e r C ( x , z ) i s g i v e n i n terms o f 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 ) , 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 t h e f o l l o w i n g r e l a t i o n ( u s i n g e q u a t i o n s (24) and  (25)):  C(x,z)  =  C(0, )  =  [(1-k) + ^  Z  X +  t  C  (  6  ' >  - <°» "  Z  C  Z  ] 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, t h e 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 p » 0  e r  a n <  ^  * the bulk s o l u t i o n concentration,  C(6,Z) must be e v a l u a t e d b e f o r e e q u a t i o n  (27) c a n 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 o b t a i n e d  from E q u a t i o n  (11) i n  terms o f l i m i t i n g c u r r e n t d e n s i t y a s ; .  _  C(6,m) FD  Limiting  (28)  (t - t )  i ln i-m  current density, i ^ ^ *  w i l l occur when t h e e x i t  of t h e d i l u t e s t r e a m C(0,m) shown i n F i g u r e 11 r e a c h e s z e r o .  concentration The l i m i t i n g  c u r r e n t d e n s i t y c a n be d e t e r m i n e d e x p e r i m e n t a l l y a s shown by Rosenberg and Tirrel  (1957), Cowan and Brown (1959) and Cooke (1961).  Once i  is  o b t a i n e d , 6 c a n be c a l c u l a t e d . The  current density r a t i o , k U s i n g F a r a d a y ' s Law and a m a t e r i a l b a l a n c e ,  the capacity i s defined  as, Cap  -  i  j  j  ^  -  F  d  n C  f  4 ±  (29)  where c a p a c i t y i s i n g - e q u i v . t r a n s f e r r e d / s e c . , n i s c u r r e n t Ap i s t h e a c t i v e membrane a r e a  efficiency,  [ i . e . area a v a i l a b l e f o r demineralization]  (cm ) , n i s t h e number o f membrane p a i r s , F i s F a r a d a y No. 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  (coulombs/g-equiv), d i  i s dialysate  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 =  i oper  C t n Ap d  d ±  f  2  amps/cm  From t h e l i m i t i n g c u r r e n t v a l u e and E q u a t i o n k, c a n be o b t a i n e d .  (30)  r  (30), the current density r a t i o ,  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  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) Based on t h e t r a d i t i o n a l t r e a t m e n t  of e l e c t r o d i a l y s i s t h e 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 t o decay e x p o n e n t i a l l y w i t h d i s t a n c e Z f r o m t h e f e e d p o i n t as shown i n F i g u r e 12a.  On  the  e v a l u a t i n g each  b u l k s o l u t i o n as a f u n c t i o n o f p a t h d i s t a n c e Z we get f o r t h e d i a l y s a t e -aZ C  d  ( Z )  =  C  d  ( 0 )  and from a m a t e r i a l b a l a n c e l e n g t h and Figure  (31)  e  on t h e s a l t a t a d i s t a n c e Z a l o n g t h e  path  t h e top of the u n i t ( a t Z = m) we get f o r t h e b r i n e ( r e f e r t o  12b): C  b  (Z)  =  [C (m) + ( | | ) C ( m ) ] - [ ( | | ) C ( 0 ) ] e " b  d  On s u b s t i t u t i n g e q u a t i o n  (31) i n t o  l o c a l c o n c e n t r a t i o n , C ( X , Z ) , can be C(x,Z)  =  [(1-k) + ~ ]  (27) a g e n e r a l e x p r e s s i o n f o r the  obtained: C(6,0) .  By s u b s t i t u t i n g v a l u e s from e q u a t i o n s ( 2 8 ) , (30) and  (33);  From e q u a t i o n s  equations (19) and  (19) and  d  "  %,d  +  R  R T  (33)  a Z  ( 2 1 ) , (22) , (23) , ( 2 5 ) , ( 2 6 ) ,  (20) can be i n t e g r a t e d .  6,d  ( Fi  -  £  d  2  J  -1  (V-^) In , — d z (Y C )_  V L  of  by:  .m m  e~  (20) t h e a p p a r e n t r e s i s t a n c e per u n i t a r e a  the d e p l e t e d d i f f u s i o n l a y e r i s g i v e n  R  (32)  a Z  d  z  2  =0 -1  +  p  m - z=0  x,z  dx  dz  (34)  57  A combined e x p r e s s i o n  f o r t h e a p p a r e n t r e s i s t a n c e s o f t h e two  d i f f u s i o n l a y e r s i s g i v e n by ( r e f e r t o F i g u r e  R  6(l-2)  +  R  10)  6(3-4) .m  m RT ( t - t ) d  ( Y  In  d  Fi  1 1 C  -1 }  z=0n  dz  z  ——s  z  W  z  -1  .m +  depleted  2m  p  z=0  L  J  x=0  dx  x,z  -1 dz  (35)  The combined a p p a r e n t r e s i s t a n c e o f t h e two e n r i c h e d 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  R  6(5-6)  +  R  6(7-8)  m RT ( t - t ) e e Fi  L  m +  J  z=0  8  z=0  ^  x=0  J -1  -i-l p  L  z  r r6  2m J  8  x.z  dx  dz  (36)  where p  i s t h e r e s i s t i v i t y a t any p o i n t ( x , z ) w i t h i n t h e e n r i c h e d Xfz diffusion layer.  (ii)  The b u l k 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 o f a s o l u t i o n - f i l l e d  compartment A cm t h i c k  is sol  CA  ohm - cm  (37)  The r e s i s t a n c e s o f t h e b u l k 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 a r e g i v e n by  58  *b  V d  =  +  R  b . - i -1  =  m(A-26)  <  ' L J z=0  (iii) The  (C,A ) dz ^ ^ z  -1  .m ( C A ) dz 6  L_  J  M38)  6  z=0  The membrane r e s i s t a n c e and p o t e n t i a l terms  r e s i s t a n c e o f a membrane cannot be c a l c u l a t e d by a s i m p l e method  but i t c a n be measured o r o b t a i n e d  from t h e m a n u f a c t u r e r .  Although  direct  c u r r e n t i s used i n electromembrane p r o c e s s e s , a l t e r n a t i n g c u r r e n t s a r e u s u a l l y used t o measure t h e e l e c t r i c a l r e s i s t a n c e o f membranes because c o n c e n t r a t i o n g r a d i e n t s t h a t a r e p r e s e n t w i t h d i r e c t c u r r e n t systems a r e n o t formed w i t h a l t e r n a t i n g c u r r e n t and t h e r e s i s t a n c e o f t h e membrane i t s e l f can be more e a s i l y d e t e r m i n e d .  However, t h e r e s i s t a n c e o f 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 t h a n t h e r e s i s t a n c e t o d i r e c t ( S p i e g l e r , 1966).  current  I f p r e c i s e v a l u e s a r e needed t h e r e s i s t a n c e t o d i r e c t  c u r r e n t s h o u l d b e d e t e r m i n e d under c o n d i t i o n s o f membrane u s e . There a r e 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 t h e m e m b r a n e - l i q u i d  inter-  f a c e i n an ion-exchange membrane a s a r e s u l t o f t h e Donnan e q u i l i b r i u m . F i g u r e 13a shows t h e 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 o f t h e a n i o n s and c a t i o n s a r e e q u a l i n t h e o u t s i d e s o l u t i o n b u t d e v i a t e from each o t h e r w i t h i n t h e membrane. c a t i o n c o n c e n t r a t i o n , C , and t h e lower l i n e i s a n i o n +  The  The upper l i n e i s  concentration.  t o t a l membrane p o t e n t i a l , E , i s t h e sum o f t h r e e p o t e n t i a l m' m  d i f f e r e n c e s a s shown i n F i g u r e 13b. E  =  m  where E<j^, E ^  a  r  E, dl e  +  *h  +  E  d  (39) 2  t h e two p o t e n t i a l jumps o c c u r r i n g a t t h e membrane f a c e s ,  w h i c h f o r m t h e Donnan p o t e n t i a l .  59  I Electrolyte  Membrane  Electrolyte  FIGURE 13 a Concentration distribution in a cation .exchange membrane ZpCp Is the concentration of fixed charge in membrane. X  FIGURE 13 b Schematic potential distribution through a cation .exchange membrane.  60  i s t h e Henderson term w h i c h i s t h e 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 t h e i n t e r i o r o f t h e membrane. The  d e t a i l e d e x p r e s s i o n s o f t h e Donnan terms and Henderson term a r e  g i v e n by V e t t e r  (1967).  A s i m p l i f i e d expression for 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 a c r o s s a membrane i n c o n t a c t w i t h u n i - u n i v a l e n t solutions of a c t i v i t i e s a  m  and a  m  electrolyte  on t h e o p p o s i t e s i d e s i s g i v e n by tt  — ( t - t ) I n ,—T\ F c c' (a')  m where t ^ , t  m  (40)  z  z  a r e t h e c a t i o n and a n i o n t r a n s p o r t numbers i n a c a t i o n - e x c h a n g e  membrane. The  membrane p o t e n t i a l s oppose t h e 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 i o n s a r e t r a n s f e r r e d f r o m l o w e r t o h i g h e r 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 a r e a due t o p o t e n t i a l s o f a c a t i o n and an a n i o n membrane i s g i v e n by R = R +R m ma mc  , mRT . + rrr- S F i S  p + p a c p  + p + p a c  F  r  -1 5 5 t ) l n , - ~ v z i dz * f J J  r  m  +  ( Y  a  (  C  -1  }  y  z  -l  m (t L-  z=0  - t ) In  ;•]  -i dz  -l  >  (41)  where s u b s c r i p t s a and c r e f e r t o a n i o n - and c a t i o n - e x c h a n g e membrane r e s pectively p , p a r e t h e a n i o n and c a t i o n membrane r e s i s t a n c e p e r u n i t a r e a Si c R . R „ a r e t h e e q u i v a l e n t r e s i s t a n c e p e r u n i t a r e a due t o a n i o n and ma mc c a t i o n membrane p o t e n t i a l .  61  The a p p a r e n t r e s i s t a n c e o f a c e l l  pair  The a p p a r e n t r e s i s t a n c e p e r u n i t a r e a o f a c e l l p a i r , R , i s g i v e n by =  d  IT  where R  d >  R, +i xv R \ j e  R , R^ and R g  (42)  + • R, "4" R m  D  a r e d e f i n e d b y e q u a t i o n s ( 3 5 ) , ( 3 6 ) , (38) and (41)  m  respectively. The a p p a r e n t r e s i s t a n c e p e r u n i t a r e a o f a c e l l p a i r c a n be e v a l u a t e d 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 t o g e t h e r w i t h t h e average bulk concentrations of the s o l u t i o n s . ( r e f e r t o F i g u r e 10)  I n C,A.,/C A 1 1 2 2 0  R  = 7  I n t h i s c a s e e q u a t i o n (42) r e d u c e s t o  <5  < 1 1 " C  TT,Z  A  C 2  I n C A /C.A. 3 3 4 4  0  0  V  ( C  3 3 " W 7  7  A  -  2  6  )  (  c f c C A 7 ) '22 "6 6 +  i  C  C A /C A  (C A  (  < 5 5 ~  A  In  +  I n C-A^/C^A, 5 5 6 6  0  +  ?  7  8  A  C  6 V  8  - CgAg)  P a  +  Pc  RT Fi  5~5  44+ (t - t ) In - + (t - t ) In a a y C c c' y  4  4  YqCq — «8"8 C  Y f  (43)  5  The s u b s c r i p t s d and e r e f e r t o t h e d e p l e t i n g and e n r i c h i n g and a and c r e f e r t o t h e a n i o n - and c a t i o n - e x c h a n g e membranes.  solutions  The n u m e r i c a l  s u b s c r i p t s r e f e r t o t h e c o r r e s p o n d i n g numbers i n F i g u r e 10. Eq. (43) i s based on t h e f o l l o w i n g a s s u m p t i o n s : (i) (ii) (iii)  V a l i d i t y o f N e r n s t i d e a l i z e d model ( r e f e r t o a p p e n d i x C) A uni-univalent electrolyte  system  S o l u t i o n - f i l l e d compartments w i t h o u t s p a c e r s ;  each o f t h e same  62  t h 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 o f t h e t h i c k ness 6 (iv)  C o n s t a n t t r a n s p o r t numbers o f t h e membranes and s o l u t i o n s o v e r the range o f c o n c e n t r a t i o n s  (v)  of i n t e r e s t  S i n g l e - i o n a c t i v i t i e s c a n be r e p l a c e d by m o l a l i t i e s and mean activity coefficients.  S i m p l i f y i n g Assumptions Even t h e s i m p l i f i e d e q u a t i o n o f t h e a p p a r e n t r e s i s t a n c e o f a d i f f e r e n t i a l a r e a o f a c e l l p a i r i . e . Eq. (43) i s cumbersome and time-consuming, I t c a n be s i m p l i f i e d by making s e v e r a l a s s u m p t i o n s , most o f w h i c h c a n 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 a s s u m p t i o n t h a t c a n be made  i s t h a t t h e two d i f f u s i o n l a y e r s i n each of t h e f l o w c h a n n e l s a r e i d e n t i c a l and t h e boundary l a y e r t h i c k n e s s on t h e two membrane f a c e s With t h i s assumption the c o n c e n t r a t i o n  i s t h e same.  p r o f i l e s become s y m m e t r i c a l i . e .  C. = C. and C = C and t h e two j u n c t i o n p o t e n t i a l s ( t h e c o n c e n t r a t i o n 1 4 5 o c  Q  p o t e n t i a l s i n t h e boundary l a y e r s ) c a n c e l o u t as shown i n F i g u r e assumption i m p l i e s (a)  14.  The  that:  (t - t )  a  =  (t - t )  c  where t , t a r e t h e t r a n s p o r t numbers o f 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 t o a n i o n -  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 t h e boundary l a y e r s i n  the f l o w channels i . e . 5  1,2  =  5  3,4  =  6  5,6  =  6  7,8  =  6  63  to  T 1 J, | Cone.  0) o c o o  Dilute E,  Cone.  Dilute  -4  c o o o 03  2rn<p  =-|rn4 .o  1  "26"  ~|3mc£  C a> o c o o  C'  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  A c c o r d i n g t o t h i s a s s u m p t i o n Eq. (43) r e d u c e s t o YeC  l1-99  R  I n C.A-/C A 2 ( t - t c) §F iI n y C f 2 6 ( C A A - C C A _A  =  c  ( -  +  where t , t  A  2  4  6  ) ctAT 2 2 (  1  4  2  ^ A 7 ) 6 6  +  +  P a  2  +  1  Pc  ]  1  I n CJV,/CJV_ C C AA r A 6  6  <  4 4 )  a r e t h e t r a n s p o r t numbers o f c o u n t e r i o n s and c o - i o n s i n t h e  £  membrane phase. Eq. (28) c a n be used t o e s t i m a t e t h e boundary l a y e r t h i c k n e s s , 6.  Other  terms w h i c h a r e n o t a c c e s s i b l e t o d i r e c t measurement i n Eq, (44) a r e t h e i n t e r f a c i a l concentrations,  and C^.  These c a n be e l i m i n a t e d a s f o l l o w s :  Eq. (10) c a n be w r i t t e n a s i£ dx  °2 " l & C  =  =  i  •  B  ( 4 5 )  ^  ;  where t h e c o n s t a n t B, w h i c h depends o n l y on t h e n a t u r e o f t h e d i s s o l v e d e l e c t r o l y t e and o f t h e membrane, i s d e f i n e d a s B  ==  (46)  (t - t )  s u b s t i t u t e Eq. (11) i n t o Eq.  6  =  (46)  B C-v-^ Him  (47)  T h e r e f o r e we g e t C  ±  =  C  2  (1 -  ~—  )  =  C  2  (1 - k )  (48)  lim  S i m i l a r l y by assuming t h e same c o n c e n t r a t i o n i n b o t h d i f f u s i o n l a y e r s we g e t  65  C  5  C  "  6 f +  "  C  6  < > 49  where n s i s t h e 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 a s s u m p t i o n s c a n be made. The e q u i v a l e n t conductance i s independent o f c o n c e n t r a t i o n over t h e l i m i t e d range o f i n t e r e s t i . e . l  A  =  A  2  =  =  A  The a c t i v i t i e s a r e e q u a l t o t h e c o n c e n t r a t i o n s , y  =  ±  Y  2  =  ' = i-o  W i t h t h e s e a s s u m p t i o n s t o g e t h e r w i t h Eqs. (48) and (49) Eq. (44) reduces to  where k and ns a r e d e f i n e d by Eqs. (26) and (50) r e s p e c t i v e l y and t , t a r e the t r a n s p o r t numbers o f t h e c o u 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 t h e membrane.  F o r i d e a l l y s e l e c t i v e membranes (t - t ) = c  1.0  I n s t e a d o f i n t e g r a t i n g o v e r t h e whole f l o w p a t h , 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 a c h i e v e d by u s i n g l o g a r i t h m i c ^ mean v a l u e s o f t h e b u l k c o n centrations, C  2  and Cg t o g e t h e r w i t h Eq. (44) o r (51) t o e v a l u a t e t h e a p p a r e n t  r e s i s t a n c e o f a complete c e l l  pair.  66  A  F i n a l l y i t s h o u l d be n o t e d t h a t a l l t h e s e e x p r e s s i o n s f o r t h e apparent r e s i s t a n c e o f a c e l l p a i r , namely Eqs. ( 4 2 ) , ( 4 3 ) , (44) and (51) have t o be m o d i f i e d t o t a k e i n t o account  t h e 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 t o s c a l e .  S c a l e s , such a s CaSO^, CaCO^,  Mg(0H)2 e t c . , c a n p r e c i p i t a t e o u t o f s o l u t i o n and d e p o s i t on t h e 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 s t a c k . resistance.  I t i s an e m p i r i c a l a p p r o a c h t o e v a l u a t e s t a c k  F o r a c e l l o f g i v e n d e s i g n and membrane t y p e , i t i s a r e l a t i v e l y  simple matter  t o u s e a l a b o r a t o r y model t o o b t a i n an e m p i r i c a l s e t o f  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 . v a l u e s may t h e n be used t o d e s i g n a f u l l - s c a l e p l a n t . e x p r e s s e d a s t h e r e s i s t a n c e o f 1 cm  2  These  T h i s d a t a may be  2 o f one c e l l p a i r i n ohm-cm , a s 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 concentrations. A l t h o u g h t h e a c t u a l c o r r e l a t i o n o f 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 t a k e t h e f o r m o f a p o l y n o m i a l power s e r i e s as R  P  = a + bC + cC  2  e t c , o r an e x p o n e n t i a l f o r m R  P  Tye ( 1 9 6 3 ) , Mason and K i r k h a m (1959) have suggested for  t h e 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  where K^, ^  P  = and  B  a s shown by  the following  expression  pair:  l  K  R  = a C  such  —  C  + K_ - L 2  C  (52)  3  a r e c o n s t a n t s f o r a g i v e n s p a c e r geometry, i o n i c com-  p o s i t i o n , membrane t y p e and t e m p e r a t u r e . c e n t r a t i o n c a l c u l a t e d from  C i s t h e l o c a l "average"  con-  67  _1_ C"  1 ( ~ + ~ ) 1 + r C. C  =  v  (53)  T  Q  C  Here C. and C a r e t h e l o c a l d i l u a t e and c o n c e n t r a t e d c r i s t h e r a t i o o f spacer  c o n c e n t r a t i o n s , and '  t h i c k n e s s e s i n t h e c o n c e n t r a t e and i n t h e 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) r e d u c e s t o t h e form l ^ C K  R  = P  + K  (54)  9 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 i s approximately  electrolytes  i n v e r s e l y p r o p o r t i o n a l t o c o n c e n t r a t i o n , and t h e e l e c t r i c a l  r e s i s t a n c e s o f c o m m e r c i a l i o n exchange membranes a r e r e l a t i v e l y 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 . (Mason, 1959).  Eq.  T h i s i s t r u e up t o about 0.1 N  Thus Eq. (54) c a n be c o n s i d e r e d  r e s i s t a n c e term,  C  independent  t o c o n s i s t of a s o l u t i o n  , p l u s a membrane r e s i s t a n c e t e r m , K .  The K„ term i n  0  (52) a l 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 c o n -  d u c t a n c e , and f o r d e c r e a s e 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 concentration.  A t 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 h i g h e r t h a n 0.1 N t h e 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  concentration  because o f t h e i n c r e a s e d c o n d u c t i v i t y o f t h e e l e c t r o l y t e i n t h e r e s i n . A l l o w a n c e s f o r membrane p o t e n t i a l s w h i c h oppose t h e a p p l i e d v o l t a g e and  t h u s r e p r e s e n t an a p p a r e n t 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  t o c o n c e n t r a t i o n g r a d i e n t s i n t h e d i f f u s i o n l a y e r s i s made i n c h o o s i n g t h e n u m e r i c a l v a l u e s o f K^,  and K^.  The K's c a n be e s t i m a t e d  from t a b u l a t e d  v a l u e s o f s o l u t i o n and membrane r e s i s t a n c e . The  s t a c k r e s i s t a n c e i s c a l c u l a t e d f r o m t h e 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 t h e 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 o v e r t h e  68  whole f l o w p a t h .  Integration  Procedure  The l o c a l v a l u e , a t any l e v e l z a l o n g t h e f l o w p a t h , o f t h e r e s i s t a n c e per u n i t a r e a o f a c e l l p a i r (R ")^ c a n be i n t e g r a t e d  o v e r t h e membrane a r e a  (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 t o o b t a i n t h e t o t a l r e s i s t a n c e o f a c e l l pair, R . P pa 1_ R  cell  da o  pair/ft  (55)  p z  where a , i s t h e a c t u a l membrane c r o s s - s e c t i o n a l a r e a , cm  (a = m x n ) ; and  p i s t h e f r a c t i o n o f membrane a r e a 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 c m  2  where n i s t h e membrane w i d t h (cm) and z i s t h e c o o r d i n a t e system a l o n g a membrane s u r f a c e  R  ( r e f e r t o F i g . 11) t r a n s p o s i n g .m dz = pn p z z=0  variables, (56)  From Eqs. ( 5 2 ) , (53) l cjiy  K  P z  +  K  K  2  3  C (z) a  (57)  and  1  C (z) a  1 + r  C (z) d  +  r  C (z)  (58)  b  V a r i a t i o n s o f 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 o f a D a  69  C ( ) a  (59)  = f(z)  Z  K, (60) Substituting  Eq.  (60) i n t o Eq. m  r  =  R  l  K  [  pn  (56),  + K  - K  2  3  f (z)]  -1  dz  o m =  { K  pn  ±  + K  f(z) - K [ f ( z ) ]  2  3  2  }  1  f ( z ) dz  f ( z ) i s o b t a i n e d by s u b s t i t u t i n g v a l u e s o f t h e b u l k s o l u t i o n s and  (32) i n t o Eq.  f ( z ) = C (z)  (61)  from Eqs.  (31)  (58)  d H - r ) ( C ( 0 ) e - ) { [ C ( m ) - ( F ^ F ^ (m) ] + [ ( F ^ C ^ O e " "-az. *]} a Z  =  d  3  b  . . .  1  ...i  . ~  •  -  - —  {[C (m) - ( F / F ) C (m)] + C ( 0 ) e b  d  b  d  d  _ C t Z  . . . . . .  [ ( F ^ )  t  Thus, s u b s t i t u t i n g i n t o Eq.  • « « o  (61) f o r f ( z ) o r C ( z ) , the c e l l p a i r  •  +  u  •  r  ]}  • i  (62)  resistance,  Si  Rp,  can be e v a l u a t e d .  S m a l l i n t e r v a l s (Az) can be chosen t o e v a l u a t e  the  i n t e g r a l as a summation C (z) a  R  =  pn  2_  Az  + K, C ( z ) a  - K  3  C (z)2  (63)  a  z=0  3.2.  Mass T r a n s f e r Models  The d i f f e r e n t i a l e q u a t i o n o f 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 t h e 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 (a) where  and  m o b i l e and  C  (b)  g  (c)  =  0  (64)  (d)  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  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 t h e d i s p l a c e m e n t v e l o c i t y ,  D i s solute d i f f u s i v i t y , e i s void f r a c t i o n . E q u a t i o n (64)  i s sometimes c a l l e d the chromatography e q u a t i o n .  terms i n t h i s e q u a t i o n e x p r e s s mass c o n s e r v a t i o n  The  contributions attributable  t o 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)  =  axial  (c)  =  a x i a l fluid-phase d i f f u s i o n  (d)  =  adsorptive  convection  phase t r a n s i e n t  T o g e t h e r w i t h an e q u a t i o n r e l a t i n g l o c a l v a l u e s of C appropriate  g  t o C^,  boundary c o n d i t i o n s , E q u a t i o n (64) a p p l i e s d u r i n g  and  every  sub-  i n t e r v a l of a c y c l i c f l o w p r o c e s s .  3.2.1.  E q u i l i b r i u m Model P i g f o r d e t a l . (1969) used E q u a t i o n (64)  model" f o r t h e r m a l p a r a m e t r i c pumping. t h a t t h e s o l i d and  The  b a s i c a s s u m p t i o n i n t h i s model i s  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 .  s i m p l i f i e s the equations since r a t e i n f o r m a t i o n a x i a l d i s p e r s i o n was t o be l i n e a r .  to develop a simple " e q u i l i b r i u m  neglected  and  This assumption g r e a t l y  i s not needed.  Tn a d d i t i o n ,  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  W i t h t h e s e a s s u m p t i o n s the r e s u l t i n g e q u a t i o n i s a  assumed hyperbolic  p a r t i a l d i f f e r e n t i a l e q u a t i o n w h i c h can be s o l v e d 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 d e v e l o p e d 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 t o show g r a p h i c a l l y t h e development of t h e s e p a r a t i o n , and  t o show  72  when s e p a r a t i o n w i l l not o c c u r ;  t h u s t h e model o f f e r s a l g e b r a i c  solutions  t h a t 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 . e q u i l i b r i u m t h e o r y was system by G r e g o r y and  generalized  by A r i s (1969) and  Sweed ( 1 9 7 0 ) , Chen and H i l l  extended by Thompson and arrangement where the two  The  extended to an open  (1971) and  Bowen (1972) t o p r e d i c t s e p a r a t i o n  i t was  further  i n a two-column  columns a r e o p e r a t e d b a c k - t o - b a c k t o m i n i m i z e  mixing. A l t h o u g h the e q u i l i b r i u m model i s compact and d i s p e r s i v e e f f e c t s which l i m i t separation p r e d i c t the u l t i m a t e steady-state  easy t o a p p l y i t i g n o r e s  i n a r e a l system, hence i t can  separation  ( R i c e , 1973).  Gupta  not  and  Sweed (1972) have extended the e q u i l i b r i u m model t o t a k e i n t o a c c o u n t a x i a l mixing.  Foo  and  Rice  (1975, 1976)  used a more g e n e r a l  t e m p e r a t u r e dependence  i n t h e l i n e a r i s o t h e r m a l o n g 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  with  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  ultimate  separation  i n c l o s e d parapumps.  p o r e d i f f u s i o n t o p r e d i c t the  Mass t r a n s f e r between t h e moving phase  t h e s t a t i o n a r y phase i s assumed t o t a k e p l a c e i n s t a n t a n e o u s l y 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  p r e d i c t e d by t h e model.  do not  enter  S i n c e the c y c l e d u r a t i o n may  possible  i n t o the  be a s s i g n e d  a r b i t r a r y v a l u e , t h e e q u i l i b r i u m model s o l u t i o n s a r e not t i m e and  i n the  and  equi-  solutions any  f u n c t i o n s of r e a l  t h e model can o n l y s e r v e as i n i d e a l i z a t i o n t h a t p r e d i c t s the  best  separation.  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 p r o c e s s e s such as e l e c t r o d i a l y s i s a r e governed by f i n i t e r a t e s of mass t r a n s f e r and t r a t i o n s f a r from e q u i l i b r i u m . the c u r r e n t  flowing  The  u s u a l l y o p e r a t e a t concen-  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  ( w i t h i n a c e r t a i n r a n g e of c o n c e n t r a t i o n )  t o some e x t e n t under the d i r e c t c o n t r o l of t h e e x p e r i m e n t e r .  and  i s thus  Cyclic  to  73  o p e r a t i o n of such systems may model t h a n by e q u i l i b r i u m 3.2.2.  t h e r e f o r e be b e t t e r r e p r e s e n t e d by a r a t e  theory.  R a t e Models Two  r a t e models w i l l be c o n s i d e r e d  here:  (a)  c o n s t a n t r a t e model  (b)  c o n c e n t r a t i o n - d e p e n d e n t r a t e model  The  b a s i c a s s u m p t i o n i n each of t h e s e models i s t h a t t h e  c o n d i t i o n may  be d i s r e g a r d e d  i n s t a t i o n a r y contact would be  a l t o g e t h e r , i . e . i f t h e two  equilibrium  phases were l e f t  f o r a s u f f i c i e n t l y l o n g p e r i o d of t i m e , the a d s o r b a t e  t r a n s f e r r e d c o m p l e t e l y i n t o one  of t h e phases.  These models a l s o  assume t h a t the c a p a c i t y o f the s t o r a g e l a y e r s i s l a r g e enough t h a t i t does not  impose a l i m i t on mass t r a n s f e r d u r i n g  the c y c l e .  neglected  and  the f l u i d i s assumed t o be i n c o m p r e s s i b l e  density.  The  complete o p e r a t i n g  intervals;  Axial dispersion i s and  have c o n s t a n t  c y c l e i s d i v i d e d i n t o a number of  whenever the f l u i d v e l o c i t y changes a t the end  sub-  of t h e s e  periods  i t i s assumed t h a t i t changes i n a s t e p w i s e manner, w h i l e i t r e m a i n s constant during  each of t h e s e s u b - i n t e r v a l s .  F u r t h e r m o r e , a system i n w h i c h  one v o i d volume i s d i s p l a c e d e v e r y h a l f c y c l e i s Concentration time, i n contrast  changes p r e d i c t e d by  considered.  the r a t e models a r e f u n c t i o n s  of  to the e q u i l i b r i u m model s o l u t i o n s w h i c h a r e f u n c t i o n s  of  the number of c y c l e but n o t of r e a l t i m e , (a)  C o n s t a n t r a t e model A c o n s t a n t r a t e of I n t e r p h a s e mass t r a n s f e r , u n i f o r m everywhere w i t h i n  the c e l l , r e q u i r e s a c o n s t a n t , Uniformity  u n i f o r m , d i s t r i b u t i o n of e l e c t r i c  current.  can be a p p r o x i m a t e d by c o n n e c t i n g a number of s h o r t s t a c k s  i n s e r i e s b o t h 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.  together  74  Dialysate Production  Br'me Production  FIGURE 16 Series connection of ED modules to approximate  constant-rate operation.  75  C o n s t a n t c u r r e n t c a n be m a i n t a i n e d  by a s u i t a b l e power s u p p l y .  This  will  e n s u r e c o n s t a n t mass t r a n s f e r u n t i l t h e s o l u t e c o n c e n t r a t i o n d r o p s l o w enough a t some p o i n t i n t h e a p p a r a t u s t h a t w a t e r s p l i t t i n g o c c u r s and s o l 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 current.  While  constant-  r a t e o p e r a t i o n i s n o t v e r y p r a c t i c a l , an e x a m i n a t i o n o f some of t h e c o n sequences o f t h i s model i s o f 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  limiting  conditions. I f t h e r a t e o f mass t r a n s f e r i s h e l d c o n s t a n t , and a x i a l d i f f u s i o n i s neglected, Equation dC •*r  (64) s i m p l i f i e s t o  ..  9C. TT-  +  =  v  dt  ac  - < ^T^-  > TT-  £  dZ  =  K (constant)  (65)  dt  d u r i n g any s u b - i n t e r v a l o f t h e c y c l e . (i)  Synchronous ( i n - p h a s e )  operation  I f t h e t o t a l c y c l e p e r i o d T i s composed o f two e q u a l s u b - i n t e r v a l s , w i t h s i m u l t a n e o u s r e v e r s a l o f b o t h t h e f l o w d i r e c t i o n and t h e d i r e c t i o n of mass t r a n s f e r , t h e n t h e c o n s t a n t  i n Equation  (65) c a n be w r i t t e n K = -  d u r i n g t h e 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 dC  £ dt"~ dC  dC  c  ~ P  =  dC  t £  -j-jT-  =  - p  s  ~ ^1  =  »  ^  o r  2  d u r i n g enrichment i . e .  demineralization  (66)  s =  K  2  ;  f o r enrichment  (67)  1 - e where p = e T I f we c o n s i d e r K then to m a i n t a i n  2  >  and d e m i n e r a l i z a t i o n t a k e s p l a c e f o r t i m e y ;  t h e m a t e r i a l b a l a n c e o f t h e system t h e e n r i c h m e n t p e r i o d  s h o u l d be A t where  76  At  T K ^  -  (68)  T l d u r i n g t h e r e s t o f enrichment h a l f c y c l e i . e . — (1 - — ) t h e v o l t a g e c a n 2 K  be s w i t c h e d The  o f f t o save power.  g r a p h i c a l s o l u t i o n o f t h e model E q u a t i o n s  following result  ( 6 6 , 67, 68) g i v e s t h e  ( r e f e r t o Appendix D):  C  T K o  T K o  -  1  +  t f  o  (  K o  1  2  - k : ^  o  ( 7 0 )  2  where C„, a r e t h e t o p ( d e m i n e r a l i z e d ) p r o d u c t and t h e b o t t o m ( e n r i c h e d ) 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 concentration; C , . = C . = C o ' f(t=0) s(t=0) o N  n From E q u a t i o n s  N  rtN  i s t h e number o f c y c l e s ( 6 9 , 70) i t i s c l e a r t h a t maximum s e p a r a t i o n o c c u r s  l K_ >> K. o r when — £• J. K by  when  K  -»• 0.  I n t h i s c a s e t h e s e p a r a t i o n f a c t o r , ns i s g i v e n  2  TK-n  n s  -  TT^ T,n  1 -  I t i s a l s o o b v i o u s t h a t when cycle.  TK n 4 C o 1  = 1^, no s e p a r a t i o n o c c u r s a f t e r t h e f i r s t  The c o n c e n t r a t i o n o f s o l u t e s t o r e d w i t h i n t h e membranes r e t u r n s t o  i t s i n i t i a l v a l u e a t t h e end o f each c y c l e and t h e a v e r a g e t o p and b o t t o m conc e n t r a t i o n s (Equations  69, 70) do n o t change a f t e r t h e 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 c c e s s i v e c o n c e n t r a t i o n p r o f i l e s i n t h e s t a c k  4  Ac  Plug Flow  Plug Flow  Plug Flow  Co  c(i)  b(i )  Btm. Resvr.  E.D. Stack  Top Resvr.  Well Mixed  Plug Flow  d(i)  Well Mixed  Axial Position  t = 0  FIGURE  t =0  Ot=T/2  d(ii)  c(ii)  b(ii)  a  t = T/2  E> t = T  t= T  Ot=3T/2  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  F o r s i m p l i c i t y i t i s assumed t h a t  the end r e s e r v o i r s have the same volume and interior.  The  the same L/D  r a t i o as 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  cell 17,  A f t e r t h e 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 a r e e i t h e r as shown i n ( b i ) ( i f no m i x i n g t a k e s 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 t h e r e s e r v o i r i s w e l l mixed).  The  fluid  end  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  t h r o u g h the column t o produce the p r o f i l e s shown i n ( c i ) or ( c i i ) a t  the  end o f 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 r e t u r n e d t o 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 a t t h e end o f t h e 3 r d h a l f c y c l e , w h i c h a r e i d e n t i c a l w i t h (b) . I n o r d e r t o 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) (ii)  make K  2  >  , or  m o d i f y 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  electric  c u r r e n t , or (iii) (iv)  m o d i f y t h e 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 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  flow, out-of-  phase o p e r a t i o n Case ( i ) has a l r e a d y been c o n s i d e r e d .  Thompson e t a l . (1974) has  dis-  c u s s e d t h e o t h e r t h r e e c a s e s as shown i n the f o l l o w i n g s e c t i o n s . (ii)  Interrupted Current  operation  T h i s i s a more g e n e r a l and more u s e f u l t y p e of o p e r a t i o n than c a s e ( i ) Here t h e c u r r e n t i s t u r n e d o f f d u r i n g a p a r t of e v e r y h a l f c y c l e . shows t h e 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 o f o p e r a t i o n .  Figure  During  the  f i r s t h a l f - c y c l e b o t h f l o w and mass t r a n s f e r t a k e p l a c e f o r p e r i o d T^, w h i c h p o i n t the c u r r e n t i s t u r n e d o f f and  18  flow continues f o r period T . 0  at A  s i m i l a r sequence,  and T^, f o l l o w d u r i n g t h e second h a l f - c y c l e .  From t h e  m a t e r i a l b a l a n c e on t h e s a l t  V i  -  K  2 3 T  ( 7 2 )  and from t h e m a t e r i a l b a l a n c e on t h e s o l v e n t  l  T  +  T  2  =  T  3  +  T  4  ( 7 3 )  I f 3 i s t h e f r a c t i o n o f t h e f i r s t h a l f - c y c l e d u r i n g w h i c h t h e c u r r e n t i s on (3 = T  ^  /  ,  r  ±  =  2  =  3  -  T  t  and  then the s u c c e s s i v e i n t e r v a l s a r e ;  T  4  =  3 ( f ) (1 - 3 ) ( | ) > *1 T (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 c o n s e c u t i v e  intervals i n a  b a t c h 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 w h i c h t h e end r e s e r v o i r s unmixed i s i l l u s t r a t e d . b e g i n n i n g o f each p e r i o d of each p e r i o d .  remain  The d o t t e d l i n e s r e p r e s e n t t h e c o n c e n t r a t i o n a t t h e and t h e s o l i d l i n e s show t h e p r o f i l e a t t h e end  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 o f t h e  c o n c e n t r a t i o n wave. The a v e r a g e t o p p r o d u c t 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 g i v e n by C o  TK TK K = l - - ^ M 2 - 6 ) - ^ M 2 - M l + ^ ) ] o o 2  and t h e a v e r a g e c o n c e n t r a t i o n o f t h e bottom  (n - 1)  (enriched) product i s  (75)  FIGURE 18 Concentration profiles-interrupted current cycle.  81  C  TK 1 + j±  = o If  = K  2  K 3 [2 - 3 ( 1 + ^ o  and 3 = 1  )] n  (76)  2  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 v a l u e o f 6 t h a t 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 of K^/K,,.  D i f f e r e n t i a t i o n of e q u a t i o n  value  (75) o r (76) shows t h a t t h e 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 o b t a i n e d when K  2  Under t h e s e c o n d i t i o n s t h e s e p a r a t i o n f a c t o r i s g i v e n by TK 1  ns  =  4cT ^  +  -  e  n  (78)  1 - - ~ 3 (n - 3 + 1) o Thus, i f K^ = K  2 >  b e s t s e p a r a t i o n i s o b t a i n e d by s e t t i n g 3 = h, so t h a t  =  T_ = x_ = T, and t h e s e p a r a t i o n f a c t o r i s 2 3 4 TK 1  ns  +  -  8cT _ 2  n  1 - -ggi (n + o n max If K  2  8C = (™ TK^  h).  >> K^, 3 = 1  (79) W  If n > n , then n must be used. max' max  and t h e s e p a r a t i o n f a c t o r i s TK 1  ns  = 1  provided  4cT ^  +  that n <  "  4C — 1 T K  n  4Co  (80) n  82  S i n c e 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 o f each c y c l e , t h e amount of separation obtained  f o r a g i v e n amount o f c u r r e n t consumed i s  the same i n e q u a t i o n s  (79) and  approximately  (80).  I f a r e a l system i s o p e r a t e d  with  > 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 c a s e ( i ) , the c o n c e n t r a t i o n i n the s t o r a g e l a y e r s must c o n t i n u a l l y d e c r e a s e i n s u c c e s s i v e c y c l e s .  After a  number of c y c l e s t h e c o n c e n t r a t i o n w i l l drop t o near z e r o p a r t way  through a  d e p l e t i o n h a l f c y c l e , c a u s i n g t h e e l e c t r i c a l r e s i s t a n c e t o become v e r y large.  I f the v o l t a g e i s c o n t r o l l e d a t a c o n s t a n t v a l u e the c u r r e n t must  t h e n become v e r y s m a l l , so t h a t , f r o m t h i s c y c l e onward, t h e 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  t h r o u g h each d e p l e t i o n  cycle.  (iii)  Interrupted flow operation  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. displacement,  Here the  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 .  c u r r e n t i s t u r n e d on a t the b e g i n n i n g o f the c y c l e , t o d e m i n e r a l i z e s o l u t i o n , b u t f l o w does not s t a r t u n t i l t h e end of pause t i m e x^. fluid  i s d i s p l a c e d upward d u r i n g p e r i o d  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 .  fluid  The the The  w h i l e the c u r r e n t r e m a i n s on  and  p o l a r i t y i s r e v e r s e d a t the  start  The  o f 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  c o m p l e t e s the c y c l e .  two pause p e r i o d s x^ and x^ and  The  c o m p l e t e c y c l e t i m e T c o n s i s t s of  the d i s p l a c e m e n t  periods  and  subsequent work based on t h i s o p e r a t i n g c y c l e t h e d i s p l a c e m e n t k e p t c o n s t a n t and  l  ( t  1  I n the  periods  the c y c l e t i m e T v a r i e s w i t h the pause t i m e used.  From the m a t e r i a l b a l a n c e  K  x^.  +  T  2  )  =  K  2  ( T  3  on t h e  +  T  4  )  the  salt  ( 8 1 )  are  83  and  from the m a t e r i a l b a l a n c e T  I f pause  T  =  2  on the  solvent (82)  4  lasts for a fraction  successive i n t e r v a l s  o f the t o t a l c y c l e t i m e T,  then the  are:  f  a( ) l  T  =  2 + K  T  T K T  2  K  =  x  K  "  2  a (  2  }  l ~ 2  T  K  and T  -  4  x  (83)  2  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  d e v e l o p s i n a c l o s e d system w i t h no m i x i n g  i n the. end  compartments.  The a v e r a g e top-compartment c o n c e n t r a t i o n a f t e r the n t h c y c l e i s g i v e n by TK  C  o  2K o  1  TK 2  K  K  o  2  -K 1 2 (84)  and  the bottom c o n c e n t r a t i o n i s  C C  I f K^ = K  2  = Q  1  + 77^ U l + ^ 4C  Q  K  ) a + 2 ( 2  the s e p a r a t i o n f a c t o r i s given  by  1  2  K  X  +  )} n  K  2  (85)  CURRENT  o o 3 O  Deplete Enrich O  23 <n c  FLOW Down  Up o  m  o o  _ CO -I*  | <o  i 5" CD  C  » QO  >o < o  ro  OJ  178  85  1 + — 2 , 1 , , l-ot 1 - _ a (n + — ) o a  ns  =  n  (  8  6  )  s  2C t h a t o < a < 1 and n = (— max TK^a If n > n , then n must be u s e d , max max o  Provided  _ -z— ) . 2a 1  a  O b v i o u s l y , b e s t s e p a r a t i o n i s o b t a i n e d a s a + 1, g i v i n g an o p 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 l o n g f l o w - p a u s e s and r a p i d d i s p l a c e m e n t . case may be r e f e r r e d t o a s i n s t a n t a n e o u s  displacement  pause o p e r a t i o n i n c o m p a r i s o n w i t h c o n t i n u o u s Case ( i ) .  As a  This  special  operation or pure-  displacement  o p e r a t i o n of  1, t h e s e p a r a t i o n i s g i v e n by TK 1  ns  +  2 C ^  n  =  (87) 1  TK 2T o  n  which i s double t h e v a l u 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 cond i t i o n s (Equation 71).  (iv)  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 t h e 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 operating w i t h the current c y c l e 90° o u t - o f - p h a s e w i t h t h e d i s p l a c e m e n t . c o n s t a n t s K^ and reservoirs.  I t i s assumed t h a t t h e r a t e  a r e e q u a l and t h a t t h e e f f l u e n t r e m a i n s unmixed i n t h e end  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 o f t h e c o n c e n t r a t i o n wave. 2T  I f t h e c u r r e n t s w i t c h i n g l e a d s t h e f l o w s w i t c h i n g by t i m e T , and y = t h e a v e r a g e t o p 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 t h e n t h c y c l e a r e  —»  FIGURE  20  Concentration profiles predicted by constant-rate modeLcontinuous cyclic displacement of fluid and mass transfer.The mass transfer cycle is 9 0 ° o u t - o f .phase with the displacement cycle.  87  given by: C  TK = 1 - • — o  TK [1 - 2 Y ] - - ^ ( 1 - Y) 2  o  C  ( n - 1)  (Y)  (88)  o  TK = 1 + o  (1 - Y)  n  (Y)  (89)  o  i n t h e i n t e r v a l o 4 y < h*  The c o n c e n t r a t i o n s change l i n e a r l y w i t h t h e  number o f c y c l e s and t h e g r e a t e s t r a t e o f change o c c u r s when y = h.  This i s  i n marked c o n t r a s t t o t h e r e s u l t s o f t h e e q u i l i b r i u m model o f p a r a m e t r i c pumping, w h i c h p r e d i c t s b e s t s e p a r a t i o n when t r a n s f e r and d i s p l a c e m e n t  cycles  a r e i n phase and no s e p a r a t i o n when they a r e 90° o u t o f phase ( P i g f o r d e t 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 g i v e n b y ns  =  i = -  -  (90)  4C  x  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 t h e s e p a r a t i o n f a c t o r i s  TK1  ns  = 1  n . max  =  +  4cT ^  n  " 4CT < o  (91) n  -  4C (— — I - %). TK^  ^  When n > n  max  , then n  max  must be used.  F i g u r e 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 o f two u n i t s operated  t o g e t h e r , w i t h t h e t o p o f one c e l l c o n n e c t e d d i r e c t l y t o t h e  top o f t h e o t h e r and t h e bottoms o f t h e c e l l s c o n n e c t e d t o g e t h e r r e v e r s i b l e pump.  through a  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 a r e needed and  the c o n c e n t r a t i o n wave b u i l d s up t w i c e a s 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 O-H/4  I  I  I T/4-H/2  I  I  I T / 2 4 3T/4  I  J  I 3T/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 t h a t 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) end of each h a l f c y c l e . r e v e r s a l or c o n t i n u o u s  i s symmetrical  at  the  Because o f t h i s symmetry e i t h e r p e r i o d i c f l o w 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 .  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  In  generated,  w h i c h grows w i t h t i m e , 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 a t 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 t o o p e r a t e  a  number of u n i t s i n s e r i e s t o g e n e r a t e a t r a v e l l i n g wave, g r o w i n g 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 d i s c u s s e d  P i g f o r d e t a l . (1969  by  b).  Comments on v a r i o u s o p e r a t i o n s o f 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 o b t a i n e d i n the f o u r c a s e s 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 ) t h a n w i t h e i t h e r of the o t h e r c a s e s c o n s i d e r e d . f e r during displacement  S i n c e mass t r a n s -  c o n t r i b u t e s l i t t l e t o t h e f i n a l s e p a r a t i o n i n pause  o p e 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 o b t a i n e d by t u r n i n g the c u r r e n t o f f d u r i n g a l l o r p a r t of the  displacement  periods.  (b)  C o n c e n t r a t i o n - d e p e n d e n t r a t e model" While i t i s p o s s i b l e to operate  the p r o c e s s  s t a n t r a t e mode, i t i s more c o n v e n i e n t electrodes.  The  i n a constant  current/con-  t o a p p l y a c o n s t a n t p o t e n t i a l t o the  l o c a l c u r r e n t d e n s i t y i s t h e n a f u n c t i o n of the concen-  t r a t i o n s a l o n g the c u r r e n t 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 i s At))' ( a f t e r ohmic l o s s e s and  the v o l t a g e a v a i l a b l e t o the  stack  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 a r e  a l l o w e d f o r ) , t h e n the c u r r e n t t h r o u g h the s t a c k i s g i v e n  by  90  -  1  ^R-^  ( 9 2 )  where A<J>^~ i s the Donnan p o t e n t i a l a c r o s s DON XT  the membranes of the s t a c k .  r  r e s i s t a n c e i s t h e sum  of t h r e e t e r m s , R  The  - 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 c h a n n e l s , 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 c o r e 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 c o m p r i s e the b u l k f l u i d  resistance  t o g e t h e r 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 o p e r a t i n g c o n d i t i o n s f o r most e x p e r i m e n t s the Donnan p o t e n t i a l was  s m a l l compared t o the a p p l i e d p o t e n t i a l , so t h a t t h e c u r r e n t d e n s i t y  m a i n l y 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 p a t h . c e n t r a t i o n s , and hence h i g h r e s i s t a n c e s , o c c u r r e d  Accordingly  con-  i n the f l o w c h a n n e l s  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 during enrichment.  Low  was  during  i n the membrane c o r e s  the ' f o l l o w i n g r a t e laws were assumed  9C g p -rr— = at  &i C^. JL t  ac  -r—ot  = - a„ C 2 s  (during depletion)  (93)  (during enrichment)  (94)  S u b s t i t u t i n g these equations i n t o equation  ( 6 4 ) , and  neglecting  axial  d i f f u s i o n , l e a d s t o a s e t of e q u a t i o n s t h a t can be s o l v e d 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 o b t a i n e d  interrupted-flow operating  cycle previously described  i s r e s t r i c t e d to the f l o w - p a u s e p e r i o d s and e q u a l t o the v o i d volume. and b r i n e c o n c e n t r a t i o n s  ^ C  o  -  P  n  ( B a s s , 1972)  provided  for  the  mass t r a n s f e r  the d i s p l a c e d f l u i d volume i s  Under t h e s e c o n d i t i o n s , the average d i a l y s t a t e after n cycles  are  (95)  91  i »  o  2  +  p  _ n _ p  p q  n _  q p  n-l  ( 1  _  p )  j-  {  4=n-l ± ] 4  ( g g )  where a  p  =  exp (  q  =  exp (  p  =  1— -- e —  a  l — T  )  2 2~ ) T  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 a p p r o a c h c a n be d e v e l o p e d by assuming a c o n c e n t r a t i o n - d e p e n d e n t mass t r a n s f e r r a t e s i m i l a r t o E q u a t i o n s ( 9 3 , 94) 9C p  \  =  C  (during depletion)  F  (97)  By c o n s i d e r i n g t h e o v e r a l l m a t e r i a l b a l a n c e f o r t h e s o l u t e and t h e l i m i t i n g s e p a r a t i o n a g e n e r a l s o l u t i o n o f t h e system i s o b t a i n e d  i n w h i c h t h e 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 a r e g i v e n by C =  -k Tn e x p ( -j— ) + k  =  -k.. Tn 2 - exp( - | — ) - k  2  -k Tn [1 - exp( -f-)]  (98)  o C  /. [1 - exp( -f_ k  2  T n  )]  (99)  o T h i s s o l u t i o n c a n be s i m p l i f i e d by assuming t h a t k^ = k^ = k^ i n t h i s case E q u a t i o n s (98, 99) r e d u c e t o C  -k Tn ) + k  -k Tn [1 - exp( - | — ) ]  o  exp(  =  k  =  -k Tn 2 + ( k - 1) exp ( - ± — ) - k  2  o  C  2  -k Tn + (1 - k ) exp ( - 1 — )  (100)  2  2  2  (101)  92  where k^, k^ a r e c o n s t a n t s w h i c h a r e 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 c h a n n e l and s t o r a g e compartment a r e o f t h e same c a p a c i t y and d i m e n s i o n s (as i s the u s u a l case) t h e n p = 1 . 0 (95, 96) w i l l be a s p e c i a l c a s e o f E q u a t i o n s  and  Equations  ( 9 8 , 99) where t h e c o n s t a n t s  a r e g i v e n by k  3.2.3.  n  = a , k„ = - 1 , k. = 0 and k. = a . 1  Comment on C o n s t a n t - R a t e M o d e l Although  t h e c o n s t a n t - r a t e model i s compact and easy t o a p p l y i t i g n o r e s  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 w h i c h 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 n o t p r e d i c t t h e u l t i m a t e s t e a d y - s t a t e  However, t h e model o f f e r s s i m p l e a l g e b r a i c s o l u t i o n s t o a system w h i c h c a n be u t i l i z e d  separation. complicated  t o show g r a p h i c a l l y t h e development o f t h e  c o n c e n t r a t i o n p r o f i l e s and t o i n d i c a t e when s e p a r a t i o n w i l l n o t o c c u r . model has been used e x t e n s i v e l y i n t h e p r e s e n t work t o 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 o f o p e r a t i o n .  The  CHAPTER 4  The C y c l i c E l e c t r o d i a l y s i s P r o c e s s O b j e c t i v e s , T e c h n i q u e s and A p p a r a t u s  4.1.  O b j e c t i v e s o f t h e Program The  primary o b j e c t i v e s of t h i s experimental  program were;  to  e x p l o r e t h e p o s s i b l e r e g i o n s o f a p p l i c a t i o n o f 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, t o s c r e e n system p a r a m e t e r s and t o d e t e r m i n e t h e i r r e l a t i v e importance. P r e v i o u s work i n a b a t c h system ( B a s s , 1972) showed t h a t t h e most important  o p e r a t i n g p a r a m e t e r s were t h e d i s p l a c e m e n t  age and t h e i n i t i a l c o n c e n t r a t i o n .  c y c l e , the applied v o l t -  These were f u r t h e r i n v e s t i g a t e d h e r e  together w i t h the e f f e c t of production r a t e .  An open system o f f e r s a h i g h  d e g r e e o f freedom w i t h r e g a r d t o i n t r o d u c t i o n o f f e e d and w i t h d r a w a l o f p r o d u c t s , and a v a r i e t y o f d i f f e r e n t o p e r a t i n g modes were c o n s i d e r e d .  The  modular c o n s t r u c t i o n o f t h e ED c e l l a l l o w e d c r u d e measurements t o be made o f t h e a x i a l d i s t r i b u t i o n o f c u r r e n t and probe v o l t a g e d u r i n g t h e c y c l e and also permitted The  the e f f e c t of channel  l e n g t h t o be i n v e s t i g a t e d .  c o n s t a n t - r a t e model d i s c u s s e d i n C h a p t e r 3 p r e d i c t e d t h a t t h e  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 t h e b e s t s e p a r a t i o n compared t o t h e o t h e r c y c l e s s t u d i e d ( s y n c h r o n o u s , o u t - o f - p h a s e and i n t e r r u p t e d c u r r e n t 93  94  cycles).  The e x p e r i m e n t a l  interrupted flow cycle.  p a r t o f t h e work was based m a i n l y on t h i s  The c y c l e i s most c o n v e n i e n t l y d e s c r i b e d  with  r e f e r e n c e t o 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 s t a c k s c l o s e coupled  i n a b a c k - t o - b a c k c o n f i g u r a t i o n were used i n most o f t h e  experimental  4.2.  work.  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 t h e sequence o f e v e n t s t h a t make up a complete operating cycle.  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 a r e a s y m b o l i z i n g t h e s o r p t i o n membrane s t a c k .  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)  a r e connected t o t h e ends o f t h e 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 t h e 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 the c y c l e .  during  F i g u r e 22 shows b a t c h o p e r a t i o n b u t i t c a n be m o d i f i e d t o  a l l o w f o r f e e d a d d i t i o n and p r o d u c t  r e m o v a l i n v a r i o u s ways d u r i n g t h e  cycle. The  i n t e r i o r of the c e l l  membranes i n t o two r e g i o n s ;  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  a s e t of flow channels connecting  t h e 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 s e t o f c l o s e d " c a p a c i t y c e l l s " o r membrane stack.  Depending on t h e d i r e c t i o n o f t h e e l e c t r i c c u r r e n t , i o n s a r e e i t h e r  t r a n s f e r r e d from t h e s o l u t i o n i n t h e f l o w c h a n n e l s t o t h a t i n t h e 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  p o t e n t i a l i s c o n t r o l l e d t o produce a p o s i t i v e square wave.  electric  The membranes  95  MOIJ  pe||ddv  96  a r e 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 equivalent  s o l u t e u p t a k e ( i . e . t h e c a t i o n i c membranes f a c e the anode).  The  to intrachannel  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 : "displacement"  a "pause" or n o - f l o w i n t e r v a l (T^) f o l l o w e d by a  i n t e r v a l ( x ) d u r i n g w h i c h the f l u i d  flows w i t h constant  2  (Q) from t h e lower t o the upper r e s e r v o i r .  Displacing fluid  entering  bottom o f t h e c e l l may  be f r e s h f e e d or " r e f l u x " r e t u r n i n g a f t e r a  downward d i s p l a c e m e n t ,  or a m i x t u r e of t h e s e .  The  w i t h a p o l a r i t y r e v e r s a l (- n) and a s i m u l t a n e o u s "pause" i n t e r v a l ( T ^ ) .  The  rate the  previous  second h a l f - c y c l e b e g i n s f l o w stoppage f o r a n o t h e r  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 s t a c k d u r i n g the whole p e r i o d o f t h i s second h a l f - c y c l e , w h i c h i s concluded  by a " d i s p l a c e m e n t "  i n t e r v a l (T^) d u r i n g w h i c h t h e s o l u t i o n i s  r e t u r n e d from t h e upper t o the lower r e s e r v o i r w i t h f l o w r a t e (- Q). displacing fluid  e n t e r i n g a t the top o f the c e l l may  be f r e s h f e e d , or a  r e f l u x s t r e a m o f d e p l e t e d s o l u t i o n o b t a i n e d d u r i n g p e r i o d (T^) b i n a t i o n of t h e s e .  The  or a com-  I n an open system p a r t i a l r e f l u x must be used t o  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 t h e o p e r a t i o n , i n some ways, i s a n a l o g o u s t o 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 t h e s o l u t e c o n c e n t r a t i o n s i n t h e system a r e i n e q u i l i b r i u m a c r o s s the membranes and  e q u a l everywhere.  of the s o l u t i o n i n the upper r e s e r v o i r and  Each c y c l e produces d e p l e t i o n 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 c o n t i n u e s ED c e l l u n t i l  t o d e v e l o p i n the  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.  I n most of the e x p e r i m e n t s r e p o r t e d h e r e symmetric h a l f c y c l e s w i t h r e g a r d t o t i m e 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 S t a c k C o n f i g u r a t i o n S i n c e some, o r a l l , of the f l u i d  displacement  i s subsequently  l e a v i n g t h e c e l l d u r i n g upward  t o be r e t u r n e d as r e f l u x , i t i s c o n v e n i e n t  connect two c e l l s t o g e t h e r as shown i n F i g u r e 23.  This d i r e c t  to  coupled-  b a c k - t o - b a c k c o n f i g u r a t i o n a v o i d s 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 e x p e r i m e n t s i n a b a t c h o p e r a t i o n showed t h a t m i x i n g i n  the end r e s e r v o i r s l o w e r s s e p a r a t i o n and a r e d u c t i o n of m i x i n g i n the s o l u t i o n e x t e r n a l t o the s t a c k h e l p s to r e d u c e t h e e f f e c t s of m i x i n g by r e d u c i n g the g r a d i e n t s o f the t r a v e l l i n g f r o n t s . s e p a r a t i o n f a c t o r was mixed) was The  internal  The  average  i n c r e a s e d by 30 - 100% when an end r e s e r v o i r  (well  r e p l a c e d by a c o i l t u b i n g ( B a s s , 1972). two c e l l s so connected ( F i g u r e 23) a r e o p e r a t e d  electically  o f - p h a s e w i t h each o t h e r and, of c o u r s e , upward d i s p l a c e m e n t i m p l i e s downward d i s p l a c e m e n t  i n the other  i n one  out-  cell  ( w i t h the p o s s i b l e e x c e p t i o n of  p e r i o d s when t h e f e e d i s b e i n g i n t r o d u c e d or p r o d u c t s  removed).  T h i s 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 operations. develop  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 a r e p r e d i c t e d t o  d u r i n g the f i r s t few c y c l e s o f o p e r a t i o n i n a c l o s e d mode, based  the c o n s t a n t 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  on  quali-  t a t i v e l y i t i s apparent t h a t a x i a l m i x i n g 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 r e s e m b l i n g a s i n e wave.  4.3.1.  Open System O p e r a t i o n o f a b a c k - t o - b a c k c o n f i g u r a t i o n I f f e e d i s to be i n t r o d u c e d , and p r o d u c t s w i t h d r a w n , c o n n e c t i o n s must  be p r o v i d e d w i t h v a l v e s t h a t a r e timed to open a t a p p r o p r i a t e moments d u r i n g the c y c l e .  S i n c e the t o t a l volume of the system r e m a i n s c o n s t a n t , f e e d must  98  Cell I  Cell  I  (—)  Reversing Pump  FIGURE  23  Back _to-back operation of two cells.  I  I  Top  Bottom  Top  Co  '  2  Pause  Displace  Pouse  Displace  3 Pause  t! f  Displace FIGURE Developing  Pause  24 concentration  profile _ two  cells operating back_to_bock in a closed system.  VO  100  be i n t r o d u c e d whenever p r o d u c t  i s withdrawn.  F o r b e s t s e p a r a t i o n i t would  seem d e s i r a b l e t o t a k e p r o d u c t s whenever maxima o r minima i n t h e c o n c e n t r a t i o n p r o f i l e s p a s s t h e a p p r o p r i a t e p o r t s , and t o i n t r o d u c e f e e d a t 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 t o t h e feed composition.  p r o f i l e around t h e l o o p c o m p r i s i n g i s approximately  I f the concentration  t h e two c e l l s and t h e i r  interconnections  s i n u s o i d a l then f e e d 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 p r o d u c t  removal p o r t s .  R e g a r d i n g t h e f e e d l o c a t i o n and t h e f e e d t i m i n g , an open system c a n be r u n under e i t h e r s y m m e t r i c , semi-symmetric o r asymmetric type o f o p e r a t i o n . I n symmetric o p e r a t i o n f e e d i s i n t r o d u c e d and p r o d u c t s  removed e v e r y  half  c y c l e w i t h t h e f e e d b e i n g i n t r o d u c e d t o t h e t o p and bottom o f each c e l l .  In  semi-symmetric o p e r a t i o n f e e d i s i n t r o d u c e d e v e r y h a l f c y c l e , b u t t o one s i d e o n l y o f each c e l l ;  w h i l e i n t h e t h i r d mode o f o p e r a t i o n n e i t h e r t h e f e e d  l o c a t i o n nor t h e feed t i m i n g i s symmetrical,  and t h e f e e d i s i n t r o d u c e d  only  once t o one s i d e of each c e l l e v e r y c y c l e . F i g u r e 25 r e p r e s e n t s a symmetric o p e r a t i o n w i t h p r o d u c t  r e m o v a l from  the mid-points  o f each c e l l .  valve timing.  I n symmetric o p e r a t i o n each c y c l e i s s u b d i v i d e d i n t o e i g h t  i n t e r v a l s t ^ ( i = 1,2, ... 8 ) .  I t shows t h e r e q u i r e d c o n n e c t i o n s  and t h e  The a c t i v i t y t a k e s p l a c e a t each t i m e i n t e r v a l  as shown i n t h e t a b l e o f F i g u r e 25 w h i c h a l s o shows t h e p o l a r i t y o f t h e of t h e e l e c t r i c f i e l d ,  t h e c o n d i t i o n o f t h e pump ( i . e . whether i d l e o r  o p e r a t i n g and i n w h i c h d i r e c t i o n ) , i t a l s o i n d i c a t e s t h e s t a t e o f t h e v a r i o u s s o l e n o i d v a l v e s and w h i c h o f them i s e n e r g i z e d  (open) and w h i c h o f  them i s c l o s e d d u r i n g t h e s p e c i f i c time i n t e r v a l c o n c e r n e d .  The d e v e l o p i n g  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 o f o p e r a t i o n i s shown i n F i g u r e 26. Here t h e amount o f f e e d i n t r o d u c e d / c y c l e i s -r- o f t h e t o t a l c i r c u l a t i n g volume.  101  V2 I  V3  X h  n V4  V5  V7  V6 -tXr-  -X-  -{XI-  F  Time Interval f  |  f  2  f  3  !  4  *5 f  6 7  f  8  v  VI  V2  V3  V4  V5 V6  V7  V8  V9  Pump P  Vol_ tage A <j)  Pause  0  0  0  0  0  0  0  0  0  0  +  B from I  0  0  0  y  0  0  0  y  0  0  +  D from II  /  0  y  0  0  y  0  0  0  Circulation  0  y  y  0  0  0  0  0  0  Pause  0  0  0  0  0  0  0  0  B from IE  0  0  0  0  0  0  y  D from I  /  y  0  0  y  0  Circulation  0  y  y  0  0  0  ^ ^^ltem Operation\^  / = Valve open 0= Item idle FIGURE  -  +  0  0  -  0  y  0  _  0  0  0  0  -  0  0  0  -v  -  = Cell 1 8 cell 11 D =Dialysate or top product  i, n  0  B = Brine  25  Flow connections and valve timing sequence  +  for symmetric operation,  Top  Bottom  tTop  I  I  F-  I  I  1  '4 Pause  Production  Circulation  B 4 ^  J  u:  Co-I  1  1  FIGURE  1  '5  •e-V  *8  Pause  Production  Circulation  26  1 Pause  Top  Bottom  Top  r-^T^B  n  n  Co"  2  f  3  Production  t 4  Circulation  5 Pause  t\t' 6 7 Production  o FIGURE 26 _ Continued  (I)  )  Bottom  1  I  II  r  li 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 i g n o r e a x i a l m i x i n g  c o n c e n t r a t i o n changes d u r i n g f e e d a d m i s s i o n omitted  f o r c l a r i t y of p r e s e n t a t i o n .  effects,  and d i s p l a c e m e n t  and  have been  The p r o d u c t w i l l undergo  „ t o t a l c i r c u l a t i n g volume . , , .. . , 2 x :;—; : c y c l e s o f enrichment or d e p l e t i o n b e f o r e t o t a l f e e d volume a  emerging under t h i s mode o f o p e r a t i o n .  I n t h e s e 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 a r r o w shows c i r c u l a t i o n of s o l u t i o n f r o m one c e l l i n t o a n o t h e r ,  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 t h e c e l l where the f e e d , F i s i n t r o d u c e d or the d e p l e t e d and  e n r i c h e d p r o d u c t s D and B a r e w i t h d r a w n .  F i g u r e 27 r e p r e s e n t s a semi-symmetric o p e r a t i o n w i t h i t s c o n n e c t i o n s and v a l v e t i m i n g sequence. the top o f c e l l I I and t h e top o f c e l l I and  Here t h e p r o d u c t s  a r e removed a l t e r n a t e l y from  the bottom o f c e l l I , w h i l e f e e d i s s u p p l i e d to the bottom o f c e l l I I .  F i g u r e 28 i s o f sawtooth shape, and c y c l e w i l l depend on how  The waveform g e n e r a t e d i n  the e f f i c i e n c y o f t h i s  operating  w e l l t h i s waveform can be m a i n t a i n e d  i n f l u e n c e of a x i a l mixing processes.  under the  I t would be e x p e c t e d t h a t 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 t o a x i a l m i x i n g t h a n the scheme shown i n F i g u r e 25.  I n the absence of m i x i n g , b o t h c y c l e s a r e p r e d i c t e d t o g i v e  e q u a l 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 . c o n s i s t s of s i x t i m e i n t e r v a l s t ^ ( i = 1,2 symmetric h a l f c y c l e s and  ...  An o p e r a t i n g c y c l e h e r e 6) t h a t c o n s t i t u t e two  non-  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 p r e s e n t s 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 t h e p r e v i o u s modes o f o p e r a t i o n (compare F i g u r e s 28 and  30).  26,  106  V4 V6 -tXr->B  V3  -txj-  n V5  f  2  V7 B  Time Interval  * 1 f  2  *3 f  4  f  5  f  6  *8  VI  V2  V3  V4  V5  V6  V7  Pump p  Pause  0  0  0  0  0  0  0  0  B from 1  y  0  0  0  0  0  y  0  D from II  0  y  0  y  0  0  0  0  Circulation  0  0  y  0  0  0  0  Pause  0  0  0  0  0  0  0  0  B from II  0  y  0  0  0  y  0  0  D from 1  J  0  0  0  y  0  0  Circulation  0  0  y  0  0  0  0  ^vjtem Operation^.  Voltage A(j)  + +  -  -  -  -  0  -  y = Valve open 0 = Item idle  FIGURE  27  Flow connections and valve timing  sequence for semi_symmetric  operation.  Top  Bottom  Top I  "1  •0  'I Pause  Production  J  '1  1  '4 Circulation  FIGURE  28  J  B  5 Pause r  f  6  Production  Production  Top  Co-  Bottom  Top  r I  '8  Pause  Circulation  FIGURE  2 8 _ Continued  (I)  Top  Bottom  Top  I  o  Circulation  FIGURE  28 _ Continued  Pause  (2)  Production  Production  Top  Bottom  Top  Co-I  f  8  Circulation  FIGURE 28 _  Continued  (3).  FIGURE 28 Developing concentration profile, semLsymmetric operation of an open system.  Ill  VI  V3  :v2  V4\  Time Item Interval Operatiorr-^  *| f  2  f  3  f  4  f  '5  !  6  VI  V2  V3  V4  Pump P  Voltage  Pause  0  0  0  0  0  B from I  J  0  0  •  0  +  D from H  0  /  /  0  0  +  Circulation  0  0  0  0  Pause  0  0  0  0  0  -  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  2  Pause  Circulation  Pause  B  'i Production  FIGURE  30  Circulation  Pause  Circulation  Top  Bottom  I  Top  I  <—  F_  F_  J)  Pause  FIGURE 30 -  Production  Continued  Circulation  (I)  FIGURE 30 Developing concentration profile ,asymmetric operation of an open system.  114  I t can be c o n c l u d e d  t h a t when a x i a l m i x i n g i s i g n o r e d a l l t h e  modes o f o p e r a t i o n c o n s i d e r e d h e r e l e a d t o the same s e p a r a t i o n . as can be seen f r o m F i g u r e s 25, 27 and system and  t h e v a l v e economy and  three  However,  29 t h e d e g r e e of c o m p l e x i t y o f  t i m i n g sequence d e c r e a s e s  the  as t h e c y c l e  becomes l e s s s y m m e t r i c .  4.4>  A p p a r a t u s and  Operation  A p h o t o g r a p h o f t h e c o m p l e t e d u n i t i s shown i n F i g u r e 31 w h i c h shows t h e c o n t r o l p a n e l b o a r d w i t h i t s t i m e r , c y c l e c o u n t e r , DC motor speed c o n t r o l l e r , DC power s u p p l y , c o n d u c t i v i t y m e t e r s , 4-pen r e c o r d e r and The  switches.  s e p a r a t i n g u n i t c o n s i s t s o f two columns o r c e l l s w h i c h a r e  d e p i c t e d i n F i g u r e 32 and a r e r e p r e s e n t e d by t h e boxes ED  I and ED  II in  F i g u r e 36 where t h e y a r e shown c o n n e c t e d to t h e p r o c e s s l i n e , r i n s e l o o p , and  the e l e c t r i c power s u p p l y . An a s y m m e t r i c c y c l i c o p e r a t i o n was  open d u r i n g t h e f i r s t h a l f - c y c l e and was (Figure 29).  During  was t  2  T h i s was  i n t r o d u c e d and an e n r i c h e d p r o d u c t was  f i r s t h a l f - c y c l e was cell t  5  enriched.  i n t o another.  direction.  was  c y c l e s t a r t e d w i t h a pause t ^ , t ^ when the f e e d  removed f r o m c e l l I f o r the  removed f r o m c e l l I I f o r a p e r i o d t ^ .  t e r m i n a t e d by c i r c u l a t i o n of the s o l u t i o n f r o m The  time  The one  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  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  opposite  The  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 ;  and a d e p l e t e d p r o d u c t was  was  c l o s e d d u r i n g t h e second h a l f - c y c l e  the f i r s t h a l f - c y c l e t h e s o l u t i o n i n c e l l I I  d e p l e t e d w h i l e t h a t i n c e l l I was period t ^ .  used h e r e i n w h i c h t h e system  6  when the s o l u t i o n was  circulated in  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 o f t h e experimental The  t e s t s t a n d i s shown i n F i g u r e 36.  f i g u r e i l l u s t r a t e s t h e way i n w h i c h f e e d s o l u t i o n f l o w s t h r o u g h t h e  s t a c k and t h e a u x i l i a r y equipment and i t i n d i c a t e s t h e p o i n t s a t w h i c h t h e c o n d u c t i v i t i e s o f t h e e f f l u e n t s t r e a m s , the v o l t a g e , t h e amperage were measured and r e c o r d e d .  The f e e d s o l u t i o n was i n t r o d u c e d i n t o t h e ED c e l l s  from a p r e s s u r i z e d tank t h r o u g h t h e p r o c e s s l i n e that terminated  l i n e , w h i c h was an open ended  i n t h e t o p and bottom p r o d u c t s  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 i n c l u d e d i n t h i s  line  t o g e t h e r 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]  driven  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 2 5 ] .  The c i r c u l a t i n g r a t e o f t h e p r o c e s s  s o l u t i o n was s e t by the motor c o n t r o l l e r o f pump P I ; was  and t h e f l o w d i r e c t i o n  c o n t r o l l e d b y t h e r e v e r s i n g s w i t c h SW I I . A s e p a r a t e 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 t h r o u g h t h e  e l e c t r o d e compartments o f t h e ED c e l l s v i a d i s t r i b u t i n g m a n i f o l d s c e n t r i f u g a l pump P2 (COLE-PARMER model MDX-3, No. 7004-10). r i n s e s t r e a m served  t o remove p r o d u c t s  by t h e  The c i r c u l a t i n g  o f e l e c t r o l y s i s and any gases  a t t h e e l e c t r o d e s were swept o u t and v e n t e d .  evolved  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 o f sodium c h l o r i d e and t h e f l o w r a t e was  about 0.47 [ l i t r e / m i n ] p e r compartment. Regulated  DC power was s u p p l i e d t o t h e ED c e l l s from S0RENSEN DCR40-10A  power s u p p l y t h r o u g h t h e r e v e r s i n g s w i t c h SW I .  A s o l i d s t a t e t i m e r was used  t o c o n t r o l t h e sequence of o p e r a t i o n , e n e r g i z e t h e s o 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 t h e p o l a r i t y o f the motor a r m a t u r e , c o n t r o l t h e p o l a r i t y o f t h e e l e c t r i c f i e l d and g i v e a n impulse end o f each c y c l e .  t o an e l e c t r o m e c h a n i c a l c o u n t e r b y t h e  118  4.3.1.  D e t a i l s o f an ED C e l l D e s i g n A modular c o n s t r u c t i o n was used f o r t h e 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 o f up t o e i g h t s e p a r a t e together  stacks or stages  connected  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  ( F i g u r e s 23, 3 2 ) .  Each s t a g e a s d e p i c t e d by F i g u r e 33 was b u i l t up f r o m e i g h t m u l t i l a y e r s o r p t i o n membrane a s s e m b l i e s ,  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 h e l d t h e g r a p h i t e  e l e c t r o d e s and i n c o r p o r a t e d f l o w c o n n e c t i o n s e l e c t r o d e r i n s e streams ( F i g u r e 3 3 ) .  Each assembled s t a g e had an a c t i v e  v o i d volume f o r t h e p r o c e s s f l u i d o f 50 cm The  f o r t h e p r o c e s s s t r e a m and t h e  3  3 p l u s a dead volume o f about 5 cm .  c o n s t r u c t i o n o f one o f t h e i n d i v i d u a l membrane a s s e m b l i e s  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 o f t h e f o l l o w i n g t h r e e components  p e r m a n e n t l y bonded  together:  (i) 7.62  An o u t e r l o w 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  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 c u t i n t o  each end. (ii)  A t r i p l e - m e m b r a n e ( c a p a c i t y c e l l ) 16.19 cm x 4.44 cm, composed o f  a c a t i o n s e l e c t i v e membrane (AMF C-100 o r IONAC MC-3142) and an a n i o n s e l e c t i v e membrane (AMF A-100 o r IONAC MA-3148) e n c l o s i n g a c o r e o f Whatman N o . l f i l t e r paper (15.56 cm x 4.13 cm). (iii)  A flow channel of polypropylene  spacer screen  (17.00 cm x  4.60 cm x 0.098 cm) V e x a r TP 23, 10 x 10 s t r a n d s p e r i n c h , c u t d i a g o n a l l y . H a l f o f t h e i o n exchange membranes were p u r c h a s e d from A m e r i c a n Machine and Foundry C o r p . , w h i l e t h e r e s t were o b t a i n e d and  from Ionac C h e m i c a l Co.  t h e s p a c e r 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 o f Canada.  119  FIGURE 33 A single stage with its two endframes.  FIGURE 34 A triple membrane _frame _spacer assembly.  120  Section at A _ A '  FIGURE  Elevation  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 ©—*^V3 HXrVI  p----( • r--i  »  i  1  Recorder 4 - Pen  Probes Rinse  I—J  Rinse Tank  £2  P2  ED n  EDI  SWI  CI  Q  V4  V2 PI Timer  swn B Motor Control  FIGURE  J  36  Schematic diagram showing solution flows and instrumentation.(Asymmetric'operation.)  L  122  The membranes were h e a t s e a l e d a l o n g b o t h s h o r t s i d e s . s i d e s remained open t o i n s e r t and t o remove t h e f i l t e r paper.  The l o n g The  poly-  p r o p y l e n e s p a c e r s c r e e n was p r e s s e d i n t o t h e frame by means o f a h e a t e d j i g . Then t h e t r i p l e membrane was heated b a r .  t a c k e d a t t h r e e c o r n e r s to the frame u s i n g a  A d e t a i l e d c o n s t r u c t i o n p r o c e d u r e i s g i v e n by Bass ( B a s s , 1972).  The m a n u f a c t u r e r ' s s p e c i f i c a t i o n s of t h e membranes used a r e g i v e n i n T a b l e V.  D e t a i l e d d e f i n i t i o n s of t h e parameters and methods f o r t h e i r  measurement a r e found i n " I o n Exchange" by H e l f f e r i c h  (1962) and " T e s t Manual  f o r P e r m s e l e c t i v e Membranes, R e s e a r c h and Development P r o g r e s s R e p o r t O f f i c e of S a l i n e Water, U.S.  4.5.  Department o f I n t e r i o r  #77,  (1964 b ) .  M e a s u r i n g and R e c o r d i n g  4.5.1.  C o n c e n t r a t i o n s , C u r r e n t , V o l t a g e and pH Measurements (i)  Concentrations  The c o n c e n t r a t i o n s o f t h e p r o c e s s 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 a u t o m a t i c t e m p e r a t u r e com-  p e n s a t o r s 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 m e t e r s A 0 t o 10 (mV) D.C.  [BECKMAN, S o l u - M e t e r RA5].  o u t p u t s i g n a l from t h e S o l u - M e t e r a l l o w e d 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 o f t h e c o n c e n t r a t i o n i n t h e ranges shown i n T a b l e V I . A c c u r a c y of t h e t y p e RA5 S o l u - M e t e r i n d i c a t i o n i s w i t h i n 2% o f t h e s c a l e span. span.  However t h e a c c u r a c y o f t h e e l e c t r i c a l o u t p u t i s w i t h i n 1% of  Table V  "  R e p o r t e d P r o p e r t i e s o f Ion-Exchange Membranes  - ^ T y p e , M a n u f a c t u r e r and —  Property  Cation-Exchange  Designa t ion  AMF C-100  ~  Anion-Exchange  IONAC MC-3142  AMF A-100  Backing  Polyethylene  Polyethylene  A c t i v e Group  Sulfonic Acid  Quaternized ammonium  Area Resistance  2 (ohm-cm )  7 (0.6N KC1)  9.1 (0.1N NaCl) 3.4 (l.ON NaCl)  8 (0.6N KC1)  0.90  0.94  0.90  IONAC MA-3142  10.1 (0.1N N a C l ) 1.7 (l.ON N a C l )  (a) T r a n s f e r e n c e number of c o u n t e r i o n ( s e l e c t i v i t y ) (0.5/1.ON KC1 o r N a C l )  :  (0.2/0.IN N a C l )  0.90  0.990  0.999  Ion Exchange C a p a c i t y  (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  60  185  50  190  10-13  < 3  12-15  < 3  Mullen Burst strength ( p s i ) D i m e n s i o n a l Changes on w e t t i n g and d r y i n g Size a v a i l a b l e  (a)  (%)  44 i n . wide rolls  40 x 120 i n .  44 i n . wide rolls  40 x 120 i n .  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 o f t h e two n o r m a l i t i e s l i s t e d .  124  Table V I C o n d u c t i v i t y and Na C I C o n c e n t r a t i o n Ranges o f BECKMAN c o n d u c t i v i t y C e l l s CEL-VDJ c o r r e s p o n d i n g t o 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]  Conductivity [micromhos/cm]  Na C I S o l u t i o n C o n c e n t r a t i o n [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 e v e r y r u n samples o f the d e p l e t e d and t a k e n and  enriched products  were  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  CEL-VH1-10] t o g e t h e r 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 w i t h s c a l e m u l t i p l i e r 10 (ii)  -2  - 10  +3  [BECKMAN, 16B2]  .  Current  The c u r r e n t i n p u t was measured as a p o t e n t i a l drop a c r o s s 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  i n t o the e l e c t r i c a l m a n i f o l d w h i c h d i s t r i b u t e d the D.C. box  SW I t o the s t a g e s .  r e s i s t a n c e s were 50.0 and 25.0  shunts were i n t e g r a t e d power f r o m s w i t c h  The w i r i n g i s shown i n F i g u r e 37.  [m^]  ± 1.5%  The  shunt  f o r t h e c u r r e n t s t o the i n d i v i d u a l  stages  [mft] f o r the t o t a l c u r r e n t .  (iii)  Voltage  P r o b e e l e c t r o d e s were prepared i n t o s t r i p s approximately  3 mm  f r o m s i l v e r w i r e c a b l e w h i c h was  wide and 0.12  mm  thick.  The  c o a t e d w i t h c o n t a c t cement (Weldwood of Canada L i m i t e d ) and removed f r o m one  s i d e of the t i p w h i c h was  Corning).  (iv)  shown i n F i g u r e 37; b u t w i t h o u t  the c o a t i n g  The  was  The  t h e s t a c k pack and  A second s e l e c t o r s w i t c h  connected t o the probes and to one r e c o r d e r pen. t o the one  s t r i p s were d i p  l o c a t e d i n s i d e the stack.  p r o b e s were i n s e r t e d between the s e p a r a t i n g membranes and s e a l e d w i t h s i l i c o n g r e a s e (Dow  hammered  c i r c u i t was  was  analogous  shunts.  £H  Samples f o r pH-checks were t a k e n f o r some r u n s j u s t p r i o r t o the e x p e r i m e n t and  immediately  t h e r e a f t e r from the two p r o c e s s p r o d u c t s  r i n s e stream and measured i n t h e u s u a l way model 101).  ( u s i n g CORNING d i g i t a l  and  electrometer  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 t o c o n t i n u o u s l y m o n i t o r the c u r r e n t i n p u t t o the c e l l s , the p o t e n t i a l drop a c r o s s the membrane s t a c k , and and  top c o n d u c t i v i t y c e l l s C l and C2 The  s t a c k v o l t a g e and  f o r each s t a g e .  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 (Figure 36).  the c u r r e n t consumption a r e measured  individually  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 c u r r e n t s i g n a l a r e r e c o r d e d a t , a t i m e 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 CORNING R e c o r d e r 840,  integrated during s e v e r a l experiments, using a  t o d e t e r m i n e the a v e r a g e c u r r e n t consumption.  CHAPTER 5 Experimental  The before  R e s u l t s and D i s c u s s i o n  primary o b j e c t i v e s of t h e experimental  (Chapter  4).  These a r e c o m p i l e d  program have been o u t l i n e d  I n t h e p r e s e n t work a l t o g e t h e r 252 r u n s were made. i n t h e main s u r v e y  t a b l e s ( T a b l e s I X - X V I ) , w h i c h show t h e  o p e r a t i n g c o n d i t i o n s , p r o d u c t i o n r a t e s and t h e s e p a r a t i o n a c h i e v e d  i n each r u n .  These s u r v e y t a b l e s a r e f o l l o w e d by group t a b l e s and diagrams t h a t i l l u s t r a t e the e f f e c t o f s i n g l e v a r i a b l e s under o t h e r w i s e 5.1.  fixed conditions.  Data C o l l e c t i o n The  c o l l e c t i o n o f raw d a t a d u r i n g t h e c o u r s e o f a c o m p l e t e r u n c o n s i s t e d  of t h e f o l l o w i n g c o n s e c u t i v e 1.  steps:  F i l l r i n s e t a n k w i t h 7.5 l i t e r s o f f r e s h r i n s e l i q u o r  d i s t i l l e d w a t e r , w i t h t h e same c o n c e n t r a t i o n a s t h e p r o c e s s  (NaCl i n  stream but not  l e s s t h a n 1000 ppm N a C l ) . 2.  Fill  t h e f e e d tank w i t h s o l u t i o n o f 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 w a t e r ) and a d j u s t t h e p r e s s u r e system w i t h t h e p r o c e s s  i n t h e f e e d tank t o about 8 p s i g .  3.  Fill  s o l u t i o n from t h e p r e s s u r i z e d feed  4.  S t a r t r i n s e pump.  5.  Set t h e t i m e r and t h e p e r i s t a l t i c pump speed and r u n t h e system w i t h  power o f f f o r few c y c l e s t o e q u i l i b r a t e s o r p t i o n membrane w i t h p r o c e s s  tank.  solution.  6.  A d j u s t check p o i n t o f c o n d u c t i v i t y m e t e r s .  7.  S e l e c t r e c o r d e r pen r a n g e s 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 o f p r o c e s s and r i n s e s o l u t i o n s ,  9.  Set the timer o f f t o b r i n g the e q u i l i b r a t e d process  a pause b e f o r e s t a r t i n g t h e r u n . 128  s o l u t i o n to  129  10.  T u r n c y c l e c o u n t e r back t o z e r o .  11.  Set o p e r a t i n g c o n d i t i o n s ( f i n a l adjustment of the t i m e r and  a p p l i e d D.C. 12.  the  voltage). Note down d a t e , 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 r e c o r d e d by  each  pen and a p p r o p r i a t e r a n g e , c h a r t speed. 13. to  Set the t i m e r on and c l o s e e l e c t r i c power c i r c u i t  simultaneously  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 t h e system approaches i t s p e r i o d i c s t e a d y s t a t e as i n d i c a t e d  by the r e c o r d e d v a l u e s of c o n c e n t r a t i o n s . Empty the p r o d u c t the volumes and n o t e the c y c l e number.  t a n k s , measure  Discard products obtained i n t h i s  transition period. 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 s w i t c h e s , and mark pen  traces accordingly.  16.  W r i t e down any o b s e r v a t i o n r e l a t e d t o  experiment.  17.  T e r m i n a t e r u n when s u f f i c i e n t p r o d u c t s a r e produced and a l l  i n f o r m a t i o n r e g a r d i n g c u r r e n t and v o l t a g e s i g n a l s a t t h e v a r i o u s s t a t i o n s have been o b t a i n e d . 18.  Measure the t o t a l amount of p r o d u c t s produced and r e a d the  total  number o f c y c l e s t o f i n d and r e c o r d t h e p r o d u c t i o n r a t e s . 19.  Take samples of p r o c e s s and r i n s e streams t o measure pH and  con-  centrations. 20. 5.2.  R e c o r d the measured v a l u e s .  Experimental The (i)  Designation  e x p e r i m e n t s r e p o r t e d h e r e f a l l i n t o two main c a t e g o r i e s : Category  R w h i c h r e f e r to the f i r s t s e t of e x p e r i m e n t s conducted  i n two columns each c o n s i s t e d o f 4 c e l l s o r s t a g e s connected t o g e t h e r i n s e r i e s h y d r a u l i c a l l y and (ii)  in parallel electrically  (Tables I X - X I ) .  C a t e g o r y M w h i c h r e f e r s to the second s e t of e x p e r i m e n t s performed  130  i n columns w i t h d o u b l e t h e l e n g t h o f t h o s e used i n C a t e g o r y  R (Tables XII-XIV),  Each e x p e r i m e n t i n t h e s e c a t e g o r i e s i s d e s i g n a t e d by e i t h e r Rna o r Mna where n i s a number w h i c h r e f e r s t o a s p e c i f i c c o m b i n a t i o n c o n c e n t r a t i o n ( C ) and a p r o d u c t i o n r a t e ( P . R . ) . Q  (C  Q  = 500, 2000  of a feed  Three feed c o n c e n t r a t i o n s  and 4 0 0 0 ppm NaCl) and f o u r p r o d u c t i o n r a t e s (P.R. = 0.0, 2 5 ,  50 and 1 0 0 c . c . / c y c l e ) have been used w h i c h r e s u l t i n 12 c o m b i n a t i o n s assumes t h e v a l u e s 1,2  12 a s shown i n T a b l e V I I .  represents a s p e c i f i c combination (T).  a i s a l e t t e r which  o f a p p l i e d v o l t a g e (A<J>) and t h e pause  T h r e e v o l t a g e s (A<(> = 1 0 , 20 and 3 0 v o l t ) and t h r e e pause t i m e s  30 and 45 sec.) have been i n v e s t i g a t e d w h i c h l e a d t o 9 c o m b i n a t i o n s s y m b o l i z e d b y any o f t h e l e t t e r s A, B 5.3.  M a i n Survey  I a s shown i n T a b l e  columns o f t h e main s u r v e y t a b l e s a r e (see T a b l e s  1.  EXP Group:  2.  time  (T = 1 5 , and a i s  VIII.  Tables  The  n-value  and n  IX-XVI):  T h i s shows t h e e x p e r i m e n t c a t e g o r y R o r M and t h e  ( n = 1, 2, .... 1 2 ) . Production Rate:  o f each p r o d u c t  ( d e m i n e r a l i z e d and c o n c e n t r a t e d )  in c.c./cycle. 3.  Feed C o n c e n t r a t i o n :  4.  EXP Symbol:  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.  t h e symbol o f a i n t h e e x p e r i m e n t a l d e s i g n a t i o n Rna  or Mna. 5.  Applied Voltage:  t h e c o n s t a n t v o l t a g e s u p p l i e d by t h e r e g u l a t e d  D.C. power s o u r c e 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.  Brine Concentration:  9.  Dialysate Concentration:  b o t h measured c o n d u c t o m e t r i c a l l y and  c o n v e r t e d b y means o f c a l i b r a t i o n c u r v e s 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 p e r million  NaCl.  131  T a b l e V I I V a l u e s of n i n E x p e r i m e n t a l D e s i g n a t i o n s Rna and Mna  ^ v ^ O p er a t i n g .. ^^-v. Parameters Value ^^v. of n TT  Feed Cone. C (ppm) q  1 2  Production Rate p.p. ( c . c . / c y c l e )  25 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 Rna and Mna  ^v^Operating ^^Parameters a  APPLIED VOLTAGE, A* (volt)  A B  Designations  PAUSE TIME, x (sec)  30 20  45  C  15  D  15  E  30  30  F  45  G  45  H I  10  30 15  133  8. 10. product  B r i n e Volume: D i a l y s a t e Volume:  streams e x p r e s s e d  11.  These a r e t h e p r o d u c t i o n r a t e s o f t h e two  i n c.c. p e r c y c l e .  Separation Factor  (ns):  D e f i n e d as t h e r a t i o o f b r i n e  product) t o d i a l y s a t e (top product)  ns  concentrations  =  The main s u r v e y and M a r e p r e s e n t e d  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  on t h e f o l l o w i n g pages.  r u p t e d by m e c h a n i c a l , 5.4.  S u c c e s s f u l means n o t i n t e r -  e l e c t r i c a l o r human f a i l u r e .  P a r a m e t e r s and Modes o f O p e r a t i o n (a)  (bottom  Investigated  Parameters  The p a r a m e t e r s w h i c h a r e s t u d i e d a r e : 1.  Demineralizing path length.  2.  Production rate.  3.  Pause t i m e , x.  The t o t a l c y c l e t i m e T i s t h e summation of pause t i m e ,  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 and p r o d u c t i o n t i m e t  p  £  which i s kept  constant  w h i c h v a r i e s between 1.5-6.0 sec depending on  t h e amount of p r o d u c t . 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 concentration, C . o  (b)  Modes o f O p e r a t i o n  The  f o l l o w i n g modes of o p e r a t i o n were c o n s i d e r e d :  6.  No-pause o p e r a t i o n .  7.  No-power d u r i n g c i r c u l a t i o n  8.  Semi-symmetric o p e r a t i o n .  operation.  Each o f t h e s e p a r a m e t e r s o r modes o f o p e r a t i o n i s a n a l y s e d  s e p a r a t e l y by  f o r m i n g groups o f e x p e r i m e n t s i n w h i c h t h e o t h e r p a r a m e t e r s a r e c o n s t a n t .  Table IX  1  EXPCROUP  Compilation of Experiments with I n i t i a l Concentration (Co) of 2000 Two Columns.Each consists of 4 Cells i n Series  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  R2  0.0  1950  1950  1950  Rl  20  1950  1 1  i I !  1  1950  10  9  11  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  CONC. (PPM)  30  3730  212  17.59  45  4310  135  31.93  C  15  3320  415  8.00  11  15  3450  239  14.44  30  4435  133  33.35  F  45  4800  101  47.52  G  45  3380  470  7.19  30  3020  550  5.49  I  15  2800  880  3.18  A  30  3560  18.80  400  19.83  8.90  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  30  3900  17.20  280  19.80  13.93  F  | 45  4025  17.73  195  19.80  20.64  C  45  3300  17.55  735  18.16  4.49  30  3010  18.10  820  18.20  3.67  2795  18.00  1020  18.13  2.74  EXPSYMBOL A  1950  8  7  5  4  20  B  30  E  10  H  20  B  30  E  10  H I  !  15  DIALYSATE  BRINE  i  VOLUME (C.C./CYCLE)  CONC. (PPM)  VOLUME (C.C./CYCLE)  SEPARATION FACTOR ns  Table IX 1  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  4  5  6  (Continued) 7  8  i EXP. GROUP  EXP» SYMBOL  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  A 1950  R3  50  1950  1950  2055  R4  100  2055  2055  9  BRINE CONC. (PPM)  VOLUME (C.C/CYCLE)  10 DIALYSATE  CONC (PPM)  VOLUME (C.C./CYCLE)  11 SEPARATION FACTOR ns  30  3200  47.38  640  48.30  5.00  45  3460  47.41  480  48.62  7.21  c  15  2850  47.88  990  48.25  2.88  D  15  3180  47.15  830  49.85  3.83  30  3500  47.34  450  49.69  7.78  F  45  3720  46.46  310  49.83  12.00  G  45  2780  47.14  1130  48.33  2.46  30  2615  47.64  1290  48.14  2.03  I  15  2370  46.54  1550  48.08  1.53  A  30  3050  96.20  1115  98.90  2.74  45  3270  96.54  870  98.75  3.76  c  15  2580  96.23  1545  97.87  1.67  D  15  2910  96.94  1190  97.11  2.45  30  3300  97.83  790  98.10  4.18  F  45  3615  97.89  515  98.21  7.02  G  45  2620  97.22  1465  98.50  1.79  30  2500  97.15  1590  98.43  1.57  15  2400  96. S8  1725  98.13  1.39  B  E  H  B  E  H I  20  30  10  20  30  10  Table X 1  EXP. GROUP  2  Compilation of Experiments with I n i t i a l Concentration (Co) of 500 PPM Two Columns/Each Consists of 4 Cells i n Series 3 4 5 6 7 8 9 10  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  EXP« SYMBOL  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  R6  0.0  530  530  530  20  530  530  CONC. (PPM)  VOLUME (C.C./CYCLE)  DIALYSATE CONC. (PPM)  VOLUME (C.C./CYCLE)  SEPARATION FACTOR ns  30  1447  24.5  59.06  45  1915  23.7  30.80  C  15  1300  28.2  46.10  D  15  1790  24.4  73.36  30  1833  19.2  95.47  A 530  BRINE  11  B  E  20  30  F  45  G  45  1332  86.0  15.49  30  1160  101,0  11.49  I  15  1042  157.0  6.64  A  30  1070  17.91  31.5  19.14  33.97  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  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  30  940  17.95  123.0  19.03  7.64  15  850  17.94  214.0  19.00  3.97  H  B  E•  H I  10  20  30  10  Table X 1  EXP. GROUP  2  3  PRODUCTION RATE  FEED CONC.  (C.C/CYCLE)  (PPM)  R7  50  510  510  500  R8  100  500  500  8  7  10  9  11  5  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  CONC. (PPM)  30  980  47.43  38  49.14  25.79  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  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  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  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  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  30  800  97.40  200  97.72  4.00  15  706  96.03  298  98.17  2.37  4  EXPSYMBOL A  510  (Continued)  B  E  H  B  E  H I  20  30  10  20  30  10  DIALYSATE  BRINE VOLUME (C.C./CYCLE)  VOLUME CONC. I (C.C./CYCLE) (PPM)  SEPARATION FACTOR ns  Table XI 1  EXP. GROUP  RIO  R9  Rll  R12  Compilation of Experiments with I n i t i a l Concentration (Co) of 4000 PPM Two Columns^Each consists of 4 Cells i n Series  2  3  PRODUCTION RATE  FEED CONC.  ' (C.C./CYCLE)  0.0  20  50  100  4  5  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  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  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  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  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  EXP« SYMBOL  (PPM)  3670  3670  3670  3720  7  8  9  BRINE CONC. (PPM)  VOLUME (C.C./CYCLE)  10 DIALYSATE  CONC. (PPM)  VOLUME (C.C./CYCLE)  U SEPARATION FACTOR ns  Table XII 1 EXP. GROUP  Compilation of Experiments with I n i t i a l Concentration (Co) of 2000 PPM Two Columns^Each Consists of 8 Cells i n Series  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  4 EXP. SYMBOL  5  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  A 2130  M2  0.0  2120 .  2120  2160  Ml  25  2170  2170  7  8  9  BRINE CONC. (PPM)  VOLUME (C.C./CYCLE)  10 DIALYSATE  CONC. (PPM)  VOLUME (C.C./CYCLE)  11 SEPARATION FACTOR ns  30  4225  120  35.21  45  4300  102  42.16  C  15  4025  177  22.74  D  15  4400  85  51.76  30  4525  70  64.64  F  45  4675  57  82.02  G  45  3900  280  13.93  30  3825  380  10.07  I  15  3650  610  5.98  A  30  4000  25.37  196  24.17  20.41  45  4075  25.52  143  24.48  27.53  C  15  3875  25.87  330  24.13  11.74  D  15  4125  24.67  140  24.50  29.46  30  4250  25.00  118  25.00  36.02  F  45  4350  24.57  94  25.71  46.28  G  45  3825  25.79  410  24.21  9.33  30  36.75  25.88  570  24.13  6.45  15  3375  25.45  840  24.66  4.02  B  E  H  B  E  H I  20  30  10  20  30  10  Table XII 1 EXP. GROUP  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  4 EXP. SYMBOL  5  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  M3  50  2120  2120  2100  M4  100  2160  2140  7  8  ?  DIALYSATE  BRINE CONC. (PPM)  10  VOLUME (C.C./CYCLE)  CONC. (PPM)  VOLUME (C.C./CYCLE)  11 SEPARATION FACTOR ns  30  3950  52.14  232  50.48  17.03  45  4025  52.55  163  51.76  24.69  C  15  3775  51.43  470  50.30  8.03  D ,  15  4050  50.09  154  50.87  26.30  30  4175  50.27  127  52.69  32.87  F  45  4300  49.12  105  51.68  40.95  G  45  3725  50.52  550  50.70  6.77  30  3400  52.73  810  52.05  4.20  I  15  3050  50.13  1270  52.39  2.40  A  30  3900  101.11  267  99.83  14.61  45  4000  98.85  192  96.75  20.83  C  15  3675'  99.09  575  98.86  6.39  n  15  4025  101.17  180  98.25  22.36  30  4125  98.88  145  96.25  28.45  F  45  4200  99.35  125  98.15  33.60  G  45  3625  100.00  640  101.18  5.66  30  3300  98.17  1100  100.00  3.00  15  2880  98.44  1440  99.88  2.00  A 2130  (Continued)  B  E  H  B  E  H I  20  30  10  20  30  10  Table XIII Compilation of Experiments with I n i t i a l Concentration (Co) of 500 PPM Two ColumnsjEach Consists of 8 Cells i n Series  EXP* GROUP  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  4  5  EXP. SYMBOL  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  M6  0.0  550  530  540  M5  25  560  530  8  9  DIALYSATE  BRINE CONC. (PPM)  10  CONC. VOLUME (C.C./CYCLE) (PPM)  VOLUME (C.C./CYCLE)  11 SEPARATION FACTOR ns  30  1130  16.5  68.48  45  1200  13.6  88.24  C  15  1090  20.2  53.96  D  15  1150  15.1  76.16  30  1280  12.0  106.67  A 550  7  B  E  20  30  F  45  G  45  1030  33.0  31.21  30  1010  44.0  22.95  I  15  970  75.0  12.93  A  30  1080  24.20  21.1  25.39  51.18  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  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  30  1000  25.07  53.0  24.78  18.87  15  960  25.62  90.0  24.84  10.67  H  B  E •  H I  10  20  30  10  Table XIII (Continued) J.  EXP. GROUP  RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  T>T?nmTrTTfiM  EXP' SYMBOL  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  M7  50  550  530  540  M8  100  540  520  CONC. (PPM)  VOLUME (C.C./CYCLE)  DIALYSATE VOLUME CONC. 1 (C.C./CYCLE) (PPM)  SEPARATION FACTOR ns  30  1050  51.82  26.3  49.24  39.92  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  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  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  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  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  30  970  98.15  80.0  98.50  12.13  15  890  97.65  139.0  99.15  6.40  A 550  BRINE  B  E  H  B  E  H I  20  30  10  20  30  10  Table XIV  1 EXP« GROUP  Compilation of Experiments with I n i t i a l Concentration (Co) of 4000 PPM Two Columns#Each consists of 8 Cells i n Series  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  M10  0.0  4175  4200  4050  M9  25  4100  t  4175  9  10  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  CONC. (PPM)  30  7450  550  13.55  45  7850  360  21.81  C  15  7125  820  8.69  D  15  8100  271  29.89  30  8175  194  42.14  F  45  8300  141  58.87  G  45  6825  1290  5.29  30  6600  1760  3.75  I  15  6025  2460  2.45  A  30  7150  26.28  810  25.47  8.83  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  30  8100  25.17  288  26.48  28.13  F  45  8150  26.78  218  26.85  37.39  G  45  6625  25.87  1700  26.65  3.90  30  6375  25.09  2240  26.86  2.85  15  5325  25.39  2650  25.84  2.20  EXPSYMBOL A  4100  8  7  5  4  B  E  H  B  E  H I  20  30  10  20  30  10  BRINE VOLUME (C.C./CYCLE)  DIALYSATE CONC. (PPM)  VOLUME (C.C./CYCLE)  SEPARATION FACTOR ns  Table XIV 1  EXP • GROUP  2  3  PRODUCTION RATE  FEED CONC.  (C.C./CYCLE)  (PPM)  Mil  50  4175  4200  4050  M12  100  4125  4200  8  10  11  6  APPLIED VOLTAGE  PAUSE TIME  (VOLT)  (SEC)  CONC. (PPM)  VOLUME (C.C./CYCLE)  30  7050  51.23  940  48.84  7.50  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  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  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  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  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  30  5600  99.41  2800  101.91  2.00  15  5000  99.18  3575  101.73  1.40  EXPSYMBOL  B  E  H  B  F. '  H I  20  30  10  20  30  10  7  9  5  4  A 4100  (Continued)  DIALYSATE  BRINE  VOLUME CONC. (PPM) ! (C.C./CYCLE)  SEPARATION FACTOR ns  T a b l e XV 1 FEED CONC.  2  EXP.  (PPM)  1980.  520  3725  D u p l i c a t e Experiments t o Test 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 o f 4 C e l l s i n S e r i e s  3  4  PRODUCTION RATE  APPLIED VOLTAGE  PAUSE TIME  (C.C./CYCLE)  (VOLT)  (SEC)  5  6  7  8  BRINE CONC. (PPM)  VOLUME (C.C./CYCLE)  9 DIALYSATE  CONC. (PPM)  VOLUME (C.C./CYCLE)  10 SEPARATION FACTOR ns  RRlA RR1D RR1E RR1F  20 20 20 20  20 30 30 30  30 15 30 45  3650 3540 3850 3900  19.72 19.33 18.50 19.60  350 415 233 207  19.52 19.13 19.33 19.70  10.43 8.53 16.52 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 RR5C RR5F RR7A RR7B RR7C RR8F  20 20 20 50 50 50 100  20 20 30 20 20 20 30  30 15 45 30 45 15 45  1050 995 1450 980 1000 960 970  18.29 19.29 17.19 49.26 48.88 49.66 98.29  28.0 35.0 23.4 44.0 34.0 55.0 46.0  19.11 19.18 19.84 48.83 49.17 49.14 98.10  37.50 28.43 61.97 22.27 29.41 17.45 21.09  20 20 50  30 30 30  30 45 45  5600 5900 5750  19.35 19.95 49.86  19.13 18.47 49.14  3.39 4.10 3.76  RR9E RR9F RR11F  1650 1440 1530  Table XVI 1  D u p l i c a t e E x p e r i m e n t s t o T e s t 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 o f 8 C e l l s i n S e r i e s  2  3  4  5  EXP.  PRODUCTION RATE  APPLIED VOLTAGE  PAUSE TIME  (C.C./CYCLE)  (VOLT)  (SEC)  99nn ^zuu  MM1B MM1D MM1F MM3C  25 25 25 50  20 30 30 20  45 15 45 15  9040  MM4A MM4E  100 100  20 30  540  MM5C MM7C MM7D MM8B MM8F  25 50 50 100 100  FEED CONC. (PPM)  6  7  8  BRINE CONC. (PPM)  9 DIALYSATE  10 SEPARATION FACTOR  VOLUME (C.C./CYCLE)  CONC. (PPM)  VOLUME (C.C./CYCLE)  4150 4100 4375 3950  25.18 26.86 25.59 49.60  133 144 106 415  24.84 24.66 24.84 48.84  31.20 28.47 41.27 9.52  30 30  3800 4150  102.32 98.13  267 129  99.23 99.57  14.23 32.17  20 20 30 20 30  15 15 15 45 45  1040 1020 1070 1040 1080  25.83 51.27 52.78 102.41 102.89  28.8 36.0 22.7 27.4 20.3  24.64 50.17 50.25 99.86 99.17  36.11 28.33 47.14 37.96 53.20  ns  4150  MM9A MM9E MM11B  25 25 50  20 30 20  30 30 45  7400 8350 7750  25.13 25.86 50.21  940 271 600  24.87 24.93 50.82  7.87 30.81 12.92  4200  MM12C MM12D MM12F  100 100 100  20 30 30  15 15 45  6600 7600 8350  97.30 97.13 98.17  1820 650 267  99.04 101.27 101.48  3.63 11.69 31.27  147  Appendix E shows t h e 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 o f s a l t s h i f t e d and a check on m a t e r i a l b a l a n c e  f o r each  r u n and l i s t s t a b l e s o f p r i n t o u t .  5.4.1.  E f f e c t of Demineralizing Path Length S i n c e t h e p r o c e s s g e n e r a t e s 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 t h e  s o l u t i o n s a t t h e two ends o f t h e ED c e l l , t h e amount o f a x i a l d i s p e r s i o n i n t h e s t a c k has a v e r y g r e a t e f f e c t on t h e f i n a l r u n s t h e c o n c e n t r a t i o n s o f t h e two p r o d u c t  separation.  I n a l l of the  streams approached l i m i t i n g  as t h e d i s p e r s i v e e f f e c t s o f a x i a l m i x i n g and o t h e r i r r e v e r s i b l e  values  processes  became e q u a l t o t h e 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 t h e number o f s t a g e s  connected i n s e r i e s t e n d s t o r e d u c e d i s p e r s i o n .  F i g u r e s 38, 39 and 40 and  T a b l e s X V I I , X V I I I and X I X show r u n s i n 4-stage columns w h i l e F i g u r e s 4 1 , 42 and 43 t o g e t h e r w i t h T a b l e s XX, X X I and X X I I show s i m i l a r e x p e r i m e n t s p e r formed i n 8-stage columns.  By comparing t h e s e f i g u r e s i t w i l l be c l e a r t h a t  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 i n a l l sets of  length  experiments.  F i g u r e s 44-49 and T a b l e s X X I I I - X X V I I I  compare t h e p e r f o r m a n c e , under  the same o p e r a t i n g c o n d i t i o n s , o f a s i n g l e column c o n s i s t s o f 8 s t a g e s t h a t o f two s h o r t columns each c o n s i s t s o f 4 s t a g e s w h i c h o p e r a t e and have t h e same p r o d u c t i o n r a t e s a s t h e s i n g l e column. was made by p l o t t i n g C / C Q  where C  o  n  versus  with  i n parallel  This comparison  the r e c i p r o c a l of t h e throughput r a t i o ;  i s t h e f e e d c o n c e n t r a t i o n and C_. i s t h e d e m i n e r a l i z e d p r o d u c t c o n D  centration.  r  I n a l l r u n s s t u 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 t h a n t h e two s h o r t p a r a l l e l columns;  however, t h e improvement i n  s e p a r a t i o n w i t h t h e c o l u m n - l e n g t h was more pronounced a t h i g h  feed  148  Table XVII  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co = 500 PPM Exp. Group # R5, R6, R7 and R8  PI EXP.  RATE  GRAPH. \  SYMBOL  ^  SEPARATION PER  ^  FACTOR  ns  \  CYCLE VOLTAGE (VOLT)  A  B  y  20  C  D E  F  G  H  I  • •  30  •  • A O  20  50  (C.C.)  (C.C.)  (C.C.)  (C.C.)  30  59.06  33.97 37.50  25.79 22.27  14.17  45  80.80  46.25  34.00 29.41  16.67  15  46.10  25.37 28.43  20.00 17.45  8.88  15  73.36  42.80  25.40  12.11  30  95.47  55.15  32.63  16.63  68.45 61.97  39.07  18.46 21.09  10.21  9.01  5.57  P A U S E \ ^  \w  (SEC)  0.0  45  10  100  45  15.49  30  11.49  7.64  6.92  4.00  15  6.64  3.97  3.60  2.37  120  149  FIGURE 38 Effect of production rate on separation. 4-Cell column ;initial cone. Ccf^SOOPPM.  150  Table XVIII  EXP.  PF.OD. RATE "\ PER  GRAPH. SYMBOL VOLTAGE (VOLT)  A B  U  20  C  D  •  E  •  F  •  G H I  • A o  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co * 2000 PPM Exp. Group # R l , R2, R3 and R4  30  10  SEPARATION FACTOR ns ^ \ CYCLE 0.0 (C.C.)  20 (C.C.)  50 (C.C.)  100 (C.C.)  30  17.59  8.90 10.43  5.00  2.74  45  31.93  13.00  7.21 6.09  3.76  15  8.00  5.71  2.88  1.67  15  14.44  7.49 8.53  3.83  2.45  30  33.35  13.93 16.52  7.78  4.18  45  47.52  20.64 18.84  12.00  7.02 5.99  45  7.19  4.49  2.46  1.79  30  5.49  3.67  2.03  1.57  15  3.18  2.74  1.53  1.39  PAUSE\. (SEC)  151  FIGURE  39  Effect of production rote on separation. 4 - C e l l column ^initial cone. CjpSOOOPPM.  152  Table XIX  EXP.  GRAPH. SYMBOL  E f f e c t of Production Rate Two Columns Each C o n s i s t s I n i t i a l C o n c e n t r a t i o n Co Exp. Group # R9, RIO, R l l  on S e p a r a t i o n of 4 C e l l s i n Series - 4000 PPM and R12  P]*0D. RATE SEPARATION FACTOR ns \. PER ^ \ CYCLE VOLTAGE PAUSlN^ 0.0 50 20 100 (VOLT) (SEC) (C.C.) (C.C.) (C.C.) (C.C.)  A  30  2.39  1.98  1.78  1.52  20 B  u  45  3.34  2.67  2.20  1.77  E  •  30  4.43  3.10 3.39  2.50  1.91  45  6.90  4.56 4.10  3.44 3.76  2.48  F  •  30  153  APPLIED VOLTAGE (VOLT)  PAUSE 15  TIME 30  (SEC) 45  10  U  20 30  FIGURE  •  B  40  Effect of production rote on separation. 4-Cell column; initial cone. C — 4000 PPM. Q  154  T a b l e XX  EXP.  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 500 PPM Exp. Group # M5, M6, M7 and M8  IOD. RATE \. PER  GRAPH. SYMBOL  SEPARATION FACTOR ns CYCLE  VOLTAGE (VOLT) A B  y  20  C  D  •  E  •  F  •  G H I  • A O  30  PAUSED. (SEC)  0.0 (C.C.)  50 (C.C.)  100 (C.C.)  30  68.48  51.18  39.92  28.33  45  88.24  65.50  53.96  40.38 37.96  15  53.96  39.92 36.11  31.21 28.33  21.04  15  76.16  55.33  44.21 47.14  32.19  30  106.67  72.61  60.77  46.52  77.85  63.07  48.43 53.20  45  10  25 (C.C.)  45  31.21  25.25  22.95  18.18  30  22.95  18.87  16.23  12.13  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 o f P r o d u c t i o n R a t e on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co - 2000 PPM Exp. Group # M l , M2, M3 and M4  P I 10D. EXP.  GRAPH.  RATE  SYMBOL  \  SEPARATION PER  \w VOLTAGE (VOLT)  A  B  a  20  C  D  E  F  G  H  I  • •  30  •  • A O  10  \  FACTOR  ns  V  CYCLE  25  50  (c.c.)  (C.C.)  (C.C.)  (C.C.)  30  35.21  20.41  17.03  14.61 14.23  45  42.16  27.53 31.20  24.69  20.83  15  22.74  11.74  8.03 9.52  6.39  15  51.76  29.46 28.47  26.30  22.36  30  64.64  36.02  32.87  28.45 32.17  45  82.02  46.28 41.27  40.95  33.60  45  13.93  9.33  6.77  5.66  30  10.07  6.45  4.20  3.00  15  5.98  4.02  2.40  2.00  PAUSEX. (SEC)  0.0  100  157  FIGURE 42 Effect of production rate on separation. 8 - C e l l column initial cone. C — 2 0 0 0 P P M . Q  158  Table XXII  EXP.  P]10D. RATE \. PER  GRAPH. SYMBOL VOLTAGE (VOLT)  A B  U  20  C  D  •  E  •  F  •  G H I  • A O  E f f e c t o f P r o d u c t i o n R a t e on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 4000 PPM Exp. Group # M9, M10, M i l and M12  30  10  CYCLE PAUSE\^ (SEC)  SEPARATION FACTOR ns 0.0 (C.C.)  25 (C.C.)  50 (C.C.)  100 (C.C.)  30  13.55  8.83 7.87  7.50  5.80  45  21.81  13.19  11.80 12.92  10.00  15  8.69  5.19  4.61  3.98 3.63  15  29.89  16.89  15.31  12.54 11.69  30  42.14  28.13 30.81  26.05  22.64  45  58.87  37.39  34.00  28.62 31.27  45  5.29  3.90  3.21  2.90  30  3.75  2.85  2.40  2.00  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 — 4 0 0 0 P P M . Q  160  Table XXIII  EXP.  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n C = 500 ppm; A<}> = 20 V  GRAPHICAL SYMBOL  PAUSE TIME (SEC)  8 C 7 C  4-CELL COLUMN 1 THROUGHPUT RATIO 2  8-CELL COLUMN  CD  4.85  1 THROUGHPUT RATIO 4  11.25 16.67  4  10.64  8  5 C  10  12.93  16  8 A  2  7 A  o  A  •  •  15  7.58  4  13.42  5 A  10  16.83  8 B  2  7 B 5 B  •  •  30  45  4 10  8.77 17.00 22.08  CD  20.53  4  15.00  8  20.91  16  25.59  4  20.77  8  27.23  16  31.58  161  4-  Pause Time  15 30 45  I  I  2 Reciprocal  8 - Cell Column  Column  ( Sec )  o I  Cell  o A  A  •  8  c  I  I  4 6 Throughput Ratio  8  I  I  I  12  16  FIGURE 4 4 Effect of demineralizing  path Jength on separation,  Co =«= 500 PPM , A(J) = 2 0 V .  162  T a b l e XXIV  EXP.  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n C - 500 ppm; A<f> = 30 V  GRAPHICAL SYMBOL  PAUSE TIME (SEC)  4-CELL COLUMN 1 THROUGHPUT RATIO 2  8 D  o  •  8-CELL COLUMN  c  D  6.58  1 THROUGHPUT RATIO  CD  4  16.88  4  12.75  8  22.73  5 D  10  21.20  16  28.43  8 E  2  4  23.48  8  30.39  7 D  7 E  A  A  15  30  4  8.77 15.94  5 E  10  25.98  16  35.69  8 F  2  9.62  4  24.22 31.25  7 F .5 F  •  •  45  4  18.89  8  10  31.55  16  37.58  163  FIGURE Effect  Pause Time  4 - Cell  8- Cell  (Sec )  Column  Column  •  15  o  30  A  •  45  •  a  45 of  demineralizing  path  length on separation.  C ^=500 P P M , A<{)=30V. 0  164  T a b l e XXV  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n C - 2000 ppm; A<j> = 20 V Q  EXP.  PAUSE TIME (SEC)  GRAPHICAL SYMBOL  4 C  4-CELL COLUMN  1 THROUGHPUT RATIO  8-CELL COLUMN  C  D  1 THROUGHPUT RATIO  c  D  2  1.33  4  3.65  4  1.97  8  4.53  1 C  10  3.36  16  6.55  4 A  2  1.84  4  7.87  4  3.05  8  9.18  1 A  10  4.88  16  11.02  4 B  2  2.36  4  10.94  4  4.06  8  13.07  10  6.72  16  3 C  3 A  3 B 1 B  o  A  •  •  A  •  15  30  45  14.59  165  Pause Time  4 - Cell  8 - Cell  ( Sec)  Column  Column  O  30  A  45  •  • m  J  1  1  1  1  1  2  4  6  8  12  16  Reciprocal  FIGURE  15  Throughput  Ratio  46  Effect of demineralizing  path length on separation.  CQ  2 0 0 0 PPM , A (J) = 2 0 V .  166  T a b l e XXVI  EXP.  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n C - 2000 ppm; A<)> = 30 V  GRAPHICAL SYMBOL  PAUSE TIME (SEC)  4 D  4-CELL COLUMN 1 THROUGHPUT RATIO  8-CELL COLUMN  c  D  1 THROUGHPUT RATIO  c  D  2  1.73  4  12.00  4  2.35  8  13.77  1 D  10  4.29  16  15.50  4 E  2  2.60  4  14.90  4  4.33  8  16.69  1 E  10  6.96  16  18.39  4 F  2  3.99  4  17.28  4  6.29  8  20.19  10  10.00  16  23.09  3 D  3 E  3 F 1 F  o  A  •  •  •  •  15  30  45  167  FIGURE Effect  47 of  demineralizing  path length on separation.  C ^ t 2 0 0 0 PPM , Q  = 30V.  168  Table XXVII  E f f e c t o f D e m i n e r a l i z i n g P a t h L e n g t h on S e p a r a t i o n C - 4000 ppm; A<j> = 20 V O  EXP.  GRAPHICAL SYMBOL  PAUSE TIME (SEC)  4-CELL  COLUMN  COLUMN  1  1 THROUGHPUT R A T I O  12 A  8-CELL  c  D  THROUGHPUT R A T I O  CD  2  1.25  4  3.40  4  1.39  8  4.36  9 A  10  1.48  16  5.00  12 B  2  1.40  4  5.59  4  1.61  8  6.56  10  1.82  16  7.17  11 A  11 B 9 B  A  •  •  II  30  45  169  Pause Time  4 - Cell  8 - Cell  ( Sec. )  Column  Column  30  45  A  •  •  •  o o  o  3  —o~  .  -a —A  —  A--  0>2  4  Reciprocal FIGURE  Throughput  6  8  J12  I 16  Ratio  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 o f D e m i n e r a l i z i n g Path Length C  EXP.  GRAPHICAL SYMBOL  Q  -  4000  PAUSE TIME (SEC)  ppm;  A(J>  =  30  4-CELL COLUMN  E  11  E  9  8-CELL COLUMN  1  Ca  1  THROUGHPUT RATIO  12  on S e p a r a t i o n  V  c  D  THROUGHPUT RATIO  CD  2  1.46  4  11.79  4  1.73  8  13.47  E  10  2.10  16  14.24  12  F  2  1.73  11  F  4  2.22  8  17.47  9  F  10  2.72  16  18.81  A  a  A  m  30  45  .  4  14.58  171  Pause Time  4 - Cell  8 - Cell  (Sec. )  Column  Column  30  A  A  45  •  •  10 a c_>  8  0  J  2  4  Reciprocal  Throughput  L  6  8  12  16  Ratio  FIGURE 49 Effect  of demineralizing  path length on separation,  C r « = 4 0 0 0 P P M , A(J)=30V Q  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 4 8 , 4 9 ) . 45 i n d i c a t e t h a t f o r a f e e d c o n c e n t r a t i o n C d e m i n e r a l i z i n g p a t h l e n g t h may  q  = 500 ppm  F i g u r e s 44  N a C l an optimum  l i e i n the v i c i n i t y o f 8 s t a g e s 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 l o n g e r d e m i n e r a l i z i n g p a t h l e n g t h s w i t h i n c r e a s i n g feed 5.4.2.  and  the  concentration.  E f f e c t of P r o d u c t i o n Rate As t h e p r o d u c t i o n r a t e  i n c r e a s e s the f e e d undergoes l e s s c y c l e s i n  the ED c e l l b e f o r e i t emerges as p r o d u c t s .  Thus t h e amount o f  i s reduced 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 .  separation  F i g u r e s 38, 41 and T a b l e s  XVII,  XX show the e f f e c t o f 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 =  ) C  for  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  NaCl. and  The  D  of about 500  ppm  p a r a m e t e r s s t u d i e d were t h e pause t i m e , T ( a t l e v e l s o f 15,  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  30  volt).  F i g u r e s 39, 42 and T a b l e s X V I I I , XXI show s i m i l a r e x p e r i m e n t s a t f e e d c o n centration C  Q  - 2000 ppm  NaCl;  w h i l e F i g u r e s 40, 43 t o g e t h e r w i t h  XIX and X X I I i n d i c a t e e x p e r i m e n t s w i t h f e e d c o n c e n t r a t i o n C  q  Tables  - 4000  ppm.  A l l t h e s e f i g u r e s r e f e r r e d t o show t h a t t h e r e i s a s t r o n g t r a d e - o f f between p r o d u c t i o n r a t e and  separation factor.  However, u s e f u l s e p a r a t i o n  can be o b t a i n e d a t a l l p r o d u c t i o n r a t e s ( p r o v i d e d t h a t h i g h e r v o l t a g e s or l o n g e r pause times and d e m i n e r a l i z i n g p a t h s a r e used w i t h h i g h concentration).  F i g u r e s 41, 42 and  and/  feed  43 show t h a t a t an a p p l i e d v o l t a g e (A<}>.)  of 30 V, a pause t i m e (T) o f 45 s e c . and a t h r o u g h p u t r a t i o o f  (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 ) , t h e 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 f e e d c o n c e n t r a t i o n s r a n g e between 30 t o 50.  To f i x i d e a s , most of the c o m m e r c i a l  ED p l a n t s a v a i l a b l e a t p r e s e n t o p e r a t e w i t h a 2:1 means t h a t a f e e d o f 1000  ppm  d e s a l i n a t i o n r a t i o , which  would be d e s a l i n a t e d t o 500 ppm  per  path.  A mark I I I s t a c k ( I o n i c s I n c . ) w h i c h 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 o f s l i g h t l y b e t t e r t h a n 2:1. used i n s e r i e s t o r e d u c e a b r a c k i s h w a t e r of 2100 down t o 500 ppm.  ( a l s o r e f e r to T a b l e I V ) .  ppm  Two  stacks  total dissolved solids  Most o f the h e a l t h  standards  (e.g. the U n i t e d S t a t e s P u b l i c H e a l t h S e r v i c e S t a n d a r d s ) r e q u i r e t h a t t o t a l d i s s o l v e d s o l i d s (TDS) hence w i t h a f e e d a t 2000 ppm  c o n t e n t of p o t a b l e w a t e r t o be 500 ppm  the  or  less;  N a C l and an e q u a l 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 n e c e s s a r y i s r e q u i r e d w i t h a f e e d a t 4000  5.4.3.  are  and a s e p a r a t i o n f a c t o r of  15  ppm.  E f f e c t o f Pause Time The  i n f l u e n c e of a pause t i m e (T) a t l e v e l s o f 15, 30 and  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  sec,  and  100  sec. f o r p r o d u c t i o n r a t e s o f 25 c . c ,  50 c . c  and  was  displacement  p e r i o d o f 36 sec. and an a v e r a g e p r o d u c t i o n p e r i o d of 1.5 6.0  45 sec.  3.0  sec.  c.c./cycle  r e s p e c t i v e l y were used. T a b l e s XXIX, XXX  and XXXI summarize t h e o p e r a t i n g p a r a m e t e r s and  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,  the  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  for  s e v e r a l groups of e x p e r i m e n t s performed i n 4-stage columns w i t h  c o n c e n t r a t i o n s between 500 ppm  and  4000 ppm  NaCl.  X X X I I I and XXXIV t o g e t h e r w i t h F i g u r e s 53, 54 and  Tables  feed  XXXII,  55 e x h i b i t r e s u l t s o f  s i m i l a r e x p e r i m e n t s conducted i n 8-stage columns. A l l t h e s e f i g u r e s show t h a t t h e s e p a r a t i o n i s improved w i t h a pause t i m e .  prolonged  However, t h e e f f e c t of pause t i m e can b e s t 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 t i m e o b t a i n e d w i t h v a r i o u s pause  times  as shown i n T a b l e s XXXV, XXXVI and XXXVII and F i g u r e s 56, 57 and  In  t h e s e f i g u r e s ns/T  i s p l o t t e d v s . pause t i m e ( x ) , where ns i s the  f a c t o r and T i s the c o m p l e t e c y c l e d u r a t i o n i n m i n u t e s .  The  58.  separation  results  are  T a b l e XXIX  EXP. GROUP and PRODUCTION RATE  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co = 500 PPM Exp. Group # R5, R7 and R8  GRAPH. SYMBOL  •  100  15  30  45  42.80  55.15  68.45 61.97  20  25.37 28.43  33.97 37.50  46.25  O  10  3.97  7.64  •  30  25.40  32.63  39.07  20  20.00 17.45  25.79 22.27  34.00 29.41  A  10  3.60  6.92  9.01  •  30  12.11  y  20  •  10  R7 (C.C./cycle)  R8 (C.C./cycle)  SEPARATION FACTOR ns  30  R5 20 ( C . C . / c y c l e )  50  PAUSE^^^ •v. TIME (SEO^v, V0LT>\^ (VOLT)  10.21  16.63  18.46 21.09  8.88  14.17  16.67  2.37  4.00  5.57  175 APPLIED VOLTAGE  PRODUCTION  RATE  (C.C./CYCLE)  20  50  100  10  O  A  •  20  Q  30  m  •  •  (VOLT)  80  60  0 0  15 PAUSE  FIGURE  30 TIME  45  (SEC)  50  Effect of pause  time on separation • 4 - Cell column ; initial c o n c * C — 5 0 0 P P M . 0  T a b l e XXX  EXP. GROUP and PRODUCTION RATE  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co - 2000 PPM Exp. Group # R l , R3 and R4  PAUSE^\^ v. TIME (SEC) GRAPH. V0LT>v. SYMBOL (VOLT)  • 20  50  100  15  30  45  30  7.49 8.53  13.93 16.52  20.64 18.84  20  5.71  8.90 10.43  13.00  O  10  2.74  3.67  4.49  •  30  3.83  7.78  12.00  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  a  20  1.67  2.74  3.76  •  10  1.39  1.57  1.79  Rl (C.C./cycle)  R3 (C.C./cycle)  R4 (C.C./cycle)  ^ \  SEPARATION FACTOR ns  FIGUR 51 Effect of pause time on separation. 4 - Cell column ; initial cone C — 2000 PPM. 0  T a b l e XXXI  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns E a c h C o n s i s t s o f 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 e n t r a t i o n Co - 4000 PPM Exp. Group # R9, R l l and R12  ^•s. EXP. GROUP and PRODUCTION RATE  R9 20 ( C . C . / c y c l e )  Rll 50 ( C . C . / c y c l e )  R12 100 ( C . C . / c y c l e )  PAUSE TIME (SEC)^\ GRAPH. V 0 L T > \ ^ SYMBOL (VOLT)  SEPARATION FACTOR ns 30  45  30  3.10 3.39  4.56 4.10  20  1.98  2.67  30  2.50  3.44 3.76  20  1.78  2.20  m  30  1.91  2.48  B  20  1.52  1.77  •  •  179  APPLIED VOLTAGE (VOLT) 20 30  or o io  <  PRODUCTION 20  •  RATE  (C.C./CYCLE)  50  100  a  •  1)  5.0  < or hi CO  2.5  ±  30 PAUSE  TIME  45  (SEC)  FIGURE 52 Effect of pause time on separation.4-Cell column ; initial c o n e . C — 4 0 0 0 PPM, 0  180  Table XXXII  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co - 500 PPM Exp. Group # M5, M7 and M8  P A U S E ^ \ ^ EXP.  GROUP  and PRODUCTION  (SEC) RATE  GRAPH. SYMBOL  • M5  25  SEPARATION  FACTOR  ns  TIME \  S  V O L T > ^ (VOLT)  15  30  45  30  55.33  72.61  77.85  20  39.92  51.18  65.50  (C.C./cycle)  36.11  o  10  10.67  18.87  25.25  30  44.21  60.77  63.07  39.92  53.96  47.14 M7  50  20  (C.C./cycle)  31.21 28.33  A  10  9.13  16.23  22.95  •  30  32.19  46.52  48.43 53.20  M8  100  (C.C./cycle)  a  20  21.04  28.33  40.38 37.96  •  10  6.40  12.13  18.18  APPLIED  RATE  PRODUCTION  (CJC./CYCLE)  VOLTAGE (VOLT)  25  50  100  10  O  A  •  A  y  A  •  20 80  30  •  60  ac  o o < li.  40  z o  <  or < o_ UJ  to 20  15  30 PAUSE  FIGURE  TIME  45  (SEC)  53  Effect of pause time on separation. 8-Cell column; initial c o n e . C — 5 0 0 P P M 0  182  Table XXXIII  EXP. GROUP and PRODUCTION RATE  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 2000 PPM Exp. Group # M l , M3 and M4  PAUSE^\^ iv. TIME (SEC) VOLTV**^ GRAPH. SYMBOL (VOLT)  •  15  30  45  30  29.46 28.47  36.02  46.28 41.27  20  11.74  20.41  27.53 31.20  O  10  4.02  6.45  9.33  •  30  26.30  32.87  40.95  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  y  20  6.39  14.61 14.23  20.83  •  10  2.00  3.00  5.66  Ml 25 ( C . C . / c y c l e )  M3 50 ( C . C . / c y c l e )  M4 100 ( C . C . / c y c l e )  SEPARATION FACTOR ns  183  APPLIED VOLTAGE (VOLT) 10 20 30  45,  PRODUCTION  RATE  (C.C./CYCLE)  25  50  100  O  A  D  •  A  y  A  •  ac o 30 I-  o 2  z o ac < 0_  UJ CO  20  3 PAUSE FIGURE  30 TIME  45  (SEC)  ,54  Effect of pause time on separation. 8-Cell column  initial cone.  2000PPM.  T a b l e XXXIV  EXP. GROUP and PRODUCTION RATE  E f f e c t o f Pause Time on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 4000 PPM Exp. Group # M9, M i l and M12  PAUSE^\^ TV. TIME GRAPH. SYMBOL  50  100  M9 (C.C./cycle)  30  45  30  16.89  28.13 30.81  37.39  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  20  4.61  7.50  11.80 12.92  10  1.70  2.40  3.21  •  30  12.54 11.69  22.64  28.62 31.27  B  20  3.98 3.63  5.80  10.00  •  10  1.40  2.00  2.90  Mil (C.C./cycle)  Ml 2 (C.C./cycle)  (SEC)^N.  V0LTV\^ (VOLT)  15  • 25  SEPARATION FACTOR ns  185 APPLIED VOLTAGE (VOLT)  PRODUCTION  RATE  (C.C./CYCLE)  40  30  o  o  ul 2 0  z o < < UJ CO  10  PAUSE  TIME  FIGURE 55 Effect of pause time on separation. 8 - C e l l column j initial cone. CQ —  4 0 0 0 PPM.  186  T a b l e XXXV  EXP.  M7 I M7 C M7 D M7 H  GRAPHICAL SYMBOL  E f f e c t o f Pause Time on S e p a r a t i o n C = 500 ppm; Group M7  PAUSE TIME, x (SEC)  o  •  CYCLE TIME, T (MIN)  ns T (MIN )  9.13  5.07  31.21  17.34  30  44.21  24.56  10  16.23  7.06  39.92  17.36  10 15  A  M7 A  SEPARATION FACTOR ns  APPLIED VOLTAGE (VOLT)  30  20  20  1.8  2.3  -1  M7 E  •  30  60.77  26.42  M7 G  •  10  22.95  8.20  M7 B  y  53.96  19.27  M7 F  •  63.07  22.53  45  20 30  2.8  187  Applied Voltage (Volt)  Pause  10  Time  15  30  45  O  A  •  A  y  •  B  20  •  30 28  r  24  -  (Sec. )  16 -  z  CO  c 8  -  0 I 0  1  1  1  15  30  45  Pause  FIGURE  Time  (Sec)  56  Effect of pause time on separation • C =ft:500 PPM 0  Group M 7 .  188  T a b l e XXXVI  EXP.  M3 I M3 C M3 D M3 H  GRAPHICAL SYMBOL  PAUSE TIME, T (SEC)  o  •  APPLIED VOLTAGE (VOLT)  CYCLE TIME, T (MIN)  SEPARATION FACTOR ns  ns T (MIN )  2.40  1.33  8.03  4.46  30  26.30  14.61  10  4.20  1.83  17.03  7.40  10 15  A  M3 A  E f f e c t o f Pause Time on S e p a r a t i o n C = 2000 ppm; Group M3  30  20  20  1.8  2.3  -1  M3 E  •  30  32.87  14.29  M3 G  •  10  6.77  2.42  M3 B  y  24.69  8.82  M3 F  •  40.95  14.63  45  20 30  2.8  FIGURE  57  Effect of pause time -on separation. C ^ i r 2 0 0 0 PPM 0  Group M3  190  T a b l e XXXVII  EXP. '  Mil I Mil C Mil D Mil H  GRAPHICAL SYMBOL  o ©  •  E f f e c t o f Pause Time on S e p a r a t i o n C = 4000 ppm; Group M i l  PAUSE TIME, x (SEC)  CYCLE TIME, T (MIN)  SEPARATION FACTOR ns  ns T (MIN )  1.70  0.94  4.61  2.56  30  15.31  8.51  10  2.40  1.04  7.50  3.26  10 15  A  Mil A  APPLIED VOLTAGE (VOLT)  30  20  20  1.8  2.3  -1  Mil E  •  30  26.05  11.33  Mil G  •  10  3.21  1.15  Mil B  y  11.80  4.21  Mil F  •  34.00  12.14  45  20 30  2.8  FIGURE Effect of  58 pause time-on  separation. C ^ 4 0 0 0 •, Group M i l , Q  192  summarized a s f o l l o w s : 1.  A t l o w v o l t a g e (A<f>) t h e s e p a r a t i o n f a c t o r p e r u n i t t i m e ns/T  v a r i e s a l m o s t l i n e a r l y w i t h t h e pause t i m e T. 2.  As t h e v o l t a g e i n c r e a s e s t h e e f f e c t o f 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 t h e c u r v e t e n d s t o l e v e l o f f . 3.  A t a f u r t h e r i n c r e a s e d v o l t a g e t h e ns/T v s . x c u r v e goes t h r o u g h  a maximum. 4.  The maximum pause t i m e t h a t c a n be u t i l i z e d w i t h o u t  s u f f e r i n g an  a d v e r s e e f f e c t on s e p a r a t i o n depends on b o t h t h e a p p l i e d v o l t a g e (A4>) and t h e f e e d c o n c e n t r a t i o n (C ) . A t 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 s e c f o r C - 500 ppm N a C l ( F i g u r e 56) and x i s about 45 sec o max r r  for C  q  = 2000 ppm ( F i g u r e 57) and a l o n g e r pause t i m e c a n be used f o r t h e  f e e d c o n c e n t r a t i o n o f 4000 ppm N a C l ( F i g u r e 5 8 ) . 5.4.4.  E f f e c t of Applied  Voltage  The e f f e c t o f t h e 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 e x p e r i m e n t s ,  each i n c l u d i n g r u n s a t 10, 20 and 30 V.  parameter v a l u e s a r e l i s t e d i n T a b l e s X X X V I I I - X L I I I  The o t h e r  system  w h i c h show e x p e r i m e n t s  w i t h f e e d c o n c e n t r a t i o n s o f 500, 2000 and 4000 ppm N a C l 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 t h e i n f l u e n c e o f t h e  a p p l i e d p o t e n t i a l (AcJ>) on t h e s e p a r a t i o n f a c t o r ( n s ) . I n c r e a s i n g t h e a p p l i e d v o l t a g e improves t h e 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 b o t h t h e pause t i m e (x) and t h e f e e d c o n c e n t r a t i o n ( C ) a s shown i n F i g u r e s 62, 63 and 64. q  1.  I n experiments w i t h feed c o n c e n t r a t i o n C  Q  The r e s u l t s a r e :  - 500 ppm N a C l t h e  s e p a r a t i o n f a c t o r (ns) i n 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 a t h i g h v o l t a g e and l o n g pause t i m e ( F i g u r e 6 2 ) .  T a b l e X X X V I I I E f f e c t o f 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 Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co 500 PPM Exp. Group # R5, R7 and R8  ^ v A P I 'LIFJJN. VOLTAGE^s. EXP. GROUP and PRODUCTION RATE  Atf)  GRAPH. SYMBOL  20  45  10.21  46.25  68.45 61.97  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  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  •  30  4.00  14.17  16.63  15  2.37  8.88  12.11  R5 20 ( C . C . / c y c l e )  100  R7 (C.C./cycle)  R8 (C.C./cycle)  30  10  •  50  (VOLT)^^ PAUSE\ (SEC)  SEPARATION FACTOR ns  •  194  PRODUCTION RATE (C.C. / CYCLE) 20  O  A  50  Q  A  75 i-  100  w c  PAUSE TIME 30 15  •  (SEC) 45  • •  A  50  ct o o < u_ z o  < or < 0w to 25  0  10 APPLIED  20 VOLTAGE  (VOLT)  FIGURE 59 Effect of applied voltage on separation. 4-Cell column initial cone C — 500 PPM. Q  195  T a b l e XXXIX  E f f e c t o f 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 Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co = 2000 PPM Exp. Group # R l , R3 and R4  ^ \ A P P L I E D \ SEPARATION  VOLTAGE  EXP.  \ .  GROUP  and PRODUCTION  20  50  RATE  Rl (C.C./cycle)  (VOLT) PAUSE^n.  SYMBOL  (SEC)  \  .  10  20  30  •  45  4.49  13.00  20.64 18.84  A  30  3.67  8.90 10.43  13.93 16.52  O  15  2.74  5.71  7.49 8.53  a  45  2.46  7.21 6.09  12.00  30  2.03  5.00  7.78  15  1.53  2.88  3.83  45  1.79  3.76  7.02 5.99  30  1.57  2.74  4.18  15  1.39  1.67  2.45  R3 (C.C./cycle)  • R4 (C.C./cycle)  FACTOR  ns  GRAPH.  -  100  A<j>  •  196  PRODUCTION RATE (C.C./CYCLE)  15  30  45  2Q  O  A  •  50  Q  A  B  A  •  2 2 5 r-  100  PAUSE  •  TIME  (SEC)  CO  c  15.0  or o \o < z o on < a. CO  7.5  0  10 APPLIED  J 30  20 VOLTAGE  (VOLT)  FIGURE 60 Effect of applied voltage on separation.4-Cell column -.initial c o n c . C — 0  2000 PPM.  T a b l e XL  EXP. GROUP and PRODUCTION RATE  20  R9 (C.C./cycle)  50  Rll (C.C./cycle)  100  R12 (C.C./cycle)  E f f e c t o f 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 Two Columns Each C o n s i s t s o f 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 e n t r a t i o n Co - 4000 PPM Exp. Group # R9, R l l and R12  GRAPH. SYMBOL  'LIEDN. VOLTAGE^*. A<|> ^\(V0LT) ^ s . PAUSE (SEC)  SEPARATION FACTOR ns 10  20  30  •  45  2.67  4.56 4.10  A  30  1.98  3.10 3.39  B  45  2.20  3.44 3.76  30  1.78  2.50  •  45  1.77  2.48  •  30  1.52  1.91  198  FIGURE 61 Effect of applied voltage on separation . 4-Cell column-, initial cone. C — 4 0 0 0 PPM. Q  Table XLI  EXP. GROUP and PRODUCTION RATE  E f f e c t o f 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 Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 500 PPM Exp. Group # M5, M7 and M8  ^ \ A P I 'LIED^s. VOLTAGE^. \ A<() (V0LT)\ GRAPH. PAUSE SYMBOL (SEC)  • 25  50  100  10  20  30  45  25.25  65.50  77.85  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  30  16.23  39.92  60.77  15  9.13  31.21 28.33  44.21 47.14  •  45  18.18  40.38 37.96  48.43 53.20  •  30  12.13  28.33  46.52  15  6.40  21.04  32.19  M5 (C.C./cycle)  M7 (C.C./cycle)  M8 (C.C./cycle)  SEPARATION FACTOR ns  •  200  APPLIED  VOLTAGE  (VOLT)  FIGURE 62 Effect of applied voltage on separation. 8-Cell column ;hitial cone. C — 5 0 0 P P M . Q  201  Table XLII  EXP. GROUP and PRODUCTION RATE  25  50  100  Ml (C.C./cycle)  M3 (C.C./cycle)  M4 (C.C./cycle)  E f f e c t o f 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 Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co = 2000 PPM Exp. Group # M l , M3 and M4  ^ \ A P PLIED^v. VOLTAGE^v A<|> \w ^\(V0LT)^\ GRAPH. PAUSEX SYMBOL (SEC)  SEPARATION FACTOR ns 10  20  30  •  45  9.33  27.53 31.20  46.28 41.27  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  30  4.20  17.03  32.87  Q  15  2.40  8.03 9.52  26.30  •  45  5.66  20.83  33.60  •  30  3.00  14.61 14.23  28.45 32.17  15  2.00  6.39  22.36  •  202  PRODUCTION RATE (C.C./CYCLE) 25 50 100  PAUSE  TIME  (SEC)  15  30  45  O  A  •  •  a  •  B  or o f— o <  < or < a. UJ CO  APPLIED  VOLTAGE  (VOLT)  FIGURE 63 Effect of applied voltage on separation. 8-Cell column Initial conc.Cg—2000 PPM.  203  Table X L I I I  EXP. GROUP and PRODUCTION RATE  M9 25 ( C . C . / c y c l e )  50  100  Mil (C.C./cycle)  M12 (C.C./cycle)  E f f e c t o f 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 Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s I n i t i a l C o n c e n t r a t i o n Co - 4000 PPM Exp. Group # M9, M i l and M12  ^\APPLIEI)N. VOLTAGE \ A<j> \. \v(V0LT) \ GRAPH. PAUSE^s. (SEC) SYMBOL  • A  SEPARATION FACTOR ns v  10  20  30  45  3.90  13.19  37.39  30  2.85  8.83 7.87  28.13 30.81  •  O  15  2.20  5.19  16.89  a  45  3.21  11.80 12.92  34.00  A Q  30  2.40  7.50  26.05  15  1.70  4.61  15.31  •  45  2.90  10.00  28.62  •  30  2.00  5.80  22.64  15  1.40  3.98 3.63  12.54 11.69  •  204  PRODUCTION RATE 40r- (C.C./CYCLE) 25 50 100  PAUSE TIME 15 30  (SEC) 45  O  A  •  •  A  a  •  B  30  or  g 20  o < u. z o or  & 10  10 APPLIED VOLTAGE  20  30  (VOLT)  FIGURE 64 Effect of applied voltage on separation. 8- Cell column-,initial conc.C — 4 0 0 0 PPM. 0  205  2.  W i t h f e e d c o n c e n t r a t i o n s o f 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 t o t h e a p p l i e d voltage. 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  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 s h o r t ( r e f e r to F i g u r e The  64) and/or the pause t i m e i s  63).  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  s t r a i g h t f o r w a r d as t h a t of the pause t i m e ( T ) .  Operating  as  at high voltage  a l w a y s r e s u l t s i n a h i g h e r energy consumption per u n i t p r o d u c t product  feed  at a f i x e d  q u a l i t y , but a t the same t i m e 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 t h e 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 p r o d u c t i o n r a t e . the d.c.  U s i n g the method o f ohmic a n a l y s i s ,  power d i s s i p a t i o n i n a g i v e n s t a c k o f c o n s t a n t a v e r a g e r e s i s t a n c e 2  R at current I i s RI  .  The amount of s a l t s h i f t e d , and hence the amount o f  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 o f d i l u a t e produced i s p r o p o r t i o n a l t o I .  Fixed  c o s t s per u n i t volume of d i l u a t e p r o d u c e d , on the o t h e r hand, a r e i n v e r s e l y p r o p o r t i o n a l t o 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 o n l y be d e t e r m i n e d by the e c o n o m i c a l 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 i t e m s c o n t r i b u t i n g to t h e t o t a l o p e r a t i n g c o s t of  ED p r o c e s s may (a)  an  be p l a c e d i n t h r e e c a t e g o r i e s :  c o s t s t h a t v a r y 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  electric  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 r e p l a c e m e n t and a m o r t i z a t i o n o f c a p i t a l i n v e s t m e n t c o s t s . L e s s membrane a r e a and densities  lower c a p i t a l c o s t s a r e r e q u i r e d a t h i g h  current  206  (c)  c o s t s t h a t a r e 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  o p e r a t i n g and maintenance l a b o r and  the c o s t of p r e t r e a t m e n t  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 t h e s e c o s t items w i t h c u r r e n t density.  The  c o s t - o p t i m i z a t i o n method d e v e l o p e d by Cowan (1960)  the t o t a l c o s t of p r o c e s s i n g y  =  (y) as the sum  expresses  of t h r e e terms:  al + Y + c  (102)  where a, b and c a r e t a k e n as c o n s t a n t s f o r a g i v e n s t a c k i f ohmic a n a l y s i s applies.  T h i s s i m p l i f i e d method has been m o d i f i e d by Lacey e t a l . (1963) and  M a t t s o n et a l . (1965). product  By d i f f e r e n t i a t i o n of Eq.  (102)  t o f i n d minimum  c o s t , the optimum c u r r e n t i s seen t o be I opt _  =  ( 7a )  (103)  h  S u b s t i t u t i n g t h i s v a l u e i n the e q u a t i o n f o r the t o t a l c o s t y, i t i s found t h a t f o r most e c o n o m i c a l o p e r a t i o n the f i r s t two costs = fixed  terms a r e t o be e q u a l  (power  costs).  T h i s optimum c o n d i t i o n can a l m o s t never be met  i n conventional  electro-  d i a l y s i s , however, because p o l a r i z a t i o n phenomena s e t an upper l i m i t t o permissible current densities;  and  the  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 c o s t t h a n they s h o u l d do under t h e 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 o p e r a t i n g c u r r e n t d e n s i t y and practical electrodialysis I t can be c o n c l u d e d  the a p p l i e d v o l t a g e i n  installations. t h a t when no e x c e s s i v e p o l a r i z a t i o n t a k e s  place  the h i g h 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 e c o n o m i c a l o p e r a t i o n of an ED p l a n t .  and  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  Concentration  Three groups o f e x p e r i m e n t s were made a t i n i t i a l c o n c e n t r a t i o n s C 500,  2000 and  4000 ppm  NaCl/R^O.  of t h e r i n s e s o l u t i o n was X L I V , XLV  1000,  W i t h t h e s e e x p e r i m e n t s the 2000 and 4000 ppm  concentration  respectively.  Tables  and XLVI summarize the o p e r a t i n g c o n d i t i o n s of s h o r t columns  (4 s t a g e s i n s e r i e s ) a t t h e t h r e e f e e d c o n c e n t r a t i o n s and F i g u r e s 66, and  67  68 d i s p l a y t h e v a r i a t i o n of t h e s e p a r a t i o n f a c t o r w i t h the f e e d con-  centration. and  of  q  T a b l e s X L V I I , X L V I I I and XLIX t o g e t h e r w i t h F i g u r e s 69,  71 r e p r e s e n t  s i m i l a r groups o f e x p e r i m e n t s performed i n l o n g e r columns  each c o n s i s t i n g of 8 s t a g e s i n s e r i e s . 1.  70  The r e s u l t s a r e summarized as f o l l o w s :  I n a l l c a s e s the h i g h e r f e e d 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  separation factor.  T h i s i s because t h e  h i g h e r 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 t o a c h i e v e t h e same s e p a r a t i o n . 2.  The  e f f e c t of the f e e d 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 t h e l o n g e r columns t h a n w i t h the s h o r t ones (Compare F i g u r e s 66-68 w i t h F i g u r e s 69-71). c o n c e n t r a t i o n d i f f e r e n c e AC c o n c e n t r a t i o n and  A t the same s e p a r a t i o n f a c t o r ns  (AC = C„ - C^)  i s h i g h e r w i t h the h i g h e r  l o n g e r columns a r e r e q u i r e d to d i m i n i s h the  the feed  concentration  AC gradient —  between the column ends and  a x i a l mixing 5.4.6.  undesirable  t h a t developed w i t h the h i g h feed c o n c e n t r a t i o n .  No-Pause The  t h u s t o s u p p r e s s the  Operation  pause t i m e x was  dropped t o z e r o i n 7 r u n s a t v a r i o u s f e e d con-  c e n t r a t i o n s t o check f i n d i n g s from the p r e v i o u s work i n a b a t c h system 1972).  T a b l e L summarizes t h e o p e r a t i n g c o n d i t i o n s and  final results  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 =  (Bass, and 0)  T a b l e XLIV  E f f e c t o f Feed C o n c e n t r a t i o n ; ( C o ) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 4 C e l l s i n S e r i e s P r o d u c t i o n R a t e - 20 C . C . / c y c l e Exp. Group # R l , R5 and R9  ^ ^ I N I T L A L ^ v ^ EXP.  GRAPH. SYMBOL  APPLIED VOLTAGE (VOLT)  A B  a  20  C  D  •  E  •  F  •  30  "\C0NC. P A U S E ^ ^ (PPM) (SEC)  SEPARATION FACTOR ns 500  2000  4000  30  33.97 37.50  8.90 10.43  1.98  45  46.25  13.00  2.67  15  25.37 28.43  5.71  15  42.80  7.49 8.53  30  55.15  13.93 16.52  3.10 3.39  45  68.45 61.97  20.64 18.84  4.56 4.10  210  APPLIED 80r-  TIME  (SEC)  VOLTAGE (VOLT)  15  30  45  20  ©  A  a  •  •  30  1000 FEED  PAUSE  •  2000  3000  CONCENTRATION  FIGURE 66 Effect of feed concentration ( C ) on separation. 4 - C e l l column-production rate— 20 C.C/cycle . 0  (PPM)  4000  T a b l e XLV  E f f e c t o f Feed C o n c e n t r a t i o n (Co) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 4 C e l l s i n S e r i e s P r o d u c t i o n R a t e = 50 C . C . / c y c l e Exp. Group # R3, R7 and R l l  SEPARATION FACTOR ns  INITIAL EXP.  GRAPH. SYMBOL  APPLIED VOLTAGE (VOLT)  A B  y  20  C  D  •  E  •  F  m  30  •^^CONC. PAUSF>v. (SEC)  (PPM) 500  2000  4000  30  25.79 22.27  5.00  1.78  45  34.00 29.41  7.21 6.09  2.20  15  20.00 17.45  2.88  15  25.40  3.83  30  32.63  7.78  2.50  45  39.07  12.00  3.44 3.76  212  FEED  CONCENTRATION  FIGURE 67 Effect of feed concentration ( C ) on separation. 4-Cell column _ production rate — 50 CC./cycle . 0  (PPM)  213  T a b l e XLVI  E f f e c t o f Feed C o n c e n t r a t i o n (Co) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 4 C e l l s i n S e r i e s P r o d u c t i o n R a t e = 100 C . C . / c y c l e Exp. Group # R4, R8 and R12  APPLIED  PAUSE  VOLTAGE (VOLT)  15  30  45  20  Q  A  B  •  G  30  •  TIME  c  FEED  FIGURE  CONCENTRATION  (PPM)  68  Effect of feed concentration (Co ) on separation. 4 — Cell column— production r a t e — 100 C.C./cycle .  (SEC)  215  Table XLVII  E f f e c t o f Feed C o n c e n t r a t i o n (Co) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s P r o d u c t i o n R a t e - 25 C . C . / c y c l e Exp. Group # M l , M5 and M9  NITIAL\. EXP.  GRAPH. SYMBOL  A  A  B  y  APPLIED VOLTAGE (VOLT)  20  C  D  •  E  •  F  •  G H I  • A O  30  10  ^\C0NC.  ^"^^  PAUSF>\(PPM) (SEC)  SEPARATION FACTOR ns 500  2000  4000  30  51.18  20.41  - 8.83 7.87  45  65.50  27.53 31.20  13.19  15  39.92 36.11  11.74  5.19  15  55.33  29.46 28.47  16.89  30  72.61  36.02  28.13 30.81  45  77.85  46.28 41.28  37.39  45  25.25  9.33  3.90  30  18.87  6.45  2.85  15  10.67  4.02  2.20  216  APPLIED VOLTAGE (VOLT)  PAUSE  TIME  (SEC)  15  30  45  10  O  A  •  20  Q  A  y  A  •  30  •  m c  or o O <  u. z o  $  or <  OL  Id  CO  2000 FEED  CONCENTRATION  3000  4000  ( PPM)  FIGURE 69 Effect of feed concentration (Co) on separation . 8 - C e l l column-Production rate 25 C.C./cycle  217  Table XLVIII  E f f e c t o f Feed C o n c e n t r a t i o n (Co) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s P r o d u c t i o n R a t e - 50 C . C . / c y c l e Exp. Group # M3, M7 and M i l  ^^^INITIAL^V. EXP.  GRAPH. SYMBOL  APPLIED VOLTAGE (VOLT)  A B  a  20  C  D  •  E  •  F  •  G H I  • A O  30  10  SEPARATION FACTOR ns  CONC. PAUSE\. (SEC)  (PPM) 500  2000  4000  30  39.92  17.03  7.50  45  53.96  24.69  11.80 12.92  15  31.21 28.33  8.03 9.52  4.61  15  44.21 47.14  26.30  15.31  30  60.77  32.87  26.05  45  63.07  40.95  34.00  45  22.95  6.77  3.21  30  16.23  4.20  2.40  15  9.13  2.40  1.70  218  APPLIED  PAUSE  TIME  (SEC)  VOLTAGE (VOLT) 10  15  30  45  O  A  • y  20 30  1000 FEED  •  2000  •  3000  CONCENTRATION  FIGURE 70 Effect of feed concentration ( C ) on separation. 8 - Cell column _ production rate — 50 C.C/cycle. 0  (PPM)  B  4000  219  T a b l e XLIX  E f f e c t o f Feed C o n c e n t r a t i o n (Co) on S e p a r a t i o n Two Columns Each C o n s i s t s o f 8 C e l l s i n S e r i e s P r o d u c t i o n R a t e - 100 C . C . / c y c l e Exp. Group # M4, M8 and M l 2  INITIAL^. EXP.  GRAPH. SYMBOL  APPLIED VOLTAGE (VOLT)  A  B  y  20  C  D  •  E  •  F  •  G H I  • A O  30  10  CONC. P A U S ^ ^ (PPM) (SEC) ^"V.  SEPARATION FACTOR ns 4000  500  2000  30  28.33  14.61 14.23  45  40.38 37.96  20.83  10.00  15  21.04  6.39  3.98 3.63  15  32.19  22.36  12.54 11.69  30  46.52  28.45 32.17  22.64  45  48.43 53.20  33.60  28.62 31.27  45  18.18  5.66  2.90  30  12.13  3.00  2.00  2.00  1.40  15  6.40  5.80  220  APPLIED VOLTAGE  PAUSE  TIME  (SEC)  15  30  10  O  A  •  20  Q  A  y  (VOLT)  30  •  45  A  co c  or o io < u.  or < a. bJ CO  1000 FEED  2000 CONCENTRATION  FIGURE 71 Effect of feed concentration (C ) on separation. 8 _ Cell column _ production rate — 100 C/Vcycle . Q  4000  221  Table  EXP.  L  GRAPH. SYMBOL  Comparison o f 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  FEED CONC. (PPM)  APPLIED VOLTAGE (VOLT)  SEPARATION FACTOR ns  45 SEC M7D  •  M3D  •  M3C  30 SEC  15 SEC  30  63.07  60.77  47.14 44.21  15.77  20  53.96  39.92  28.33 31.21  11.91  30  40.95  32.87  26.30  7.56  20  24.69  17.03  9.52 8.03  3.56  2.40  1.60  500  M7C  2000  NO-PAUSE OPERATION  PAUSE OPERATION  M3I  A  10  6.77  4.20  M l ID  •  30  34.00  26.05  15.31  3.13  M11C  a  20  12.92 11.80  7.50  4.61  2.16  4000  222  APPLIED  FEED  CONCENTRATION  (PPM)  VOLTAGE 80  (VOLT)  500  2000  A  10 20 30  0  y  Q  •  •  15 PAUSE  FIGURE  4000  m  30 TIME  (SEC)  72  Comparison of pause and no_ pause operations . 8 —Cell column_ production rate — 50 C.C./cycle .  223  w i t h t h e normal or p a u s e - o p e r a t i o n  (x = 15, 30 and  45 sec.) under  otherwise  identical conditions. One  can see t h a t r e d u c i n g t h e pause t i m e t o z e r o i n a l l c a s e s s t u 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 . f i n d i n g s t h a t f l o w pauses a t the b e g i n n i n g important 5.4.7.  f e a t u r e s o f the c y c l i c ED  Pure-Pause  This confirmed  previous  of each h a l f c y c l e r e p r e s e n t  operation.  Operation  I n pure-pause o p e r a t i o n t h e e l e c t r i c power i s o f f d u r i n g and  the  circulation  i n t e r p h a s e mass t r a n s f e r t a k e s p l a c e o n l y d u r i n g pause p e r i o d s i n each  cycle.  T h i s mode o f 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 c o u l d r e s u l t i n  l a r g e power s a v i n g s .  T a b l e L I l i s t s 12 r u n s ;  h a l f of them were conducted  w i t h power on d u r i n g c i r c u l a t i o n w h i l e the o t h e r h a l f were performed w i t h pure-pause o p e r a t i o n under o t h e r w i s e  identical conditions.  Figure  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 a c h i e v e d by the two modes o f  73  operation.  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, b u t r e s u l t s i n poor  separation. 2.  5.4.8.  T h i s e f f e c t i s more pronounced w i t h s h o r t pause t i m e .  Semi-Symmetric  Operation  I n semi-symmetric o p e r a t i o n f e e d i s i n t r o d u c e d and p r o d u c t s  withdrawn  e v e r y 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 d u r i n g t h e f i r s t h a l f c y c l e ( r e f e r t o Chapter 4 ) .  S i x e x p e r i m e n t s were performed  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 u s i n g semi-symmetric o p e r a t i o n . 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.  Table L I I These  e x p e r i m e n t s were compared w i t h s i m i l a r r u n s 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  SEPARATION FACTOR ns GRAPH. SYMBOL  EXP.  APPLIED • VOLTAGE (VOLT)  M3A M3B  B  ©  20  M3C M3D M3E M3F  • •  30  PAUSE TIME (SEC)  POWER ON DURING CIRCULATION  POWER OFF DURINC CIRCULATION  30  17.03  4.34  45  24.69  7.32  15  8.03 9.52  2.45  15  26.30  3.37  30  32.87  7.02  45  40.95  11.49  225  APPLIED VOLTAGE  POWER  DURING  CIRCULATION OFF  ON 20  a  30  •  •  4 Or-  30  U  o O < 20  z o  <  OL UJ CO  10  15 PAUSE  FIGURE  30 TIME  (SEC)  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 .  45  T a b l e L I I Semi-symmetric O p e r a t i o n Feed C o n c e n t r a t i o n Co - 2000 ppm P r o d u c t i o n r a t e = 100 C.C./Cycle o f each p r o d u c t  BRINE FEED CONC. • (PPM)  EXP.  PRODUCTION RATE (C.C./CYCLE)  APPLIED PAUSE VOLTAGE • TIME (VOLT) (SEC)  2110  VOLUME CONC. (PPM) • (C.C./CYCLE)  VOLUME CONC. (PPM) • (C.C./CYCLE)  SEPARATION FACTOR ns  30  3825  98.57  355  101.71  10.77  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  30  4100  98.60  204  101.67  20.10  45  4150  99.40  186  102.08  22.31  SS-M4A  2080  DIALYSATE  SS-M4B  SS-M4E  SS-M4F  100  100  20  30  227  shown i n T a b l e L I I I .  F i g u r e 74 c o n t r a s t s t h e p e r f o r m a n c e ' o f t h e s e two modes.  I n a l l c a s e s t h e semi-symmetric o p e r a t i o n r e s u l t s i n a lower  separation  factor. F i g u r e s 75 and 76 show t h e i d e a l d e v e l o p i n g  concentration  profiles  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 t h e mass t r a n s f e r t a k e s p l a c e d u r i n g b o t h pause and d i s p l a c e m e n t  periods.  The  d o t t e d l i n e s i n t h e s e f i g u r e s show s e p a r a t e l y t h e p r e v i o u s c o n c e n t r a t i o n and  t h e change i n t h i s p r o f i l e due t o t h e mass t r a n s f e r d u r i n g  circulation.  S o l i d l i n e i s t h e summation of t h e two d o t t e d l i n e s u s i n g t h e f e e d as t h e z e r o l e v e l .  These f i g u r e s show t h a t when s t e a d y  concentration  s t a t e i s reached the  two modes o f o p e r a t i o n s h o u l d r e s u l t i n t h e same s e p a r a t i o n . summarizes F i g u r e s 75 and 76 and l i s t s t h e a v e r a g e p r o d u c t expressed  profile  Table LIV  concentrations,  i n a r b i t r a r y u n i t s , w h i c h would be e x p e c t e d d u r i n g t h e t r a n s i e n t  p e r i o d s and a t t h e p e r i o d i c s t e a d y s t a t e . The  l o w s e p a r a t i o n a c h i e v e d 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 t o e x t e r n a l m i x i n g o u t s i d e t h e 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 t o w i t h d r a w t h e d e p l e t e d and t h e e n r i c h e d  products  s u c c e s s i v e l y d u r i n g t h e two h a l f - c y c l e s . Any m a t e r i a l from t h e p r e v i o u s c y c l e t h a t mixed w i t h t h e new p r o d u c t would i m p a i r 5.5.  separation.  Comment on pH-Changes Checks on t h e pH o f b o t h t h e p r o c e s s  s i g n i f i c a n t changes f o r most r u n s . The  half-  and r i n s e streams showed no  T y p i c a l r e s u l t s a r e l i s t e d i n T a b l e LV.  r i n s e stream r e m a i n s a l m o s t unchanged and o n l y shows a s l i g h t  i n i t s pH-value w h i l e t h e p r o c e s s  s o l u t i o n tends t o be a s l i g h t l y  fluctuation acidic  w i t h a drop i n t h e pH-value of about 0.3 from i t s i n i t i a l a v e r a g e v a l u e o f 5.9.  A n o t i c e a b l e exception to t h i s a r e the experiments w i t h low feed  c o n c e n t r a t i o n ( C = 500 ppm) w h i c h i n v o l v e r e l a t i v e l y l o n g pause t i m e (T = Q  45 s e c . ) and/or h i g h v o l t a g e (A(j> = 30 V) as e x e m p l i f i e d by e x p e r i m e n t s M7 F,  228  Table L I I I  Comparison o f 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./Cycle Feed C o n c e n t r a t i o n Co - 2000 ppm  SEPARATION FACTOR ns EXP.  APPLIED VOLTAGE (VOLT)  GRAPHICAL SYMBOL  PAUSE TIME (SEC)  SEMI-SYMMETRIC OPERATION  ASYMMETRIC OPERATION  30  10.77  14.61 14.23  45  15.93  20.83  M4 C  15  5.54  6.39  M4 D  15  15.04  22.36  30  20.10  28.45 32.17  45  22.31  33.60  M4 A M4 B  M4 E M4 F  Q  •  a  m  20  30  229  APPLIED  MODE  OF  OPERATION  VOLTAGE 4 0 r-  (VOLT)  SEML SYMMETRIC  a  Q  •  20 30  ASYMMETRIC  •  30  CO c  or o  S  20  z o or < o_ UJ  CO 10  _J 30 PAUSE FIGURE  TIME  (SEC)  74  Comparison of semi symmetric and asymmetric operations. 8 - Cell column- production rate 100 C.C./cycle. Feed concentration C 2 0 0 0 PPM . 0  45  Bottom  Top  A  t  4  Pause • sr. cycle  Circulation  I? A •  '4'  f  5  Production  t  '6  Pause  Circulation  2  FIGURE  75  cycle  »3 Pause  «3 Pause FIGURE 75 -  II  yi  Continued I  N3  t  •  •JN  H  Pause 3  Pause  cycle FIGURE 75  — Continued 2  t N  N  N N  N N 1/1  H  Pause 4 ^ cycle FIGURE  75 -  Continued 3  B  D  .iv  4' 5  T  T  Pause FIGURE  75  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.  T a b l e L I V Average p r o d u c t s c o n c e n t r a t i o n s i n a r b i t r a r y u n i t s o b t a i n e d under semi-symmetric and asymmetric o p e r a t i o n s  SEMI-SYMMETRIC CYCLE NUMBER  FIRST HALF-CYCLE  SECOND HALF-CYCLE  ENRICHED PRODUCT C  1  / /  1 2  / /  2 3  / /  3 4  / /  4 5 5  / /  .  B  OPERATION  ASYMMETRIC OPERATION  DEPLETED PRODUCT  ENRICHED PRODUCT  C  D  Co + 3  Co - 3  Co + 8.5  Co - 8.5  Co + 13  Co - 13  Co + 16.5  Co - 16.5  Co + 19  Co - 19  Co + 20.5  Co - 20.5  Co + 18  Co - 18  Co + 18 Repeat  C  B  DEPLETED PRODUCT C  D  Co + 8  Co - 8  Co + 12  Co - 12  Co + 16  Co - 16  Co - 18  Co + 18  Co - 18  Repeat  Repeat  Repeat  242  T a b l e LV  EXP.  pH-Changes f o r Some ED Runs a t v a r i o u s f e e d c o n c e n t r a t i o n s and o p e r a t i n g conditions  FEED CONC. Co (ppm)  RINSE pH  PROCESS pH Initial  Final  Initial  Final  5.7  5.4  5.7  5.4  5.6  5.0  5.6  5.7  5.8  5.6  M3  A  M3  F  M3  E  5.8  5.3  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  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  5.9  5.7  5.9  5.6  6.2  6.0  6.2  5.9  Mil F  5.7  5.3  5.7  5.8  Mil I  6.1  6.0  6.1  6.2  2000  500  Mil A Mil B  4000  •  243  M7  B and M7  5.6.  E ( r e f e r to Table LV).  Temperature Measurements  The  i n i t i a l and  f i n a l t e m p e r a t u r e s of t h e p r o c e s s  stream f o r s e v e r a l  r u 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 were measured u s i n g an i n s e r t e d mercury thermometer. v a l u e of 23-25°C was  5.7.  An average t e m p e r a t u r e r i s e o f 3-5°C from i t s i n i t i a l o b s e r v e d i n most c a s e s .  P r e s s u r e Drop Measurements The  p r e s s u r e drop a c r o s s an 8-stage ED column was  f l o w r a t e s u s i n g a mercury manometer. L V I and a p l o t o f AP F i g u r e 77. 16.7  (mm  Hg)  measured a t v a r i o u s  Measured v a l u e s a r e l i s t e d i n T a b l e  vs. flow r a t e (c.c./sec) i s displayed i n  Most o f the r u n s i n the p r e s e n t work i n v o l v e a f l o w r a t e of about  c.c./sec.  The mean h y d r a u l i c r a d i u s of t h e f l o w c h a n n e l was  about  2.76  -2 x 10 5.8.  cm w h i c h g i v e s r i s e t o a R e y n o l d s number of about Probe V o l t a g e , A p p a r e n t R e s i s t a n c e and  Current  760.  Consumption  I n a l l e x p e r i m e n t s d e s c r i b e d h e r e the a p p l i e d v o l t a g e s u p p l i e d by D.C.  power s o u r c e was  h e l d c o n s t a n t d u r i n g each h a l f c y c l e .  drop a c r o s s the s t a c k (as measured by probe e l e c t r o d e s ) was  The  the  voltage  primarily 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  o v e r p o t e n t i a l s as shown i n T a b l e L V I I and F i g u r e B o t h the s t a c k v o l t a g e (probe v o l t a g e ) and  electric  78. the c u r r e n t consumption v a r y  s y s t e m a t i c a l l y d u r i n g the c y c l e and a l o n g the d e m i n e r a l i z a t i o n p a t h .  Typical  examples of t h e s e f l u c t u a t i o n s a r e shown i n F i g u r e s 79 and  voltage  80 f o r the  T a b l e L V I P r e s s u r e Drop Measurements 8-Stage ED S t a c k Time P e r i o d t , = 63.5 s e c  MANOMETER READING (mm Hg)  VOLUME (C.C.)  FLOW RATE (C.C./SEC)  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  EXP. GROUP  M7  GRAPH. SYMBOL  •  Average Probe V o l t a g e ( S t a c k V o l t a g e ) over a complete c y c l e f o r v a r i o u s f e e d 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  ^APPLIED VOLTAGE FEED (VOLT) CONC. (ppm)  AVERAGE PROBE VOLTAGE (VOLT) '10  20  30  500  8.95  18.00  27.25  M3  •  2000  8.60  17.15  25.50  Mil  •  4000  8.25  16,65  24.85  247  FIGURE 78 Average stack voltage (probe voltage) vs. applied voltage for various feed concentrations. Pause time ^ = 45 sec , EXFJ group M 3 , M 7 Q M II.  FIGURE 79 Traces of probe voltage recording during a cycle at four points along the demineralizing path. EXP. M7F .  FIGURE  80  Traces of current recording during a cycle at different points along the demineralizing  path. E X P  M7F.  250  Traces of probe voltage recording EXP. M IIF.  during a cycle at four points along the demineralizing path  251  252  and c u r r e n t r e s p e c t i v e l y a t t h e f e e d c o n c e n t r a t i o n C  q  - 500 ppm.  Figures  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 o f s t a c k v o l t a g e and c u r r e n t c o n s u m p t i o n d u r i n g t h e c y c l e and a l o n g t h e d e m i n e r a l i z a t i o n p a t h f o r t h e f e e d c o n centration C  q  - 4000 ppm.  Average v a l u e s o f t h e s e v a r i a t i o n s a l o n g t h e  d e m i n e r a l i z a t i o n p a t h a r e i n d i c a t e d i n T a b l e L V I I I and F i g u r e 83 f o r t h e s t a c k v o l t a g e and i n T a b l e s L I X and LX and F i g u r e s 84 and 85 f o r t h e c u r r e n t consumption. The c u r r e n t consumption d e c r e a s e s w i t h i n c r e a s i n g s e p a r a t i o n , t h u s i t d r o p s a l o n g t h e d e m i n e r a l i z a t i o n p a t h as we move f r o m t h e f e e d end towards t h e p r o d u c t  end ( r e f e r t o 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  f e e d c o n c e n t r a t i o n ( r e f e r t o F i g u r e 8 5 ) . The main i n f l u e n c e c a u s i n g t h e wide v a r i a t i o n s i n t h e c u r r e n t was t h e d e p l e t i o n o f s o l u t e i n e i t h e r t h e f l o w c h a n n e l s o r t h e c a p a c i t y c e l l s towards the'end o f each h a l f c y c l e . The s t a c k v o l t a g e , a s shown i n F i g u r e 8 3 , approaches t h e a p p l i e d v o l t a g e as t h e c u r r e n t consumption d r o p s due t o e i t h e r a h i g h s e p a r a t i o n o r a l o w feed  concentration. T a b l e s L X I , L X I I and L X I I I show v a r i a t i o n s o f probe v o l t a g e , c u r r e n t ,  a p p a r e n t r e s i s t a n c e and power consumption a l o n g t h e d e m i n e r a l i z a t i o n p a t h f o r v a r i o u s r u n s w i t h t h e a p p l i e d v o l t a g e a t l e v e l o f 10, 20 and 30 v o l t and f e e d c o n c e n t r a t i o n s C  q  o f 500, 2000 and 4000 ppm  NaCl.  T a b l e LXIV and F i g u r e 86 show t h e v a r i a t i o n o f a v e r a g e s t a c k 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 a v e r a g e s t a c k r e s i s t a n c e d e c r e a s e s w i t h  i n c r e a s i n g f e e d c o n c e n t r a t i o n and w i t h d e c r e a s i n g 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 t h e v a r i a t i o n o f s t a c k r e s i s t a n c e a l o n g t h e dem 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 . as t h e p r o c e s s  stream becomes more d e p l e t e d  The r e s i s t a n c e i n c r e a s e s  towards t h e p r o d u c t end.  253  Table L V I I I  EXP.  V a r i a t i o n of probe v o l t a g e a l o n g t h e 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 M l I F  GRAPH. SYMBOL  FEED CONC. (PPM)  STAGE NUMBER APPLIED VOLTAGE (VOLT)  PROBE VOLTAGE/APPL. VOLT. 4 FEED END  3  2  1 PROD. END  M7 F  •  500  30  0.883  0.917  0.943  0.960  Mil F  •  4000  30  0.787  0.850  0.883  0.917  254  Symbol  Feed ConeC ( PPM.) 0  • •  500 4000  LOO  I  0-751  4 Feed End  I  3 Stage  I  2 Number  1 1 Product End  FIGURE 83 Variation of stack voltage (probe voltage) alonge the demineralizing path for various feed concentrations. E X P . M 7 F 8 i M I I F .  255  T a b l e L I X V a r i a t i o n o f c u r r e n t consumption a l o n g t h e d e m i n e r a l i z a t i o n path during the depletion h a l f c y c l e a t various applied voltages. Co - 2000 ppm Exp. M3 B, M3 F and M3 G.  >v EXP.  M3 G M3 B M3 F  GRAPH. SYMBOL  A  •  •  STAGE >v NUMBER  APPLIED VOLTAGE (VOLT)  CURRENT CONSUMPTION (mA) 4 FEEDEND  •3  2  1 PRODEND  10  167  161  150  109  20  323  273  192  126  30  463  347  232  153  \. >v  256  Variation  of current consumption along the demineralization  applied voJtages.  C =^ 2 0 0 0 PPM , Q  EXP.  M3 B ,  path at various M3F  8M3G  257  T a b l e LX  V a r i a t i o n o f c u r r e n t consumption a l o n g t h e d e m i n e r a l i z a t i o n path d u r i n g t h e 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 concentrations. A<j> = 30 V Exp. M3 F, M7F and M i l F  1——  —1 >v  EXP.  M7 F M3 F Mil F  GRAPH. SYMBOL  A  •  •  CURRENT CONSUMPTION (mA)  STAGE \v  NUMBER 4 FEEDEND  '3  2  500  225  105  55  29  2000  463  347  232  153  4000  1050  640  409  288  FEED CONC. (PPM)  >v \ .  1 PRODEND  258  Variation of current consumption along the demineralization various feed concentrations. AO" = 3 0 V ,  EXP  path at  M3F.M7F  8MIIF.  Table LXI Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 500 ppm, Exp. M7 B, M7 F and M7 G  EXP.  APPLIED VOLTAGE (VOLT)  STAGE NUMBER VARIABLE Probe Voltage (Volt) Current (mA)  M7 B  20  Apparent Resistance (f!) Power (Watt) Probe Voltage (Volt) Current (mA)  M7 F  1  2  •3  4  18.5  17.9  17.3  16.8  31  56  97  596.8  319.6  178.4  0.57 28.3  1,00 .27.3  43  77  658.1  354.5  1.68 26.0  167 100.6 2.81 25.0  DEPLETION HALF CYCLE AVERAGE VALUES  1  2  3  4  AVERAGE VALUES  17.6  19.1  18.8  18.1  17.5  18.4  88  21  40  76  298.9  909.5  470.0  238.1  1.52 26.7  132  232  121  197.0  107.8  329.4  0.40  0.75  28.8  28.3  29  55  993.1  514.5  1.38 27.5  158 110.8 2.77 26.5  74 432.1 1.33 27.8  105  225  104  261.9  117.8  471.8  30 Apparent Resistance (fl) Power (Watt) Probe Voltage (Volt)  M7 G  ENRICHMENT HALF CYCLE  10  Current (mA) Apparent Resistance (fl) Power (Watt)  1,22  2.10  3.43  5.80  3.14  0.84  1.56  2,89  5.96  2.81  9.1  8.9  8.6  8.4  8.8  9.5  9.3  9.0  8.7  9.1  25  47  74  84  58  18  37  57  81  48  364.0  189.4  116.2  100.0  192.4  527.8  251.4  157.9  107.4  261.1  0.23.  0.42  0.64  0.71  0.50  0,17  0.34  0.51  0.70  0.43 IS)  Table LXII  EXP.  APPLIED VOLTAGE (VOLT)  Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 2000 ppm, Exp. M3 B, M3 F and M3 G  VARIABLE Probe Voltage (Volt) Current (mA)  M3 B  20  Apparent Resistance (£!) Power (Watt) Probe Voltage (Volt) Current (mA)  M3 F  30  Apparent Resistance (£2) Power (Watt) Probe Voltage (Volt) Current (mA)  M3 G  DEPLETION HALF CYCLE  ENRICHMENT HALF CYCLE  STAGE \ ^ NUMBER 1  2  3  4  18.0  17.3  16.3  15.4  167 107.8 3.01  27.0 197 137.1  228 75.9 3.94  25.8 278 92.8  324 50.3 5.28  24.4 371 65.8  5.32  7.17  9'. 05  9.0  8.6  8.2  139  192  210  352 43.7 5.42  22.4 510 43.9 11.42  7.8 220  AVERACE VALUES 16.8 268 69.4 4.41  24.9 339 84.9  1  2  3  4  18.7  18.0  17.1  16.3  126 148.4 2.36  28.0  192 93.8 3.46  27.0  153  232  183.0  116.4  273 62.6 4.67  25.5 347 73.5  8.24  4.28  6.26  8.85  8.4  9.3  9.0  8.6  190  109  150  161  323 50.4 5.26  24.0 463 51.8 11.11  8.2 167  AVERAGE VALUES 17.5 229 88.8 3.94  26.1 299 106.2 7.63  8.8 147  10 Apparent Resistance (fl) Power (Watt)  64.7 1.25  44.8 1.65  39.0 1.72  35.5 1.72  46.0 1.59  85.3 1.01  60.0 1.35  53.4 1.38  49.1 1.37  62.0 1.28  Table LXIII  EXP.  APPLIED VOLTAGE (VOLT)  N.  Variation of probe voltage, current, resistance and power consumption along the demineralizing path. Co = 4000 ppm, Exp. M i l B, M i l F and M i l G  STAGE NUMBER  VARIABLE Probe Voltage (Volt)  Mil B  Current (mA)  Power (Watt) Probe Voltage (Volt) Current (mA)  2  3  4  17.3  16.3  15.6  15.0  517  639  759  880  AVERAGE VALUES 16.1 699  1  2  3  4  AVERAGE VALUES  18.3  17.6  16.7  16.0  17.2  393  500  685  833  603  33.5 8.94 26.0 391  25.5  20.6  17.0  24.2  10.42  11.84  13.20  11.10  24.5  23.2  21.7  23.9  540  711  1097  685  46.6 7.19 27.5 288  35.2 8.80 26.5 409  24.4  19.2  31.4  11.44  13.33  10.19  25.5  23.6  25.8  640  1050  597  30 Apparent Resistance (fi)  66.5  45.4  32.6  19.8  41.1  Power (Watt)  10.17  13.23  16.50  23.80  15.93  8,5  8.1  7.7  7.5  8.0  Probe Voltage (Volt)  Mil G  1  DEPLETION HALF CYCLE  20 Apparent Resistance (£2)  Mil F  ENRICHMENT HALF CYCLE  Current (mA)  •347  443  460  469  430  95.5 7.92 8.9 323  64.8  39.8  22.48  55.6  10.84  16.32  24.78  14.97  8.6  8.4  8.1  8.5  383  403  460  392  10 Apparent Resistance (fi) Power (Watt)  24.5 2.95  18.3 3.59  16.7 3.54  16.0 3.52  18.9 3.40  27.6 2.87  22.5 3.29  20.8 3.39  17.6 3.73  22.1 3.32  T a b l e LXIV  E f f e c t o f I n i t i a l C o n c e n t r a t i o n on t h e e q u i v a l e n t r e s i s t a n c e o f ED s t a c k Exp. Group M7, M3 and M i l  FEED CONC. EXP.  GRAPH. SYMBOL  (ppm)  APPLIED VOLTAGE (VOLT)  EQUIVALENT STACK RESISTANCE (ohm) 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  T a b l e LXV V a r i a t i o n o f ED S t a c k R e s i s t a n c e a l o n g t h e 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 cycle a t various applied voltages. Co - 500 ppm Exp. M7 B, M7 F and M7 G  >v EXP.  M7 G M7 B M7 F  GRAPH. SYMBOL  •  •  •  STAGE >v NUMBER  APPLIED VOLTAGE (VOLT)  X. \ X.  RESISTANCE, R = A<j>/I (ft) 4 FEEDEND  3  2  1 PRODEND  10  107.4  157.9  251.4  527.8  20  110.8  238.1  470.0  909^5  30  117.8  261.9  514.5  993.1  265  Symbol  1000  1 o  Applied Volt AO  (Volt )  •  30  •  10  800  600 0>  o c o tn  or 400  c <u o a. o. <  200  3 Feed End  I  Stage  Number  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 t h e p l o t o f t h e s t a g e a p p a r e n t 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 . t h e s t a g e p o s i t i o n a l o n g t h e 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 a r e f i t t e d by  s t r a i g h t l i n e s w h i c h suggest t h a t t h e a p p a r e n t r e s i s t a n c e o f an ED may be e x p r e s s e d In  R  stack  by an e m p i r i c a l r e l a t i o n o f t h e form: =  £  C  +  ±  (104)  CZ 2  where R ^ i s t h e l o c a l r e s i s t a n c e a t d i s t a n c e I f r o m t h e f e e d i n l e t and C2 a r e c o n s t a n t s .  and  I f we a r e concerned o n l y w i t h t h e a v e r a g e v a l u e o f t h e  s t a g e r e s i s t a n c e t h e n we have I  =  nV  (105)  where £' i s a s i n g l e s t a g e l e n g t h and n i s t h e s t a g e number end).  S u b s t i t u t e Eq. (105) i n t o Eq. In  where R  N  R  n  =  C.  1  +  (n = 1 a t f e e d  (104): (106)  C„n J  i s t h e a v e r a g e r e s i s t a n c e o f s t a g e number n.  F i g u r e 89 shows t h e v a r i a t i o n o f t h e a v e r a g e s t a g e r e s i s t a n c e w i t h t h e s t a g e p o s i t i o n on a s e m i - l o g a r i t h m i c s c a l e when t h e f e e d C  q  concentration  - 2000 ppm and a p p l i e d v o l t a g e was a t l e v e l s o f 10, 20 and 30 V.  Various  p o i n t s under t h e same o p e r a t i n g c o n d i t i o n s a r e f i t t e d by s t r a i g h t l i n e s . The s l o p e o f t h e s e 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 t h e s e l i n e s a r e e x t r a p o l a t e d they tend t o merge i n t o a s i n g l e p o i n t (a p o l e ) . For f e e d c o n c e n t r a t i o n C  q  = 2000 ppm t h e p o l e l i e s a t t h e p o i n t P (0.70,  45 ) ( r e f e r t o F i g u r e 8 9 ) . In  R  n  The v a l u e o f  =  In  45  F o r t h i s c a s e Eq. (106) c a n be w r i t t e n as +'C  Q  3  (n - 0.70)  (107)  c a n be o b t a i n e d from t h e s l o p e o f t h e l i n e s i n F i g u r e 89  267  Symbol  • 1000  Initial Cone. ( PPM) 500  O  2000  A  4000  800 600  400  1 0 1  4 Feed End  3 Stage Number  2  I Product 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 .  M3F.M7F  a Mil F (refer to Tables L X I - L X I U . )  268  FIGURE  89  Variation of apparent ED stack resistance along the demineralization using a semi-log-scale. (refer to Table  LXll)  2000 PPM EXP.M3B ,M3F S  6  path  M3G .  269  as  follows:  and  C  3  *  0.43  f o r A<j>  =  30 V  C  3  =  0.34  f o r Atj) =  20 V  C  3  -  0.17  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)  be d e t e r m i n e d f o r t h e o t h e r f e e d c o n c e n t r a t i o n s under v a r i o u s  can  operating  conditions.  5.9.  Voltage  Efficiency  V o l t a g e e f f i c i e n c y may voltage that i s u t i l i z e d  A<t>  r, v  =  "  A(f,  be d e f i n e d as the f r a c t i o n of the a p p l i e d  i n s e p a r a t i o n (probe v o l t a g e ) .  con " A<j>  A < { ,  el —  •* 100  (108)  where A<j>  =  applied voltage  Acb  =  v o l t a g e drop i n t h e c o n n e c t o r s °  =  v o l t a g e drop due  con  A<|>g£  r  to the r i n s e s o l u t i o n  and  electrode  overpotentials T a b l e L X V I 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 r u n s under v a r i o u s operating conditions.  5.10.  The v o l t a g e e f f i c i e n c y r a n g e s between 82.50 and  C u r r e n t d e n s i t y and  90.83%.  efficiency  I n the p r e s e n t work t h e 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 o n c e n t r a t i o n and The  c u r r e n t d e n s i t y c o r r e s p o n d s t o o p e r a t i o n w i t h a low a small applied voltage.  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  feed  T a b l e LXVI  Voltage E f f i c i e n c y  APPLIED VOLTAGE (VOLT)  UTILIZED VOLTAGE (VOLT)  VOLTAGE EFFICIENCY  M3 B  20  17.15  85.75  M3 F  30  25.50  85.00  M3 G  10  8.30  83.00  M7 B  20  18.00  90.00  M7 F  30  27.25  90.83  M7 G  10  8.95  89.50  Mil B  20  16.65  83.25  Mil F  30  24.85  82.83  Mil G  10  8.25  82.50  EXP.  %  271  n  TI  =  n  „ sn mn w  (B.7.)  When t h e s e l e c t i v i t y o f the membrane i s 0.90 t h e t r u e c u r r e n t efficiency, n  i s u s u a l l y about 80%.  The c u r r e n t u t i l i z a t i o n f a c t o r o r t h e  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^ c a n be d e f i n e d as  a c t u a l amount o f s a l t t r a n s p o r t e d I  theoretical  amount o f s a l t  (109)  A  transported  where t h e t h e o r e t i c a l amount o f s a l t t r a n s p o r t e d i n g - e q u i v a l e n t VAC  =  1  '  Z  '  1  0  ZF  ,6•  i s g i v e n by (  M  1 1 0  >  where V  = the volume o f f l u i d d e m i n e r a l i z e d f l o w channel  d u r i n g time t i n a  (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)  The  I  = c u r r e n t passed (amp)  t  = d u r a t i o n o f the c u r r e n t passage  Z  = v a l e n c e (g-equiv./g-mole)  F  = F a r a d a y ' s c o n s t a n t = 96500 (coulomb/g-equiv.)  M  = M o l e c u l a r w e i g h t o f s o l u t e = 58.44 (g/g-mole)  (sec)  o v e r a l l c u r r e n t e f f i c i e n c y a s d e f i n e d above i n c l u d e s t h e t r u e  current e f f i c i e n c y ,  t o g e t h e r w i t h any i n e f f i c i e n c i e s i n the p r o c e s s 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 l e a k a g e 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 e v a l u a t e d  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 T a b l e L X V I I .  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 c a s e s ;  runs w i t 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 .  high  P r e v i o u s work i n t h e 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. FEED CONC (ppm)  CURRENT  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  EXP.  (Amp)  OVERALL CURRENT EFFICIENCY %  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 t h e f i r s t c y c l e , d e c r e a s i n g r a p i d l y f o r subsequent c y c l e s , and t e n d i n g t o z e r o as t h e s e p a r a t i o n approached s t e a d y 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 c o u l d 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 s h o r t r e g e n e r a t i o n s t e p compared w i t h t h e d e m i n e r a l i z i n g s t e p and by u s i n g a l o n g e r d e m i n e r a l i z i n g p a t h . as most o f t h e u s e f u l s e p a r a t i o n t a k e s p l a c e d u r i n g pause p e r i o d s c i r c u l a t i o n time may r e s u l t i n an i n c r e a s e d c u r r e n t  5.11.  Also  decreasing  efficiency.  Comments on S t a c k R e s i s t a n c e Models F o u r e x p e r i m e n t 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 have been used t o  t e s t t h e non-ohmic model.  The f o l l o w i n g s i m p l i f i e d e q u a t i o n  (Eq. 51) was  used t o p r e d i c t t h e a p p a r e n t r e s i s t a n c e o f an ED s t a g e a t t h e p r o d u c t end. 2RT R  = P  FT  r  [(t  .  N  " V  l  n  2FD (t - t ) A i , A - 26 + _ D D  ns + k ,  — T  ]  1 + k/ns 1 - k  . A - 26 + _ C C U  . + p  A  , + p  a  (51)  C  where R  i s the r e s i s t a n c e per u n i t area  P  R  2 (ohm-cm )  i s t h e gas l a w c o n s t a n t =  8.3144 ( J o u l e - g m o l e  .T  =  t h e a b s o l u t e t e m p e r a t u r e (°K)  F  =  Faraday's constant  i  =  c u r 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 o f c o u n t e r - i o n s i n membrane and s o l u t i o n respectively  - 1  - °K ) _ 1  (Coulomb/g.equiv) 2  274  t  =  c  t r a n s p o r t number o f c o - i o n s i n t h e membrane  D  =  2 e q u i v a l e n t s o l u t i o n c o n d u c t a n c e (mho.cm /gmole) 2 d i f f u s i v i t y (cm / s e c )  ns  =  separation factor  A  =  =  k  =  —— D r a t i o of the operating to l i m i t i n g current density  A  =  f l o w channel  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)  =  t h e a n i o n and c a t i o n membrane r e s i s t a n c e p e r u n i t a r e a  C  (ohm  t h i c k n e s s (cm)  - cm^)  System D a t a and A s s u m p t i o n s Room t e m p e r a t u r e = 25°C = 298°K M o l e c u l a r w e i g h t o f N a C l = 58.44 E q u i v a l e n t c o n d u c t a n c e o f aqueous sodium c h l o r i d e s o l u t i o n , A, i s g i v e n by T a b l e L X V I I I and F i g u r e 90. D i f f u s i v i t y o f aqueous sodium c h l o r i d e , D, i s g i v e n by T a b l e L X V I I I and F i g u r e 91. A - 26  -  A 2  E l e c t r o d e a r e a = 61.23 cm Spacer t h i c k n e s s = 0.098 cm Exposed a r e a o f spacer = 0.50 Membrane s e l e c t i v i t y = 90% = 0.90 (t - t ) c  (t - t ) av  = 0.45 =  k  19.2 ft-cm  = 0.80  2  275  Table LXVIII  CONC. o f NaCl (ppm)  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 *  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 C o n v e r s i o n E n g i n e e r i n g D a t a Book, Second E d i t i o n , U.S. O f f i c e o f 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 2 5 ° c . •  1.47  ;l  I  I  J  0  1000  2000  3000  1  I  I  I.  4000  5000  6000  70C0  Concentration , PPM FIGURE 91 Diffusivity  of aqueous  sodium chloride solutions at 2 5 ° c .  1  8000  278  Sample o f 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 1 0 " cm /sec 5  2  2 C„ = 4300 ppm ; A„ = 113 mho. cm /gmole ns = 4 0 . 9 5 ; i = 2.858 mA/cm av 2  1 s t term (membrane p o t e n t i a l term) =  (2)(8.3144)(298)(0.9) (96500) (2.858)10  < t > , m  R  -  U  R  '  =  8  .  5  l  1 + 0.0195 O  n  _ 3  solution resistance  R  =  solution resistance  (11.45) 1 0 (4300)(113)  , _  7  c m  2  1  o, '  1 9 1 Z  2  0  " "  C  m  2  =  38.40 n - cm  =  868.58'n - c m  term)  6  5 t h term ( e n r i c h e d  3  term)  (0.098)(58.44)10 (0.5)(105)(125.6)  d  >  Z  m  4 t h term ( d e p l e t e d  6  term)  (2)(96500)(1.599) 1 0 " (2.858) (0.45) (125.6)10-3  3rd term (membrane r e s i s t a n c e  40.95 + 0.8  n  J  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 p 6  l  2  term)  6  c, ° "  2  n  =  2 3  '  5 7  C  m  The a p p a r e n t r e s i s t a n c e per u n i t a r e a o f a c e l l p a i r , R^ i s g i v e n b y R = R p  X  The p r e d i c t e d  + R .  cj>,m  o  + R + R , +R m  d  e  stage r e s i s t a n c e i s given by  =  1048.04 fi - c m  2  279  Measured s t a g e r e s i s t a n c e ... «. the p e r c e n t a g e e r r o r  =  = 136.93 - 160.05 . ^ 1(  Q  160.05 ft .._ - 14.44%  =  T a b l e LXIX l i s t s v a l u e s o f 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 e x p e r i m e n t s and b r e a k s down t h e t o t a l p r e d i c t e d r e s i s t a n c e  into  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 t h e c o n t r i b u t i o n o f each element towards t h e o v e r a l l v a l u e .  Figure  92 d i s p l a y s t h e d i s c r e p a n c y  between p r e d i c t e d and measured v a l u e s o f an ED s t a g e r e s i s t a n c e .  The  d i s c r e p a n c y may be a t t r i b u t e d t o t h e assumed v a l u e s used i n t h e c a l c u l a t i o n or t o t h e s i m p l i f y i n g a s s u m p t i o n s i n v o l v e d i n t h e model o r t o b o t h o f them. From T a b l e LXIX i t c a n be seen t h a t t h e membrane p o t e n t i a l term together with the d i f f u s i o n layer resistance contribute  about 20% w h i l e  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 t h e o v e r a l l r e s i s t a n c e value.  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 c a n be used  s a t i s f a c t o r i l y t o predict the stack The  b a s i c e q u a t i o n o f ohmic a n a l y s i s i s g i v e n a s  ll  P  where K^, average  resistance.  K = — C and  i + Ko - KoC  (52)  are constants for a given  system and C i s t h e l o c a l  concentration.  Measured s t a g e r e s i s t a n c e s i n s e v e r a l r u n s were p l o t t e d v s . t h e r e c i p r o c a l o f t h e average c o n c e n t r a t i o n 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 .  as shown i n F i g u r e  The model c o n s t a n t s were d e t e r m i n e d  from t h e s l o p e and i n t e r c e p t o f t h e graph as f o l l o w s : *  and  K  2  *  K  3  -  216484 191.34 0.0  93 and T a b l e LXX.  Table LXIX  D i s t r i b u t i o n of the predicted resistance of an ED stage, R , between i t s r e s i s t i v e elements  M3 F 2000 ppm RESISTIVE ELEMENT  VALUE  a  M3 B 2000 ppm  % age of R s  VALUE n  M7 G 500 ppm  % age of R s  VALUE  a  Mil F 4000 ppm  % age of R s  VALUE n  % age of R s  Membrane P o t e n t i a l  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  D i f f u s i o n Layer Resistance  4.07  2.97  4.91  4.97  33.30  8.27  2.11  3.26  Depleted Bulk S o l . Resistance  113.48  82.88  73.45  74.27  269.96  67.02  50.34  77.71  Enriched Bulk S o l . Resistance  3.08  2.25  3.28  3.32  12.29  3.05  1.69  2.61  Predicted t o t a l Resistance Value  136.93  Measured Resistance Value  160.05  Discrepancy as % Age  - 14.44  100  98.90  100  128.1  - 22.80 i  402.74  100  64.78  445.90  81.00  - 9.68  - 20.03  100  520  7T  i  Voltage (Volt)  Initial Cone. 480  (PPM)  10  500  O  400  20  30  2000  •  4000  B  o  320  240  160  /  /A  /  80  V  /  / 80  160 Measured  FIGURE  4-  240  320  Value of ED Stage  400  480  Resistance (ohm )  92  Discrepency  between predicted and measured value d an ED stage .  520  T a b l e LXX  V a l u e s o f l o c a l average c o n c e n t r a t i o n , C and measured s t a g e r e s i s t a n c e  PRODUCT CONC (ppm) EXP. C  B  C  D  LOCAL AVERAGE CONC. (ppm)  STAGE RESISTANCE («)  M3 B  4025  163  313  128  M3 F  4300  105  205  160  M3 G  3725  550  958  75  M7 B  1090  20.2  40  753  M7 F  1110  17.6  35  826  Mil B  7375  625  1152  40  Mil F  8125  239  464  81  Mil G  6450  2010  3065  26  283  900  FIGURE  93  Variation of apparent resistance of an ED stage with the reciprocal of Ihe average  product concentrations.  284  5.12  Comparison w i t h P r e v i o u s Work i n C l o s e d  (i)  Separation  System  B a s s (1972) r e p o r t e d some e x p e r i m e n t s performed i n a b a t c h - r e c i r c u l a c i o n mode o f o p e r a t i o n i n w h i c h a 90% d e m i n e r a l i z e d p r o d u c t was i n t e r m i t t e n t l y r e p l a c e d by f r e s h f e e d e v e r y e i g h t c y c l e s .  E x p e r i m e n t s under t h i s mode o f  o p 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 o f 16 w i t h a f e e d C  q  concentration  = 1250 ppm, a p p l i e d v o l t a g e A<}> = 10 V, pause t i m e x = 10 s e c , d i s p l a c e d  volume 6 = 2/3 t h e a c t i v e volume and a t h r o u g h p u t r a t i o o f about 0.075. I n t h e p r e s e n t work e x p e r i m e n t s w i t h  = 20 V, x = 15 s e c r e s u l t i n a  A<j>  s e p a r a t i o n f a c t o r o f 20 a t a t h r o u g h p u t r a t i o o f 0.25 w h i c h i s t h e same magnitude o f s e p a r a t i o n p e r u n i t power c o n s u m p t i o n as i n t h e p r e v i o u s  case.  However, t h e p r e v i o u s work does n o t show any c o n s i s t e n t e f f e c t o f i n i t i a l concentration, C (ii)  q  on t h e f i n a l  R e s i s t a n c e and C u r r e n t The  separation.  Consumption  i n i t i a l r e s i s t a n c e and c u r r e n t consumption i n t h e c l o s e d system  were g e n e r a l l y o f t h e same magnitude a s i n t h e p r e s e n t work and they e x h i b i t t h e same t r e n d o f v a r i a t i o n a l o n g t h e d e m i n e r a l i z i n g p a t h . (iii)  Analysis of A x i a l Dispersion The a x i a l d i s p e r s i o n i n t h e ED c e l l s has been d e t e r m i n e d p r e v i o u s l y  u s i n g t h e s t e p r e s p o n s e method.  The r e s u l t i n g F-diagrams d i d n o t suggest  excessive channelling or by-passing. was e s t i m a t e d  From t h e s l o p e o f r e s p o n s e c u r v e i t  t h a t t h e system c o r r e s p o n d s t o about 50 e f f e c t i v e m i x i n g  I n t h e spacer used i n b o t h works t h e r e a r e 10 x 10 s t r a n d s p e r i n c h and t h e r e a r e about 55 h o l e s a l o n g t h e f l o w p a t h i n t h e ED c e l l .  stages.  285  (iv)  E f f e c t o f Pause Time The p r e v i o u s work i n t h e b a t c h o p e r a t i o n showed t h a t f l o w pauses  at  t h e b e g i n n i n g o f each h a l f c y c l e r e p r e s e n t i m p o r t a n t f e a t u r e s o f t h e c y c l i c  process operation.  5.13  T h i s i s i n l i n e w i t h t h e f i n d i n g s i n t h e p r e s e n t work.  Reproducibility  S e v e r a l o f t h e r u n s 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 r e p e a t e d to t e s t t h e r e p r o d u c i b i l i t y o f t h e r e s u l t s .  T a b l e LXXI l i s t s t h e d u p l i c a t e  e x p e r i m e n t s and compares them w i t h t h e i n i t i a l ones conducted i n 4-stage columns.  T a b l e L X X I I makes t h e same c o m p a r i s o n f o r e x p e r i m e n t s 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 a r e  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  SEPARATION FACTOR n s EXP. OLD Rl A  8.90  Rl D  7.49  DISCREPANCY  NEW  AS PERCENTAGE OF ( n s ) Av,  10.43  + 15.83  8.53  + 12.98  Rl E  13.93  16.52  + 17.01  Rl F  20.64.  18.84  -  R3 B  7.21  6.09  - 16.84  R4 F  7.02  5.99  - 15.83  R5 A  33.97  37.50  +  R5 C  25.37  28.43  + 11.38  R5 F  68.45  61.97  -  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  +  R9 F  4.56  4.10  - 10.62  Rll F  3.44  3.76  +  9.12  9.88  9.94  8.94  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 OLD  NEW  DISCREPANCY AS PERCENTAGE OF ( n s ) Av.  Ml B  27.53  31.20  + 12.50  Ml D  29.46  28.47  -  Ml F  46.28  41.27  - 11.44  M3 C  8.03  9.52  + 16.98  M4 A  14.61  14.23  -  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  M9 E  28.13  30.81  +  9.09  Mil B  11.80  12.92  +  9.06  M12 C  3.98  3.63  -  9.20  Ml 2 D  12.54  11.69  -  7.02  M12 F  28.62  31.27  +  8.85  EXP.  3.42  2.64  - 11.50  CHAPTER 6  C o n c l u s i o n s and Recommendations  The p r e s e n t work has p r o v e n t h e f e a s i b i l i t y  of c o n t i n u o u s  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.  cyclic  The 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 d e m i n e r a l i z i n g p r o c e s s competes m a i n l y w i t h d i s t i l l a t i o n and i t a p p e a r s t o be more a t t r a c t i v e e c o n o m i c a l l y 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 salt).  ( w i t h c o n c e n t r a t i o n s o f up t o about 10,000 ppm d i s s o l v e d  However, 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 s u b j e c t t o e x c e s s i v e ,  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 f o r m a t i o n 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 .  Cyclic  p r o m i s e s t o overcome t h e s e problems by t h e r e v e r s e d p o l a r i t y  electrodialysis  technique.  I n t h e p r e s e n t work no e x c e s s i v e p o l a r i z a t i o n was n o t i c e d i n most o f t h e r u n s  (up t o t h e maximum v o l t a g e a p p l i e d o f 30 v o l t s )  and i n e x p e n s i v e g r a p h i t e e l e c t r o d e s proved r e a s o n a b l y l o n g p e r i o d of t i m e .  The p r o c e s s 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 t o 50 a t a throughput B D a desalinationratio  t o be s a t i s f a c t o r y over a  r a t i o o f 0.25 w h i c h i s e q u i v a l e n t i.<  ( d e f i n e d as C /C_) o f about 25 compared w i t h t h e o D  d e s a l i n a t i o n r a t i o per p a t h o f about 2 i n most c o m m e r c i a l p l a n t s c u r r e n t l y i n operation. The p r i m a r y o b j e c t i v e s o f t h e e x p e r i m e n t a l program u n d e r t a k e n  were  to e x p l o r e t h e p o s s i b l e r e g i o n o f 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, t o s c r e e n system p a r a m e t e r s , 288  and t o determine.  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 d e s i g n and o p e r a t i n g p a r a m e t e r s  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  (ii)  Semi-symmetric and asymmetric modes o f o p e r a t i o n  (iii)  Pause and no-pause o p e r a t i o n s  (iv) b)  length  Pure-pause o p e r a t i o n w i t h power o f f d u r i n g  Operating (v)  circulation  Parameters  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 t o 0.50.  (vi) (vii) (viii)  A p p l i e d v o l t a g e A<|) a t l e v e l s o f 10, 20 and 30 v o l t , Pause t i m e x a t l e v e l s o f 1 5 , 30 and 45 s e c . Feed c o n c e n t r a t i o n C  q  a t l e v e l s o f 500, 2000 and 4000 ppm  The r e s u l t s o f t h e s t u d y c a n be summarized i n t h e f o l l o w i n g : 1.  D e s p i t e t h e s t r o n g 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 , t h e s e p a r a t i o n f a c t o r ranged from 30 ( f o r 4000 ppm f e e d ) t o 50  ( f o r 500 ppm f e e d ) a t t h e h i g h e s t 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 t i m e proved t o be an i m p o r t a n t  Decreasing  o p e r a t i n g parameter.  t h e pause t i m e below 15 s e c . r e s u l t e d i n c o n s i d e r a b l y  lower  separation. 3.  The maximum pause t i m e t h a t c a n be u t i l i z e d w i t h o u t an a d v e r s e  e f f e c t on s e p a r a t i o n depends on b o t h t h e a p p l i e d v o l t a g e Acj> and t h e f e e d concentration C . o C  q  - 500 ppm and i t was about 45 s e c . f o r C 4.  The  A t an a p p l i e d v o l t a g e A<}> = 30 V;  x  was about 30 s e c . f o r max  q  - 2000 ppm.  I n a l l c a s e s i n c r e a s i n g t h e a p p l i e d v o l t a g e improves t h e s e p a r a t i o n .  separation f a c t o r increases at l e a s t p r o p o r t i o n a l l y with the applied  290  voltage.  The e f f e c t o f a p p l i e d v o l t a g e was more pronounced when t h e f e e d  c o n c e n t r a t i o n was h i g h and/or t h e pause t i m e was s h o r t . 5.  With t h e feed c o n c e n t r a t i o n C  Q  - 5 0 0 ppm t h e optimum c o n d i t i o n s  are thought t o 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 t h e v i c i n i t y o f 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 t h e range about 30 s e c .  20-30  v o l t and a pause time o f  An i n c r e a s e o f pause t i m e above 3 0 s e c . 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 o f p o l a r i z a t i o n . 6.  As t h e f e e d c o n c e n t r a t i o n C  q  increases the separation  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,  decreases. higher  v o l t a g e and l o n g e r pause t i m e . 7.  Pure-pause o p e r a t i o n saves e l e c t r i c power a t t h e expense o f poor  separation. 8. drawal,  V a r i a t i o n s i n the methods o f f e e d i n t r o d u c t i o n and p r o d u c t  with-  such a s s y m m e t r i c , 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 m i x i n g  i s ignored a l l  t h e s e modes p r e d i c t t h e same f i n a l s e p a r a t i o n as shown by t h e g r a p h i c a l solutions.  However, t h e degree o f c o m p l e x i t y  o f t h e system, t h e number o f  v a l v e s and t h e number o f s u b d i v i s i o n s i n t h e t i m i n g sequence, d e c r e a s e a s t h e o p e r a t i o n becomes l e s s symmetric. 9.  When semi-symmetric and asymmetric o p e r a t i o n s were compared  e x p e r i m e n t a l l y under o t h e r w i s e lower  separation.  i d e n t i c a l c o n d i t i o n s t h e former r e s u l t e d i n  T h i s may be a t t r i b u t e d m a i n l y  to the e x t e r n a l mixing  outside the a c t i v e demineralizing area. 10.  The e x p e r i m e n t a l  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-  strated.  The p r o c e s s  results aregenerally highly reproducible.  l o o k s p r o m i s i n g and i t d e s e r v e s f u r t h e r study a l o n g t h e  291  following a)  lines: The  p r e s e n t work has been l i m i t e d by the f o l l o w i n g d e s i g n  parameters: (i)  A d e m i n e r a l i z i n g p a t h o f maximum l e n g t h o f 8 s t a g e s i n series  (ii)  A D.C.  power s u p p l y o f 400 w a t t s  (a maximum a p p l i e d  v o l t a g e of about 30 v o l t s ) (iii)  A maximum t i m e i n t e r v a l o f about 50  sec.  To e x p l o r e f u l l y t h e whole o p e r a t i n g domain a t f e e d c o n c e n t r a t i o n h i g h e r t h a n 500 ppm the p r o c e s s b)  Q  modifying  design.  The  f e e d c o n c e n t r a t i o n s h o u l d be extended t o the range C  10,000 - 15,000 c)  a l l t h e s e p a r a m e t e r s need t o be r e l a x e d by  C  Q  =  ppm.  Other o p e r a t i n g p r o c e d u r e s s h o u l d be i n v e s t i g a t e d .  i t i s proposed t o d i s c o n n e c t  t h e e l e c t r i c power f r o m t h e ED  p a r t of t h e d i s p l a c e m e n t .  A l s o , the system may  w i t h f e e d i n t r o d u c t i o n and  product withdrawal  In p a r t i c u l a r  stacks during  be r u n i n s e m i - b a t c h o p e r a t i o n  once e v e r y 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 o t h e r t h a n t h e p r e s e n t 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 t h e two h a l f c y c l e s .  T h i s may  r e s u l t i n a b e t t e r power  economy. d)  The proposed s t a c k 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 t h e e x p e r i m e n t a l  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 o f the c o n s t a n t - r a t e model based on t h e s t a c k r e s i s t a n c e c o u l d 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 s c a l e - u p and an o p t i m i z a t i o n s t u d y of the system a r e  f o r e v a l u a t i o n o f the p r o c e s s  economics and  scale w i t h other competitive  processes.  f)  essential  i t s c o m p a r i s o n on a c o m m e r c i a l  Other s o l u t e s s h o u l d be i n v e s t i g a t e d , b o t h i n b i n a r y and  in  multicomponent m i x t u r e s . g)  By u s i n g c a t i o n and a n i o n 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 i o n s o n l y , t h e system can be used t o s e p a r a t e monovalent i o n s from d i v a l e n t and o t h e r i o n s .  NOMENCLATURE  Typical Unit membrane a r e a  cm  i o n i c a c t i v i t y o f c a t i o n (+) o r a n i o n (-)  g-mole litre  r a t e constant during d i l u t i o n h a l f cycle  sec  r a t e constant d u r i n g enrichment half cycle  sec  membrane a r e a  2  -1 -1  cm g-mole litre  solute concentration  or ppm constant cm / s e c  diffusion coefficient p o t e n t i a l drop p e r c e l l p a i r  volt  p o t e n t i a l drop  volt  the f r a c t i o n d e s a l t e d Faraday's  A.sec/g-equiv. litre/sec.  constant  or f l o w r a t e o f p r o c e s s  stream mA/cm^  current density  A  current  2  ionic flux vector  (g-mole)/(cm ) ( s e c )  electrical conductivity o r t h e 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 293  mho/cm  294  Typical  Unit  constant rate constant or c e l l c o n s t a n t  cm  -1  constant channel  length  a s i n g l e stage  cm length  cm  phenomenological c o e f f i c i e n t l e n g t h o f t h e membrane or t h e d e m i n e r a l i z i n g p a t h  cm  number o f c y c l e s or number o f membrane p a i r s or w i d t h o f membrane separation  factor  normality of s o l u t i o n exp  (- a  ]L  cm g-equiv.litre  — )  o r p e r m s e l e c t i v i t y o f i o n exchange membrane or membrane a r e a u t i l i z i n g f a c t o r exp  (- a  2  )  flow rate  cm / sec  heat f l o w v e c t o r d i m e n s i o n l e s s r a t i o o f spacer t h i c k n e s s i n t h e c o n c e n t r a t e and t h e d i l u a t e compartments areal resistance or t h e gas l a w c o n s t a n t  ohm cm ( j o u l e s ) /(°K) (mole)  t r a n s p o r t number or t e m p e r a t u r e cycle  time  sec °K  or a b s o l u t e t e m p e r a t u r e ionic  mobility  t o t a l chemical p o t e n t i a l  (cm  )/(volt)(sec)  295  Typical Unit v .  =  displacement  velocity  v  =  velocity vector  cm/sec cm/sec 3  V  =  volume  cm  w x  = =  w a t e r t r a n s p o r t number distance co-ordinate  cm  y  =  l a t e r a l distance co-ordinate  cm  z  =  v a l e n c e o f charged s p e c i e s or d i r e c t i o n o f f l o w  (g-equiv)/(g-mole)  Greek Symbols a  =  f r a c t i o n of h a l f  cycle  g  =  f r a c t i o n of h a l f  cycle  Y  =  phase l a g  =  t h e mean i o n i c a c t i v i t y  6  =  thickness of Nernst layer or d i f f u s i o n layer  cm  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 o f p a c k i n g  n  =  efficiency  ri  =  e l e c t r i c f i e l d vector  A"  =  e q u i v a l e n t conductance  Y  +  coefficient  volt/cm 2 (mho) (cm  )/(g-equiv) 3  v v  +  =  p a r t i a l m o l a r volume  =  stoichiometric coefficients for electrolyte M  cm /mole  v +  p  =  electrical resistivity  p  =  (1 - E)/E = r a t i o o f volume o f p a c k i n g t o v o i d volume  x  =  pause t i m e or t r a n f e r e n c e number o f w a t e r  ohm-cm  sec  296  Typical Unit A<|>  =  applied electric potential  volt  Acb  =  Donnan p o t e n t i a l  volt  =  divergence operator or gradient operator  Don  V  Subscripts 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 o f t i m e i n t e r v a l d u r i n g a c y c l e ; (T ,T ) 1  2  +  f o r p o s i t i v e l y charged  species; ( t )  -  f o r n e g a t i v e l y charged  species; ( t _ )  a  f o r anion-exchange membrane; ( or an a v e r a g e v a l u e ; (C ) cL b r i n e product; (C, ) b b r i n e (enriched) product; (C )  b B  +  a  )  B  c  c a t i o n - e x c h a n g e membrane; ( t ) or c o n c e n t r a t e p r o d u c t ; (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;  d^,d  fc  £  2  Donnan terms;  (C^)  (EQ^E^)  D  d i a l y s a t e (depleted) product;  e  enriched product; (C ) or e l e c t r o d e ; ( 1 ) ' e  f  fluid  F  Faraday;  H  Henderson term;  i  r e f e r s to i n l e t ;  I  current  ; (y  j  co-ion;  (C^)  o r m o b i l e phase; (n^,) (E^) (C^)  (C^)  (C^)  297  k  counter-ion; (C^) ^ o r s p e c i e s k; (J^)  SL  refers to l o c a l value at distance feed i n l e t ; (R^)  m  manifold; ( n ) o r membrane; ( F ^ ) or membrane s o l u t i o n i n t e r f a c e ; (C )  I from t h e  m  m  n  s t a g e number;  (^ )  o  r e f e r s to i n i t i a l s t a t e ;  p  cell pair;  R  resistance;  S  s o l i d o r s t a t i o n a r y phase; or p e r m s e l e c t i v e l y ; (n )  n  (C ) o  (R^) (n^) (C )  g  T  total; (E ) or t o p ( d e m i n e r a l i z e d ) p r o d u c t ; or t e m p e r a t u r e ; (V^U) T  (Cj)  w  water t r a n s p o r t ;  ( )  IT  u n i t area per c e l l p a i r ;  v  r e f e r s t o the average c o n c e n t r a t i o n  °°  refers to i n f i n i t e d i l u t i o n ;  n  w  (R^) of s a l t ;  (A ) ra  Superscripts =  r e f e r s t o p r o p e r t y i n membrane;  (C,,C.)  k or t o n e g a t i v e l y .+  =  charged s p e c i e s ;  3  (t~)  r e f e r s t o p o s i t i v e l y charged s p e c i e s ;  (t^)  (^ ) v  REFERENCES  A c r i v o s , A., I n d . 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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, M a r c e l D e k k e r , I n c . , New Y o r k , 1971.  Appendix A  Electrode  A.l.  Electrode  System  Materials  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 a r e i n u s e , f o r example, g r a p h i t e and stainless  s t e e l , which a r e gradually attacked  must be r e p l a c e d .  i n oxidizing  c o n d i t i o n s and  P l a t i n u m - c o a t e d m e t a l s (e.g. t i t a n i u m , t a n t a l u m , o r  z i r c o n i u m ) , w i t h a h i g h l e v e l o f 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 o f s e v e r a l y e a r s , a r e now f r e q u e n t l y u s e d , e s p e c i a l l y  a s anodes.  O x i d e s o f some m e t a l s  such a s l e a d and r u t h e n i u m have p r o v e n t o be s u f f i c i e n t l y c o n d u c t i v e and i n s o l u b l e i n a c i d s t o be used a s c o a t i n g f o r anodes (Thangappan, e t a l . , 1970). M a g n e t i t e 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 , b u t t h i s m a t e r i a l i s v e r y f r a g i l e ( D a v i s and Brockman, 1972).  A.2.  Electrode  Reactions  Throughout t h e 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 o f an e l e c t r o d i a l y s i s  s t a c k , and i n t h e i n t e r v e n i n g membranes, e l e c t r i c a l c o n d u c t i o n i s i o n i c .  At  the e l e c t r o d e s , however, t h e mechanism o f e l e c t r i c a l c o n d u c t i o n changes a b r u p t l y from i o n i c t o e l e c t r o n i c .  The t e c h n o l o g y o f e l e c t r o d e  reactions  i s h i g h l y d e v e l o p e d i n many r e s p e c t s , b u t t h e r e 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 c o n c e r n i n g mechanisms and t h e r e l a t i v e i m p o r t a n c e o f competing reactions that occur a t the electrodes 304  ( D a v i s and Brockman, 1972).  305  The c a t h o d e o r n e g a t i v e l y changed  electrode  i s t h e source o f e l e c t r o n s ,  and a t t h e c a t h o d e , t h e e l e c t r o n s must be t r a n s f e r r e d from t h e 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 a r e t y p i c a l r e a c t i o n s by  w h i c h t h i s t r a n s f e r o f c h a r g e may be a c c o m p l i s h e d : M" 0  2  + xe  + 2H 0 + 4e' 2  2H  +  + 2e'  2H 0 + 2e" 2  -> M°  metal deposition  (A.l.)  -* 40H  r e d u c t i o n o f gaseous oxygen  (A. 2.)  ->  H2 ( a c i d i c s o l u t i o n )  -> H  Metal-deposition  2  + 20H  (basic solution)  e v o l u t i o n o f gaseous  (A.3.)  hydrogen  (A.4.)  r e a c t i o n s a r e u s e f u l i n p r o c e s s e s such a s e l e c t r o -  p l a t i n g and t h e r e c o v e r y o f spent p i c k l e l i q u o r . oxygen i s r e d u c e d a r e i m p o r t a n t i n f u e l c e l l s .  Reactions i n which  gaseous  The p r i n c i p a l c a t i o n s  p r e s e n t i n t y p i c a l b r i n e a r e much l e s s r e a d i l y d i s c h a r g e d t h a n hydrogen i o n , and t h e n e t r e s u l t o f t h i s i s t h a t t h e cathode r e a c t i o n i s a l m o s t i n v a r i a b l y the cathodic  h a l f o f t h e 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~ 2 2  E  O  =  0  (A. 5.)  There i s u s u a l l y a l m o s t no d e t e r i o r a t i o n o f t h e c a t h o d e , and a l m o s t any c o n d u c t o r t h a t i s c o m p a t i b l e w i t h t h e r e s t o f t h e system c a n be used a s a cathode.  Carbon s t e e l i s a commonly used c a t h o d e m a t e r i a l .  Heavy m e t a l  i o n s such a s copper and i r o n may p l a t e o u t on t h e c a t h o d e , a n d , i n a d d i t i o n , t h e s h i f t i n pH caused by t h e cathode r e a c t i o n may cause t h e p r e c i p i t a t i o n o f a v a r i e t y o f s u b s t a n c e s t h a t may f o u l t h e system.  The  p r i n c i p a l problems a r e a p t t o be due t o CaCO^, M g ( 0 H ) , and Fe(0H).j. 2  Depending on t h e c o m p o s i t i o n o f t h e s o l u t i o n , pH, anode c o m p o s i t i o n , and c u r r e n t d e n s i t y , one o r more o f t h e f o l l o w i n g r e a c t i o n s may o c c u r a t t h e anode:  306  +x M°  ->• M  M° + xOH~  + xe ;  -> M ( 0 H )  2M° + 2xOH~ H  —  -> M 0 2  x  + xe"  x  2H 0  0  40H~  •*• . Q  2C1~  -> C l + 2e  Oxidation  2  2  o x i d a t i o n of e l e c t r o d e  (A.7.) (A. 8.)  2  o x i d a t i o n o f gaseous hydrogen  +  2  (A. 6.)  + xH 0 + 2xe~  -»• 2 H + 2e~  2  metal d i s s o l u t i o n  + 4H  + 4e~ ( a c i d i c s o l u t i o n s )  +  + 2H 0 + 4e~ ( b a s i c s o l u t i o n s ) 2  2  ,  (A.9.)  e v o l u t i o n of  (A. 10.)  gaseous oxygen  (A. 1 1 ) .  e v o l u t i o n o f gaseous c h l o r i n e  (A.12).  o f gaseous hydrogen i s an i m p o r t a n t r e a c t i o n i n f u e l - c e l l  Metal 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 electrode. i s oxidized, hydroxyl  i o n s a r e consumed.  When t h e anode  U n l e s s p r o v i s i o n i s made f o r  removing t h e companion hydrogen i o n s o r s u p p l y i n g s o l u t i o n w i l l become a c i d i c .  operation.  hydroxyl  ions, the electrode  Most m e t a l o x i d e s and h y d r o x i d e s a r e s o l u b l e  in acidic solutions. M 0 2  x  + 2xH  ->  +  2M  + X  + xH 0  (A. 13.)  2  or M(0H)  + x H -»• M ^ + x H 0 +  x  (A.14.)  4  2  The n e t r e s u l t i s t h e d i s s o l u t i o n o f e l e c t r o d e  metal.  R e a c t i o n s i n w h i c h gaseous oxygen o r c h l o r i n e i s e v o l v e d a r e commonly encountered i n e l e c t r o d i a l y s i s when n o b l e m e t a l anodes a r e u s e d .  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 a s seawater c h l o r i d e i o n s may be o x i d i z e d a t t h e anode t o produce h y p o c h l o r i t e : C l ~ + 20H~ - 2e~ •* 0C1~ + H 0 2 o  E  =0.94 v o l t  (A.15.)  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 a t the anode w i l l be c a r r i e d of t h e c e l l i n t h e anode r i n s e s t r e a m ( a n o l y t e ) , and a p o r t i o n may as c h l o r i n e gas.  2  escape  C h l o r i n e r e m a i n i n g 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 f o r m  an e q u i l i b r i u m m i x t u r e a c c o r d i n g Cl  + H0  =  2  to  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 , c h l o r i d e w a t e r , we w i l l f i n d t h a t the anode r e a c t i o n d i s c h a r g e s from the water w i t h the simultaneous p r o d u c t i o n H0 o  - 2e~  ->  h0*  Z  + 2H  E  +  s u l f a t e , and  taneously.  We  low-  oxygen  of hydrogen i o n s :  £  =1.23  volts  (A. 18.)  O  T y p i c a l b r a c k i s h water contains and  out  s i g n i f i c a n t amounts of b o t h c h l o r i d e  f r e q u e n t l y b o t h c h l o r i n e and  oxygen a r e e v o l v e d  simul-  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  of s u c c e s s because the r e a c t i o n s a r e p r i n c i p a l l y c o n t r o l l e d by k i n e t i c s r a t h e r t h a n by any  degree  electrode  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 p r o d u c t s , c u r r e n t d e n s i t i e s and  such as C10^,  may  o c c u r , depending on  the n a t u r e 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 a r e not u s e d , 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 p r o d u c t s of the e l e c t r o d e s . produce i r o n o x i d e s  local  oxidative  I r o n or s t e e l anodes, f o r example, w i l l  i n v a r i o u s d e g r e e s , and  c a r b o n anodes w i l l produce c a r b o n  dioxide. The operation provide  electrode reactions necessarily associated with introduce  two p r o b l e m s :  f i r s t , added power must be s u p p l i e d  the e l e c t r o d e r e a c t i o n energy;  r e a c t i o n s may  electrodialysis  second, the p r o d u c t s o f the  be h a r m f u l t o the e l e c t r o d i a l y s i s s t a c k or may  to  electrode  i n t e r f e r e with  308  the c o n t i n u e d  o p e r a t i o n o f the system.  The  f i r s t o f t h e s e 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 discussed i n process and  efficiency section;  t h e r e i s no s i n g l e s i m p l e We  the second i s more  be  complicated  solution.  can e x p e c t t h a t the c h l o r i n e or o t h e r o x i d i z i n g m a t e r i a l s formed  a t t h e anode may  cause r a p i d d e t e r i o r a t i o n of the s t a c k components;  the a l k a l i n e cathode m a t e r i a l , i f allowed l i k e l y t o produce p r e c i p i t a t i o n .  t o e n t e r the s t a c k , i s o b v i o u s l y  Because o f t h i s i t i s u s u a l t o  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 s t r e a m compartments a t ends of the d i a l y s i s s t a c k s .  and  the  F r e q u e n t l y i s o l a t i o n of t h e s e 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 f e e d w a t e r i s a l l t h a t i s a t t e m p t e d by of c o n t r o l l i n g the p o s s i b l e h a r m f u l  way  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 s t r e a m , t o a v o i d f o r m a t i o n of c h l o r i n e , has been d e s c r i b e d by W i e c h e r s (1954).  the  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 t o the cathode stream. t r i e d or p r o p o s e d .  S e v e r a l more n e a r l y c l o s e d systems have a l s o been  I n p r i n c i p l e we  c o u l d c i r c u l a t e sodium s u l f a t e o r  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 t o oxygen and hydrogen g e n e r a t i o n . volume c o u l d be m a i n t a i n e d  I f t h i s were a l l t h a t happened, e l e c t r o l y t e  by a d d i n g v e r y s m a l l q u a n t i t i e s of p u r e w a t e r f r o i  t i m e to t i m e or by r e a c t i n g the two gases. been suggested by R o b e r t s (1957), who  An even more s u b t l e a p p r o a c h  has p a t e n t e d  r e d o x s o l u t i o n between the two. compartments.  The  the r e d u c t i o n a t t h e cathode t h e o r e t i c a l l y b a l a n c e  has  the c i r c u l a t i o n of a o x i d a t i o n a t the anode and each o t h e r i n t h i s  case.  U n f o r t u n a t e l y , none o f t h e s e " 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 t o c o n f i n e a g i v e n i o n t o 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 s t r e a m tend t o 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 o f o x i d a t i o n , pH s h i f t , and A.3.  fouling inevitably  arise.  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 p r o c e s s e s o c c u r r i n g a t the  electrodes  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 g i v e n 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 t h r o u g h each o f t h e e l e c t r o d e compartments  involve three (1)  steps:  The  t r a n s f e r of i o n s from the b u l k of the s o l u t i o n t o t h e  s u r f a c e 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  f o r m a t i o n of the f i n a l p r o d u c t s o f the r e a c t i o n and  their  r e m o v a l 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 a r e i n v o l v e d : (i)  Concentration overpotential  When the c u r r e n t i s f l o w i n g , the i o n s t h a t d i s c h a r g e m i g r a t e 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 g r a d i e n t a c r o s s the t h i n l a y e r a t the e l e c t r o d e s u r f a c e .  diffusion  T h i s phenomenon i s e x a c t l y a n a l o g o u s t o  the c o n c e n t r a t i o n g r a d i e n t t h a t o c c u r s 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 l e a d s t o a change i n e l e c t r o d e p o t e n t i a l o f \on  _ RT  Sulk  ,  "  C  ( A  T  ± n  I surface  . -  1 9  *  )  310  (ii)  The  Chemical o v e r p o t e n t i a l  chemical o v e r p o t e n t i a l ,  » i s defined  t o be t h a t p o t e n t i a l  i n e x c e s s o f t h e d i s c h a r g e p o t e n t i a l f o r t h e g i v e n r e a c t i o n w h i c h must be a p p l i e d t o the c e l l i n order t o maintain a f i n i t e r a t e of discharge. C h e m i c a l o v e r p o t e n t i a l o c c u r s a s a r e s u l t o f s t e p s ( 2 ) and ( 3 ) above.  The  value of n , f o r t h e e l e c t r o d e r e a c t i o n i s g i v e n by T a f e l ' s F o r m u l a : chem ° J  n ,  a + —r=r  =  chem  In i  a F  (A. 20.)  where a' (iii) The  =  h. and a = c o n s t a n t (depends on n a t u r e o f c a t h o d e ) ,  Ohmic o v e r p o t e n t i a l  ohmic o v e r p o t e n t i a l , n  c o n s i s t s o f two p a r t s , namely t h e  v o l t a g e drop w h i c h o c c u r s i n t h e b u l k s o l u t i o n o f c o n s t a n t  concentration  p l u s t h e v o l t a g e drop a c r o s s t h e d i f f u s i o n l a y e r where t h e c o 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 current n , ohm  =  n , + ru sol 6  =  i R ,  density  (A.21.)  ohm  where R , c o n s i s t s o f two s e r i e s r e s i s t a n c e s , ohm R . ohm R  =  R  . + R sol o  , c a n be e v a l u a t e d sol  X  (A. 22.)  i n terms o f t h e mean r e s i s t i v i t y o f t h e b u l k  solution, R  where-  sol  =  P  meany Ap  (A. 23.)  311  p mean  =  t h e mean r e s t i v i t y o f t h e e l e c t r o d e s o l u t i o n , ft - cm  y  =  b u l k s o l u t i o n t h i c k n e s s , . cm  Ap  =  a c t i v e membrane a r e a , cm  K  2 may be e v a l u a t e d by s p e c i f y i n g t h e 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 t h e d o u b l e i n t e g r a l o f t h i s f u n c t i o n a s d i s c u s s e d i n S e c t i o n 3.1.1. 1_ R,  -1 1  J z-0  p(x,z)dx  dz  x=0  Thus, t h e 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 summing t h e s e s e p a r a t e A. 4.  e >  (A.24.)  c a n be e v a l u a t e d by  components.  E l e c t r o d e F l o w System  The  two e l e c t r o d e compartments p r e s e n t  i n each multimembrane s t a c k  a r e 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 s e p a r a t e h y d r a u l i c system.  recirculating  I n p a s s i n g t h r o u g h t h e c e l l c a t h o l y t e becomes b a s i c and  a n o l y t e becomes a c i d i c , when t h e s e a r e 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 s h o u l d be made i n e l e c t r o d e system f o r d i s c h a r g e e l e c t r o d e g a s e s , and a s m a l l d i s c h a r g e  of the  of electrode s o l u t i o n i s required  t o p r e v e n t b u i l d u p o f i o n s produced by e l e c t r o d e r e a c t i o n s . b l e e d 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.  A feed-and-  Stacks Gases  ±  Rinse]" Tank  Liquid Discharge  €5" Make. Up Water  1x  FIGURE A _ | Electrode system flow sheet  Appendix B  The C u r r e n t 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 , n^., i s r e l a t e d  t o t h e Faraday  efficiency,  rip by t h e r e l a t i o n n  =  n  I where n  w  (B.l.)  n F*  w  i s the w a t e r t r a n s f e r  term,  The F a r a d a y 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 o f t h e s a l t  shifted  r  to the t h e o r e t i c a l c u r r e n t r e q u i r e m e n t ( e q u i v a l e n t of s a l t t r a n s p o r t e d ) ( F a r a d a y s of e l e c t r i c i t y passed)(number of membrane p a i r s  F  =  employed)  I ^ O E In  (B.2.)  where F = F a r a d a y ' s c o n s t a n t , 96500 A / ( s e c ) ( e q u i v a l e n t ) AN = change i n p r o d u c t s t r e a m 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 p r o d u c t s t r e a m , l i t e r / s e c I = t o t a l c u r r e n t passed through t h e 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 b o t h the r  a c t u a l membrane used and the amount o f l e a k a g e c u r r e n t t h a t a s t a c k d e s i g n may  p e r m i t and i t e x p r e s s e s the performance  w . r . t . the c u r r e n t .  particular  of t h e p r o c e s s  I t i s o f t e n d e t e r m i n e d by an i n e x a c t method  v a l u e s ) f o r b r i n e and d i a l y ' s t a t e streams i n d e p e n d e n t l y : 313  (apparent  314  V i D  n  -  D  ^B  -  VF  , (B.3.)  s  nl  =  ( B  '  4 > )  where TV.* ^ 1  a p p a r e n t F a r a d a y e f f i c i e n c i e s based on t h e 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 , m l / s e c . 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  an(  *  D r  i  e f f l u e n t concentrations r e s p e c t i v e l y  n e  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 s t r e a m a r e n o t i d e n t i c a l because o f : (a)  w a t e r t r a n s f e r by osmosis and  (b)  a minor volume change r e s u l t i n g from t h e s a l t d i s p l a c e m e n t  The t r u e F a r a d a y e f f i c i e n c y , rip, i s d e f i n e d  electro-osmosis  by:  n  D  =  n  F  (1 - 18 w D )  (B.5.)  n  B  =  n  F  (1 - 18 w B )  (B.6.)  x  1  where w = moles o f water t r a n s p o r t e d 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  number o f i o n s ) e.g. f o r N a C l , w Determination  of n  a n c  D (Wilson,  j n D  3.  w  C  a r e w a t e r t r a n s p o r t numbers (-  = 4, w  C  hydration  =8.  e n a b l e b o t h r\„ and w t o be c a l c u l a t e d r  1960).  The f a c t o r s t h a t may  c o n t r i b u t e towards low c u 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 s t a c k a r e m e c h a n i c a l and e l e c t r o c h e m i c a l  ones:  315  (1)  I m p e r f e c t s e l e c t i v i t y of membranes o r d e t e r i o r a t i o n o f membranes.  The f a c t t h a t t h e membranes a r e n o t p e r f e c t l y s e l e c t i v e means t h a t more than t h e t h e o r e t i c a l c u r r e n t must be p a s s e d . (2)  E l e c t r i c a l l e a k a g e 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 p a t h s  through the s t a c k m a n i f o l d . (3)  S h o r t - c i r c u i t i n g o f membrane p a c k s .  (4)  I n t e r n a l and e x t e r n a l w a t e r l e a k a g e .  A l a r g e w a t e r t r a n s f e r may  accompany t h e c u r r e n t f l o w a c r o s s t h e membrane due t o osmosis and e l e c t r o o s m o s i s , w h i c h r e s u l t s i n l o s s of p r o d u c t w a t e r .  A l s o t h e r e may be h y d r a u l i c  l e a k a g e s between c e l l s and/or e x t e r n a l l e a k a g e s . (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 o r unwanted i o n t r a n s f e r .  At  s u f f i c i e n t l y h i g h 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 OH  +  and  i o n s n o r m a l l y p r e s e n t i n water w i l l b e g i n t o p a r t i c i p a t e i n t h e c u r r e n t -  carrying process. Assuming t h a t o b v i o u s p r o b l e m s , 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 t h r o u g h b o l t s and c o n t a i n e r s , g r o s s l e a k s between t h e p r o d u c t and waste compartments, and water s p l i t t i n g , have been p r o p e r l y t a k e n c a r e o f , we c a n e x p r e s s 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 , n^., a s t h e p r o d u c t o f t h e s e efficiencies: n  T  I  =  n n n s m w  =  run F w  (B.7.  where ri : s  t a k e s c a r e of e f f e c t s due t o t h e p e r m s e l e c t i v i t y of t h e i n d i v i d u a l membranes  n : m  accounts f o r the e f f e c t s of c u r r e n t leakage through the manifold  316  ri : w  i s the r e s u l t of w a t e r t r a n s p o r t  The q u a n t i t i e s r i , n. and s  i d e a l l y t h e y approach (i)  t h r o u g h the membranes,  are a l l d e f i n e d  m  i n such a way  that  1.0.  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 d e f i n e d  as  n t - P c + n t + P a 's  n t + n t, c a +  where a r e numbers of c a t i o n and a n i o n - p e r m e a b l e membranes  n ,n c a t ,t  a r e 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 a n i o n  +  respectively Pc,Pa  a r e p e r m s e l e c t i v i t y of c a t i o n and a n i o n - p e r m e a b l e membranes r e s p e c t i v e l y  Pc  =  = "  1  Pa  =  t —  c  "  C  =  t - t ~-  (B.9.)  11  -  r e f e r t o t r a n s p o r t numbers of c o u n t e r - i o n s  +  n  +  - t 1  where t , t  fc  i n membranes.  Mien  = n , Eq.(B.8.) r e d u c e s t o : a ^ n  =  t  =  ( t + t_) - 1  t  =  a n i o n t r a n s p o r t number i n the c a t i o n - p e r m e a b l e membrane  t_^  =  c a t i o n t r a n s p o r t number i n t h e a n i o n - p e r m e a b l e membrane  s  -  Pc + t , Pa + +  =  1 - ( t ^ + t*)  (B.10.)  where  317  -  ( t + t * ) i s i m p e r f e c t s e l e c t i v i t y f a c t o r o r p e n e t r a t i o n of C  c o - i o n s i n t o a membrane. If t  = t  = 0.5, =  s (ii)  then n  w i l l be e q u a l t o the a v e r a g e p e r m s e l e c t i v i t y  s  ( Z l+ i i ) I  (B.H.)  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 s t a c k by c o n d u c t i o n manifolds  and s t r a y p a r a l l e l c u r r e n t p a t h s consume power w i t h o u t  through  producing  any u s e f u l r e s u l t s , t h u s r e d u c e 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 i n h e r e n t e n g i n e e r i n g d e s i g n 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 s t r e a m w i t h i n the s t a c k i s c o n n e c t e d , 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 s t r e a m s .  S i n c e the c o n c e n t r a t i o n s t r e a m i s more c o n d u c t i v e  t o e l e c t r i c i t y t h a n the  d i l u t e s t r e a m , i t would be e x p e c t e d t h a t a h i g h f r a c t i o n of leakage  non-productive-  c u r r e n t would f l o w t h r o u g h t h e c o n c e n t r a t i o n s t r e a m . Leakage c u r r e n t c a l c u l a t i o n s have been d e v e l o p e d by W i l s o n  and M a n d e r s l o o t and H i c k s  (1966) and p r e s e n t e d  by B e l f o r t and  (1960)  Guter  (1968). U s u a l l y the e f f e c t of c u r r e n t l e a k a g e r e d u c t i o n i n e f f i c i e n c y o f l e s s t h a n 5%,  t h r o u g h the m a n i f o l d  is a  B e l f o r t and G u t e r (1968) i n  t h e i r s t u d y 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 t h a t c u r r e n t l e a k a g e has  o n l y minor e f f e c t .  be e s t i m a t e d by a s s e m b l i n g  The  current f o r a given design  can  a sample s t a c k w i t h i n s u l a t i n g s h e e t s of p l a s t i c  i n p l a c e o f the membranes, t h e r e b y the l i q u i d f l o w .  leakage  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 , b u t  The n o r m a l o p e r a t i n g v o l t a g e i s then a p p l i e d and  c u r r e n t measured i s r e g a r d e d  as b e i n g t h a t due  to leakage  not  the  t h r o u g h the  entire  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 p a t h o f t h e s t a c k .  (iii)  Water t r a n s f e r term, n. w  Some w a t e r i s t r a n s p o r t e d t h r o u g h t h e membranes a l o n g w i t h t h e e l e c t r o l y t e s due t o e l e c t r o - o s m o s i s .  The amount o f 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 t y p e , 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 solution.  When t h e f e e d i s o f l o w s a l i n i t y o r when moderate q u a n t i t i e s o f  s a l t a r e removed from b r a c k i s h w a t e r , t r a n s p o r t i s seldom a problem. However, i n more c o n c e n t r a t e d  s o l u t i o n s o r i n systems i n v o l v i n g a h i g h  degree o f d e s a l i n a t i o n , w a t e r t r a n s f e r c a n have i m p o r t a n t  e f f e c t s on t h e  current 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 (a)  r e q u i r e t h e use o f a d d i t i o n a l c u r r e n t t o meet t h e d e s a l t e d product  (b)  will:  quality  specifications,  r e d u c e t h e q u a l i t y of p r o d u c t  o b t a i n a b l e from a g i v e n amount o f  f e e d t o t h e d i l u t e stream. The e f f e c t o f water t r a n s p o r t on t h e c u r r e n t e f f i c i e n c y i s g i v e n by: nx w  (0.018) m. 1  (B.12.)  n. w  1 -  m. x  the m o l a l i t y o f t h e f e e d w a t e r  where  T  w  t r a n s f e r e n c e number o f w a t e r d e f i n e d as t h e number o f moles w a t e r t r a n s f e r r e d p e r Faraday  n  number of membrane  pairs.  Appendix C  N e r n s t I d e a l i z e d Model of W a l l  C.l.  The F l o w F i e l d i n an E l e c t r o d i a l y s i s  Layers  Cell  I n a l m o s t a l l electromembrane p r o c e s s e s  t h e s o l u t i o n s t o be t r e a t e d  f l o w between p a r a l l e l p l a n a r ion-exchange membranes.  The f l o w c h a n n e l s a r e  f i l l e d w i t h s p a c e r m a t e r i a l s t h a t cause complex f l o w p a t t e r n s .  The v e l o c i t y  o f t h e s o l u t i o n s p a s t t h e membranes and t h r o u g h t h e s p a c e r 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 m i x i n g o f t h e s o l u t i o n i n t h e c e n t e r p o r t i o n s o f t h e f l o w c h a n n e l s , b u t t h e m i x i n g i s l e s s near t h e s u r f a c e s o f t h e membranes, where t h e s o l u t i o n i s a l m o s t s t a t i c .  C.2.  N e r n s t 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 t h e s i m p l i f i e d N e r n s t model. 1904)  T h i s i s an i d e a l i z e d model  (Nernst,  based on t h e f o l l o w i n g a s s u m p t i o n s : - there are l a y e r s adjacent  are completely  t o t h e membranes i n w h i c h t h e s o l u t i o n s  s t a t i c or i n laminar  flow.  - t h e s o l u t i o n i n t h e b u l k ( i . e . between t h e w a l l l a y e r s ) i s t h o r o u g h l y mixed so t h a t t h e c o n c e n t r a t i o n o f e l e c t r o l y t e a t any p o i n t i n t h i s zone i s the same as t h a t a t any o t h e r p o i n t . - t h e r e i s no change o f e i t h e r t h e t h i c k n e s s of t h e w a l l l a y e r s o r the c o n c e n t r a t i o n g r a d i e n t s a l o n g t h e f l o w 319  channel.  320  D e s p i t e t h e c o m p l e x i t y i n a r e a l system, N e r n s t model a f f o r d s a s i m p l i f i e d mathematical  approach w h i c h r e s u l t s i n e x p r e s s i o n s t h a t a r e  easy t o u s e and t h a t p r e d i c t performance a d e q u a t e l y f o r use i n t h e d e s i g n of electromembrane p r o c e s s e s .  C.3.  Some d e r i v a t i o n s o f t h e Model S i n c e f r e q u e n t u s e i s made o f t h e a s s u m p t i o n t h a t t h e c o n c e n t r a t i o n  g r a d i e n t i n t h e w a l l l a y e r o f 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 o f t h i s a s s u m p t i o n w i t h t h e o t h e r main a s s u m p t i o n s 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 n o t do so i n the complete absence o f o t h e r e f f e c t s .  I t s m o t i o n i s accompanied by a  f l o w o f e l e c t r i c c u r r e n t , and t h e r e may a l s o be a f l o w o f heat and a f l o w of s o l v e n t .  We a r e f a c e d w i t h t h e p r o b l e m o f d e s c r i b i n g s i m u l t a n e o u s l y a  minimum o f f o u r 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 h e a t .  I n 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 a r e c o u p l e d , i t i s sometimes c o n v e n i e n t of i r r e v e r s i b l e p r o c e s s e s .  t o make use o f t h e t h e o r y o f t h e thermodynamics A l t h o u g h an a n a l y s i s made i n t h e s e terms cannot  d e a l w i t h t h e u n d e r l y i n g c a u s e s o f t h e phenomena t h a t may be o b s e r v e d , i t i s o f g r e a t v a l u e 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 t h a t must n e c e s s a r i l y h o l d between t h e v a r i o u s f o r c e s and f l o w s when t h e system i s i r the s t e a d y  state.  The g e n e r a l e q u a t i o n s f o r f l o w may be w r i t t e n ( H i l l s e t a l . , 1961) as:  321  -y  =  l -> 2  =  J  \ -> Q where  T  - 24  V l n  T  12 T 2 "  - 12 T 1 "  L  22 T 2  - 13 T 1 "  L  23 T 2 "  L  33 T 3  - L-.Vln T 34  " 14 T 1 "  L  24 T 2 "  L  34 T 3  - L-.Vln T 44  V  L  =  V l n  L  V  L  =  14  13 T 3 "  - 11 T 1 " L  J  V  L  V  U  U  U  U  V  V  V  V  U  U  -  U  U  L  V  L  2 3  U  V U T  V  V  U  U  3  L  L  (CI.)  a r e p h e n o m e n o l o g i c a l c o e f f i c i e n t s and t h e s u b s c r i p t s 1,2,3,and 4  r e f e r t o t h e p o s i t i v e i o n s , n e g a t i v e i o n s , water and h e a t  respectively.  V^U i s t h e g r a d i e n t o f t o t a l c h e m i c a l p o t e n t i a l , t a k e n a t c o n s t a n t t e m p e r a t u r e , and Q i s t h e f l o w o f h e a t . I f we c o n s i d e r an i s o t h e r m a l p r o c e s s i n which b o t h 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 t h e i o n s t o g e t h e r w i t h e l e c t r o - o s m o s i s a r e n e g l e c t e d , t h e n a l l t h e terms e x c e p t t h e f i r s t w i l l drop o u t and t h e i o n i c f l u x , J i s g i v e n by  k  J  =  "kkVk = - V k V k L  (c  -2  }  2 where  i s t h e f l u x o f an i o n i c s p e c i e s 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 d e f i n e d as t h e average v e l o c i t y i m p a r t e d t o t h e s p e c i e s under t h e a c t i o n o f a u n i t g e n e r a l i z e d f o r c e ( p e r m o l e ) , and  is  t h e 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 c h e m i c a l p o t e n t i a l , U, i s meant t o i n c l u d e e f f e c t s due t o e l e c t r i c i t y , as w e l l as t e m p e r a t u r e , p r e s s u r e , 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 t h a t g r a v i t a t i o n a l f i e l d s a r e u n i m p o r t a n t , t h e n V U = Z F VE + — • Vp + | £ VC T dp dC where  VE i s t h e e l e c t r i c f i e l d  i n volts/cm  F i s t h e Faraday c o n s t a n t i n coulombs/g.equiv. Z i s the valence  (C.3.)  322  I n r e a l e l e c t r o d i a l y s i s systems t h e modest d i f f e r e n c e s i n t e m p e r a t u r e and  p r e s s u r e have no s i g n i f i c a n t e f f e c t on t h e c u r r e n t f l o w i n g as l o n g a s  even v e r y s m a l l p o t e n t i a l negligible.  For i d e a l U  where U  o  =  U  o  differences exist.  solution,  + RT l n a  (C4.)  i s the standard chemical p o t e n t i a l  d i l u t e solutions  3U HJ T h e r e f o r e — Vp term i s  and a i s t h e a c t i v i t y .  c o n c e n t r a t i o n c a n be used i n s t e a d o f a c t i v i t y  For  (a = yC ^ C ) .  From Eq.(C.4.) we g e t {2.  •?  vc  A term i n c l u d i n g  (C.5., the d e r i v a t i v e  o f t h e a c t i v i t y c o e f f i c i e n t c o u l d be  i n c l u d e d ( s e e f o r example, H i l l s , e t a l . , 1 9 6 1 ) , b u t t h i s does n o t 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 ,  o m i s s i o n o f t h e t e r m t h a t would  a r i s e f r o m d i f f e r e n t i a t i o n o f t h e a c t i v i t y c o e f f i c i e n t i s no worse t h a n some of t h e o t h e r a s s u m p t i o n s t h a t a r e needed t o f a c i l i t a t e t h e i n t e g r a t i o n o f t h e s e e q u a t i o n s when they a r e used t o 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 t h e p r e s s u r e t e r m RT  k  J  The  =  " k k k u  c  ( z  ionic mobility,  F V E +  c7 k> k vc  (c  '6  )  u ^ ( g - m o l e s ) ( s q . c m ) / ( j o u l e ) ( s e c ) , c a n be r e l a t e d  to t h e 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) t h r o u g h t h e N e r n s t - E i n s t e i n  relation: u  k  =  V  R T  (c  -7  )  where T i s t h e a b s o l u t e t e m p e r a t u r e , °K., and R i s t h e gas c o n s t a n t , 8.3143 joules/(°K)(mole).  Eq.(C.7.) i s t r u e o n l y when t h e a c t i v i t y  coefficient  323  is unity,  t h a t i s , a t i n f i n i t e d i l u t i o n (Chapman, 1969).  From Eqs.(C.6.) and  J  - Vk  = k  (C.7.)  F  c  k  V E  - V k c  (c  - -> 8  Eq.(C.8.) i s the well-known N e r n s t - P l a n c k e q u a t i o n of i o n i c f l u x w i t h n e g l i g i b l e c o n v e c t i o n ( i . e . C^y  = 0, where v i s the  A l t h o u g h the N e r n s t - P l a n c k e q u a t i o n has i t s rigorous applications  stream v e l o c i t y ) .  a number of s h o r t c o m i n g s w h i c h  t o d i l u t e s o l u t i o n s , we  w i l l use  a c c o m p l i s h e s a g r e a t s i m p l i f i c a t i o n of a complex problem. we any  t r a n s p o r t e.g.  t h i s however, neglect  For  a more thorough a n a l y s i s  c o n c e n t r a t e d multicomponent s o l u t i o n s ,  between  of  ionic  i t i s necessary to  a more complete f l u x e x p r e s s i o n (Chapman, 1969).  C.3.2.  Ionic For  Fluxes  a u n i - d i r e c t i o n a l f l o w of a 1-1  can be w r i t t e n J  +  C  +  e l e c t r o l y t e E q s . ( C 7 . ) and  (C.8.)  as -  - 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  and  To do  s o l v e n t 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  the f l u x e s o f the charged s p e c i e s .  use  i t because i t  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 g r a d i e n t s i n the  limit  = C_  = C  +  i n the  ( £  )]  solution  phase (CIO.)  f o r mono-monovalent e l e c t r o l y t e Z  +  =  - Z_  =  1.0  (C.ll.)  324  I n t h e membrane, t h e n u m e r i c a l v a l u e o f t h e f l u x r a t i o , — - , i s e q u a l t o t h e 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 o f the steady  s t a t e t h e f l u x e s a r e independent o f p o s i t i o n x ( p e r p e n d i c u l a r t o membrane f a c e ) , t h e same f l u x r a t i o p r e v a i l s a l s o i n t h e s o l u t i o n : i± J_  =  |± J_  =  _|± t_  1±__ (1 - t )  =  (C.12.)  +  The n e g a t i v e s i g n i s i n t r o d u c e d because t h e J ' s a r e v e c t o r s .  I n the  membrane J+ and J _ have o p p o s i t e s i g n s , w h i l e t+ and t _ a r e a l w a y s t a k e n a s positive.  I t s h o u l d be noted t h a t t h e i o n f l u x r a t i o i s e q u a l t o t h e r a t i o  o f t h e i o n t r a n s p o r t numbers i n t h e membrane o n l y when i o n t r a n s p o r t i n membranes t a k e s 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 . U n l e s s t h e membrane i s i d e a l l y p e r m s e l e c t i v e , t h e r e 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 t o d i f f u s i o n a c r o s s t h e membrane caused by t h e 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 t h e s o l u t i o n s a t t h e two membrane f a c e s .  T h i s back d i f f u s i o n o f t h e s a l t  will  be n e g l e c t e d h e r e , however, because a l m o s t i d e a l l y p e r m s e l e c t i v e membranes a r e 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 a r e i n g e n e r a l much l a r g e r than t h e 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 a r e used w h i c h a r e n o t f u l l y permselective. From E q s . ( C 9 . ) and (C.12.): = - t - J+ t+ D_ OR  FC R  T  dE dc dx ~ dx  325  substitute  Eq.(C.13.) i n t o  +  +  d  . _ . 2D4  j + J  =  +  (C.9.)  t+ D_  x  x  + Z + °+ l  d  d  J  t+ D_  x  - 2D+ dc _ ~~Z dx" 1 - (D+ t_/D_ t+)  (C.14.)  flX  and " 1 - (D_ t+/D+ t _ ) 2 D  Since f l u x e s ,  (C.15.)  d G d  X  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 a r e c o n s t a n t , i t f o l l o w s t h a t — i s c o n s t a n t a l s o . ' dx the a p p l i c a t i o n  I n o t h e r words,  o f t h e N e r n s t - P l a n c k e q u a t i o n w i t h t h e above a s s u m p t i o n s  l e a d s t o a l i n e a r c o n c e n t r a t i o n g r a d i e n t i n t h e boundary I t i s o f t e n more c o n v e n i e n t t o e x p r e s s t h e f l u x e s  layer. i n terms o f t h e  d i f f u s i o n c o e f f i c i e n t o f t h e e l e c t r o l y t e , D, r a t h e r t h a n t h e i o n i c coefficients, D D+ D_ and  +  =  and D_. t+ t_  Noting that i n free  solution  t+ (1 - t )  =  solution  ! - ! ( ! + ! ) D  2  (C.16.)  +  u s i n g t h e N e r n s t e x p r e s s i o n f o r t h e d i f f u s i o n c o e f f i c i e n t o f 1-1  lyte i n dilute  OR  diffusion  D  +  D_  electro-  326  From Eq.(C.16.)  D  +  D_ + D_  =  t _ + t+  t_ =  (1 - t )  (C.18.)  +  S u b s t i t u t e E q . ( C 1 8 . ) 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  1 - ( t + t _ / t _ t+)  d  =  - 2D  +  (l-t ) l +  dc  +  ( t _ t+ - t + t _ )  X  d  ( C i 2 ( J < )  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 - ^ (t  - t )  +  d  (c  . .) 22  x  +  Similarly  J  •-  D i  -  Ct. - t _ )  =  £ d  D t  -  ( t -  x  +  4S. d  (C.23.)  x  t + )  F o r 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 a n i o n exchange membrane t_= 1.0  J, +  =  0;  J  -  = -  [ ~ 4 ] t dx £  D  (C.25.)  +  Note t h a t b o t h Eqs.(C.24.) and (C.25.) a r e o f t h e t y p e o f F i c k ' s l a w , b u t t h e  327  ratio ^  r e p l a c e s t h e i o n i c c o e f f i c i e n t D± ( i . e . t h e f l u x i s h i g h e r because  the e l e c t r i c f i e l d p r o v i d e s a d d i t i o n a l d r i v i n g  force).  The c u r r e n t d e n s i t y , i , i s g i v e n by F a r a d a y ' s l a w i  =  Substitute f o r J i  F ( J - J_)  (C.26.)  +  +  and J _ f r o m Eqs.(C.22.) and (C.23.)  =  2 L — Ct  +  "  V  dc d  FD  =  dc  ( t _ - t_)  X  d  ?  x  I f i , D and t h e t r a n s p o r t numbers a r e c o n s t a n t , Eq.(C.27.) t h e n , 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 e q u a t i o n s , t h e c o n c e n t r a t i o n gradient i n the w a l l layer i s l i n e a r .  C.4.  Wall layer thickness  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 and  i t varys along the flow path.  s t e a d y s t a t e h a s been r e a c h e d .  inlet  I n t h e N e r n s t model i t i s assumed t h a t a  I t i s a l s o assumed t h a t t h e h y d r a u l i c f l o w  c o n d i t i o n s o f t h e s o l u t i o n s a r e chosen such t h a t v a r i a t i o n a l o n g t h e membrane can be n e g l e c t e d .  I n t h i s case, the s o l u t i o n concentration 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 n o t v a r y a l o n g t h e membrane. A c c o r d i n g t o t h e N e r n s t model an a p p r o x i m a t e a v e r a g e v a l u e ( o r a c r i t i c a l v a l u e ) o f 6 i s used and t h e p r o b l e m c a n be s o l v e d w i t h o u t over t h e whole f l o w p a t h .  S t u d i e s w h i c h s t r e s s t h e hydrodynamic a s p e c t s o f  t h e problem and t h e i n f l u e n c e o f non-uniform published  integration  ( S o n i n and P r o b s t e i n , 1968;  d i f f u s i o n l a y e r s have been  S o l a n and Winograd, 1969).  I t i s of  i n t e r e s t t h a t t h e hydrodynamic a n a l y s i s l e a d s t o j u s t i f i c a t i o n o f N e r n s t ' 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 o f u n i f o r m t h i c k n e s s ] a s a fairly  good a p p r o x i m a t i o n  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 c o n c l u d e d t h a t t h e N e r n s t 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 N e r n s t - P l a n c k e q u a t i o n s and t h e use o f  an a v e r a g e t h i c k n e s s of t h e d i f f u s i o n  layer.  Appendix D  G r a p h i c a l S o l u t i o n o f C o n s t a n t - R a t e Model  G r a p h i c a l s o l u t i o n f o r synchronous ( i n - p h a s e ) chapter  ( 3 ) ] w i l l be c o n s i d e r e d  here.  operation  [case  (i) -  Graphical s o l u t i o n s f o r the other  c a s e s can be d e v e l o p e d i n a s i m i l a r manner. The system c o n s i s t s o f a s e p a r a t o r as shown i n F i g u r e D - l ( a ) .  (ED s t a c k ) and two end r e s e r v o i r s  I n i t i a l l y the separator  and t h e bottom r e s e r v o i r  a r e f u l l o f s o l u t i o n o f c o n c e n t r a t i o n C , t o p r e s e r v o i r i s empty. q  abseissa i n Figure D - l ( b ) , which represents  The  the v e r t i c a l coordinate i n  Figure D - l ( a ) , i s divided i n t o three sections: Section I  :  -I -4 z ^ o  ,  t h e bottom r e s e r v o i r  Section I I :  o 4 z 4 I  ,  the separator  Section I I I :  I 4 z 4 2H ,  Operation  s t a r t s w i t h up-stroke  the top r e s e r v o i r  (demineralization half cycle).  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 f r o m t h e m o b i l e phase i n t o t h e s t o r a g e compartments o f t h e s e p a r a t o r .  By t h e end o f t h e f i r s t h a l f c y c l e t h e  c o n c e n t r a t i o n p r o f i l e s o f s o l u t i o n i n t h e s e p a r a t o r and t h e t o p r e s e r v o i r a r e i n d i c a t e d by t h e l i n e s a b c , cde r e s p e c t i v e l y i n F i g u r e D-2. of s o l u t e s t o r e d i n t h e s e p a r a t o r rectangle afgh  The amount  d u r i n g t h i s h a l f c y c l e i s g i v e n by t h e  ( F i g u r e D-2) w h i c h has t h e same a r e a a s t h e two t r i a n g l e s  a c f and c e f ( i . e . c f = f g ) .  The s t o r e d m a t e r i a l i s r e t u r n e d  phase d u r i n g t h e 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 329  to the mobile between  330  c c  <D U  c o o  E  I Bottom Reservoir  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 a b c d e and amount of material stored a f g h at the end of the first half cycle.  332  r e g i o n s 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 t h e r a t i o o f t h e l mass t r a n s f e r r a t e s i n t h e two h a l f - c y c l e s , — K K  where  2  dC  f  =  - K, 1  : '  for demineralization  (D.l.)  =  K  ;  f o r enrichment  (D.2.)  dt dC dt  f  2  T If K  2  £  K^ and d e m i n e r a l i z a t i o n i s assumed t o t a k e p l a c e f o r t i m e  then to maintain 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  s h o u l d be A t , where  At  =  TK ^  (D.3.) K  l  G r a p h i c a l s o l u t i o n s o f t h r e e d i f f e r e n t c a s e s of .the r a t i o —  will  be  2 considered. K  (a)  l  K  i =  1.0  2 I n t h i s c a s e La = Z.3 as shown i n F i g u r e D-3(a) where a = t a n  and  g = tan ^ K ; 2  K^  and t h e s t o r e d 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  r e g i o n s I I and I I I d u r i n g t h e second h a l f c y c l e .  Each p o i n t a l o n g t h e 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 g i v e n by t h e l e n g t h o f t h e corresponding  a r r o w v e r t i c a l l y above i t ( c o n c e n t r a t i o n s a t p o i n t s a and e  r e m a i n c o n s t a n t w h i l e t h a t a t p o i n t c shows t h e maximum jump).  F i g u r e D-3(b)  shows t h a t by t h e end o f t h e f i r s t c y c l e a l l p o i n t s a l o n g t h e 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 t o 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 o b t a i n e d i n this  case.  FIGURE  D_3(a)  Mass transfer during the second half cycle (enrichment half cycle) K =K, 2  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  l In t h i s case — 2 K  ->  0.  From E q u a t i o n  (D.3.) At  -*• 0, w h i c h means  K  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 instantaneously to r e g i o n I I ( i . e . Z,B  90°).  F i g u r e D-4(a) shows t h e mass t r a n s f e r d u r i n g t h i s h a l f  c y c l e , where t h e v e r t i c a l arrows i n d i c a t e t h e 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 a l o n g a b C ^ , w h i l e F i g u r e D-4(b) shows t h e c o n c e n t r a t i o n p r o f i l e s a t t h e b e g i n n i n g and a t t h e end of t h e second ( e n r i c h m e n t ) h a l f cycle.  Due t o t h e i n s t a n t a n e o u s  mass t r a n s f e r t h e r e 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 a t t h e boundary o f t h e two r e g i o n s Every c y c l e the depleted product by t h e t r i a n g l e  e  (points  C.^  and  CJ-J-J) •  s u f f e r s a l o s s of m a t e r i a l  represented  ^ ( F i g u r e D-4(a)) w h i l e t h e e n r i c h e d p r o d u c t  a n e t i n c r e a s e o f s i m i l a r amount.  The average top and bottom  gains  concentrations  a f t e r t h e n t h c y c l e a r e g i v e n by: C  K Tn 1 - ^ o  N  - i S o  -  (D.4.)  and C_  K. Tn o  (c)  K  >  2  K  2  K  o  x  i s assumed t o be l a r g e r t h a n K^, b u t b o t h a r e o f t h e same o r d e r o f  magnitude e.g. K At  =  = 2K^.  2  r 4  I n t h i s case Equation  (D.3.) g i v e s t h a t (D.6.)  The mass t r a n s f e r d u r i n g t h e 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  Cm  Ui  S  FIGURE D_4(a)  FIGURE  Mass transfer during the second half cycle (enrichment half cycle),  Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle-  K  2 >  K  I  K  2 >  K  D_4(b)  I  FIGURE  D_5(a)  Mass transfe during the second half cycle (enrichment half cycle). K = 2K, 2  FIGURE D_5(b) Concentration profile at the beginning (dotted line) and at the end (solid line) of the second half cycle. K =2K, 2  337  A f t e r t h e f i r s t h a l f c y c l e t h e m a t e r i a l l o s t by t h e t o p ( d e m i n e r a l i z e d ) p r o d u c t i s g i v e n by A ceo ( F i g u r e D-5(a)) where 1 A ceo  T 1 ( \ ) ( -j=- ) T K  =  (D.7.)  and t h e a v e r a g e c o n c e n t r a t i o n o f t h e t o p p r o d u c t i s g i v e n by TK C  T,1  =  o - —  C  ( D  - '  )  -  9  8  Then e v e r y c y c l e t h e t o p p r o d u c t w i l l l o s e a m a t e r i a l g i v e n by K T ' K T ± ( - J _ ) ( i ) - A ( _ ± _ ) (At) 1  A ceo - Ac'od'  =  K T  T  •  i  (  At K  " i  r  i  )  (  D  0  and t h e a v e r a g e c o n c e n t r a t i o n change w i l l be g i v e n by m a t*e r i•a ln l-.o s s (T/2)  _ "  _K.T 1 4  K^T 1 K 4  (D.10.)  2  The a v e r a g e t o p c o n c e n t r a t i o n a f t e r t h e n t h c y c l e i s g i v e n by C_,  TK =  o  i  -  TK  ^ o  ^  K o  -  K  T  0).ll.)  2  S i m i l a r l y e v e r y c y c l e t h e bottom p r o d u c t g a i n s t h e m a t e r i a l g i v e n by t r a p e z i u m ab'c'o - t r i a n g l e aoc  =  1  K  1  T  T  T  K  1  T  K  I  (  "T"  )  (  T  K T  1  T  l  " Kj  1  1  -  }  (D.12.)  The a v e r a g e bottom c o n c e n t r a t i o n a f t e r t h e n t h c y c l e i s g i v e n by B,n ~to C  T  -  1  +  i r ^  K  i ! - F > 2 K  ( 1  K  0  n  ( D  1 3  -  )  APPENDIX E  COMPUTER PROGRAMS  338  Appendix E  Symbols used i n Computer Program  i)  DATA CB  =  Brine Concentration  (ppm)  CD  =  Dialysate Concentration  (ppm)  VB  =  Volume o f B r i n e p r o d u c t  (c.c./cycle)  VD  =  Volume o f d i a l y s a t e p r o d u c t  CF  =  Initial  (c.c./cycle)  (Feed) C o n c e n t r a t i o n  (ppm)  Numbers 1, 2, .... 9 s t a n d f o r Exp. l e t t e r s A, B, .... I .  ii)  RESULTS (A) T h i s f i r s t p a r t o f t h e program computes: a)  S e p a r a t i o n f a c t o r NS  b)  M a t e r i a l b a l a n c e and % e r r o r ERR  where PP  iii)  %  =  (  ? P F  p  F  F  =  CB/CD  ) 100  =  BB + DD  ( S a l t i n product  streams)  BB  =  CB * VB  (Salt i n brine)  DD  =  CD * VD  (Salt i ndialysate)  FF  =  CF * (VB + VD)  ( S a l t i n feed)  RESULTS (B) T h i s second p a r t o f t h e program computes t h e amount o f s a l t  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  shifted  $r * w a t f l v scards=exp 5=ml •EXECUTION BEGINS  2 3 1*  5 6 7 8 9 10 11 12  $COMPILE DIMENSION X(12,5) ,BB(12),DD(12),PPC12),VF( 1 2 ) , F F U 2 ) , 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) 15 WRITE(6,6) FORMAT(IX, DATA'//1X;12X, C8 ,9X,'VB ,8X, CD' 6 18X, VD',8X, CF') DO 60 1=1,N 60 WR!TECG,26)l,XCI,l>,XCl,2),XCI,3),X(l,l»),XCI,5) F0RMATC1X, I7,5F10.2) 26 WRITEC6,36) F0RMATC//1X,'RESULTSCA)'/IX,'MATERIAL BALANCE & SEPARATION 36 1//1X 1!*X BB',11X 'DD ,11X 1'PP',11X, 'FF' , 10X, 'MB'^X, 'ERRS',7X, 'NS*) DO 80 1=1,N BBCI)=X(1,1)*X(I,2 ) DD( I ) =X ( I , 3 ) *X ( I , 1*) PP(I)=BB(I)+DD( I ) VF( I )=X( I , 2 ) +X ( I , 1*) FF(I)=VF(I)*X(I,5) MB(I)=PP(I )-FF( I ) ERR(I)=MB(I)*100.0/FF( I ) NS(I)=X(I,1)/X(I,3) CBF(l)=X(l l)-X(l 5) CDF(I)=X(I,5)-X(I,3) BF(I)=CBF(I)*X(I,2) DF( I ) = CDF( I )*X( I ,i*> A S ( I ) = 8F(I ) + DF( I ) 1  31*  35 36 37  ,  ,  1  ,  80 1*5  90 66 86 '76  FACTOR'  ,  /  /  /  $DATA DATA  ,  /  1  /  13 li» 15 16 17 18 19 20 21 22 23 21* 25 26 27 28 29 30 31 32 33  ,  2 3  /  /  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 , 7 6 ) I , C 3 F ( I ) , B F C I ) , C D F ( I ) , D F ( I ) , A S C I ) FORMAT(//IX,'RESULTS(B)'/IX,'AMOUNT OF SEPARATION ) FORMATC//IX,13X, CB-CF',7X,'BF ,10X,'CF-CD',8X,»DF ,12X,'AS') FORMAT C 1X,I7,I»F12.2,F11*.2) STO? END 1  1  1  1  i« 5 6 7 8 9 10 il 12 13 11* 15 16 17 18 19 20 21 22 23 21* 25 26 27 28 29 30 31 32 33 31*  35 36 37 38 39 1*0 1*1 1*2 CO  •po  GROUP M l C3  1 2 3 i* 5 6 7 8  9  VB  U 000 .00 U 07 5 .00 3875 .00 1(125 .00 1*250 .00 1*350 .00 3825 .00 3675 .00 3375 .00  RESULTS(A) MATERIAL 8ALANCE  & SEPARATION  BB  196.00 11*8.00 330.00 11*0.00 118.00 9 1 * . 00 1*10.00 570.00 81*0.00  CF  21*.17 21* .1*8 21*. 13 21*. 50 25.00 25*7} 21*.21  21*.13 21*.66  2160.00 2160.00 2160.00 2170.00 2170.00 2170.00 2170.00 2170.00 2170.00  FACTOR  DD  1011*79.90 103991*.00 10021(5.10 101763.60 106250.00 106879.50 986U6.69 95109.00 85893.69  VD  cn  25.37 2 5 .52 25 .87 214.67" 25.00 21*.57 25.79 25 .88 2S.U5  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  MB  FF  107006.30 108000.00 108000.00 106698.80 108500.00 109107.60 108500.00 108521.60 108738.60  ERR% •0.737 -0.355 0.194 •1.1*11 0.645 0.173 0.067 0.315 •1.959  -789.13 -3C3.00 209.06 -1505.19 700.00 188.56 72.75 31*1.38 -2130.63  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 - CF  1 2 3 I* 5 6 7  8 9  BF  181*0 .00 1915 .00 1715 .00 1955 .00 2080 .00 2180 .00 1655 .00 1505 .00 1205 .00  CORE USAGE DIAGNOSTICS COMPILE TIME"  1*6680 .79 438 70 .80 1*1*367 . 0 1 * 1+8229 . 8 1 * 52000 .00 53562 .61 1*2682 .1*1* 3 8 9 1 * 9 .1*1  30667 .25  OBJECT CODE"  C F - CD  DF  1961* .00 2012 .00 1830 .00 203 0 .00 2052 .00 2076 .00 1760 .00 1600 .00 1330 .00  1*71*69. 88  2608 BYTES,ARRAY AREA"  NUMBER OF ERRORS" 0.15 .SEC,EXECUTION  $STOP #EXECUTION TERMINATED #  1*9253 .75 1*1*157. 91 1*9735 .00 51300. 00 53373. 97 1*2609.61 38608. 01 32797. 80  AS 91*150.63 98121*.50 88521*.91* 97961*.81  103300.00 106936.50 85292.00 77557.38 631*65.05 8 6 1 * BYTES,TOTAL  0, NUMBER OF WARNINGS" TIME"  0.15 SEC,  AREA AVAILABLE-  1021*00  0, NUMBER OF EXTENSIONS-  WATFIV - JUL 1973 V1L4  16:45:00  BYTES 0  FRIDAY  21 NOV 75  •*> *->  $r * w a t f i v s c a r d s - e x p 5-m4 •EXECUTION BEGINS  par-nollst  $COMPILE $DATA DATA 1 2 3 4 5 6 7 8 9  VB 101.11 98 .85 99.09 101.17 98 .88 99.35 100.00 93.17 98.44  CB 3900.00 4000.00 3675.00 4025.00 4125.00 4200.00 3625.00 3300.00 2880.00  CD 267.00 192.00 575.00 180.00 145.00 125.00 640.00 1100.00 1440.00  VD 99.83 96.75 98 .86 98.25 96.25 98.15 101.18 100.00 99.88  CF 2100.00 2100.00 2100.00 2160.00 2160.00 2160.00 2140.00 2140.00 2140.00  RESULTS(A) MATERIAL 8ALANCE & SEPARATION FACTOR 1 2 3 4 5 6 7 8 9  BB 394329. 00 395400. 00 364155. 60 407209. 10 407880. 00 417270. 00 362500. 00 323960. 90 283507. 10  PP 420983 .50 413976 .00 421000 .10 424894 .10 421836 .20 429533 .60 427255 .10 433960 .90 427334 .30  no 26654 .61 18576 .00 56344 .50 17685 .00 13956 .25 12268 .75 64755 .20 110000 .00 143827 .10  FF 421974 .00 410760 .00 415694 .90 430747 .10 421480 .70 426600 .00 430525 .10424083 .70 424404.80  MB -990 .44 3216 .00 5305 .25 -5853 .00 355 .50 2938 .69 -3269.94 9877 .19 2929 .56  ERR% -0.235 0.783 1.276 -1.359 0.084 0.689 -0.760 2.329 0.690  NS 14.607 20.833 6.391 22.361 28 . 448 33.600 5.664 3.000 2.000  RESULTS(B} AMOUNT OF SEPARATION  1 2 3 4 5 6 7 8 9 CORE USAGE  CB-CF 1800 .00 1900 .00 1575 .00 1865 .CO 1SG5 .0 0 2 04 0.00 14SS .00 1160 .00 740 .00  3F 181998 .00 1S7815 .00 156066 .60 133632 . 00 194299 .10 202674 .00 143500 . oo 113S77 .10 72845 .56  03JECT COOE=  CF-cn 1833 .00 1908 .00 1525 .00 1980. 00 2015 .0 0 2035 . 00 1500. 00 1040. 00 700. 00  OF 13 2 9 3.30 8 184599 .00 150761 .50 194535 .00 193943 .70 199735 .10 151769 .90 104000 .00 69916 .00  2608 BYTES,ARRAY ARF.A=  NVM'JER OF ERRORS"  AS 364986.30 372414.OC 306828.10 383217.00 383242.90 402409.10 300269.90 217877.10 142761.50 864 BYTES,TOTAL AREA AVAILABLE"  0, nUMSER OF WARNINGS*  102400  0, TJM3ER OF EXTENSIONS-  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  $C0MPILE $DATA DATA 1 2 3 it  5 C 7 8 9  CD 21.10 17.10 26.30 19.70 15.70 11). 90 1)0.00 53.00 90.00  VB 2U.20 2«*. 11* 2U .38 24.25 23.8lt 2U.13 25.3U 25.07 25.62  CB 1080.00 1120.00 1050.00 1090.00 11U0.0O 1160.00 1010.00 1000.00 960.00  RESULTSCA) MATERIAL BALANCE ti SEPARATION 1 2  3  ii 5 6 7 o 9  BB 26136.,00 27035,.80 25599,,00 26U32,.50 27177,.59 27990,.80 25533,.39 25070,.00 21)595,.20  VD 25 .39  25.31) 25.30 25.25 25 .65 25.95 25.11 21).78  21).81)  CF 5U0.00 51)0.00 51)0.00 560.00 560.00 560.00 530.00 530.00 530.00  FACTOR  DD 535. ,73 i»i)l.,86 665. ,39 U97.,1)2 1*02,.35 386, ,65 1001)..1)0 ' 1313, ,31) 2235,.60  PP 26671.72 271)78 . 66 26251).39 2G929.92 27580.U5 28377.U6 • 26597 .79  26383.31) 26830.79  FF 26778.60 . 26989.20 26827.20 27720.00 27720.00 28 0i)U.80 26738.50 261)20.50 2671)3 .79  MB -106. ,88 1)89,.1.6 -5 62..81 -790, .08 -139, .55 332, .66 -mo, .70 -37 , .16 87, .00  ERR* -0.399 1.811) -2.098 -2.850 -0.503 1.136 -0.526 -0.1U1 0.325  NS 51.185 65 .1)97 39.921) 55.330 72.611 77 . 352 25.250 13.868 10.667  RESULTSCB) AMOUNT OF SEPARATION  1 2 3  1* 5 6 7 8 9  USAGE DIAGNOSTICS COMPILE TIME-  CB-CF 51)0.00 580.00 510.00 530.00 580.00 600.00 1*80.00 1*70.00 1*30.00  BF 13068 .00 H 0 0 1 .20 121)33 .80 12852 .50 13827 .20 11)1*78.00 12163 .20 11782 .90 11016 .60  OBJECT' CODE NUMBER OF 0.03  1  CF-CD 518.90 522.90 513.70 5i)C30  51)1).30  DF 13171). 87 13511.73 12996.61 1361)2.57 13966.73  51)5.10 U9O.00 1)77.00 1*1)0.00 2608  BYTES, ARRAY AREA*  ERRORS"  SEC,EXECUTION  11)11)5.31)  12303.90 11320.06 10929.60  AS 2521)2 .86 27512.93  251)30.1)1  261*95 . 07 27793.93 28523.3U 21)1)67.09 23602.95 2131)6.20 861*  8YTES  0, NUMBER OF WARNINGSTIME"  0.15 SEC,  0, NUMBER OF  WATFIV - J U L 1973 V1LU.  CO  EXTENSIONS16:11:U5  FRIDAY  21 NOV  75  CO  tr *watfiv scards-exp 5-m7 par-nollst  #EXECUTION BEGINS  $C0MPILE $DATA DATA 1 2 3 U 5 6 7 8 9  VB 51. 82 50. 17 51. 91 50. 09 50. 77 50. 50 50. 25 50. 94 50. 77  CB 1050.00 1090.00 1030.00 1070.00• 1100.00 1110.00 1010.00 990 . 00 950.00  CD 26.30 20.20 33.00 24.20 18.10 17.60 UU.OO 61.00 104.00  VD 49. 24 51. 50 49. 03 51. 00 51. 49 51. 57 51. 25 49. 5C U9. 67  CF 550. 00 550. 00 550. 00 550. 00 550. 00 55 0. 00 530. 00 530. 00 530. 00  RESULTS(A) MATERIAL BALANCE & SEPARATION FACTOR 1 2 3 U 5 6 7 8 9  BB 5UU11 .00 34G35 .30 53U67 .30 53596 .29 55 8 U7.00 56055 .00 50752 .50 50430 .60 U8231 .50  PP 55706 .02 55725 .59 55085 .29 5U830 .U9 56778 .97 56962 .63 53007 .50 53450 .10 53397 .18  DD 1295.01 10U0.30 1617.99 123U.20 931.97 907.63 2255.00 3019.50 5165.68  FF S55S3. ,00 55918,,50 55517.,00 555 99,.50' 56243,,00 56138..50 53795,.00 53233,.20 53233,.20  MB 123.01 -192.90 -431.71 -769.00 535.97 82U.13 -737.50 216.90 163.98  ERRS 0.221 -0.345 -0.778 -1.383 0.953 1.46S -1.U6U 0.U07 0.308  NS 39.92U 53.960 31.212 4U.215 GO* 71 63.068 22.955 16.230 9.135  RESULTS(B) AMOUNT OF SEPARATION  1 2 3 U 5 6 7 8 9 USAGE DIAGNOSTICS COMPILE TIM5  CB-CF 500.00 540.00 U80.00 520.00 550.00 560.00 480.00 460.00 420.00  DF CF-CO 5 23 J TJ 25736.,99 27284,,69 529.80 25348.,51 517.00 525.80 - 26315..79 27387..53 531.90 27U55,,86 532.40 24907,.50 480.00 23 215 .50 U63.00 21159 .42 U26.00  BF 25910.00 27091.80 24916.80 26045.80 27923.50 28280.00 24120.00 23432.40 21323.40  03JECT CODE-  2608 3YTES, ARRAY AREA" '  NUMBER OF ERRORS0.03 SEC,EXECUTION TIME-  AS 51596.99 54376.48 50265.31 52362.59 53311.03 55735 . 86 U9027.50 46647.90 42482.82 864 3YTES  0, NUMBER OF WARNINGS-  0, NUMBER OF EXTENSIONS-  0.15 SEC, WATFIV - JUL 1973 V1L4  16:16:11  0 FRIDAY  21 NOV 75  $r * w a t f i v s c a r d s " e x p ' 5 » m 8 p a r - n o l l s t 'EXECUTION BEGINS  JCOMPILE $OATA  DATA 1 2 3 (*  5  6 7 8 9  CB 1020.00 1050.00 1010.00 1030.00 1070.00 -1080.00 1000.00 970.00 890.00  V8 9 9 . 72 9 9 . 09 9 9 . U5 98. 50 9 7 . 32 9 7 . 69 9 8 . 73 9 8 . 15 9 7 . 65  cn 36.00 26.00 1*8.00 32.00 23.00 2^.30 55.00 80.00 139.00  vn 98.12 98.18 98.79 99.65 99.92 99.82 98.55 98.50 99.15  CF 5U0. 00 540. 00 5 4 0 . 00 SUO. 00 5tt0. 00 51)0. 00 5 2 0 . 00 520 .00 5 20.00  RESULTS(A) MATERIAL BALANCE ft SEPARATION FACTOR 1 2 3  k  5 6 7 8 9  BB 10171'*.30 10UOUU.UO 1001*!* I*.1*0 1C11*55 .00 101*132.30 105505.10 98729.9U 95205 .1*1* 8 6 9 0 8 .1*1*  PP 10521*6.60 106597..00 105186 .3C 101*61*3 .70 1061*30 .50 107830 .90 10U150 .10 103085 .1*0 100690 .20  DD 3 5 3 2 . 32 2552. 68 1*71*1.92 3188. 80 2298 .16 2325 . 81 51*20.25 7 8 8 0 . 00 1 3 7 8 1 . 85  FF 106833 .50 1065 25 10701*9 .50TJ 107000 .90 105509 .50 106655 .30 102585 .50 102257 .90 102335 .90  j  K3 -1586 .88 71 .31 -1853 .25 -2357 .19 -79 .06 1175 .56 1561* .63 827 .50 -161*5 .69  ERR? - 1 ..1*35 0..067 - 1 ..71*1 -2,,203 -0,.071* ,102 • 1, 1,.525 0,.809 - 1 ,.608  NS 28.333 1*0.385 21.01*2 32.188 1*6.522 itS.SiO • 18.182 12.125 6.403  RESULTS(B) OF SEPARATION  1 2 3 i»  5  C 7 8 9  C3-CF 1*80.00 510.00 U7O.00 1*90.00 530.00 51*0.00 1*80.00 1*50.00 370.00  CORE USAGE DIAGNOSTICS COMPILE T I M E -  OBJECT CODE'  CF-CD 501* .00 5 ] l * .00 1*92 .00 503 .00 517 .00 515 .70 1*65 .00 1*1*0 .00 381 .00  BF 1*7865 . 60 50535 .89 1*671*1.50 1*8265 . 00 51579.60 52752.60 1*7390. 39 1*1*167.50 36130.50  2608 BYTES,ARRAY AREA-  NUMBER OF ERRORS0.03 SEC,EXECUTION TIME-  AS 97318 .06 101000 .30 9531*5.13 98887 .19 10323S .10 101*329 .50 93215 .13 87507 .1*1* 73906 .63  DF 1*91*52.1*8 501*61*. 52 l*850i*.68 50622.20 51658 . 61* 51576.99 1*5825 .75 1*331*0.00 3 7 7 7 6 . 11* "  86U BYTES,TOTAL AREA A V A I L A B L E -  0, NUMBER OF WARMINGS0.15 SEC,  102U0O  0, NUMBER OF EXTENSIONS-  WATFIV - J U L 1973 V1L1*  16:20:1.5  BYTES 0  FRIDAY  21 NOV 75  .*>Ln  t r *watf!v scards-exp 5-m9 #EXECUTION BEGINS  par«noltst  $COMPILE JDATA DATA 1 2 3 it 5 S 7 8 9  VB 26.28 26.00 26.34 26.50 25.17 26.78 25.37 25.09 25.39  C3 7150.,00 7450.,00 6800.,00 7600..00 8100,.00 3150,.00 6625 .00 6375 .00 5825 .00  CD 810.00 565.00 1310.00 450.00 288.00 218.00 1700.00 2240.00 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  PP 208532.60 207825.00 212241.80 213019.00 211503.10 224110.10 216693.60 220115.00 216372.60  DD 20630.70 14125.00 33129.33 11619.00 7626.24 5853.30 45304.99 60166.40 63475.94  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 .385 3 897 2 ,346 2 .198  RESULTS(B) AMOUNT OF SEPARATION  1 2 3 4 5 6 7 8 9  CB-CF 3100. 00 3400. 00 2750.,00 3500.,00 4000,,00 4050,.00 2450,.00 2200 .00 1650 .00  CORE USAGE DIAGNOSTICS COMPILE TIME-  BF 81467.94 88400.00 72434.94 92750.00 100679.90 108458.90 63331.48 55197.99 41893.50  OBJECT CODE-  CF-CD 3240. 00 3485..00 2740..00 3650..00 3812,,00 3332,.00 2475 .00 1935 .00 1525 .00  DF 825 22 j 5 87125 .00 69234.56 94243.00 100941.60 104231.60 65958.69 51974.10 39405 .99  2608 8YTES,ARRAY AREA"  NUMBER OF ERRORS0.03 SEC,EXECUTI ON TIME-  AS  163930.60 175525.00 141723.50. 136393.00 201621.60 212630.60 123340.10 107172.00 81299.44 864 BYTES,TOTAL AREA AVAILABLE"  0. NUMBER OF WARNINGS0.15 SEC,  102400  0, NUMBER OF EXTENSIONS-  WATFIV - JUL 1973 V1L4  16: 25 :07  0 FRIDAY  21 NOV 75  ON  Jr * w a t f l v scards»exp' 5=mll par»nollst #EXECUTION BEGINS  JCOMPILE $DATA DATA 1 2 3 It 5  6  7 8 9  VB 51.23 51.39 51.20 51.86 50.15 1*9.21 50.11* 1*9.70 1*9.52  C8 7 050.00 7375 .00 6775. 00 7500. 00 8 075.00 8125. 00 6IJ50.00 5975 .00 5300. 00  CD  91*0. 00  625 .00 1£*70.00 1*90.00 310. 00 259 .00 2010. 00 21*90.00 3125. 00  VD 1*8.81* 1*9.61 1*9.93 !*9.1l* 50.15 50.86 50.61* 50.97 50.85  CF 1*100.00 1*100.00 1*100.00 1*175.00 1*175.00 1*175.00 1*200.00 1*200.00 1*200.00  RESULTS(A) MATERIAL BALANCE & SEPARATION FACTOR 1 2  3  i»  5  6 7 8 9  B3 361171.1*0 379001,,10 31*6879,,90 388 950,.00 1*01*961,.10 399331,.20 3231*02,.90 295957,.1*0 2621*56,.00  PP 1*07031..00 1*10007.,1*0 1*20277..00 U1302S..50 1*20507,.60 1*11935,.70 1*25189.,30 1*23872,.60 1*21362,.20  DD 1*5909.,59 31005,.25 73397,.06 21*078 .60 , 1551*6,.50 12155,.51* 101786,.30 126915.20 158906.20  FF 1*10286.90 1*11*100.00 1*11*632.90 1*21575 .00 413752 .<»0 1*17792 .20 1*23275 .90 1*22813 .90 . 1*21551*.00  MB -3205 .94 -1*092 .56 561*1*.06 -85l<6 .1*1* 1755 .19 -5805 .50 1913 .38 1058 -191 .753  j  ERR? -0,721 -0.988 1.361 -2.050 0.1*19 -1.390 0.1*52 0.250 -0.01*5  NS 7.500 11.800 i*.G09 15.306 26.01*8 33.996 3.209 2.1*00 1.696  RESULTS(B) AMOUNT OF SEPARATION  1 2  3  (*  5  6 7 8 9  CB-CF 2950,.00 3275,.00 2675 .00 3325 .00 3900 .00 3950 .00 2250 .00 1775 .00 1100.00  CORE USAGE DIAGNOSTICS COMPILE TIME-  BF 151128 .1*0 163302 .10 136959 .90 1721*31* .50 195581* .90 191*379.5 0 1128H* .90 88217 .1*1* 51*1*72.00  OBJECT CODE-  OF 151*331* .30 172391* .70 131315 .80 181080 .80 193329 .60 200181* .90 110901 .50 87158 .69 51*663 3 2608 BYTES,ARRAY AREACF-CO 3160,.00 31*75..00 2630.00 3685,.00 3865 .00 3936 .00 2190 .00 1710 .00 1075 .00  NUMBER OF ERRORS0.03 SEC,EXECUTION TIME-  j  AS 3051*62 .80 31*0696 .90 268275 .80 353515 .30 3891*11*.60 391*561*.1*0 223716 .50 175376 .10 109135 ; TJ 86U BYTES,TOTAL AREA AVAILABLE-  0, NUMBER OF WARNINGS0.15 SEC,  1021*00  0, NUMBER OF EXTENSIONS-  WATFIV - JUL 1973 V1LU  16:29:27  3YTES 0  FRIDAY  Co 21 NOV 75  %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  V3 101.33 93.75 99.15 101.75 99.11 99.25 99.11 99 .1.1 93.18  C3 6900 .00 7250.,00 665 0.,00 7400.,00 7925..00 8100,.00 6400 .00 5600 .00 5000 .00  1 2 3 4 5 6 7 8 9  VD 101.50 33.50 101.75 39.15 99.11 100.81 101.58 101.31 101.73  CD  1190.00 725.00 1670.00 590.00 350.00 283.00 2210.00 2800.00 3575.00  Cr  4050.00 4050.00 4050.00 4125.00 4125.00 4125.00 4200.00 4200.00 4200.00  MATERUL BALANCE S SEPARATION FACTOR A  1 2 3 4 5 6 7 8 9  8B 699177.00 723187.50 659347.40 752950.00 785446.70 803925 . .00 634304..00 556696.00 495899.90  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  MB FF -1439.50 821451.50 806962.50 -11637.50 15625.00 813644.90 823712.40 -17264.SO 8 17 657 .5 0 2477.75 7206.75 825247.40 15337.75 842893.00 -3500.00 845544.00 15762.69 843821.30  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  CORE USAGE D.AGNOSTICS COVP.LE T.Mr-  BF 288790.50 319200.00 257789.90 335231.20 376618.00 394518.70 218042.00 139174.00 79343.94  OBJECT CODE-  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  2608 BYTES,ARRAY AREA-  NUMBER OF ERRORS0.03 SEC,EXECUTI ON TI ME-  AS 579080.50 650037 .50 499954.90 683726.40 750758.20 781830.70 4201S6.10 28184S.00 142925.10 864 BYTES,TOTAL AREA  0, NUMBER OF WARNINGS0.15 SEC,  102400  0, NUMBER OF EXTENSIONS-  WATF.V - JUL 1973 V1L4  16:33:51  BYTES 0  FRIDAY  21 NOV 75  OJ •O-  00  — $ i—*w a t f ! v-s card s - co rt-5 •- r-1#EXECUTION  -1 — 2 —3 4 5 _ 7 8 -9 5  10 11 12 13 -lit  1 5  16 17 -18 19 20 21 22 23 -24 25 26 27 28 28 29 -30 31 32 .33 34 35 -36 37 38 39  BEGINS  $C0MPILE UMrMLt DIMENSION X ( 1 2 4 ) B B ( 1 2 ) D D ( 1 2 ) , P P ( 1 2 ) V F ( 1 2 ) F F ( 1 2 - > v 1ERR(12),CBF(12),CDF(12),BF(12),DF(12),AS(12) REAL MB(12),NSU2) N»9 READ(5,5)CF 5 FORMAKF10.2) READ(5,15)((X(l>-J)>J»l l») -l-l-,N> 15 FORMAT(4F10.2) WRITE(6,6) 6—FORMAKIX/' DATA V71X>-12Xv-'CB ^^X>—VB-V8X^—C^'— 18X,'VD') DO 60 1=1,N 60- WRITE(6,26)I,X(I,1),X(I,2)>X(I>3),X(l>4) 26 FORMAT (IX, I 7,4F10.2) WRITE(6,36) 36—FORM AT ( //1X> RESULTS (A) /lXv—MAT-ER-l AL--BALANCE—&—SE-PARAT-4-ON—F-AGTOR 1//1X,14X,'BB',11X,'DD'^IX, 1 ' P P M I X , 'FF',10X, ' M B ' ^ X / E R R S ' ^ X / N S ' ) DO 80 1 = 1,N BBO)=X(I,1)»X(I,2) DD(I)=XCI,3)*X(I,4) PP( I )°BB( I )+DD( I) VF(I)=X(I,2)+X(I,4) FF(I)=VF(I)*CF MB( I ) = PP( I )-FF( I ) ERR(I)=MB(I)*100.0/FF(I) NS(I)=X(I,1)/X(I,3) CBF( I )=X( l , l ) - C F CDF(I) = CF-X( I ,3) BF(I)=CBF(I)*X(1,2) DF( !)=CDF( I )*X( 1,4) AS(I) RF(I)+DF( A SlI) = =B F ( I J + D F l I I; ) 80 W R I T E ( 6 , 4 6 ) I , B B ( I ) , D D ( I ) , P P ( I ) , F F ( I ) , M B ( I ) , E R R ( I ) , N S ( I ) 4 6—FORMATC 1X> I 7> 4F13 . 2, F l l . 2 , 2F10.3 ) WRITE(6,66) WR!TE(6,86) DO 90 l=l,N - — 90 W R I T E ( 6 , 7 6 ) I , C B F ( I ) , B F ( I ) , C D F ( I ) , D F ( I ) , A S ( I ) 66 FORMAT(//lX,'RESULTS(B)'/IX,'AMOUNT OF SEPARATION') 8 6--FORMAT(//lX>13X, CB-CF',-7X^ 76 FORMATCIX,I7,4F12.2,F14.2) STOP END /  /  v  >  1  J  $DATA  /  /  /  -1 2 3 ~~k~ 5 6 7 8 9  CS 3560.-00 3770.00 3310.00 341 Or 0 0 3900.00 4025.00 3300.00 3010.00 2795.00  VB 18-.80 18.19 17.90 17-. 9 4 17.20 17.73 17.55 18.10 18.00  RESULTS(A) MATERIAL BALANCE ft SEPARATION BB -66928.-0068576.25 59248.98 -61175.4167079.94 71363.19 -57915.0154481.02 50310.00  2 3 ...»+_.. 5 6 -7— 8 •9  CD 40 0.00 290.00 580.00 4 5 5vO 0 280.00 195.00 735.00 820.00 1020.00  VD 19.8319.80 18.30 18 -.--11 19.80 19.86 18.16 18.20 18.15  FACTOR PP -74860.00 74318.25 69862.94 -69415 .44 — 72623.94 75235.88 -7126 2.-5 6 — 69405.00 68802.56  DD 7932.005742.00 10614.00 8240.05 5544.00 3872.70 13347.5014924.00 18492.60  M3 FF 4 68r50-75328-r50237.75 74080.50 • -727.00 70589.94 -70297.50- -•—88 2.06473.94 72150.00 1935.44 73300.44 -69634.5 0- — 1 6 2 8.0 6-1380.00 70785.00 -1650.94 70453.50  ERR? -0.6220.321 •1.030 -1.255 0.657 2.640 -2.-338 -1.950 -2.343  NS —S-r90013.000 5.707 -7.495 13.929 20.641 —4v4903.671 2.740  RESULTS(B) -AMOUNT—OF—SEPARATION-CB-CF— 1610.00 1820.00 -1360.0 0 1460.00 1950.00 2075.00 1350.00 1060.00 845.00CORE USAGE DIAGNOSTICS -COMP1LE-TIME*  — BF 30268 ,00 33105 ,80 -24343 ,9926192 .40 33539 .99 36789 .74 23692 .50 19186 .00 -15210 ,00-  OBJECT CODE=  -CF-CD — 1550.00 1660.00 -1370.001495.00 1670.00 -1755 .00 1215.00 1130.00 — 930.00-  -DF30736.50 32868.00 -2 5071-. 0027074.45 33066.00 -34854.30 22064.40 20566.00 -16860.90-  2600 BYTES,ARRAY AREA-  NUMBER OF ERRORS"  -—- AS 61004.50 65973.75 -49414.9953266.85 66605.94 71644.0045756.91 39752.00 -32070.90816 BYTES,TOTAL AREA^AVAILABLE-  0, NUMBER OF WARNINGS-  —0-.18-SEC, EXECUTION -TIME--  :  0.13-SEC—-WATFIV —  102400  0, NUMBER OF EXTENSIONS" VERS ION-1 LEVE L:-3 MARCH—1971  BYTES 0 DATE"—07-30-74CO  •EXECUTION #  $STOP TERMINATED  O  $COMPILE 4 DATA DATA CB __ 1 3200.00 2 3it60.00 3 2850.00 U 3180. 00 5 3500.00 -6 37 20.00 7 2780. 00 8 2615.00 - 9 — 2 3 7 0 . 00  _VB 47.38 i»7.t*l 4 7.88 1*7.15  CD 61*0.00 480.00 990.00 830.00 1*7.31* 1*50.00 1*6.-1*6 310.00 1*7. 11* 1130.00 l»7.6t* 1290.00 1 * 6 . 5 1 * — 1 5 5 0,00 —  VD 1*8.30 48.62 1*8.251*9.85 1*9. 69 i»9;831*8. 33 i*8.H» 1*8.08  RESULTS(A) MATERIAL  BALANCE  h SEPARATION  BB 151616.00 161*038.50 -1361*58.00- — 11*9936.90 165689.90 172831.10 — 13101*9.10 121*578 .50 -110299 . 7 0 —  1 2  -3U 5 -6  7 8  -9-  FACTOR pp 182528. 00 187376. 10 -181*225; 50191312, t»0 188050, 1*0 -188278, 1*0185662, 00 186679. 10 -181*823, 70-  — DD 30912.00 23337.60 -1*7767.501*1375 .50 22360.50 -151*1*7.30 51*612.90 62100.60 -71+52U .00  -MB FF-1*01*8.00 186576.00 117.69 187258. 1*0 -1871*53.50- — 3 2 2 8.002162.t»i* 189150.00 -1158.00 189208 .1*0 -512.91* 187765.50 -501*.Ui* 186165.50 -91.81 186770.90 -181*508 ;90- — 311*. 81-  —ERR%— -2.170 0.063 — 1.7221.11*3 -0.612 - 0.273-0.271 -0.01*9 -0.171-  —NS 5.000 7.208 -2T879831 778 -12.000 1*60  027 529-  RESULTSCB)AMOUNT OF SEPARATION CB-CF 1250.00 1510.00 900.00 1230.00 -15 5 0 001770 00 830.00 665.00 1*20.00 —CORE-USAGE DIAGNOSTICS COMPILE TIME-  #EXECUTION  BF 59225, 00 -71589. 0 . 1*3092. 00 r  57991*,  1*9  -7 33 76,9 i * 82231*. 19 39126, 20 -31680, 6 0 1951*6, 80  OBJECT-CODE-  CF-CD 1310.00 -11*70.00960.00 1120.00 -1500.00161*0.00 820.00 - 660.00 1*00.00  -71*535 .00-  81721.19 39630.60 31772.UO 19232.00  2600- BYTES,-ARRAY AREA-  NUMBER OF ERRORS'0.03 SEC,EXECUT1 ON TIME-  $STOP • TERMINATED  DF 63273.00 •711*71.381*6320.00 55832.00  AS 1221*98.00 -11*3060.1*0891*12.00  113826.1*0 -11*7911.90163955.30 78755.75 —  631*53.00  38778.80 816 BYTES,-TOTAt—AREA~A-VA-|-tABtE-—102!r00—BYTES  0, NUMBER OF WARN INGS= 0.12 SEC,  0, NUMBER OF EXTENSIONS*  WATFIV - VERSION  1 LEVEL 3 MARCH  1971  0 DATE-  07-30-7U  u>  $ COM PI LE -$DATADATA -CB3050. 00 1 3270. 00 2 - 3 — 2580. 00 2910. 00 i» 3500. 00 5 -3615. 00 -6 2620. 00 7 2500. 00 8 2400. 00 9  V3 96.20 96.54 —96.2396.94 97.83 — 97.8997.22 97.15 -96.88  CD 1115.00 870.00 -1545.001190.00 790.00 -515.001465.00 1590.00 -1725.00  -RESULTS (A) MATERIAL BALANCE & SEPARATION 1 2 -3  BB 293409. 90 315685. 70 2482 73-. -30 282095. 30 322839, 00 - 353872 30 — 254716 30 242874 90 —232512 0 0 —  DD 110273 85912 151209 115560 77499 -50578 144302 156503 -169274  —VD 98.90 98.75 -97.87 97.11 98.10 -98.2198.50 98.43 98.13  FACTOR PP 403683.30 401598.20 399482:50397656.20 400338.00 404450.40 399018.80 399378.60 401786v20-  ,40 ,50 r-10 ,80 ,00 ,15 ,50 ,60 r20  FF400930.40 401320.80 -3S8875-.40398772.70 402636.10 402935.50402204.50 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 02.445 4.177 .019 ,788 .572 .391-  RESULTS(B) AMOUNT OF SEPARATION CB-CF 995.00 -1215.00525.00 855.00 -1245.001560.00 565.00 - 445.00 345.00 CORE-USAGE DIAGNOSTICS COMPILE TIME=  •EXECUTION t  BF 95718.94 -117296 0050520.75 82383.69 -12 17 98". 3 0152708.30 54929.30 - 43231.75 33423.60  OBJECT-CODE=-  DF CF-CD 940.00 92965.94 1185 .00- — 117018.70 510.00 49913.70 865.00 84000.13 -12'55.00 — 1 2 4 0 9 6 . 5 0 151243.30 1540.00 58115.00 590.00 -465.00 --45769.95 32382.90 330.00 -2600- BYTESyARRAY-AREA=  NUMBER OF ERRORS* 0.03 SEC,EXECUTION  $STOP. TERMINATED  AS 188684.80 -234314.80 — 100434.40 166883.80 -245894.80 — 303951.70 113044.20 - 89001.69 65806.50  -816 - BYTES7TOTAL-—AREA—AVAItAB LE"=—102400—BYTES-  0, NUMBER OF WARNINGSTIME-  0, NUMBER OF EXTENSIONS-  0.13 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH  1971  0 DATE-  07-30-74  u>  •GKOUP K5  $COMPf LEDATA-  $DATA VB 7.917.19 7.94 7-v7515 14 9795 94  CB •1070:001110.00 1040.00 -1070.001125.00 1150.00 -• 970.00 940.00 850.00  VD CD 19.-14—31.-5 019.38 24.00 19.11 41.00 19.8 0—2 5-. 0 0 19.79 20.40 19.82 16.80 -95.00 — - 19.1619.03 123.00 19.00 214.00  RESULTS(A) MATERIAL- BALANCE &-SEPARATION-FACTOR BB -19163; 7019080. 90 18657, 60 - 18992, 5019293, 74 19711, 00 -17430, 9016873, 00 15249, 00  —  DD - 6 0 2:91465.12 783.51 -495.00403.72 332.98 -18 20.202340.69 4066.00  PP -19766r6119546.02 19441.11 19487.5019697.46 20043.97 19251.1019213.68 1931?.00  FF —19636v5019382.10 19636.50 — 19901.50 19578.19 19588.80 —19678.9019599.39 19578.20  MB -130.-11163.92 •195.39 -414.00119.27 455.17 •427.80 -385.71 -263.20  NS ERR? —0.663- — 3 3 : 9 6 8 46.250 0.846 25.366 -0.995 - 42.800-2.080 55.147 0.609 68.452 2.324 - 2 r l 7 4 - —10.2117.642 -1.968 3.972 -1.344  RESULTS(B) AMOUNT-OF—SEPARATI ON -CB-CF— 540.00 580.00 -510.00 540.00 595.00 620.00 440.00 410.00 -320.00CORE USAGE DIAGNOSTICS -COMPILE TIME-  —BF 9671.40 9970.20 —91I-1.409585.00 10204.25 10626.80 7906.80 7359.50 — 5 74 0.80-  03JECT CODE-  CF-CD— 498.50 506.00 -489.00505.00 509.60 513.20435.00 407.00 -316.00-  2600 BYTES,ARRAY AREA-  NUMBER OF ERRORS0:03-SEC;EXECUT ION "TIME-  $STOP •EXECUTION TERMINATED  DF 9541.29 9806.28 —9344:799999.00 10084.98 10171.63 8334.60 7745.21 -6004.00-  AS19212.69 19776.48 -18 494.1919584.00 20289.22 20798.42 16241.40 15104.70 11744.80816 BYTES,TOTAL AREA AVAILABLE-  0, NUMBER OF WARNINGS0.-12-SEC;—WATFIV  102400  0, NUMBER OF EXTENSIONSVERS I ON !" LEVEL" 3 "MARCH -  -  1971  BYTES 0 DATE-—07-30-74Co Cn Co  GROUP R7  $C0MP1LE -$DATA • •DATA 1 2 -3 4 5 -6 7 8 -9  CB 980.00 1020.00 960.0 0 1016.00 1044.00 1055 .00 928.00 900.00 796.00  —RESUtTS (A) MATERIAL  VB 47.43 46.15 47.8 7 46.17 46.14 46;-13 46.96 47.85 47.89  —  —  ;  '  VD 49.14 48.30 48.1049.63 49.89 49.8748.04 49.13 48 .11-  —  BALANCE ft SEPARATION - BB 46481. 39 47072. 99 -45955; 2046908. 71 48170. 16 -48667. 1543578. 88 43065. 00 -38120. 44-  CD 38 .00 30.00 48.00 40.00 32.00 27.00 103.00 130.00 2 21.00  FACTOR  -DO — 1867. 32 1449. 00 -2 308; 801985, 20 1596, 48 -1346. 49 4948, 12 6386, 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 -4894477048853.00 48975.30 -48960.0048450.00 49459.80 -48960.00-  —MB -901.99 352.50 --63 0.-7135.91 791.34 -105 3.6477.00 -7.90 -207.25-  —ERR?— -1.831 0.732 -17-3910.074 1.616 -2.1520.159 -0.016 -0.423-  — NS 25.789 34.000 -2 0.-00025.400 32.625 -39.074,010 ,923 -3.602-  RESULTS(B) AMOUNT OF SEPARATION CB-CF 470.00 -510.00" 450.00 506.00 -534:00545.00 418.00 -390.00 286.00  8 9 CORE tlSAGE" -  DIAGNOSTICS COMPILE TIME=  •EXECUTION •  BF 22292.09 -23536. 5 0 21541.50 23362.02 -24638.76"25140.85 19629.28 -18 661.50-13696.54  OBJECT-CODE=  CF-CD 472.00 -480.00462.00 470.00 "478.00 483.00 407.00 380.00 289.00  —2&OO-BYTES7ARRAY  NUMBER OF ERRORS0.03 SEC,EXECUTION  $STOP TERMINATED  DF 23194.08 -2 318 4.0022222.20 23326.10 -2 3847.4224087.21 19552.27 " 18669.40 13903.79  TIME"  AREA  AS 45486.17 46720.50" 43763.70 46688.12 -48486.1849228.06 39131.55 37330.90 27600.33  3  — 8 1 6 BYTES7TOTAL—AREA-AVAttABtE"—102400—BYTES"  0, NUMBER OF WARNINGS" 0, NUMBER OF EXTENSIONS" 0.12 SEC, WATFIV - VERSION 1 LEVEL 3 MARCH 1971  0 DATE"  07-30-74  $COMPILE $DATA DATA CB 935.00 950.00 915.00 920.00 948.00 96 0.0 0 852.00 800.00 -706.0 0  1 2 -3 4 5 -6 7 8 9 —  —  VB 96.94 96.72 96.-16 97.80 96.30 9 6.15 96.26 97.40 96.03  RESULTS ("AO MATERIAL BALANCE & SEPARATION BB— 90638. 88 91884. 00 -8798 6.-3 889976. 00 91292. 38 92303. 94" 82013. 50 77919. 94 67797. -1-3-  CD 66.00 57.00 103.00 76.00 57.00 5 2:0 0 153.00 200.00 298.0 0  VD 97.14 97.80 97.8498.28 96.87 9 8v31~ 97.59 97.72 98 .17'  FACTOR  DO 6411.24 5574.60 -10077.527469.28 5521.59 -5112.12 14931.27 19544.00 -29254.66-  pp 97050.06 97458.56 -98 063r8 897445.25 96813.94 -97416.0096944.75 97463.94 -97051.75-  -FF97040.00 97260.00 -97000.-0C98040.00 96584.94 -97229.9496924.94 97559.94 -97099.94-  -MB10.06 198.56 -1063.8 8-594.75 229.00 - 186.0619.81 -96.00 —-48.19-  ERR%0.010 0.204 097607 237 ,191" ,020 ,098 '0.050-  -NS14.167 16.667 —8~. 88 312.105 16.632 -18.462 569 000 "2.369-  -RESULTS(B) AMOUNT OF SEPARATION BF CB-CF 435.00 42168.90 450.00 — -435 2 4.00 415.00 39906.40 420.00 41076.00 -448 .00 — -43142-.40460.00 44229.00 352.00 33883.52 -300.00 — 29220.00206.00 19782.18 CORE-USAGEDIAGNOSTICS COMPILE TIME"  •EXECUTION #  OBJECTCODE=  CF-CD 434.00 443.00397.00 424.00 -443.00448.00 347.00 300.00 202.00  2600 BYTES",i\RRAY AREA=  NUMBER OF ERRORS" 0.03 SEC,EXECUTION TIME"  $STOP TERMINATED  DF 42158.76 43325.-4038842.48 41670.72 -42913.4144042.88 33863.73 29316.0019830.34  AS 84327.63 86849.3878748.88 82746.69 -86055.7588271.88 67747.19 58536.00 39612.52 816" BYTES/TOTAL—AREA-AVAILABLE"—l-02Wt>—BYTES-  0, NUMBER OF WARNINGS" 0.12 SEC,  0, NUMBER OF EXTENSIONS"  WATFIV - VERSION  1 LEVEL 3 MARCH  1971  0 DATE-  07-30-74  $r » w a t f t v scards con 5 r 9 par>»noltst B  •EXECUTION  a  BEGINS  $COMPILE $DATA DATA VB 17.73 17 ".SOl S . 61 18.13  CB 4900.00  I  51*00.00 51*20.00  2  3  k  6150.00  CD  VD . 19.18 19.20 18.72 18.96  21*75.00  2020.00 1750.00 1350.00  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  ERR* ^07821-0.653 -2.1*63 0.716"  -3371*.88  -  975.19-  NS -1T9802.673 3.097  -U.556-  "RESULTStBT AMOUNT OF  SEPARATION CB-CF 1230.00 173070 0 1750.00 21*80.00  1 2 3 1* CORE USAGE TjrAGNOSTTCS COMPILE  TIME-  OBJECT CODE=  CF-CD 1195.00 r6 5 0T0 0 1920.00 2320.00  DF 22920.09 316 797^ 9 3591*2.1*0 1*3987.21  2592 BYTES,ARRAY AREA"  NUMBERS TERRORS0.03 SEC,EXECUTION  $STOP # EXECUTION TERM INATED" #  BF 21807.39 30791*70 0 32567.50 1*1*962.1*1  AS 1*1*727.98 621* 71* 70 0 68509.88 8891*9.63 816 BYTES,TOTAL AREA AVAILABLE-  07-NUMBER-OF-WARNTNGSTIME-  0.08 SEC,  1021*00  Or NUMBER—OF EXTENSIONS  WATFIV - VERSION  -  -  1 LEVEL 3 MARCH  3  1971  BYTES 0~ DATE-  07-30-71*  CO Cn  j r * w a t r i v s c a r d S " c o n i°ril "EXECUTION BEGINS  par=noiist  $COMPILE $DATA DATA CB 4700.00 5 0 2 0'.- 0 0 5300.00 5700.00  1 "2 3 4  VB CD 47.50 2645.00 4-772 4 2 28 0.0 0 47.45 2120.00 46.85 1655.00  VD 48.75 48 .3 4' 48.25 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 T 2 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 "T77772.202 2.500 "37444"  RESULTS(B) AMOUNT OF SEPARATION CB-CF 1030.00 "135070 0" 1630.00 2030.00 CORE USAGE  -DTAGNOSTrCS COMPILE  TIME"  BF 48925.00 "6377470X'" 77343.44 95105.50  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"  TCUMBER"OF~ERR"ORS= 07"NUMBER""aF"WAWrNGS=^ 0.03 SEC,EXECUTION TIME"  $STOP ?EXECUnON"TERmiTATED i  0.08 SEC, WATFIV - VERSION  102400  BYTES  LT7 NUMBERTTJF-TXTENSTTWS"—0 1 LEVEL 3 MARCH  1971  DATE-  07-30-74  r *watflv scard scards-con 5 - r l 2 p a r - n o l l s t „5r_*watfIv "EXECUTION  BEGINS  "$ COMPILE" SDATA  DATA 1 2 3 (*  CB 1*520.00 4700.00 1*850.00 533070TT  "RESULTS ("A3 MATERIAL BALANCE  _  VB 96:25 96.10 96.71* 96.62  _  CD "2970.00 2660.00 251*0.00 2150.00  & SEPARATION  BB 1*35050.00 1*51670. 00 I* 69189700" 511*981*.50  VD 98.35 98.35 98.00 98.85  FACTOR  PP  DT)  292099.50 261611.00 "71*8920.00" 212527.50  72711*9.50 713281.00 "718109700" 727512.00  FF 723912.00 723351*.00 "721*1*32.80 72711*8.30  MB 3237.50 -10073.00 "-6323.81" 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"  CORE USAGE  BF rO'DTJTDTT 91*178.00 109316.lu ""155558710-  OBJECT CODE=  DIAGNOSTICS  CF-CD 750-70 TJ" 1060.00 101*251.00 1180.00 11561*0.00 "15 70.0 0" ""155191+ .50" 2592 BYTES,ARRAY AREA=  NUMBER OF ERRORS-  -COMPUT-TiMF-  0T03-SEC7EXECUTrON"TIME-  "$STOP * EXECUTION TERMINATED #  AS T5D7UZT3TT 1981*29.00 221*956.10 "310752.60"  —  816 BYTES,TOTAL AREA AVAILABLE-  0, NUMBER OF WARNINGS-  1021*00  0, NUMBER OF EXTENSIONS-  07 09 "SECT WATFI V — "VERSHOITTTEVEL~3~HAR-CH"~I"97I -  BYTES 0 DATE"  07-30-71*"  r_  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 for a Desalting Process  F.l.  Minimum Work of S e p a r a t i o n  The m i x i n g of two s u b s t a n c e s always r e s u l t s i n an i n c r e a s e i n e n t r o p y , due t o the i n c r e a s e i n "randomness" of t h e system.  This increase  i s accompanied by a c o r r e s p o n d i n g d e c r e a s e i n f r e e energy, so t h a t t h e s e p a r a t i o n o f t h e r e s u l t i n g m i x t u r e under t h e r m o d y n a m i c a l l y  reversible  c o n d i t i o n s r e q u i r e s t h e s u p p l y o f an e q u a l amount of energy t o c o u n t e r a c t n a t u r e ' s tendency t o mix r a t h e r t h a n unmix s p o n t a n e o u s l y . In  g e n e r a l , heat and work b o t h depend on the p a r t i c u l a r p a t h , and  one  cannot c a l c u l a t e the minimum r e q u i r e m e n t of e i t h e r w i t h o u t 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 p r o c e s s - t h e  i s o t h e r m a l r e v e r s i b l e p r o c e s s - f o r w h i c h t h e work i s measured by t h e change i n the H e l m h o l t z f r e e energy of  ( t h e work f u n c t i o n ) , A.  The term "minimum work  s e p a r a t i o n " i s u s u a l l y used t o mean t h e thermodynamic r e v e r s i b l e work o f  s e p a r a t i o n f o r an i s o t h e r m a l p r o c e s s and hence i t i s independent of t h e p r o c e s s mechanism and dependent o n l y on t h e i n i t i a l and f i n a l  states.  The minimum work t o s e p a r a t e one mole of a f e e d s o l u t i o n of c o m p o s i t i o n x^ i n t o two p r o d u c t s o l u t i o n s o f c o m p o s i t i o n s  and x^ r e s p e c t i v e l y i s  g i v e n by (Dodge, 1944)* * Dodge, B.F., Ed., " C h e m i c a l E n g i n e e r i n g Thermodynamics", McGraw H i l l New Y o r k , 1944. 359  Co.,  360  f x .2  ~  v  W. . . ideal  =  - AA  =  - RT  (1 - x ) ( _ 2 3 2  X l  X  X  - x )  - x  2  3  x  B 2  1  P  0  - x )  3 1 2 - 3  1  X  A? ln— P P  —  p ln B1  3  X  (1 - x„)(x +  I— L x  J  X  (x - x ) p l 2 3 A1 3  2  L  A 3  n  X  p  + A l  x  P  1  i - B 3 | B1 n  P  (F.l.)  where p I s t h e p a r t i a l p r e s s u r e and s u b s c r i p t s  1, 2 and 3 r e f e r t o  f e e d , f i r s t p r o d u c t , and second p r o d u c t , 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 t o t h e components. Spiegler  (1966 a) d e v e l o p e d  energy r e q u i r e m e n t  a g e n e r a l e q u a t i o n f o r t h e minimum t h e o r e t i c a l  t o s e p a r a t e s a l t from a s a l i n e .  p r o c e s s i n w h i c h a 1-1 e l e c t r o l y t e s o l u t i o n product s o l u t i o n s  U  =  o f cones. C  and C  d  1.377 x AN (  o f cone. Cf i s c o n v e r t e d i n t o two  a t 25°C, t h e minimum energy  £  p  —  F o r any d e s a l t i n g  )  i s g i v e n by  (F.2.)  ot — J-  J.  3  where U  i s t h e energy i n kwh/m  AN = t h e n o r m a l i t y d i f f e r e n c e  between f e e d and p r o d u c t  solution N  = the normality N N~~ c f  =  subscripts respectively.  ;  a  (g-equiv/lit) N NT d f  =  f , d, c i d e n t i f y f e e d , p r o d u c t  ( d i l u a t e ) and c o n c e n t r a t e  361  F.2.  P r a c t i c a l Energy  The  Requirements  t h e o r e t i c a l energy r e q u i r e m e n t s f o r a d e s a l t i n g p r o c e s s u s u a l l y  r e p r e s e n t s m e r e l y a s m a l l p o r t i o n o f the a c t u a l energy r e q u i r e m e n t .  When  the minimum work r e q u i r e m e n t 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 t h e a c t u a l r e q u i r e m e n t of o p e r a t i n g p r o c e s s , i t i s found t h a t t h i s l a t t e r • have an energy e f f i c i e n c y of t h e o r d e r of o n l y 2 t o 5%  (Dodge and  Eshaya,  I960)*. These low e f f i c i e n c i e s a r e , o f c o u r s e , a t t r i b u t a b l e t o t h e d r i v i n g f o r c e s w h i c h a r e n e c e s s a r y i n any p r a c t i c a l p r o c e s s , as c o n t r a s t e d w i t h t h e r e v e r s i b l e p r o c e s s t h a t assumes z e r o d r i v i n g f o r c e s . are  These d r i v i n g f o r c e s  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 . , w h i c h a r e n e c e s s a r y 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 a l w a y s e n t a i l s an  i n c r e a s e i n s i z e and hence c o s t o f equipment and because t h e t o t a l c o s t s o f a d e s a l t i n g p r o c e s s a r e 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 r e a c h e s a c o s t minimum a t 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 t h a n 20%. The main i r r e v e r s i b l e e f f e c t s t h a t make t h e a c t u a l p r o c e s s d i f f e r s t h e i d e a l r e v e r s i b l e one a r e : i) ii) iii) iv) v)  P r e s s u r e drop i n l i n e s and equipment due t o f l u i d  friction,  T h r o t t l i n g processes. F i n i t e t e m p e r a t u r e d i f f e r e n c e between f l u i d s e x c h a n g i n g h e a t . Heat c o n d u c t i o n a l o n g s o l i d s . Heat l e a k i n t o t h e system from t h e s u r r o u n d i n g s .  * Dodge, B.F. and A.M. Eshaya, i n : " S a l i n e Water C o n v e r s i o n " Number 27 i n Advances i n C h e m i s t r y S e r i e s , American C h e m i c a l S o c i e t y , Washington, D.C., 1960.  from  362  vi)  F l u i d m i x i n g when t h e r e i s a d i f f e r e n c e i n t e m p e r a t u r e o r concentration.  vii) viii) ix) x)  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 , Joule heating i n e l e c t r i c current flow, Polarization effects at electrodes, Mechanical  f r i c t i o n , a s i n pumps and c o m p r e s s o r s .  These e f f e c t s c a n never be c o m p l e t e l y  e l i m i n a t e d and f r e q u e n t l y must  r e m a i n o f c o n s i d e r a b l e magnitude, i f t h e s i z e o f t h e equipment i s t o be k e p t w i t h i n reasonable  bounds [Dodge B.F. and A.M. E s h a y a , I 9 6 0 ] .  

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