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A Cyclic electrodialysis process : investigation of closed systems Bass, Dieter 1972-12-31

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^ 0 %  A CYCLIC ELECTRODIALYSIS PROCESS Investigation  of Closed  Systems  by  DIETER BASS Dipl.  Ing., Universitaet  F r i d e r i c i a n a Zu K a r l s r u h e , 1968  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS  FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  t h e Department of  CHEMICAL ENGINEERING  We a c c e p t required  this  thesis  as c o n f o r m i n g  to the  standard  THE UNIVERSITY OF B R I T I S H Decembe r , 19 72  COLUMBIA  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and  study.  I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may by h i s representatives.  be granted by the Head of my Department or  It i s understood that copying or publication  of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of  ^<Of C  The University of B r i t i s h Columbia Vancouver 8, Canada  ABSTRACT  The cyclic electrodialysis process combines two concepts. The idea of flow reversal from parametric pumping is applied to an electrically driven absorption-desorption  process operating with a  stack of three-layer, ion-selective membranes. The cyclic process was investigated for the demineralization of aqueous NaCl solutions in a closed system. The standard parametric pumping operation was found to be generally very inefficient because of the finite rates of mass transfer.  Flow pauses after each polarity reversal substantially  improved both the rate and the limit of separation. Two designs of the electrodialysis cell were studied. system parameters were analysed on a simple bench scale c e l l .  Ten Final  separations were limited by large axial dispersion and ranged between 1 and 40.  A second electrodialysis cell consisted of up to eight  single stages (15 [cm] channel length) which were usually operated in series hydraulically and in parallel e l e c t r i c a l l y .  Final separation  factors ranged between 2 and ~6000. Large separation factors were achieved for long channels, long pause times, and high applied potentials. The i n i t i a l rate of ii  separation appeared to be a maximum for a channel length of approximately one meter and pause times of about ten seconds.  During the f i r s t  few cycles the separation factor could be approximated by an exponential function of time. The potential of the process for continuous separation in open systems was  demonstrated.  Models of the closed systems are presented and are used to discuss the experimental results.  iii  TABLE OF CONTENTS Page ABSTRACT  i i  LIST OF TABLES  x  LIST OF FIGURES  xiii  ACKNOWLEDGEMENTS  xxiii  Chapter 1  INTRODUCTION AND SCOPE  2  PROCESS PRINCIPLES 2.1  . . . . 4  Electrodialysis  4  2.1.1  Origin  of s e p a r a t i o n  5  2.1.2  Membrane s e l e c t i v i t y  8  2.1.3  T r a n s p o r t processes through ion s e l e c t i v e membranes  12  M u l t i c e l l e l e c t r o d i a l y z e r and its applications  14  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 and other problems i n s t e a d y - s t a t e electrodialysis  16  Current  21  2.1.4 2.1.5  2.1.6 2.2  1  reversal  techniques  Parametric pumping, h e a t l e s s a d s o r p t i o n and s i m i l a r c y c l i c s e p a r a t i o n processes  iv  . . 24  Chapter  3  Page Parametric pumping  25  2.2.2  Other  33  cyclic  operations  EFFECT OF FINITE MASS TRANSFER RATES ON PARAMETRIC PUMPING AND PURE PAUSE OPERATION. . . . 37 3.1  General  3.2  C o n s t a n t , Uniformly D i s t r i b u t e d  3.3  4  2.2.1  37 Rates  of Mass T r a n s f e r  39  3.2.1  Parametric pumping o p e r a t i o n  41  3.2.2  Pure pause o p e r a t i o n  51  C o n c e n t r a t i o n Dependent  Rates of  Mass T r a n s f e r  52  3.3.1  Pure pause o p e r a t i o n  54  3.3.2 3.3.3  Parametric pumping o p e r a t i o n Comparison o f pause and parametric pumping o p e r a t i o n s . . . . . . . . . .  56  3.4  Summary  56 60  3.5  Comment on an E q u i l i b r i u m Model with Instantaneous Displacement  61  THE CYCLIC ELECTRODIALYSIS PROCESS OPERATION AND APPARATUS  65  4.1  D e s c r i p t i o n of the Batch Operation  65  4.2  The F i r s t Bench Module  68  4.2.1  E l e c t r o d i a l y s e r No. 1 (EDI)  71  4.2.2  Membrane spacer stacks  75  4.2.3  Process  83  4.2.4  Timing  4.2.5  Rinse  4.2.6  Measuring  flow and switch boxes  loop  v  84 88  and r e c o r d i n g  88  Chapter  4.3  5  Page  The Mini P i l o t P l a n t Module  90  4.3.1  Electrodi alyser  90  4.3.2  Rinse d i s t r i b u t i o n system  4.3.3  Current and voltage measurements  EXPERIMENTAL  No. 2 (ED 11)  98 . . . 98  RESULTS AND DISCUSSION. . . . . . . .  101  5.1  Data C o l l e c t i o n  102  5.2  Main Survey Tables  104  5.3  The F i r s t E l e c t r o d i a l y s i s C e l l  (EDI). . . . .  108  5.3.1  Parameters  108  5.3.2  E f f e c t of a p p l i e d v o l t a g e . . . . . . .  109  5.3.3  E f f e c t of pause time  120  5.3.4  Effect  5.3.5  E f f e c t of d i s p l a c e d volume  135  5.3.6  Effect  141  5.3.7  E f f e c t of i n i t i a l  5.3.8  E f f e c t of i n t e r n a l flow d i s t r i b u t i o n and a x i a l d i s p e r s i o n . . . 151  5.3.9  E f f e c t of e x t e r n a l mixing i n brine r e s e r v o i r  of s u p e r f i c i a l v e l o c i t y  of dead volumes  . . . .  128  c o n c e n t r a t i o n . . . . 147  5.3.10 E f f e c t of c a p a c i t y c e l l  159  t h i c k n e s s . . . 164  5.3.11 E f f e c t of t h i c k n e s s and hydrodynamic p r o p e r t i e s of spacer screens  165  5.3.12 Comment on pH-changes  167  5.3.13 Comment on c u r r e n t e f f i c i e n c i e s . . . . 167 5.3.14 Comment on true l i m i t s and on r e p r o d u c i b i l i t y of batch runs  vi  170  Chapter  Page 5.4  Summary of Experience Gained on First Electrodialysis Cell  5.5  173  The Second E l e c t r o d i a l y s i s C e l l  (EDI I) . . . . 175  5.5.1  Data r e d u c t i o n  and p r e s e n t a t i o n . . . . 176  5.5.2  E f f e c t of channel  5.5.3  E f f e c t of pause time  194  5.5.4  E f f e c t of a p p l i e d  voltage  205  5.5.5  E f f e c t of i n i t i a l  c o n c e n t r a t i o n . . . . 205  5.5.6  E f f e c t of d i s p l a c e d  5.5.7  E f f e c t of dead volumes  5.5.8  E f f e c t of s u p e r f i c i a l v e l o c i t y  5.5.9  Reproducibility  length  178  volume  211 221 . . . .  226  5.5.10 Comment on the m a t e r i a l balance f o r the s o l u t e 5.5.11 Comment on the performance of i n d i v i d u a l stages 5.5.12  5.6  Experimental t e s t of the constant rate model .  229 . 231 239  5.5.13 Comment on the e f f e c t of end mixing  241  5.5.14 Production of 90% d e m i n e r a l i z e d solution  243  Summary of Results and Experience on  6  221  the Second ED Module  247  MATHEMATICAL MODELS  250  6 .1  Spacer Model  250  6.1.1 6.1.2  252  Model equations Considerations related process o p e r a t i o n s  vi i  to c y c l i c 261  Chapter  Page 6.1.3  Solutions  262  6.1.4  Backward D i f f e r e n c e scheme with Gauss-Seidel i t e r a t i o n  264  6.1.5  R e s u l t s of computer s i m u l a t i o n s . . . . 269 6.1.5.1  Accuracy  6.1.5.2  E f f e c t of o p e r a t i n g parameters  270  Comparison with r e s u l ts . . .  271  6.1.5.3 6.1.6  Concluding  and convergence.  . . 269  experimental  comments on the  spacer model 6.2 7  Rate Model  CONCLUSIONS  278 279  AND RECOMMENDATIONS. . . . . . . . . .  280  NOMENCLATURE  284  REFERENCES  289  APPENDICES A DETAIL DRAWINGS, PICTURES OF THE MODULES AND MANUFACTURING PROCEDURES . . . . . . . . . . .  295  A.l  ELECTRODIALYZER NO. 1  296  A.2  ELECTRODIALYZER NO. 2  302  A. 3  MANUFACTURING PROCEDURE FOR MEMBRANESPACER FRAME MATHEMATICAL DERIVATIONS  305 308  DERIVATION OF CONCENTRATION TRANSIENTS FOR CONSTANT, UNIFORMLY DISTRIBUTED RATES OF MASS TRANSFER. PARAMETRIC PUMPING OPERATION  309  DERIVATION OF CONCENTRATION TRANSIENTS FOR CONCENTRATION DEPENDENT RATES OF MASS TRANSFER PURE PAUSE OPERATION  313  RATE THEORY OF PARAMETRIC PUMPING  318  B •B.l  B. 2  B.3  vi i i  APPENDICES B.4 B. 5  Page  MULTIPLE STEP DISPLACEMENT MODEL (STOP-GO ALGORITHM) DERIVATION OF CONCENTRATION  TRANSIENTS  325 FOR  EQUILIBRIUM CONTROLLED PURE PAUSE OPERATION. . . . 330 C  COMPUTER PROGRAMS  336  C. l  EVALUATION OF EDI EXPERIMENTS  337  C.2  EVALUATION OF E D I I EXPERIMENTS  378  C.3  SPACER MODEL  408  ix  LIST OF TABLES Tab 1 e 1.  Page Computer S i m u l a t i o n s o f Pure P a u s e , P a r a m e t r i c Pumping^and M u l t i p l e Step D i s p l a c e m e n t O p e r a t i o n s f o r 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 Rates  59  2  E l e c t r o d i a l y s e r No. 1 ( E D I )  75  3  P r o p e r t i e s o f Neosepta  76  4  S t a c k Pack V e r s i o n s  5  Piston  6  C o n d u c t i v i t y and NaCl 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 CELrVDJ 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 f r o m a Beckman S o l u - m e t e r RA5  89  7  E l e c t r o d i a l y s e r No. 2 (EDI I )  97  8  Compilation  of Experiments  on EDI-S1-8  9  Compilation  of Experiments  on EDI-S2-15  10  Compilation  of Experiments  on EDI-S2-16  11  Compilation  of Experiments  on EDI-S3-12  12  Compilation  of Experiments  on EDI-S3-13  13  Compilation  of Experiments  on ED 11-S1-8  Membranes  Used i n F i r s t  ED C e l l  . . . . 79  Pump S p e c i f i c a t i o n s  x  84  107  Tab 1 e 14  Page E f f e c t of Applied EDI-SI-8  V o l t a g e (A$)  15  Effect of Applied EDI-S2-15  V o l t a g e (A$)  on  16  E f f e c t o f A p p l i e d V o l t a g e (A$) EDI-S3-12 and E D I - S 3 - 1 3  on  17  Effect and  on 116  o f P a u s e Time  ( x ) on  EDI-S2-15  EDI-S2-16  122  18  Effect  on P a u s e Time  ( T ) on EDI-S3-12  19  Effect  o f P a u s e Time  ( x ) on E D I - S 3 - 1 3  20  Effect  of S u p e r f i c i a l V e l o c i t y  (v)  21  on EDI-SI-8 Effect of S u p e r f i c i a l Velocity on E D I - S 2 - 1 6 , EDI-S3-12  (v)  131  22  E f f e c t of S u p e r f i c i a l V e l o c i t y on E D I - S 3 - 1 3  23  E f f e c t o f D i s p l a c e d Volume (s) E D I - S 2 - 1 5 and E D I - S 3 - 1 3 . .  24  25  E f f e c t o f Dead Volumes EDI-S3-12 and E D I - S 3 - 1 3 Effect  of I n i t i a l  EDI-S3-12  (<SR/6 1 T)  (v)  on EDI-S1-8, 137 on E D I - S 2 - 1 5 ,  . .  142  C o n c e n t r a t i o n ( c 0 ) on  and E D I - S 3 - 1 3  148  26  Step Response Experiments  on EDI-S1-8  27  Step Runs Step Runs  on  28  Response E x p e r i m e n t s #1-14 Response E x p e r i m e n t s #15-24  xi  157  EDI-S3-12 157  on  EDI-S3-12 158  Table  Page  29  Step Response  Experiments on EDI-S3-13  30  E f f e c t of End Mixing on EDI-S3-12 .  31  E f f e c t of Capacity C e l l Thickness on E1 e c t r o d i a l y z e r  No. 1  158 162  166  32  pH-Changes i n Some EDI-S3-12 Runs  167  33  Results Second Effect Second  180  34  35  36  37  38  39  40  41  42  of Step-Response Tests on ED C e l l s of Channel Length (MS) on E1 e c t r o d i a l y z e r  184  E f f e c t of Pause Time (x) on Second Electrodi alyzer  196  E f f e c t of A p p l i e d Voltage (A$) on Second E l e c t r o d i a l y z e r  206  E f f e c t of I n i t i a l C o n c e n t r a t i o n ( c 0 ) on Second E l e c t r o d i a l y z e r . . . . . . . . . . . .  212  E f f e c t of D i s p l a c e d Volume (6) on Second E l e c t r o d i a l y z e r  217  E f f e c t of S u p e r f i c i a l V e l o c i t y Second El e c t r o d i a l y z e r  223  (v) on  Spacer Model No. I , E f f e c t of Layer Thickness  272  Spacer Model No. I , E f f e c t of F o u r i e r Number  273  Spacer Model Potential  274  No.I, E f f e c t of A p p l i e d  XI i  LIST OF FIGURES  Fi gure  Page  1  The  2  T r a n s p o r t processes s e l e c t i v e membrane  3  4  electrodialysis  principle. across an  . . . .  6  anion13  Multicell electrodialysis (schemati c) Concentration p o l a r i z a t i o n s e l e c t i v e membrane  stack 13 of an i o n 18  5  Thermal parametric pumping .  18  6  C h a r a c t e r i s t i c s of batch s e p a r a t i o n v i a e q u i l i b r i u m theory of parametric pumping . . . .  30  Concentration t r a n s i e n t s for equilibrium theory of parametric pumping ( a c c o r d i n g to P i g f o r d , 1969a)  32  7  8  9  10  11  Heatless a d s o r p t i o n a i r d r y i n g system, used by Skarstrom ( 1959) C y c l i c zone a d s o r p t i o n (proposed P i g f o r d , 1969b)  by  E l e c t r o d i a l y s i s systems with c o n s t a n t , uniformly d i s t r i b u t e d r a t e s of mass t r a n s f e r C o n c e n t r a t i o n p r o f i l e s during the f i r s t c y c l e of a c y c l i c e l e c t r o d i a l y s i s process operated in parametric pumping mode under c o n d i t i o n s of e q u a l , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d rates of mass t r a n s f e r  xi i i  34  35  . .  40  43  Fi gure 12  13  14  15  16  17  18  19  20  Page Product c o n c e n t r a t i o n t r a n s i e n t s f o r c y c l i c e l e c t r o d i a l y s i s process operated i n param e t r i c pumping mode under c o n d i t i o n s of equal , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d r a t e s of mass t r a n s f e r  44  Product concentration transients f o r c y c l i c e l e c t r o d i a l y s i s process operated i n parametric pumping mode under c o n d i t i o n s of unequal , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d rates of mass t r a n s f e r  45  Development of s t a n d i n g waves i n a parametric pumping o p e r a t i o n under c o n d i t i o n s of e q u a l , constant and u n i f o r m l y d i s t r i b u t e d rates of mass t r a n s f e r when v a r i a b l e s are switched one-quarter cycle out of phase  47  Product c o n c e n t r a t i o n t r a n s i e n t s f o r c y c l i c e l e c t r o d i a l y s i s process operated i n parametric pumping mode under c o n d i t i o n s of e q u a l , cons t a n t and u n i f o r m l y d i s t r i b u t e d r a t e s of mass t r a n s f e r , when p e r i o d i c v a r i a b l e s are switched one-quarter c y c l e out of phase  48  Average top and bottom product t r a n s i e n t s f o r phase s h i f t o p e r a t i o n of a constant r a t e c o n t r o l l e d parametric pump  50  L a t e r a l c o n c e n t r a t i o n p r o f i l e and c o - o r d i n a t e systems i n flow channel and t r i p l e membrane. . .  50  E f f e c t of the number of segments (N) on the product c o n c e n t r a t i o n t r a n s i e n t s f o r conc e n t r a t i o n dependent r a t e s of mass t r a n s f e r _1 ( a i = a 2 = 0 . 0 1 sec ,T=20 s e c , p=1.0, 6=1.0). . .  58  Product c o n c e n t r a t i o n t r a n s i e n t s f o r e q u i l i b r i u m c o n t r o l l e d pure pause o p e r a t i o n  63  Batch o p e r a t i o n of c y c l i c process  66  xi v  electrodialysis  Fi qure 21  Page Time v a r i a t i o n of a p p l i e d p o t e n t i a l (a) and flow r a t e (b) f o r c y c l i c e l e c t r o d i a l y s i s process  22  Block diagram of experimental  23  First electrodialysis (exploded  cell  testing station.  view, schematic)  25  Glass f i b r e  26  Floating  27  Automatic s w i t c h i n g arrangement f o r c y c l i c el e c t r o d i a l y s i s process P i s t o n Pump D r i v e . E l e c t r i c c i r c u i t f o r motor r e v e r s a l  30  31  32  33  1  80,81,82  spacer screen  l i d expansion  69  72  E l e c t r o d i a l y s e r No.  29  . .  EDI  24  28  66  78  tank  85  85 87  Clamping arrangement of e i g h t stages i n mini p i l o t p l a n t module  91  Schematic assembly of one second e l e c t r o d i a l y z e r  87  stage of the  ' I n t e g r a t e d membrane-spacer frame f o r e l e c t r o d i a l y z e r No. 2. Parts and assembly  . . . .  93  E l e c t r o d i a l y s e r No. 2. E l e c t r o d e end frames of a s i n g l e stage  94  Process flows through second d i a l y s i s c e l l (schematic)  96  electro-  34  Current monitoring c i r c u i t  35  EDI-S2-15/#l5. Traces of c u r r e n t and probe v o l t a g e r e c o r d i n g during the f i r s t f i v e cycles  xv  99  Ill  Fi gure 36  37  38  39  40  Page Stack voltage f i r s t ED c e l l  vs. electrode voltage f o r 112  EDI-S1-8/#36. Example o f c o n c e n t r a t i o n t r a n s i e n t s i n p a r a m e t r i c pumping o p e r a t i o n when mass t r a n s f e r r a t e s a r e c o n s t a n t  113  EDI-S2-15/#9. Example o f c o n c e n t r a t i o n t r a n s i e n t s i n p a r a m e t r i c pumping o p e r a t i o n when mass t r a n s f e r r a t e i s concentration dependent. . .  113  E f f e c t o f a p p l i e d v o l t a g e on f i n a l c o n c e n t r a t i o n s , s e p a r a t i o n f a c t o r , and c u r r e n t . Second s t a c k e x p e r i m e n t s i n no-pause operation. EDI-S2-1 5/#7 ,8 ,9 ,10 ,1 7 . . . . . . . . E f f e c t o f a p p l i e d v o l t a g e on f i n a l p r o d u c t concentrations f o r t h i r d stack experiments. EDI-S3-12/#17,18,19,1-2 and E D I - S 3 - 1 3 / #6,7,11 ,8,22,9  .117  118  41  E f f e c t o f a p p l i e d v o l t a g e on f i n a l s e p a r a t i o n f a c t o r f o r t h i r d s t a c k e x p e r i m e n t s . EDI-S3-12/ #17,18,19,1-2 and EDI-S3-1 3/#6 ,7 ,11 ,8 ,22 ,9 . . . . 119  42  E f f e c t o f p a u s e t i m e (x) on s e p a r a t i o n f o r s e c o n d and t h i r d s t a c k e x p e r i m e n t s  43  44  45  46  factor 123  E f f e c t o f p a u s e t i m e on f i n a l r e s e r v o i r c o n centrations f o r t h i r d stack experiments. ED I S3-12/#24 ,18,21 ,22 ,23 and EDI-S3-13/#10 ,11 , 7 , 12,2,13,1 ,14  124  E f f e c t o f p a u s e t i m e (x) on f i n a l s e p a r a t i o n factor f o r t h i r d stack experiments. EDI-S3-12/ #24 ,18 ,21 ,22 ,23 and EDI-S3-1 3/#10 ,11 ,7 ,12 ,2 , 13,1 ,14  124  D i a l y s a t e - c o n c e n t r a t i o n - t r a n s i e n t of EDI-S3-12/#6-0  125  E f f e c t o f p a u s e t i m e (x) on c o n c e n t r a t i o n t r a n s i e n t s of t h i r d stack experiments  126  xvi  Fi gure 47  48  49  50  51  52  Page C o n t r a s t i n g pause and no-pause o p e r a t i o n f o r t h i r d stack e x p e r i m e n t s . EDI-S3-13/ #21 ,32  127  E f f e c t of s u p e r f i c i a l v e l o c i t y (v) on f i n a l r e s e r v o i r c o n c e n t r a t i o n s f o r pause and nopause o p e r a t i o n . EDI-S3-13/#l5 ,3 ,16,25,17, 32,18,31 and EDI-S3-13/#20 ,19 ,21  132  E f f e c t of s u p e r f i c i a l v e l o c i t y (v) on f i n a l s e p a r a t i o n f a c t o r s f o r pause and no-pause operation. EDI-S3-13/#l5,3,16,25,17,32,18, 31 and EDI-S3-1 3/#20 ,19 ,21  132  E f f e c t of s u p e r f i c i a l v e l o c i t y (v) on conc e n t r a t i o n t r a n s i e n t s f o r no-pause o p e r a t i o n . EDI-S3-13  133  E f f e c t of s u p e r f i c i a l v e l o c i t y (v) on conc e n t r a t i o n t r a n s i e n t s f o r pause o p e r a t i o n . EDI-S3-13  134  E f f e c t of d i s p l a c e d volume ( 6 ) on f i n a l r e s e r v o i r c o n c e n t r a t i o n s f o r pause o p e r a t i o n . EDI-S3-13/#4,3S2,12,5  138  53  E f f e c t of d i s p l a c e d volume ( 6 ) on f i n a l s e p a r a t i o n f a c t o r f o r pause o p e r a t i o n . EDI-S3-13/#4 ,3 , 2,12,5 138  54  E f f e c t of d i s p l a c e d volume ( 6 ) on concentrat i o n t r a n s i e n t s f o r pause o p e r a t i o n . EDI-S3-13  139  E f f e c t of d i s p l a c e d volume ( 6 ) on r e a l t r a n s i e n t s f o r no-pause o p e r a t i o n  140  55  56  E f f e c t of dead volumes tion  57  transients.  transients.  concentra-  EDI-S2-15  E f f e c t of dead volumes tion  (Sg/S T ) on  time  (S B /<5 T ) on  EDI-S3-1 3  xvi i  143 concentra144  Fi gure 58  Page E f f e c t of dead volumes (Sg/6 T ) on factor transients.  59  60  61  62  63  64  65  66  67  68  69  salting  EDI-S2-15  146  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c 0 ) dialysate concentration t r a n s i e n t s . EDI-S3-1 2  on 149  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c 0 ) on c o n c e n t r a t i o n t r a n s i e n t s . EDI-S3-13  150  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c 0 ) on c o n c e n t r a t i o n t r a n s i e n t s . EDI-S3-13  150  I n t e r n a l m i x i n g . E f f e c t of number of e f f e c t i v e mixing stages (m) on response to step change in feed c o r i c e n t r a t i on: . _ (a) response f u n c t i o n x ( t ) ; ( b ) ' s l o p e ( x ( t ) ) of response curve (di mensi on!ess )  155  Maximum slope stages (m)  156  (x) v s . number of mixing  Step response of second stack (schemati c)  versions 156  E f f e c t of i n t e r n a l d i s p e r s i o n . T r a n s i e n t s of s e p a r a t i o n f a c t o r and d i a l y s a t e product c o n c e n t r a t i o n f o r second stack v e r s i o n s  160  Q u a l i t a t i v e model of the c o n c e n t r a t i o n p r o f i l e s in a c y c l i c e l e c t r o d i a l y s i s process in pause time o p e r a t i o n with i n t e r n a l d i s p e r s i o n and well mixed end r e s e r v o i r s  163  Uniqueness and r e p r o d u c i b i l i t y of f i n a l s e p a r a t i o n f a c t o r f o r second stack experiments  171  Uniqueness of f i n a l s e p a r a t i o n second stack experiments  172  factor for  Dimensionless slope of step response curves f o r second ED c e l l as f u n c t i o n of the number of e l e c t r o d i a l y s i s stages xv i i i  179  Fi gure 70  71  72  73  74  75  76  77  78  79  80  81  82  83  Page E f f e c t of channel separation factor  length (MS) on transients  E f f e c t of channel length concentration transients  (MS) on . . . . .  E f f e c t of channel length current d i s t r i b u t i o n  (MS) on  185  186  187  E f f e c t of channel length (MS) on separation factor transients . . .  188  E f f e c t of channel length current d i s t r i b u t i o n  189  E f f e c t of channel separation factor  (MS) on  length (MS) on transients  E f f e c t of channel length concentration transients  (MS) on  E f f e c t of channel length current d i s t r i b u t i o n  (MS) on  190  191  192  E f f e c t of channel length (MS) on i n i t i a l rate of s e p a r a t i o n (a)  193  E f f e c t of pause time ( x ) on s e p a r a t i o n factor transients  197  E f f e c t of pause time tion transients  ( x ) on concentra198  E f f e c t of pause time distribution  ( x ) on c u r r e n t  E f f e c t of pause time factor transients  ( x ) on s e p a r a t i o n  E f f e c t of pause time distribution  ( x ) on c u r r e n t  .199  200  xi x  201  Fi gure 84  85  86  87  88  89  90  91  92  93  94  95  96  97  Page E f f e c t of pause time (x) on s e p a r a t i o n factor transients.  202  E f f e c t of pause time (x) on concentration transients  203  E f f e c t of pause time (x) on i n i t i a l of s e p a r a t i o n (a)  204  E f f e c t of a p p l i e d separation factor  rate  v o l t a g e (A$) on transients  207  E f f e c t of a p p l i e d v o l t a g e (A$) on separation factor transients  208  E f f e c t of a p p l i e d v o l t a g e (A$) on separation factor transients  209  E f f e c t of a p p l i e d v o l t a g e (A$) on i n i t i a l rate of s e p a r a t i o n (a)  210  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c 0 ) on s e p a r a t i o n f a c t o r t r a n s i e n t s  213  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c 0 ) on s e p a r a t i o n f a c t o r t r a n s i e n t s  214  E f f e c t of i n i t i a l c o n c e n t r a t i o n (co) on s e p a r a t i o n f a c t o r t r a n s i e n t s  215  E f f e c t of d i s p l a c e d volume (6) on separation factor transients  218  E f f e c t of d i s p l a c e d volume (6) on separation factor transients  219  E f f e c t of d i s p l a c e d volume (6) on separation factor transients  220  E f f e c t of dead volumes  (6g/6 T ) on  concentration transients  xx  222  Fi gure 98  99  Page E f f e c t of s u p e r f i c i a l v e l o c i t y separation factor transients  (v) on  E f f e c t of s u p e r f i c i a l  (v)  separation  velocity  224 on  factor transients  225  100  R e p r o d u c i b i l i t y of second stack experiments. . . . 227  101  R e p r o d u c i b i l i t y of second stack e x p e r i m e n t s . . . . 228  102  Overvoltage-current d i a l y s i s stages  103  104  105  106  107  curves  of the  electro232  Time-space d i s t r i b u t i o n l i m i t i n g conditions  of c u r r e n t at  Time-space d i s t r i b u t i o n at l i m i t i n g c o n d i t i o n s  of probe  236 voltage 237  I n f l u e n c e of phase s h i f t (y) on t r a n s i e n t s f o r constant rate o p e r a t i o n  240  E f f e c t of end transients  242  mixing on  concentration  C o n c e n t r a t i o n t r a n s i e n t s of top and bottom r e s e r v o i r c o n c e n t r a t i o n s during p r o d u c t i o n run #3 compared to batch run #26 (low concentration)  245  C o n c e n t r a t i o n t r a n s i e n t s of top and bottom r e s e r v o i r c o n c e n t r a t i o n s during p r o d u c t i o n run #5 compared to batch run #6 (high concentration)  246  109  D e r i v a t i o n of the spacer  253  110  E f f e c t of width r a t i o (6) on s e p a r a t i o n f a c t o r t r a n s i e n t s p r e d i c t e d by Spacer Model . . . . . . .  108  xx i  model equations  275  Fi gure 111  112  Page Comparison of computer s i m u l a t i o n with experimental r e s u l t s on runs #22,23,24 ( f i r s t stack)  276  Comparison of computer s i m u l a t i o n with experimental run #36 ( f i r s t s t a c k )  277  xxii  ACKNOWLEDGEMENT  I wish to thank direction  Dr. D.W. Thompson, under whose  t h i s work was conducted, f o r h i s h e l p f u l  and encouragement throughout t h i s  investigation.  I a l s o wish to thank the f a c u l t y Chemical  guidance  and s t a f f  E n g i n e e r i n g Department of the U n i v e r s i t y  of the  of B r i t i s h  Columbi a. I am indebted to the U n i v e r s i t y of B r i t i s h the N a t i o n a l  Research C o u n c i l , and Environment  Columbia,  Canada f o r  f i n a n c i a l support. I would l i k e Jacqueline  to express my g r a t i t u d e to my w i f e  f o r her c o n t i n u a l  support and forebearance  throughout these y e a r s .  xxi ii  Chapter 1  INTRODUCTION AND SCOPE  Electrodialysis  has achieved  only p a r t i a l  success  in 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 problem areas  in electrodialysis  s c a l e formation design  over other d e s a l t i n g p r o c e s s e s .  The  p r a c t i s e are f o u l i n g and  on the membranes and the r a t h e r complex  of the multicompartment e l e c t r o d i a l y s i s  cell.  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 reduce p o l a r i z a t i o n on the membranes.  effects Lacey  electrodialysis  stacks to  and d e p o s i t i o n of p a r t i c u l a t e s  (1965) invented  an e l e c t r o s o r p t i o n  stack of much s i m p l e r c o n s t r u c t i o n than c o n v e n t i o n a l dialysis  stacks.  In t h i s  apparatus s a l t i s absorbed b y , or  desorbed from, the stack depending on the d i r e c t i o n electric  current.  electro-  The process  of the  resembles packed bed a d s o r p t i o n /  d e s o r p t i o n or i o n exchange systems. Wilhelm et al. (1966) i n v e s t i g a t e d a temperature cycled adsorption-desorption of the f l u i d  process  i n which the d i r e c t i o n  flow was reversed synchronously  1  with  the temperature  2  switching. recently  This  p r o c e s s , known as parametric pumping, has  a t t r a c t e d a great deal  large s e p a r a t i o n s The  of a t t e n t i o n  because very  were e x p e r i m e n t a l l y obtained f o r one  system.  concept of t h i s work i s to combine c y c l i c e l e c t r o -  sorption-desorption temperature c y c l e d The  with the  flow r e v e r s a l employed i n  the  parametric pump.  purpose of t h i s  study i s to analyze the  of a c y c l i c e l e c t r o d i a l y s i s process f o r l a r g e  potential  separations,  to develop s u i t a b l e modules f o r experimental t e s t s , and investigate systematically the  performance of The  three main  the  . closed  material  e f f e c t of process v a r i a b l e s  systems.  of t h i s  t h e s i s has  been arranged in  parts: The  second  which  chapter reviews  are combined  dialysis  process,  presents  some  controlling standard ing) pause  In  cyclic  with  a new  and  the  principles  cyclic  the t h i r d  electrochapter  considerations  and  contrasts  process cyclic  of  the  (parametric operation  the  pump-  (pure  mode).  the. f o u r t h  laboratory fifth  in the  basic  steps  chapter details  apparatus are  chapter presents  experimental  to  results.  of  given,  and  the and  discusses  the  on  3  A mathematical  model  of the standard  operation  of the e l e c t r o d i a l y s i s  developed  in the sixth  includes  a numerical  equations, with  solution  and compares  experimental  chapter,  cyclic  stacks i s which  also  o f t h e model  computer  simulations  results.  Conclus i ons and recommendati ons , based on the results  of t h i s  work, are  contained  i n the seventh  chapter.  Chapter 2  PROCESS PRINCIPLES  This s e c t i o n which  2.1  reviews the b a s i c process  principles  are combined i n 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 .  Electrodi alysis Electrodialysis  in an i o n i c s o l u t i o n . electrodialysis methods"  i s a unit operation f o r separations  Along with other membrane processes  belongs to the c l a s s of " s e l e c t i v e  transport  ( S h a f f e r and M i n t z , 1966). Since e l e c t r o d i a l y s i s  gained commercial  s t a t u s some  f i f t e e n years ago, a l a r g e number of p u b l i c a t i o n s have  appeared  on fundamental  appli-  a s p e c t s , membrane phenomena, p o t e n t i a l  c a t i o n s , process t e c h n o l o g y , and process economics.  Wilson's  monograph (1960) i s the only major work e n t i r e l y devoted to the f i e l d .  Chapters on e l e c t r o d i a l y s i s  d e a l i n g with d e s a l i n a t i o n Sporn  (1966), Popkin  Rickles  (1967), Lacey  are i n c l u d e d i n books  p r o c e s s e s , e.g. S p i e g l e r  (1962,1966),  (1968); or with membrane p r o c e s s e s , e.g. (1972).  4  5  In t h i s work the term e l e c t r o d i a l y s i s the conventional t i o n s , although discussed  2.1.1  i s used in  s e n s e , i . e . r e l a t e d to s o l u t e - s o l v e n t i t i s not  restricted  separa-  to such processes  as  below.  O r i g i n of s e p a r a t i o n . Consider  trolytic  cell  the system i n Figure 1 i n which an  i s d i v i d e d i n t o two  s e l e c t i v e membrane.  Anode and  compartments by an i o n -  cathode are connected to a  power source (not shown i n Figure 1) which maintains electric  elec-  a  constant  p o t e n t i a l d i f f e r e n c e between the e l e c t r o d e s .  the a p p l i e d p o t e n t i a l d i f f e r e n c e (or v o l t a g e ) so that c u r r e n t flows  through the  e l e c t r o l y t e s o l u t i o n of a simple  Suppose  i s l a r g e enough  c e l l , which i s f i l l e d  with  s a l t such as sodium c h l o r i d e  (NaCl). The according  c u r r e n t i s t r a n s p o r t e d by  to t h e i r t r a n s p o r t numbers.  sport numbers i s u n i t y i n the  anions and  cations  The  sum  and  i n the membrane,  solution  of these  v + + v_ = v + + v_ = 1 solution  but  equal  i n the two  (1)  membrane  the t r a n s p o r t numbers of the  sarily  tran-  phases.  i o n i c species  i s not  neces-  Membrane  Figure  I.  The  electrodialysis  principle  7  If selective.  v_ > v_  the membrane i s s a i d to be anion  T h i s means  that the number of anions which c a r r y  c u r r e n t i s l a r g e r i n the membrane than i n the s o l u t i o n . The  number of moles of anions  (n_) which are s e l e c -  t i v e l y t r a n s f e r r e d through an a n i o n i c membrane by e l e c t r o l y s i s i s p r o p o r t i o n a l to the number of Coulombs and the d i f f e r e n c e in t r a n s p o r t numbers (v_ - v _ ) . given by the time i n t e g r a l  The number of Coulombs i s  of the c u r r e n t ( I )  l  tl  I(t)dt  "'o  Thus  V n_ =  - v f ~ F '  1 1  I(t)dt  ,  (2)  0  where  z_  i s the valence  of the a n i o n s , and F i s Faraday's  constant. Because of the c o n d i t i o n of e l e c t r o n e u t r a l i t y , the number of moles of c a t i o n s the membrane i s i d e n t i c a l The  molar c o n c e n t r a t i o n  volume  (V)  i s given as  (n+)  which are r e j e c t e d by  f o r e q u i v a l e n t ions  change  (z_=z+ = z).  (Ac) of the s o l u t i o n  with  8  Ac  =  v  - v I(t)dt  -TTT  (3  o  The two solution-membrane concentration  i n t e r f a c e s experience  changes which are of i d e n t i c a l  of o p p o s i t e s i g n .  magnitude but  The s i d e f a c i n g the cathode i s depleted  and the s i d e f a c i n g the anode i s e n r i c h e d . Enrichment and d e p l e t i o n s e l e c t i v e membrane, which v+  are i n v e r t e d  i s characterized  at a c a t i o n  by the i n e q u a l i t y  > v+ . The c o n c e n t r a t i o n  changes  are c a r r i e d i n t o the  membrane and s o l u t i o n bodies by d i f f u s i o n a l mass t r a n s p o r t . enriched  Demineralized s o l v e n t  and/or  convective  ( d i a l y s a t e ) and  s o l u t i o n ( b r i n e ) may, t h e r e f o r e , be withdrawn  from  o p p o s i t e s i d e s of the membrane. The s e p a r a t i o n  of s o l u t e and s o l v e n t  t h e r e f o r e , from a d i f f e r e n c e i n t r a n s p o r t species  i n membrane and s o l u t i o n .  s e l e c t i v i t y , and i s the s u b j e c t  2.1.2  Membrane  This  originates,  number of i o n i c  difference is called  of the f o l l o w i n g  section.  selectivity.  Commercially a v a i l a b l e membranes are almost e x c l u s i v e l y of the resinous  ion-exchange t y p e .  The s e l e c t i v i t y i s  9  achieved by i n c o r p o r a t i n g  a large number of f i x e d i o n i c  groups  * in a matrix of i n e r t m a t e r i a l . The  presence of a high  groups has an e x c l u s i o n  concentration  of f i x e d  ionic  e f f e c t on ions with the same s i g n as  these groups. According to the Gibbs-Donnan p r i n c i p l e , e q u i l i b r i u m between s o l u t i o n and membrane phase means e q u a l i t y of the chemical and  p o t e n t i a l s of the s o l u t e .  neglecting  For a f u l l y  ionized  salt  osmotic pressure terms, one has a  +  a+  a_  • a_  _ a  = a+  +  • a_  where the a's denote i o n a c t i v i t i e s  (4)  and the a's s t o i c h i o m e t r i c  c o e f f i ci ents. In s i m p l i f i e d by  concentrations  form, when a c t i v i t i e s  and assuming e q u i v a l e n t  ions  are r e p l a c e d equation (4)  reduces to  c+  • c  = c+ • c  (5)  * An e x c e l l e n t summary of p r e p a r a t i v e methods found i n the patent l i t e r a t u r e i s given by Placek (1970).  10  In an anion  s e l e c t i v e membrane i n which  groups of c o n c e n t r a t i o n  X  anionic  are p r e s e n t , the e l e c t r o n e u t r a 1 i t y  c o n d i t i o n has the form c  The i o n i c c o n c e n t r a t i o n s solute concentration  = X + c,  (6)  i n the s o l u t i o n  (c)  because  are i d e n t i c a l  to the  of the assumption of  e q u i v a l e n t anions and c a t i o n s : (7)  c = c+ = c Combining  ( 5 ) , ( 6 ) and ( 7 ) one f i n d s c+  • (X + c + ) = c  D i v i d i n g both s i d e s by the f i x e d  :  (8)  ion concentration  yields  equation (9)  1 +  +  (9)  T  which may be approximated f o r d i l u t e  solutions  ( c + << X)  by  (io) Equation in an anion  (10) shows that the c a t i o n  concentration  s e l e c t i v e membrane v a r i e s as the square of the  11  solution  concentration  and  ing the number of f i x e d The  may  be  kept very  i o n i c groups  (X)  small  i n the membrane.  c o n t r i b u t i o n of c a t i o n s to the c u r r e n t flow i s  a c c o r d i n g l y s m a l l , s i n c e the f l u x of c a t i o n s electric  potential gradient  ->•  j  where  u~+  +  = - u+  (j+)  • c+  • z+  i s the m o b i l i t y of the  The  as the  isolated  actual  and  of other s p e c i e s  dependences.  (11)  c a t i o n s i n the membrane.  pressure results  gradients i n very  c o n d i t i o n s and  p r o j e c t those r e s u l t s dominate the present The t e r i z e d by defined  complicated  be  aspects.  found i n Wilson's  Guides (1960)  (1962) books.  A l s o , most of the steady-state  as well  I t i s beyond the scope of t h i s work to  l i t e r a t u r e may  or i n H e l f f e r i c h ' s  (11) i s  to a p o t e n t i a l g r a d i e n t .  account f o r the various treatments of these to the p u b l i s h e d  an  • grad($)  ion f l u x due  presence of c o n c e n t r a t i o n  as the m i g r a t i o n  along  (grad(O)) i s  It must be kept in mind that equation written  by i n c r e a s -  results  reported  are l i m i t e d  i t i s d i f f i c u l t or i m p o s s i b l e  to unsteady-state  to to  s i t u a t i o n s which  process.  selectivity  of the membranes i s o f t e n  a quantity called  ( W i l s o n , 1960), as  charac-  p e r m s e l e c t i v i t y (P) which i s  12  - v  v P =  ~ - v+  1  (12)  where p o s i t i v e s u b s c r i p t s r e f e r to c a t i o n s e l e c t i v e membranes and  negative  signs to anion  selective  ones.  The permselectivity therefore expresses the increase in transport number over the value in free solution as a fraction of the maximum possible increase3 i.e. the increase that would be observed in the case of an ideally selective membrane ( W i l s o n , 1960).  2.1.3  Transport The  taneously catalogued processes  processes  various  through  through i o n - s e l e c t i v e membranes.  t r a n s p o r t processes  which occur  simul-  i o n - s e l e c t i v e membranes are b r i e f l y  in this  section.  f o r an anion  a l y t i c separation.  Figure 2 i l l u s t r a t e s  s e l e c t i v e membrane during  I t a l s o shows the l a t e r a l  these electrodi-  concentration  profi1e. a) preference others  Gegen-ion  f o r some ions  (co-ions).  gegen-ions  transport:  The membrane e x h i b i t s a  (gegen-ions) and d i s c r i m i n a t e s  I d e a l l y the t o t a l  against  c u r r e n t i s c a r r i e d by  alone. b)  Co-ion  the c u r r e n t flow  transport:  Any co-ion p a r t i c i p a t i o n i n  uses energy but y i e l d s  no s e p a r a t i o n .  13  Membrane Electric  Field  *~ Co-ion  Transport  Solute  Diffusion  1-  I  f  Gegen-ion  Transport  Osmosis + Electroosmosis  Distance  Figure  2.  Brine  Transport selective  processes across membrane.  an  anion-  Oialysate  -FT \ \ \ \ \ \ \ \ \ \ \ \ Rinse  Cathode  Rinse Feed  Figure  3.  Multlcell  electrodialysis  stack  (schematic).  14  So I u t e  c)  A concentration  diffusion:  develops i n s i d e the membrane as a r e s u l t of the changes.  Solute d)  dilutes  d i f f u s e s back along  Solvent  the e n r i c h e d  transfer  due  this  to  i n t e r f a c e , but  and  the  ion solvation  experiences  frictional f)  Solvent  The  to each  ionic  of the membrane.  i n the membrane  f o r c e s imparted by  Osmos i s :  usually  t h i s depends upon the  a c t u a l degree of s e l e c t i v i t y  EIectro-osmos i s:  e)  concentration  gradient.  e f f e c t i v e number of s o l v e n t molecules attached species  gradient  the moving  difference in solvent  ions.  activities  in the a d j o i n i n g s o l u t i o n s f o r c e s s o l v e n t through the membrane.  Osmotic e f f e c t s Wilson  these e f f e c t s  and  reduce the extent of  separation.  (1960) presented a d e t a i l e d d i s c u s s i o n of Schlbgel  (1964) wrote an e x c e l l e n t monograph  on membrane t r a n s p o r t phenomena i n general  ( i . e . not  restricted  to i o n - s e l e c t i v e membranes).  2.1.4  Multicell The  was  e l e c t r o d i a l y z e r and  multicell  its applications.  e l e c t r o d i a l y z e r which i s p r e s e n t l y  proposed by Meyer and  Strauss  (1940).  Figure  used  3 is a  _  In t h i s d i s c u s s i o n the e l e c t r o d e r e a c t i o n s have been d i s r e g a r d e d because they provide merely a l i n k between e l e c t r o n i c and e l e c t r o l y t i c c u r r e n t t r a n s p o r t in e l e c t r o d i a l y s i s systems. The energy requirements to maintain the e l e c t r o d e r e a c t i o n s are only a small f r a c t i o n of the t o t a l energy input in a m u l t i c e l l arrangement.  15  sketch  of such a m u l t i c e l l  channels cation  arrangement.  (1 ,2,3,••• ,n) i s formed by an array of i n t e r l e a v e d  (c) and anion  i s placed  (a) s e l e c t i v e membranes.  between f l a t e l e c t r o d e s .  (1 ,3 ,5 , ••• ,Figure  This  stack  Feed s o l u t i o n flows up-  ward through the s t a c k , becomes depleted  Figure  A number of p a r a l l e l  3 ) , and e n r i c h e d  i n one s e t of channels  i n another s e t ( 2 , 4 , 6 , » « « ,  3 ) . D i a l y s a t e and b r i n e have to be c o l l e c t e d and drawn  off separately.  Electrode  r e a c t i o n products are removed by  independent r i n s e streams ( F i g u r e 3 ) . I t i s not e s s e n t i a l to have both anion and c a t i o n s e l e c t i v e membranes i n the s t a c k . In the t r a n s p o r t d e p l e t i o n s e l e c t i v e , membranes r e p l a c e see  process n e u t r a l , or non-  the anionic ones i n the s t a c k ,  e.g. Kollsman (1959), Lacey (1962), Lang et aZ.(1968),  Huffman  (1969). Only one kind of s e l e c t i v e membranes form the stack  of the e l e c t r o d e c a n t a t i o n intermediate  l o c a t i o n to the flow  achieved by d e n s i t y Kollsman  process.  Feed i s i n t r o d u c e d channels.  Separation i s  induced c o n v e c t i o n , see F r i l e t t e  (1958), B i e r (1959), F r i e d l a n d e r and R i c k l e s Electrodialysis  s o l u t e s from s o l v e n t .  i s conventionally  at an  (1957), (1965).  a p p l i e d to separate  The membranes d i s c r i m i n a t e a l s o between  ions of d i f f e r e n t charge and s i z e but of the same s i g n . Based on t h i s membrane  property, p u r i f i c a t i o n  processes have  16  been proposed f o r mixed e l e c t r o l y t e s o l u t i o n s by G i l l 11 and  ( 1956), and On  s e v e r a l others  ( W i l s o n , 1960).  i n which monovalent ions  (above a l l NaCl) are s e l e c t i v e l y extracted and by e l e c t r o d i a l y s i s  (Tsunoda, 1965;  concentrated  Yamane, 1969).  Exchange r e a c t i o n s i n the e l e c t r o l y t i c of a p p l i c a t i o n  Electrodialysis cesses  and  n a t i o n and  conventional pollution  problems with  and  a commercial s c a l e , t a b l e s a l t i s produced from  sea water i n Japan by a process  another f i e l d  Dewey  ( W i l s o n , 1960:  competes with  Cohan, 1965).  other membrane pro-  s e p a r a t i o n techniques  control.  state is  i n water  desali-  It i s a t t r a c t i v e whenever  minor i m p u r i t i e s ( l e s s than 10,000 ppm)  arise  ( F r i e d l a n d e r , 1966).  2.1.5  Concentration  polarization  in s t e a d y - s t a t e The and  solution  problems  electrodialysis.  causes l o c a l  i n the v i c i n i t y  controlled  other  d i f f e r e n c e i n t r a n s p o r t numbers between membranes  at the i n t e r f a c e s , and  s o l u t i o n may  and  d e p l e t i o n and  lateral  concentration  of the membranes.  l i m i t these layers.  enrichment of s o l u t e  Stirring  concentration  gradients of the  gradients  to  develop  bulk diffusion  I f the concept of a Nernst l a y e r i s  adopted,the s t e a d y - s t a t e  c o n d i t i o n f o r the s o l u t e f l u x at an  17  anion  s e l e c t i v e membrane corresponds to  ^^-irr see  1  c  -JK  Figure 4 and compare with  where  (c  zero.  (13  »  equation (3) 2  i  current density  [ampere/cm ]  D  diffusion  [cm /sec]  6  Nernst f i l m t h i c k n e s s  Co  bulk  concentration  [g-moles/1itre]  c',c"  solution concentrations at the membrane s u r f a c e  [g-moles/1itre]  alone, a l i m i t i n g  The corresponding  2  coefficient  I f the l a y e r t h i c k n e s s conditions  c  - °> = f « - ;>  [cm]  i s c o n t r o l l e d by the flow  case e x i s t s when  limiting  c^  current density  becomes ^ ^ n  m  is  Wltm-.  "  , • ° C  (  In aqueous s o l u t i o n s , no true l i m i t e x i s t s because or hydrogen ions w i l l low  concentrations  as water  1  4  hydroxyl  take p a r t i n the i o n i c t r a n s f e r at very  of s o l u t e .  T h i s i s u s u a l l y r e f e r r e d to  splitting. Effects  of c o n c e n t r a t i o n  branes on the e l e c t r o d i a l y s i s  polarization  process  are always  of the memundesirable:  )  18  Figure  4.  Concentration membrane.  Figure  5.  Thermal  polarization  parametric  o f an  pumping.  ion-selective  19  a) requires  larger b)  one,water sibly  The mass t r a n s f e r membrane  are l i m i t e d .  This  areas.  If t h e c u r r e n t  splitting  rates  density  is close to the  reduces t h e c u r r e n t  efficiency  limiting  and p o s -  t h e pH o f t h e p r o d u c t .  increased  c)  The s t a c k  resistance  d)  The Donnan p o t e n t i a I , (He I f f e r i c h ,  and t h e e f f e c t i v e  stack  is increased.  voltage  is  1962) i s  therefore  + reduced. The by  Wilson  e a r l y work on t h i s phenomenon was summarized  (1960).  in the f o l l o w i n g  The more recent l i t e r a t u r e may be three  divided  classes:  1.  Fundamental a s p e c t s of 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 p h e n o m e n a , Cook ( 1 9 6 1 , 1 9 6 5 ) ; Mandersloot (1965); S p i e g l e r (1971); F o r g a c s ( I 972) .  2.  T h e o r e t i c a l p r e d i c t i o n of the e f f e c t i v e s t a c k r e s i s t a n c e m a i n l y b a s e d upon s o l u t i o n s of t h e flow f i e l d i n t h e channels, B e l f o r t (1968); Sonin (1968); S o l a n ( 1 9 6 9 , 1 9 7 1 ) ; P n u e l i ( 1 9 7 0 ) ; Mas ( 1 9 7 0 ) , and an e x p e r i m e n t a l s t u d y o f t h e hydrodynamic c o n d i t i o n s e x i s t i n g in a c t u a l ED s t a c k s ( B e l f o r t , 1972).  Compared to h o r i z o n t a l across the f i l m s . See  equation  concentration p r o f i l e s  ( 2 4 ) , page 53 f o r d e t a i l s .  20  3.  E n g i n e e r i n g s t u d i e s u s i n g mass t r a n s f e r correlations to characterize individual s t a c k p e r f o r m a n c e s , e.g. Rosenberg (1957); Cowan ( 1 9 5 9 ) ; W e i n e r ( 1 9 6 4 ) ; M a n d e r s l o o t (1965); Kitamoto (1970,1971); Sata (1969); Yamane ( I 969a ) .  Concentration p o l a r i z a t i o n  i s often  other problems in actual e l e c t r o d i a l y s i s  Scale  formation.  Supersaturation  cause some components of the the  membrane s u r f a c e .  B i c a r b o n a t e s and channels of the  Fouling  and  linked  practise.  l o c a l pH  changes  feed water to p r e c i p i t a t e  In p a r t i c u l a r  Calcium  and  i s caused by  suspended s o l i d s  has  accumulate on  stack r e s i s t a n c e .  the  membrane s u r f a c e ,  Korngold  commercial anion s e l e c t i v e  been observed t h a t f o u l i n g  (1970) pre-  Cook, 1965;  i s apparently r e s t r i c t e d  under a c i d i c  conditions  of  It to  organic  (Kressman,  1969;  S o l t , 1965).  Po i son i ng i s d e f i n e d as fixed  fouling  membranes.  a n i o n i c membranes, mainly because p r e c i p i t a t i o n matter occurs often  concentrate  present i n many w a t e r s .  sented a comprehensive experimental study of the behaviour of ten  at  (Matz, 1965).  These p a r t i c l e s d e p o s i t and thus i n c r e a s i n g the  may  Magnesium  Sulphatesmay form d e p o s i t s i n the stack  with  a reaction  i o n i c groups of the  of i o n i c s p e c i e s with  membrane m a t r i x .  the  There seems to  be  21  a close  r e l a t i o n to the f o u l i n g mechanism and i t i s e x p e r i -  mentally d i f f i c u l t to d i s t i n g u i s h  between  both.  Kobus  (1972)  reported cases of soap p o i s o n i n g i n which a n i o n i c membranes e v e n t u a l l y became c a t i o n  s e l e c t i v e a f t e r complete p o i s o n i n g .  These membranes d i d not only lose but  their selective  properties  a l s o showed an i n c r e a s e i n r e s i s t i v i t y . Other problems in p r a c t i c a l ED o p e r a t i o n may  summarized  as f o l l o w s  (Matz, 1965; W i l s o n , 1960;  be  Furukawa,  1968; Tsunoda, 1965; C a l v i t , 1965): (i) (ii)  E l e c t r i c a l leakage through di st r i b utors.  manifold  H y d r a u l i c and e l e c t r i c a l l e a k a g e due to gasketting difficulties.  (iii)  I r r e g u l a r f l o w d i s t r i b u t i o n between c h a n n e l s , and a r e a s o f s t a g n a t i o n i n individual channels.  (iv)  A l i g n m e n t d i f f i c u l t i e s and p l a s t i c d e f o r m a t i o n o f sealant as w e l l as o f t h e memb r a n e s .  The l a t t e r problems are b a s i c a l l y mechanical and design d i f f i c u l t i e s which are r e l a t e d construction  2.1.6  of c o n v e n t i o n a l  Current r e v e r s a l  e l e c t r o d i a l y s i s equipment.  techniques.  Current r e v e r s a l reduce s c a l e  to the complicated  has been proposed as a measure to  formation, fouling  in two forms (Matz, 1965).  and p o i s o n i n g and i s employed  22  Reversed p o l a r i t y .  At p e r i o d i c i n t e r v a l s . ( u s u a l l y  hours) the e l e c t r o d e p o l a r i t y  i s r e v e r s e d , e i t h e r f o r a short  time during which the e f f l u e n t s a r e g u l a r c y c l e with  are u s u a l l y d i s c a r d e d , or i n  continuous p r o d u c t i o n .  o p e r a t i n g method r e q u i r e s interchange dialysate. ful  p i p i n g f o r b r i n e and  the periods between d i s m a n t l i n g  stacks when operated  current.  in this  The usual  c y c l e periods  counterpulses The  of the  current d i r e c t i o n  is periodically  inverted  polarity.  are i n the order o f s e v e r a l seconds, with  lasting  fractions  b a s i c idea of t h i s  the c o n c e n t r a t i o n  success-  mode.  i n t e r r u p t e d by s h o r t c u r r e n t pulses with The  The l a t t e r  Matz s t a t e s that many p l a n t s are p a r t i a l l y  i n extending  Pulsed  several  of a second only  technique  (Matz, 1962).  i s to f r e q u e n t l y d i s t u r b  l a y e r s , s i n c e i t has been found that s c a l e  forming p r e c i p i t a t e s  as well  some i n d u c t i o n p e r i o d before  as f o u l i n g c o l l o i d s  require  permanent d e p o s i t i o n  ( S p i e g l e r , 1961; K o r n g o l d , 1970).  Tests  Webster, South Dakota, showed some success  of t h i s  occurs method i n  in scale  at the p r i c e of a moderate r e d u c t i o n i n c u r r e n t  reduction  efficiency  ( C a l v i t , 1965).  Electrosorption-desorption. investigated technique.  a process  Lacey (1965,1968) conceived and  which i s based on the reversed  The standard  electrodialysis  stack was  polarity  converted  23  i n t o an a b s o r p t i o n s t a c k , which contained flow channels.  only one s e t of  The channels were separated  sheets which c o n s i s t e d of an anion  by t h r e e - l a y e r  and a c a t i o n s e l e c t i v e  membrane and a n o n - s e l e c t i v e inner l a y e r or c o r e . composite sheets were sealed along They served  compartments f o r  of the a p p l i e d e l e c t r i c  Feed s o l u t i o n , which flowed became d e m i n e r a l i z e d  the four edges.  as temporary storage  s o l u t e during one p o l a r i t y  These  c o n t i n u o u s l y through the c h a n n e l s ,  and was drawn o f f as d i a l y s a t e  f o r the d u r a t i o n of t h i s  potential.  product  a b s o r p t i o n part of the c y c l i c  o p e r a t i on. The  p o l a r i t y was reversed before  the compartments  reached a s t a t e of s a t u r a t i o n , i . e . before c a p a c i t y was f i l l e d .  their  storage  Subsequent r e g e n e r a t i o n of the membrane  compartments e n r i c h e d the feed s o l u t i o n , and the r e s u l t i n g b r i n e e f f l u x was u s u a l l y r e j e c t e d .  Cycle times ranged  between 15 minutes and one hour. This stack m o d i f i c a t i o n has some i n t e r e s t i n g consequences: F i r s t , the process nature  i s no longer continuous i n  but resembles more a f i x e d bed a d s o r p t i o n  o p e r a t i n g with  an e l e c t r o c h e m i c a l p o t e n t i a l  system  driving  force.  D i a l y s a t e and b r i n e are produced s u c c e s s i v e l y i n a s i n g l e set of channels i n s t e a d of s i m u l t a n e o u s l y as i n a c o n v e n t i o n a l  multicell  i n adjacent  electrodialyzer.  channels  24  Second, the stack has  less  leakprone  i s much s i m p l e r i n d e s i g n .  distribution  m a n i f o l d s , a s m a l l e r number  of c h a n n e l s , and improved membrane u t i l i z a t i o n the membranes are not used to separate and  may t h e r e f o r e be as small  It  factors  since  b r i n e and d i a l y s a t e  as the a c t i v e  i n t e r i o r of the  stack. T h i r d , the r e g e n e r a t i o n additional savings  2.2  energy, the cost of which must be balanced  resulting  Parametric  from the s i m p l i f i e d  The  with  cell  and S i m i l a r  Processes  term parametric  pumping was i n t r o d u c e d by Wilhelm  f o r a temperature c y c l e d a d s o r p t i o n - d e s o r p t i o n  r e v e r s i n g flow d i r e c t i o n .  cycled  (1967) c a l l e d h e a t l e s s a d s o r p t i o n and  employed to upgrade hydrogen.  Wilhelm and h i s co-workers  i n v e s t i g a t e d temperature c y c l e d a d s o r p t i o n of l i q u i d s theoretically  process  Skarstrom (1959) had used a  s i m i l a r p r o c e s s , b e f o r e , to dry a i r i n a pressure o p e r a t i o n which A l e x i s  against  design.  Pumping, Heatless A d s o r p t i o n  C y c l i c Separation  (1966)  step u s u a l l y r e q u i r e s -  and e x p e r i m e n t a l l y :  both  Wilhelm and Sweed (1968),  Wilhelm et al. (1968), Sweed and Wilhelm (1969), Rolke and Wilhelm (1969).  This system has a l s o been s t u d i e d by Wakao  et al. (1968), P i g f o r d et al. (1969), A r i s Lin  (1969), Horn and  (1969), H a r r i s (1970), Baker I I I (1970), Gregory and  25  Sweed (1970), Rhee and Amundson (1970), Sweed and (1971) , Chen and H i l l (1972) .  (1971), Chen et al.  Temperature c y c l e d gas  gated by Jenczewski (1972).  Gregory  (1972), Butts et  a d s o r p t i o n has been  investi-  and Myers (1968,1971) and P a t r i c k et  S a b a d e l l and Sweed (1970) showed the  al.  al.  applicability  of the parametric pumping p r i n c i p l e to pH c y c l e d packed bed adsorption. Batta  Heatless a d s o r p t i o n was  r e v i v e d by Eluard  (1971), and Shendelman and M i t c h e l l  (1972).  Although Sweed (1971) presented an e x c e l l e n t on parametric pumping up to the year 1970 b a s i c concept and P i g f o r d et al.'s are b r i e f l y tion  (1970),  review  i n c l u s i v e , the  (1969) e q u i l i b r i u m model  i n t r o d u c e d i n the next s e c t i o n .  Heatlass adsorp-  and some other c y c l i c s e p a r a t i o n processes are  subse-  quently r e l a t e d to parametric pumping.  2.2.1  Parametric pumping. Consider the c l o s e d system  of a j a c k e t e d  i n F i g u r e 5.  t u b u l a r column and two  end  It consists  reservoirs.  The  column i s packed with a bed of a d s o r b e n t , the temperature which i s c o n t r o l l e d by the temperature The  of the j a c k e t  of  fluid.  mixture to be separated i s contained i n the bottom  r e s e r v o i r No. 2 and system  i n the void spaces of the column.  The  i s a c l o s e d one, i . e . there i s n e i t h e r feed of f r e s h  solution  nor removal  of p r o d u c t s .  This s i t u a t i o n i s  26  analoguous to the f a m i l i a r t o t a l r e f l u x operation of a d i s t i l l a t i o n column, and i t w i l l , t h e r e f o r e , be r e f e r r e d to as t o t a l r e f l u x mode. Most workers describe a parapump cycle of the t o t a l r e f l u x system, shown i n Figure 5, as a sequence of these steps: (i)  Displace  upward t h r o u g h  a heated  (ii)  Displace  downward t h r o u g h  bed.  a cooled  bed.  I n i t i a l l y the bed i s u s u a l l y hot, the concentration i s uniform, and s o l u t i o n and adsorbent are everywhere i n equilibrium.  I f the coupled c y c l i n g of bed temperature and  f l u i d displacement i s c a r r i e d out,the average concentration of the e f f l u e n t s from top and bottom r e s e r v o i r s w i l l change as function of the number of cycles ( t r a n s i e n t s ) . During the f i r s t upward displacement,the concentrations remain at t h e i r i n i t i a l e q u i l i b r i u m values.  After this  displacement i s complete, the temperature i s lowered and the flow moves downward.  Solute r e d i s t r i b u t e s between the phases  and s o l u t i o n which i s depleted i n adsorbate emerges from the  bottom end of the column. The second cycle begins by reversing the flow d i r e c -  tionand r a i s i n g the temperature to the i n i t i a l l e v e l .  If  conditions are properly chosen,the top e f f l u e n t w i l l be enriched i n adsorbate, and the bottom e f f l u e n t w i l l be even f u r t h e r depleted during t h i s second c y c l e .  27  Very l a r g e and  concentration  differences  between  top  bottom e f f l u e n t s have been e x p e r i m e n t a l l y achieved  for  repetetive  c y c l i n g by Wilhelm (1968a) f o r a toluene-heptane-  silica  system.  gel  d e f i n e d as top  the  The  separation  r a t i o of the  f a c t o r (ns) which has  average e f f l u e n t  compared to bottom, i n c r e a s e d beyond 10 Favourable c o n d i t i o n s  s  concentrations, in t h i s system.  f o r temperature c y c l e d  m e t r i c pumping of l i q u i d s i n packed bed  been  adsorption  para-  columns  are: 1.  L a r g e t e m p e r a t u r e c h a n g e s and t e m p e r a t u r e sensitive adsorption isotherms.  2.  Packing with  3.  No b r e a k t h r o u g h  4.  E q u i l i b r i u m between s o l u t i o n  5.  Large heat t r a n s f e r  6.  Minimal  7.  Synchronous s w i t c h i n g of and f l u i d d i s p l a c e m e n t .  axial  et al.  Pigford which must be  regarded as  separations.  This  i t d e s c r i b e s the form.  I t has,  large adsorption of  capacity.  concentration  fronts.  and a d s o r b e n t .  coefficients.  dispersion. bed  temperature  (1969a) developed a simple model l i m i t i n g case f o r parametric pumping  "equilibrium  model" has  concentration transients  the  advantage that  in closed  t h e r e f o r e , been used e x t e n s i v e l y  b a t c h , semicontinuous and  simulate  continuous systems ( G r e g o r y ,  Chen, 1970,1972; B u t t s , 1972;  Shendelman, 1972).  Gregory (1970) showed that t h i s model i s u s u a l l y to d e s c r i b e experimental  to  mathematical  results  quantitatively.  1970;  However, inadequate  28  The  following  assumptions c h a r a c t e r i z e  the e q u i l i b -  rium theory: (a)  instantaneous interphase e q u i l i b r a t i o n , i . e . no mass t r a n s f e r r e s i s t a n c e ,  (b)  linear  (c)  no a x i a l  (d)  instantaneous  Upon close  equilibrium  isotherms,  dispersion, temperature  inspection  changes.  of these assumptions, one  sees that they account f o r c o n d i t i o n s 4, 5, and 6 above. remaining c o n d i t i o n s may For  be e x t e r n a l l y  conservation  £  I  dz  +  8 cr f 3t  +  void volume  temperature square wave, the mass  equation ( f o r a s l i c e  dc  where  set by the experimenter.  square wave displacement of one  combined with a synchronous  The  of t h i c k n e s s  /-. \ (1 -e) . e  dz)  3c„ s = 0 9t  velocity  (15)  v  constant i n t e r s t i t i a l  Cp  fluid  concentration  [g-moles solute/ 3 cm solution]  c„ s  solid  concentration  [g-moles solute/ 3 cm solid]  z  direction  t  time  e  f r a c t i o n a l void volume of the packing  of flow  [cm/sec]  [cm] [sec]  29  becomes  9c  9c  f  f  Here cs = M • cf  (17)  M = l i n e a r e q u i l i b r i u m constant and m =  The  —  M  hyperbolic d i f f e r e n t i a l  equation  s o l v e d by the method of c h a r a c t e r i s t i c s ( A c r i v o s , 1956).  The  are s t r a i g h t l i n e s .  characteristics Since  cf  (16)  may  be  f o r each h a l f c y c l e  in the  ( z , t ) plane  remains constant along  any  c h a r a c t e r i s t i c,  ^dt = T1 - +T —m  The may  be  (18)  movement of c o n c e n t r a t i o n  displayed g r a p h i c a l l y .  The  waves i n the  analytical  thus based on keeping t r a c k of c o n c e n t r a t i o n travel  through the  bed  solutions bands as  they  bed.  Figure 6 i s a h y p o t h e t i c a l example of a c l o s e d system.  The  bed  number of c y c l e s .  length The  i s shown as o r d i n a t e l i n e s have  slopes  against  are  the  Figure  6:  C h a r a c t e r i s t i c s of batch s e p a r a t i o n v i a t h e o r y of p a r a m e t r i c p u m p i n g .  equilibrium o  31  d u r i n  T T i  9  f i rst half cycles ,  HOT and  1  +  ~m  v  — COLD  upward.  t h e n e t m o t l  m  Since is  during second h a l f c y c l e s .  <  H 0 T  m  coLD'  '  o n  °f the bands  The top or bottom e f f l u e n t c o n c e n t r a t i o n  is a  mixture of bands which o r i g i n a t e i n known c o n c e n t r a t i o n s of preceding  cycles.  emerges with  the same c o n c e n t r a t i o n  A f t e r an i n i t i a l on the i n i t i a l Aris equations top  A band which t r a v e l s  i t had when i t e n t e r e d .  s t a r t - u p p e r i o d the bands no longer  (1969) has shown that a p a i r of d i f f e r e n c e  always e x i s t s , which completely  number of c y c l e s .  d e s c r i b e average  as f u n c t i o n s of the  Gregory (1970) extended the a n a l y s i s to  f o r dead volumes  i n the top and bottom r e s e r v o i r s and  displacements of l e s s than one void  volume.  The common r e s u l t of these the p r e d i c t i o n that the c o n c e n t r a t i o n column  depend  concentration.  and bottom product c o n c e n t r a t i o n s  allow  from bottom to top  analytical  solutions is  at the bottom of the  tends to that of pure s o l v e n t as the number of c y c l e s  increases.  Figure 7 i s a p l o t of the normalized  bottom c o n c e n t r a t i o n equations  for m  t r a n s i e n t s according  = 0.227 and m _  = 0.5.  top and  to P i g f o r d et al. 's  32  Figure  7.  Concentration t r a n s i e n t s for e q u i l i b r i u m theory o f p a r a m e t r i c pumping ( a c c o r d i n g t o P i g f o r d , 1969a).  33  In r e a l i t y d i s p e r s i v e e f f e c t s heat t r a n s f e r rates linear equilibrium  and f i n i t e mass and  l i m i t the s e p a r a t i o n , as a l s o may nonisotherms (Rhee and Amundson, 1970).  Wilhelm and h i s co-workers  developed models which  take some or a l l of those n o n - i d e a l i t i e s  into  account  (Wilhelm, 1966; Wilhelm and Sweed, 1968; Wilhelm et al. , 1968; Sweed and Wilhelm, 1969; Rolke and W i l h e l m , 1969; Sweed and Gregory, 1971).  T h e i r numerical s o l u t i o n s  agreed  q u i t e well with experimental r e s u l t s .  2.2.2  Other c y c l i c  Heatless  operations.  adsorption,  the o r i g i n a l  cyclic  adsorption  system, works on the pressure dependence of the gas a d s o r p t i o n equilibrium.  The system i s much more a t t r a c t i v e  practical  point of view because  initiated  almost i n s t a n t l y  cooling  in thermally forced Skarstrom's  illustrated  pressure changes  from a may be  compared to the slow h e a t i n g and systems.  (1959) double column arrangement i s  i n Figure 8.  When column A adsorbs under high p r e s s u r e , column B i s backwashed under low pressure with a purge stream of dry a i r .  Very high p u r i f i c a t i o n s  are achieved when the  v o l u m e t r i c purge flow rate exceeds the feed flow Shendelman (1972) obtained s i m i l a r r e s u l t s  rate.  f o r a system  34  C0 2  i n He, as d i d A l e x i s  c a r b o n s , and Batta  (1967) with  (1971) with  the system H2  i n hydro-  O2 i n a i r .  Dry A i r Valve I _ 1—t=*<J  T 1  T  Valve 2  ><—,  Purge V a l ve  Wet A i r  4  4 Way V a l v e  Wet A i r  Figure  8:  Heatless adsorption Skarstrom (1959).  Heatless  a i r drying  system,  a d s o r p t i o n must be considered  o p e r a t i o n which resembles more a conventional s e p a r a t i o n or a f i x e d pump.  used by  a one-cycle  chromatographic  bed ion exchange than a parametric  The r e g e n e r a t i o n step f o r each column i s a counter  35  c u r r e n t backwashing product.  This  Cyclic was  with a purge stream from the other column's  i s the only r e f l u x i n the system.  zone adsorption  C y c l i c zone  devised by P i g f o r d et al. (1969b).  shown i n Figure 9, c o n s i s t s tion  —  columns.  The  of two  The  adsorption  system, which i s  temperature c y c l e d adsorp-  temperature c y c l e s of the columns are one-  h a l f c y c l e out of phase, i . e . one adsorbs ( c o l d ) w h i l e the other one desorbs (hot) and v i c e v e r s a .  A four-way  valve i s  switched synchronously with the temperature of the beds.  Purified  Feed  Figure 9.  C y c l i c zone a d s o r p t i o n I 969b).  (proposed  by P i g f o r d ,  36  O b v i o u s l y , the two  be considered  as  independent s e p a r a t o r s which have been synchronized  in  such a way  as to achieve  twin  columns may  'continuous  production  streams of d i f f e r e n t c o n c e n t r a t i o n s , one than t h a t of the  f e e d ' ( P i g f o r d , et al.3  higher  of and  1969b).  r e f l u x between the columns, which are regenerated solution  in co-current  one  lower  There i s no using  feed  flow.  Electrosorption-desorpt-Con The  two  ( L a c e y , 1965 ,1968)  —  e 1 e c t r o s o r p t i o n p r o c e s s , d e s c r i b e d i n S e c t i o n 2.1.6, i s  a l s o a one-cycle  s e p a r a t i o n process  analoguous to a s i n g l e alternately  without r e f l u x .  It is  column c y c l i c zone a d s o r b e r , which  produces e n r i c h e d and  depleted  solution.  Chapter 3  EFFECT OF FINITE MASS TRANSFER RATES ON PARAMETRIC PUMPING AND PURE PAUSE OPERATION  3.1  General The  strates  e q u i l i b r i u m theory of parametric  the process  the a n a l y t i c a l  p r i n c i p l e with great s i m p l i c i t y .  solutions  provided by t h i s  t a t i v e l y with experimental  systems (Gregory  and  illuAlthough  theory agree  quali-  r e s u l t s on some a d s o r p t i o n separa-  t i o n systems, the equations real  pumping  are not s u i t a b l e f o r d e s i g n i n g  Sweed, 1970).  In p a r t i c u l a r  e q u i l i b r i u m theory n e g l e c t s a l l r a t e p r o c e s s e s .  Rolke  the and  Wilhelm (1969) a t t r i b u t e d the small s e p a r a t i o n s obtained  on  a NaCl/mixed ion exchange r e s i n system f o r water d e m i n e r a l i z a t i o n to slow r a t e s of i n t r a p a r t i c l e mass t r a n s f e r . An  electrodialysis  process may  be operated  with  comparatively high mass t r a n s f e r r a t e s at c o n c e n t r a t i o n s far  removed from e q u i l i b r i u m and may  t h e r e f o r e be b e t t e r  represented by a rate model than by the e q u i l i b r i u m Two models w i l l  be  very simple but p h y s i c a l l y investigated  reasonable  theoretically.  37  The  theory. rate  b a s i c assumpti  38  of these models i s that neglected.  the e q u i l i b r i u m  may be  In other words, i f the two phases were i n s t a t i o n a r y  contact f o r an i n d e f i n i t e be  condition  period  of t i m e , the adsorbate would  t r a n s f e r r e d completely i n t o one o f the phases. It i s f u r t h e r assumed that  n e g l i g i b l e , that  the f l u i d  d e n s i t y , that no l a t e r a l d e v e l o p , and that  axial dispersion i s  i s i n c o m p r e s s i b l e and has constant  concentration  the f l u i d  gradients  e x i s t or  v e l o c i t y changes i n a stepwise  manner and remains constant during the time i n t e r v a l s between steps. Using the same n o t a t i o n  as i n S e c t i o n  mass balance equation f o r a h o r i z o n t a l dz  slice  2.1, the  of t h i c k n e s s  i s again  3c f  TT where  p =  dc + v  Tz  1-£ = volume e  I.  T T~  <'>  0  5  ratio.  Two simple rate  These rate  3c  f  + p  laws w i l l  be c o n s i d e r e d :  a)  C o n s t a n t and u n i f o r m l y d i s t r i b u t e d i n t e r p h a s e mass t r a n s f e r r a t e s .  b)  Mass t r a n s f e r r a t e s w h i c h a r e p r o portional to the concentration in one o f t h e p h a s e s .  laws are i n v e s t i g a t e d  f o r two o p e r a t i o n a l  modes  Continuous d i s p l a c e m e n t o r p a r a m e t r i c pumping: b o t h v a r i a b l e s ( e . g . f l u i d d i s p l a c e m e n t and e l e c t r i c potential) are continuously "on" at a l l t i mes.  39  (i)  potential  (ii)  the  (i)  potential  "on" —  (ii)  potential  "off"  (iii)  potential no f I o w ,  "on"  (iv)  potential  "off"  of the  subsequent  upward d i s p l a c e m e n t ,  no  —  —  in  reverse p o l a r i t y  —  void  two  obey such rate  laws.  arrangements.  The  In the  downw.ard d i s p l a c e m e n t .  volume i s d i s p l a c e d  Figure 10  electrodes  are  power s u p p l y .  systems which would  i s a sketch of the  supposed to be  meandering flow v e r s i o n of the  physical  sorption  channel  reached the  (Figure  stacks  10.a)  outer c h a n n e l s .  flows to the  l a s t channel  connected to a r e g u l a t e d The  be  i o n - s e l e c t i v e membranes.  e f f l u e n t from t h i s f i r s t i t has  will  Rates of Mass T r a n s f e r  electrodialysis  i s i n t r o d u c e d i n t o one  etc. until  —  analysis.  stacks are  composed of p e r f e c t  flow,  upward d i s p l a c e m e n t ,  C o n s t a n t , Uniformly D i s t r i b u t e d There are  fluid  —  p o t e n t i a l " o n " in r e v e r s e p o l a r i t y downward d i s p l a c e m e n t .  system in which one  basis  3.2  1 1  E x c h a n g e - d i s p l a c e o r p u r e p a u s e : when one v a r i a b l e i s " o n " t h e o t h e r i s " o f f " and v i c e v e r s a . In p a r t i c u l a r t h e s i m p l e s t p e r i o d i c f o r m o f t h i s mode, i s c o n s i d e r e d h e r e , w h i c h c o n s i s t s of f o u r s t e p s .  2.  A closed  "on  channels should be  The  adjacent  in the  constant  short to  the  channel,  stack. current  eliminate  The  40  unequal p o t e n t i a l  d i s t r i b u t i o n s due to r e s i s t a n c e  changes  in the s o l u t i o n .  t  Out  El. Held Flow IrT'  Out  t CONSTANT  Flow In  OPERATION  (a) M E A N D E R I N G  Figure  CURRENT  10:  FLOW  (b) M E A N D E R I N G  CURRENT  E l e c t r o d i a l y s i s systems with c o n s t a n t , u n i f o r m l y d i s t r i b u t e d r a t e s o r mass transfer.  The meandering c u r r e n t v e r s i o n  i s b a s i c a l l y a seg-  mented or staged e l e c t r o d i a l y s i s c e l l , the stages of which are  connected  in series  electrically  as well  A g a i n , the D.C. power supply i s operated mode, and the stages should be s h o r t .  as h y d r a u l i c a l l y .  i n constant c u r r e n t  41  Both devices allow an e x t e r n a l c o n t r o l  of the mass  t r a n s f e r rates , or  dcf  Obviously  equation  dc = -p  d t  (19) w i l l  = K = constant  (19)  break down as one  of the con-  c e n t r a t i o n s approaches z e r o , s i n c e the a p p l i e d p o t e n t i a l must then can  i n c r e a s e beyond a l l bounds.  p r e d i c t negative  Since the  equation  c o n c e n t r a t i o n s i t must be used with  caution.  3.2.1  Parametric If  of  pumping o p e r a t i o n .  the rate constants  are of equal  o p p o s i t e s i g n during the two  pumping o p e r a t i o n , one  h a l f c y c l e s of a  but  parametric  has  o  dt  magnitude  d C  s  -K  for dilution (20)  dt  The  = -  P  K  dt  f o r enrichment  s o l u t i o n of t h i s system of d i f f e r e n t i a l  trivial.  Suppose the i n i t i a l  cs(t=0) = c 0 .  The  condition is  equations  cf(t=0) = c0 ,  e f f l u e n t c o n c e n t r a t i o n during the  (demineralization) half cycle is  is  first  42  Cf(t) The  = c 0 - Kt  average product c o n c e n t r a t i o n  CT  -j  becomes  T/2 r  'T , 1  cf(t)dt  T/2  - K  'o where  T = cycle period  (T < 2c 0 /K , f o r non-negative  values  of c f ( t ) ) . If direction it  the p o l a r i t y  of the f l u i d  i s straightforward  concentration  during  of the e l e c t r i c  p o t e n t i a l and the  displacement are s i m u l t a n e o u s l y  switched  to show that the average bottom product the next part c y c l e i s  C  B,1 ~  C o  During the next d e m i n e r a l i z a t i o n the top product concentration i s  C  which i s i d e n t i c a l  to  T,2  c  reached w i t h i n the f i r s t internal  _  C o  T,l  "  K  ' 4  Final  cycle.  Figure  and product c o n c e n t r a t i o n  11.a), a f t e r the f i r s t  c o n d i t i o n s are t h e r e f o r e 11 i l l u s t r a t e s the  profiles  initially  (Figure  h a l f c y c l e ( F i g u r e 11.b), and a f t e r  the second h a l f c y c l e ( F i g u r e  11.c).  43 - v  z o  \<  or iz  Co  Co  UJ  >  o z o o  Reservoir  Reservoir ED .stack 2  1  -f  i  o  it  -e  (a)  Figure  For  II:  (b)  C o n c e n t r a t i o n p r o f i l e s during the f i r s t c y c l e of a c y c l i c e l e c t r o d i a l y s i s process operated in p a r a m e t r i c pumping mode u n d e r c o n d i t i o n s o f e q u a l , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d r a t e s o f mass transfer.  s i m p l i c i t y i t i s assumed that the end r e s e r v o i r s are  packed with i n e r t m a t e r i a l  having the same void volume as the  separator. A p l o t of the average top and bottom product concentration  transients  i s shown i n Figure 12.  decrease i n top product c o n c e n t r a t i o n the  starting  The  initial  i s c l e a r l y a r e s u l t of  conditions.  If the more general case of unequal rate is c o n s i d e r e d , the r e s u l t i n g  constants  product c o n c e n t r a t i o n s are  44  O <  or »z  LxJ O Z  o o  TIME  Figure  12:  Product concentration transients for c y c l i c e l e c t r o d i a l y s i s process operated in p a r a m e t r i c pumping mode u n d e r c o n d i t i o n s of e q u a l , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d r a t e s o f mass t r a n s f e r .  shown in Figure 13.  Here i t i s assumed, that  for demineralization  and  K2  Although  the  equation  (20).  changes a f t e r the sidered  as  transients due  first  Kx  f o r enrichment, see c o n c e n t r a t i o n s show  applies also further  c y c l e , these changes cannot be  true s e p a r a t i o n because top remain p a r a l l e l .  and  con-  bottom product  C o n c e n t r a t i o n s continue to change  to r e d i s t r i b u t i o n of s o l u t e  between s o l u t i o n  and  sorption  45  K,<K  2  ^  C  L -  < z  c - K--  o z: o o  7/2  2T  3T TIME  Figure  13: Product c o n c e n t r a t i o n transients e l e c t r o d i a l y s i s process operated pumping mode u n d e r c o n d i t i o n s o f s t a n t , and u n i f o r m l y distributed transfer.  membranes. the  O b v i o u s l y , the model w i l l  concentrations  reaches z e r o .  of the model are d i s c u s s e d  for c y c l i c i n parametri c uneq ua I , c o n r a t e s o f mass  break down i f one of  These p h y s i c a l  restrictions  above.  Up to t h i s point standard parametric pumping seems to have no s e p a r a t i o n p o t e n t i a l trolled  by a constant t r a n s f e r  when used i n a system conrate.  This i s i n c o n t r a s t to  46  experimental  results  on a thermal parapump system which i s  operated c l o s e to e q u i l i b r i u m , see It was when the two  c o n t r o l v a r i a b l e s were switched  e q u i l i b r i u m theory  see  P i g f o r d et  quarter  Sweed (1968).  found t h a t maximum s e p a r a t i o n was  The  occurred  Wilhelm and  al.  substantiated this  (1969a).  i f temperature and c y c l e out  simultaneously.  finding  In t h e i r work no  achieved  theoretically,  separation  displacement were switched  one  of phase.  T h i s behaviour i s i n v e r t e d when the system i s controlled  by  constant t r a n s f e r r a t e s .  separation one  i s obtained  quarter  c y c l e out  Figure  when the e l e c t r i c of phase to the  14 i l l u s t r a t e s  two  c y c l e s i n steps  is  assumed that the  In t h i s  of one-half  the  case maximum  polarity  flow  i s switched  reversal.  consecutive  action for  c y c l e from the s t a r t .  rate constants  are equal  It  (Ki = K 2 ) ,  and  that the e f f l u e n t remain unmixed i n the end r e s e r v o i r s . For convenience i t i s , a g a i n , assumed that the r e s e r v o i r s are packed with  inert material  as the s e p a r a t o r .  The  abscissa  d i v i d e d i n t o three  sections:  - £ < z < 0  * average top  having the i n Figure  same void volume 14 i s , t h e r e f o r e ,  f o r the bottom r e s e r v o i r  0 < z < %  f o r the  separator  % < z < 2£  f o r the top r e s e r v o i r  This assumption does not a f f e c t the values and bottom e f f l u e n t c o n c e n t r a t i o n s .  of  the  •4  t=0 z o  A  cc tz UJ  t =T  VI  o o o  -e  21  -t  3T  t=2T  V -e F i g u re  14:  e  zt  D e v e l o p m e n t o f s t a n d i n g waves i n a p a r a m e t r i c pumping o p e r a t i o n u n d e r c o n d i t i o n s of e q u a l , c o n s t a n t , and u n i f o r m l y distributed r a t e s of mass t r a n s f e r i f v a r i a b l e s a r e s w i t c h e d 1/4 c y c l e o u t of p h a s e .  48  A symmetric s t a n d i n g wave of i n c r e a s i n g i s generated as a r e s u l t of the p e r i o d i c product t r a n s i e n t s  Figure  15:  forcing.  (see Figure 15) are s t r a i g h t  amplitude The  average  lines.  Product concentration t r a n s i e n t s for c y c l i c e l e c t r o d i a l y s i s process operated in parametric pumping mode u n d e r c o n d i t i o n s o f e q u a l , c o n s t a n t , and u n i f o r m l y d i s t r i b u t e d r a t e s of mass t r a n s f e r , when p e r i o d i c v a r i a b l e s a r e s w i t c h e d one q u a r t e r out of p h a s e .  49  The general any phase s h i f t  y  case of unequal rate  i s summarized  constants and  i n the f o l l o w i n g  f o r the average top and bottom product t r a n s i e n t s  equations (0 < y < j)  which are d e r i v e d i n Appendix B . l .  = c o - KiJ+ ( K 2 +  Cj  K j X i  +  2  T  where T 3T 2 ' 2  5T ' 2  •• • (21)  and Cg  -  Co  +  fK2-Ki  K2+Kx  +  2—  Y  T  where t = T , 2T  , 3T  ,  o  The t r a n s i e n t s  •  are s t r a i g h t  a p l o t f o r three values of K2  •  lines.  Figure 16 i s  y = 0» T/8, T/4, assuming  > Kx . The important r e s u l t s of t h i s s e c t i o n  as  are summarized  follows: 1.  C o n s t a n t , u n i f o r m l y d i s t r i b u t e d r a t e s o f mass . t r a n s f e r lead t o g e n e r a l l y poor s e p a r a t i o n s i n a p a r a m e t r i c pumping o p e r a t i o n .  2.  The i n f l u e n c e o f t h e p h a s e r e l a t i o n s h i p f o r t h e s e r a t e laws i s o p p o s i t e t o t h e e q u i l i b r i u m t h e o r y of p a r a m e t r i c pumping.  K,<K  l  1  1  0  T/2  T  1  1  2  1  2T  r —  3T  TIME  Figure  16.  A v e r a g e t o p and b o t t o m p r o d u c t t r a n s i e n t s f o r phase s h i f t o p e r a t i o n of a c o n s t a n t r a t e c o n t r o l l e d p a r a m e t r i c pump.  Figure  17:  Lateral concentration p r o f i l e and co-ordinate systems in flow channel and t r i p l e membrane.  en O  51  3.2.2  3.  A n a l y t i c a l s o l u t i o n s f o r the average product c o n c e n t r a t i o n s as f u n c t i o n s of t h e c y c l e t i m e have been d e r i v e d . These t r a n s i e n t s are straight lines.  4.  The b r e a k i n t h e t o p t h e i n f l u e n c e of t h e distribution.  Pure pause The  Figure 10  do  externally the  rate  transient reflects concentration  operation.  mass t r a n s f e r not  product initial  depend on  controlled.  rates  model systems  flow c o n d i t i o n s ,  I t may,  constants Ki and  in the  K2  rather  t h e r e f o r e , be  are  of  they  are  assumed that  equal f o r pure pause  parametric pumping o p e r a t i o n , although t h i s w i l l  not  and be  valid  f o r other systems. The  solutions  simple i n t h i s c a s e . trations  cT  obey the  of the  The  transients  of the  (13)  are  product concen-  ( *41  for t  T 3T 5T 2 ' 2 ' 2 ' (22)  and cD  very  relations  Ki £ - (K2+Kx)|  — co  model equations  = c0  +  K2  where again the  -  (K2+Ki)^  phase s h i f t  t  f o r t = T , 2T , 3T ,  i s d e f i n e d i n the  interval  52  0 < Y <  J  i . e . the s w i t c h i n g of the p o t e n t i a l  leads the flow  switching  by Y • One  can  recognize  by s i m u l t a n e o u s l y  that maximum s e p a r a t i o n i s obtained  s w i t c h i n g the two  the product t r a n s i e n t s have twice pump with equation  3.3  one-quarter  variables.  In t h i s  the slope of a  c y c l e phase s h i f t  and  21).  Concentration  Dependent Rates of Mass T r a n s f e r  rate e l e c t r o d i a l y s i s In conventional  process, this  electrodialysis  i s not very  a constant  u s u a l l y a p p l i e d to the e l e c t r o d e s .  density  parametric  (see Figure 15,  While i t might be p o s s i b l e to operate  is  case  ( i ) i s then  The  a  constant  practical.  electric local  potential  current  a f u n c t i o n of the c o n c e n t r a t i o n s  along  the current path. For p e r f e c t l y s e l e c t i v e membranes i n steady the concept of the Donnan p o t e n t i a l Helfferich  (1962).  of the e f f e c t i v e  The  be  adopted, see  c u r r e n t d e n s i t y ( i ) i s then  stack v o l t a g e and  u n i t membrane area  may  state  the t o t a l  the  ratio  r e s i s t a n c e per  53  Figure the  lateral  17 i l l u s t r a t e s the co-ordinate  concentration  electrosorption  stack:  profile  i n the s m a l l e s t  2.1.6.  The a p p l i e d  i s diminished by the Donnan p o t e n t i a l  A$  The integral  = 2RT in zF  Don  total  u n i t of an  a flow channel and an adjacent  l a y e r membrane, see a l s o S e c t i o n (A$)  system and  three-  potential  (A$Don).  (24) at membranes  r e s i s t a n c e of the u n i t i s the sum of the  s o l u t i o n r e s i s t a n c e s , Rf and R s .  rb  Rf =  RT z  z  2z F D  -7?yT (25)  RT S  and  2  2  2z F D  dy' c,(y')  the r e s i s t a n c e of both membranes (R_) x m  Substituting  (24) and (25) i n t o (23) gives  54  2RT zF at membranes ra  RT 2  dy  to the  Donnan p o t e n t i a l w i l l  applied p o t e n t i a l .  + R  cs T T J  2  2z F D  The  dy'  The  u s u a l l y be  lowest c o n c e n t r a t i o n  path.  i s low  concentration  d e p l e t i o n , and  m  small  compared  current density i s therefore  mainly c o n t r o l l e d by the The  (26)  i n the flow  in the membrane core  i n the  channels  current during  during enrichment.  rate laws subsequently assumed are based on these  The  approxima-  tions:  9t  +aiC  f  during  dilution (27)  9t  3.3.1  Pure pause The  considered details Appendix  = -a 2 c  during  operation.  exchange-displace type of process  f i r s t , because i t may  of t h i s B.2.  enrichment  step-by-step  be s o l v e d  calculation  operation is  analytically.  The  are r e f e r r e d to i n  55  For  one  void volume d i s p l a c e m e n t , without phase  s h i f t , the product c o n c e n t r a t i o n t r a n s i e n t s  Co  are  v  (28)  '1  ^Co =  pq" - qp""  2+p  (1-p)  n-l I 1=0  where p = exp  (-  aiT/2)  q = exp  (- a 2 T/2)  p = i s as d e f i n e d b e f o r e . In  equation (28) the bottom product  concentration  decreases e x p o n e n t i a l l y , whereas the top product c o n c e n t r a tion  i s l i m i t e d by the o v e r a l l The  separation  mass b a l a n c e .  factor  (ns) i s here d e f i n e d as the  r a t i o of bottom and top product c o n c e n t r a t i o n s . tion  f a c t o r i n c r e a s e s without  approaches  l i m i t as the number of c y c l e s  infinity. Although the product t r a n s i e n t s  to  are of s i m i l a r  form  those f o r parametric pumping under e q u i l i b r i u m c o n t r o l , a  fundamental d i f f e r e n c e e x i s t s . of  This separa-  real  Equations (28) are f u n c t i o n s  t i m e , whereas the e q u i l i b r i u m theory e s s e n t i a l l y  excludes time from the mathematical  solution.  56  3.3.2  Parametric  pumping  I f equations balance may,  (15)  the  operation.  (27)  are s u b s t i t u t e d i n t o the mass  resulting partial  differential  i n p r i n c i p l e , be s o l v e d f o r any  equations  h a l f c y c l e , see  Appendix  B. 3. A numerical  solution  to the problem was  preferred  h e r e , however, s i n c e the number of terms i n the f i n i t e solution numerical  grows g e o m e t r i c a l l y with calculation  scheme was  a l g o r i t h m , developed by Sweed and In t h i s equations ential  placement of one and  are d e s c r i b e d  identical  (ODE)  Wilhelm  void volume.  ordinary N  differ-  times f o r a d i s -  A conceptual  i n Appendix  model of  the  B.4.  to numerical  the  In t h i s  N=l  is equivalent  results  s e c t i o n the  f o r three values  to a  of computer s i m u l a t i o n s  evaluations  Comparison of pause and  simulations  differential  a FORTRAN IV program f o r computer s i m u l a t i o n s  pure pause o p e r a t i o n , and are i d e n t i c a l  (1969).  N  which are s o l v e d  The  to the STOP-GO  continuous p a r t i a l  I n c i d e n t a l l y , the case  3.3.3  number of c y c l e s .  are approximated by a set of  equations  algorithm  scheme the  the  series  of equations  parametric  pumping  (28).  operations.  r e s u l t s of a number of computer of  N(N  = 1,4,50)  are  compared.  57  Figure 18 shows the normalized c o n c e n t r a t i o n sients  for  p = 1.0  a x = a 2 = 0.01  (ii)  (iii)  ]  , T = 20 [ s e c ] ,  and  N = I o r p u r e p a u s e o p e r a t i o n shows u n h i n d e r e d and u n l i m i t e d s e p a r a t i o n . N = 4 r e p r e s e n t s an o p e r a t i o n w h i c h c o n s i s t s o f f o u r p a u s e s and f o u r o n e quarter displacements. The t r a n s i e n t s i l l u s t r a t e a g r a d u a l t r a n s i t i o n from pure pause t o c o n t i n u o u s d i s p l a c e m e n t . A break in the top product t r a n s i e n t a f t e r t h e f i r s t c y c l e may be r e c o g n i z e d . N = 50 o r p a r a m e t r i c pumping shows v e r y l i t t l e a d d i t i o n a l separation a f t e r the f i r s t cycIe . NOTE: The r e s u l t s f o r N = 100 a r e virtually identical.  Table 1 l i s t s  normalized top and bottom  and the corresponding s e p a r a t i o n  f o r various parameter v a l u e s . as  -1  f o r one void volume displacement: (i)  tions  [sec  tran-  concentra-  f a c t o r a f t e r 50 c y c l e s  The r e s u l t s may  be  summarized  follows: 1.  Best s e p a r a t i o n i s always achieved with a pure pause o p e r a t i o n .  2.  Longer c y c l e p e r i o d s g e n e r a l l y improve t h e separation. This is equivalent to increasing the rate c o n s t a n t s ai and a by e q u a l factors. 2  3.  If t h e r a t e c o n s t a n t f o r e n r i c h m e n t i s i n c r e a s e d ( e q u i v a l e n t to longer second h a l f c y c l e ) the s e p a r a t i o n is improved. However, the t r a n s i e n t s d r i f t s i m u l t a n e o u s l y toward h i g h e r c o n c e n t r a t i o n s for Run No. I I .  58  N  SYMBOL  I  O  4  A  50  •  PURE PAUSE PARAPUMP  ,05  Figure  18:  E f f e c t o f t h e number of s e g m e n t s on t h e p r o d u c t concentration transients for concentration d e p e n d e n t r a t e s of mass t r a n s f e r ( a i = a = 0 . 0 I s e c " T = 20 s e c , p = 1 . 0 , 6 = 1 . 0 ) . 2  Table 1 Computer S i m u l a t i o n s of Pure Pause, Parametric Pumping, and M u l t i p l e Step Displacement Operations f o r Concentration Dependent Mass Transfer Rates SIMULATION RUN NO.  RATE  CONSTANTS  CYCLE PERIOD  VOLUME RATIO  DISPLACED VOLUME  NO. OF SEGMENTS  NO. OF CYCLES nc  CONCENTRATIONS BOTTOM  ai [ - ] 1  [sec  -1  .01  3  a2  P  <5  N  [sec]  [-]  [-]  [-]  20  1  1  2 3 4  40  1  1  5 6  X  TOP X  ns  [- ]  B [- ]  1  50  2.9 5  [- 3  4  50  1 .66  .450  3.70  50  50  1.11  .894  1 .24  1  [sec- ] .01  T  SEPARATION FACTOR  T  .0067  1  50  3.00  .0000  4  50  1 .87  .303  [- 3  438.  66067. 6.17  50  50  1.21  .806  1 .50  1  1  4  50  2.04  .207  9.85  8  1  1  50  50  1 .38  .661  9  1  1  1  50  2.99  .0067  10  4  50  2.01  11  50  50  1 .36  1  50  2.46  .0067  13  4  50  1 .38  .378  3.66  14  50  50  .92  .747  1 .24  7  12  15  80 .01  .01  ,02  .01  20  20  1/2  1/4  1  1  16  .488 1 .04  1  50  2.21  .0067  4  50  1 .24  .342 .672  2.08 443. 4.11 1 .30 365.  328. 3.63  50  50  .83  2  50  3.64  .0067  19  8  50  1 .56  .328  4.77  20  100  50  .92  .710  1.29  4  50  4.56  .0067  16  50  1.58  .328  17 18  21 22  1/2  1/2  1/4  1 .24 540.  677 . 4.83  60  4.  A d e c r e a s e i n volume r a t i o ( l e s s a d s o r b e n t o r t h i n n e r membrane c o r e ) r e d u c e s t o p and b o t t o m p r o d u c t c o n c e n t r a t i o n s and may l e a d to a steady d e c l i n e of bottom product c o n c e n t r a t i o n i n p a r a m e t r i c pumping o p e r a t i o n (N=50).  5.  I f l e s s t h a n one v o i d volume i s d i s p l a c e d w i t h t h e same c y c l e p e r i o d t h e s e p a r a t i o n i s i mp r o v e d . Note  3.4  that 5 = i r e q u i r e s N = 2 f o r pure pause o p e r a t i o n , 6 = £ r e q o i r e s N = ketc.  Summary In t h i s chapter two simple laws f o r the rate of  mass t r a n s f e r i n c y c l i c  s e p a r a t i o n processes have been analyzed  to determine t h e i r e f f e c t on the t r a n s i e n t systems with continuous or pulse l i k e rate  laws are p h y s i c a l l y well  response of closed  displacement.  founded f o r an e l e c t r o d i a l y s i s  process and may be viewed as l i m i t i n g c o n d i t i o n s to the l o c a l  equilibrium  The  complementary  concept.  I t i s shown that the standard parametric pumping operation transfer  i s generally rates  is n e g l i g i b l e . limitations  very i n e f f i c i e n t  i f the i n f l u e n c e  of an e q u i l i b r i u m  mass relationship  A pure pause o p e r a t i o n overcomes much of these  and leads to u n l i m i t e d  It i s also  between the f o r c e d  separations.  demonstrated that f o r constant and  u n i f o r m l y d i s t r i b u t e d mass t r a n s f e r  equilibrium  for finite  variables  r a t e s , the phase r e l a t i o n  i s c o n t r a r y to that f o r the  theory of parametric pumping.  The maximum  61  separation to one  effect will  quarter  be  of a t o t a l  obtained i f the cycle.  The  separation  i s , however, s t i l l  small  3.5  E q u i l i b r i u m Model with  Comment on  an  phase s h i f t  amounts  in this  compared to a pure pause  case  operation.  Instantaneous  Displacement At t h i s  point  the  question  the e f f e c t of a pure pause o p e r a t i o n trolled at the  system?  Is the  beginning of the  may on  be  asked, what i s  an e q u i l i b r i u m  con-  instantaneous s o l u t e  redistribution  h a l f c y c l e s the  separating  true  mechanism?  Or  tion  enough that equi1ibriurn i s always maintained?  slowly  The in  i s i t , a l s o , necessary to d i s p l a c e the  d e r i v a t i o n of the model equations i s contained  Appendix B.5.  of the  solu-  The  product c o n c e n t r a t i o n s  number of c y c l e s are  described  by the  as  functions  following  equati ons:  CASE 1:  The s t a t i o n a r y phase i s i n i t i a l l y unloaded or in the low e q u i l i b r i u m s t a t e . The f i r s t d i s placement i s up without changing the e q u i l i b r i u m  62  _ i = 1 +  K  ~  p-1  x  KA-1  C n  n-1  (29)  and  II Co  where  K = 1 + mi  A  1  K - A  K  K  KA-1  ,  and  n-1  A = 1 + m2  ;  mi & m2  are d e f i n e d  i n S e c t i on 2.2.1.  CASE 2:  The s t a t i o n a r y phase i s i n i t i a l l y l o a d e d . displacement i s down without changing the equi 1 i b r i urn  _B_ c0  f-Ll KA  * + IA  A  KA-  First  n-1  and  (30)  Co  KA-1  1 - f 1  Figure 19 i l l u s t r a t e s and  A  =  1.25.  n-1 1  KA  the t r a n s i e n t s  for  K = 1.5  63  A" 1,25  Figure  19:  Product concentration transients for e q u i l i b r i u m c o n t r o l l e d p u r e pause o p e r a t i o n ( o r p a r a m e t r i c pumping w i t h i n s t a n t a n e o u s d i s p l a c e m e n t ) .  It can be seen that l i m i t i n g c o n d i t i o n s are reached a few is  cycles.  finite  The  l i m i t i n g separation  within  f a c t o r f o r both  cases  and i d e n t i c a l :  £-tm(ns) = llm _P_  =  K-1  X-l  =  mx m2  (31)  64  The two  equilibrium states  concentration The  s o l u t e merely r e d i s t r i b u t e s according  i n such a manner that the adsorbent  asymptotically  time i n t e r v a l  to the  approaches a constant  of a c t i v e s e p a r a t i o n  value.  i s comparatively  short. In answer to the above questions one can t h e r e f o r e deduce t h a t , i n the standard parametric pumping finite  flow rates  are e s s e n t i a l f o r s u c c e s s f u l  operation, separation  when the system i s c o n t r o l l e d by e q u i l i b r i u m . Another aspect of t h i s model emerges i f a combinat i o n of rate and e q u i l i b r i u m c o n t r o l pure pause o p e r a t i o n . (29)  i s considered  Obviously the t r a n s i e n t equations  or (30) c o n s t i t u t e the maximum s e p a r a t i o n  obtained i n such a system. where the r a t i o limitation  mi/m2  for a  which can be  For e l e c t r o d i a l y s i s , however,  i s u s u a l l y extremely l a r g e , t h i s  does not a r i s e i n p r a c t i s e .  Chapter 4  THE CYCLIC ELECTRODIALYSIS PROCESS OPERATION AND APPARATUS  4.1  Description Figure  of Batch Operation 20 i l l u s t r a t e s  constitute a single cycle. shown s c h e m a t i c a l l y division  the four b a s i c steps which  The e l e c t r o d i a l y s i s  as a r e c t a n g u l a r  box with a  f o r membrane s e p a r a t o r s ) .  The composite  membranes are represented by a d o u b l e - l a y e r .  cell.  diagonal  i n d i c a t i n g the membranes (a symbol which i s found  frequently  (circles  (ED) c e l l i s  i n Figure  Partial  sorption  Two r e s e r v o i r s  20) are connected to the ends of the ED  shading of the c i r c l e s  i n d i c a t e s the l i q u i d  content of these r e s e r v o i r s at d i f f e r e n t stages during the cycle. The direction left  first  half cycle i s characterized  of the e l e c t r i c  - cathode r i g h t ) .  field  (n) ( s i g n c o n v e n t i o n : anode  This w i l l  p o l a r i t y of the a p p l i e d p o t e n t i a l positioned  be r e f e r r e d to as p o s i t i v e (A<J>).  The membranes are  i n such a way t h a t p o s i t i v e p o l a r i t y  65  by p o s i t i v e  i s equivalent  T,  66  First Hnlf Cycle PG  use  Displacement Second Half Cycle  21 Figure  20.  Batch operation  of  c y c l i c e l e c t r o d i a l y s i s process  (a)  UJ <  (b) ? o _i  Tl ME  Li-  Figure  21.  Time v a r i a t i o n flow rate (b) p rocess.  of a p p l i e d p o t e n t i a l ( a ) and for c y c l i c e l e c t r o d i a l y s i s  67  to s o l u t e The  intrachannel  first  s o l u t i o n becomes depleted  during  the e n t i r e  h a l f c y c l e which c o n s i s t s of a "PAUSE" or no-flow  interval The  uptake, i . e . the c a t i o n i c membranes face the anode.  followed  ( T J  fluid  by a "DISPLACEMENT" i n t e r v a l  flows with rate  (T ). 2  (Q) from the lower to the upper  reservoi r . The  second h a l f c y c l e begins with a p o l a r i t y  reversal  (- n) and s i m u l t a n e o u s l y the flow stops f o r another "PAUSE" interval  ( T 3 ) . The i n t r a c h a n n e l  f o r the d u r a t i o n by  of t h i s  solution receives  solute  second h a l f c y c l e , which i s concluded  a "DISPLACEMENT" i n t e r v a l  (x.J.  Solution  i s thus  from the upper to the lower r e s e r v o i r with flow rate In t h i s  wave m a n n e r . is  reversed  during  but t h e magnitude  pulses  magnitude  potential  At the beginning  (ii) Positive  to the f o l l o w i n g  The a p p l i e d  the entire  operation,  The f l o w  rate  alternate  and d u r a t i o n  (iii)  (- Q) .  study the parameters A<j> , Q , x.. ( i = 1 ,  2, 3, 4) are s u b j e c t (i)  returned  conditions: (A<|)) c h a n g e s  of every half  i s regulated Figure  negative  (x2 = T i * ) ,  of ( i i )  this  the sign  t o remain  in a pulse ones  constant  means  like  fashion.  o f t h e same  see Figure  In m o s t e x p e r i m e n t s t h e p a u s e  (xi = X 3 ) a n d b e c a u s e  cycle  21a.  (Q) v a r i e s  with  i n a square  21b.  times  a r e equal  symmetric half  cycles.  68  (iv) are a d j u s t e d is equal in the  or  Flow r a t e so t h a t  the  less than  lower  ( Q ) and d i s p l a c e m e n t total  the  reservoir. therefore,  excess  in the  In  F i g u r e 20  a finite  Starting  4.2  The  two  the  reservoirs  number of  conditions  displaced  volume  2  (Q •  T  initially  remains  2  completely  from  )  contained  d i s p l a c e d volume may v a r y  (x = Ti»)  filled  and any  run t o  run.  (or dead volumes) are shown.  The b a s i c c y c l e  is  repeated  in the  same  order  times.  are  always  (a)  uniformly  (b)  The f i r s t h a l f c y c l e i s a d e m i n e r a I i z i n g one w i t h upward d i s p l a c e m e n t .  distributed  concentrations.  F i r s t Bench Module The  on  but  no e x c e s s v o l u m e s  (v) for  solution  The ED c e l l  with s o l u t i o n , volumes  volume  times  ED  cell  experimental  part of t h i s work was  v e r s i o n s , the  in t h i s s e c t i o n . f o r both modules. but  at the  the  equipment w i l l  first  Most of the  auxilary  be  the  shown as  electrodialysis cell rinse  of the  a block diagram. cell  loop and  described identical  repetitions,  presentation, This  v e r s i o n s , see  (ED)  the  be  equipment was  clarity  diagram i s i d e n t i c a l f o r both ED  process l i n e , the  of which w i l l  In order to avoid unnecessary  same time r e t a i n  The  performed  block  Figure  i s connected to  e l e c t r i c power.  the  22.  0 CM  F i g u r e 22.  Block  d i a g r a m of e x p e r i m e n t a l  testing  station.  70  The pump P2.  r i n s e loop c o n s i s t s of tank 12, valve V3 and  The process  line  i s open-ended and terminates i n  the top r e s e r v o i r T above ED and i n the bottom r e s e r v o i r B below ED.  In the same l i n e  are found the c o n d u c t i v i t y c e l l s  CI and C2, pump P I , and valve V I , and a branch l e a d i n g through valve V2 to tank T l which contains  the stock  solution  (NaCl/H20). The b i n d i n g posts  DC power i n p u t may be t r a c e d from the e l e c t r i c EP1 and EP2, through the switch box SB1 to the  r e g u l a t e d DC r e c t i f i e r . A second e l e c t r i c r a t e and the d i r e c t i o n  c i r c u i t indicates  t h a t the flow  of flow d e l i v e r e d by the p o s i t i v e  displacement pump PI may be c o n t r o l l e d by means of a motor c o n t r o l l e r and a switch box SB2. A t i m e r , which i s t r i g g e r e d by P I , i n i t i a t e s the s w i t c h i n g of SB1 and SB2. Four s i g n a l s tinuously:  are recorded  The s o l u t i o n  simultaneously  concentrations  c e l l s , the c u r r e n t input to the ED c e l l and  the a c t u a l p o t e n t i a l  drop across  and con-  i n the c o n d u c t i v i t y measured by shunt A,  the stack pack measured  by r e v e r s i b l e probe e l e c t r o d e s . The  c u r r e n t s i g n a l was i n t e g r a t e d during some of  the experiments to determine the average c u r r e n t  consumption.  71  4.2.1  E l e c t r o d i a l y s e r No. The  identify  1  (EDI)  primary o b j e c t i v e  of t h i s f i r s t  important parameters of the  study t h e i r e f f e c t s q u a l i t a t i v e l y . view of EDI, Appendi x  u n i t was  to  c y c l i c process and Figure 23  reduced machine drawings are  shows an  is  A.1.  following  Simple c o n s t r u c t i o n  2.  No l i q u i d  ing.  O n l y two s e a l s  4.  Membrane-spacer stack of  which  T h i c k n e s s of  The  liquid  is  manufacture.  because  flow  required. is  a separate block,  d e t e r m i n e d by t h e  sorption these  centre  the  frame o p e n -  membranes a n d / o r s p a c e r s c r e e n s limits.  centre i s recessed at top  Perspex and  plate.  bottom to  d i s t r i b u t i o n chambers i n which d i s t r i b u t o r  p l a t e s , each c o n t a i n i n g The  manifolds  centre frame i s made from a 1"  opening i n the  form two  distribution  i s easy to  internally.  may be v a r i e d w i t h i n  The  which  3.  size  chosen  reasons:  1.  dispersed  overall  exploded  contained i n  A constant t h i c k n e s s centre frame design was f o r the  to  32  x 0.032"* h o l e s , are  mounted.  process s o l u t i o n which flows through the  frame i s p h y s i c a l l y separated by  two  centre  s i n g l e membranes from  the  72  End F r a m e  Centre  End  Frame  Frame  Stack-Pack Gasket Nut  Gasket  Bolt  Bolt  — i -  Nut  : 31  Electrode  Electrode  Spacer Membrane  F i gu re  23.  Spacer Membrane  F i r s t e l e c t r o d i a l y s i s c e l l EDI (exploded view, schematic).  73  electrode assemblies.  Each of these  assemblies  c o n s i s t s of  a 1" p o l y e t h y l e n e  p l a t e , a f l a t graphite e l e c t r o d e , a graphite  b o l t with  n u t , a spacer  a nylon  rubber gasket.  Two  the wash s o l u t i o n .  s c r e e n , and a r e s i l e n t  r i n s e ports provide Detail  inlet  silicon  and o u t l e t o f  drawings of the e l e c t r o d e end  frame (see Appendix A . l ) show how the r i n s e stream i s d i s tributed  and c o l l e c t e d . E l e c t r o d e s were cut from a g r a p h i t e block of unknown  origin plates. led  and f i t t e d  i n the r e s e t s provided  Some unsuccessful  finally  to the threaded  These had a c o n i c a l with  experimenting  i n the p o l y e t h y l e n e with  brass  g r a p h i t e b o l t s shown  head to provide  were sanded f l a t a f t e r assembly.  i n Figure 23.  a larger contact  the counter-sunk e l e c t r o d e p l a t e s .  connectors  area  B o l t s and e l e c t r o d e s  S p e c i a l Nylon nuts were  made to t i g h t e n the b o l t s . The blocks with  e l e c t r o d e s were permanently set i n t o the end  a bed of s i l i c o n  The  s e p a r a t i n g membranes were of the same kind as  used i n the stack The  rubber.  (see below).  whole assembly was held together by a clamping  device which c o n s i s t e d of two r e c t a n g u l a r frames from 1" square pipes) and four t i e rods Appendi x A . 1 ) .  (manufactured  (see d e t a i l  drawing,  74  The wire.  probe e l e c t r o d e s were made from  1 [£2/ft]  Four threads t w i s t e d i n t o a s i n g l e wire  (10"  silver  long)  were p r o t e c t e d by a s l e e v e of SCOTCH tape except the ends. One  2  end was  s o f t s o l d e r e d to a 1 x 2 [mm ]  silver  (0.020" t h i c k ) and the p o i n t of c o n t a c t was t a c t cement.  This probe was  plate  covered with  always i n s e r t e d  i n t o the  compartment with the unprotected s i d e of the p l a t e  con-  rinse  facing  the e l e c t r o d e and the covered s i d e touching the s e p a r a t i n g membrane.  The  probes  measured, t h e r e f o r e , the p o t e n t i a l  across the stack and the two The in  4.2.2  s e p a r a t i n g membranes.  main f e a t u r e s of the f i r s t  the f o l l o w i n g Table  drop  ED c e l l  are summarized  2.  Membrane-spacer s t a c k s . Three  stack v e r s i o n s were t e s t e d  t h i s work by combining  two  i n the course of  types of spacer screens with  two  d i f f e r e n t s o r p t i o n membranes.  The  Sorption  Membranes  Resinous  ion exchange membranes were purchased  Tokuyama Soda, Japan. The  manufacturer's  from  These were commercially used membranes.  specifications  are given i n Table  3.  75  Tab l e 2 EIectrodia Iyser  I (EDI)  R i g i d C e n t r e Frame S i n g l e Stage  Des i gn  230  [cm ]  Volume  630  [cm ]  40  [cm ]  #x Inherent  Membrane  Rinse  2  Area  E1ectrode  A c t i ve  No.  Dead  Volume  Utilization  3  m  #**  83  System  Single  One  Gaskets  Mate r i a l s  3  on  Pass  Each E l e c t r o d e Frame  C e n t r e Frame E l e c t r o d e Frame Electrode Te rm i n a 1 Gaskets  Plexiglass L.D. P . E . Graphite Graph i t e S i l i c o n Rubber  * r e f e r s t o the space which w i l l membrane s p a c e r s t a c k c a l c u l a t e d from t h e dimensions d i s t r i b u t i o n chambers  be  f iI led with  of t h e two  **#  f r a c t i o n o f t o t a l membrane circulating solution.  area  exposed  to  flow  the  76  Table 3 Properties  of  NEOSEPTA M e m b r a n e s ,  f rom Yamane  Type  (1969)  CL 25T c a t i o n s e 1 e c t i ve  AV4-4T anion s e l e c t i v e  PVC  PVC  Back i ng Th i c k n e s s  1)  Burst  2)  strength  Ion e x c h a n g e Water  c a p a c i t y 3)  content  Electric  resistance  Transport  number  0.15  -0.17  3 -  0.15  4  0.17  5 - 7  1 .8 - 2 . 0  1.5  -  2.0  4)  . 30 -  .40  .20 -  .25  5)  2.7  -  3.2  3.5  -  4.5  >  .98  >  .98  6)  1)  [mm]  2)  [kg/cm !]  3)  Cmeg/gram  4)  e q u i l i b r a t e d w i t h 0 . 5 N NaCI s o l u t i o n Cgramm H 0 / g r a m dry membrane i n N a - f o r m ,  2  d r y membrane  in N a - f o r m ,  or  Cl-form]  2  5)  -  equilibrated [ft c m ]  with 0.5N  NaCI  solution  at  or 25  CI-form] [°C]  2  6)  m e a s u r e d by e l e c t r o d i a l y s i s i n 0 . 5 N NaCI c u r r e n t d e n s i t y 10 [m A/cm 3 a t 25 [ ° C ]  solution,  2  The s o r p t i o n membranes, or "capacity c e l l s , " were made i n two versions with a large core and with zero core. the f i r s t case the core was 1/32" t h i c k ,  c o n s i s t i n g of a  sturdy SPURLDITE frame, and a double l a y e r of p l a s t i c  coated  In  77  glass f i b r e  screen  thick) f i t t e d and  (14/18 strands  per i n c h , approx. 1/64"  i n t o the c e n t r a l opening of the frame.  An anion  a c a t i o n s e l e c t i v e membrane of the same s i z e as the frame  were placed edges with  on opposite  s i d e s and s e a l e d around the f o u r  SCOTCH t a p e .  Care had to be  taken to keep the membranes always moist because they not only s h r i n k upon d r y i n g but may develop c r a c k s . d e s i r e d to produce c a p a c i t y c e l l s  A l s o , i t was  i n which no a i r bubbles  were entrapped. The  membranes could be permanently cemented onto  the frame using  Eastman 910  adhesive (Armstrong Cork Co.)  which was found to form a s a t i s f a c t o r y bond between the damp membrane and SPURLDITE i f both s u r f a c e s had been sanded. PVC,  Since  the s t r e n g t h e n i n g  slightly  f a b r i c of the membranes i s  the sanding procedure probably exposed the PVC f i l a m e n t s .  This method was not used i n the experimental c e l l s  since i t  seemed d e s i r a b l e to be able to i n s p e c t the c a p a c i t y interior  cell  and to modify the c o r e . In the "zero"  core  v e r s i o n , the c a p a c i t y c e l l s  s i s t e d of the two membranes and the s e a l i n g t a p e .  con-  A g a i n , the  a i r pockets were completely removed before s e a l i n g .  The  Spacers  B e l f o r t and Guter (1968) i n v e s t i g a t e d the flow p a t t e r n produced by various  s c r e e n s , and found t h a t m u l t i p l e  78  l a y e r s of n e t - l i k e develop  showed the l e a s t tendency to  areas of s t a g n a t i o n . The  first  same glass f i b r e  spacer was  made of four l a y e r s  screen used f o r the f i r s t  core.  The  strips  (10" x 1/4"  the  fabrics  sketch below i n d i c a t e s  capacity c e l l  the f o l d i n g .  x 1/32") strengthened  of the  SPURLDITE  the s t r u c t u r e  along  sides.  Figure 25:  The p l a s t i c net: which was  Glass f i b r e spacer s c r e e n .  second spacer m a t e r i a l was  a c o n v e n t i o n a l VEXAR  L 12 (12/12 s t r a n d s / i n c h , c l e a r  kindly  polypropylene)  s u p p l i e d by DuPont DeNemours of Canada.  79  It was cut p a r a l l e l  to one s t r a n d d i r e c t i o n  single  Thickness  layer only.  approx. 0.81  and used as a [mm].  The  spacers  are a l s o shown i n Figure 24a. The f o l l o w i n g membrane spacer  stacks were  combined  and i n v e s t i g a t e d i n t h i s work:  Table 4 S t a c k P a c k V e r s i o n s Used  ^^v. Property  ED C e l l  Stack Version 1  2  3  8  15 o r 16  12 o r 13  ^ - v .  No. o f u n i t s Space r mate r i a l Channe1 t h i c k n e s s [cmU Membrane  in First  glass  f i b re  0.205  material  Cap ac i t y ce 1 1 type F r e e2 f1ow vo1ume [cm ]  VEXAR® LI2 0 . 127 o r 0.116  glass 0.165  f i b re o r 0.155  NEOSEPTA CL 25T & AV4T  with  core  282  no  core  387 o r 373  no  core  389 o r 370  The stacks were assembled to form packs using two PVC clamps as shown i n Figure 24b.  These packs f i t t e d  centre frame opening and were i n s e r t e d as one block to  Figure 24c.  i n t o the  according  80  Figure  24.  L I e c t r o d i a I y z e r N o . I. (a) capacity c e l l core (scale :  Spacer screens inches).  and  F i g ure  2 4.  E I e c t r o d i a I y z e r No. r i g i d c e n t r e frame  I. (b) (scale :  Stack-pack and inches).  Figure  24.  E I e c t r o d i a I y z e r No. assemblinq (scale :  I. (c) C e l l inches).  ready  for  83  4.2.3  Process  flow.  It was planned that the volume of each pulse would be of the same magnitude as the f r e e of the e l e c t r o d i a l y s e r . piston The  ,  flow volume  Since t h i s was r e l a t i v e l y s m a l l , a  pump d r i v e n by a v a r i a b l e  features  displacement  speed D.C. motor was f e a s i b l e .  of t h i s combination a r e :  1.  Positive  2.  Pump body and end r e s e r v o i r  3.  R e v e r s i b l e with minimal  4.  Short  5.  No dead  6.  Accurate  7.  Piston displacement for timing.  8.  May be m o d i f i e d square p u l s e s .  9.  S i m p l e c o n s t r u c t i o n , may be m a n u f a c t u r e d according t o s p e c i f i c a t i o n s in workshop.  10. The drawal pump. specifications The  displacement.  start-up  time  a r e one  part.  time l a g .  (i.e.  square  pulses).  volume. flow  rate  setting.' i s natural  t o produce o t h e r  R e l i a b l e because very reciprocating  trigger  piston  little  than  wear.  acted as an i n f u s i o n - w i t h -  The pump was manufactured a c c o r d i n g to the given i n Table 5. cylinder  of the p i s t o n  tank at one end of the process  line.  pump formed the storage The o p p o s i t e end of the  84  Table 5 Piston  Pump  Specifications  2  P1STON FACE AREA Ccm ]  PUMP  MAXIMUM PISTON  22 . 88  MOVEMENT  DISPLACED VOLUME  0 to 630  [cm ]  FLOW RATE [cmVsec] DRI VE  27.5  [cm]  3  2.5  to 75  1/4 hp DC MOTOR SCR MOTOR CONTROL REDUCTION  BOSTON RAD 1OTROL E25  GEAR RATIO  1 /48  P I N I O N ^ a n d RACK  l i n e was  connected to a f l o a t i n g  shown i n Figure  4.2.4  l i d expansion tank which i s  26.  Timing and  switch  boxes.  As mentioned i n the previous  s e c t i o n , the  linear  placement of the p i s t o n i s used to t r i g g e r timing and ing  circuits.  under 4.1  In the c y c l i c  not  time.  independent v a r i a b l e s and provided  for these.  switch-  operation described in d e t a i l  the n a t u r a l c o n t r o l v a r i a b l e  placed volume and  dis-  for switching i s d i s -  However, the pause times  separate  are  timing devices have to be  117 V G  60  ~  L  N  6.5 "  -7'  !  4  m1  • • ft — • n— • Q  <S  9  D2  R4  00  ro \  \  VA  R3  V V  DI  Rl  my  / / / /  R2 R j l /  +  —e  9> -Sj-  Figure 26.  &  Floating  l i d expansion  ro  "7  1  \  ^ D2  —  4  I  R4  tank  SWI  SW2  PUMP  Fi gure  27.  DISPLACEMENT  Automatic s w i t c h i n g arrangement f o r c y c l i c e l e c t r o d i a l y s i s process S = s w i t c h , R = r e l a y , D = time delay C = electromechanical counter, SW = m i c r o sw i t c h .  00  relay  86  Figure 27 shows how d i s p l a c e d volume and pause times are c o n t r o l l e d :  A cam i s attached  which d r i v e s the p i s t o n .  to the r e c i p r o c a t i n g  T h i s cam operates  rack  microswitches  SW1 and SW2 which are a d j u s t a b l y mounted.  Relays  Rl and R2 are used to reverse the p o l a r i t y  armature (see Figure 28). solid  s t a t e delayed  of the motor  Both a r e , however, delayed by  r e l a y s DI and D2 ( P o t t e r and B r u m f i e l d  CDB38-70004, a d j u s t a b l e from 0.6 to 60 s e c o n d s ) .  Relays  R3 and R4 c o n t r o l the p o l a r i t y  of the e l e c t r i c  which i s a p p l i e d to the e l e c t r o d i a l y s i s DCRA 40-10A power s u p p l y .  potential  cell  from a S0RENS0N  The r e l a y c i r c u i t  i s i d e n t i c a l to  the one shown i n Figure 28 except that the input comes from the DC power supply  and the output goes to the c e l l .  When the p i s t o n i s moving the c i r c u i t s contacts  are s e l f - h o l d i n g  using  R3/1 or R4/1.  An e l e c t r o m e c h a n i c a l by means of contact  The  counter  C r e c e i v e s one i n p u l s e every  cycle  Rl/1.  switch boxes SB1 and SB2 i n Figure 22 c o n s i s t  of the f o l l o w i n g components which are combined i n one network:  m z  R2 3  m 3  9 90  a  R2 2  <>6  a  87  ?o  IN  &-9  OUT  0 D.C.  - +  M O T O R S P E E D  '  + B O S T O N  CONT. R A D I  Figure 28.  P i s t o n Pump D r i v e . reve rs a I .  Electric  circuit  O T R O  f o r motor  E L E C T R O D E  A N I O N I C  C A T I O N I C  E L E C T R O D E  E N D  M E M B R A N E  M E M B R A N E  E N D  F R A M E  8 E L E C T R O D E  L  F R A M E  C E N T R A L F R A M E S  I.  E L E C T R O D E  V A N I O N I C M E M B R A N E  S P A C E R  Figure  30.  Schematic assembly eIectrod i a Iyzer.  S P A C E R  o f one  s t a g e of t h e  second  88  4.2.5  Rinse  SB1  : r e l a y s R3  SB2  : r e l a y s Rl , R2 , DI , D2  e l e c t r o d e wash l i q u o r was  pump from a p l a s t i c frames.  pumped by a p e r i s t a l t i c  tank through a flow s p l i t t e r It returned  streams were remixed.  Plastic  to each e l e c t r o d e to be  4.2.6  R4  loop.  The  trode end  and  Measuring and  to the  to the h o l d i n g tank where tubing allowed  the  flow  rates  balanced.  Sodium c h l o r i d e c o n c e n t r a t i o n  continuously  measured c o n d u c t o m e t r i c a l l y .  tivity  (Beckman I n s t r . , CEL-VDJ s e r i e s ) used with  reading  monitored the c o n c e n t r a t i o n s  provided.  cell.  A 0 to 10  Meter allowed  of the s o l u t i o n  flows  D.C.  potentiometric  in the f o l l o w i n g ranges  output s i g n a l  r e c o r d i n g of the  (see Table  6).  direct RA5)  at both  Automatic temperature compensation [mV]  was  Flow type conduc-  c o n d u c t i v i t y meters (Beckman I n s t r . , Solu-Meter  ends of the ED  the  recording.  Concentrations:  cells  elec-  from the  was  Solu-  concentration  89  Table  Conductivity  and NaCI  Conductivity  6  Concentration  Cells  CEL-VDJ  0-IOCm V ] D . C . s i g n a l  The  concentration  CppmD  2,500  0 -  1,300  20  0 --  10,000  0 -  5,480  50  0 -- 25,000  0 -  15,370  accuracy  of the output s i g n a l  every  The  c u r r e n t was  recorded  experiment a D.C. to f u l l  The  using  r e c o r d e r (see below). and  shunt Prior  the  Current  continuously.  p r e p a r a t i o n of probe e l e c t r o d e s  been d e s c r i b e d in d e t a i l  the s t a c k .  potential  of known magnitude  s c a l e of the r e c o r d e r pen  The  picked up by these  (16 gauge).  current signal  s c a l e v e r n i e r of the  Voltage:  as the  scale.  to the length of the w i r e .  t h e r e f o r e measured d i r e c t l y  across  i s ±0.5% of f u l l  a Nichrome r e s i s t a n c e wire  calibrated  sliding  was  solution  0 --  resistance varied according  was  NaCI  5  drop across  was  RA5  Con d u c t i v i t y Cm i c r o m h o s / c m ]  Current:  to  Corresponding to a  f r o m a BECKMAN  So I u - M e t e r  Ce11 C o n-s1 t a n t K [cm ]  Ranges o f BECKMAN  in S e c t i o n 4.2.1.  probes represented  The  signal  has which  the voltage drop  Continuous r e c o r d i n g of t h i s probe voltage  90  allowed the average stack local  p o t e n t i a l to be determined.  changes could be used to i d e n t i f y p o l a r i z a t i o n  Recorder:  the f u l l  pH:  effects.  The above s i g n a l s were traced by a  WATANABE 4 pen r e c o r d e r , model MC6-11S4H. utilized  The  A l l four pens  chart width of 25[cm].  Samples f o r pH-checks were taken f o r some runs  j u s t p r i o r to the experiment and immediately t h e r e a f t e r from both process and r i n s e stream and measured i n the usual  4.3  The Mini  P i l o t P l a n t Module  The to the f i r s t  way.  p r i n c i p l e m o d i f i c a t i o n of t h i s module compared one c o n s i s t e d of a complete redesign  electrodialysis  cell.  the r i n s e loop  as well  This  of the  n e c e s s i t a t e d m o d i f i c a t i o n s to  as a d d i t i o n s to c u r r e n t  and voltage  measuring systems.  4.3.1  E l e c t r o d i a l y s e r No. 2 (EDI I) Based on the experience with  the f i r s t  ED c e l l  a  staged e l e c t r o d i a l y s e r was developed which c o n s i s t e d of e i g h t equal s t a g e s , each composed of e i g h t membrane-spacer frames and  two e l e c t r o d e end frames. The  ing  device  e i g h t stages  as i l l u s t r a t e d  were mounted i n a two l e v e l i n Figure 29.  The stages  clamp-  were  91  F i gu r e  29 .  Clamping arrangement of e i g h t s t a g e s in mini p i l o t p l a n t module ( s c a l e : c e n t i m e t e r s ) .  92  numbered from 1 to 8 s t a r t i n g from the d i a l y s a t e stages were always connected i n s e r i e s usually  in parallel e l e c t r i c a l l y .  end.  hydraulically  The  and  Less than e i g h t stages  could be operated on l i n e by changing tube connections and d i s c o n n e c t i n g the i d l e stages from the e l e c t r i c power. Each stage was a complete e l e c t r o d i a l y t i c c e l l , i n itself.  Apart from the l o c a t i o n  of r i n s e  and process  flow  ports i n the e l e c t r o d e end frames the stages were i d e n t i c a l . In c o n t r a s t to the f i r s t  ED c e l l , which had a r i g i d  centre  frame to hold the membrane-spacer s t a c k , the new design tures a m u l t i p l e - f r a m e centre p a r t . the  A schematic p i c t u r e of  assembly i s given i n Figure 30, (page 87). Each c e n t r a l  frame c o n s i s t e d of three components  which were permanently j o i n e d (i)  (ii)  (iii)  The The  fea-  t o g e t h e r , see Figure 31:  An o u t e r s e a l i n g frame ( 8 - 7 / 8 " x 3 " x 1 / 1 6 " ) w i t h keyshaped l i q u i d d i s t r i b u t i o n slots, made o f low d e n s i t y p o l y e t h y l e n e . A t r i p l e membrane 6 - 3 / 8 " x 1 - 3 / 4 " , composed o f two i o n e x c h a n g e membranes ( C I 0 0 and A I 0 0 , c a t i o n and a n i o n s e l e c t i v e r e s p e c t i v e l y , A m e r i c a n M a c h i n e and F o u n d r y C r o p . ) and a l a y e r o f Whatman f i I t e r p a p e r N o . I. A spacer screen 6-14/16" x 1-7/8" x 0.038" Vexar® T P 2 3 , 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 , made o f c l e a r p o l y p r o p y l e n e . membranes were heat s e a l e d along both short  sides.  long s i d e s remained open to i n s e r t and to remove the f i l t e r  paper.  93  polypropylene spacer screen  welded spacer frame  triple membra ne  a  ssemb I y  poIyethyIene f rame  F i g u re  31.  Integrated membrane-spacer d i a l y z e r No. 2. P a r t s and  frame f o r e l e c t r o assembly ( s c a l e : inches)  94  Figure  32.  E i e c t r o d i a I y z e r No. s i n g l e stage (scale  2. Electrode : inches).  end  frames  of  a  95  The  polypropylene spacer screen was  the frame by means of a heated j i g . was  tagged  into  Then the t r i p l e membrane  at three corners to the frame using a heated  A more d e t a i l e d d e s c r i p t i o n may  pressed  be found  of the manufacturing  in Appendix A.3.  bar.  procedure  I t should be noted that although  approximately 20 d i f f e r e n t o p e r a t i o n s were necessary to produce one  u n i t , a l l 64 membrane-spacer frames showed e x c e l l e n t  s i mi 1ari t y .  ing  (or  The  e l e c t r o d e end  frames had  1.  Hold the e l e c t r o d e s  2.  Provide  3.  Distribute  the  follow-  tasks:  from)  a rinse  t h e membrane Provide  4.  with t h e i r  (or c o l l e c t )  the  double  the process  flow  into  stack.  shows how  face. the end  meet these demands, see also Figure The  terminals.  chamber.  a sealing  Appendix A.2  of  to f u l f i l l  pass  r i n s e was  frame was  designed to  32. an important  characteristic  construction. The  external  pipe connections f o r the process  t i o n were l o c a t e d i n the e l e c t r o d e end illustrates  the i n t e r n a l  flow  frames.  solu-  Figure 33  distribution.  H y d r a u l i c leaks between r i n s e and  process  could be avoided by 0 - r i n g s e a l s as i n d i c a t e d  stream  i n Figure  33.  96  These were the only gaskets i n a d d i t i o n  to the  separating  membranes, see a l s o Figure 30» (page 87).  OUT  Figure  33:  Process flow through second e I e c t r o d i a Iyser stage.  Table 7 summarizes the s p e c i f i c a t i o n s of the second electrodi alyser:  97  Table Electrodialyser  Des i gn Eight  Membrane-Spacer F rame  E1ectrode  7 No. 2  M u l t i p l e Frame S t a c k S t a g e s w i t h E i g h t Frames  * Vo1ume  Inherent  Dead  Membrane  Utilization  Volume  **  Rinse  System  * Gas k e t s  M a t e r i a 1s  per  Each  Composite Pop-In U n i t , 3 P a r t s Permanently Joined  Area  A c t i ve V o i d  (EDM)  2  60  [cm ]  50  [cm ]  10  [cm ]  97  [*]  Doub1e  3  3  Pass  2 S e p a r a t i n g Membranes 4 0-Rings f o r Process Flows  S t a c k Frame E l e c t r o d e Frame Electrode Te rm i na1  Polyethylene Plexiglass Graphite Graph i t e  stage  ** f r a c t i o n of t o t a l transfer.  membrane  area  available  for ionic  98  4.3.2  Rinse  distribution  system.  wash l i q u o r  (10,000  The was  pumped by a c e n t r i f u g a l  from a two-gallon fold  and  tank.  the  The  Current  and  Current individually  returned +  measured at 0.90  did not  Q"O8  require special  to the  holding  [litre/min]  control.  voltage measurements. consumption and  f o r each sta.ge..  number of pens, only one recorded  pump (Cole Parmer, model MDX-3)  compartments and  rate was  per compartment and  4.3.3  aqueous NaCl s o l u t i o n )  p l a s t i c tank through a d i s t r i b u t i o n mani-  16 r i n s e  flow  [ppm]  stack  v o l t a g e were measured  However, because of the  c u r r e n t and  one  limited  voltage s i g n a l  were  simultaneously.  Current Shunts were prepared  from NICHR0ME r e s i s t a n c e wire  (14 gauge), and  i n t e g r a t e d i n t o the e l e c t r i c a l  manifold  distributed  D.C.  (see  22)  the  to the s t a g e s . The  power from switch box The  w i r i n g i s shown i n Figure  Figure  34.  shunt r e s i s t a n c e s were 50.0[mft] ± 1.5%  c u r r e n t s to the i n d i v i d u a l current.  SB1  stages  and  25.0  which  mfi f o r the  f o r the total  99  SELECTOR SWITCH  TO RECORDER  Figure  34.  Current monitoring  circuit.  100  Voltage Probe e l e c t r o d e s were prepared from s i l v e r wire cable (8 leads of l [ f i / f t j into strips  r e s i s t a n c e wire) which was hammered  approximately 1/8" wide and 5/1000" t h i c k .  The  s t r i p s were dip coated with waterproof c o n t a c t cement (Canadian  I n d u s t r i e s L i m i t e d ) and the c o a t i n g was removed  from one s i d e of the t i p which was l o c a t e d The  i n s i d e the s t a c k .  probes were i n s e r t e d between the s e p a r a t i n g membranes  and the stack pack and s e a l e d with s e l f - s e t t i n g  silicon  rubber g e l . A second  s e l e c t o r switch was connected  and to one r e c o r d e r pen. one  shown i n F i g u r e 34.  to the probes  The c i r c u i t i s analoguous  to the  Chapter 5  EXPERIMENTAL RESULTS AND DISCUSSION  In t h i s chapter the experiments correlated  complete details  are compiled and  i n three ways: a.  Survey t a b l e s f o r each s t a c k c o n t a i n t h e o p e r a t i n g c o n d i t i o n s and t h e l i m i t i n g , steady - p e r i o d i c state r e a c h e d a f t e r a c e r t a i n number o f cy I c e s .  b.  Group t a b l e s and d i a g r a m s i I l u s t r a t e the e f f e c t of s i n g l e v a r i a b l e s under otherwise fixed conditions.  c.  I n d i v i d u a l t a b l e s and d i a g r a m s p r e s e n t a record of the t r a n s i e n t s f o r s i n g l e test runs.  The  c o l l e c t i o n of raw data during the course of a  batch  run w i l l  be d e s c r i b e d f i r s t , f o l l o w e d by  about the p r o c e s s i n g of these data i n t o  Subsequently, a discussion  of the v a r i a b l e s  the main f e a t u r e s of the process phenomena. section  of t h i s chapter the a p p l i c a t i o n  results  to the o p e r a t i o n of a continuous  di cussed. 101  will  table  form.  illustrate  In the c o n c l u d i n g  of these batch system w i l l  be  system  5.1  Data  Collection A complete batch run c o n s i s t e d of the f o l l o w i  consecutive  steps:  1.  F i l l r i n s e t a n k w i t h 6 t o 8- l i t e r s o f f r e s h r i n s e l i q u o r (NaCI i n d i s t i l l e d water, varying concentration).  2.  F i l l system with process s o l u t i o n of d e s i r e d c o n c e n t r a t i o n (NaCI i n d i s t i l l e d wate r ) .  3.  Start  4.  S t a r t p i s t o n pump t o e q u i l i b r a t e s o r p t i o n membranes w i t h p r o c e s s s o l u t i o n .  5.  A d j u s t check p o i n t meters.  6.  C a l i b r a t e r e s i s t a n c e of c u r r e n t shunt u s i n g r e c o r d e r pen ( f i r s t ED c e l l o n l y ) .  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 pH s a m p l e s o f p r o c e s s and r i n s e solution.  9.  S e t o p e r a t i n g c o n d i t i o n s (pump d i s p l a c e m e n t , dead v o l u m e s , pump s p e e d , p a u s e times, applied D.C. voltage).  rinse  pump.  of  conductivity  10.  N o t e 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 e a c h pen and appropriate range, chart speed.  11.  Check t o t a l  12.  Turn  13.  C l o s e e l e c t r i c power c i r c u i t a f t e r comp l e t i o n of next foreward s t r o k e of p i s t o n pump ( t h e membrane a r r a n g e m e n t and t h e e l e c t r o d e p o l a r i t y i s s e t t o demineralize the s o l u t i o n during t h i s f i r s t h a l f eye I e ) .  counter  cycle period with  stop  watch.  b a c k t o z e r o , and  103  14.  R e c o r d c u r r e n t and v o l t a g e f o r d i f f e r e n t s t a t i o n s by i n g s e l e c t o r s w i t c h e s , and t r a c e s a c c o r d i n g l y (second only).  signals manipulatmark pen ED c e l l  15.  W r i t e down any o b s e r v a t i o n to experiment.  related  16.  Change r e c o r d e r pen r a n g e s i n o r d e r t o u t i l i s e maximal c h a r t w i d t h .  17.  T e r m i n a t e run when s t e a d y p e r i o d i c s t a t e i s r e a c h e d by d i s c o n n e c t i n g power s u p p l y , and s t o p p i n g p i s t o n pump i n t h i s o r d e r .  18.  Read t o t a l down .  19.  Take pH s a m p l e s o f p r o c e s s and r i n s e streams, or e q u i l i b r a t e c o n c e n t r a t i o n o f p r o c e s s s o l u t i o n t o c h e c k mass ba I ance f o r s o l u t e .  20.  T e s t pH s a m p l e s and n o t e  The information  number of  c y c l e s and  down  note  results.  r e c o r d e r chart thus contained a l l the  related  to the  were e x t r a c t e d from the  test run.  The  following  original details  chart.  a.  Mean p r o d u c t c o n c e n t r a t i o n s i n end r e s e r v o i r s a f t e r each c y c l e . These were c o n v e n i e n t l y o b t a i n e d as t h e r e f l u x c o n c e n t r a t i o n s s i n c e both r e s e r v o i r s were r e a s o n a b l y w e l l m i x e d .  b.  Mean c u r r e n t c o n s u m p t i o n f o r any h a l f cycle. The l o c a l c u r r e n t t r a n s i e n t s were a v e r a g e d e i t h e r pI a n i m e t r i c a I Iy o r by an i n t e g r a t o r r e c o r d e r . The t o t a l c u r r e n t c o n s u m p t i o n of t h e s e c o n d ED c e l l module was r e c o r d e d c o n t i n u o u s l y d u r i n g t h e f i r s t c y c l e s , and i n a r o t a t i n g sequence with the i n d i v i d u a l stages t h e r e a f t e r .  104  5.2  c.  Mean s t a c k v o l t a g e f o r e a c h h a l f c y c l e . T h i s was e v a l u a t e d pI a n i m e t r i c a I I y . A g a i n , t h e s t a g e s were r e a d i n r o t a t i o n f o r t h e s e c o n d ED c e l l .  d.  L o c a l t r a n s i e n t s of c u r r e n t , v o l t a g e , and e f f l u e n t c o n c e n t r a t i o n s c o n t a i n e d a d d i t i o n a l i n f o r m a t i o n r e l a t e d t o mass t r a n s f e r m e c h a n i s m s and i n t e r n a l c o n c e n tration distributions.  Main Survey Tables Current and  proper units of the  by  c o n c e n t r a t i o n data were converted  means of c a l i b r a t i o n c u r v e s .  main survey t a b l e s Run number  1.  are  (see  (#):  The  were numbered c h r o n o l o g i c a l l y order.  Two  and  numbers separated by  Tables 8 to  they are  Initial  NaCI i n d i s t i l l e d  3. solution tivity  in t h i s  indicate  a change  (c ) 0  i n parts per  million  water.  (6)  as  contained i n the  f r a c t i o n of the  system between the  free conduc-  cells.  4. second.  each stack  run.  concentration  D i s p l a c e d volume  volume V0  listed  a dash (-)  columns  13):  experiments on  in o p e r a t i n g c o n d i t i o n s during the  2.  The  into  Superficial  This i s based on  velocity the  (v)  active  i n centimeters  void  volume ( V ) a  per of  the  105  stack  and  the t o t a l  length  {&)  of the e l e c t r o d e s  i n flow  di r e c t i on.  where  Q = volumetric pump.  5.  Pause t i m e  flow  (x)  rate d e l i v e r e d by  in s e c o n d s .  given when the pause times f o r f i r s t were equal .  and  piston  A s i n g l e number i s second h a l f c y c l e  For unequal pause times the n o t a t i o n  f o r 10 sec during  6.  10/5  d e m i n e r a l i z a t i o n , 5 sec during  Cycle  p e r i o d (T)  in s e c o n d s .  stands  enrichment.  Since  the  flow  rates Q were equal f o r both h a l f c y c l e s T i s c a l c u l a t e d as  V  T1 = ? ° ' *• Q  where t T and and  8  +  TT  +  T  TT  B  Tg are the pause times f o r d e m i n e r a l i z a t i o n  enrichment r e s p e c t i v e l y .  7. voltage  Applied  i s given  8.  potential  because t h i s  Number of  in v o l t s  (A$).  The  electrode  i s the true independent v a r i a b l e .  e y e Ies ( n c ) .  The  subsequent columns  r e f e r to c o n d i t i o n s which e x i s t a f t e r nc c y c l e s from s t a r t - u p .  106 Total  9. is for  the a r i t h m e t i c  current  ( I ) in amperes.  mean of the average c u r r e n t consumption  d e m i n e r a l i z i n g and e n r i c h i n g  half  Brine concentration  10.  This base c u r r e n t  cycles.  ( x D ) and D—  Dialysate concentration  11.  with r e s p e c t to the i n i t i a l  brine  of dead volumes* 6g  and  respectively  (6g  free solution  volume  and  6T  8j  V0  in brine  second ED  (see item 3 ) ) , whether  *  reservoir,  limiting  and the number of stages f o r  cell.  main survey t a b l e s  presented on the f o l l o w i n g  interrupted  and d i a l y s a t e  are given as f r a c t i o n s of the  are reached or n o t ,  The are  (top product) c o n c e n t r a t i o n  T h i s c o l u m n c o n t a i n s comments o n : The presence  13.  the  ( n s ) d e f i n e d as the r a t i o of  (bottom product) to d i a l y s a t e  conditions  normalized  concentration c 0 .  Separation factor  12.  (x^-) both  of a l l s u c c e s s f u l  pages.  Successful  by m e c h a n i c a l , e l e c t r i c a l , or human  Or excess volumes.  experiments means not  failure.  Table 8 C o m p i l a t i o n of Experiments on EDI-S1-8  J  2  RUN NO.  2  JL  _5  6  Z  8  9  VOLTAGE CYCLE CURRENT CONCENTR. VOLUME VELOCITY PAUSE CYCLE DISPLACED SUPERFICIAL TIME INITIAL PERIOD APPLIED NO. TOTAL  in  CONCENTRATION BRINE  %  [-] 1 2 3 4 5 6 7 8 9 10-0 -1 14 15-0 -1 21 22 23 24 29 30 31 32 33 34 35 36 37 38 39 40 41 42  X  Co [ppm]  6 [-]  1090 1050 1040 1050 1090 1080 1090 1090 1080 1110  1.10 1.10 1.10 1.10 1.10 1 .73 1 .73 1 .73 1 .73 1 .73  1020 1020  1.00 1.00  770 775 760 765 850 700 710 720 710 700 700 700 720 725 710 760 760 760  1 .00 1 .00 1.00 1.00 0.42 1.75 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1.00 1 .80 1.80 1 .00 1 .00 1 .00  '  • V  T  T  AO  nc  I  B  [cm/sec]  [sec]  [sec]  [volt]  [ -]  [ampere]  [ - J  1.21 1.21 1.77 2.33 1.21 1 .21 1.21 . 1.662.62 0.65 1 .21 1 .21 1.21 0.65 0.65 1.21 1 .21 1.21 2.33 1 .77 1 .77 1.77 2.33 2.89 1 .21 0.65 0.65 1.21 1 .21 1.21 1.21 1.21  * Probe v o l t a g e , hand r e g u l a t e d .  _  -  -  -  • -  -  ._  -  '  53.3 53.3 36.4 27.6 53.3 84.3 84.3 61 .4 39.0 157.4 84.3 50.2 50.2 93.8 93.8 50.2 50.2 50.2 8.7 57.1 34.3 34.3 26.1 21 .0 50.2 93.8 93.8 87.3 87.3 50.2 50.2 50.2  4 6 6 6 6 4 6 6 6 8 8 6 6 4* 5* 5* 11 7.55 7.55 12.5 12.5 12.5 12.5 12.5 5.0 15.0 20.0 6.0 10.0 20.0  10 7 8 9 8 6 9 12 10 9 16 7 9 13 7 10 • 10 10 40 10 13 6 10 9 9 8 5 6 5 8 7 7  _  0.37 0.385 0.40 0.35 0.23 0.37 0.39 0.41 0.52 0.57 0.32 0.32 0.30 -  -  . 1 .00 0.35 0.55 0.60 0.65 0.55 0.50 0.20 0.60 0.75 0.28 0.44 0.78  n  1 .020 0.995 0.999 0.998 1 .005 1 .030 1 .020 1 .010 1 .010 1.110 1 .020 0.969 0.970 0.965 0.950 0.955 0.956 0.962 1 .10 1 .03 0.99 0.95 0.965 0.975 0.96 1 .04 1 .02 1 .02 1 .07 0.986 0.956 0.972  12 SEPARATION FACTOR  REMARKS  s  L = l i m i t reached NL = l i m i t not reached 6g/5y = dead volumes  D I A LX Y S A T E  T  11  n  [ -]  [ -]  1 .020 0.999 0.996 1 .000 1 .000 0.974 0.938 0.955 0.972 0.900 0.928 0.983 0.997 0.972 1 .000 1 .010 1 .010 1 .020 0 .969 0.973 1 .00 0.97 0.985 0.99 0.96 0.935 0.98 0.862 0.86 0.995 0.975 0.954  1 .00 1 .00 1 .00 1 .00 1 .01 1 .06 1 .09 1 .06 1 .04 1 .23 1.10 0.99 0.97 0.99 0.95 0.95 0.95 0.95 1.13 1 .06 0.99 0.98 0.98 0.985 1 .00 1.11 1 .05 1.19 1 .25 0.991 0.980 1 .02  NL NL NL NL NL L L L L L NL NL L L NL L L L L L L L L L L L L L L L L L  Table 9 Compilation of Experiments on EDI-S2-15  1 RUN  7 NO.  5  6  7  8  9  VOLTAGE CYCLE CURRENT CONCENTR. VOLUME PAUSE CYCLE VELOCITY DISPLACED SUPERFICIAL TIME PERIOD APPLIED TOTAL INITIAL NO.  #  c0  6  [-]  [ppm]  [-]  1 2 3 4 5-0 -1 6 7 8 9 10 11 12-0 -1 13 14 15 16 17 18 19 20 21 22 23 24 26 27 28-0 -1 -2 -3 29 30-0 -1 31 32 33  n  3  T  T  A<t>  nc  [cm/sec]  [sec]  [sec]  [volt]  [-]  1.29 0.47 1.41 1.41 2.11  0 20 10 10 5 10 10 0 0 0 0 5 5 10 10 15 15 25 0 14 7 7 7 0 0 3.5 15 15 5 10 15 : 5 0 7 14 25 3.6 15  V  930 890 910 910 930  0.95 0.95 0.47 0.47 0.47  990 940 950 970 960 960 940  1.00 1.00 1.00 1.00 1.00 ' 1.00 ' 1.00  '  2.23 0.88 0.88 • 0.88 0.88 • 2.23 2.23  930 980 960 975 1025 1010 1020 1040 980 1050 1020 1020 1020 1090 1070  1.00 1.00 1.00 0.59 1.0 1.0 0.5 0.5 0.5 0.5 1.0 0.25 1.0 1.0 1.0  2.23 2.23 ' 0.47 0.47 0.88 1 .70 1.70 1 .70 1.70 0.88 1.70 1.70 0.47 2.23 2.23  1070 1010  1.54 0.5  0.88 1.77  1030 1120 1150  0.59 0.25 1.0  0.47 1.70 2.23  35 137 36 36 21 31 42 '55 55 55 55 32 32 42 42 52 132 111 • 55 56 28 28 '28 28 29 14 132 52 32 42 52 32 84 28 42 111 14 52  4 10 16 16 16 20 8 16 24 32 32 32 16 16 16 16 40 • 40 40 40 40 40 32 40 24 32 32  40 16 16 . 40 32  I  in  CONCENTRATION  1? SEPARATION FACTOR  BRINE DIALYSATE X  B  [ampere] [ - ]  10 0.23 8 0.30 15 0.60 14 0.60 14 ' 0.74 25 0.62 14 0.75 10 0.40• 0.70 10 10 0.85 10 1 .00 14 1 .25 1 .25 10 • 16 0.90 0.65 10 10 0.60 7 0.43 15 0.30 10 1 .30 7 1.15 14 • 1.40 15 1 .28 22 1 .32 10 1 .25 1 .44 10 1.72 65 8 0.48 0.96 10 4 1.38 7 1.18 11 1 .00 18 1 .30 6 1.05 21 0.80 34 0.52 13 0.36 1 .70 60 11 0.90  11  1 .00 1 .45 1 .37 1 .50 1 .25 1 .50 1 .23 1 .01 1 .01 1.07 1.14 1 .29 1 .31 1 .41 1.28 1 .32 1 .42 •1 .60 1.14 1 .54 1.72 1 .50 1 .54 0.98 1 .00 1 .42 1.51 1.46 1 .25 1 .37 1 .45 1.28 1.20 1 .27 1 .41 1 .55 1 .63 1 .39  X  T  n  s  [-]  [ - ]  0.990 0.580 0.566 0.582 0.722 0.563 0.641 0.935 0.858 0.801 0.750 0.631 0.623 0.548 0.671 0.607 0.585 0.397 0.747 0.561 0.529 0.463 0.568 0.950 0.888 0.468 0.582 0.537 0.719 0.615 0.540 0.644 0.670 0.621 0.486 0.449 0.494 0.517  1 .01 2.50 2.42 2.59 1.73 2.67 1.92 • 1 .08 1.18 1.33 1 .52 2.05 2.10 2.58 1 .91 2.17 2.43 4.03 1 .52 2.75 3.24 3.24 2.72 1 .03 1.13 3.02 2.60 2.72 1 .74 2.23 2.69 1 .99 1 .80 2.05 2.91 3.45 3.31 2.70  13 REMARKS L = l i m i t reached NL = l i m i t not reached = dead volumes L NL L, « I  NL NL L L L L L L L NL L NL L NL, L L L NL, NL, L, NL NL, L L NL NL NL L L L, L L, NL L  B  -  5 B = .35  6 B = .5 SB=<5T = 1.0 «B = 1-5 6 B = -75  <5B = -5 «B.»  Table 10 Compilation of Experiments on EDI-S2-16  1  2  3  4  5  6  7  8  9  CONCENTR. VOLUME PAUSE CYCLE VOLTAGE CYCLE CURRENT VELOCITY RUN NO. INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL #  Co  6  [-]  [ppm]  [-]  V  [cm/sec]  T  T  [sec] [sec]  AO [volt]  nC  I  11  1?  13  CONCENTRATION  SEPARATION FACTOR  REMARKS  BRINE DIALYSATE T B  ns  10  X  X  [ -][ampere] [ - ] [ " ]  1  1100  1.00  2.32  15  52  32  2  1070  1.00  0.92  15  85  32  9  3-0  1175  0.61  0.92  15  52  32  14  25  72  20  4  1220  0.61  0.92  25  72  32  14  5-0 -1  1250  0.61  0.92  15 25  52 72  32  -2  0.49  25  111  -3  1 .77  25  -4  0.92 0.92  0.484  0.71  1 .55  0.476  3.25  L  0.70  1 .88  0.341  5.52  NL  0.60  2.04  0.274  7.46  L  0.70  2.11  0.278  7.58  L  13 21  0.70 0.50  1 .36 1 .41  0.238 0.179  5.71 7.88  NL, 6 B = 1.84 L, 6 B - 1.8*.  32  40  0.40  1 .46  0.158  9.24  L, 6 B = 1.84  67  32  50  0.45  1 .44  0.176  8.18  NL, 6 B = 1.84  25  72  16  60  0.30  1 .40  0.222  6.32  NL, 6 Q = 1.84  -1  15 25  52 72  16 16  . 16 22  0.50 0.40  1 .29 1 .32  0.308 0.250  4.18 5.28  L, 6 B = 1.84 L, 6 B = 1.84  -2  15  52  40  38  0.63  1 .43  0.196  7.05  L,  6 R - 1.84  0.52  1 .41  '0.142  10.10  L,  6 B - K84  1 .50  1.11  0.585  1 .88  L, 6 B = 1.84  1 .54  L  6-0  1225  0.61  -3 7 8-0  1250 1240  0.61 0.61  0.92 0.92  -1 9-0 -1  1200  1.00  0.92 0.49  25  72  40  45  0  22  40  50  0.84  L  1.47  -1  10  [- ]  L = l i m i t reached NL = l i m i t not reached 6g/6y = dead volumes  3.04  0  22  32  30  1 .41  1.10  0.714  0  22  40  50 "  1 .60  1 .22  0.630  1 .94  L  0  53  40  15  1 .26  1 .31  0.589  2.22  L  99  40  19  0.84  1 .48  0.447  3.31  NL  o cr  Table 11 Compilation of Experiments on EDI-S3-12  1 RUN NO.  2  3  4  5  fi  7  8  q  PAUSE CYCLE VOLTAGE CYCLE CURRENT VELOCITY CONCENTR. VOLUME TOTAL INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO.  in  CONCENTRATION BRINE  [-] 1-0 -1 -2 -3 -4 2-0 -1 -2 3-0 -1 -2 4-0 -1 5-0 -1 -2 -3 6-0 -1 -2 -3 -4 ' 7 7a 8 8a 9-0 -1 -2 -3 10-0 -1 11 11a 12-0 -1 -2 13  Co  6  [ppm]  [-]  [cm/sec]  1225  1 .00  1.33 0.92  1220  0.59  0.49 0.92  1230  0.59  0.49 0.92  1245  0.59  0.49 0.92  1280  0.59  1280  0.47 0.29 0.29  0.92 0.49 0.49 0.49 1 .33 0.92 0.49  1280 1280 1270 1270 4800  0.12 0.59 0.59 1 .00 1 .00 1 .00  0.49 0.49 0.49 0.92 0.92 0.92  4680  0.59  0.92  4560 4600 4690  1 .00 1 .00 0.59  4830  1 .00  V  T  T  [sec] [sec]  0.92 0.92 0.92 0.49  0 0 5 15 15 15 25 25 15 25 25 15 25 25 25 25 25 10 10 10 20 20 20 20 20 20 0 5 10 15 15 • 25 15 15 15 30  36 52 62 82 129 62 82 111 62 82 111 62 82 82 111 96 80 31 36 50 70 52 .100 100 93 93 53 63 73 83 62 82 83 . 83 62 120  0.92  15  83  AG  nc  I  [volt]  [-]  [ampere]  32  10 18 25 30 35 20 25 31 16 24 30 16 23 16 20 28 36 50 60 70 80 145 15 15 10 12 5 10 20 35 15 20 11 15 20 29 33 10  1.50 1 .35 1.20 1.00 0.70 0.90 0.70 0.62 0.80 0.60 0.50 0.90 0.70 0.75 0.70 0.65 0.56 0.65 0.60 0.55 0.45 0.35 0.85 0.75 0.95 0.75 3.10 3.00 2.70 2.30 3.20 2.80 3.60 3.10 2.00 1.30 1.40 2.20  32 32 32 32  32  32 32 32 32 16  32 32 32 16 16 24 16  IT  X  B  SEPARATION FACTOR  REMARKS  D1ALYSATE X  T  [- ] [ - ] 0.821 0.705 0.526 0.411 0.316 0.265 0.217 0.175 0.194 0.136 0.110 0.259 0.218 0.237 0.217 0.091 0.055 0.131 0.111 0.106 0.083 0.048 0.222 0.191 0.376 0.255 0.922 0.898 0.636 0.545 0.273 2.00 0.205 1 .52 0.386 1 .76 0.267 0.341 0.216 0.157 . 1 .30 0.533 1 .07 1.18 1 .41 1 .56 1 .72 2.04 2.21 2.32 1.37 1 .43 1 .47 2.03 2.17 2.12 2.21 2.33 2.38 1 .36 1 .38 1 .39 1 .43 1 .47 2.09 2.29 1 .64 1 .83  13  17  L = NL =  ns  [- ] V T 6  1 .31 1 .67 2.69 3.81 5.46 7.72 10.20 13.28 7.06 10.52 13.40 7.85 9.97 8.98 10.19 25.70 43.00 10.41 12.48 13.17 17.14 30.50 9 . 38 12.00 4.36 7.18  —— — — —  ——— — — 10.00  — ——  —— — 2.44  3.94 6.60  =  limit reached l i m i t not reached d e a d v o 1 umes  L L L L L L L L L, 6 B - 1.75 L,. = 1.75 ! 6B L, 6 B 1 . 7 5 L L NL NL L, 5 B = 0.12 L, 6B = 0.30 L, 6 B = 2.06 NL, 6 B = 2.06 L, 6B = 2.06 L, 6 B = 2.06 L, 6 B = 2.18 NL L, b r i n e u n m i x e d L NL, b r i n e unmi x e d L NL NL NL L L L L, b r i n e u n m i x e d NL, 6 B = 1.75 NL, 6 B = 1.75 L, 6 B = 1.75 ' L 6 CONTINUED  Table 11 (Continued)  2  1 O H M  M rt  KUN  NU •  if  [-] 14 15 15 17 18 19 20 21 22 23 24  3  4  5  6  7  8  9  PAUSE CYCLE VOLTAGE CYCLE CURRENT CONCENTR. VOLUME VELOCITY TOTAL INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. f_  Co  [ppm] 5000 1000 980 1130 1080 1175 1160 1230 1200 1200 1170  A 0  [-] 1 .00 1.00 1 .00 1 .00 1 .00 1 .00 0.25 1.00 1.00 1.00 1.00  \f V  [cm/sec] 0.92 1.32 1.32 0.90 0.90 0.90 0.90 . 0.90 0.90 0.90 0.90  T  [sec] 25 5 5 5 5 5 20 10 15 20 0.6  T 1  A d> Li * r  [sec]  [volt]  103 46 46 64 64 64 54 74 84 94 55  16 20 20 10 20 30 30 20 20 20 20  II V*  [-] .8 18 18 18 18 16 50 ]0 17 16 15  T  10  rnwrpMTD/iTTnw BRINE  1  DIALYSATE A  [ampere] [ - ] 2.10 0.95 0.90 0.53 0.84 1.06 0.75 0.81 0.74 0.69 1.09  11  1 .42 1.29 1.27 1 .20 1 .32 1 .34 2.67 1 .39 1 .49 1 .52 1.14  12  13  SEPARATION FACTOR  DFMUDIc'C  r\ L nMK NO  nc 11 o  [ - ]  [ - ]  0.496 0.588 0.598 0.700 0.578 0.473 0.211 0.508 0.486 0.469 0.703  2.86 2.19 2.12 1 .72 2.28 2.85 12.64 2.73 3.04 3.23 1:62  I U  ——  l i m i t " l i m i t ,  r*o3/*ho*H I C d t l l c U  NL » l i m i t not reached 60/6_ = dead volumes D  1  L L L L L L L L L L L  o CL  Table 12 Compilation of Experiments on EDI-S3-13  1 RUN NO.  2  3  H  5  6  7  8  • 9 . . . 10  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  CONCENTRATION BRINE  #  C0  6  V  [-]  [ppm]  [-]  [cm/sec]  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 18 19 20 21 22 24 25 25 27 28 2930 31 32 33 34 35 36 37 38 39 40 40a 41 42  1240 1250 1228 1240 1270 1300 1270 1260 1135 1045 1250 1282 1205 1125 1265 1275 1270 1180 1195 1185 1205 1205 1260 1250 1260 1260 1210 1270 1280 1300 1290 1280 1200 1200 1260 4640 4500 4890 5560 5275 5125 5215  1 1 0.5 0.25 1.5 1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 1 1  .90 .95 .95 .95 .95 .95 .95 .95 .95 .95 .95 .95 .95 .95 .50 1 .40 1 .85 2.36 .50 .27 1 .85 .95 . 1 .40 1 .40 1 .40 1 .40 1 .40 1 .40 2.36 2.36 1.85 1 .85 1 .85 1.85 1.85 0.95 0.95 1 .40 1 .40 1.40 1 .40 .16  T  [sec] 20 10 10 10 10 5 5 5 5 0.6 5 10 20 30 10 10 10 10 0.6 0.6 0.6 5 10/5 10/10 10/10 10/5 10/5 10/10 10/5 10/10 10 10 10 10 10 5 5 10 10 10 10 0.6  T [sec]  nc [volt]  93 71 45 34 96 61 61 61 61 52 61 71 91 111 68 37 33 30 50 90 14 61 32 37 37 32 49 54 25 30 33 33 33 33 33 61 35 37 37 74 54 285  22 22 22 22 22 10 22 30 40 22 22 22 22 22 22 22 22 22 22 22 22 30 22 22 10 10 10 10 22 22 22 22 22 22 22 10 10 10 15 15 15 5  11  [ - ]  I [ampere]  [ - ]  19 18 36 65 10 17 17 15 22 23 18 20 19 13 28 34 45 45 50 45 160 18 40 35 40 50 • 20 16 35 30 30 60 70 40 60 15 40 35 34 35 15 15  .70 .85 .77 .73 .91 .62 1 .00 1 .20 1 .28 .99 .96 .87 .69 .50 .62 .80 .79 .70 .87 .60 1.69 1 .05 .91 .81 .54 .65 .59 .54 .92 .80 .81 .77 .71 .60 1.00 1 .65 1.73 1 .54 2.44 2.35 2.58 0.60  1 .69 1 .60 2.08 2.34 1 .33 1 .31 1 .52 1.61 1 .77 1 .28 1 .52 1 .61 1 .71 1 .79 2.14 2.08 2.10 2.12 1 .26 1 .72 0.90 1.61 2.03 2.14 1 .83 1 .65 1 .38 1 .48 2.01 2.16 2.15 2.05 1 .99 1 .57 2.82 1.15 1 .25 1 .54 1 .70 1 .70 1 .57 1 .27  X  B  DIALYSATE XT T [-  12  13  SEPARATION FACTOR  REMARKS  ns  ]  [ - ]  .349 .398 .278 .236 .531 .603 .432 .389 .330 .570 .424 .372 .324 .301 .239 .248 .242 .240 . 540 .350 .856 .375 .228 .228 .344 .376 • .535 .•515 .228 .233 .230 .217 .235 .171 .326 .684 .644 .462 .333 .330 .495 .586  4.85 4.03 7.46 9.90 2. 50 2.18 3.53 4.15 5.36 2.24 3.59 4.33 5.27 5.95 8.93 8.35 8.71 8.83 2.33 4.91 1 .05 4.29 8.90 9.35 5.33 4.39 2.59 2.86 8.85 9.27 9.33 9.43 8.44 9.16 8.66 1 .68 1 .95 3.33 5.10 5.14 3.18 2.17  V  6  L  =  limit  NL  = =  limit not reached dead v o l u m e s  T  L L NL NL L L L L L L L L L L NL NL L L L L NL L L NL L L NL - L NL L L L. NL, L, NL, L NL NL L L L NL  reached  6B = <ST=0.5 SB=<5T = 1 -0 6 b = ST"=0 .0  6B=6T = 1 .0  Table 13 Compilation of Experiments on EDII-S1-8  1 RUN  2 NO.  3  4  5  6  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  CONCENTRATION BRINE  Co  6  [-]  [ppm]  [-]  6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 35a 36 37 38 39 40  5700 5700 5300 5400 4800 5300 4300 5100 5050 5400 5500 5100 5300 4900 5500 5200 2600 2650 2650 1250 1290 1250 1280 1260 1270 1220 1240 1200 1280 1220 1220 1250 1150 1250 1260 1290  2/3 2/3 2/3 2/3 2/3 1 1/4 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 1 1 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3  V  [cm/sec] 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 3 .0 1 .6 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 5 .4 1 .4 3 .0 1 .4 2 .2  T  T  A*  nc  [sec]  [sec]  [volt]  [ -]  10 0.6 5 20 5 5 5 5 0.6 0.6 5 10 10 10 10 10 20 10 10 0.6 10 20 5 10 0.6 0.6 5 10 20 5 10 10 0.6 0.6 10 10  40 50 60 80 50 68 25 50 70 129 50 50 39 29 30 59 80 61 60 40 60 80 50 79 60 41 50 59 78 50 60 60 135 71 145 92  10 10 10 10 10 10 10 5 10 10 15 10 10 10 10 15 10 10 15 10 10 10 10 10 10 15 15 15 15 5 10 5 10 10 10 10  40 30 45 25 46 26 90 55 40 20 30 33 30 40 45 34 25 30 30 45 30 30 35 16 25 34 26 25 25 35 30 40 30 40 30 25  I [ampere] [ - ] 5.6 3.8 3.2 2.0 4.1 4.6 2.6 2.0 5.7 5.5 6.9 2.6 1.7 0.9 1.0 3.4 1 .5 2.1 3.0 2.4 1 .4 1.1 1.8 1 .8 2.6 3.4 2.8 2.0 1 .8 1.1 1 .4 0.8 1.6 2.2 1.5 1.6  11  2 .51 1 .48 2 .38 2 .63 2 .35 1 .91 3 .50 1 .87 1 .60 1 .75 2 .55 2 .40 2 .27 2 .13 2 .16 2 .69 2 .86 2 .68 2 .91 2 .32 2 .84 3 .18 2 .70 2 .19 1 .94 2 .49 2 .90 3 .17 3 .70 2 .34 2 .87 2 .57 2 .99 2 .46 3 .40 3 .00  12 SEPARATION FACTOR  DIALYSATE X1  13  ns  [- ]  [- ]  0 .011 0 .507 0 .023 0 .008 0 .026 0 .159 0 .004 0 .219 0 .324 0 .155 0 .011 0 .0 30 0 .072 0 .130 0 .132 0 .004 0 .004 0 .019 0 .012 0 .068 0 .014 0 .009 0 .012 0 .029 0 .092 0 .024 0 .005 0 .001 0 .001 0 .054 0 .012 0 .0.26 0 .011 0 .021 0 .006 0 .008  224 3 104 348 91 12 874 9 5 11 231 80 32 16 16 . 648 710 143 250 34 202 362 222 74 21 103 546 3600 6100 43 247 99 285 118 552 373 '  REMARKS MS = L = NL = =  No. of stages limit reached l i m i t not reached dead v o l u m e s  NL L  NL L  NL L L L L L  NL L , MS = 6 NL, MS = 4 L, MS = 2 L, MS = 2 L L L L L L L L L L L L NL NL NL L L L L NL NL  CONTINUED  Table 13 (Continued)  1 RUN NO.  2  3  4  5  6  7  : 8  .9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  11  CONCENTRATION  12  13  SEPARATION FACTOR  REMARKS  BRINE DIALYSATE Co  6  V  i-1  [ppm]  [-]  [cm/sec]  41  1300  1/4  5.4  42  1175  1/4  5.4  43  1210  2/3  5.4  44  1225  2/3  5.4  45  1275  2/3  5.4  46  1240  2/3  5.4  47  1225  2/3  5.4  48  1250  2/3  5.4  49  1270  2/3  5.4  50  1290  2/3  2.2  #  T  X  T  ns  [ - ] [ampere] [- ]  [- ]  [- ]  V  B  5  MS = No. of s tages L = l i m i t reached NL = l i m i t not reached T - dead volumes  0.6  16  10  no  3.4  2.56  0.169  15  NL  35  10  54  0.9  5.18  0.006  810  NL  31  10  60  2.2  2.20  0.095  23  L, MS = 6  10  50  10  26  1.0  2.74  0.022  122  NL, MS = 6  10  40  10  34  0.7  2.67  0.040  66  L, MS = 4  21  10  80  1.5  1.75  0.320  5  L, MS = 4  21  10  50  0.4  2.61  0.095  28  L , MS = 2  11  10  100  1.2  1.30  0.657  2  L , MS = 2  20  80  10  40  1.2  3.46  0.008  452  10  91  10  20  1.5  3.31  0.013  262  10 0.6  0.6 10 0.6  2/3  5.4  52  1250  2/3  5.4  10  5.4  X  [volt]  1280  - 2/3  I  [sec]  51  1280  nc  [sec]  10  53  T  10  NL NL *  40  10  no  0.6  3.19  0.051  63  40  10  60  0.6  2.30  0.040  58  40  10  55  0.6  2.70  0.072  CONCENTRATIONS MEASURED IN WELL MIXED END RESERVOIRS, TWO STAGES ON EACH END INACTIVE. CONCENTRATIONS MEASURED BETWEEN ACTIVE AND INACTIVE STAGES.  '  6  B  " T -  unmixed  i  NL, MS = 4, 6 B = 6y = i **  38  6  NL, MS = 4  =  NL, MS = 4, * B " « T * unmi xed  108  Tables the ED  8 to 12 c o n t a i n experimental  first cell  results  ED c e l l , Table 13 shows r e s u l t s  obtained  from the  with  second  in batch mode. The  f o l l o w i n g type of a b b r e v i a t i o n w i l l  be  used  subsequently: EDI T h i s stands f o r the the second stack  - S2  5.3.1  The  (S2)  ( E D I ) , used  v e r s i o n , which contained refers  to run  First Electrodialysis Cell  with  fifteen  number f i v e  (15)  (#5).  (EDI)  Parameters. The  cell  15/#5  f i r s t electrodialyser  spacer-membrane u n i t s , and  5.3  -  (EDI)  may  parameters which were s t u d i e d on t h i s f i r s t be d i v i d e d i n t o the  Operating  f o l l o w i n g two  parameters:  1.  Applied  voltage  A$  2.  Pause time  T  3.  Superficial  velocity v  4.  Displaced  5.  Dead volume  6.  Initial  volume 6 ^ B ^ T  concentration  c0  groups:  ED  109  Design  All  except  sections. 5.3.8  parameters:  7.  I n t e r n a l flow d i s t r i b u t i o n axial dispersion  8.  E x t e r n a l mixing  9.  Thickness of c a p a c i t y c e l l  core  10.  Thickness and hydrodynamic of spacer s c r e e n .  properties  two  in brine  of these parameters  Items 7. and 8. are d i s c u s s e d i n f u l l d e t a i l  constant.  the end of each  survey  i s analysed  i n which the other  separately parameters  These groups are presented i n t a b l e s which  d i s p l a y the o p e r a t i n g parameters experiment  and the f i n a l  conditions  i n the same order as the main  tables. The  for  under  and 5.3.9, r e s p e c t i v e l y .  by forming groups of experiments  at  reservoir  are d e f i n e d i n preceding  Each of these ten parameters  are  and  a series  versions.  t r a n s i e n t response  of the ED c e l l  of s y s t e m a t i c runs on the second  was  evaluated  and t h i r d stack  Appendix C.l d e s c r i b e s the computer c a l c u l a t i o n s  which were performed  on the raw  data f o r each  c y c l e and  lists  t a b l e s of p r i n t o u t .  5.3.2  E f f e c t of a p p l i e d v o l t a g e . The  main survey t a b l e s  list  voltage s u p p l i e d by the r e g u l a t e d D.C.  values of the constant power s o u r c e , s i n c e  110  this  i s the true  independent v a r i a b l e .  the  stack i s p r i m a r i l y  but  i t varies  a function  systematically  The v o l t a g e drop  of t h i s a p p l i e d  during the c y c l i c  Figure 35, which i s a copy of the t r a c e s  voltage  operation.  A t y p i c a l example of these f l u c t u a t i o n s in  across  i s shown  of probe v o l t a g e  (potentiogram) and c u r r e n t (electrogram) recorded during the first  five  cycles  of the e l e c t r i c but  the  potential  i s indicated  fields  of EDI - S2 - 15/#15. i s suppressed  The p o l a r i t y  i n the potentiogram  by p o s i t i v e and negative signs  below the c u r v e .  The f o l l o w i n g  reversal  trends  i n the time characterize  potentiogram: a.  Probe v o l t a g e i s g e n e r a l l y w e l l below t h e e l e c t r o d e v o l t a g e due t o t h e s o l u t i o n r e s i s t a n c e of the r i n s e s t r e a m , the e l e c t r o d e o v e r p o t e n t i a I s , and t h e r e s i s tances in the connectors.  b.  P e a k s r e s u l t from e a c h p o l a r i t y r e v e r s a l . The p e a k s r e f l e c t t h e b a t t e r y e f f e c t o f t h e membrane s t a c k , and a p p e a r t o be s h a r p e r when s w i t c h i n g f r o m p o s i t i v e t o n e g a t i v e p o l a r i t y than v i c e v e r s a . This b a t t e r y e f f e c t i s most p r o n o u n c e d f o r c a p a c i t y c e l l s with " z e r o " core because of t h e very large c o n c e n t r a t i o n changes i n t h o s e c e l l s (DONNAN e f f e c t ) . However, the peaks a r e o f moderate magnitude compared t o t h e l e v e l of t h e a p p l i e d p o t e n t i a l . T h i s i n d i c a t e s t h a t t h e DONNAN p o t e n t i a l has l i t t l e i n f l u e n c e .  c.  The p e a k s d e c a y w i t h i n a few s e c o n d s . Subsequent changes of t h e probe v o l t a g e are a n t a g o n i s t i c t o the c u r r e n t changes, and must t h e r e f o r e be a s s o c i a t e d w i t h t h e electrode reactions.  APPLIED  VOLTAGE  *!6[v]  11  POTENT IOG RAM  ELECTROGRAM  NO. of CYCLES Figure  35.  [-]  EDI-S2-I5/#I 5. T r a c e s o f c u r r e n t and p r o b e voltage recording during the f i r s t f i v e c y c l e s .  112  F i gu re  36.  Probe voltage ED c e l l .  vs. electrode  voltage  for  first  I.I 113  BRINE  o  ITH 2UJ  1.0  o  z o o  DIALYSATE 0.9Figure  37.  ED I - S I - 8 / # 3 6 . Example of c o n c e n t r a t i o n t r a n s i e n t s i n p a r a m e t r i c pumping o p e r a t i o n when mass t r a n s f e r rates are c o n s t a n t .  38.  EDI - S 2 — I 5 / # 9 . Example of c o n c e n t r a t i o n t r a n s i e n t s i n p a r a m e t r i c pumping o p e r a t i o n when mass t r a n s f e r r a t e s are c o n c e n t r a t i o n d e p e n d e n t .  O DC  UJO z o o  Figure  114  A p l o t of the mean probe v o l t a g e v s . a p p l i e d for  a l l three membrane packs may  illustrated l i n e and * runs.  fitted  points f a l l  concentration  (A$)  second, and  on  averaging 14, 15 and  final  third  16 show  conditions  stack  consumption i n c r e a s e s The potential  versions,  for  the  high  Little  (see Table  transients  values  be  concentration  and  respectively.  with The  of A $ , and  first,  the  is  current  increasing  of the other parameters.  reservoir concentration  The  f o r zero pause t i m e ,  An  i n s p e c t i o n of the  characteristics  Figure 37 i s a t y p i c a l  concentration  of the model  discussed  example of the The  real  top  ( d i a l y s a t e ) drops s h a r p l y f o r the  both c o n c e n t r a t i o n s  upward f o r subsequent c y c l e s .  See page 147.  applied  separation  time t r a n s i e n t s of the r e s e r v o i r c o n c e n t r a t i o n s .  *  the  l a r g e s o r p t i o n c a p a c i t y of the mem-  shows a l l the  c y c l e , and  by i n -  identified.  14).  S e c t i o n 3.2.1.  of  experiments  or no improvement occurred  f a s t displacement,  first  diagonal  simultaneously.  depend on the may  as  v a r i a t i o n s in  effect  improvements i n s e p a r a t i o n with  f o l l o w i n g trends  in  and  lines  method.  g e n e r a l l y improved f o r l a r g e r values  branes  below the  c o n c e n t r a t i o n , p o s i t i o n i n g of the p r o b e s , and  Tables  1.  by s t r a i g h t  s c a t t e r of the p o i n t s i s caused by  a c c u r a c i e s of the  voltage  The  are d i v i d e d in low  The  process  in Figure 36.  be  voltage  remain p a r a l l e l  Separation  i s thus  and  drift  completed  115  a f t e r one  cycle.  The  improvements which may  an i n c r e a s e d p o t e n t i a l are r e s t r i c t e d  be  achieved  to the f i r s t  by  cycle,  and  t h e r e f o r e remain s m a l l .  The  c u r r e n t consumption i n c r e a s e d almost p r o p o r t i o n a l l y to  the a p p l i e d p o t e n t i a l . changed very  little  1. e. the e l e c t r i c  2.  In these  experiments the  compared to the  initial  r e s i s t a n c e of the stack  concentrations  concentration,  stayed  almost  Small improvements were observed f o r zero pause t i m e ,  slow d i s p l a c e m e n t ,  and  branes (see the f i r s t  small  s o r p t i o n c a p a c i t y of the mem-  group i n Table  t i o n t r a n s i e n t s of these  15).  Typical  clearly ing  v i s i b l e , but  the s e p a r a t i o n  the next c y c l e s .  with  The  the model presented  Figure 39  illustrates  potential  (A<1>) on  voir concentrations  to  (Xg  curves  38.  cycle is  is further increased  shape of these  dur-  agrees w e l l  in S e c t i o n 3.3.2.  d i r e c t l y the  final  concentra-  experiments are shown i n Figure  A break of the d i a l y s a t e t r a n s i e n t a f t e r the f i r s t  The  constant.  separation and  i n f l u e n c e of the factor  x ^ ) , and  final  c u r r e n t consumption i s seen to r i s e  applied  (ns), final  reser-  current ( I ) .  l e s s than p r o p o r t i o n a l  the a p p l i e d p o t e n t i a l up to approximately 32  [V].  This  behaviour i s a t t r i b u t e d to the simultaneous i n c r e a s e in bottom  Table 14 E f f e c t of Applied Voltage (A4>) on EDI-S1-8  1 I\ U It  2 tx u -  3  f}  5  6  7  8  10  9  CONCENTR. VOLUME . VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  rnMrrwTOATTnw LUINUtN 1 KA 1 I UN BRINE  #  Co  6  [-]  [ppm]  [-]  [cm/sec]  [sec]  14 1-5-0 40 41 35 42  1020 1020 760 760 700 750  1.00  1.21  _  50.2  6.0 6.0 6.0 10.0 12.5 20.0  7 9 8 7 9 7  0.32 0. 32 0.28 0.44 0.55 0.78  6 7 38 39  1080 1090 725 710  1.73 1.73 1 .80 1.80  1.21  _  84.3 84.3 87.3 87.3  4.0 6.0 15.0 20.0  6 9 6 5  37 15-1 36  720 1020 700  1.00  0.65  _  93.8  5.0 6.0 12.5  3 31 32  1040 710 720  1.10 1 .00 1 .00  1.77  _  36.4 34.3 34.3  6.0 7.55 12.5  V  T  T [sec]  nc [volt]  11  I  B  [ampere] [" ]  12 SEPARATION FACTOR  DIALYSATE X T  1  ns  13 n r II ri  •  c-\  0.969 0.970 0.986 0.956 0.960 0.972  0.983 0.997 0.995 0.975 0.960 0.954 -  0.99 0.97 0.99 0.98 1 .00 1 .02  NL L L L L L  0.23 0.37 0.60 0.75  1 1 1 1  0.974 0.938 0.862 0 .860  1 .06 1 .09 1 .19 1.25.  L L L L  5 13 8  0.20 0.30 0.50  1 .02 0.965 1.04  0 .980 0.972 , 0.935  1 .05 0.99 1.11  L L L  8 13 6  0.39 0.35 0.55  0.999 0.99 0.95  0.996 1 .00 0.97  1 .00 0.99 0.98  NL L L  .03 .02 .02 .07  r  L — limit reached NL = l i m i t not reached 6g/6-j- = d e a d v o l u m e s  [ - ]  [- ]  t/  REMARKS  Table 15 E f f e c t of Applied Voltage (A$) on E D I - S 2 - 1 5  1 D 1! v r\ U11  2 wn  IX u .  #  CONCENTR. INITIAL  3  H  5  7  8  9  10  VOLUME PAUSE CYCLE VELOCITY VOLTAGE CYCLE CURRENT DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  [-3  6  V  [ppm]  [-]  [cm/sec]  7 8 9 10 17  940 950 970 960 1025  1.00  0.88  0.0  • 13 6 12-1  930 990 940  1.00  2.23  14 27 28-2 33  980 1090 1070 1150  1.00  1250 1225 1250 1225  0.61  Co  6  T  T  nc  I  11  PfiMPrMTrjflTTriM  12  13  SEPARATION FACTOR  REMARKS  UUNLcIN 1 KA 1 I UN  BRINE D1ALYSATE ns  [- ]  1  _  L—  [volt]  [-]  [ampere]  [ -]  T [- J  55  8 16 24 32 40  10 10 10 10 10  0.40 0.70 0.85 1.00 1.30  1.01 1 .01 1 .07 1.14 1.14  0.935 0.858 0.801 0.750 0.747  1.08 1.18 1 .33 1 .52 1 .52  L L L L L  10  42  15 20 32  10 14 16  0.65 0.75 0.90  1 .28 1 .23 1.41  0.671 0.541 0. 548  1 .91 1 .92 2.58  L L NL  2.23  15  52  15 32 32 32  10 10 11 11  0.60 0.96 1.00 0.90  1 1 1 1  .32 .46 .45 .39  0.607 0.537 0. 540 0.517  2.17 2.72 2.69 2.70  NL L NL L  0.92  25  72  16 16 32 40  0.30 0.40 0.50 0.52  1.40 1.32 1 .41 1.41  0.222 0.250 0.179 0.142  6.32 5.28 7.88 10.10  [sec] [sec]  B  NL =  l i m i t reached l i m i t not r e a c h e d dead vo1umes  EDI - S 2 - 1 6 5-4 6-1 5-1 6-3  60 22 21 45  NL, 6B L , 6B L , 6B L , 6B  = = = =  1.84 1.84 1.84 1-84  CT. CD  Table 16 E f f e c t of Applied Voltage (A*) on EDI-S3-12 and EDI-S3-13  1 RUN NO.  3  2  5  6  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT TOTAL INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO.  [-]  Co [ppm]  17 18 19 1-2  1130 1080 1175 1225  6 7 11 • 8 22 9  4  1300 1270 1250 1260 1205 1135  6  V  T  T  AO  nc  [-]  [cm/sec]  [sec]  [sec]  [volt]  [- ]  10 20 30 32  18 18 16 25  1.00  1.00  .90 .90 .90 .92 .95  5  5  64 64 64 62 61  10 22 22 30 30 40  17 17 18 15 18 22  I  10  CONCENTRATION BRINE D1ALYSATE  B [ampere] [- ] 0.53 0.84 1 .06 1.20 .62 1.00 .96 1.20 1.05 1.28  11  X  1.20 1 .32 1 .34 1.41 1 1 1 1 1 1  .31 .52 .52 .61 .61 .77  12 SEPARATION FACTOR ns  13 REMARKS L = l i m i t reached NL = l i m i t not reached Sg/Sy = dead volumes  T [- ]  [ - ]  0.700 0.578 0.473 0.526  1 .72 2.28 2.85 2.69  L L L L  2.18 3.53 3.59 4.15 4.29 5.36  EDI-S3-13 L L L L L • L  X  0.603 0.432 0.424 0.389 0.375 0.330  en  CONCENTRATION  zu  b ro SEPARATION  [-]  !>> b) FACTOR [-]  118  0)  = 1200 [ppm], 6 = 1.0  ure 4 0 .  [ - ] , v = 0.95  [ c m / s e c ] , x = 5.0 [ s e c ]  E f f e c t o f a p p l i e d v o l t a g e on f i n a l p r o d u c t c o n centrations for t h i r d stack experiments. EDI — S 3 - I 2 / # I 7 , 1 8 , 1 9 , 1 - 2 and ED I-S3-I3/#6,7,I I , 8 , 22 , 9 .  119  REDUCED POTENTIAL [v] 1200 [ppm], 6 = 1.0  Figure 41.  [ - ] , v = 0.95  [ c m / s e c ] , T = 5.0 [ s e c ]  E f f e c t o f a p p l i e d v o l t a g e on f i n a l P^a+<on factor f o r t h i r d stack experiments. EDl-io-.z/ #17 1 8 , 1 9 , 1 - 2 and ED I-S3-I3/#6,7,I I , 8 , 2 2 , 9 . s e  120  r e s e r v o i r c o n c e n t r a t i o n , and r e s i s t a n c e due The  r i s e of the  concentration  3. on  to p a r t i a l  reflects  the  changes i n stack  removal of s o l u t e from the  c u r r e n t with A$  is accelerated  stagnates between 32 and  40  as the  (see Tables  t h i r d stack  15 and  tial  (A$)  on  final  tion  f a c t o r of the  16).  The  version  brine  of the f i r s t  operations  ED  cell  i n f l u e n c e of the a p p l i e d  r e s e r v o i r concentrations groups i n Table 16  cell.  [V].  Large improvements were recorded f o r pause time the second and  ED  and  poten-  final  are shown i n  separa-  Figures  * 40  and  41  respectively.  The  final  creased l e s s than p r o p o r t i o n a l This  current  to the  applied p o t e n t i a l .  confirms the concept of an o v e r a l l  within  the stack  f o r enhanced  5.3.3  E f f e c t of pause time.  consumption i n -  resistance  increase  separation.  The influence of equal pause times (T) at the beginning of each h a l f c y c l e was versions.  Table 17, 18, and  parameters and ments, and the  studied  the  final  Figures 42 , 43  pause time on  concentrations  final  on the second and  19 summarize the  conditions and  for several  stack  operating  reached in these e x p e r i -  44 d i r e c t l y  separation  third  d i s p l a y the  f a c t o r s and  final  effect  of  reservoir  groups of experiments.  * The a b s c i s s a i s the a p p l i e d p o t e n t i a l per number of flow c h a n n e l s . This reduced p o t e n t i a l allows comparison between stacks c o n t a i n i n g d i f f e r e n t numbers of flow c h a n n e l s .  121  The  r e s u l t s show that the s e p a r a t i o n  i s improved  f o r prolonged pause t i m e s , and that b e t t e r s e p a r a t i o n i s always accompanied by reduced c u r r e n t consumption. some i n d i c a t i o n t h a t the f i n a l reach and  limiting  separations  will  There i s  eventually  l e v e l s s e t by the amount of i n t e r n a l  45 shows the t r a n s i e n t - S3 - 12/#6-0.  Section  3.3.1.  The i n i t i a l  part of the curve i s a f i n e  decay p r e d i c t e d by the model i n  However, a f t e r twenty c y c l e s the curve begins  to a s y m p t o t i c a l l y approach a f i n i t e e f f e c t s which are d i s c u s s e d The tions  real  l i m i t s e t by d i s p e r s i v e  in Section  5.3.8.  time t r a n s i e n t s of the r e s e r v o i r  concentra-  f o r the EDI - S3 - 13 group (see Table 19) are shown  in  Figure 46.  15  [min] i n a l l experiments.  is  Figure  of the top r e s e r v o i r c o n c e n t r a t i o n f o r  example of the exponential *  the  -  the combined i n f l u e n c e s of molecular d i f f u s i o n , DONNAN  e q u i l i b r i u m , and c a p a c i t y of the s o r p t i o n membranes.  EDI  mixing,  Final  c o n d i t i o n s are reached a f t e r  approximately  The break i n the t r a n s i e n t s of  top r e s e r v o i r c o n c e n t r a t i o n  disappears  as the pause time  lengthened and the s o l u t i o n i n the bottom r e s e r v o i r accumu-  l a t e s more and more of the t o t a l  solute.  T h i s model does not account f o r the mass t r a n s f e r during d i s p l a c e m e n t , which happened i n the experiment due to the continuous a p p l i c a t i o n of the e l e c t r i c p o t e n t i a l ( A $ ) . Since the d i s p l a c e d volume (6) was small and the v e l o c i t y of displacement was l a r g e , the r a t i o of pause time to r e s i d e n c e time was a l s o l a r g e . S e c t i o n s 5.3.4 and 5.3.5 demonstrate that the m a t e r i a l t r a n s f e r r e d during displacement c o n t r i b u t e s very l i t t l e to the s e p a r a t i o n under such c o n d i t i o n s .  Table 17 E f f e c t of Pause Time (x) on EDI-S2-15 and EDI-S2-16  1 D U N  KUH  wn  li U •  2  3  4  5  6  7  8  5  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  M r* T f l l T Pi ( I T T  Co  6  [-]  [ppm]  [-]  11 12-0 28-3 27 28-2 33  960 940 1070 1090 1070 1150  1 .00  8-0 3-0 3-1 4  1240 1175 1175 1220  7 6-2 6-3  1250 1225 1225  •  V  T  A*  nc  12  13  SEPARATION FACTOR  REMARKS  DIALYSATE  I [ampere]  [ -]  [- ]  [- ]  1.25 1.25 • 1.30 0.96 1.00 0.90  1 .29 1 .31 1 .28 1 .46 1.45 1.33  0.631 0.623 0.644 0.537 0.540 0.517  2.05 2.10 1 .99 2.72 2.69 2.70  B  X T  r  ns  [volt]  [ -]  32 32 32 52 52 52  32  14 10 18 10 11 11  0 15 25 25  22 52 72 72  32  30 14 20 14  1.41 0.70 0.60 0.70  1.10 1 .88 2.04 2.11  0.714 0.341 0.274 0.278  1 .54 5.52 7.46 7.58  0 15 25  22 52 72  40  50 38 45  1 .50 0.63 0.52  1.11 1 .43 1.41  0.567 0.196 0.142  1 .96 7.05 10.10  [cm/sec]  [sec]  2.33  5 5 5 15 15 15  0.61  0.92  0.61  0.92  -  T [sec]  AM  CONCENTRATION BRINE  #  U  L NL  6g/6y  = limit reached = l i m i t not reached =• d e a d v o l u m e s  L L L L NL L EDI-S2-16 L NL L L L, 6 B - 1.84 L, <SB = 1 .84 L, 6 B = 1.84  ro ro  Table 18 E f f e c t of Pause Time (T) on EDI-S3-12  1 RUN NO.  2  3  n  5  6  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  CONCENTRATION BRINE  #  Co  6  V  C-]  [ppm]  [-]  [cm/sec]  1-1 1-2 1-3 8  1225 1225 1225 1270  1.00  0.92  0 5 15 20  24 18 21 22 23  1170 1080 1230 1200 1200  1.00  0.90  9-0 9-1 9-2 9-3  4800  . 1.00  0.92  T  T  [sec] [sec]  nc  11  I  T  13  SEPARATION FACTOR  DIALYSATE X  [ampere] [ - ]  12  ns  REMARKS L = NL =  limit reached l i m i t not reached d e a d v o 1 times  [volt]  [- ]  52 62 82 93  32  18 25 30 10  1.35 1.20 1.00 0.95  1.18 0.705 1.41 . 0.526 1 .56 0.411 1.64 0.376  1 .67 2.69 3.89 4.36  L L L L  0.6 5 10 15 20  55 64 74 84 94  20  15 18 20 17 16  1.09 0.84 0.81 0.74 0.69  1.14 1 .32 1.39 1 .49 1.52  1 .62 2.28 2.73 3.04 3.23  L L L L L  0 5 10 15  53 63 73 83  16  5 10 20 35  3.10 3.00 2.70 2.30  —  [- ]  0.703 0.578 0.508 0.486 0.469 0.922 0.89 8 0.636 0.545  [- ]  —  6 B /6 T =  L NL  NL NL  ro ro  Table 19 E f f e c t of Pause Time (T) on EDI-S3-13  1 RUM NO.  2  3  4  5  6  7  8 :  9  CONCENTR. VOLUME PAUSE CYCLE VOLTAGE CYCLE CURRENT VELOCITY INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  #  Co  6  C-]  [ppm]  [-]  14 11 7 12 2 13 1 14  1045 1250 1270 1285 1250 1205 1240 1125  24 16 25  V  [cm/sec]  T  [sec]  T [sec]  AO [volt]  10  11  CONCENTRATION  BRINE DIALYSATE X X I T B [ "] [ ] [ampere] [ -] nc  12  13  SEPARATION FACTOR  REMARKS  ns  L = l i m i t reached NL = l i m i t not reached 6g/5-p = dead volumes  [- ]  L L L L L L L L  52 61 61 71 71 91 91 m  22  23 18 17 20 18 19 19 13  0.99 0.96 1.00 0.87 0.85 0.69 0.70 0.50  1 .28 1 .52 1 .52 1 .61 1 .60 1 .71 1.69 1.79  0.570 0.424 0.432 0.372 0.398 0.324 0.349 0.301  2.24 3.59 3.53 4 . 3 3 •• 4.03 5.27 4.85 5.95  10/5 10/10 10/10  32 37 37  22  40 34 35  0.91 0.80 0.81  2.03 2.08 2.14  0.228 0.248 0.228  8.90 8.35 9.35  L NL NL  1.40  10/5 10/10  32 37  10  50 40  0.65 0.54  1 .65 1.83  0.376 0.344  4.39 5.33  L L  2.36  10/5 10/10 10/10  25 30 30  22  35 30 45  0.92 0.80 0.70  2.01 2.16 2.12  0.228 0.233 0.240  8.85 9.27 8.83  NL L L  1.00  0.95  1260 1275 1250  0.50  1.40  27 26  1260 1260  0.50  30 31 18  1280 1300 1180  0.50  0.6 5 5 10 10 20 20 30  Figure  42.  E f f e c t of p a u s e t i m e ( x ) on s e p a r a t i o n s e c o n d and t h i r d s t a c k e x p e r i m e n t s .  factor  for  UJ » — — — J> •  N> -) -+» \ Q) -+> =*fc -+ C D N> — O J> O -+ >• 3 — C O o 00 -t> M O "O — I D )  c ro -4 co ro 3- C D N  4  T  UJ CL  —  3  D ) C O C D 3 -4 Q. 0) O O 3 m TT  0  -+>  — C D — 1 X 3 W D 01 UJ C D — I I • -J UJ 3 C D \ C D C O  =* 3 ro  h -i o co <  -  •  O  m  <•  — l o o v O — I 3  —  ro co o  -  ro  —  Ul C D i 3 i  m  =**: -(•> M  «.  O  )  -  *  — 4-, -t, J> -4 C D • — O O 00-1-4 n  ro -+. o — o -h * i ro  M  "o  4 0) ZT cz  ro — co U J -i  C D  CL  D J -4 3 C O —• O . -4 3 0) C D m  n  — H i ro ^ C O x Ul "d o I C D 3 — I U J —• + >  \ 3 — %  —  C D 3  3D)  O H — 1/1  —  — . co  — C D v. XJ ~j  —  m  O  oj I D)  ro i -4 •• co — ro U J o —  | 3  U J  ro  125  Figure  45.  Dia I y s a t e - c o n c e n t r a t i o n - t r a n s i e n t  o f ED I-S3-I2/#6-0.  126  Figure  46.  E f f e c t o f p a u s e t i m e ( x ) on c o n c e n t r a t i o n t r a n s i e n t s of t h i r d s t a c k e x p e r i m e n t s .  127  TIME 400 1  [sec] 1600  1200  __l  _J _ _ Q  r » BRINE  6=  ^8DIALYSATE  LEGEND RUN S Y M B O L [sec] 21 O 0.6 A 32 10 Z  Co - 1250 [ppm], 6 = 0.5 [ - ] , v = 1 . 8 5  Figure  47.  [cm/sec], A $ = 2 2  C o n t r a s t i n g p a u s e and n o - p a u s e o p e r a t i o n stack experiments. EDI—S3—I3/#2I,32.  [V]  for third  128  Figure 47 contrasts the concentration t r a n s i e n t s of standard parametric pumping operation (no-pause) with pause operation (x = 10 [sec]) under otherwise ditions.  i d e n t i c a l con-  The l a t t e r are p a r t i c u l a r l y favourable f o r the  pause operation because they combine small displaced volume (6 = 0.5), f a s t displacement  (v = 1.85  [cm/sec]), and moderate  applied p o t e n t i a l (A* = 12.5 [ V ] ) . The  l a s t group of Table 19 contains experiments with  unequal pause times.  In p a r t i c u l a r , , the brine producing h a l f  cycle was shortened, since the current consumption during these periods became u s u a l l y very small (see the electrogram in Figure 35).  The pause times f o r these part cycles were  halved without s i g n i f i c a n t e f f e c t s on the f i n a l c o n d i t i o n s .  5.3.4  E f f e c t of s u p e r f i c i a l  velocity.  The s u p e r f i c i a l v e l o c i t y (v) was varied f o r groups of experiments on a l l three stack v e r s i o n s . ameters and f i n a l conditions are compiled  Operating  par-  i n Table 20, 21 and  22 f o r f i r s t , second and t h i r d s t a c k , r e s p e c t i v e l y . The e f f e c t of the s u p e r f i c i a l v e l o c i t y on f i n a l  r e s e r v o i r concen-  t r a t i o n s and f i n a l separation f a c t o r s i s g r a p h i c a l l y displayed in Figure 48 and 49, r e s p e c t i v e l y , f o r the groups of Table 22. Figures 50 and 51 show the real time t r a n s i e n t s of the reserv o i r concentrations of these groups.  129  The  results  are q u i t e d i f f e r e n t depending  value of the pause t i m e , and may 1.  No-pause o p e r a t i o n . ably improved ment.  The  be summarized as  Final  separation  f o r slow v e l o c i t i e s  on the  follows.  i s consider-  of d i s p l a c e -  improvement i n s e p a r a t i o n i s  accompanied  by reduced c u r r e n t  consumption.  T h i s agrees with the models presented i n Chapter 3.  I f the c y c l e p e r i o d  the  flow r a t e , the r e s i d e n c e time w i l l be propor-  tionally  i s prolonged by r e d u c i n g  i n c r e a s e d , but at the same time the  rate of mass t r a n s f e r w i l l be decreased according  to some power f u n c t i o n of v.  Generally,  in packed beds and i n flow channels with lence promoters, the steady s t a t e coefficients to  n  transfer  have been found to be  v , where n = 0.5  to 0.8  proportional  (see e.g.  1968; Yamane, 1969b; and Kitamoto et It may  turbu-  al.  Hicks,  ,  1971).  be expected t h a t the i n f l u e n c e of the  r e s i d e n c e time i s p r e v a i l i n g  i n the case of  unsteady-state mass t r a n s f e r i n the e l e c t r o dialysis  system, t o o .  The experiments with no-pause time c o n f i r m train  of t h o u g h t s , and Figure 50  this  illustrates  130  that a r e d u c t i o n i n v e l o c i t y tration pause  2.  leads to concen-  t r a n s i e n t s which resemble those of  operations.  Operations  with  moderate pause t i m e .  Final  separation  is virtually  independent of  superficial  velocity.  The rate at which  this  l i m i t i s approached may be improved by i n c r e a s i n g the v e l o c i t y . is  The i n c r e a s e i n r a t e  at the expense of a higher  c u r r e n t con-  sumpti on.  The  improved rate of s e p a r a t i o n  accord with is  i s i n complete  the concept that the pause time  the true cause of a s u c c e s s f u l  o p e r a t i o n of the e l e c t r o d i a l y s i s  cyclic p r o c e s s , at  l e a s t i n the parameter regime i n v e s t i g a t e d .  The  pause periods  of the c y c l i c o p e r a t i o n  seem to be  responsible f o r a certain  amount of s e p a r a t i o n which i s inde-  pendent of the v e l o c i t y .  The displacement may, t h e r e f o r e ,  be  implemented as f a s t as m e c h a n i c a l l y  des i r a b l e .  feasible  or e c o n o m i c a l l y •  Table 20 E f f e c t of S u p e r f i c i a l  1 RUN NO.  2  3  4  5  6  7  Velocity  8  (v) on EDI-S1-8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  #  Co  6  [-]  [ppm]  [-]  V  [cm/sec]  2 5 3 4  1050 1090 1040 1050  1.10  1.21 1.21 1.77 2.33  7 8 9  1090 1090 1080  1 .73  1.21 1.66 2.62  36 35 32 33 34  700 700 720 710 700  1.00  0.65 1.21 1.77 2.33 2.89  T  T  AO  [sec]  [sec]  [volt]  -  nc  I  10  11  CONCENTRATION BRINE X  B [ - ] [ - ] [ampere]  D I A LX Y S A T E  12  13  SEPARATION FACTOR  REMARKS L =-•  ns  T [- ]  [- ]  5  limit reached l i m i t not reached = dead volumes  NL ==  V T =  53.3 53.3 36.4 27.6  6  7 8 8 9  0.37 0.35 0.39 0.40  0.995 1 .005 0.999 •0.998  0.999 1 .000 0.996 1 .000  1 .00 1.01 1 .00 1.00  NL NL NL NL  84.3 61.4 39.0  6  9 12 10  0.37 0.39 0.41  1 .02 1 .01 1 .01  0.938 0.955 0.972  1 .09 1 .06 1 .04  L L L  93.8 50.2 34.3 26.1 21.0  12.5  8 9 6 10 9  0.50 0.55 0.55 0.60 0.65  1.04 0.96 0.95 0.965 0.975  0.935 0.96 0.97 0.985 0.990  1.11 1 .00 0.98 • 0.98 0.985  L L L L L  —  Table 21 E f f e c t of S u p e r f i c i a l Velocity  2  1  4  5  6  7  8  (v) on EDI-S2-16, EDI-S3-12  9  VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT RU;i NO. CONCENTR. VOLUME INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  9  Co  6  C-]  [ppm]  [-]  5-2 5-1 5-3  1250  0.61  V [cm/sec] 0.49 0.92 1 .77  T  T  [sec] [sec] 25  111 72 67  A*  nc  [volt]  [-]  32  40 21 50  IG  11  CONCENTRATION  BRINE DIALYSATE X X B T [- ] [ampere] [ - ] I  0.40 0.50 0.45  1 .46 1 .41 1 .44  0.158 0.179 0.176  12 SEPARATION FACTOR ns [- ] 9.24 7.88 8.18  13 REMARKS L = l i m i t reached NL » l i m i t n o t reached 5g/6T >» dead volumes L, 6 L, 6 NL, 6  B B B  = 1.84 = 1.84 = 1.84  EDI-S3-12 6-2 6.-1 6-0  1280  0.29  0.49 0.92 1.83  10  50 36 31  32  70 60 50  0.55 0.60 0.65  1.39 1 .38 1 .36  0.106  o.m  0.-131  13.17 12.48 10.41  L, 6 NL, 6 L, 6  B B B  = 2.06 = 2.06 = 2.06  CO CD  Table 22 E f f e c t of S u p e r f i c i a l  1  2  3  k  5  6  7  Velocity  S  (v) on EDI-S3-13  O  C0(ICEi'<TR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED no. TOTAL  S  V [co/sec]  nc  CONCENTRATION  6 P. 1 !JDIALYSATE £ I r 6 [ampere] [ -3 [- 3  n  13  SEPARATION FACTOR  REMARKS i  [-3  [PP=I]  C-]  15 3 15 25 17 32 18 31  1265 1228 1275 1250 1270 1290 1180 1300  0.50  0.50 0.95 1 .40 1 .40 1 .85 1 .85 2.36 2.36  10  68 45 37 37 33 33 30 30  22  28 36 34 35 45 30 45 30  0.62 0.77 0.80 0.81 0.79 0.81 0.70 0.80  2.14 2.08 2.08 2.14 2.10 2.15 2.12 2.16  0.239 0.278 0.248 0.228 0.242 0.230 0.240 0.233  8.93 7.46 8.35 9 .35 8.71 9.33 8.83 9.27  NL NL NL NL L L L L  20 '19 21  1185 1195 1205  0.50  0.27 0.50 1.85  0.6  90 50 14  22  45 50 160  0.60 0.87 1.69  1 .72 1 .26 0.90  0.350 0.540 0.856  4.91 2.33 1 .05  L L NL  C-3  ns  m  6  [sec]  A* [volt]  11  Co  T  T [sec]  10  [-•]  L 11ra11 rc&cncd NL " l i m i t r o t reached fig/Sy " dead vo1urr.es  Figure  48.  E f f e c t o f s u p e r f i c i a l v e l o c i t y ( v ) on f i n a l r e s e r v o i r c o n c e n t r a t i o n s f o r p a u s e and n o - p a u s e operation. E D ! - S 3 - I 3 / # I 5 , 3 , 1 6 , 2 5 , 1 7 , 3 2 , 18,31 and ED I - S 3 - I 3 / # 2 0 , 19,21 .  Figure E f f e c t o f s u p e r f i c i a l v e l o c i t y ( v ) on f i n a l s e p a r a t i o n f a c t o r s f o r p a u s e and n o - p a u s e o p e r a tion. E D I - S 3 - I 3 / # l 5 , 3 , 1 6 , 2 5 , 1 7 , 3 2 , 1 8 , 3 1 and ED I - S 3 - I 3 / # 2 0 , 1 9 , 2 1 .  Figure  50.  E f f e c t of s u p e r f i c i a l v e l o c i t y ( v ) on c o n c e n t r a t i o n t r a n s i e n t s for no-pause o p e r a t i o n . EDI —S3—I 3 .  134  Figure  51.  E f f e c t o f s u p e r f i c i a l v e l o c i t y (v) on c o n c e n t r a t i o n t r a n s i e n t s f o r pause o p e r a t i o n . EDI-S3-I3.  135  5.3.5  E f f e c t of d i s p l a c e d The  displaced  of experiments. final  conditions.  final  volume ( 6 ) was v a r i e d  i n three groups  Table 23 summarizes o p e r a t i n g parameters and Figures 52 and 53 show, r e s p e c t i v e l y , the  e f f e c t of d i s p l a c e d and  volume.  separation  volume on f i n a l  reservoir  concentrations  f a c t o r f o r the group of experiments with  10 seconds pause time.  The r e a l time t r a n s i e n t s  bottom r e s e r v o i r c o n c e n t r a t i o n s are i l l u s t r a t e d for  the same group of experiments.  real time t r a n s i e n t s  of top and i n Figure 54  Figure 55 shows analoguous  f o r two experiments with no pause t i m e .  Reducing the d i s p l a c e d  volume ( 6 ) has the f o l l o w i n g  effects. 1.  No-pause o p e r a t i o n :  The f i n a l  separation is  reduced.  Most o f t h e r e d u c t i o n o c c u r s d u r i n g t h e f i r s t  The  current  final  2. separation down.  is unaffected.  Pause o p e r a t i o n  i s improved.  The f i n a l  (x ~ - 10 L~sec]):  The r a t e  current  The f i n a l  of s e p a r a t i o n i s slowed  is reduced.  These r e s u l t s agree with a model i n which mass t r a n s f e r rates follows  finite  are c o n t r o l l i n g , and may be e x p l a i n e d as  using t h i s model. I.  occurs  cycle.  For no-pause o p e r a t i o n :  during the f i r s t  Most o f t h e s e p a r a t i o n  c y c l e as shown i n C h a p t e r 3. The  136  local  effluent  creases  concentration  m o n o t o n i c a I Iy w i t h  centration  therefore  during  time.  d i s p l a c e d volume  half  cycle.  Thus, the  tion  during  all  first  concentration  consumption  is  time  effluent  cycle  When t h e  The  the  trend.  of is  the  the  duration  effluent  reduced.  case the  ratio  The  of  pause time  therefore,  as t h e  the  well  the  the  front  flow,  the  mixed b r i n e  well  pause  reservoir.  low c o n c e n t r a t e d reservoir  solution  time  time disappears. approaches respond  exponential  The r e s u l t s  front  the  cycle  for  confirm finite  When t h e  emerges from  t h a t emerges becomes c o m p l e t e l y  mixed d i a l y s a t e  reversed  to  i.e.  concentrations  concentration  large  be e x p e c t e d t o  pause o p e r a t i o n ,  final  situations  gradually  large  in the  over-  current  d i s p l a c e d volume  concentration.  limited  of  volume  of  each  Since the  is very  a r e c a u s e d by d i s p e r s i o n e f f e c t s :  The p a r t  time.  concentra-  limiting  influence  system would  a pure  dialysate  Two  placement is  de-  con-  of  s m a l l , the  displacement  initial  is obtained  more and more as t o  this  half  concentration,  limit  In t h i s  d e c a y of  cycle  unaffected.  zero.  The o t h e r zero.  mean v a l u e  i n c r e a s e s and t h e  approaches on t h e  shortens  changes are g e n e r a l l y  may be c o n s i d e r e d . cycle  half  The a v e r a g e e f f l u e n t  For pause o p e r a t i o n :  2.  first  a l s o d e c r e a s e s m o n o t o n i c a I Iy w i t h  Reducing the  the  the  Similarly,  dis-  displaced the  stack.  dispersed  during  breaks through  and becomes c o m p l e t e l y  into  dispersed  Table 23 E f f e c t of Displaced Volume {&) on EDI-S1-8, EDI-S2-15 and EDI-S3-13  1 RUN i"iO.  /  3  l\  5  6  7  8  3  COi'lCil iiTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE ClTxP.EiYT Iii IT IAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED HO. TOTAL  10  11  CO liCEKT RATIO!!  "P SEPARATION FACTOR  6RWJE CtALYSATE t  Co  [-] 14 15-0 40 2 5 7  1020 1020 760 1050 1090 1090  6  V  C-]  [cm/sec]  1.00 1 .00 1.00 1.10 1.10 1 .73  1.21  nc [sec] [sec] [volt] [-3 [ampere] [-3 T  T  50.2 50.2 50.2 53.3 53.3 84.3  AO  6  I  7 9 8 7 8 9  0.32 0.32 0.28 0.37 0.35 0.37  0.969 0.970 0.986 0.995 1 .005 1 .02  C- 3  ns [-3  0.983 0.997 0.995 0.999 1 .000 0.938  0.99 0.97 0.99 1 .00 1 .01 1 .09  *T  33 REMARKS L • lJr.lt reached UL " l i c i t not reached Sg/S-j. •> deed votu.-r.es NL L L NL NL L EDI-S2-15  22 17 29  1050 1025 1070  0.50 1 .00 1.54  0.88  0  28 55 84  40  10 10 6  1.25 1 .30 1 .05  0.98 1.14 1 .20  0.95 0.747 0.670  1 .03 1.52 1 .80  L, 6 B = 1.5 L EDI-S3-13  4 3 2 12 5  1240 1230 1250 1280 1270  0.25 0.50 1.00 1.00 1.50  0.95  10  34 45 71 71 96  22  65 36 18 20 10  0.73 0.77 0.85 0.87 0.91  2.34 1 .99 1 .56 1 .57 1 .31  0.236 0.278 0.398 0.372 0.531  9.90 7.15 3.93 4.22 2.46  NL NL L L L  Co =  1250  [ppm], v = 0.95  [cm/sec], T -  10  [ s e c ] , A4> = 22  0-1 0  ,  ,  . 5 . 1  [V]  .  15  DISPLACED VOLUME [-]  CO CO  F i g u re 52 .  F i g u r e 53 .  E f f e c t of d i s p l a c e d volume (6) on f i n a l r e s e r v o i r c o n c e n t r a t i o n s f o r pause o p e r a t i o n . EDI-S3-I3/#4,3,2, 12,5.  E f f e c t o f d i s p l a c e d volume (6) on f i n a l s e p a r a t i o n f a c t o r f o r pause o p e r a t i o n . EDI-S3-I3/#4,3,2,12,5.  .2 Figure  54.  E f f e c t o f d i s p l a c e d volume (6) on c o n c e n t r a t i o n t r a n s i e n t s f o r pause o p e r a t i o n . EDI—S3—13.  co  A  = 1050  Figure  EDI-S2-I5/#29 , <f = l.54 M  [ppm], v = 0.88  55.  [cm/sec] , x = 0.0  [sec],  E f f e c t o f d i s p l a c e d volume (6) on r e a l t r a n s i e n t s f o r no-pause o p e r a t i o n .  40  time  141  therein. vent  When t h e  d i s p l a c e d volume  breakthrough,  passing  dispersion  and c h a n n e l i n g  sion effects  are  deta i I under  5.3.7.  5.3.6  Effect The  end  final  are  duct is a re  and w i l l  to  pre-  mixing,  internal  by-  disper-  be d i s c u s s e d  in  real  time t r a n s i e n t s  first  group (see  of Table 24  The p r e s e n c e of  separation If  dead volumes*in  grouped i n Table 24.  Figure 57)  2.  to  These  experiments with v a r i a b l e  c e n t r a t i o n s f o r the  the  stack.  always present  t o g e t h e r with the  1.  restricted  enough  of dead volumes.  reservoirs  group (see  in the  is  is small  of the  results, product con-  Figure 56)  may  be  and  the  summarized as  dead v o l u m e s  does n o t  third follows:  influence  factor.  the  concentrations  These  the  dead v o l u m e s are  s l o w e d down, h o w e v e r ,  are equal  unchanged. as t h e  the  The r a t e  dead v o l u m e s  of  final  pro-  separation  in each  reservoir  i ncreased. 3.  unequal  Experiments with equal  dead v o l u m e s  concentrations smaller  are  when 6 D D  confirms  in  lower  > 6-,-,  the  total  reservoirs  and t h e  and v i c e  dead volume  show t h a t  current  consumption  v e r s a when 6 D  I  t h e c o n c e p t of a d e v e l o p i n g Or excess volumes.  the  b  < 6T.  but final  much This  I  concentration  wave,  which  Table 24 Effect of Dead Volumes ( « R / « T ) on EDI-S2-15, EDI-S3-12 and EDI-S3-13  1 RUN NO.  2  3  Q.  ,  5  6  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  11  CONCENTRATION  12 :  13  SEPARATION FACTOR  REMARKS  BRINE D1ALYSATE #  Co  <5  V  [-]  [ppm]  [-]  [cm/sec]  19  1020  20  1040  21  0.5  1.70  T  [sec] [sec] 7  nc  T  28  [volt] 40  9 80  I  [ -]  [ampere]  B [- ]  T [- ]  ns C- ] . 3.24-  X  X  14  1.40  1 .72  0.529  15  1.30  1 .50  0.463  3.24  22  1.35  1 .54  0.568  2.72  L NL V  6  L,  1220  0.59  0.92  -1 -2 3-0  1230  62 82  32  6B = 0.0, 6T  20  0.90  2.04  0.265  25  0.70  2.21  0.217  10.20  L  13.28  L  7.72  111  31  0.62  2.32  0.175  15  62  16  0.80  1.37  0.194  25  82  24  0.60  1 .43  0.136  10.52  L , 6 B = 1 .75,  30  0.50  1.47  0.110  13.40  L, 6 8 -  111  = 1.0  L  25  25  6T  EDI-S3-12  0.92 0.49  = 0.0  L , 6 B = 0.5, 6 T = 0.0  0.49  -1 -2  15 25  reached not reached = dead volumes  NL, 6 B = 1.0,  • 2-0  T  = limit = limit  7.06  L . 6 B = 1 .75, 5 T " 0.0 5 T = 0.0  1.75, 6 T - 0.0  EDI-S3-13 32  1290  0.5  1.85  10  33  22  . 30 •  0.81  2.15  0.230  9.33  L , 6 B = 0.0, 6 T - 0.0  33  1280  60  0.77  2.05  0.217  9.43  L , 6 B " 0.5, 5 T = 0.5  34  1200  70  0.71  1 .99  0.235  8.44  NL, 6 B = 1.0, 6 T ° 1.0  35  1200  40  0.60  1 .57  0.171  9.16  L , 6 B = 1.0, 6 T = 0.0  36  1260  60  1.00  2.82  0.326  8.'66  NL, a B = 0 .0 , 6 T - I .0 j>  i  143  1000  [ppm], <5 = 0.5  Figure 56.  [-], v =  1.70  [ c m / s e c ] , T = 7.0  E f f e c t o f dead v o l u m e s ( 6 g / 6 ) transients. EDI-S2-I5. y  on  [ s e c ] , A$ =  concentration  40  144  Figure 57.  E f f e c t of dead v o l u m e s ( < 5 / 6 ) transients. ED I - S 3 - I 3. R  T  on  concentration  145  is  pushed out  i n t o the  volume means a s m a l l reenters the  the  current  brine  reservoir.  concentration  e I e c t r o d i a Iyzer consumption  change.  during  is smaller  A large  every if  Since odd  the  reservoir the  half  front  front cycle,  has a  low  concentration.  4. of  solute  as t h e are  A "salting  added t o t h e  amount  and t h e  (c  T  brine  respect  displaced  - c )(5v 0  0  - c )(6v 0  A plot the  of  0  solute  =  1  f  [xT-  "  ,1 1  + v ) x_  -  1  0  these  factors  as f u n c t i o n s  of  be used as a c o n t i n u o u s  reservoir  v o l u m e s were  amount  of  salt  to  opposite  would  amount factor"  The  factors  concentra-  1 +  i -J r  B  <5v  device could  the  initial  GO  c  product.  *  xT-  0  the  + Vj)  0  B  and a " d e s a l t i n g  dialysate  to  as t h e  volume:  c „ <5v  (c  may be d e f i n e d  product  removed from t h e  normalized with  tion  factor"  infinite  be removed  one d u r i n g  real  time  solute  f r o m one  each c y c l e  reservoir  (see  1  Figure  ^ B-  5  J  shows  pump.  and we I I m i x e d , a  <5 1 +  that If  the  constant and added 58).  146  Figure 58.  E f f e c t of dead v o l u m e s ( 6 / 6 ) transients. EDI-S2-I5. R  T  on s a l t i n g  factor  147  5.3.7  E f f e c t of i n i t i a l The  ~ 1250  ppm  concentration  to ~ 5000 ppm  ments (see the  initial  Table 25).  solutions.  e f f e c t on  the  separation  the  transients  f a c t o r was  (see  the  EDI-S2-12 group.  The h i g h e r  voltage 2.  branes tion  in the  are  the  current  range  less  to  are necessary to densities  investigated  (23),  pause times are  retarding limiting  proportionally  same s e p a r a t i o n . maintain  the  in-  effective  36).  of  of  the  i o n e x c h a n g e memsolution  (D'A Iessandro, current  concentra-  1971). density  This (compare  3.3.  long or the  l e s s pronounced ( F i g u r e  The  of  v o l t a g e than  reduce the  reduces the  Section  a  in  are:  achieve the  independent  r e s i s t a n c e term  had  requires  The s p e c i f i c c o n d u c t i v i t y  with equation If  concentration  (see a l s o F i g u r e  i s more o r  constant  a smaller applied  1.  o v e r p o t e n t i a Is w h i c h  stack  of  EDI-S3-13 runs which  reasons f o r t h i s behaviour  rates  resistances  Figure 59,60,61).  The  creased electrode  experi-  concentration  higher c0  reduced f o r the  s h o r t e r pause times and  The  same time the  In a l l cases the  mass t r a n s f e r  changed from  same r a t i o between the  had  larger  was  i n c r e a s e d from 2,000 to 10,000 ppm  order to maintain the two  (c0)  NaCl/H 2 0 i n three groups of  At  r i n s e s o l u t i o n was  the  concentration.  59).  v o l t a g e h i g h , these  effects  Table 25 E f f e c t of I n i t i a l  1 RUN NO.  2  5  '  5  H  6  Concentration ( c 0 ) on EDI-S3-12 and EDI-S3-13  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL  10  11  CONCENTRATION  12  13  SEPARATION FACTOR  REMARKS  BRINE DIALYSATE #  C-] 4-0 -1 10-0 -1  Co  6  V  [ppm]  [-]  [cm/sec]  1245  0.59  0.92  4680  T  T  [sec] [sec] 15 25 15 25  62 82 62 82  AS  [volt] 32  nc  C-3 16 23 15 20  I  [ampere] 0.90 0.70 3.20 2.80  X  B [- ] 2.03 2.17 2.00  X  T  ns  [-3  [- ]  0.259 0.218 0.273 0.205  7.85 9.97 10.00  5  L - l i m i t reached NL " l i m i t not reached dead volumes  V x "  L L L L  EDI-S3-13 6 37  1300 4640  1.00  0.95  5  61  10  17 15  0.62 1.65  1 .31 1.15  0.603 0.684  2.18 1 .68  L L  26 39 •  1260 4890  0.50  1.40  10  37  10  40 35  0.54 1 .54  1 .83 1 .54  0.344 0.462  5.33 3.33  L NL  149  F ig u r e  59 .  E f f e c t of i n i t i a l c o n c e n t r a t i o n ( c o ) on concentration transients. EDI—S3—12.  dialysate  S -  1.0  Figure 60.  [ - ] , v - 0.95  [ c m / s e c ] ' , T - 5.0  [ s e c ] . At - 10  E f f e c t of I n i t i a l concentration ( C o ) on concentration t r a n s i e n t s . EOI-S3-I3.  [V]  151  5.3.8  Effect axial  of i n t e r n a l  flow d i s t r i b u t i o n  dispersion.  The  flow d i s t r i b u t i o n  and  longitudinal  measured using a step response method. axial  of r e s i d e n c e t i m e s .  d i s c u s s e d by Danckwerts (1953) who diffusion function  of a system  inlet.  with  concept has been  a l s o measured the  response  to a step change i n c o n c e n t r a t i o n  a mixing  a l s o employed by McHenry and Wilhelm  tinuous model using an a x i a l  diffusion  f o r more than about 25 mixing c e l l s .  coefficient  response of  tanks to a step change of the i n l e t  (1957).  coincide  The mixing c e l l  m  concept  (1958), and  Young (1957), i n p a r t i c u l a r , gives an  The equation may  analytical  equal mixing  concentration.  be m o d i f i e d to account f o r the  i n h e r e n t dead volumes of the f i r s t ED c e l l  design.  I f these  dead volumes are assumed to be well mixed, the normalized effluent  concentration  equation ( 3 2 ) .  cell  model and the con-  f u r t h e r advanced by Young (1957), E p s t e i n  e x p r e s s i o n f o r the e f f l u e n t  at  mixing by a frequency response  (1957) showed that the mixing c e l l  many o t h e r s .  axial  i n v o l v e d the  Kramers and Alberda (1953) proposed  method, which was  was  Flow systems  The  c o e f f i c i e n t by a method which  model and measured the a x i a l  Aris  mixing were  d i s p e r s i o n have often been s i m u l a t e d by models based  on d i s t r i b u t i o n s  the  and  is a function  of time a c c o r d i n g to  1 52  m x =  -  L  T  -  +  m  r  exp  r - l  (32) m+l-j + exp(-  mt)  (m+ 1 - j )  I ^ fJ / - 1 + ( m - j ) j=o '  r  — m  where v„ - v. 2  i n h e r e n t dead volume  v„ - v.  v.  v, = a c t i v e stack a T  _. t Q v  t =  time  a Q = flow  x =  c c  This f u n c t i o n was for  initial  evaluated  r = 0.04  using  first  = final  concentration  a digital  values  of r .  computer. The  d e r i v a t i v e of (32) w.r.t. time t .  The  The upper  the f u n c t i o n ( 3 2 ) , the  63 shows the dependence of the maximum slope two  concentration  are shown in Figure 62.  part of the diagram i l l u s t r a t e s part i s the  rate  C l  " c o ~ 1 Cj  results  void volume  (x) on  lower  Figure m  curves go through a minimum at m =  for 2,  153  i n c r e a s e monotonically  f o r l a r g e r m, and approach a f i n i t e  l i m i t which i s given by  Hm\(k)\ m  According of  to equation  the flow  step  =  ^  - H »  (32) the response should  r a t e , the d i r e c t i o n  be independent  of f l o w , and whether the  i s an i n c r e a s e or a decrease i n c o n c e n t r a t i o n . The  r e s u l t s f o r t e s t s on the f i r s t  v e r s i o n s are presented  i n Table  26 to 29.  +  and t h i r d  stack  The s i g n of the  slopes  i n d i c a t e s response to an i n c r e a s i n g (+) or a d e c r e a s i n g & (-) s t e p , t i s the time at which the maximum slope o c c u r r e d , _*  and  x  the corresponding The  concentration.  response curves  of the second stack  versions  could not be evaluated  i n the same way, s i n c e pronounced by-  passing was observed.  T y p i c a l response curves  in  Figure 64.  The c o n c e n t r a t i o n  are sketched  i n experiments with  decreased very soon a f t e r the step had entered  EDI-S2-15  the s t a c k ,  passed through a p l a t e a u , and descended f i n a l l y toward the inlet  concentration.  Another spacer  plus s o r p t i o n membrane  added to the same pack almost e l i m i n a t e d the p l a t e a u , but the shape of the curve was not of the F type p r e d i c t e d by a +  The step response method may be u t i l i z e d to measure the void volume between the c o n d u c t i v i t y d e t e c t o r s .  154  mixing  cell  model.  This may be due to a nonuniform flow  distribution. The  spacer screens  p l a s t i c netting flowed  c o n s i s t e d of a s i n g l e  cut p a r a l l e l  to one s t r a n d .  t h e r e f o r e i n many p a r a l l e l  a random p a c k i n g .  groves  l a y e r of  The s o l u t i o n  r a t h e r than  The flow r a t e s through  the groves  through varied  because the spacing was not c o n t r o l l e d a c c u r a t e l y . The  response  resembled those  curves  of EDI-S1-8 stack most c l o s e l y  p r e d i c t e d by a mixing  cell  model (see Table  The mean value of the maximum slopes was k = 1.27 and  26).  _* occurred a f t e r t mixing  stages The  = 0.965.  T h i s corresponded  to 10 e f f e c t i v e  (see F i g u r e 6 3 ) . third  stack was t e s t e d with  plus s o r p t i o n membranes.  By-passing  12 and 13 spacers  ( o r c h a n n e l l i n g ) was  n o t i c e d f o r the former and i s manifested i n the high value _* of t = 1.11. The a d d i t i o n of another u n i t i n c r e a s e d the value of the slope from x = 1.26 to x = 1.42 and shortened —*  +  the time lapse to t stages  The e f f e c t i v e  number of mixing  i s m = 12 or 13, see Figure 63. The  third  as the f i r s t one. flexible sion  = 1.01.  stack comprised  the same spacer  screens  The i n c r e a s e d m i s a r e s u l t of the more  capacity c e l l s .  They d i s t r i b u t e  the areal  compres-  from the e l e c t r o d e end frames more evenly than the All  values  averaged.  155  Figure  62.  Internal mixing. E f f e c t o f number o f e f f e c t i v e m i x i n g s t a g e s (m) on r e s p o n s e t o s t e p change_ i n feed c o n c e n t r a t i o n : (a) r e s p o n s e f u n c t i o n x ( T ) ; (b) s l o p e ( x ( t ) ) o f r e s p o n s e c u r v e ( d i m e n s i o n I e s s ) .  156  T r T r 30 25 15 20 NUMBER OF MIXING STAGES m [-} Figure  63.  Maximum s l o p e  ( x ) v s . number o f m i x i n g  EDI-S2-I5  Figure 64.  Step  response of second  stages  (m)  EDI-S2-I6  stack  versions  (schematic).  157  Table Step  Flow  Rate  0 Hem /seel  Response Experiments  D i sp 1 acement Up/Down  Rate  Q CcmVsecH  14.1 14.1 20 . 8 20.8  0 . 856 0 .960 1. 1 1 1 .03 1 .02  D i s p 1 a c e m e nt Up/Down L-l  0 . 5 17 0.564 0 . 423 0.549 0.570  27  Response Experiments  Up Down Up Down  X  L-l  - 1 .27 - 1 .26 + 1.21 - 1 . 38 -1 . 2 4  Runs  Flow  —*  C o n c e n t r a t i on  X  Table Step  EDI-SI-8  T i me t*  •  Dow n Up Down Up Down  14. 1 14. 1 14.1 20 . 8 20.8  on  Maximum S I ope  L-I  3  26  on  EDI-S3-I2  #1-14  Max i mum S 1 ope  • x L-l -1.12 + 1.07 - 1 .09 + 1.14  T i me t* L-l 1.19 1.21 1 . 20 1.17  C o n c e n t r a t i on X *  L-l  -  1 58  Table Step  Response Experiments Runs  Flow  Rate  3 Q [cm /sec]  D i sp1acement Up/Dow n  Maximum Slope  Rate  C-] -1.174 +1.210 + 1 .057 -1.210 - 1 . 148 +1.275 +1.123 -1.131 - 1 .349 +1.336 +1.227 - 1 .249  Q Ccm V s e c ]  X*  n-D  1.1 8 1 1 .031 1 . 1 59 1 .054 1 .204 1 .024 1 . 1 48 1.125 1.155 1 .058 1 .005 1.155  0 .592 0 .469 0 . 426 0.570 0.497 0.518 0 . 5 12 0 . 5 12 0.520 0.568 0 .600 0.506  29  Response Experiments  D i sp1acement Up/Down L>]  C o n c e n t r a t i on  c-:  X  Table  Flow  T i me T*  •  Dow n Up Dow n Up Dow n Up Down Up Down Up Dow n Up  Step  on E D I - S 3 - I 2  #15-24  L>:  7.03 7.03 7.03 7.03 14.1 14.1 14.1 14.1 28.3 28.3 28.3 28.3  28  Maximum S 1 ope  •  on E D I - S 3 - I 3  T i me t*  L>:  C o n c e n t r a t i on X*  C-D  X  7.03 7.03 7.03 7.03 14.1 14.1 14.1 14. 1 28.3 28.3 28.3 28.3  Down Up Down Up Down Up Down Up Dow n Up Dow n Up  [-3  -1.259 +1.416 +1.326 -1 .351 -1.468 +1.598 +1.327 - 1 .427 -1.429 +1.743 +1.374 - 1 .324  1 .049 0 .940 1 .005 1 .020 1 .086 0.978 1 .032 1 .032 0 .974 0 .967 1 .029 1 .008  .604 .336 .393 . 596 .59 1 . 388 . 340 .639 .623 .45 1 .371 .640  1 59  combination of sturdy in the f i r s t s t a c k . the stacks  frames and strengthened  A comparison of the s e p a r a t i o n  shows that the v e r s i o n s with  by-passing,  spacers  c h a n n e l l i n g , e t c . achieved  less  present  runs on  axial d i s p e r s i o n ,  much b e t t e r s e p a r a t i o n  f a c t o r s , see Figures 40,41; 44,45; 65. The  internal  dispersion effects  mainly r e s p o n s i b l e f o r the f i n i t e operations. of  this  interpretation  conditions  5.3.9  Figure 51 presents  are, therefore,  separation  l i m i t of pause  f u r t h e r evidence i n favour  of the r e s u l t s , s i n c e the l i m i t i n g  are shown to be independent of the flow  E f f e c t of e x t e r n a l mixing i n b r i n e  rate.  reservoir.  Three p a i r s of experiments were performed on the EDI-S3-12 stack to study the e f f e c t of mixing of the e f f l u x c o n c e n t r a t i o n on the performance. had  the usual  The f i r s t run of each  complete mixing of both r e s e r v o i r s but i n the  second run the b r i n e r e s e r v o i r was r e p l a c e d by a c o i l I.D.  TYGON tubing  reduced.  (8 m l o n g ) .  to  from the r e s u l t s  as w e l l as i n power listed  p a i r #7-#7a shows the l e a s t improvement. the small  d i s p l a c e d volume as e x p l a i n e d  A qualitative  of 5/16"  Consequently, the mixing was  The improvement i n s e p a r a t i o n  requirement i s evident The  pair  i n Table 30. T h i s i s due  subsequently.  p i c t u r e of the c o n c e n t r a t i o n  in the r e s e r v o i r s and i n the ED c e l l  at l i m i t i n g  profiles  conditions  160  Figure 65.  E f f e c t of i n t e r n a l d i s p e r s i o n . T r a n s i e n t s of s e p a r a t i o n f a c t o r and d i a l y s a t e p r o d u c t c o n c e n t r a t i o n f o r second s t a c k v e r s i o n s .  161  i s presented i n Figure 66, which i s s i m i l a r l y c o n s t r u c t e d to Figures end  reservoirs  that the lines i ng  11 and  , Section  are well  total  are  14  void  3.2.1.  It i s assumed that  mixed a f t e r each d i s p l a c e m e n t ,  volume of the  f o l l o w e d through one  and  stack i s d i s p l a c e d .  cycle  according to the  the  The operat-  sequence :  (0)  t = 0  The ED e e l I and t h e b r i n e t a n k c o n t a i n s o l u t i o n , the d i a l y s a t e tank is empty. D i a l y z a t i o n s t a r t s , flow is stopped.  (1)  t = T  At t h e end of t h e f i r s t p a u s e t i m e t h e i n t e r n a l c o n c e n t r a t i o n p r o f i l e is lowered  (ii)  t = ^-  The w e l l mixed b r i n e volume i s f l o w e d t h r o u g h t h e ED c e l l p r o d u c i n g t h e d i a l y s a t e p r o f i l e ( i i ) which i s then w e l l m i x e d , i . e . the d i a g o n a l l y shaded a r e a s above and b e l o w ( i i i ) a r e e q u a l .  (iii)  +  (iv)  The  =  5 "  +  T  T  n  e  to  t = T  • n i"e r n a I p r o f i l e i s r a i s e d f r o m ( i i i ) d u r i n g the e n r i c h i n g pause  The e f f l u e n t p r o f i l e ( i v ) i n t h e b r i n e tank i s w e l l mixed t o y i e l d ( v ) . Since l i m i t i n g c o n d i t i o n s were assumed ( v ) c o i n c i d e s w i t h (0) e x t e r n a l l y , and ( i v ) w i t h (0) i n s i d e t h e ED c e l l , and t h e loop i s t h u s c l o s e d .  cross shaded areas i n d i c a t e  maintain the lines  (with  (ii) time.  the  c u r r e n t requirements  steady p e r i o d i c  concentration  fronts.  arrows) show the  concentration  changes of some  volume elements as  they r e c i p r o c a t e  Several e f f e c t s may  be  in the  The  to dotted  module.  e x p l a i n e d by  t h i s model:  Table 30 E f f e c t of End Mixing on EDI-S3-12  1  2  3  4  5  6  7  8  9  COi.'CtfiTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT RUIi iiO. INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED fin. TOTAL §  C-3  Co [ppm3  S C-3  V  [cm/sec]  nc £sec] [sec] [volt] C - l T  T  AO  10  11  CONCENTRATION  12 SEPARATION FACTOR  8 R1; J E DIALYSATE  I  x  X  3  T  [2tipere3  C-3  C-3  73  ns [- 3  REMARKS L l i m i t reached NL « l i m i t not reached a dead volumes a  7 7a  1280 1280  0.59  0.49  20  100  32  15 15  0.85 0.75  2.09 2.29  0.222 0.191  9.38 12.00  NL L, brine unmixed  8 8a  1270 1270  1 .00  0.92  20  93  32  10 12  0.95 0.75  1 .64 1 .83  0.376 0.255  4.36 7.18  L NL , brine unmixed  11 11a  4560 4600  1 .00  0.92  15  83  32  11 15  3.60 3.10  1 .52 1 .76  0.386 0.267  3.94 6.60  L • L, brine unmixed  CD  ro  163  Figure  66.  Q u a l i t a t i v e model of t h e c o n c e n t r a t i o n p r o f i l e s in a 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 i n pause t i m e o p e r a t i o n w i t h i n t e r n a l d i s p e r s i o n and w e l l mixed end reservoirs.  164  1. the  internal  are smoother, 2. through  dispersion  centration  effective  and t h e b r e a k t h r o u g h  renders  because the g r a d i e n t s  occurs  later.  S m a l l e r d i s p l a c e d volumes a l s o p r e v e n t  Current consumption  peaks r e s i d e o n l y  ED c e l l ,  5.3.10  a break-  i s reduced i f t h e high  f o r short  i . e . i f the e f f l u x  E f f e c t of c a p a c i t y First  tion  less  profile  of t h e f r o n t s . 3.  active  A p r e s e r v a t i o n of the e f f l u x  cell  time  cells.  in the  peaks a r e p r e s e r v e d .  thickness.  and t h i r d stacks only d i f f e r  of the c a p a c i t y  periods  con-  i n the c o n s t r u c -  However, a comparison of e x p e r i -  ments under s i m i l a r o p e r a t i n g c o n d i t i o n s  is d i f f i c u l t for  two reasons: 1.  The e f f e c t i v e  t h i c k n e s s of the flow  c h a n g e d when t h e f r a m e s were This  i s probably  a result  channels  removed f r o m t h e c a p a c i t y  of t h e i n c r e a s e d f l e x i b i l i t y  cells. of t h e  ceI I s . 2. be d i f f e r e n t  The i n t e r n a l (see Section  The b a s i s cussion.  m i x i n g o f t h e s t a c k s was f o u n d t o 5.3.8).  of comparison i s t h e r e f o r e  Only two p a i r s  open to d i s -  of experiments were s e l e c t e d  from  165  the d a t a , see Table to  31.  (Note, the a p p l i e d v o l t a g e  the p o t e n t i a l per spacer  plus s o r p t i o n membrane.)  runs were no-pause operations The  actual value  f a c t o r s should above.  One  A reduction  f a c t emerges n e v e r t h e l e s s  i n the  thickness  The  separation. was  not  high  of the  quite  separation  reasons  given  clearly:  core  rates of mass t r a n s f e r i n c r e a s e  at the  limited.  increases  i s q u i t e important f o r a pause  U n f o r t u n a t e l y , the  realized  and  of the c a p a c i t y c e l l  This  The  were t h e r e f o r e rate  s t r e s s e d because of the  the c u r r e n t consumption. operation.  and  of the c o n c e n t r a t i o n s  not be  i s reduced  the  importance of the pause times  time experiments on the f i r s t  stack  were performed.  5.3.11  E f f e c t of t h i c k n e s s of  spacer The  and  screens.  second and  third  study the e f f e c t of the spacer was  hydrodynamic p r o p e r t i e s  stack  v e r s i o n s were designed  screen.  b e l i e v e d to have a s i m i l a r e f f e c t  capacity c e l l .  The  channel  to the  thickness  thickness  of  step response measurements, S e c t i o n  r e v e a l e d however, that the i n t e r n a l d i f f e r e n t mechanisms f o r the two difficult  The  d i s p e r s i o n i s caused  s t a c k s , and  to d e f i n e a common b a s i s f o r the  i t becomes runs.  to  the  5.3.9, by very  Table 31 Effect  1 RUN NO.  C-]  2  3  4  of Capacity C e l l Thickness on E l e c t r o d l a l y z e r  5  6  7  8  9  CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL Co  6  [ppm]  [-]  V  T  T  [cm/sec]  [sec]  [sec]  -  42 1-0  750 1225  1.00 1.00  1.21 1.33  36 24  700 1170  1.00 1 .00  0.65 0.90  -  nc [volt]  [ -]  10  No. 1  11  CONCENTRATION  BRINE 01ALYSATE X X T B [ ] [] [ampere] I  12 SEPARATION FACTOR ns  '[- 3  13 REMARKS L = 1 tmi t reached NL <* l i m i t not reached 6Q/6J = dead volumes  50.2 36  2.5 2.7  7 10  0.78 1.50  0.972 1.07  0.954 0.821  1.02 1 .31  L, EDI-SI-8 L, EDI-S3-12  94 55  1.56 1 .66  8 15  0.50 1.09  1.04 1.14  0.935 0^70 3  1.11 1 .62  L, EDI-S1-8 L, EDI-S3-12  167  5.3.12  Comment on  pH-changes.  At f i r s t checked before  and  changes o c c u r r e d . discontinued. ments with the pH  the pH  of process  a f t e r each r u n . The  systematic  Occasional  However, no pH  was  significant  sampling was,  therefore,  solution  high v o l t a g e s , d i s c l o s e d that becomes more a c i d i c , but  r i n s e stream remains e s s e n t i a l l y are l i s t e d  rinse solutions  l a t e r checks, e s p e c i a l l y f o r experi-  long pause times and  of the process  and  below in Table  unchanged.  Typical  the  results  32.  Table  32  pH-Changes f o r some EDI-S3-I2 Runs  \ .  pH RINSE  PROCESS Run  before  after  before  1 1  6.3  5.6  7.6  7.7  13  6.4  6.35  7.5  7.6  14  6.3  5.8  7.5  7.5  22  6.6  6.35  7.5  7.5  23  6.35  6.18  7.4  7.5  5.3.13  Comment on c u r r e n t The  of  after  efficiency.  change in c u r r e n t e f f i c i e n c y  a number of experiments are l i s t e d  during  in Table  the  course  C . l . l to C.1 .66  168  (see  Appendix C . l ) .  parameters start  ( s e e T a b l e s 9 t o 13), the c u r r e n t  b e t w e e n 25 and 50% f o r t h e f i r s t  rapidly tion  D e p e n d i n g on t h e v a l u e s  of the operating efficiencies  c y c l e , decrease  f o r s u b s e q u e n t c y c l e s , and t e n d t o z e r o  approaches s t e a d y , When t h e s e  steady-state  as t h e  quite separa-  periodic state.  results  a r e compared t o 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 , batch  and c o n t i n u o u s  systems  may be d i s t i n g u i s h e d . (i) for  Most c o n t i n u o u s s y s t e m s  demineraIizing  concentration. South 1600  t h e feed  water t o the s p e c i f i e d  The e l e c t r o d i a l y s i s  Dakota, operated  with  require several  test  four stages,  The a v e r a g e c u r r e n t e f f i c i e n c y  and  demineraIized  (Calvit  per stage  f r o m 92 t o 83$ as t h e s t r e a m became p r o g r e s s i v e l y The  overall  solved  current efficiency  solids  The c u r r e n t e f f i c i e n c y  system decreases  electrodialysis efficiencies  Sloan,  decreased depleted.  19% iota  in time s i m i l a r  process.  Mandersloot  i n a batch  I dis-  recircula-  to the present ( 1 9 6 4 ) reporte'd  o f 85% f o r 94$ d e m i n e r a I i z a t i o n  sodium c h l o r i d e The  f o r removing  and  was 9 0 $ .  (ii) tion  product  bed i n W e b s t e r ,  ppm b r a c k i s h w a t e r t o 350 ppm p r o d u c t  1965).  stages  o f 0.05N  cyclic current aqueous  solution.  reasons  f o r much s m a l l e r  e x p e r i m e n t s on t h e f i r s t  ED c e l l  current e f f i c i e n c i e s f o r  a r e as f o l l o w s :  169  N a t u r e of d e n s i t y i s uniform  the c y c l i c and  operation:  c o n s t a n t , one  Suppose the  void volume i s d i s p l a c e d ,  the membranes are p e r f e c t l y s e l e c t i v e , and zero. first  In t h i s  eralized  i s e x a c t l y 50%  solution  in time.  s i n c e only one-half  According  remain  number of c y c l e s . experiments was  remains current  the stack during  pause t i m e s ,  the  decreased g r a d u a l l y as f u n c t i o n s of  The  d i s p l a c e d volume i n most of  l e s s than a v o i d volume.  It was  effluent  unchanged.  e f f i c i e n c y , as d i d the  electric  of the demin-  to t h i s model the  In r e a l i t y , when o p e r a t i n g with current e f f i c i e n c i e s  the  current  of subsequent c y c l e s are z e r o , s i n c e the  concentrations  separation.  The  volume i s r e c o v e r e d , the other h a l f  in the e l e c t r o d i a l y z e r . efficiencies  the pause time i s  c a s e , the e f f l u e n t c o n c e n t r a t i o n during  h a l f c y c l e decreases l i n e a r l y  efficiency  current  the  these  This reduced  the  presence of dead volumes.  a l s o found that the c u r r e n t consumption of displacement c o n t r i b u t e d very  It may  be more e f f i c i e n t  power during d i s p l a c e m e n t s ,  little  to d i s c o n n e c t  to  the  the  or d i s p l a c e at very  high  flow r a t e s .  I n t e rnaI centration  front.  mixing results  in d i s p e r s i o n of the  These d i s p e r s i v e e f f e c t s  must be  con-  balanced  by e l e c t r i c energy input at steady p e r i o d i c c o n d i t i o n s , i . e . a l a r g e r and  l a r g e r amount of the  c u r r e n t i s consumed to main-  t a i n the c o n c e n t r a t i o n wave as the s e p a r a t i o n  progresses.  170  Channeling and/or  unequal  flow  n e a r l y stagnant volume elements which  distribution  become  causes  periodically  d e m i n e r a l i z e d and e n r i c h e d but never emerge as p r o d u c t s .  5.3.14  Comment on true  limits  and r e p r o d u c i b i l i t y of  batch r u n s . The o p e r a t i n g c o n d i t i o n s were changed during the course of some experiments uniqueness of the f i n a l Appendix  i n such a manner as to t e s t the  c o n c e n t r a t i o n s , see the t a b l e s i n  C.l f o r runs: #28 #5,6,8,9  (EDI-S2-I6) (EDI-S2-I6)  Figure 67 shows the s e p a r a t i o n the number of c y c l e s  factor  (ns) as a f u n c t i o n of  (nc) f o r runs #27 and #28 on EDI-S2-15,  and Figure 68 i s a s i m i l a r p l o t f o r runs #8 and #9 on ED IS2-16.  Both f i g u r e s demonstrate  uniqueness of the f i n a l The  the r e p r o d u c i b i l i t y  separation  reproducibility  and the  factor.  of the r e s u l t s was t e s t e d  fre-  quently throughout the experimental program and was found to be e x c e l l e n t i n most c a s e s .  Tables 14, 15, 16, 17, 19, 22,  23 and Figures 40, 41, 43, 44, 46 may be r e f e r r e d comparison tribution  of r e p l i c a t e experiments.  to f o r a  However, the flow d i s -  and consequently the i n t e r n a l  dispersion  appeared to  be d i f f e r e n t when the same stack was dismantled and reassembled. This i n f l u e n c e d the r e p r o d u c i b i l i t y of s e p a r a t i o n  runs.  Figure 67.  U n i q u e n e s s and r e p r o d u c i b i l i t y of f i n a l s e p a r a t i o n f a c t o r f o r second s t a c k e x p e r i m e n t s .  Figure  68.  U n i q u e n e s s of f i n a l stack experiments.  separation  factor  for  second ro  173  5.4  Summary of Experience Gained on F i r s t ED C e l l The experimental work on the f i r s t  meet s e v e r a l a)  Serve as p r e l i m i n a r y i n v e s t i g a t i o n t o e x p l o r e t h e p o s s i b i l i t i e s of a p p l y i n g c y c l i c o p e r a t i o n s t o an e I e c t r o s o r p t i o n stack.  b)  Test p r e d i c t i o n s of s e v e r a l t h e o r e t i c a l models.  simple  c)  S c r e e n o p e r a t i n g and d e s i g n to determine t h e i r r e l a t i v e f o r such c y c l i c o p e r a t i o n s .  parameters importance  d)  Provide a basis f o r understanding the phenomena i n v o l v e d i n o r d e r t o d e s i g n an i m p r o v e d s t a c k and ED m o d u l e .  The c y c l i c ED p r o c e s s i s a l m o s t e n t i r e l y  by t h e r a t e s  o f mass t r a n s f e r  E q u i l i b r i u m plays only 2. usually  very  centration during or  long  completed and produced the  results: 1.  trolled  had to  objectives:  This program was s u c c e s s f u l l y following  ED c e l l  a subordinate  The s t a n d a r d inefficient  transients  the f i r s t residence  parametric  a c r o s s t h e membranes. role. pumping o p e r a t i o n  under t h e s e c i r c u m s t a n c e s .  show t h a t t h e main s e p a r a t i o n  c y c l e , except times.  con-  f o r large  applied  is  The c o n occurs  v o l t a g e s an  174  The a d d i t i o n  3. reversal  improves  order  magnitude.  of  a flow  separation  Internal  4. channelling  the  of  factors  in  a pause  each  polarity  by more t h a n  dispersion effects  and b y - p a s s i n g a r e t h e  separation  pause a f t e r  which  an  include  main c a u s e f o r  limited  operation.  5.  The a p p l i e d  voltage  is the  6.  The c u r r e n t  consumption  second  important  p a rameter.  proportional identical found t o  with the  conditions.  separation  but  final  is  alter  the  approximately  at  separation lower  otherwise factor  is  limiting  end r e s e r v o i r s  values.  delay  the  limit. may be r e d u c e d t o  obtain  separation.  also 10.  separation  do not  in the  The d i s p l a c e d volume  9.  set  However, the  Dead v o l u m e s  8.  mixing  concentration  be s l o w e d down and a p p r o a c h e s 7.  better  initial  increases  External  mixing  reduces s e p a r a t i o n  when  internal  present. The s u p e r f i c i a l  in pause o p e r a t i o n s  by pumps o r m e c h a n i c a l  velocity  has a m i n o r  and may be  limitations.  effect  increased to  a  on level  175  5.5  The Second The  Electrodialysis Cell  results  a second module. 1.  2.  on the f i r s t  (EDII)  ED c e l l  The f o l l o w i n g o b j e c t i v e s were pursued:  D e s i g n and p r o d u c e in  new s t a c k  -  is simple  -  may be m a n u f a c t u r e d  -  is reliable  -  is readily  -  a l l o w s t h e pack s i z e or decreased,  -  may be used w i t h t h e same e q u i p m e n t as t h e p r e v i o u s  -  might be e a s i l y scaled up.  this  Investigate  4.  Study e f f e c t  accurately,  a s s e m b l e d and d i s a s s e m b l e d ,  -  p a u s e t i me  -  initial  -  d i spIaced  -  applied  -  fIow  t o be i n c r e a s e d auxilary cell,  new e l e c t r o d e  end frames  pack.  effect  of channel  of o p e r a t i o n  concentration voIume  voItage  rate  which  in performance,  stack  3.  pack  construction,  D e s i g n and p r o d u c e for  were used to design  length.  parameters:  176 Test  5.  theoretical  uniform  model  b a s e d on c o n s t a n t  r a t e o f mass t r a n s f e r .  The  equipment and i t s f e a t u r e s are d e s c r i b e d  and  the manufacturing procedures f o r stack u n i t s and e l e c t r o d e  end  frames are contained The  i n Chapter 4.3,  i n Appendix A.3.  length of the flow  channels was a d j u s t a b l e  the new ED module c o n s i s t e d of e i g h t i d e n t i c a l stages  in parallel connection  transfer. ated  electrically.  was used to analyze  uniform  r a t e s of mass  c u r r e n t mode, whereas the r e g u l a r t e s t  f o r the more r e a l i s t i c  constant  t e s t s were performed on the f u l l  5.5.1  In four runs an e l e c t r i c  In the l a t t e r case the D.C. power supply was oper-  i n constant  called  The  were always connected i n s e r i e s h y d r a u l i c a l l y and  usually series  stages.  since  Data r e d u c t i o n The  data  v o l t a g e mode.  series  These  number of s t a g e s .  and p r e s e n t a t i o n .  obtained  from those on the f i r s t  on the second ED module d i f f e r e d  one as e x p l a i n e d  required d i f f e r e n t processing  i n S e c t i o n 5.2.  and modified  This  p r e s e n t a t i o n of the  results. The  form of the main survey t a b l e i s r e t a i n e d to  allow e a s i e r comparison with Table of  13 l i s t s  operating  the r e s u l t s  on the f i r s t  ED c e l l .  parameters and c o n d i t i o n s at the end  experiments #6 to #53 i n c h r o n o l o g i c a l o r d e r .  I t can be  177  seen that the below 1%  final  of the  d i a l y s a t e concentrations  initial  measuring system i s not Section with  4.2.6, and  the  concentration.  The  are  often  well  conductometric  very accurate i n t h i s  regime, see  t a b l e s h o u l d , t h e r e f o r e , be  used  caution. C o n s e q u e n t l y , i t i s more meaningful to compare  rates  of s e p a r a t i o n  purpose the  instead  concentration  of f i n a l  changes and  were e v a l u a t e d as f u n c t i o n s are d e s c r i b e d  and  of t i m e .  for  The  corresponding  tables  factors  The  initial  The  rates  C.2. t r a n s i e n t s of  of s e p a r a t i o n  initial  (33)  which w i l l  rate of s e p a r a t i o n  be  i s a l s o the reported  a  mation was total  compiled and current  mean c u r r e n t , and  _  was  was  initial  approximated  c p n s t j  definition  of the  by  ( 3 3 )  rate  constant(a)  subsequently.  Complementary to the  final  the  were determined from  drawing a s t r a i g h t l i n e through the  d log(ns) _  Equation  tables  f a c t o r s are p l o t t e d i n semi-1ogarithmic diagrams  graphs by  points.  this  separation  groups of experiments i n which a s i n g l e parameter  varied. the  For  the  contained in Appendix  From these e v a l u a t i o n separation  conditions.  transients, additional  grouped i n t a b l e s f o r i n i t i a l  consumption, a p p l i e d e l e c t r o d e  mean probe voltage  in each stage  inforand  voltage, (see  178 Appendix C.2). Operating tion in  (a), initial  process  and f i n a l  total  i n t a b l e s 35 to  E f f e c t of channel The  c u r r e n t , and the pH changes  ^9 •  length.  e f f e c t of the channel  length on i n t e r n a l  p e r s i o n was analyzed using the step response described. ing  r a t e of separa-  and r i n s e streams of the same groups of experiments  are presented  5.5.2  conditions, i n i t i a l  The r e s u l t i n g  dis-  method p r e v i o u s l y  F-diagrams d i d not suggest c h a n n e l l -  or b y - p a s s i n g , and the f r o n t s were much sharper than f o r  the previous ED c e l l . are l i s t e d curves  The r e s u l t s of these  response  i n Table 33, and the dimensionless  tests  slope x o f the  i s g r a p h i c a l l y d i s p l a y e d i n Figure 69 as a f u n c t i o n of  the number of stages ( L ) . One can see that the shape of the curve to  the t h e o r e t i c a l  graphical  one shown i n Figure 63.  personal  l i m i t of the slope f o r i n c r e a s i n g  caused by mixing liquid  stages t h i s  touch.  The  number of stages i s  i n the i n t e r c o n n e c t i n g pipes and i n the  distribution  systems i n the s t a c k .  l i m i t i s n e a r l y reached.  flow i n the channels although  However, the  d e t e r m i n a t i o n of the s l o p e s i s not only r a t h e r i n -  accurate but a l s o s u b j e c t to a c e r t a i n finite  is similar  For more than 6  In other words, the  may be c o n s i d e r e d to be p i s t o n  there i s s t i l l  internal  mixing  flow,  i n the system.  (A  179  F i gu re 69 .  D i m e n s i o n I e s s s l o p e of s t e p r e s p o n s e c u r v e s s e c o n d ED c e l l as f u n c t i o n o f t h e number of electrodialysis stages.  for  180  Table  33  Results of Step-Response Tests on Second ED  F1ow  Stages in Series  Rate 0  C-3  T i me La£_se  Maximum Slope  t *  X  Cells  Concent rat i on —* X  Ccm /sec3  Csec3  C-3  C-3  2.81 3.60  37. 1 29.3  -1.95 -2.03  0 .62 0.66  3  #i  #5  & #6  7.40  21.7  -2.56  0.58  #7  &  7.72  19.1  -2.58  0.68  #5  to  #8  14.3 14.1  20.2 19.8  -3.60 + 3.60  0.6 1 0.55  #3 to  #8  14.25  28.5  -3.90  0.66  #1  #8  6.4 14.1  84.0 37.7  -3.50 -4.07  0.62 0.55  to  value  #8  of  x ~ 4.0  corresponds to at l e a s t 50 e f f e c t i v e  mixing  stages.) The was  e f f e c t of the channel  length on  s t u d i e d i n three sets of experiments with  stages  connected i n s e r i e s  (see Table  f a c t o r t r a n s i e n t s of the three 70, 73, and  i n Figure 71  2, 4, 6, and  The  8  separation  groups are d i s p l a y e d i n Figure  75; the c o n c e n t r a t i o n  are i l l u s t r a t e d  34).  separation  and  t r a n s i e n t s of two 76, and  the  local  groups current  consumptions at steady p e r i o d i c c o n d i t i o n s are p l o t t e d i n  181  Figures 72, s t a n t (a) results  74  and  77.  is plotted  cm t o  124 cm)  order  of  A fourfold  increase  r a i s e s the  final  The  initial  may be a p p r o x i m a t e d  3. but  appears to  maxima f o r  group  the  channel  separation  If  to  10 C s e c H ) t h e  to  a higher  5.  the  con-  (MS).  The  length  by a t  ( f r o m 31  least  one  separation  factor  function  a maximum. at  about  channel  For the  high  MS = 5 .  The  g r o u p s l i e between MS = 6 and MS =  8.  pause t i m e  0.6  with  is  the  increased (from T =  v s . MS c u r v e seems  constant  no c h a n g e  show an i m p r o v e m e n t to  the  i n c r e a s e s w i t h the  maximum i s  The c o n c e n t r a t i o n  some s i m i l a r i t y  of  (a)  go t h r o u g h  rate  level  transient  constant  this  other  4.  I.  in  by an e x p o n e n t i a l  The r a t e  concentration  ED ceI  number of stages  rate  magnitude.  2.  group  a g a i n s t the  the  are: 1.  length  F i n a l l y , in Figure 78,  to  be d i s p l a c e d  in s h a p e .  transients  for  the  no-pause  i n s e p a r a t i o n w i t h MS, w h i c h  effect  of  the  p a u s e t i m e on t h e  has first  :e. IS 2. dc^s  not" e*i<s t~  183 For t h e  6. appears to  be  less  last  group  affected  i n T a b l e 34 t h e  by MS.  T h i s group  and a pause t i m e  transients  F i g u r e 76 show p o i n t s  in  amount o f  solute  is  constant  almost  stant  rate  believed the  that  sorption  proportional  behaviour  further  The to  to  by t h e  initial  current  does n o t  ternal  The  local  mass t r a n s f e r  periodic gradients  which  They  first  It  as e x p e c t e d .  effect  of  higher  con-  The  depend on MS f o r  and  the  A large  last  stage  ratio the  no-pause  reflect  a v e r a g e d o v e r one c y c l e a t illustrate  is  approximately  distributions  have d e v e l o p e d .  c o n s u m p t i o n between  is  at  a con-  5.5.3).  d e c r e a s e s in the  current  rates  conditions.  but  noticeable  the  stream  decrease at  a saturation  current  length,  i.e.  product  see S e c t i o n  channel  g r o u p s w i t h x = 10 U s e e ] ,  8.  is only  total  dialysate  in S e c t i o n 3 . 3 .  reflects  details  initial  the  model  The  inflection,  removed f r o m t h i s  membranes w h i c h (for  of  p e r c y c l e and does n o t  this  7.  final  is  as p r e d i c t e d  centrations  of  which  of  constant  has a h i g h  T = 10 U s e e ] .  concentration  rate  case.  the  in-  steady  concentration difference is  in  identical  current to  I a rge s e p a r a t i o n .  9. off  toward  the  Most of  the  current  b o t t o m end ( s t a g e  distribution No. 8 ) .  This  curves reflects  level the  Table 34 E f f e c t of Channel Length (MS) on Second  RUN NO. #  [-]  NO. OF PAUSE STAGES TIME MS  [-]  x [sec]  INITIAL CONC. Cn [ppm]  APPLIED VOLTAGE  DISPL. VOLUME $  SUPERF. VELOCITY y [cm/sec]  INITIAL RATE  TOTAL  CURRENT  INITIAL  FI NAL  INITIAL  FINAL  INITIAL  FI NAL  [min~ ]  [ampere]  [ampere]  [-1  [-]  [-]  [-]  PROCESS pH  RINSE pH  AO [volt]  [-]  1250 1240 1210 1250  10  2/3  5.4  .028 .064 .077 .077  0.88 1.44 2.60 3.00  1.16 1 .48 2.16 2.40  5.2 5.7 5.9 6.1  6.3 6.0 5.5 5.3  5.7 5.2 5.1 6.0  5.8 5.1 5.1 5.8  6.5 6.4 6.5 6.1 7.2  6.3 6.0 5.0 5.5 6.3  5.4 5.4 5.2 5.8 5.2  5.6 5.2 5.6 5.7 5.6  _  _  _  5.3  5.2  5.9  -  -  l  48 46 43 25  2 4 6 8  47 45 44 26 35a  2 4 6 8 8  10  1225 1275 1225 1290 1220  10  2/3  5.4  .109 .140 .170 .170 .170  0.70 1 .32 1 .88 2.70 2.60  0.36 0.68 1 .04 • 1.40 1 .40  19 20 18 17 6  2 2 4 6 8  10  4900 5500 5300 5100 5700  10  2/3  5.4  .087 .087 .096 .096 .086  1.45 1.75 . 3.00 4.70 5.60  0.88 1 .00 1 .72 2.60 3.20  0.6  »  Electrodialyzer  _  -  6.1 _ _  -,  CO  Figure  70.  Effect factor  of c h a n n e l length transients.  (MS)  on  separation  Figure  71.  E f f e c t of channel trans i ents.  length  (MS) on  concentration  187  Figure  72.  E f f e c t of channel d i s t r i b ut i o n .  length  (MS) on  current  Figure  73.  Effect factor  of c h a n n e l l e n g t h transients.  (MS) on  separation  189  Figure  74.  E f f e c t of c h a n n e l distribution.  length  (MS) on  current  Figure  75.  Effect factor  of c h a n n e l l e n g t h transients.  (MS) on  separation  Figure  76.  E f f e c t of c h a n n e l transients.  length  ( M S ) on  concentration  192  Figure  77.  E f f e c t of c h a n n e l distribution.  length  (MS) on  current  0.2  Figure 78.  E f f e c t of channel l e n g t h of s e p a r a t i o n ( a ) .  (MS) on i n i t i a l  rate  194  penetration  of  the  concentration  a complete  cycle.  Also,  separation  results  in  the  channel, although  the  fact  5.3.3  that  the  into  one can s e e t h a t  larger  currents  some of  this  runs w i t h s h o r t e r  at  the  the the  effect  ED s t a c k  during  more s u c c e s s f u l bottom  end  of  i s o b s c u r e d by  c h a n n e l s have  less segments.  E f f e c t of pause t i m e . The  pause time (T) was  experiments from 0.6 ation  to 20  factor transients  tions rate  i n Figure 81, constant (a)  summarized as  magnitude  improves the  Table 35.  separ-  The  85;  82,  i n Figure 86.  84;  current d i s t r i b u -  e f f e c t of pause time on The  This  pause time  results  for  the high  (see a l s o  to  below).  no-pause  pause time  the  is  the are  least  operation.  10 C s e c H  (c )  a saturation one o b s e r v e d  10  final  at  beyond  concentration  coincides with  is s i m i l a r  in  to  as t h e  concentration  s m a l l e r than  of  from 0 . 6  s e p a r a t i o n as w e l l  dialysate  separation  80, which section  the  in the  of  Increasing  a low o n e .  vious  rate  The f i n a l  2.  Figure  and  is plotted  C s e c 3 enhances the  of  of  d i s p l a y e d in Figure 79,  i n Figure 80,  An i n c r e a s e  separation.  f o r three sets  follows:  1.  an o r d e r  82;  varied  s e c o n d s , see  are  concentration transients  for  front  0  but  effect, in the  not see pre-  195  3. sition front  The c u r r e n t  illustrate  from n o - p a u s e t o pause o p e r a t i o n . is gradually  dialyzer  creasing fairly  The i n i t i a l ,  The c o n c e n t r a t i o n  and p u s h e d o u t o f t h e e l e c t r o -  total  x f o r t h e groups w i t h  constant  current  built-up  the tran-  as x i n c r e a s e s .  4.  f o r high  current  decreases with i n -  low c o n c e n t r a t i o n s ,  concentration  runs.  but remains  The f i n a l  always decreases with x .  Note on the s a t u r a t i o n the  distributions  capacity c e l l  changes.  effect:  I f the c o n c e n t r a t i o n i s l a r g e ,  core experiences d r a s t i c  concentration  During a b s o r p t i o n the i n c r e a s e may reach the l e v e l  where the membranes become f l o o d e d with s o l u t e and  gradually  the  membrane p o l a r i z a t i o n  absorption  loose t h e i r i o n s e l e c t i v i t y .  further  i s much l a r g e r  reduced.  from w i t h i n  At the same t i m e ,  and the r a t e of  A c e r t a i n amount of s o l u t e has  to be accumulated i n the c a p a c i t y c e l l s  before the e f f e c t  becomes apparent. At rates  low i n i t i a l  concentrations  are probably more c o n t r o l l e d  than by p o l a r i z a t i o n e f f e c t s . the  dialysate  products decrease  the mass  transfer  by high s o l u t i o n  resistance  T h e r e f o r e the t r a n s i e n t s of exponentially.  Table 35 Effect of Pause Time (T) on Second Electrodialyzer  D 11;  I  RUN  K.  A  NO.  #  MO. OF STAGES  PAUSE TIME  MS  x [sec]  [ppm]  0.6 5 5 10 20  [-]  C-3  7 8 10 6 9  8  25 28 26 35a 27  8  31 32 33 34  8  INITIAL COKC.  APPLIED VOLTAGE  DISPL. VOLUME  SUPERF. VELOCITY  A* [volt]  [-]  [cm/sec]  5700 5300 4800 5700 5400  10  2/3  5.4  0.6 5 10 10 20  1250 1280 1290 1220 1250  10  0.6 5 10 20  1220 1240 1200 1280  15  Cn v rj  INITIAL RATE SL  2/3  2/3  5.4  5.4  TOTAL  CURRENT  INITIAL  FINAL  PROCESS pH INITIAL  RINSE  Fl NAL  INITIAL  Fl NAL  [-]  [-]  _  _  _  [-3  -  5.7 -  5.6 -  -  -  5.3  6.0  5.8  5.2 5.4  5.7 5.6 5.3  5.7 6.0 5.7 6.3  6.1 6.0 5.6 6.8  1  [mln- ] [ampere] [ampere]  pH  [-]  j  .018 .063 .063 .086 .108  5.6 5.6 5.1 5.6 5.5  5.6 3.8 4.1 3.2 2.0  5.7  .077 .120 .170 .170 .170  '3.0 2.7 2.6 2.7 2.2  2.4 1 .8 1.4 1 .4 1 .1  6.1 6.1 7.2 6.2  5.5  .148 .229 .255 .229  4.4 4.2 3.5 3.0  3.4 2.8 2.0 1.8  6.1 6.2 6.4 6.9  4.7 5.3 5.7 6.0  -  6.3 5.6  -  5.8  _  6.5  -  F i g u re  79 .  E f f e c t of p a u s e t i me ( T ) on s e p a r a t i o n transients.  factor  Figure  80.  E f f e c t of p a u s e t i m e trans i ents.  (x)  on  concentration  199  Figure  81.  Effect  of  pause time  (T)  on c u r r e n t  distribution.  F i g u re  82 .  E f f e c t of p a u s e t i m e t rans i ents .  (x)  on s e p a r a t i o n  factor  201  Figure  83.  Effect  of  pause t i m e  (x)  on c u r r e n t  distribution.  202  Figure  84.  E f f e c t of p a u s e t i m e transients.  (T)  on s e p a r a t i o n  factor  203  F i g u re  85.  E f f e c t of p a u s e t i m e trans i ents.  ( T ) on  concentration  204  Figure  86.  E f f e c t o f pause t i m e sepa r a t ion ( a ) .  (x)  on i n i t i a l  rate  of  205  5.5.4  E f f e c t of a p p l i e d The a p p l i e d  in  voltage. ( A $ ) was  e l e c t r o d e voltage  increased  three groups of experiments from 5 to 10 to 15 v o l t s .  The  other system parameter values are l i s t e d  i n Table 36, and  the  are shown i n Figures  transients  87, 88, 89.  of the s e p a r a t i o n  factors  The r e s u l t s a r e :  1.  Initial  rate  and f i n a l  separation  i m p r o v e d by an i n c r e a s e o f t h e a p p l i e d  2. function the  is approximately  a linear  of A $ , see Figure 9 0 .  From t h e o r e t i c a l  considerations  3. is  potential.  constant  function  The r a t e  a r e much  has t o pass t h r o u g h  The c u r r e n t  proportional  4.  consumption  (both  of  origin.  initial  and f i n a l )  toA$.  The h i g h  concentration  ration  effect  5.5.5  E f f e c t of i n i t i a l The  the point  w h i c h was n o t i c e d  initial  r u n s show t h e same  satu-  previously.  concentration.  concentration  ( c 0 ) was i n c r e a s e d f o r  three groups of experiments from 1200 to 2500 to 5700 ppm NaCI.  The r i n s e s o l u t i o n  remained at 10,000 ppm NaCI.  Table  Table 36 E f f e c t of Applied Voltage (A*) on Second E l e c t r o d i a l y z e r  RUN NO. a  V  NO. OF STAGES  PAUSE TIKE  INITIAL CONC.  APPLIED VOLTAGE  MS  T  Co [ppm]  AO  6  ••  [volt3  C-3  [cm/sec]  1220 1280 1240  5 10 15  2/3  5.4  DISPL. VOLUME  [-3  C-3  [sec3  35 28 32  8  5  36 26 35a 33  8  10  1250 1290 1220 1200  5 10 10 15  2/3  13 8 10 16  8  5  5100 5300 4800 5500  5 10 10 15  2/3  SUPERF. VELOCITY V  INITIAL RATE  TOTAL  PROCESS pK  CURRENT  INITIAL FINAL a [rain- } [ampere3 [arcpere3 1  IH  RINSE pH  FINAL  INITIAL  FINAL  C-3  [-3  C-3  C-3  1T1 AL  .072 .120 .229  1 .3 2.7 4.2  1.1 1.8 2.8  7.2  7.0  6.5  5.2  6.2  5.3  6.0  6.0  5.4  .088 .170 .170 .255  1.4 2.6 2.7 3.5  0.8 1.4 1.4 2.0  6.6 6.1 7.2 6.4  6.2 5.5 6.3 5.7  5.3 5.8 5.2 5.7  5.3 5.7 5.6 5.6  5.4  .030 .063 .063 .116  2.2 5.6 5.1 9.5  2.0 3.8 4.1 6.9  5.7  5.9  5.7  6.5  5.7 6.0  5.7 5.5  5.6 5.4  6.5 5.4  ro o cn  207  Figure  87.  Effect factor  of a p p l i e d v o l t a g e transients.  (A$)  on  separation  208  Fi gure 8 8 .  Effect factor  of a p p l i e d v o l t a g e transients.  (A$)  on  separation  209  Figure  89.  Effect factor  of a p p l i e d v o l t a g e transients.  (AO) on  separation  210  Figure 90.  E f f e c t of a p p l i e d v o l t a g e o f sep a r a t i o n ( a ) .  (A$)  on i n i t i a l  rate  211  37  summarizes the  93  d i s p l a y the  operating  separation  conditions  and  Figure 91,  factor transients.  The  92  and  results  are: 1. higher  The  initial  n o t e on  results.  in  concentrations  The  the  than  limiting  final  (see  i s reduced  also Figure  separation  In F i g u r e 91  the  final  factor  ns  96  and  The  c0  = 2500 ppm  and  curve  the  o t h e r two  i n F i g u r e 92  value  in Figure  93.  i n c r e a s e s w e l l beyond conductivity  meter  3  IO .  i s not  by  foot-  the  meters  lowest rises  but =  consistent  independent concentrations  t o a much  reaches a  1200  ppm  capable  higher  lower  transient  stressed e a r l i e r  actually  changes.  of t h e  c0  I t was  large concentration accuracy  The  shows no  seems t o be  same a p p l i e s f o r h i g h e s t  Figure 92.  level  r a t e of s e p a r a t i o n  page 2 2 1 ) •  2.  of c 0 ;  initial  that  of m o n i t o r i n g  the such  It i s b e l i e v e d , however, t h a t  i s not  the  primary  c a u s e of  this  scatte r .  3. c 0 , but  5.5.6  Both  initial  at a d e c r e a s i n g  final  increase  with  volume.  d i s p l a c e d volume (6)  of experiments and  current  rate.  E f f e c t of d i s p l a c e d The  and  was  i n c r e a s e d from 1/4  varied for to  2/3  to  three  sets  1 total  void  Table 37 Effect  F.Ui. ?«G.  iiO. OF STAGES  PAUSE TIHE  INITIAL CQKC.  i  MS  T  [-3  C-3  C9  [sec]  [ppn]  27 22 9  8  20  26 35a 23 6  8  33 24 21  8  of I n i t i a l  APPLIED VOLTAGE  Concentration  CISPL. VOLUME  SUPERF. VELOCITY  <5  V  ( c 0 ) on Second  INITIAL RATE a [mln-1]  Electrodialyzer  PROCESS r>;  TOTAL  CURRENT  INITIAL  F111 At.  INITIAL  Ft HAL  INITIAL  FINAL  [srcpere]  C-]  C-]  C-]  C-]  RINSE pK  [volt]  C-]  1250 2600 5400  10  2/3  5.4  .150 .150 .108  2.2 4.0 5.5  1.1 1.5 2.0  6.2 6.2  5.6 5.3  5.4 6.1  5.3 5,5  10  1290 1220 2650 5700  10  2/3  5.4  .170 .170 .141 .086  2.7 2.6 4.2 5.6  1 .4 1 .4 2.1 3.2  6.1 7.2 5.8  5.5 6.3 4.3  5.8 5.2 5.0  5.7 5.6 5.2  10  1200 2650 5200  15  2/3  5.4  .255 .200 .170  3.5 5.8 8.8  2.0 3.0 3.4  6.4 5.7 5.9  5.7 4.3 4.8  5.7 4.9 6.0  5.6 5.3 6.8  [cm/sec]  '  [atapore]  213  Figure  91.  E f f e c t of i n i t i a l c o n c e n t r a t i o n tion factor transients.  (co)  on  separa-  214  F igu re  92 .  E f f e c t of i n i t i a l c o n c e n t r a t i o n tion factor transients.  (co)  on  separa-  215  20  30 TIME [min]  Fi g u r e  93.  E  f  f  ect  tion  of  initia,  factor  concentration  transients.  (=.)  on  separa-  216  volume, see Table 38. plotted  The s e p a r a t i o n  i n Figure 94, 95 and 96.  factor  transients  The f o l l o w i n g  are  findings  have  been e x t r a c t e d : 1. the  initial  with  In a n o - p a u s e o p e r a t i o n , rate  is largest  6 , see F i g u r e 9 4 .  (or part  2.  of  low c o n c e n t r a t i o n s ,  f o r 6 = I and d e c r e a s e s  The f i n a l  separation  l a r g e 6 ' s because of the b r e a k t h r o u g h front  at  In pause o p e r a t i o n  effect  remains  i s the continued  of the c o n c e n t r a t i o n  a t t h e same c o n d i t i o n s  d i s a p p e a r s more o r l e s s , rise  small  effect  6 ' s than  redistributed almost is  For high  of t h e t r a n s i e n t  The f i n a l because,  between s o l u t i o n per c y c l e .  The r e a l separation although  has a c e r t a i n  (c  causes the t r a n s i e n t s  for large ones.  constant  small.  concentrations  time  0  the front  amount o f  measuring system.  = 5500 ppm) t h e  to rise  and s o r p t i o n  The c y c l e p e r i o d  faster  if  that  is small  dispersion.  is  6 is  if 6  accelerated. large,  does n o t b r e a k t h r o u g h , t h e  internal  for  membranes i s  are, therefore,  i s a l s o much s m a l l e r  What  f o r 6 = 1/4,  The amount o f s a l t  transients  this  see F i g u r e 9 5 .  b e y o n d t h e bounds o f a c c u r a c y o f t h e p r e s e n t  saturation  is smaller for  it).  initial  3.  slightly  system  Table 38 E f f e c t of Displaced Volume (6) on Second  PAUSE TIME  INITIAL CONC.  T  Co  [-]  [sec]  [ppm]  41 25 30  8  0.6  42 26 35a 29  8  12 8 10 11  8  DIIM  M f\  RUN NO. #  [-]  NO. OF STAGES MS  10  5  APPLIED VOLTAGE  DISPL. VOLUME  SUPERF. VELOCITY  INITIAL RATE  v  a  [volt]  [-]  1300 1250 1270  10  1/4 2/3 1  5.4  1175 1290 1220 1260  10  1/4 2/3 2/3 1  5.4  4300 5300 4800 5300  10  1/4 2/3 2/3 1  5.4  [cm/sec]  [mi n~*]  Electrodialyzer  TOTAL  CURRENT  INITIAL  FINAL  [ampere] . [ampere]  PROCESS pH INITIAL  F  1 NAL  RINSE pH INITIAL  FINAL  [-]  [-]  [-]  [-]  .057 .077 .091  3.6 3.0 3.0  3.4 2.4 2.6  6.1 6.1  5.8 5.3  5.3 6.0  5.3 5.8  .159 .170 .170 .170  2.6 2.7 2.6 • 2.7  0.9 1.4 1.4 1.8  6.2 6.1 7.2  5.9 5.5 6.3  5.1 5.8 5.2  5.3 5.7 5.6  .091 .063 .063 .046  5.4 5.6 5.1 5.5  2.6 3.8 4.1 4.6  5.4  5.7  5.5  6.5  _  _  5.7 6.3  5.6 6.8  6.5 6.7  -  -  -  -  _  5.7 6.2  -  -  218  219  Figure 9 5 .  Effect factor  o f d i s p l a c e d volume transients.  ( 6 ) on  separation  220  0 Figure  96.  10 Effect factor  20  30 TIME [min]  of d i s p l a c e d volume transients.  (6)  on  40  separation  221  The i n i t i a l  4. of the  6 except  consumption  f o r the no-pause group.  amount o f s e p a r a t i o n  5.5.7  current  The f i n a l  is  independent  current  a t t h e end o f e a c h r u n .  E f f e c t of dead volumes. The  +  dead volumes were i n c r e a s e d  for a single  of runs (#45 & #52, on 4 stages) to check f i n d i n g s first the  the  ED c e l l .  separation  5.5.8  in  One can see that the  volume i n each end r e s e r v o i r s  slows  at which the l i m i t i s approached.  E f f e c t of s u p e r f i c i a l The  from the  i s the same f o r both e x p e r i m e n t s , although  presence of 1/2 void  down the rate  pair  The r e s u l t i s shown i n Figure 97 i n terms of  product c o n c e n t r a t i o n t r a n s i e n t s .  final  reflects  flow rate  velocity.  of the process s o l u t i o n was  three groups of e x p e r i m e n t s , which are l i s t e d  t o g e t h e r with t h e i r o p e r a t i n g c o n d i t i o n s .  altered  i n Table 39  Again, separation  factor transients *  are d i a g r a m m a t i c a l l y shown i n Figure 98 and  99.  are s i m i l a r to those obtained on the f i r s t  The r e s u l t s  ED c e l l :  for the  Figure 98 contains r e s u l t s on no-pause experiments high and low c o n c e n t r a t i o n s . The r e t a r d i n g i n f l u e n c e of i n i t i a l c o n c e n t r a t i o n i s very c l e a r from t h i s graph. +  0 r excess volumes in the end reservoirs.  222  Figure  9 7 .  E f f e c t of dead v o l u m e s trans ients.  ( 6 / 6 - )  on  concentration  Table 39 E f f e c t of S u p e r f i c i a l Velocity (v) on Second E l e c t r o d i a l y z e r  RUN NO. #  NO. OF STAGES  PAUSE TIHE  MS  T  C-3  [sec3  37 38 25  8  0.6  39 40 26 35a  8  15 14 7  8  [-3  10  0.6  INITIAL CONC. Co  APPLIED VOLTAGE  DISPL. VOLUME  SUPERF. VELOCITY  INITIAL RATE  A*  <5  V  a  TOTAL  CURRENT  INITIAL  FINAL  PROCESS pH  RINSE pH  INITIAL  FINAL  INITIAL  Fl NAL  [-]  [-]  [-]  [-3  [volt]  [-]  [cm/sec]  [m1n- ]  1150 1250 1250  10  2/3  1 .35 3.00 5.4  .100 .091 .077  2.0 2.7 3.0  1.6 2.2 2.4  6.6 6.4 6.1  5.6 5.4 5.3  5.4 5.8 6.0  6.0 5.6 5.8  1260 1290 1290 1220  10  2/3  1 .42 2.15 5.4 5.4  .125 .141 .170 .170  2.1 2.3 2.7 2.6  1 .4 1.6 1 .4 1 .4  6.1 6.5 6.1 7.2  5.7 5.9 5.5 6.3  5.4 5.4 5.8 5.2  . 6.2 5.5 5.7 5.6  5400 5050 5700  10  2/3  1 .6 3.0 5.4  .021 .022 .018  5.6 5.5 5.6  5.5 5.7 5.6  5.8 5.5  5.9 5.5  7.2 5.0  7.1 6.9  [ppm]  1  [ampere]  [ampere]  ro ro co  224  x = 0.60  0  Figure 98.  10  [sec]  20  30  40 50 TIME [min]  E f f e c t of s u p e r f i c i a l v e l o c i t y tion factor transients.  (v)  on  60  separa-  225  Figure  99.  E f f e c t of s u p e r f i c i a l v e l o c i t y tion factor transients.  (v)  on  separa-  226  1.  In c o n t i n u o u s  displacement for  improves t h e r a t e  low c o n c e n t r a t i o n ,  At h i g h  concentrations  independent current  2.  5.5.9  the i n i t i a l  independent  initial  consumption  rate  slow  separation is smaller.  becomes e s s e n t i a l l y small.  The  of v.  performance.  f o r t h e slow  as t h e f i n a l  v , but i s a l s o very  In p a u s e o p e r a t i o n  does n o t depend on v . smaller  as w e l l  and t h e c u r r e n t  of the v e l o c i t y  is also  a better  d i s p l a c e m e n t mode ( n o - p a u s e )  an i n c r e a s e o f v r e s u l t s  The f i n a l  The i n i t i a l  separation  current  in  factor  consumption  is  displacement r u n .  Reproducibi1i t y . Several of the runs were repeated to t e s t the r e -  producibility  of the r e s u l t s .  The f o l l o w i n g  p a i r s may be  compared (see Table 34, 35; Figure 82, 100, 101): #8  & #10  ,  #26 & #35a  #27  & #49  ,  #40 & #50  The  initial  dialysate  transient  are  generally  the  top product t r a n s i e n t  extremely well  and a l l of the b r i n e  reproduced.  dialysate  The f i n a l  i s s u b j e c t to the l i m i t e d  of the conductometric measuring system. the  ,  The f i n a l  transient branch of accuracy  values of  c o n c e n t r a t i o n s are f o r most runs l e s s than 3%  Figure  100.  Reproducibility  of  second stack  experiments.  228  F i g u re  10 1.  Reproducibility  of  second s t a c k  experiments.  229  "of the i n i t i a l c o n c e n t r a t i o n . ing  Small  v a r i a t i o n s of the operat-  c o n d i t i o n s may i n f l u e n c e the a c t u a l  following  accuracies Flow  are estimated rate  Applied Pause  voltage  times  Displaced  volume  Concentrations  5.5.10  Comment on the m a t e r i a l  to apply  to these  : ±2 $  A$  : ±1 $  T  :  <5  : ±0.5$  c  T  , c  R  The  parameters:  ±0.5%  : ±0.5$  balance f o r the s o l u t e . conservation  The e l e c t r o d i a l y s i s  liquid  streams which are separated  Solute  or s o l v e n t w i l l  of the t o t a l  process i n v o l v e s two  by i o n s e l e c t i v e  membranes.  permeate through the membranes, and  s o l u t i o n may seep from one stream into the other ical  reached.  Q  A c l o s e d system r e q u i r e s mass i n the system.  limit  through mechan-  leaks. Any  exchange of m a t e r i a l would be detected  volume or as c o n c e n t r a t i o n situations process  have been considered  Three  to check the changes i n the  stream. I.  solutions stream  change of the two streams.  e i t h e r as  T h e s y s t e m was f i l l e d  o f known  volumes.  was a l w a y s s m a I l e r  with  rinse  The c o n c e n t r a t i o n  than  and p r o c e s s of t h e process  the concentration  of the rinse  230  stream.  The volume of  when t h e  s y s t e m was a l lowed t o  circulation  or  the  process s o l u t i o n stand  applied potential.  for  the  remainder.  p a n i e d by s o l u t e  flux  low t o  in the  process  stream c o n c e n t r a t i o n  removal  a l o n e would  while  equilibration branes, over  neither  a period  taken.  opposite  at  concentration direction,  different  process s o l u t i o n  the •  was  since the  accomthe  water  one  was u s u a l ly o u t the  concentrations  power s u p p l y . with  day.  before  From these r e s u l t s  of  the  and After  sorption  mem-  stream changed  runs  of  After  was e q u i l i b r a t e d  in which to  be u n c h a n g e d b u t  b a l a n c e by up t o two o r t h r e e  and a f t e r  the  membranes are  before  no pH s a m p l e s were  +5%  the  con-  for  the  experiments,  r u n s were e q u a l ,  i t i s concluded that no  that the  the  of  hour.  The p r o c e s s s o l u t i o n  runs of  concentrations,  volume n o r c o n c e n t r a t i o n  some s e p a r a t i o n  e x i s t e d , but  responsible  through  i n c r e a s e d more t h a n  The v o l u m e s were f o u n d  centration first  the  of  3. and a f t e r  high  was  transport  d i s c o n n e c t e d from t h e  of  no  explain.  and p r o c e s s s o l u t i o n  circulated  days w i t h  The s y s t e m was f i I l e d w i t h m e a s u r e d v o l u m e s  2. rinse  transfer  The o s m o t i c w a t e r  s e p a r a t i n g membranes f r o m  several  slightly  E v a p o r a t i o n may have c a u s e d  some v o l u m e c h a n g e and o s m o t i c w a t e r for  decreased  the  however.  mechanical  q u i t e permeable to  leaks solute.  231  The  increase  in solute concentration  i n the f i r s t  may be an e f f e c t of a change i n the d i s t r i b u t i o n between s o l u t i o n and s o r p t i o n membranes.  Since  daily  runs  of s o l u t e the e x p e r i -  ments were always stopped a f t e r the completion of a f u l l c y c l e , the i n i t i a l  distribution  hours of r e s t i s l i k e l y  i n the stack  a f t e r some 12  to be d i f f e r e n t f o r that at the end  of a r u n .  5.5.11  Comment on the performance of i n d i v i d u a l The  stages.  f o l l o w i n g t e s t s were performed to d e t e c t whether  d i f f e r e n c e s between i n d i v i d u a l  stages of the e l e c t r o d i a l y z e r  e x i s t e d , and how these d i f f e r e n c e s a f f e c t e d the s e p a r a t i n g performance. a)  Overpotential-current i nformation.  The  mean probe voltage  each stage were evaluated  and the mean c u r r e n t i n  and are t a b u l a t e d  i n Appendix C.2.  From these t a b l e s o v e r p o t e n t i a l - c u r r e n t diagrams were pared f o r each s t a g e , see Figure  102.  p o i n t s , which are p l o t t e d f o r runs with voltage  (A$ = 1 0  points s h i f t s large currents  v ) , i s considerable.  from small  currents  f o r the eighth  pre-  The s c a t t e r of the constant a p p l i e d A l s o , the bulk  f o r the f i r s t  of the  stage to  s t a g e , because these c o n s t i t u t e  the d i a l y s a t e and the b r i n e end of the assembly, r e s p e c t i v e l y .  232  0  Figure  102..  .2  .4  .6  .8 I [A]  OvervoItage-current stages.  0  .2  .4  c u r v e s of t h e  .6  .8 I [A]  electrodialysis  Figure  102.  OvervoItage-current dialysis stages.  curves  of t h e  electro-  234  The in the  experimental the  points  range of c u r r e n t s  approximated b y . s t r a i g h t  investigated  represent mainly the  the  s o l u t i o n , and  The  flow rate to the  Any  be  l i n e s show a v a r i a t i o n of 0.80  slopes  so  may  the  i .16  resistances  The  fi  various  of the  i n slope  solid  be  of These  connectors,  r i n s e chambers.  r i n s e chambers was may  slopes  ( ± 20%).  d i v i d i n g membrane in the  that the hydrodynamic c o n d i t i o n s difference  here.  lines  almost e q u a l ,  assumed  identical.  s h o u l d , t h e r e f o r e , i n d i c a t e unequal  * contact  resistances. Figure  resistances  102  than the  b)  shows that  stages 1, 2, 7, 8 have l a r g e r  others.  Comparison of  local  current  and p r o b e  voltage t r a n s i e n t s during a s i n g l e The by  the  shape of the  multipen r e c o r d e r  conditions a typical  run  (#49).  The  general  The  first  103  voltage  and  104,  curves  transients will  be  limiting  stage number.  of a pause time followed absorption  traced  respectively, for  numbers r e f e r to the  h a l f c y c l e i s an  course of the  and  during a complete c y c l e at  i s copied i n Figure  Each h a l f c y c l e c o n s i s t s ment.  current  cycle.  by  displace-  half cycle.  described  The  first:  * The g r a p h i t e connectors c o n s t i t u t e d some problems i n the present c e l l s . They broke f r e q u e n t l y and were too porous. Small amounts of r i n s e s o l u t i o n seeped through the g r a p h i t e , causing c o r r o s i o n of the m e t a l l i c parts of the e l e c t r i c manifold.  235  The eralizing  pause t i m e .  concentration this  currents  stage  enters  are r e l a t i v e l y small When the flow  during  the demin-  s t a r t s , solution  the e i g h t h s t a g e .  The c u r r e n t  of high  through  i n c r e a s e s s h a r p l y , goes through a maximum, and  remains at a f a i r l y  high  level.  When the c o n c e n t r a t i o n  front  reaches the seventh sta^e the c u r r e n t here shows a peak, e t c . Although the displacement i s 2/3 void volumes, the concentration  f r o n t j u s t reaches the f o u r t h stage  by the end of  the displacement p e r i o d , which shows the retarded the  c o n c e n t r a t i o n wave i n the a b s o r p t i o n  c u r r e n t peak i s observed i n the s i x t h The  currents  stack.  v e l o c i t y of The h i g h e s t  stage.  i n c r e a s e i n a step-wise manner at the  s t a r t of the e n r i c h i n g pause time f o l l o w e d by r a p i d decays which i n d i c a t e the d e p l e t i o n of the s o r p t i o n membranes. the s i x t h  stage  part of t h i s show l i t t l e f1ow  shows a very high  peak.  During the displacement  h a l f c y c l e the c u r r e n t s decrease f u r t h e r and i n f l u e n c e of the hydrodynamic c o n d i t i o n s i n the  channel. The  probe v o l t a g e s  are s e t i n r e l a t i o n  measured e l e c t r o d e voltage while power supply  i s constant.  time because there  to the  the output v o l t a g e  of the  The e l e c t r o d e v o l t a g e v a r i e s i n  are s e v e r a l r e l a y contacts  as well  r e s i s t a n c e s of the measuring shunts i n s e r i e s with cell.  Again  as the  the ED  236  I.CH  UJ  rr or  . z> o o UJ  rr 3  < UJ  20  40  60  80  TIME  [sec]  Pause j-Displ. Pause |oispl.-| 1st, half  2 n d , half  CYCLE  Fi gure  103.  Time-space d i s t r i b u t i o n con d i t i o n s .  of  current  at  limiting  237  12-  ELECTRODE VOLTAGE  8UJ CD <  o > a  Ul or  3 CO  < Ul  2j  i 40 60 80 20 •PauseJ-Displ.- Pausejoispl. Ist. half  TIME [sec]  2nd. half  CYCLE  Figure  104.  Time-space d i s t r i b u t i o n limiting conditions.  of probe v o l t a g e at  238  The  probe v o l t a g e s  are higher than the a p p l i e d  e l e c t r o d e v o l t a g e during most of the is  first  pause time.  a t t r i b u t e d to the membrane b a t t e r y e f f e c t in  operation. the  During the displacement the  probe v o l t a g e  When the p o l a r i t y This  i n d i c a t e s the  falls  current increases  reversed  the probe voltages  battery e f f e c t .  The  tages pass through a minimum as the h e l p f u l polarization level  disappears  No.  and  7 and  No.  8.  No.  No.  minimum during  stages  No.  the second part  level  i s higher  despite The  the  performance  i t shows the  Runs w i t h s e l e c t e d  lowest  The  previous  stages.  d i s c u s s i o n shows d i f f e r e n c e s between No.  7 & 8.  A real  p a i r s (see runs #19  life  & #20,  t e s t was Table  s e p a r a t i o n t r a n s i e n t s c o i n c i d e almost p e r f e c t l y . current consumption of run #20 higher  vol-  cycle.  c)  formed on the two  stack  voltage.  p a r t i c u l a r l y poor and  5 & 6, and  increase.  6 seems to perform much b e t t e r than  Its voltage  7 seems to be  one.  concentration  f a c t that i t consumes almost as much c u r r e n t . of  and  i n c r e a s e subsequently toward a  d i s t i n c t l y below the e l e c t r o d e A g a i n , stage  unsteady-state  t h e r e f o r e below the a p p l i e d  i s switched  This  i s probably  per-  34). The  caused by  The  higher the  10%  concentration. It  i s concluded  that the d i f f e r e n c e s between  which are a r e s u l t of the manufacturing procedure  do  stages  not  239  seriously  influence  the performance of the stages with  to t h e i r s e p a r a t i n g t a s k . final  respect  They may, however, i n f l u e n c e the  l i m i t of s e p a r a t i o n .  5.5.12  Experimental  t e s t of the constant rate  model.  Four experiments were performed to t e s t the constant rate  model proposed i n Chapter 3.  connected i n s e r i e s  hydraulically  The e i g h t stages were and e l e c t r i c a l l y .  power supply was operated i n constant c u r r e n t mode. c u r r e n t s had to be f a i r l y  The D.C. These  s m a l l , as the maximum output v o l t a g e  of the D.C. supply was l i m i t e d to 40 V. In two runs the e l e c t r i c phase with the flow  potential  (y = 0, see equations  was switched i n  (21)).  The phase  s h i f t i n the other runs amounted to one q u a r t e r c y c l e The transients  results  are shown i n form of c o n c e n t r a t i o n  (see Figure 105), (i)  (ii)  (iii)  (y =  and c o n f i r m  that:  the s e p a r a t i o n i s v i r t u a l l y completed a f t e r the f i r s t c y c l e f o r in-phase s w i t c h i n g , the concentration transients are s t r a i g h t l i n e s with equal a b s o l u t e values of the s l o p e s f o r e q u a l r a t e s when t h e s w i t c h i n g i s one q u a r t e r c y c l e o u t - o f - p h a s e . This holds experimentally only f o r the f i r s t c y c l e s , b e c a u s e t h e power s u p p l y c o u l d n o t m a i n t a i n c o n s t a n t c u r r e n t a t a h i g h enough voltage, the decrease i n d i a l y s a t e c o n c e n t r a t i o n during the f i r s t c y c l e i s l a r g e r f o r in-phase o p e r a t i o n than f o r o u t - o f - p h a s e one.  .  C o = 1250  Figure  [ppm], 6 =  105.  1 [-], v -  4.3  [ c m / s e c ] , T = 0.6  I n f l u e n c e of phase s h i f t constant rate operation.  (y)  [sec]  on t r a n s i e n t s  for  ro o  241  5.5.13  Comment on the e f f e c t of end End mixing  may  ED module as f o l l o w s . electrically as i n e r t  be suppressed  was  chosen:  and  for  the l o c a t i o n of the c o n d u c t i v i t y c e l l s : and  13, were i d e n t i c a l  A comparison run  (#52)  idle was  (Sg = 6 T = 1/2)  volume of two The 106.  The  i d l e stages results  experiments  i n runs  The  taper o f f .  This indicates  end  mixing  two  reasons  #51  and  separates  in  runs  that p a r t i a l  does not improve the f i n a l  #51  and  I.  #53  Solute  run as  are shown i n F i g u r e initially  i n run  i s stored  at a r a t e  (#51  and  #53),  transients  s u p p r e s s i o n of the  separation.  c o n d i t i o n s are much slower  than  the  #53.  c o n d i t i o n s before the other  that f i n a l  between  dead volumes i n the  i n t e r m e d i a t e to those of the other experiments its final  and  stage on each s i d e f o r run  of the three t e s t s  but reaches  except  between the  were the same i n t h i s  comparison run (#52)  Runs  performed with the same f o u r  centre stages but no i d l e s t a g e s . reservoirs  line  four active  the l a s t i d l e stages f o r run #51,  the l a s t a c t i v e and the f i r s t #53.  flow  i d l e ones on e i t h e r s i d e .  #51  reservoirs  see Table  connected  dispersion.  f o l l o w i n g combination  stages b r a c k e t t e d by two  are  remain i n the process  (or i d l e ) beds with small  #53,  i n the m u l t i p l e stage  I f l e s s than e i g h t stages  the others may  The  mixing.  There are approached  #52.  i n the s o r p t i o n  when t h e ED s t a g e s a r e used as dead v o l u m e s .  membranes The  brine  242  Figure  106.  Effect  of  end m i x i n g  on c o n c e n t r a t i o n  transients.  243  concentration the  tends toward  dialysate transient  2.  i s equal  p l a c e d volume  is  idle  In t h i s  case t h e r e s e r v o i r  t o t h e volume  in experiments  in the i d l e  reservoir  small.  solutions  5.5.14  P r o d u c t i o n of 90% d e m i n e r a l i z e d  of t h e i d l e  mittently closed  The d i s -  dispersion of t h e  and t h e c o n c e n -  s t a g e s a r e damped.  solution.  l i n e a r decay of the d i a l y s a t e  transients  of the process f o r a continuous  demonstrate t h i s , t w o p r o d u c t i o n  performed  stages.  rate,  transients  To  i f the displaced  Hence, the c o n c e n t r a t i o n s  changed at a slow  cates the p o t e n t i a l  concentrations  and t h e i n t e r n a l  tration  The  i n t h e ED s t a g e s  #5 1 and #53 e x c e e d e d t h o s e o f  s t a g e s by 1/6 v o i d , o n l y ,  comparatively  t h e r e f o r e , and  dispersion  n o t e x p e r i e n c e any c h a n g e w h a t s o e v e r  volume  the  limit,  i s damped.  Suppose t h e i n t e r n a l  may be n e g l e c t e d . will  a higher  indi-  system.  runs (#3 and #5) were  i n which a 90% d e m i n e r a l i z e d product was i n t e r r e p l a c e d by f r e s h  feed.  during these e x p r i m e n t s .  i n the b r i n e  reservoir,  The b r i n e s i d e S a l t accumulated  remained continuously  therefore.  Operating c o n d i t i o n s were i d e n t i c a l to those f o r batch runs #6 and #26. and  brine  reservoirs  The c o n c e n t r a t i o n  changes i n d i a l y s a t e  are shown i n F i g u r e s 107 and 108,  244  r e s p e c t i v e l y f o r low ( c 0 = 1250 ppm) and high  ( c 0 = 5500  ppm)  c o n c e n t r a t i ons. In Figure  107 the product was removed seven  Each d e m i n e r a l i z a t i o n  lasted eight c y c l e s .  m i n e r a l i z a t i o n was continued were reached. obtained  with  The f i n a l a final  until  times.  The e i g h t h de-  steady p e r i o d i c c o n d i t i o n s  separation  f a c t o r of ns = 322 was  b r i n e product c o n c e n t r a t i o n  of c l o s e to  9000 ppm.  Compared to run #26 which reproduced the i n i t i a l  transients  of #3 f a i r l y w e l l , the f i n a l  separation  appears to be improved at the h i g h e r b r i n e This the  i s i n l i n e with initial  the previous  #6, i s shown.  concentration.  f i n d i n g s on the e f f e c t of  c o n c e n t r a t i o n , see S e c t i o n  In Figure  5.5.5.  108 a s i m i l a r p a i r of e x p e r i m e n t s , #5 and  The d i a l y s a t e product was removed f o u r times  a f t e r every 15th c y c l e i n run #5.  The product  begins to i n c r e a s e a f t e r the second production the f i n a l  separation  initial  The production  a final  t r a n s i e n t s of run #5 are p e r f e c t l y  a final  separation  brine concentration  factor  of 14,000  ppm.  mean c u r r e n t consumption i n c r e a s e s during the  runs by a small  concentration.  c y c l e , and  ppm.  reproduced i n run #6, which reaches a f i n a l of ns = 185 a g a i n s t  concentration  f a c t o r i s only ns = 76, a g a i n s t  b r i n e product of almost 25,000 The  factor  amount due to the l a r g e r b r i n e  The c u r r e n t s  108 f o r each production  are recorded  cycle.  i n Figures  107 and  245  Figure  107.  C o n c e n t r a t i o n t r a n s i e n t s o f t o p and b o t t o m reservoir concentrations during production run #3 compared t o b a t c h run #26 (low concent rat i o n ) .  tn c-i o o  o o to CD  100  NUMBER OF CYCLES C-3  o  •o •o  > ro  o  3  PRODUCTION EXPERi  CD  n  ro  Fi  g u r e 10 8, C o n c e n t r a t i o n  t r a n s i e n t s of t o p and b o t t o m r e s e r v o i r concentrations during production r u n #5 c o m p a r e d t o b a t c h r u n #6 ( h i g h concentrat i on).  247  The  results  of the  cyclic electrodialysis  has  over a l a r g e c o n c e n t r a t i o n The  high  dence  concentrations  runs confirm  that  p o t e n t i a l f o r a continuous  system  range (up to at l e a s t 10,000  r e q u i r e more r e c y c l e or longer  ppm). resi-  times. It should  to optimize applied in  production  be pointed  the p r o d u c t i o n  out that no  process.  The  voltage were r a t h e r s m a l l , and  l a r g e batches at the  low  attempt was  pause time and  the feed was  concentration end,  made the  introduced  i n s t e a d of in  s m a l l e r p o r t i o n s during each c y c l e at a l o c a t i o n where the averaged c o n c e n t r a t i o n the feed c o n c e n t r a t i o n .  of the  travelling  S i m i l a r l y , one  product i n t e r m i t t e n t l y during  f r o n t c o i n c i d e s with would withdraw  each c y c l e in any  the  realistic  open system.  5.6  Summary of Results ED  and  Experience  on the  Second  Module  1.  I t was demonstrated that simple stacks may be produced on a l a b o r a t o r y s c a l e . The stacks c o n s i s t e d of i n t e grated frames which held the spacer screens and the a b s o r p t i o n membranes and which d i s t r i b u t e d the flow i n t o the c h a n n e l s .  2.  A segmented module was b u i l t which c o n s i s t e d of e i g h t individual stages. The stages seem to a l l perform approximately e q u a l l y in s e p a r a t i n g NaCl-H 2 0 s o l u t i o n s , although some problems with the e l e c t r i c manifold were encountered.  248  3.  Uniform flow d i s t r i b u t i o n and small i n t e r n a l c h a r a c t e r i z e d the stack hydrodynamics.  mixing  4.  The i n f l u e n c e of the channel length was i n v e s t i g a t e d by o p e r a t i n g up to e i g h t stages i n s e r i e s h y d r a u l i c a l l y . The r e s u l t s show improvements of the l i m i t of s e p a r a t i o n s i m i l a r to the i n f l u e n c e of the pause t i m e , as the residence time i s i n c r e a s e d . A l s o , there i s l e s s i n t e r n a l d i s p e r s i o n f o r longer c h a n n e l s . The i n i t i a l rate of s e p a r a t i o n appears to be a maximum f o r a channel length of approximately one meter.  5.  Systematic p e r t u r b a t i o n s of four o p e r a t i n g parameters and of the i n i t i a l c o n c e n t r a t i o n were performed on the e i g h t stage module: + l  :  in _ ! ° _l_0 0  r L s e c-iJ  Pause time  (t)  AppIied  (A*)  \0_ J5  (6.)  2/3 ±L±  (v)  . +0.0 5 .4 _ 4 j  +  voltage  Displaced  volume  Superficial Initial  velocity  concentr.  (co)  [volt]  + l / 3  -5/12  r L - Ji r  , -, Lcm/secJ  _ K A +4450 r -, 250 _ | 0 0 LppmJ  6.  The for  s e p a r a t i o n f a c t o r s range from 3i n s i g n i f i c a n t (ns = 3, run #7) to very l a r g e (ns > 10 f o r runs #33, #34).  7.  The pause times remain an e s s e n t i a l f e a t u r e of the c y c l i c e l e c t r o d i a l y s i s process o p e r a t i o n even f o r long c h a n n e l s , but they may be kept short (approximately 10 seconds or l e s s ) i f the other c o n d i t i o n s are f a v o u r a b l e .  8.  The i n i t i a l rate of s e p a r a t i o n i n c r e a s e s almost l i n e a r l y with the a p p l i e d v o l t a g e . The production may t h e r e f o r e be a c c e l e r a t e d but only at the expense of a d d i t i o n a l energy because the c u r r e n t consumption r i s e s i n prop o r t i o n to the v o l t a g e .  9.  In a pause o p e r a t i o n the v e l o c i t y of displacement has l i t t l e e f f e c t on the s e p a r a t i o n and may be kept as l a r g e as p o s s i b l e .  249  10.  I f the pause time i s o m i t t e d , slow displacement i s necessary to keep the residence time l o n g , which in turn slows down the rate of s e p a r a t i o n . U s u a l l y such an o p e r a t i o n is i n e f f i c i e n t .  11.  The d i s p l a c e d volume should be small enough to prevent breakthrough of the c o n c e n t r a t i o n f r o n t . I f i t i s reduced the f i n a l s e p a r a t i o n i n c r e a s e s almost without 1 i mi t .  12.  The i n i t i a l c o n c e n t r a t i o n has a r e t a r d i n g e f f e c t on the i n i t i a l rate of s e p a r a t i o n . The i n f l u e n c e on the f i n a l s e p a r a t i o n could not be e s t a b l i s h e d f o r the c o n d i t i o n s tested.  13.  The presence of dead volumes i n the end r e s e r v o i r s slows down the rate of change of the c o n c e n t r a t i o n s . There i s no e f f e c t on the l i m i t s which are e v e n t u a l l y r e a c h e d .  14.  Two p r e l i m i n a r y production runs on the module showed the p o t e n t i a l of the c y c l i c e l e c t r o d i a l y s i s process to separate NaCl-Water s o l u t i o n s up to at l e a s t 10,000 ppm. No attempt was made to optimize o p e r a t i n g c o n d i t i o n s .  15.  A t h e o r e t i c a l model which assumes constant and uniform rate of mass t r a n s f e r through the membranes was confirmed e x p e r i m e n t a l l y .  16.  pH changes i n process and r i n s e s o l u t i o n were g e n e r a l l y s m a l l , but there i s a trend toward higher a c i d i t y of the product stream f o r high voltages and long pause times.  Chapter 6  MATHEMATICAL MODELS  6.1  Spacer Model Sonin and Probstein (1968) derived general mass  balance equations f o r mass transfer channels.  in electrodialysis  They made the f o l l o w i n g assumptions and s i m p l i f i -  c a t i ons: 1. s o l v e n t a n d an i s not  The f l u i d  consists  infinitely  of  dilute,  un-ionized  fully  (nonpolar)  ionized  salt  which  so I v a t e d . 2.  The f l u i d  is  incompressible  and a t  constant  temperature. 3. constant ions,  The membranes  electrical  and a r e  are  conductivity  perfectly with  impermeable  with  4.  No c h e m i c a l  reaction  5.  Nernst-Einstein  holds.  250  respect  respect to  takes  equation  selective, to  the  solvent  have gegen-  molecules.  place.  for  the  ion  mobilities  251  6.  Two-dimensional  7.  No i n t e r p h a s e mass t r a n s f e r  8.  Diffusion  and n e g a t i v e  geometry.  coefficients  resistance.  and v a l e n c e s o f  positive  ion are e q u a l .  Under these assumptions the mass c o n s e r v a t i o n tions  f o r any  volume element may  be  equa-  reduced to  2  |c_L + v . v c ' = D • V c '  (35)  and  V ( c ' . v *) -  0  (36)  where c' = s o l u t i o n t' =  [g-mole/cm ] [sec]  time  -> V  = fluid  V  =  D  = solute diffusion c o e f f i c i e n t  [cm /sec]  $  = electric  [volt]  initial  to c a l c u l a t e  velocity  vector  [cm/sec] 1  gradient  Equations and  3  concentration  (35)  [cm- ]  potential  and  (36)  and  2  appropriate  c o n d i t i o n s have been used by Sonin and the s t e a d y - s t a t e  concentration  and  boundary Probstein  current  252  distributions  i n channel  lent velocity  profiles.  flow assuming laminar and/or turbu-  In t h i s work d i f f e r e n t hydrodynamic c o n d i t i o n s w i l l be assumed based on the m o d i f i e d stack d e s i g n .  In  particular,  the presence of a spacer m a t e r i a l in the flow channels gests t h a t the channels cells.  The  identical  effective  cell  be d i v i d e d i n t o a s e r i e s of w e l l mixed  number of c e l l s  i s not  necessarily  to the number of spacer holes but must be  experimentally.  sug-  It w i l l  be  f u r t h e r assumed t h a t each  c o n s i s t s of a t u r b u l e n t core and  across which only d i f f u s i o n  determined  and  two  stagnant  mixing  sublayers  e l e c t r o l y t i c migration  take  pi ace.  6.1.1  Model  equations.  Figure 109  illustrates  the dimensions of the j section  i n the stagnant  volume i s occupied by shaded bars  t  h  the c o - o r d i n a t e systems  mixing  cell  the adjacent j  s o r p t i o n membrane.  by s o l i d  cell  by the  where  I  length of flow  d  effective  which reduce the f r e e ratio  m  number of mixing  m  channel  length of mixing cells.  h  This i s indicated  d %l  t  Some of the. channel  spacer m a t e r i a l .  across the channel  length of the mixing  and  and  cell  flow  253  Figure  109.  D e r i v a t i o n of the spacer model e q u a t i o n s .  254  The  two p a r t i a l  differential  equations  (35) and (36) w i l l be  r e p l a c e d by a system of d i f f e r e n c e equations and PDEs ing  to the f o l l o w i n g p r o c e d u r e .  c  was chosen, where  accord-  The n o t a t i o n  j,k  k = 1 f o r turbulent = 2 f o r stagnant  ocre sublayer  == 3 f o r stagnant i n n e r l a y e r and  For t u r b u l e n t  j = 1 , 2, •• • , m  core:  del dt'  d  pj-1  b^26  *  V C  (37)  j,2 y =6  with  the i n i t i a l  condition  For stagnant s u b l a y e r s :  @ t' = 0  (v = 0)  c  j,l  =  c  °  255  with  initial  condition  @ t' = 0  boundary c o n d i t i o n s  inner layer:  '  ' j,3 9 t"  initial  c  9c j,2 9 yTi— "^  -  s  C  =  ' j,2  c  2zF  anion selective membrane  j,i  (v = 0)  9  C  with  o ~ o  0 ,D  r  For stagnant  c  > \  = D  2  c' j,3  (39)  9y'  condition  0 , c. , = c0 'j ,3 3c  boundary conditions  0 ,D  .;.3  ^1 2zF  l'  c a t i on selective membrane  8 C  a J,3 2 ' 9y'  N.B.  The f l u x of s a l t due t o the e l e c t r i c c u r r e n t must be c o r r e c t e d a c c o r d i n g t o the d i f f e r e n c e i n f r e e volume between flow channel and i n n e r l a y e r .  The (38)  current densities  and (39) over t h e i r boundary c o n d i t i o n s .  drop across a flow channel has  ( i . ) couple equations ( 3 7 ) ,  a constant value A $ .  The p o t e n t i a l  and an adjacent s o r p t i o n  membrane  Due to assumption 8 there i s no  256  charge p o l a r i z a t i o n at the membranes and the equation f o r the  current  density  i s simply  A  1J  where  A $  D0n  total  tot  duced:  2 A3>  R5  —  (40)  tot  resistance  Donnan p o t e n t i a l and the t o t a l  given by equation The  $  Donnan p o t e n t i a l  R,. ^  The  -  (26) i n S e c t i o n  following  r e s i s t a n c e are  3.3.  dimension 1 ess  q u a n t i t i e s were i n t r o -  257  cj., k  k  co  and  =  =  v =  1 ,2,3  ; j =  1 ,2,3,-.. , m  K—  Jl/v (41) P - TT  B  ~ b  Fo =  j  b P gyv  2  2  K =  V z F  ( F o u r i e r Number)  b  D c,  R . • 2 z membrane b RT  2  F  2  D c,  258  The  resulting  dimensionless equations  boundary c o n d i t i o n s  and  their i n i t i a l  are  d c dt  9  C  .i,2 3t  3 c 3t  m  b-1,1  a  _1_ Fo  and  2  F o ( i - B)  •j.ij  '  V  C  (42)  J,2 y=3  c. LA  (43)  9 y'  3  J Fo  @ t = 0  2  ,  c  (44)  c. , = c . 3c  y = 0  3 , 2  9y 3c  1^3  =  ay  y-3  = P. 2  = c. - = 1.0  9  ,  c 3C.  »  j  j  2  -  l .  C  j  ~  J >3 3y  0  J  •  ir  (45)  259  where  c. A^ - 2 In -C J - ^ j,2  y=0  (46)  i . = J 1 - 26  dy_  + 2  + 2  the c o n c e n t r a t i o n  p o i n t an a d d i t i o n a l profile  duced.  The c o n c e n t r a t i o n  plifies  equations  tions  assumption  regarding  i n the stagnant s u b l a y e r profile  is linearized.  is introT h i s sim-  ( 4 2 ) , ( 4 3 ) , (46) and some boundary  condi-  in (45). The  for  5  0  0  At t h i s  +  final  s e t of equations  f o r the spacer  model i s  j = 1 ,2 ,3 , • • • , m.  •  (47)  260  d c = - m  dt  •j.ij (48)  2(1 - 3)  C  2  Fo • 3 (1 - 23)  JJ  C  "  m J,2J  3 • Fo  2  3c  JL1 _  at  a c  j _  (49)  Fo  3 y"  wi th  t >0  t  =  °  ,  '  cQ  C  j,l  1  = 1 .0  = C  J  5  2  =  c  j53 =  1  -  0  (50) 9  C  i  3c 2  3  J\3 9y  261  and  m Aip - 2 In C  2B In 1 - 23 C  +  j,l  dy  + 2  m  j,l  (51) P/2  m  _ c  m j,2  C  c j,2 C  j,3  + K  where the s u p e r s c r i p t (m) denotes the c o n c e n t r a t i o n solution  of the  at the i n t e r f a c e , and c n -j i s the feed to the f i r s t  mi xi ng eel 1 . The  s e t of model equations  (47) to (51) may be  c l a s s i f i e d as  system of m directly coupled pairs of first order ordinary differential-difference equations coupled by nonlinear boundary conditions with m independent linear second order partial differential equations. Looking at the ODE's a l o n e , t h i s  i s an i n i t i a l  value  problem,  whereas the PDE's are of the p a r a b o l i c type and c o n s t i t u t e an i n i t i a l - b o u n d a r y problem.  6.1.2  Considerations The  system of equations  p e r i o d s t a r t i n g with tions.  r e l a t e d to c y c l i c  uniformly  process  operations.  (47) to (51) d e s c r i b e s a  distributed  In g e n e r a l , any c o n c e n t r a t i o n  initial  distribution  concentraat t = 0  262  may r e p l a c e the i n i t i a l for c y c l i c operating  operations  condition in (50).  This  of the e l e c t r o d i a l y s i s  i s important  stack.  When  parameters are changed i n s t e p s , the time axis  may be transposed m a t h e m a t i c a l l y , because i t i s g e n e r a l l y more convenient to s t a r t parameter values  c a l c u l a t i o n s at t = 0 f o r constant-  than to d e f i n e the step  changes of the  parameters as f u n c t i o n s of time. The  thickness  of the stagnant s u b l a y e r s  g e n e r a l l y a f u n c t i o n of the flow  conditions  ated  from mass t r a n s f e r c o r r e l a t i o n  able  (see a l s o S e c t i o n  tion  i s a v a i l a b l e on the unsteady-state  must be c o n s i d e r e d (6)  5.3.4).  data  (6) i s  and may be evalu-  i f these are a v a i l -  However, very  little  informa-  mass t r a n s f e r which  in a c y c l i c operation.  The t h i c k n e s s  i s , t h e r e f o r e , t r e a t e d as an independent v a r i a b l e . The  concept of stagnant s u b l a y e r s  down as the v e l o c i t y  will  break  approaches z e r o , i . e . as the flow  becomes more and more l a m i n a r .  The model equations must,  t h e r e f o r e , be used with  under those c o n d i t i o n s .  caution  the present form they cannot be a p p l i e d to pause  6.1.3  operations.  S o l u t i ons. The  nonlinear  makes a n a l y t i c a l likely.  In  form of the c o u p l i n g  c o n d i t i o n (51)  s o l u t i o n s of the model equations very un-  A s e m i - a n a l y t i c a l approach  i s , in p r i n c i p l e , possible  263  if  the c u r r e n t d e n s i t i e s  constant.  are assumed to remain  However, the r e s u l t i n g s e r i e s  to be e v a l u a t e d n u m e r i c a l l y in any f i n d d i r e c t numerical the system equations  solutions  stepwise  solutions  case.  I t was  would have  preferred  based on approximations  to  of  (47) to ( 5 1 ) .  A number of standard numerical  integration  have been c o n s i d e r e d , see e.g. McCracken and  Dorn  schemes  (1964),  Hamming ( 1962) : -  Fourth order  R u n g e - K u t t a (RKS)  -  Milne f i f t h order predictor u s i n g a RKS i n i t i a l i s a t i o n  - Common d i f f e r e n c e  corrector  scheme  - B a c k w a r d d i f f e r e n c e scheme - C r a n k - N i c h o l s o n scheme The first  first  two  order PDEs and  integration  are o f f e r e d  schemes are s u i t a b l e f o r  by most computing c e n t r e s  as l i b r a r y s u b r o u t i n e s with f i x e d and/or v a r i a b l e  step  length. In the present system of equations space d e r i v a t i v e was difference  r e p l a c e d by the c o n v e n t i o n a l  e x p r e s s i o n to t e s t the RKS.  of the unsteady s t a t e test case. a finite  Carslaw  the second order  An  analytical  d i f f u s i o n equation (49) was  and Jaeger  (1959) give such  slab with constant heat i n f l u x through  boundaries.  central solution  used as  a solution both  264  It was found that  RKS diverges i n some cases when  i n t e g r a t i n g with f i x e d step s i z e s , although a r e d u c t i o n i n time step s i z e u s u a l l y The using  l e d to s a t i s f a c t o r y convergence.  stability  of the d i f f e r e n c e methods was  e-schemes. It was found that  the common d i f f e r e n c e scheme i s  unstable f o r the unsteady s t a t e d i f f u s i o n e q u a t i o n . Crank-Nicholson scheme showed i n s t a b i l i t y The  tested  The  f o r equation ( 4 7 ) .  backward d i f f e r e n c e scheme was s t a b l e i n a l l c a s e s . Since RKS, as well  as M i l n e , r e q u i r e  approximations of some p a r t i a l  difference  d e r i v a t i v e s , i t was  finally  decided to use the s t a b l e backward d i f f e r e n c e scheme i n the an  present model.  This  i s an i m p l i c i t method which  i t e r a t i o n method as the f o l l o w i n g  6.1.4  Backward D i f f e r e n c e The  first  d e r i v a t i o n shows.  scheme with Gauss S e i d e l  iteration.  backward d i f f e r e n c e scheme approximates the  time d e r i v a t i v e by - c At  and  requires  the second p o s i t i o n d e r i v a t i v e by  (52)  265  C  2  3 c  lay'  2  y+Ay,t ~  c  y,t Ay  y ,t  +  C  .y-Ay,t  (53)  2  Suppose the i n n e r l a y e r of the s o r p t i o n membrane i s d i v i d e d i n t o 2n p a r a l l e l  A  slices  to  (54)  * = 2n"  This i s e q u i v a l e n t to expanding of the c o n c e n t r a t i o n s  of t h i c k n e s s  k =  the second s u b s c r i p t (k)  l ^ , " - ,  n + 3.  i e n t to c o n s i d e r h a l f of the l a y e r t h i c k n e s s the c o n c e n t r a t i o n  profile  It i s s u f f i c only  because  i s symmetric.  In a d d i t i o n to the two-dimensional space ( s u b s c r i p t s , j,k) a time g r i d has been i n t r o d u c e d (52). the new  This w i l l  grid by equation  be l a b e l e d by s u p e r s c r i p t s (1) and  time value and the o l d one r e s p e c t i v e l y . The f o l l o w i n g a b b r e v i a t i o n s are used:  Z l  _  2 • At Fo • 3  (0) f o r  266  z  = m • At  z  =  k  The  system  following  s  2 • At Fo • 3 • (1 -  of equations implicit  23)  (47) to (51) i s transformed  a l g o r i t h m to c a l c u l a t e  the new  into  c'. K'S. J »K  For  C  j,l  j  "  1 ,2 , ••• , m  C  j,l  C  i  c . 0 0.3  C  j,4  C  =  Z  * *  o  j,2  C  ( j-l,l  C  j j ) "  2 5  C  ( j - 1 ,1  o  C  C  * ( JJ  I  "  C  j,l  + z, • 1  J,3  - c. 'j,4. = z  ~  'j,5  - 2 cC ' + C c' j,4 j,3  j,2  1  - c j,2  the  267  C  l j ,n+2  "  c  o _ j ,n+2 ~  c' - cc° J,n+3 j,n+3  C  z  3  =L 2  c  A i | ; - .2 •  C  J,n+2  •  j,n+2 "  c  +  c  j,n+l  j ,n+3  In  J  flLl)  In 1 - 26 + c'. , J ,1  2  l J,n+3  2Q  C  h,2i  -T  + £+ S  C  j,l  " j,2  where S*  3  "K  4  2  1  - + C— 7 — +c— 7 — + ... +c — r —  3  If  j,4  j,5  SIMPSON'S rule  j,n+3  i . were constant a l i n e a r matrix equation  could  3  be e s t a b l i s h e d Seidel  and s o l v e d  by standard methods.  i t e r a t i o n was employed i n the f o l l o w i n g 1.  2.  Calculate  Calculate  i . for  c'. .  D - Max|c^k k = 1 ,2 3.  c.  0  - values  J >K  values and f i n d -  c°  j k  |  , n+3  I f D > i t e r a t i o n e r r o r go to 1  The Gaussway:  268  A computer program was w r i t t e n which c o n s i s t e d of a main program and three s u b r o u t i n e s . parameter v a l u e s , i n i t i a l i z e d organized  The main program  the c o n c e n t r a t i o n  the i n t e g r a t i o n , adjusted  matrix,  time step s i z e  track of the averaged c u r r e n t consumption as well e f f l u e n t concentrations  and the m a t e r i a l b a l a n c e .  p e r i o d i c s w i t c h i n g of e l e c t r i c fluid for to  polarity  read  and kept as of the The  and d i r e c t i o n of  flow was a l s o performed a u t o m a t i c a l l y by the program  a given number of c y c l e s .  The p r i n t o u t v a r i e d  according  the i n f o r m a t i o n t h a t was d e s i r e d . The  subroutines  CURRENT, PAMPA, and GASE c a l c u l a t e d ,  r e s p e c t i v e l y , the c u r r e n t d e n s i t y , the values according  to i n c r e a s i n g or d e c r e a s i n g  performed the Gauss-Seidel A listing  of the FORTRAN  time step s i z e , and  IV program i s presented the r e q u i r e d input  data.  i n t e g r a t i o n step s i z e was c o n t r o l l e d by the  following c r i t e r i o n : with  • • ,6)  iteration.  in Appendix C.3, which a l s o d e t a i l s The  of z^(£.=l  Each i n t e g r a t i o n was performed  the c u r r e n t time step  (At) and with A t / 2 .  If  DD = Max  c*jk(At)  - c^k(At/2)  j = 1 ,2,«-', m k = 1,2, —  , n + 3  > ERROR  twice  269  the c u r r e n t step s i z e was halved step was r e p e a t e d .  If  and the same  DD < 0.05 * ERROR  integration  the c u r r e n t  step  s i z e was doubled. The  two values  of the new c o n c e n t r a t i o n s were a l s o  used to c o r r e c t the actual c o n c e n t r a t i o n s the estimated  6.1.5  6.1.5.1  on the b a s i s of  truncation e r r o r .  Results of computer s i m u l a t i o n s . The  o b j e c t i v e s of s i m u l a t i o n runs were:  a)  To t e s t a c c u r a c y and c o n v e r g e n c e o f the i n t e g r a t i o n .  b)  To i n v e s t i g a t e pa r a m e t e r s .  c)  To compare t h e model mental res uIts .  e f f e c t s of operating with  experi-  Accuracy and convergence. The  i n t e g r a t i o n was t e s t e d by  - v a r y i n g t h e number o f s l i c e s s o r p t i o n membrane ( n ) - adjusting the tolerable integration errors  in the  i t e r a t i o n and  - m o d i f y i n g t h e program from to r e l a t i v e error control  absolute  270  The  results  are:  1.  Between  membrane a r e u s u a l l y 2. error  and  iteration  integration  iterations between  lies  1/64  and s i x s l i c e s  and  per h a l f  error  error  should  control  both  be s m a l l e r  integration  than  to  e r r o r , e.g. I0  -I+  - 3  . than  3  size is  1/256, w h e r e a s t h e t i m e s t e p s i z e  The m a t e r i a l  of  ± 0.1$, but t h e r e  the  number o f c y c l e s 4.  especially  decreases  (I t o 2) i n  l i m i t s , e.g. i f both  balance  are s e t  error  control  of s y s t e m a t i c  drifts  as  control  very well  with  becomes  small.  results  obtained  (at least 3 s i g n i f i c a n t f i g u r e s ) .  parameters.  found that small  t h i c k n e s s , high p o t e n t i a l s  i s very time consuming  concentration  generally  E f f e c t of o p e r a t i n g It was  in the order  is increased.  when t h e d i a l y s a t e  under a b s o l u t e e r r o r  is generally  are i n d i c a t i o n s  Relative  r e s u l t s compare  6.1.5.2  - 3  . 3.  The  IO  v s . I 0 ~ , t h e number o f  b e t w e e n 3 and 5 and t h e t i m e s t e p  case of comparable e r r o r IO  5 *  i s one o r d e r o f m a g n i t u d e s m a l l e r  and t h e number o f i t e r a t i o n s becomes v e r y s m a l l the  sorption  s u f f i c i e n t i f p < I.  For absolute e r r o r  If t h e i t e r a t i o n the  four  and  F o u r i e r numbers, small  small  thickness r a t i o s  layer  lead to  271  good s e p a r a t i o n typical  results  6.1.5.3  Tables  of s y s t e m a t i c  Comparison with Figure 111  tion  40, 41  and  42, and  show  computer s i m u l a t i o n s .  experimental  illustrates  results.  the experimental  t r a n s i e n t s f o r EDI-SI-8/#22, #23,  simulations  Figure 110  #24  concentra-  runs and  computer  f o r a set of parameters which were p a r t l y  calcu-  l a t e d from the o p e r a t i n g c o n d i t i o n s (M, Fo, AIJJ, 6, p, c 0 ) , p a r t l y estimated The  and  adjusted  f o r a reasonable  experiments were s p e c i f i c a l l y  t e s t of the s i m u l a t i o n program. 5.3.2  the probe v o l t a g e was  a way the  v o l t a g e was,  as to maintain  runs l i s t e d  line) and. experimental  were adjusted  in Section  s u b j e c t to c h a r a c t e r i s t i c A<£>.  The  The  D.C.  t h e r e f o r e , hand r e g u l a t e d i n such  a constant  probe v o l t a g e s i g n a l  for  again.  It was  shows a comparison of c a l c u l a t e d ( s o l i d (points) concentration transients for  previously f i t t e d  t r a n s i e n t reasonably  parameters 8 and £  Although the model p r e d i c t s the well, i t fails  dialysate  to do so f o r the b r i n e .  a l s o found that the model breaks down f o r  small membrane core t h i c k n e s s i n combination with voltages.  fluc-  above.  Figure 112  EDI-SI-8/#36.  performed f o r a  As e x p l a i n e d  t u a t i o n s , whereas the model assumed constant power supply  f i t (6,£).  Negative c o n c e n t r a t i o n s  occur  large applied  at some stages  during  Table 40 Spacer  Model No. I , E f f e c t of Layer  Thickness  Parameters RUN NO.  M  Fo  20  2  P  B  5  6  3.2  1  0.05  3  16  1  8  1  0.1  CURRENT CYCLE NO.  TOP CONCENTRATION C  1 2 3 4 5 6 7 8 9 10 11 12  BOTTOM CONCENTRATION C  T  SEPARATION FACTOR  DEPLETING  ENRICHING 1  ns  B  - E  3  8  3  8  3  8  1 .66 1.98 2.17 2.28 2.34 2.37 2.38 2. 39 2.40 2.40  1 .64 1.95 2.15 2.27 2.35 2.40 2.43 2.45 2.46 2.47 2.47 2.48  .234 .160 .089 .050 .032 .024 .020 .019 .018 .018  .246 .193 .122 .075 .050 .037 .030 .026 .024 .023 .023 .022  7.1 12.4 24.4 45.7 72.6 97.9 116.8 127.5 133.2 136.1  6.7 10.1 17.6 30.1 47.2 65.6 81.6 93.4 101.1 105.8 108.5 110.1  3  8  1 .47 1 .42 2.01 2.08 2.04 2.04 2.03 2.00 1 .98 1 .95 1 .94 1 .92 1.92 1 .89 1 .91 1 .88 1 .90 1 .87 1 .90 1 .86 1 .86 1 .86  3  8  2 .29 2.25 2.12 2.12 2.08 2.12 2.02 2.05 1 .97 1 .99 1.94 1.95 1 .92 1 .92 1 .91 1 .89 1 .91 1 .88 1.91 1 .87 1 .86 1 .86  Table 41 Spacer Model No. I , E f f e c t of F o u r i e r Number Parameters RUN NO.  M  Fo  3  P  Af  TT  0.05  1  16  1  ?  6  3.2  1  20  2 20 3  2  CUR RENT CYCLE NO.  TOP CONCENTRATION C  1 2 3 4 5 6 7 8 9 10  BOTTOM CONCENTRATION  SEPARATION FACTOR  c: B  T  2  -3  1 .00 1.01 1 .02 1.02 1.03 1.03 1.03 1 .04 1 .04  1.66 1.98 2.17 2.28 2.34 2. 37 2. 38 2.39 2.40 2.40  2 .87 .87 .87 .87 .88 .88 .88 .89 .89  DEPLETING  ns  i  3  2  3  .23 .16 .089 .049 .032 .024 .020 .019 .018 .018  1.16 1.16 1.17 1.17 1.17 1.17 1.17 1.17 1.17  7.1 12.4 24.4 45.7 72.6 97.9 116.8 127.5 133.2 136.1  2  ENRICHING -i  D 3  2  E 3  ro —i co  Table 42 Spacer Model No. I , E f f e c t of A p p l i e d  Potential  Parameters RUN NO.  M  Fo  B  P  0.05  3 20  K  6  1  3.2  1  16  2  1  4  TT  0.1  8  Compari son CURRENT CYCLE NO.  1 2 3 4 5 6 7 8 9 10  TOP CONCENTRATION  BOTTOM CONCENTRATION  c T  c  SEPARATION FACTOR ns  B.  3  4  3  4  1 .66 1 .98 2.17 2.28 2.34 2. 37 2.38 2.39 2.40 2.40  1 .28 1 .44 1 .55 1.62 1.67 1 .72  .234 .160 .089 .049 .032 .024 .020 .019 .018 .018  .487 .507 .485 .455 .429 .408  3 7.1 12.4 45.7 72.6 97.8 116.8 127.5 133.0 136.0 138.0  DEPLETING 1  ENRICHING 1  D  4  3  2.6 2.9 3.2 3.6 3.9 4.2  1 .47 2.01 2.04 2.03 1 .98 1.94 1 .92 1 .91 1 .90 1 .90  - E 4  -  3 2.29 2.12 2.08 2.02 1.97 1 .94 1 .92 1.91 1 .91 1 .91  4  --  275  SIMULATION M = 20  Figure  110.  ,  Fo= 2  PARAMETERS ,  16 ,  S*  10  , /3= 0.1  , £ = 3.2  E f f e c t of w i d t h r a t i o ( ? ) on concentration t r a n s i e n t s p r e d i c t e d by S p a c e r M o d e l .  factor  276  .04O  EXPERIMENT  —  SIMULATION  NUMBER OF CYCLES  o o  M = 8 0.6  Fo = 135 /3= 0.1  AV= ^ =  24.3  6=  1.00  0.6  1.04  Fi gure  111.  Comparison of computer s i m u l a t i o n w i t h e x p e r i m e n t a l r e s u l t s on r u n s #22,23,24 (f i r s t s t a c k ) .  277  <  cc fZ Ul  1.00  o z o o 2  NUMBER  OF CYCLES  .95-  — t O CD  M = 8 5 * 0.6  Fo = 72.2 /3=  *f=  0.08  44.3  5=  6 = 1.00  1.0  1.05A  z o H  SIMULATION 1.00-  CC  Q. O I-  T"  l  8  4  <  ui o z o o  EXPERIMENT  NUMBER  OF CYCLES  .95-  75-  .90-  .85  Fi gu re  112.  Comparison of computer s i m u l a t i o n with experimental run #36 ( f i r s t s t a c k ) .  278  the Gauss-Seidel i t e r a t i o n loop and lead  to program  i nterrupts.  6.1.6  Concluding comments on the spacer model. The  spacer model i n i t s present form p r e d i c t s the  e f f e c t of system  parameters  operations q u a l i t a t i v e l y . experiments practical  on the s e p a r a t i o n of no-pause I t may be used  q u a n t i t a t i v e l y , but these f i t s  significance.  f o r very large  rates  to f i t s i n g u l a r do not have much  In p a r t i c u l a r , the model breaks  of mass t r a n s f e r ;  down  t h i s i s probably due  to the l i n e r i z a t i o n of the c o n c e n t r a t i o n p r o f i l e s i n the stagnant  sublayers. Modifications 1.  layers, script  of the model may  Nonlinear concentration  i . e . expanding the l a t e r a l k) i n t h e f l o w  include:  profiles  in the sub-  concentration  grid  (sub-  channels.  2.  Include  water  transfer  3.  Account f o r d e n s i t y  due t o s o l v a t i o n  of the  ions.  sorption  membranes.  induced free  convection  in  279  4.  Include  sorption  c a p a c i t y of  5.  Replace c o n c e n t r a t i o n s  6.  Modify equations to allow  ion exchange  membranes.  the  b e g i n n i n g of each h a l f  6. 2  pauses at  Rate Model  improved along the f o l l o w i n g 1. operations potential  is continuously  Allow  ducing t h e m i x i n g  3.  lation  density  data  the flow  pauses at  dispersion effects  by  intro-  concept.  law by i n c l u d i n g more  approximation  terms  (equation (27).  M e a s u r e r a t e s o f mass t r a n s f e r  of o p e r a t i n g  pumping  cycle.  for internal  cell  be  in which the e l e c t r i c  applied while  Modify the rate  the current  4.  3.3 may  lines.  to a parapause o p e r a t i o n  b e g i n n i n g of each h a l f  function  in Section  Combine p u r e p a u s e and p a r a m e t r i c  2.  of  f o r flow  cycle.  The rate model presented  the  by a c t i v i t i e s .  e x p e r i m e n t a l l y as  and s y s t e m p a r a m e t e r s and u s e t h e s e  i n form of s e m i - e m p i r i c a I  transfer  equations.  corre-  Chapter 7  CONCLUSIONS AND RECOMMENDATIONS  The  purpose of  t h i s work was  to i n v e s t i g a t e  to develop a 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 , both and  theoretically.  following  separations  (ns  > IO ) 3  The  the  by t h e  rate  direction of  a closed  the  very  large  system.  of  the  polarity  of  the  fluid  of  the  stacks electric  displacement  Equilibrium  to  is  field  governed  conditions  have  influence.  Flow p a u s e s a t  important  Moderate  pause t i m e s  both the  rate  pared to  no-pause  of  can a c h i e v e  eIectrosorption  mass t r a n s f e r .  little  3.  in  r e s p o n s e of  alternations  and o f  represent  of t h i s study lead to  Cyclic electrodialysis  2.  generally  results  experimentally  conclusions. 1.  periodic  The  and  the  features (up  of  beginning the  cyclic  10 CsecU)  to  separation  and t h e  operation.  280  of  each h a l f  process  considerably  limiting  cycle  operation. improve  separation  com-  281  4.  The e f f e c t  s t u d i e d on a s i m p l e featured factors cyclic  a rigid  operation  ten  system parameters  bench s c a l e e l e c t r o d i a l y s i s  centre  between I  of  frame  design.  and 40 were o b t a i n e d gave b e s t  separation  m o d e r a t e pause t i m e s , high a p p l i e d v o l t a g e , small d i s p l a c e d volume, small i n t e r n a l mixing, uniform flow d i s t r i b u t i o n , small s o r p t i o n c a p a c i t y of l a r g e f1ow rate. Simple  5.  plant This Small  stacks  were  module and m a n u f a c t u r e d resulted  in  uniform  ing the  A high  flow  channel  of  separation  of  approximately  7.  final  length  I meter  the  for  were, thus,  few c y c l e s can be a p p r o x i m a t e d  =  mini-pilot  10  (ns)  procedure. channels.  achieved.  is obtained  and p a u s e t i m e s  ns  a  in the  pause t i m e .  factor  The  stack,  The  be a maximum f o r  The s e p a r a t i o n  separation  for  designed  separation  be  which  experimentally.  distribution  or the  appears to  cell,  using a standardized  dispersion coefficients  6.  Final  could  by  initial  a channel of  increas-  about  during  length  10 s e c o n d s .  the  by an e x p o n e n t i a l  first  function  a • t  whe re  a  is  the  rate  constant  and  t  is  the  real  time  in  in  rate  Cmin ]] - 1  Cmin3  282  Axial  dispersion  f ronts  The p o t e n t i a l  f o r large  concentration was  the separation  as s t e e p  of the c y c l i c  separations  range  from  electrodialysis  i n an open s y s t e m o v e r t h e t o at  1,000  least  10,000 CpprnJ NaCI  demonstrated.  9.  M o d e l l i n g o f t h e c l o s e d s y s t e m h a s met o n l y  partial  success.  A qualitative  model  which  tration  dependent  mass t r a n s f e r  rates  explains  experimental numerical predict  results.  techniques,  experimental  10. reproducible  inaccurate,  A more r i g o r o u s may be f i t t e d results  if  a standardized  f o r very  I. trodes  model, which  requires  t o some d a t a b u t c a n n o t  are g e n e r a l l y  testing  procedure  is  highly followed.  m e a s u r i n g s y s t e m becomes  small  concentrations.  On the b a s i s of the r e s u l t s recommendations  most o f t h e  results  concentration  however,  assumes c o n c e n -  a priori.  The e x p e r i m e n t a l  The c o n d u c t o m e t r i c  ing  concentration  deveI o p .  8. process  limits  of t h i s study the f o l l o w -  can be made.  The d e s i g n o f e l e c t r i c  s h o u l d be i m p r o v e d .  connectors  to the e l e c -  283  P r o v i s i o n should  2. concentration  in  binary  the  ranges, e . g .  Other  and  in muIticomponent  4.  Different of  could  power  lead to  polarity  Also,  separation  is  c l o s e the large  procedures  proposed to  effect  of  of  should  at  both  moderately  initial  the This  reduced between  electri  concentration It  may be four  on  final  desirable  sides  for  10,000 p p m ) .  An open s y s t e m s h o u l d introduced  investi-  be a n a l y z e d .  membranes a l o n g a l l (>  analyze  displacement.  a phase s h i f t  should  be  disconnect  during  s h o u l d be c h e c k e d .  concentrations  intermittently  cells.  conditions.  power s a v i n g s  sorption  conductivity  mixtures.  ED s t a c k s  The e f f e c t  factors  7. is  it  and pump r e v e r s a l s  6.  very  operating  the  different  s p a c e r s c r e e n s may be used t o  from the large  measure  s h o u l d be i n v e s t i g a t e d ,  hydrodynamic  In p a r t i c u l a r  separation.  to  solutes  the  Other  5.  electric  by p a r a l l e l  3.  influence  gated.  be made t o  be d e s i g n e d  and p r o d u c t s  are  in which  drawn  off.  feed  NOMENCLATURE Typical a  3±  =  t h i c k n e s s of inner l a y e r of adsorpt i o n membrane  Inion (-)  =  iVity  °  f C a t i  °  n  ( + )  °  r  L  Unit  rcml J  [g-mole/litre]  ai  =  r a t e constant during cycle  dilution  half  a2  =  rate constant during half cycle  enrichment  b  =  t h i c k n e s s of spacer screen of flow channel  c  =  concentration  d  =  effective  length  D  =  diffusion  coefficient  F  =  Faradays constant = 96 .5 x 10  Fo  =  F o u r i e r number  i  =  current  I  =  current  j  =  integer  j  =  f l u x vector  or width  -JI-,  LR s e c  - i -J ,  L r s e c  r  .L  i  cmm j  [g-mole/litre] of mixing c e l l s  [cm] 2  [cm. /sec] 3  [A s e c / g - e q u i v . ]  2  density  [A/cm ] [A]  ["fl-mole ~ 2 (_ cm sec_  284  285  Typical k  =  integer  K  =  rate constant  Unit  number  f9:  m o 1 e  —  \J l tre-sec_ I  =  channel  m  =  M  =  M(l- e )/e , or number of mixing cells l i n e a r e q u i l i b r i u m constant  n  =  number of gram i n t e g e r number  nc  =  number of c y c l e s  ns  =  separation  N  =  number of segments of STOP-GO a l g o r i thm  p  =  exp(-aij)  P  =  permselectivity  Ps Pd  or =  length  or i n t e g e r  [cm]  3  cm3 [cm  moles or  of s o l u t i of s o l i d r  , n [g-mole]  factor  of i o n exchange membrane  S a l t i n g or Desalting factor  q  =  expC-az^-)  Q  =  flow  r  =  dimension 1 ess  R  =  areal  t  =  real  3  rate  [cm /sec] volume  resistance time  ratio 2  [fi cm ] [sec]  286 Typical =  [sec]  c y c l e time  t  i o n i c mobi 1 i ty  =  s u p e r f i c i a l v e l o c i t y of f l u i d i n packing or channels  [cm/sec]  =  velocity  [cm/sec]  =  volume  =  dimensionless  lateral  vector  3  [cm ] concentration  distance  charge  co-ordinate  valence of charged s p e c i e s or d i r e c t i o n of flow i  2  ern g-mole 1 V sec g-equivj  =  c o n c e n t r a t i o n of f i x e d i o n i c in membrane matrix  z  Unit  =  calculation  constants  g-mole g-dry membrane [cm] [g-equiv/g-mole] [cm]  ( i = l,2,*--,6)  Greek Symbols a  =  stoichiometric coefficient  6  =  dimensionless  Y  =  phase l a g  6  =  thickness fraction  layer thickness  of Nernst l a y e r or  [cm] [ -]  of v o i d volume d i s p l a c e d  e  =  fractional  void volume of packing  r\  =  electric  field  G  =  absolute  temperature  vector [°K]  287  Typical 1  X  +  mi  1 + m2  v  =  transport  £  =  dimensionless  TT  =  length  P  =  (l-e)/e = ratio void volume  T'  Units  =  number membrane r e s i s t a n c e  fraction of volume of packing to  a^/2  T  =  pause time  [sec]  V  =  f i n i t e d i f f e r e n c e symbol or divergence o p e r a t o r or gradient vector  [cm-1] [cm ]  A$  =  applied e l e c t r i c  A<J>Don=  Donnan p o t e n t i a l  Aip  dimensionless  =  -1  potential  [V] [V]  potential  S u b s c r i pts +  for positively  charged s p e c i e s  (cations)  for negatively  charged s p e c i e s  (anions)  0  r e f e r s to i n i t i a l  state  Lim  at l i m i t i n g , s t e a d y - p e r i o d i c  s  solid  or adsorbent phase  state  f  fluid  phase  T  top r e s e r v o i r  B  bottom  reservoir  Supers c r i pts  m  =  r e f e r s to property i n membrane  =  r e f e r s to membrane s o l u t i o n  interface  REFERENCES Acrivos, A., I&EC, 48, 703 (1956). D'Alessandro, S., A. Tantillo, Desalination, 9_, 225 (1971 ). A l e x i s , R.W., A r i s , R.,  Chem. Eng. P r o g r . , 63, No. 5, p. 69  I&EC f u n d . , 8, 603  A r i s , R. , N.R. Baker  I I I , B.,  B a t t a , L.B.,  (1969).  Amundson, A. I. Ch. E. J . , _3 , 280 I&EC f u n d . , 9, 686  U.S.  B e l f o r t , 6., G.A.  patent 3,564,816  (1971).  G u t e r , D e s a l i n a t i o n , 5, 267  "Electrophoresis: Acad. P r e s s , N.Y.  B u t t s , T . J . , R. Gupta, N.H. (1972).  (1957).  (1970).  , D e s a l i n a t i o n , 1_0 , 221 B i e r , M.,  (1967);  (1968). ( 1972).  Theory, Method, and A p p l i c a t i o n s , " (1959). Sweed, Chem.Eng. S c i . , 27, ~~  855  C a l v i t , B.W., J . J . S l o a n , i n P r o c . F i r s t I n t e r n . Symp. Water D e s a l i n a t i o n , Washington, D . C , Oct. 3-9, 1965, V o l . 2, p. 11. C a r s l a w , H.S., J.C. J a e g e r , "Conduction of Heat i n S o l i d s , " 2nd e d . , Clarendon P r e s s , Oxford (1959). 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No. 135 (1965).  292  L a c e y , R.E., " D e m i n e r a l i z a t i o n by t r a n s p o r t d e p l e t i o n , " u S O f f . S a l i n e Water Res. Dev. Rep. No. 80 (1962). Lang, E.W.,  E.L. Huffman, R.E. 115, 88c (1968).  Lacey, J . Electrochem.  Soc,  McCracken, D.D., W.S. Dorn, "Numerical Methods and FORTRAN programming," W i l e y , N.Y. (1964). McHenry, K.W.  J r . , R.H.  Wilhelm, A. I. Ch. E. J . , 3, 83  M a n d e r s l o o t , W.G.B., R.E. 304 (1965).  H i c k s , IE&C p r o c . des. dev.,  Mas, L . J . et al. , D e s a l i n a t i o n , 7_, 285  (1957). 4,  (1970).  Matz, R. i n " P r o c . I n t e r r e g i o n a l Seminar Economic Appl . Water Desal.," N.Y., 22 Sept. to 2 O c t . , 1965, p. 79. Matz, R. et al. , U.S. Meyer, K.H.,  W.  patent 3,029,196  (1962).  S t r a u s s , H e l v , c h i m - a c t a , 2_3, 795  (1940).  P a t r i c k , R.R., J . T . S c h r o d t , R.I. Kermore, S e p a r a t i o n S c i . , 7, 331 (1972). P i g f o r d , R.I., E. Baker I I I , D.E. (1969a).  Blum, I&EC f u n d . , 8,  144  , I&EC f u n d . , 8,  848  (1969b). Placek, C ,  "Ion Exchange Resins," Noyes Data Corp.,  P n u e l i , D.,  G. Grossman, D e s a l i n a t i o n , 7_, 297  P o p k i n , R.,  "Desalination,"  Rhee, H.K.,  N.R.  F.A.  P r a e g e r , N.Y.  Amundson, I&EC f u n d . , 9_, 303  R i c k l e s , R.N., "Membranes, Technology Develop. Corp. (1967).  1970.  ( 1970). (1968). ( 1970).  and Economics,"  Noyes  293  R o l k e , R.W.,  R.H. Wilhelm, I&EC f u n d . , 8, 235 (1969).  Rosenberg, N.W.,  C.E. T i r r e l l , I&EC, 49_, 780 ( 1957).  S a t a , R. et al. , B u l l . Chem. Soc. J a p a n , 4_2, 279 ( 1969). S a b a d e l l , J . E . , N.H. Sweed, S e p a r a t i o n S c i . , 5_, 1 71  ( 1970).  Schlb'gel, R. , " S t o f f t r a n s p o r t durch Membranen," S t e i n k o p f , Darmstadt (1964). S h a f f e r , L.H., M.S. M i n t z , " E l e c t r o d i a l y s i s , " i n : " P r i n c i p l e s of D e s a l i n a t i o n , " e d . K.S. S p i e g l e r , Acad. P r e s s , N.Y. , 1966 , pp. 200-290. Shendelman, L.H., J . E . M i t c h e l l , Chem. Eng. S c i . , 27, 1449 (1972). Skarstrom, C.W., Ann. N.Y. Acad. S c i . , 77, 751 (1959). S o l a n , A., Y. Winograd, The Phys. of F l u i d s , U_, 1372 (1969). S o l a n , A., Y. Winograd, U. K a t z , D e s a l i n a t i o n , 9 , 89 (1971). S o l t , G.S. i n : "Proc. F i r s t I n t e r n . Symp. Water D e s a l . , Washington, D.C. , O c t . 3-9 , 1965 , V o l . 2, p. 219. S o n i n , A.A., R.F. P r o b s t e i n , U.S. O f f . S a l i n e Water Res. Dev. Rep. No. 375, 1968. S p i e g l e r , K.S. ( e d ) , "Salt-Water P u r i f i c a t i o n , " Son, N.Y. , 1962; :  , "Principles  John Wiley &  of D e s a l i n a t i o n , " Acad. P r e s s ,  N.Y. , 1966 . , D e s a l i n a t i o n , 9 , 367 (1971). , Adv. Chem. S e r . , 38 , 179 (1961 ) . Sporn, P., "Fresh Water from S a l i n e Waters," Pergamon P r e s s , O x f o r d , 1966.  294  Sweed, N.H., R.H. Wilhelm, I&EC f u n d . , 8, 221 Sweed, N.H., R.A. Gregory, A i c h e y , 1_7, 171  (1969).  (1971b).  Sweed, N.H., F.B. H i l l , "Parametric Pumping," i n : "Progress in S e p a r a t i o n and P u r i f i c a t i o n , " (E.S. P e r r y , e d . ) , W i l e y , N.Y. (1971), V o l . 3, p. 171-240. Tsunoda, Y. i n : " P r o c . 1st I n t e r n . Symp. Water D e s a l i n a t i o n , Washington, D.C., O c t . 3-9, 1965, V o l . 2, p. 325. Wakao, N., H. Matsumoto, K. Juzuki , A. Kawahara, Kagaku Kogaku, 32, 169 (1968). Weiner, S.A., P.M. R a p i e r , W.K. 3, 126 (1964).  Baker, I&EC p r o c . d e s . dev.,  Wilhelm, R.H., A.W. R i c e , A.R. B e n d e l i u s , I&EC f u n d . , 5, 141 (1966). Wilhelm, R.H., N.H. Sweed, S c i e n c e , 195, 522 Wilhelm, R.H., A.W. R i c e , R.W. 7, 337 (1968b).  (1968a).  R o l k e , N.E. Sweed, I&EC f u n d . ,  W i l s o n , J.R. ( e d . ) , " D e m i n e r a l i z a t i o n by B u t t e r w o r t h , London, 1960.  Electrodialysis,"  Yamane, R. et al. , I&EC p r o c . d e s . dev., 8, 159  (1969a).  , B u l l . Chem. Soc. J a p a n , 42^, 2741 ( 1969b). Young, E.F. J r . , Chem. Eng., Feb. 1957, p. 241.  APPENDIX A  DETAIL DRAWINGS, PICTURES OF THE MODULES AND MANUFACTURING PROCEDURES  295  APPENDIX  A.l  ELECTRODIALYZER NO. 1  296  Figure  A. I.2.  EIectrodia Iyzer  No.  I  <?n  situ>.  299  Figure A . I . 3 .  Dimensions  o f EDI  electrode  end  frame.  300  1  i  I -7'  F i gure  j«P.rJ-  A.I.4.  Dimensions of EDI  centre  frame.  Figure  A.1.5.  Dimensions  of  EDI c l a m p i n g  frame.  APPENDIX  A.2  ELECTRODIALYZER NO. 2  302  Figure  A.2.I  Laboratory  testing  station.  o  F i g u r e A.2.2  Dimensions of EDM  electrode  end  frame.  APPENDIX A.3  MANUFACTURING PROCEDURE FOR MEMBRANE-SPACER FRAME  Each membrane spacer frame c o n s i s t e d of 5 parts which were permanently j o i n e d t o g e t h e r .  Figure A-3-1  shows  an exploded view of the assembly.  i  Polyethylene Frame  Anionic _ Membrane Polypropylene  Filter Paper  Spacer  Cationic — Membrane  23 Figure A-3-1:  Exploded view of membrane-spacer assembly.  305  306  CUTTING; The polyethylene edge. was  The  supporting sheets  frame was  punched out of low  (1/16" t h i c k n e s s ) with  a double-knife-  outer edge cut measured 3" x 8-7/8", the i n n e r  1-1/2" x 6-11/16".  t h e r e f o r e marked at one  The  corner f o r f u t u r e r e f e r e n c e .  holes on the e l e c t r o d e end  p l a t e s , see Appendix A.2.  Resets  were punched out using a s i n g l e -  (1-7/8" x 6-11/16").  f i t t e d to the r e s e t s of the  Spacers were then  aqueous NaCI s o l u t i o n  individually  frames.  Membranes were pre-cut  knife-edge  inside  frames.  Spacer screens knife-edge  Flow  stream  (1/8" wide x 0.035" deep) were m i l l e d out along both lengths of the  one  frames were unsymmetric, and were  d i s t r i b u t i o n s l o t s were punched to f i t the process  0.5N  density  and  and  soaked f o r 24 hours i n  punched out using a s i n g l e -  (1-3/4" x 6-3/8"). Filter  paper (Whatman No.  1) was  cut i n t o 1-1/2"  x 6-1/16" p i e c e s .  ASSEMBLING: Each membrane p a i r was a heated bar filter  (seal  paper was  approximately  s e a l e d along both widths with 1/8"  wide).  A piece of  i n s e r t e d between the s e a l e d membranes.  307  The spacers were welded to the frames by means of a heated j i g which was mounted on a crank s h a f t punch.  The  temperature of the j i g was c o n t r o l l e d by a r h e o s t a t to approximately 240 ° F . paper were p o s i t i o n e d  S p a c e r , frame, and a sheet of t h i n under the hot j i g .  The paper was used  to a i d s e p a r a t i o n of the j i g a f t e r completion of the j o i n i n g process of frame and s p a c e r .  i  Jig with Heating Cable  "LT  -Paper 33  - F r a me Spacer  /////\\\\\  Figure A-3-2:  Welding of spacer  and f r a m e .  The hot j i g was lowered and pressed down with g r a d u a l l y i n c r e a s i n g pressure f o r approximately 1 minute. spacer frame was then q u i c k l y water b a t h .  The j o i n e d  removed and quenched  in a cold  The paper was removed.  A s o r p t i o n membrane was tagged to the frame by means of a heated b a r .  APPENDIX B  MATHEMATICAL DERIVATIONS  308  APPENDIX B.l  DERIVATION OF CONCENTRATION TRANSIENTS FOR CONSTANT, UNIFORMLY DISTRIBUTED RATES OF MASS TRANSFER PARAMETRIC PUMPING OPERATION  Since  axial  dispersion i s neglected  i t is sufficient  to c o n s i d e r what happens to the uniform c o n c e n t r a t i o n  of one-  end  with  r e s e r v o i r during  feeding  any complete c y c l e , which s t a r t s  the r e s e r v o i r s o l u t i o n to the s e p a r a t o r . The  concentration at d i f f e r e n t  brine cycle i s i l l u s t r a t e d profiles  i n b r i n e tank and s e p a r a t o r  i n s t a n t s during  the (k+1)  0 - refers to the initial the b r i n e t a n k . 1 - after  time  switched 2  - after  3 - after  i n Figure B - l .  cycle:  (polarity  to negative).  one-half time  cycle  t = T/2.  t = T/2 + y.  4 - a f t e r time t = T - y (polarity t o pos i t i ve ) . 5 - a t end o f c y c l e t = T.  309  are shown  concentration in  t = T/2 - y  back  The  3 09  Figure B.I.  A  C o n c e n t r a t i o n c h a n g e s i n b r i n e ( a ) and d i a l y s a t e ( b ) r e s e r v o i r d u r i n g a c y c l e i n p a r a m e t r i c pumping o p e r a t i o n .  310  The shaded area i s the e f f l u e n t concentration p r o f i l e at the end of the cycle i n d i c a t e s the r i s e i n c o n c e n t r a t i o n . The c a l c u l a t i o n of the l i n e s 5 i s s t r a i g h t f o r w a r d . The corners are l i s t e d clockwise s t a r t i n g from the leftmost lower one:  concentrations are given f i r s t , time next, separ-  ated by a comma.  C  [ B,k  [ B,k C  +  (  K  2"  K  i )J  • °]  +  'B,k  2  5  K  i Y  » \  ~  v\  2  The t o t a l area i s simply  A =K2Y  2  +h  ( K 2 - K O J + 2(K 1 +  K2)Y  (y- 2Y) + ^  (K2-Ki)T  + 2KlY  Thus the c o n c e n t r a t i o n c  B,k+l  "  C  change i s given by  B , k  =  f  A  = (  K 2  -  K l  >!  +  +  By s i m i l a r i t y , the d i a l y s a t e change d u r i n g the (£ + 1)  c y c l e (see a l s o  C  C  T,* + 1  c C T,1  7  T  A s i m i l a r area a n a l y s i s  (T 2-Y  (I  {  2Ki  \ K:  TY +  r  c. •• - c T,0 t,l  -  K x +2Ki  2  -  Hence  (K1+K2)J  d i a l y s a t e producing h a l f c y c l e must  separately.  - Cc T,0  is:  " T,* = (Ka-K,) , -  The f i r s t calculated  Figure 3.1 .b)  K  2  r  2  Y  gives  K2Y  -  K2Y  :  312  In g e n e r a l , f o r  n £ 1  K 2 -Ki  K i | + (K 2 + K  T,n = c T,0  4  "  Ki+K2 x ( n - l ) T 2  and  c  B,n  C  B,0  +  K  2  - K i  4  .  Ki+K2 2  x  T  nT  1  APPENDIX B.2  DERIVATION OF THE CONCENTRATION TRANSIENTS FOR CONCENTRATION DEPENDENT RATES OF MASS TRANSFER PURE PAUSE OPERATION  In a similar analysis to the previous  section the concentrations  in s t a t i o n a r y and moving parts of the systems may be as b l o c k s .  considered  One void volume displacement i s assumed. For the n  t h  dilution  h a l f c y c l e one h a s , a c c o r d i n g  to the assumed r a t e law  C  e  s  C  T B  T  3t  n = - a x  and  n r  3t  n  c  at  s u b j e c t to the i n i t i a l for  t = 0  1  conditions (  •  C  T n J  V.  N c  n-l  ( i)»-( s]»-l c  313  314  Hence  C  Hn " ( T]n-l  eX  (  3lt)  P "  (B.2.1)  C  n " ( s)n-1  Similarly  C  T  1  +  K^Jn-lC  1  "  «P(-»lt>]  f o r the n.th enrichment h a l f  3t  n  cycle  a2  and  9t  n  s u b j e c t to the i n i t i a l for  t = 0  - P  3t  n  conditions ( 1 C B n  f  C  1 B  r  •  cS  I J n  =  n-l  i c!  n  315 Hence  1)n  n  exp(-a2 1 (B.2.2) f  [ B J n-1  'n  The (B.2.2) may ing  and the  1 - exp(-a2  • H. - hi - (  abbreviations  and  exp  hi)  q = exp - a 2 are  used. n= 1  1 + l(l-p)  (cs)  (cgj^-  = q  +  f ( l -  P  )  1 + P(l-q) +  (B.2.1) and  The  to be  p =  t)  J  stepwise as f o l l o w s .  i s chosen  t =0  for  *>  systems of d i f f e r e n c e equations  be solved  condition  il  C  (l-q)(l-p)  global  start-  316  n=2 (  c  t  P  2  = q • l(l-p)  k)  c  q 2  +  ^  ( 1  •  "P  }  Ip(l-p)  +  pq  "  p )  "  (cBj  = 1 + p(l-q) + (l-q)(l-p) + p(l-q)[q + ^ 0 - p f |  +  F  ( 1  ( s)  (l-q)(l-p)p  -  1 + p(l-q)(l+q) +  -  P  (l-q)(l-p)(l+p+q)  n=3  [ C ;]  = q  [cl  = q  ^  3  2  3  + q(l-p)l(p+q)  + \  2  p (l-q)  2  + q ( l - p ) l ( p + q ) + q(l-p) 1 p  2  '3  = q[q  (cBj  2  + £(1-P)(P  2  + q  2  +  pq)]  2  = l + (l-q)[p(l+q) + (l-p)(l+P+qf|+p(l-q)[q + q(l-p)l(p+q)] + (l-p)(l-q)q 2  2  2  2  = 1 + (1-q) pp(l+q+q ) + ( 1-p) (1+q + p+q + pq + p )J  317  n = 4  2  C V.  .  B  2  2  = 1 + p ( l - q ) ( l + q + q ) + (1-q)(1-p)(1+p+q+q +pq+p ) + J  3  2  3  2  p ( l - q ) [ q + ( l - p ) £ ( p q + q + pq )]  2  p(l.q*)-p*-q*+  +  I p -* k  q*  £=1  2 + p ( l V ) - p* - q(l-p) I  + (l-q)(l-p)p  :  5  \ p "* q*  +  H=l  p "* q* 3  i=0  The  general r e c u r r e n c e scheme i s c l e a r now and the  r e s u l t becomes  cT I T ( 1 c  n n =  p  n  = 2 + (l-q ) - p - ( l - p ) p n  P  n  q  i n  f fa  APPENDIX B.3  RATE THEORY OF PARAMETRIC PUMPING  The  n  cycle consists  of a d i l u t i o n h a l f  followed by an enrichment h a l f c y c l e . of the rate one  cycle  After substitution  laws (19) i n t o the mass balance equation ( 6 ) ,  has f o r the f i r s t  3cf  _t  part c y c l e  3cf  + V  _ L  + a i C f =  0  f  (B.3.1) 3C.  3t and  3 1  ~  C  f  *  f o r the second part c y c l e  3t  = - a 2 c, (B.3.2)  3cf Tt  3c _L _ 3z  1 2 .  p  318  C  s  =  0  319  The method of c h a r a c t e r i s t i c s  ( A c r i v o s , 1956), i s  a p p l i e d and the f o l l o w i n g sets of o r d i n a r y  differential  equa-  t i o n s are obtained:  The f i r s t  equation of ( i ) i s r e w r i t t e n as  dc.  dz = - a! • c.  dt  or  dz dt  The p a r t i a l is  identical  and  differential  s dt  since  there  =  dt  (B.3.3)  - ai  of the second equation i n (B.3.1)  to the t o t a l  dc  d In c 1  derivative  3c 3c . s , s_ dz^= 3t 3z * dt  ac s_ at  i s no flow i n the s t a t i o n a r y phase (dz/dt = 0)  Hence dc  s _ ai c. p "f  (B.3.4)  dt  Similarly, f i nds  f o r the s e t of equations  (B.3.2) one  320  ^  1  dt  a2  cs  (B.3.5)  ,  and  dcf dz = v , and dt ~dT  (B.3.6)  P 9 2 c(  Because of (B.3.5) i t i s not p o s s i b l e to e l i m i n a t e the c o n c e n t r a t i o n of e q u a t i o n s .  i n the s t a t i o n a r y phase, c s , from the s e t  The l o c a l  concentration  profiles  phases have to be c a l c u l a t e d step by s t e p . equations take i n t o  i n both  The f o l l o w i n g  account that the frames of r e f e r e n c e f o r  equations (B.3.3) and (B.3.6) are t r a v e l l i n g with velocity written  v, whereas equations  (B.3.4) and (B.3.5) are  f o r a s t a t i o n a r y frame of r e f e r e n c e .  plane i s considered  the f l u i d  I f the ( z , t )  one can c a l c u l a t e the necessary  and average c o n c e n t r a t i o n  profiles.  local  321 For the f i r s t  part  cycle:  c u=e ,t) 4  Cf(z,t=T/2) T/2)  T/2  cf(A,t) = cf(£-vt,0)  exp(-ait)  T/2  t,n  z  c U , t ) dt  T  f  :  '2  B,n-l  ex  a z  P  z/v f  fz I  1  cc(z s  0) + * i  '  c ^ ( z - v t , 0 ) e x p ( - a i t ) dt +  p  p  fi  2  c  B,n-l  ex  a iz  P  322  For the second  part  cycle  c (z,t) 5  c^(z,t)  c^(z ^=0,t)  c (z,T) = cs  Tl  f  s  exp - a 2 \  j  4  T/2  cf(z,T) = c T  n  r  + pa  z + I - vt, j  e x p ( - a 2 t ) dt  z/v (  r)  c f ( 0 , t ) - c f vt , j  +  f  B,n  c f ( 0 , t ) dt  T T/2  v t _ s  T/2  T  /"  c  pa2  vs , j  Tl  e x p ( - a 2 s ) ds  323  In Table B-l the c o n c e n t r a t i o n time and and  space are presented f o r four s u c c e s s i v e  under the  p = 1. as w e l l . used.  d i s t r i b u t i o n s in  The  r e s t r i c t i o n s , c^- = c g = 1.0  time and  The  x' = aT/2  cycles  at t = 0, ai = a 2 =  space average c o n c e n t r a t i o n s  abbreviations  half  and  are  £ = az/v  included are  a,  Table B.l : Average and local Concentrations During the F i r s t Two Cycles of a Parametric Pumping Operation for Concentration Dependent Rates of Mass Transfer. — •-  1/2  3/Z  /  AVERAGE EFFLUENT  •  AVERAGE SOLUTIOA/  AVERAGE  ADSORBED  LOCAL SOLUTIOA'  2e.pH)+£^-Z  LOCAL  2<* (-z)-  AD-SOR&EA/T  f  2-(/*j- Z)  axf>6-J)  L  expM')j| exp(- j )  2  APPENDIX B.4  MULTIPLE STEP DISPLACEMENT MODEL (STOP-GO ALGORITHM)  In the conceptual phases may areas  model of t h i s  scheme the two  be represented by two-dimensional p l a t e s .  of the p l a t e s i n d i c a t e the volumes of each of the phases.  Since the frame of r e f e r e n c e may be attached the phases, i t w i l l  be assumed  The displacement  occurs  d i v i d e d i n t o segments of i d e n t i c a l the number of steps  and  to the s o l u t i o n .  stepwise. length  (see Figure B-2).  i s d i s p l a c e d , there w i l l  sents a separate well mixed  adjacent  cells  The p l a t e s are Az = £ / N  according  I f one v o i d volume  be N segments on the moving  2N segments on the s t a t i o n a r y one.  During  to e i t h e r of  t h a t the adsorbent (or adsorp-  t i o n membrane) i s d i s p l a c e d r e l a t i v e  to  The  Each segment  plate repre-  cell.  the STOP periods mass i s t r a n s f e r r e d  f o r time i n t e r v a l s  At = T/2N.  During  between each GO  step the segments are d i s p l a c e d by one increment without mass transfer taking p l a c e .  At the end of each h a l f c y c l e the  325  326  segments on the s t a t i o n a r y p l a t e , which have no neighbours on the moving p l a t e , may be intermixed mixing  to satisfy-  the end  condition.  4  N  CM  Direction of Displacement  2N  Figure  B-2:  P l a t e r e p r e s e n t a t i o n of m u l t i p l e step d i s p l a c e m e n t model (STOP-GO a l g o r i t h m ) .  A FORTRAN digital  IV program was prepared f o r an IBM 360/67  computer to simulate c o n c e n t r a t i o n  t r a n s f e r rates according The program i s w r i t t e n  to equations  dependent mass  ( 2 7 ) , see S e c t i o n  3.3.  i n double p r e c i s i o n because round-off  e r r o r s a f f e c t e d the o v e r a l l mass balance f o r l a r g e N's. The FORTRAN program i s l i s t e d followed  on the next page  by the computer p r i n t o u t of a s i m u l a t i o n  run f o r  327  N = 100 , 6 = \ , a  a  = O.OUsec- ] , p = 0.5 , T = 10[sec] 1  2  = O.OlCsec" ] , 1  2  1  c  2 3 4 5 6 7 8  C C C  9  C  24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52  M U L T I P L E STFP I) I SI'LACF MFNT MODEL C0NCEN1 *ftT t UN nt?LNl>FNT RATES DF H\SS TRANSFE* OOUniE P R C C I S I O N P . 0 , P 1 , 01 ,.:F FF , S? , S I . DE X P , X I 203 ) , Y ( 2 0 0 » REAL A I , A 2 ,.'4 , F A U » P A , B S , S F P READ 1 5 , 1 ) M . N O . U . A l , A ? , K , T A J FORMAT ( 3 I 3 , 4 r f > . 4 )  1  10 11 12 13 14 15 16 17 18 19 20 21 22 23  328  2 C  WRITE ( 6 , 3 ) M , N , N 0 , M , A l , A 2 , . * , T A J FORMAT ( 1H I / / / • D I S P E R S I O N MODEL 3 F RATE THEORY • / / 1 1 0 X , ' ENDS WELL M I X E D , EXCHANGE' - D I S P L A C E 2 « NUMBER OF COMPARTMENTS = 13/ 3 ' NUMBER OF C Y C L E S = •••13/ 4 ' D I S P L A C E D VOLUME = ' ,\it'/' tlif 5« I N I T I A L CONCENTRATION = 1.0 • / 6« D E S A L I N A T I O N KATE C O E F F I C I E N T = •,F6.4,'!l/SECJ•/ 7< CONCENTRATION RATE C O E F F I C I E N T = • , F 6 . 4, • t 1 / SEC ) ' / 8 ' VOLUME RATIO = SF6.3/ 9» CYCLE TIME = '.F6.1 ,'(SECI'///» WRITE ( 6 , 4 ) FORMAT Ii' CYCLE NO. B*IN6 DIALYSATB SEPARATI3N BALANCE ( ? ) !•>  3  4  C C FIRST C  5 1C  11  X(I)=CEFF C C SECCNC HALF CYCLE C 0 0 2 0 1=1,NO !=ND1-L OC 1 5 K=1,K 1=1*1 X{I)=X(I)»Y(I)*C1 15 Y(I-1)=Y(I)*C 2C CCNTINUE S1=0.0 S2=0.0 S3=0.0 OC 2 1 1=1.f S1=S1*X(I) 21 S3=S3*Y(ll  DC 2 2 I = H t H 2 22  S2=S2*X(II BS=«SHS7»S3«K)*EA S2=S2/ND SEP=S2/CEFF  23  X U ) = S2  76  CC 2 3 I'fl,f>2  77 C C C  PRIMCUT  81 82 63 84 85  FKC  CF FILE  DC 1 0 L = 1 , N 0 l =F + L OC 5 K = 1 , V 1=1-1 Y(I*l)=Y(1)*X(I)«P1 X(I)=X(I)»P CCNTINUE \ CEFF=0.0 OG 1 1 1=1,NO CEFF=C6FF*X( II CEFF=CEFF/ND  0 0 1 2 1=1,NO  72 73 74 75  79 8C  CYCLE  12  71  78  HALF  DO 1 0 0 J = 1 , N  53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70  Ml=Hfl N01=ND»1 M2=M«ND P=-Al*rAU/ND P=DEXP(P| Q=-A2*TAU/ND ;= DfiXPO) Pl=(l.DO-PI/R Ql=(l.DU-tfl*R BA=100./(MH',*R*N0> DO 2 1=1,M2 X(I)=1.00 YUM1.00  WRITf 25 ICO  (6,25)  J,S2,CEFF,SEP,8S  FCR^AI (I7.4FI2.4) CCMINUE SICP ENC  329  D I S P E R S I C N PCCEL  OF RATE THEORY  ENDS KELL  MXEO,  EXCHANGE - D I S P L A C E  NLCeER CF CCKPARTPENTS NIPSER CF CYCLES DISPLACEC VCLL"E INITIAL CCNCEMRATICN D E S A L I N M 1 C K RATE C C E F F I C I E N T CCNCENTRATICN RATE C C E F F I C I E N T VCLL'PE RAT1C CYCLE T I C E  CYCLE  NC.  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 STCP exccuncN  BRINE 0.9821 0.S668 0.9539 0.9430 0.9338 0.9260 0.9195 0.9140 0.9C94 0.9C55 0.9024 0.8SS8 0.8976 0.8959 0.8946 0.8936 0.6928 0.8923 0.8920 0.8918 0.8918. 0.8920 0.8922 0.8926 0.8930 0.8935 0.8941 0.8947 0.8954 0.8962 0.8970 0.8978 0.8966 0.8995 0.9CC4 0.9013 0.9022 0.9032 0.9C42 0.9052 0.9C62 0.9072 C.9C82 0.9C92 0.9102 0.9113 0.9123 0.9133 0.9144 0.9154 0.9165 0.9175 0.9ie6 0.9197 0.92C7 0.9218 0.9228 0.9239 0.9249 0.9260 0 I CHP I K  M  EC  DIALYSATE 0.95C7 0.9293 0.9105 0.8939 0.8793 0.8663 0.e548 0.8445 0.8352 0.8269 0.8194 0.8126 0.8063 0.8CC6 0.7954 0.7905 0.7861 0.7ei9 0.778C 0.7743 0.7708 0.7676 0.7645 0.7615 0.7587 0.756C 0.7535 0.751C 0.7486 0.7463 0.744C 0.7419 0.7398 0.7377 0.7357 0.7338 0.7319 0.73CC 0.7282 0.7264 0.7247 0.723C 0.7213 0.7197 0.7181 0.7165 0.7149 0.7134 0.7119 0.7104 0.7089 0.7075 0.706C 0.7C46 0.7032 0.7019 0.7CC5 0.6992 0.6979 0.6966  ICO 60 50/1C0 1.0 0.01CCIl/SECl 0.01CCI1/SECI C.5CC 10.01 S E C )  SEPARATION 1.C330 1.C404 1.C477 1.0549 1.0620 1.0689 1.0757 1.0823 i.oea8 1.C951 1.1C13 1.1073 1.1132 1.119C 1.1247 1.1303 1.1358 1.1412 1.1465 1.1518 1.1569 1.1620 1.1671 1.1721 1.1770 1.1818 1.1867 1.1914 1.1962 1.2C09 1.2C55 1.2102 1.2147 1.2193 1.2238 1.2283 1.2328 1.2372 1.2416 1.2460 1.2504 1.2547 1.2590 1.2633 1.2676 1.2719 1.2761 1.2803 1.2e45 1.2887 1.2928 1.297C 1.3011 1.3C52 1.3C97 1.2133 1.3173 1. 2214 1.3254 1.3293  BALANCE 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.«»998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.9998 99.999H 99.9998 99.9998 99.9998  APPENDIX B.5  DERIVATION OF CONCENTRATION TRANSIENTS FOR EQUILIBRIUM CONTROLLED PURE PAUSE OPERATION  CASE A: Initial  equilibrium  constant K 2 .  First  displacement  downward. It i s s u f f i c i e n t tions  of the adsorbent  (c ) and of the s o l u t i o n i n the end s and i n s i d e the s e p a r a t o r ( c ^ and C g ) .  reservoirs The for  to c o n s i d e r the o v e r a l l concentra-  mass balances during the n  the f i r s t h a l f  c  S  cycle are:  cycle  cB  cB  and the second h a l f  t h  +  n  cycle  330  P C  cB  > n-1  331  C  C  Substitute  ( T]  +  p  c  =  ( s)  C  .  ( T)  +  p  c  ( s  B  equilibrium  relations  rc v.  s  0 J n  = K2f<  and  Ki  and  let  X =  and  1 + pK2  and  1 +  pK  x  use  n- 1  One  K =  has  to s o l v e  the  J  n  system of d i f f e r e n c e  equations  332  C  ( B)  +  ,  1  "  -  )  1  !  '  n-1  • for +  n > 1  X -1  n- 1 K  s u b j e c t to the  initial  conditions  C  ( B]  "  (T C  E.g. n = 1  Cp  c-  +  - i )c0  ( x  K  —  „  x  Co  — K  n = 2 1 + =  C o l  X/  l Tj C  (<-!)•£  c,  Co-  +  X -1  f,  +  1 X  1 X  1  + -r  K  11 K  -  c,  x  _  i  f  i  _  r  "  333  n = 3  Co.  1  +  X  i  X  M Co 1 + x  = J  3  =  The  l  £0-  K  c,  K ^X  M  form of the equation  X  1  + (K  K_  '  +  +  11 K  i s now  K  K  j _  KX  ( X - 1) +  1 +  ( X - 1)  (1  1 K  1 +  ^x  7x  o b v i o u s , so t h a t i n general  334  n-2  = 1 +  [X  K  I  (1  = 1 +  £=0  1  fl U  n-  1  KX KX  or  h)  K-X  ' n = 1 + KX - 1  X K  1 K  KX  (KX)  K-X - 1  n-  1  (KX)  n-1  CASE B: Initial  equilibrium  constant K i .  First  displace-  ment up. By analogy with case A, the mass balances the system of d i f f e r e n c e  equations  lead to  335  (cT) V.  +  ' n -  1  U-l)(cB. J  V  > n. for n > 1 f  1 c,  Subject to the i n i t i a l  +  (K -  n-1  c  conditions  H. - K The  1)  = c,  solution is  c0  * + 1  K  KX  -X - 1  (•cX)  n-1  APPENDIX C  COMPUTER PROGRAMS  336  APPENDIX C . l  EVALUATION OF EDI EXPERIMENTS  The raw data from the recorder chart was processed on a d i g i t a l  computer.  The flow chart of the corresponding  computer program i s shown in Figure C . l . columns involve the f o l l o w i n g  The p r i n t o u t  calculations.  1  : Cycle number (ncyc) i s part of the input  2  : Real time (t)  in seconds  t - 2 *  3 & 4  data  + ^  -  • ncyc  (C-l-1)  : Average bottom ( c ) and top (Cj) r e s e r v o i r concent r a t i o n s in parts per m i l l i o n NaCI i n H 0 converted from [mV] reading using c a l i b r a t i o n data f o r conductivity c e l l . B  2  5 & 6  : Concentrations ( x and X y ) normalized w . r . t . i n i t i a l concentrations.  7  : Separation f a c t o r (ns) as r a t i o of average bottom and top product concentrations  g  337  the  338  : Average current consumptions during e n r i c h i n g and d i a l y z i n g ( I ) h a l f cycle i n amperes. Converted from [mV] reading using r e s i s t a n c e c a l i bration data.  8 & 9  2  1 0 & 1 1 : Current e f f i c i e n c i e s of d i a l y z i n g ( E ) and e n r i c h ing ( E ) h a l f c y c l e i n per cent according to the usual d e f i n i t i o n (see e . g . W i l s o n , 1 9 6 0 ) . x  2  a c t u a l c o n c e n t r a t i o n change ^ 100 theoretical concentration change  (C-l-2)  The t h e o r e t i c a l concentration change i s c a l c u l a t e d assuming perfect membranes and n e g l e c t i n g water t r a n s f e r as w e l l as the volume changes due to the salt transfer. Consider a flow channel of volume V / n , where V a  a  i s the a c t i v e void volume of the stack and n i s the number of spacer s c r e e n s . The t h e o r e t i c a l concent r a t i o n change, i n [ppm], of the s o l u t i o n 1n t h i s channel i s given by I • t • 10 * M theor. zF • V , / n a where I mean current t duration the current I i s passed z valence 6  An"  A c  F  9  F  ^ 5 0 0  a y  '  S  C  °  n  S  t  a  n  t  =  M molecular weight of solute = 5 8 . 4 5  i  (r ( C  " "  [A] [sec] [g-equiv./g-mole] [A s e c / g - e q u i v . ] r„,„ [g/g-mole]  I t i s assumed that the d i s p l a c e d volume ( 6 • Vo) of concentration Co + c i s mixed with the dead volume i n the r e s e r v o i r which receives the e f f l u x . The t h e o r e t i c a l concentration change i s t h e r e f o r e f o r the e n r i c h i n g h a l f c y c l e  1  o\ 1  3 )  339  Ac  I, • U zF  theor,I  - n  .  6  V  V  ' o/ a  *  1 0  •  « • v + v 0  f o r the d i a l y z i n g  AC  I2  theor,2  Finally  C  E, =  • t zF  2  half  •n  B  cycle  6 • V 0 /V a  f o r the coulombic  • 10  6  •M  6 • V0 + V T  e f f i c i e n c i e s i n [%]  C  B,ncyc'~ B , n c y c - l Ii • t i • n  M  6  V  ' 6  °  B V 0 /V a  +  V  0.165  (C-l-4) cT - cT 6 Vo + V T T , ncyc- I T, ncyc T • 0.165 I2 • t 2 • n * 6 V 0 /V a  Equations solutions  ( C - l - 4 ) are reasonably accurate f o r d i l u t e provided water t r a n s f e r i s n e g l i g i b l e .  Power e f f i c i e n c y E^ i n per cent i s d e f i n e d as  theoretical  minimum, r e v e r s i b l e work of s e p a r a t i o n ,n f ) a c t u a l work performed *  For i d e a l d i l u t e s o l u t i o n s the numerator i s given as the r e v e r s i b l e work of mixing per g-mole of s o l u t i o n  340  •Aw  = R0  rev  where .Q  i =1  i= 1  and ( 2 )  r e f e r to the s t a t e before and a f t e r m i x i n g , and the  y.  are the mole f r a c t i o n s of the the components j i n the state Q or ( 2 )  R  universal  gas constant =  8.317  0  The  actual  Aw  where  K  Wsec g-mole  absolute temperature = 298 [°K]  work performed i s  j ncyc act  th  l,k  • average c u r r e n t during k enriching half cycle  2,k  average c u r r e n t during k th d i a l y z i n g half cycle  The r e v e r s i b l e work has to be c a l c u l a t e d f o r each r e s e r v o i r s e p a r a t e l y , m u l t i p l i e d by the number of moles i n the r e s e r v o i r , and the d i a l y z i n g work sub' t r a c t e d from the e n r i c h i n g work.  341  Thus  [-Aw v  E = P  r e v  ] ;  •  enr. A<{)  [ 6 V 0 + V B ] - (• Aw  ^  '  c  k=l  K  ^  1  k  rev d i a l +  !  2,k  («sv +v 0  T  13770.0 [%]  342  READ:  C a l i b r a t i o n constants f o r concent r a t i o n s , flow r a t e , c u r r e n t  1 READ : Run no., i n i t i a l c o n c e n t r a t i o n , o p e r a t i n g c o n d i t i o n s , no. o f cards  1 CALCULATE  : o p e r a t i n g parameters In proper u n i t s  PRINT : t a b l e heading  T i = 1, no. of cards  READ : Cycle no., c o n c e n t r a t i o n s , currents, k  yes  no  READ : s e t of new o p e r a t i n g conditions  RECALCULATE  CALCULATE : C o n c e n t r a t i o n s , s e p a r a t i o n (+ PRINT) currents, efficiencies  : operating parameters  factor  •  PRINT : stack d e t a l I s , o p e r a t i n g  Figure C.I.:  parameters  Flow c h a r t of e v a l u a t i o n program f o r EDI runs  343  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 J 19 1 20 21 22 23 24 25 26 27 I 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52  53 54 56 57 58 59 60 f>l  c  C PROGRAM TC EVALUATE FIRST ED CELL EXPERIMENTS C READ (5,1) NS,NC,VOL,VA 1 FORMAT ( 2 I 3 . 2 F 6 . 4 ) RE AC (5,2) AC,A1,B1,A2,B2 2 FORMAT (5FIC.2) REAC (5,3) NC,NCARD,SPE,CISP,PHI,DVB,OVT,DTF,DTS,CBV,CTV 3 FORMAT (21 3,F4.1,8F6.4 ) IF (SPC-.GT;4C.01 GO TO 4 A3=0.689 03=0.686 GO TO 5 4 A3=C.79l B3=-3.43 5 V={A3*SPE*B3)*24.1/VA CBG=CBV*(Al*Cev*Bl) CTC=CTV*(A2*Crv*e2) YC=(CB0+CTG)/6494444.4 X1M=Y0*AL0G(YO) VC=2.288*DISP VB=2.288*DVB VT=2.288*CVT HT1=DTS+VC/V*24.1/VA HT2=0TF+V0/V«24.1/VA T=HT1+;HT2 HE1=0.165*(VC+VB)/V0«VA/NC/HTI HE2= 0.165*(V0+VT)/V0*VA/NC/HT2 HEP=2754C.00/PHl/T C C SUMMATION CONTROL VARIABLES C L=0 :\ Zl=1.0 Z2=100.0 CU=0.0 CB1=CB0 CT1=CT0 TIME=0.0 C C PRINT TABLE HEAD C WRITE (6,6) (1,1=1,12) 6 FORMAT (1H1, • • 214,17,18,17,18,17,19,ie,17,18,17,18// 3'CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT "4 CURRENT POKER'/ 5* NO. TIME BOTTOM TOP NORMALIZED FACTOR ENR. OIA 6L.EFFICIENCY EFFICIENCY'// 7'NCYC T CB CT XB XT NS II 12 8 El E2 EP •/• I-) (SEC) (PPM) (PPM) (-) (  9-)  (-)  (A)  It)  (A)  WRITE (6,7) l—i  :  m '.  (*)•/» « / )  C C PRINT INITIAL CCNOITICNS C WRITE (6,8) l,CU,CR0,CTC,Zl,Zl,2l,CU,CU,Z7,Z2,22 8 FORMAT (I4,F9.l,F8.0,F7.C,Ffl.2,F7. 3,F9.2,Ffl.3,F7.3,F8.t,F6.1,F9.3 I  3  4  4  62 C 63 C REAC CYCLE CONDITIONS 64 C 65 DC 100 1=1,NCARD 66 READ (5,9) NCYC,CBV.CTV.CURF,CURS,K 67 9 FORMAT (I 3,4F10.1,I 3» 68 IF (K.EO.l) GO TC 20 69 WRITE (6,10) 70 10 FORMAT (• • » 71 IF (K.EQ.O) GO TC 20 72 WRITE (6,7) 73 READ (5,11) SPE1.PH11,CTFI,OTS1 74 11 FORMAT (4F>>.2) 75 IF (SPEI.GT.4C.0) GC TC 12 76 A3=0.689 77 B3=0.686 78 GO TO 13 79 12 A3=0.79l 80 B3=-3.43 81 13 V1=(A3*SPE1*:B3)*24.1/V» 82 HEl=HET*HTl 83 HE2=HE2*l-T2 84 HEP=HEP*T 85 HT1=DTS1+V0/V1*24.1/VA 86 HT2=DTF1+VC/V1*24.1/VA 67 T=HT1+HT2 88 HE1=HEI/HT1 89 HE2=HE2/HT2 90 HEP=HEP/T 91 20 TIME=TIME+(NCYC-L)*T 92 CB=CBV*(A1*CEV+B1) 93 CT=CTV*(A2*CTV*B2) 94 XB=CB/CBO 95 XT=CT/CTO 96 SEP=XD/XT 97 CUl=AC*CURS 98 IF (AC.LT.I.C) CL'1=CU1/HT1 S9 CU2=AC*CURF ICO IF (AC.LT.I.C) CL'2=CU2/HT2 101 ECU1=(CB-CB1)/CUl*HEl/(NCYC-L) 102 E0U2=(CTl-CT)/CU2*HC-2/(NCYC-L1 I 103 CU=CU+(CL'KCL 2)*INCYC-L) 104 Yl=CB/3247222.2 1C5 Y2=CT/3247222.2 1C6 EP=( ( V 0 + V B ) * ( X 1 M - Y 1 * A L C G ( Y l ) ) • ( V O * V T ) * ( Y 2 * A L C G ( Y 2 ) - X l M ) ) / C U » H E P 107 CB1=CB 108 CT1=CT 1C9 L=NCYC UO WRITE (6,8) NCYC,TIME,CB.CT.XB,XT,SEP,CU1,CU2,ECUI,ECU2,EP 111 100 CONTINUE 112 WRITE (6,10) 113 WRITE (6,7) 114 READ (5.1C5) NT 115 1C5 FORMAT (12) 116 WRITE (6,110) NT,NS,NC,NC 117 110 FORMAT (//• TABLE C.1.NI2,' • NUMERICAL EVALUATION OF EXPER , 118 1IMENT'/22X,'ECI-S ,I1,•-•.12,«/»•,12//) 119 WRITE (6,120) L 120 12C FORMAT (1HI.I3) 121 STOP 122 END ENC CF FILE  345 3  2  1  RC A l lift  CYCIE KC.  NCYC l-l  4  crscr-MRAi I C N UCI1CM  (TP*)  CP  CI (PPM)  T (SEC)  (CP  5  NTWAI I C N SfCARATIO*1 NURMAl Ur.O • F A C T O R XI!  XT  l-»  l->  o.c  1032.  Kill.  1  55.5 111.1  127R.  774.  I.CO 1.24  6 7 1 . 622. 593.  1.37 1.45 1.49  582.  3  l(k.6  1416. 1497.  4  5  2 2 2 . 2 217.7  1542. 157C.  6  3 3 3 . 2  1564.  570.  1.52 1.53  7  lee.e  1569.  56e.  1.54  TABLE  C.l. 1  n  ?  1 .ceo 0 . 164 0 . 6 6 2 0 . 6 1 4 C . « 8 6 0.576 U.563 0.561  NS l-l  9  CUHHTN f L' 1 A l .  CONCI  0 7  6  r.NH. 11  IA)  10  11  ClWRCNf EFFICIENCY  12 IA)  El It)  C? Itl  12 POWIR  trr icitNCY FP I D  I.CO  0.0  CO  100.0  100.0  100.oco  1.62 2.07  1 . 1 (.0  1.120 1.700 1.180 1. 160  37.5  37.7  IP.O  13.2 6.4  7.371 1.678  1. 120 1.100  1.6 1.8  1.8  1.100  0.7  0.4  1.160 1.2C0 1.2C0  2 . 16 7.55 2.64 2.73  2.75  1.700 1.7C0 1.2C0  10.)  5.7  3.0 1.4  1.3CI 1 . 0 5 7  0.661 0. 7 5 7 0.655  « N U » E R I C A l EVALUATICN OF EXPERICENT E01-S2-15/418  1  2  CYCLE NO. NCYC l-l  3  REAL TI"E  4  CCNCENTRATICN BCTTCM TCP  5  CB IPPMI  CT IPPMI  xe «-)  4 5 6  0.0 27.6 55.5 83.3 111.1 138.9 166.6  7  1V4.4  8 9  222.2 249.9 277.7 3C5.5 333.2 361.0 3E8.6  1C13. 1122. 1212. 1303. 1377. 1447. 15CC. 1564. 1584. 1626. 1654. 1679. 1702. 1722. 1739.  1019. 929. 851. 787. 735. 697. 664. 639. 626. 606. 587. 570. 559. 546. 539.  I.CO 1.11 1.20 1.29 1.36 1.43 1.48 1.54 1.56 1.60 1.63  1 2 3  1C 11 12 13 14  TABLE  C.l. 2  7  8  CCNCENTRATICN SEPARATION N0RMALI2E0 FACTOR  T ISEC)  0  6  1.66  1.68 1.70 1.72  XT l - l  l.CCC 0.911 0.e35 0.777 0.722 C.684 C.652 0.627 0.614 0.595 C.576 0.559 C.548 0.536 0.529  CURRENT ENR. C I A L . 1 1 (Al  NS «->  I.CO 1.21 1.43 1.67 l.RB  2.09 2.77  2.46 2.55 2.70 2.R3 2.96 3.06 3.16 3.24  9  0.0 1.440 1.4C0 1.4C0 1.400 1.400 1.4CC 1.400 1.4C0 1.400 1.4C0 1.4C0 1.4C0 1.4C0 1.400  ' 12 IAI  CO 1.300 1.400 1.400 1.390 1.380 1.360 1.360 1.360 1.360 1.360 1.360 1.360 1.360 1.360  1 0  11  CURRENT EFFICIENCY El IT!  100.0 23.1 19.8 19.9 16.1  15.2 11.6 14.1 4.3 9.2 6.2 5.6 4 . 9  4.3  3.7  E? It)  100.0 21.3 16.9  14.1 11.4 8.6  7.3 5.8 2.9 4.4 4.4 3.8 2.6  2.3  2.0  1 2  POWER EFFICIENCY EP It)  100.000  0.739 0.682 0.648 0.604 0.564 0.523 0.497 0.450 0.426 0.401 0.379 0.358 0.339 0.322  : NUMERICAL EVALUATICN OF EXPERIMENT EDI-S2-13/I19  2  1  4  3  CCNCENTRATICN BCTTCP TCP  5  6  CYCLE KG.  REAL TIME  NCYC l-l  T ISEC)  CB (PPM)  CT (PPM)  XB l-l  XT l-l  0.0 27.8 55.5  1036. 1100. 1155.  1042. 942. 676.  I.CO 1.C6 1.11  l.CCO C.903 0.640  111.1 166.6 222.2 277.7 333.2 3(8.8 416.6  1261. 1347. 1416. 1475. 1517. 1547. 1558.  738. 656. 599.  1.22 1.30 1.36 1.42 1.46 1.49 1.50  0.708 C.63I 0.574 0.532 C.5C0 C.474 0.463  0 1  2 4 6 8 10 12 14  IS  tARLF  C.l. 1  555.  521. 494. 462.  8  7  CCNCENTRATICN SEPARATION FACTOR NORMALIZED  9  CURRENT ENR. C I A L . 11 IA)  12 IA)  1.00 1.17 1.32  0.0 1.360 1.320  CO 1.220 1.400  1.72 7.06 2.38 2.67 2.92 3.15 1.74  1.320 1.370 1.370 1.3C0 1 .2 80 1.2P0 1.280  1.360 1.320 1.300 1.280 1.260 1.760 1.760  NS l-l  I NUMERICAL FVALL'AIICN CF EXPERIMENT IOI-S2-15/I2C  10  11  CURRENT EFFICIENCY El  (II  E2 It)  100.0 27.8  100.0  25.3  14.4  24.8 19.9 16.1 13.8 10.0 7.4 5.4  15.6 9.3 7.0  25.3  5.3  4.1 3.3  2.B  12 POWER EFFICIENCY EP Itl  100.000 0.880 0.774 0.731 0.651 0.568 0.536 0.488 0.446 0.426  346  ,  |  ?  CYCLE NO.  CCNCFN1HM ICN  Tier  I'dicK  NCYC  T  (-»  c  2 4 6  fl  IC 12 1* 16 ie 20 22  Cn  (SEC)  IPI'M  O.C 55.5 111.1 1(6.6 222.? 277.7 333.2 3E8.8 444.3 459.9 555.4 610.9  978. 1C59. 1133. 1196. 125C. 1306. 135C. 1388. 142S. 1458. 14 86. 1511.  TABLE  C.l.4  1  2  CYCLE  REAL TI'E  NCYC l-l  0 1 2  3  4  5  6 7  a  9  10  4  J  REH  5  irp  KCH^ALI/IL'  Cl  XI!  |PP»>  9HC • H4C. 839. 73C. 739. 699. 675. 645. 619. 596. 575. 557.  (-1  1.C0 i.ce 1.16 1.22 1.28 1.33 1.38 1.42 1.46 1.49 1.52 1.54  4  3  CONCENTRATION TCP 8CTTC»«  5  XT  l-l  I.CCO C.90H 0.65S 0. 796 C.754 C.713 0.688 0.658 C.632 C.608 0.587 0.568  i«cinn  I N K .  C I A I .  10  II  CUKHfNT  rrricirNCY  I ?  tmciiNCv  12  Fl  F2  CP  IAI  IAI  l t »  1*1  H I  0.0 1.360 1.340 1.320 1.320 1.320 I . 120 1.320 1.320 1.320 1.320 1.370  CO 1.160 1.340 1.320 1.32C 1.320 1.320 1.320 1.320 1.320 1.320 1.320  l-l  100.0 10C.0 27.5 30.5 25.2 17.7 21.9 20.2 19.1 14.4 19.2 13.9 15.4 e.5 13.5 10.3 12.6 9.0 11.6 8.1 9.7 7.2 P.8 6.3  6  8  7  CT (PPM  xe (-i  0.0 50.2 ICO.4 150.6 2C0.e 251.0 301.3 351.5 4C1.T 451.9 502.1  1C29. 1237. 1358. 1416. 143C. 1466. 1483. 1489. 1494. 15C0. 1503.  1038. eo5. 70C. 663. 613. 596. 584. 573. 569. 564. 557.  l.CO 1.20 1.32 1.38 1.39 1.42 1.44 1.45 1.45 1.46 1.46  9  CURRENT ENR. C1AL.  XT (-1  NS l-l  tl (Al  12 IAI  I.CCC 0.7 75 0.675 C.639 0.590 0.574 0.563 0.552 0.548 C.543  l.CO 1.55 1.96 2. 15 2.35 2.48 2.56 2.62 2.65 2.68 2.72  0.0 1.120 1.120 I.ICO 1.060 1.C20 l.ccn 0.960 0.960 0.960 0.960  CO 1.000 1.040 l.COO 1.000 0.980 C.960 C.960 0.960 C.960 C.960  C.537  * NUMERICAL EVALUATION OF EXPERIMENT E01-S2-I3/I2T  10  11  CURRENT EFFICIENCY El m  E2 1X1  100.0 100.0 31.4 39.6 18.4 17.0 9.0 6.3 2.2 A.5 6.0 2.9 2.8 2.1 , 1.0 2.1 0.7 1.0 0.9 1.0  o.s  1.1  .  POWCR  II  NS  I.CO I. 19 I. 35 1.54 1. 70 1.87 2.01 2. 16 2.31 2.45 2.59 2.72  4  CURRFNT  CONCENTRATION SEPARATION FACTOR NCRKALWEO  C8 (PPP)  C.l.S  II  7  100.000 0.985 0.862 0.817 0.757 0.720 0.668 0.631 0.599 0.570 0.542 0.516  t NUMERICAL EVALUATION OF EXPERIMENT EDI-S2-15/I21  T (SEC)  TABLE  6  CPNCfNT R A T ICN St I'ARAT I C N  12 POWER EFFICIE EP IX)  100.000 2.957 2.231 1.713 1.410 1.213 1.054 0.931 0.829 0.750  0.666  347 ' 1  3  f  CCNCFNTHAI ICN P.FH t If fc UCITCM TCP  CYCLE ,NC. NCYC (-1  CB 1PPMI  CT |PPM|  xe I-)  0.0 30.2  I02e.  9C6 120.8  1C 11. 1127. 1196. 124B. 1272.  885. 819. 765. 739.  151.0 161.3 211.5  1339. 1372. 1397.  XT l-l  NS (-1  l.CO 1.11 1.17 1.22 1.25  l.CCO U.861 0.797 0.744 C.719  1.00 1.47 1.65 1. 74  6B4. 655. 632.  1.31 1.35 1.37  C.665 0.637 0.615  246.7 1441.' 2ei.9 1464.' 317.1 1477. 352.3 1480.  593. 571. 560. 555.  1.41 1.44 1.45 1.45  377.5  60C 618. 642. 654. 655. 660. 662.  1.39 1.35 1.32 1.31 1.29 1.29 1.28  60.4  4  5 6  7  8 9 10 11  12 13 14 15 16 IT IB  4C2.7  427.9 453.1 478.3 5C3.6 528. e  TABLE  1  1419. 1377. 1344. 1330. 1317. 1314. 1303.  C . l . 6  2  CYCLE NC.  4  REAL TI"E  CCNCENTRATICK BOTTOM TCP  NCYC l-l  T ISEC)  CB I PPM)  0  CO 50.2 ICO.4 150.6 2C0.E 251.0 2C1.3 351.5 401.7 451.9 5C2.I  11C0. 1347. 148C. 1544. 1587. 1603. 1617. 1620. 1617. 1617. 1615.  1 2 .3 4 5 6 7 8  9 10  TABLE  C . l . 7  I  5  1096. 851. 722. 639. 600. 574. 555. 548. 542. 535. 530.  NUMERICAL  1.440 1.4 40  1.98' 2. 11 2.23  1.240 1.240 1.2C0  1.140 1.160 1.120  C.577 0.556 0.545 0.540  2.45 2.58 2.66 2.69  l.OCO 1.040 1.C20 l.OCO  l.COO 1.000 I.000 C.960  C.5B3 0.601 0.625 0.636 0.637 0.642  2.39 2.25 2.11 2.05 2.03 2.01 1.99'  1.2P0 1.320 1.4C0 1.360 1.320 1.320 1.320  1.200 1.160 1.240 1.260 1.280 1.280 1.2B0  0.644  CF  6  0.0  1.29  l.CO 1.22 1.35 1.40 1.44 1.46 1.47 1.47 1.47 1.47  l.CCO 0.776 C659 0.5B2 0.547 0.524 0.506 0.500 0.494 0.488  1.47  0.484  EVALUATION  8  NS |-|  l.CO 1.58 2.04 2.41 2.64 2.78 2.91 2.95 2.98  3.01  3.04  OF  10  II  CURRENT EFFICIENCY El IXI  E2 IX)  12 POWER EFFICIENCY EP IXI  100.0 too.o 20.1 31.0 13.0 13.6 10.2 11.6 4.R 5.5  100.000 2.077 1.6CR 1.387 1.154  22.5 11.3 8.8  IC.3 5.2  1. 169 1.087 1.013  17.3 9.0 5.8 1.2  6.6 3.7 2.0 0.9  0.866 0.828 0.781 0.730  4.4  -20.2 -10.6 -13.3 -4.4 -10.0 -5.6 -4.3 -4.4  -2.6 -0.3  - 0 . 9 - 3 . S  -I.1 - 0 . 3  0.825 0.705 0.601 0.538 0.491 0.455 0 . 4 2 0  EXPERIMENT  7  XT (-)  1  12 IAI  CO 1.300 1.360 1.320 1.320  XB <-)  EDI-S2-16/*  CURRCNT CI At..  INK.  11 I.M  CONCENTRATION SEPARATION NORMALIZED FACTOR  CT IPPM)  9  1.520 1.4P0  < NUMERICAL EVALUATION EOl-S2-13/#2B  3  fl  7  6  CONCENTRATICN SEPARATION NORMAL IUU MCIOR  r  ISEC)  0 1 2 3  5  4  CURRENT ENR. CIAL. II |A)  0.0 l.OCO 0.960 0.920 0.880 0.860 0.840 0.840 0.840 0.840 0.840  EXPERIMENT  9  12 IA)  CO C.900 0.920 C900 C.880 C.860 C840 C.830 0.830 C.R30 0.830  1 0  11  CURRENT EFFICIENCY El E2 (X) IX)  100.0 100.0 37.8 41.T 21.3 21.5 10.7 14.3 7.3 6.7 3.0 4.6 2.6 3.5 O.S 1.2 -0.5 1.2 0 . 0 1.2 -0.5  1.0  12  POWER EFFICIENCY EP IX)  100.000 3.748 2.885 2.334 1.936 1.639 1.429 1.248 1.105 0.994 0.902  348 4  3  5  6  l  2  CYCLE NC.  REAL TIME  NCYC l-l  T (SEC)  IPI'M)  cn  CI (PPM)  XC (-)  XT l-l  0.0 83.6 167.6 251.3 335.1 418. "J 5C2.7 566.4 670.2 754.0  1C67. 1355. 1517. 1623. 1643. 1662. 1671. 1665. 1662. 1654.  1067. 784. 645. 577. 544. 526. 516. 513. SIC. 506.  I.CO 1.27 1.47 1.52 1.54 1.56 1.57 1.56 1.56 1.55  l.CCC C.735 0.605 0.541 0.51C C.493 0.484 0.481 0.478 0.476  0 1 7 3 4 5 6 7 8 9  TABLE  ' 1  CCNCENTRATICN 8CIICM 1CP  C.l. 8  4  CYCLE NC.  REAL TIME  CCNCENTRATICN 8CTTCM TCP  NCYC l-l  T (SEC)  CB CT IPPM) (PPM)  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14  0.0 81.6 163.3 244.9 326.5 4C8.2 469.8 571.4 653.1 734.7 816.3 898.0 979.6 1C61.2 1142.9  TABLE  1237. 1598. 1867. 2C68. 2227. 2344. 2418. 2477. 2507. 2551. 2566. 2561. 2590. 2599. 2608.  C.l. 9  Cl'NClNIRAI ICN SFPARATION NCHMAl l/EC fAC10H  CURRENT CNR. CIAL.  NS l-l  I.CO I.7J 2.35 2.61 3.C2 3. lb 3.24 3.24 3.76 3.25  <»  II 1AI  0.0 O.RHC 0.620 o.nco C.7RO 0.760 0.760 0.720 0.770 0.770  17 IA) CO C.740 C760 0.740 C.720 C. 700 C.700 C700 C.700 C.700  10  11  CURRENT EFFICIENCY El 111  E2 Itl  100.0 100 0 30.0 35 1 16. I 16.8 12.2 8.5 2.3 4.1 2.4 2.4 1.0 1.4 -0.7 0.3 -0.4 0.5 -l.l 0.2  12 POWFR ETF ICIENCV EP IX)  100.000 3.049 2.358 1.910 1 .575 1.279 1.093 0.945 0.834 0.742  « NUMERICAL EVALUATICN CF EXPERIMENT E0I-S2-16/* 2  3  2  8  7  1219. 955. 755. 619. 529. 464. 426. 393. 381. 366. 355. 346. 346. 342. 339.  5  6  8  7  CURRENT ENR. OIAL.  CONCENTRATION SEPARATION NORMAL 12EC FACTOR XB l-l  I.CO 1.29 1.51 1.67 1.60 1.90 1.96 2.CO 2.C3 2.C6 2.C7 2.C9 2.C9 2.10 2.11  9  XT (-)  NS l-l  11 IA)  12 IA)  l.COO 0.783 0.619 0.508 0.434 0.281 0.349 C.223 0.312 0.302 0.291 C.286 0.2e4 0.280 0.278  1.00 1.65 2.44 3.29 4.15 4.9R 5.60 6.21 6.49 6.84 7.13 7.30 7.38 7.49 7.58  0.0 0.760 0.750 0.730 0.720 0.710 0.700 0.7C0 0.7C0 0.7C0 0.700 0.7C0 0.700 0.700 0.700  CO C.720 C.700 C.700 C.700 C.700 C.700 C.700 C.700 C.700 C.700 C.700 C.700 0.700 0.700  I NUMERICAL EVALUATION OF EXPERIMENT EOI-S2-I6/I 4  10  11  CURRENT EFFICIENCY El l«)  E2 (XI  12 POKER EFFICIENCY EP (SI  100.0 100.0 100.000 44.8 34.6 2.212 33.8 26.9 1.930 26.0 18.2 1.689 20.9 12.2 1.492 15.5 e.7 1.327 9.9 5.2 1.177 7.9 4.3 1.058 4.0 1.7 0.947 6.0 1.7 0.665 2.0 1.7 0.790 2.0 0.9 0.726 1.2 0.3 0.669 1.2 0.5 0.672 1.2 0.3 0.581  349 4  9  8  10  1  2  CYCLE NO.  REAL TI»E  NCYC l-l  T ( SEC I  CB CFPf 1  CT IPPMI  XB l-l  XT l-l  NS l-l  II IA)  o.c  1264. 1344. 1408. 1466. 1514. 1564.  1749. lois. 845. 7IC.  I.CCC 0.816  0.568 0.4R6 0.424  2.04 2.47 2.92  CO 0.960 0.950 0.940 0.970 0.9CO  CO 0.900 C920  529.  I.CO 1.C6 1.11 1.16 1.20 1.24  I.CO  61.6 123.3 iei.9 246.5 3C8.2  C.900 C.860  27.9  431.4 554.7 678.C eci.2  1676. 1665. 1696. 1716.  419. 361. 322. 297.  1.29 1.32 1.34 1.36  C. 336 0.289 0.258 0.238  3.R3 4.55 5.20 5.71  0.820 o.7ec 0.740 0.700  C.800 C.760 C700 C.680  IB.8 12.6 10.5 7.1  e57.9  0 I 2 3  4 5 T  9  It 13  3  CCNCFNTRATICN BCTIC" TCP  606.  7  }  CONCCNT RATICN SEPARATION NCRMAll/EO FACTOR  0.677  I . 30 1.65  CURRENT  LNR. C I A L . 17 1 A)  C.900  CURRFN1 EFFICIENCY El Itl  100.0 31.R 31.5 73.6 31.0 18.8  41.6 25.7  514.5 lC27.e 1141.0 1254.3  1730. 1742. 1759. 1173. 1781.  284. 27C. 239. 228. 223.  1.37 1.38 1.39 1.40 1.41  C.227 0.216 0.191 C. 183 0 . 179  6.C2 6.38 7.28 7.67 7.88  0.5C0 0.5C0 0.5C0 0.5C0 0.5C0  C480 C.480 0.480 C480 C.480  27.5 22.0 16.5 13.R 8.3  23 27 29  1347.6 1534.1 1627.3  1773. 1767. 1767.  243. 252. 259.  1.40 1.40 1.40  C194 0.201 0.208  7.22 6.94 6.73  0.580 0.570 0.570  C.560 C.560 0.560  -7.1 -2.4 0.0  30 32 36  1684.0 1797.2 2C23.8  1776. 1793. 1798.  245. 231. 218.  1.40 1.42 1.42  0.196 0.185 0.175  7.16 7.67 8.15  0.490 0.460 0.450  C.440 C440 C.440  37 39 41  21C9.2 22eC.O 2450.6  1813. 1827. ie47.  213. 201. 197.  1.43 1.45 1.46  0.170 0.161 0.158  8.41 8.97 9.24  0.4C0 0.4CC 0.400  C.4G0 C.400 C.400  43 45 47 51  2533.2 2615.6 2658.C 2662.8  1824. 1618. 1815. 1815.  205. 215. 217. 219.  1.44 1.44 1.44 1.44  0.164 0.173 0.174 0.176  6.78 8.34 8.27 6.18  0.460 0.460 0.450 0.450  C.450 C.440 0.440 C.440  ,52 154 56 58  2919.4 3C32.7 3146.C 3259.2 3372.5  179C.1781. 1776. 1776.  ieic  230. 252. 264. 275. 277.  1.43 1.42 1.41 1.40 1.40  0.184 0.201 0.212 0.22C 0.222  7.79 7.03 6.65 6.38 6.32  0.300 0.260 0.280 0.260 0.2R0  C.320 C.300 C.300 C.300 C.300  TABLE  C.l.lC  J NUMERICAL EVALUATION OF EXPERIMENT E01-S2-16/* 5  E? It)  100.0  14 IS 17 19 21  to  11  14.3  11.2  17 POWFR EFFICIENCY EP Itl  100.oco 2 . 140 1.851 1.69? 1.543 1.458  8.6 4.8  1.775 1.117 1.007 0.905  2.5  0.964 0.943 0.899 0.852 0.804  3.5 2.4  2.8  3.0 1.0 0.5  -2.2  -0.5 -0.9  0.889 0.769 0.721  16.9 18.0 3.1  3.0 1.5 0.7  0.5e9 0.577 0.537  18.1 9.1 12.7  0.9 1.0 0.3  0.357 0.351 0.348  -45.1 -11.8 -6.0 0.0  -1.0 -1.4 -0.2 -0.2  0.675 0.645 0.621 0.582  -18.5 -34.6 -14.8 -9.9 0.0  -3.0 -3.4 -2.0 -1.6 -0.4  0.415 0.394 0.360 0.369 0.362  350 1  2 RIAL Jiff.  CYCLE NC.  4  3  CCNCl:N 1RAT ICN OCHCM It P  0  6  CONCENTRATION  1 SEPARATION FACIHH  T (SEC)  CR (PPM)  CT IPPMI  NUHMAL 1 1(0 XT XO l-l (-1  0 1 2 3 4  0.0 61.6 123. 3 184.9 246. 5  2435. 1263. 1 307. 1347. 1337.  1725. 1045. 90"). 793. 716.  l.CO 0.52 0.54 0.55 0.57  I.COO 0.85 1 C.742 C.647 0.584  1.00 C M 0 . 72 C . 85  6 e 10 12 .14 16  369.8 493.1 616.3 739.6 662.9 986.1  1448. 14<»C 1519. 1515. 1554. 1562.  574. 51C. 451. 413. 39C. 377.  0.59 0.61 0.62 0.63 0.64 0.64  17 18 2C 22  1C42.8 IC99.4 1212.7 1325.9  1575. 1581. 1599. 1(05.  355. 339. 32C. 306.  23 24 26 28 30  1272.6 1419.2 1512.4 16C5.7 1699.0  1605. 1602. 1597. 1594. 1591.  313. 322. 332. 337. 339.  37  2C25.4  1674. 24C.  45  2478.5  51  2758.3  NCYC (-1  TABLE  CURRENT ENR. C I A L .  11  CUKHTNT EFFICIENCY  El (tl  F2  12 POWER EFFICIENCY EP IXI  C.9f  0.0 0.760 0 . 7.'0 0.720 0.7C0  C O C.680 C.700 C.680 C660  100.0 -770. 1 31.1 27.5 28.3  100.0 33.2 24.2 21.3 14.6  IOO.OCO -13.473 -5.757 -7.639 -1.425  0.468 0.416 C.360 C.337 C.318 0.307  1.27 1.47 1.69 1.87 2.01 2.09  0.6C0 0.670 0.520 0.5C0 0.490 0.490  C.600 C560 C520 CSOO C490 C480  25.4 1 7.1 14.0 8.0 9.5 4.1  14.8 7.2 7.0 4.8 3.0 1.7  -0.333 0.053 0.239 0.305 0.351 0.347  0.65 0.65 0.66 0.66  C289 0.277 0.261 0.249  2.23 2.34 2.52 2.64  0.38C O.'iCO 0.400 0.4C0  C400 C . 380 0.370 C.370  34.1 13.0 22.7 6.5  5.2 3.8 2.5 1.8  0.422 0.434 0.468 0.461  0.66 0.66 0.66 0.65 0.65  0.256 C.263 0.271 0.275 C277  2.58 2.50 2.42 2.38 2.36  0.420 0.440 0.460 0.460 0.460  0.420 0.440 C.450 C450 C.450  0.0 -5.9 -5.6 -2.8 -2.8  -2.3 -2.6 -1.3 -0.7 -0.4  0.533 0.499 0.444 0.405 0.373  0.69 0.196  3.51  0.650  0.600  17.7  3.0  0.490  1741. 174.  0.71 0.142  5.03  0.560  0.500  14.5  1.6  0.436  1720. 217.  0.71 0.177  3.99  0.6C0  .0.540  -5.8 -1.6  C.l.11  IT)  0.418  : NUMERICAL EVALUATION OF EXPERIMENT E0I-S2-16/* 6  4  3  CYCLE NC.  REAL TIME  CCNCENTRATICN BCTTCM TCP  T ISEC)  CB CT IPPM) (PPM)  XR I-)  XT (-)  0 1 2 3 4  0.0 31.6 63.3 54.9 126.5  1242. 1257. 1263. 1273. 127e.  1251. 1148. 1099. 1060. 1027.  l.CO l.CI 1.C2 1.03 1.C3  l.COC C.918 0.8 78 C.e47 0.821  8 12 16 20 24 28 32 36 40  253.1 379.6 5C6.1 637.7 759.2 ee5.7 1CI2.2 me.e 1265.3  1305. 1376. 1337. 1347. 1352. 1 358. 1358. 1358. 1258.  933. 873. 832. 804. 784. 77C. 761. 753. 743.  1.05 1.C7 1.08 1.C8 1.C9 1.C9 I.C9 I.C9 1.C9  47  1486.7  1363.  T3I.  1.10  C.l.(2  NS I-)  10  12 (A)  2  TABLE  9  11 (A)  1  NCYC l-l  R  5  6  7  B  CCNCENTRATICN SEPARATION FACTOR NORMALIZED  9  CURRENT ENR. C I A L .  NS l-l  10  11  CURRENT EFFICIENCY E2 (X)  POWER EFFICIENCY  11 (A)  12 (A)  l.CO 1.10 1.16 1.21 1.25  0.0 1.520 1.520 1.560 1.580  0.0 1.380 1.480 1.520 1.500  100.0 l o c o 6.7 18.2 6.7 8. 1 6.6 6.2 3.2 5.4  100.000 0.441 0.381 0.346 0.306  0.745 0.698 C.665 C.642 0.627 0.615 C.608 0.602 0.594  1.41 I.53 1.62 1.68 1.74 1.78 I.BO 1.8.2 1.14  1.540 1.520 1.5C0 1.500 I.SCO 1.5C0 I.SCO I.SCO 1.500  1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 I.5CU  4.2 3.8 3.4 2.4 1.7 1.7 0.4 . 1.2 1.7 0.8 0.9 0.6 0.0 0.4 0.0 0. 3 0.0 0.4  0.240 0.203 0.171 0 . 146 0.131 0.117 0 . 103 0.093 0.0B4  0.589  I.en  i.5co  i.soo  0.9  0.074  I NUMERICAL EVALUATION CF EXPERIMENT tlll-Si-lt/t f  El It)  12  0.)  EP IXI  351  1  2  3  4  6  CYCLE KC.  REAL TIME  NCYC l-l  T ISECI  CB IPPM  CT IPPP)  X8 l - l  c  1 2 3 4 5  CO 31.6 63.3 54.9 126.5 158.2  1226. 1247. 1263. 1278. 1254. 1305.  1238. 1142. 1104. 1076. 105C. 1C31.  l.CO 1.C2 I.C3 I.C4 1.C6 1.C6  1.000 C922 0.892 0.e69 0.648 0.832  1C 15 2C 25 3C  316.3 474.5 632.7 790.8 549.0  1347. 1360. 1366. 1368. 1344.  965. 931. 909. 897. 884.  I.10 1.11 1.12 1.10  32 35 4C 45 50  1C12.2 11C7.1 1265.3 1423.5 1561.6  1405. 1440. 1472. 1485. 1496.  52 56 60 65  17C2.4 1S44.C 2185.6 2487.7  67 70 75 60  2550.9 2645.8 2eC4.C 2962.1  TABLE  CCNCENTRATICN 8GT1CM TCP  5  7  8  CONCENTRATION SEPARATION NCRPALUEO FACTOR  CURRENT CNR. CIAL.  11  CURRENT EFFICIENCY E2 IXI  POKER EFFICIENCY  1.00 I. 10 1. 16 1.20 1.25 1.28  0.0 1.320 1.340 1.360 1.380 1.390  CO 1.280 1.340 1.350 1.360 1.37.0  0.779 0.752 C.734 0.724 0.714  1.41 1.48 1.52 1.54 1.54  1.420 1.420 l;420 1.420 .1.420  1.400 1.400 1.400 1.400 1.400  1.4 0.5 0.2 0.1 -0.8  2.3 1.2 0.8 0.4 0.4  0. 184 0.137 0.109 0.090 0.073  862. 835. 806. 791. T8C  1.15 0.696 1.17 .0.674 1.20 0.651 1.21 0.639 1.22 0.630  1.65 1.74 1.84 1.90 1.94  1.620 1.640 1.640 1.640 1.640  1.580 1.600 1.600 1.600 1.600  4.6 1.7 0.9 0.4 0.3  1.7 1.4 0.9 0.5 0.3  0.080 0.081 0.076 0.070 0.064  1645. 1795. 1SIC. 1962.  686. 581. 537. 519.  1.34 1.46 1.56 1.60  0.554 0.469 0.433 0.419  2.42 3.12 3.60 3.82  1.080 l.COO 0.960 0.96C  1.160 1.130 1.100 1.100  8.8 4.8 3.3 1.4  5.2 3.0 1.3 0.4  0.044 0.052 0.056 0.056  1822. 1696. 1594. 1546.  581. 658. 722. 742.  1.49 1.28 1.30 1.26  0.469 0.531 0.583 0.599  3.17 2.60 2.23 2.11  1.6C0 1.620 1.620 1.620  1.520 1.560 1.560 1.560  -10.6 -6.1 -3.0 -1.4  -5.0 -4.0 -2.0 -C.6  0.089 0.071 0.055 0.047  t NUMERICAL EVALUATION OF EXPERIMENT ECl-52-U/t 6  El Itl  12  12 IAI  C.l.13  NS 1-1  10  II IA)  l.ll  XT (-1  9  100.0 100.0 3.9 18.4 2.9 6.8 2.8 5.1 2.8 4.6 1.8 3.4  EP IXI  IOO.OCO 0.535 0.398 0.336 0.302 0.270  352 10  CCNCFNTRATICN BCITCM TCP  CYCLE NC.  HEAL 1I*E  NCYC l-l  T I SEC I  IFPMI  0.0 51.9 103.8 155.6 2C7.5 259. 4 311.3 363. 1 415.C 466.9 518.8 570.7 622.5 674.4  I20C. 1184. 1202. 993. 1381. 903. 845. 14'.2. 806. 1466. 1517. 77 7. 1 5 35. 755. 742. 1546. 1551. 733. 1551. 725. 1554. 72C. 715. 1554. 711. 1551. 707. 1546.  773.5 872.5 571.6 1C70.6 1169.7 1268.8  16 34. 1688. 1714. 1741. 1752. 1754.  1320.6 1272.5 1424.4 1476.3 1528.1 158C.C 1621.9 1663.8 1735.7 1787.5  1674. 1621. 1566. 1562. 1541. 153C. 1522. 1517. 1511. 15C6.  0 1 2 3 5 6  T 8 9 ic ii 12 13  14 15 16 17 18 19  20 21 22 23 24 25 26 27 28 29  v  TABLE  1' CYCLE NC. NCYC l-l  cn  C.l.14  2  t2 ITI  EP Itl  l.CCC 0.828 C.753 C.704 C.672 0.647 C.629 o.6ie 0.611 C.604 0.6CC 0.596 C.592 0.589  I.CO 1.33 1.55 1. 73 I.FT I .98 2.06 2. It 2. 15 2.17 2.19 2.20 2.21 2.22  0.0 1.0«0 1.160 1.180 1 .2C0 1.2C0 1.2C0 1.240 1.240 1.240 1.240 1.240 1.240 1.240  CO 1 . 160 1.240 1.260 1.280 1.2*0 1.230 1.280 1.280 1.280 1.280 1.280 1.280 1.280  636. 593. 56e. 553. 542. 537.  1.38 1.43 1.45 1.47 1.48 1.48  C53C 0.495 0.473 0.461 0.452 0.447  2.60 2.88 3.06 3.19 3.28 3.31  0.760 0.780 0.8C0 0.8C0 0.8C0 O.BCO  C.900 C.9C0 C.880 C.880 C.880 C.BBO  9.0 5.3 2.6 2.6 1.0 0.3  6.1 3.7 2.3 1.3 1.0 0.5  0.166 0. 173 0.173 0.172 0.168 0. 162  587. 626. 645. 662. 670. 673. 675. 675. 676. 677.  1.41 1.37 1.34 1.32 1.30 1.29 1.29 1.28 1.28 1.27  0.4B9 0.522 C.538 0.552 0.556 0.561 0.562 0.562 0.563 C.S65  2.89 2.63 2.49 2.39 2.33 2.30 2.79 2.28 2.27 2.25  1.160 1.180 1.2C0 1.2C0 1.2C0 1.2G0 1.2C0 1.2C0 1.200 1.200  1.200 1.220 1.240 1.240 1.240 1.240 1.240 1.240 1.240 1.240  -10.3 -6.T -4.3 -3.0 -2.6 -1.3 -1.0 -0.7 -0.7 -0.7  -6.2 -4.7 -2.3 -2.0 -C.9 -0.5 -0.2 0.0 -0.2 -0.2  0.262 0.228 0.205 0.167 0.173 0. 162 0.154 0.147 0.140 0.134  4  CCNCENTRATICN 8CTT0M TCP  5  6  7  8  CCNCENTRATICN SEPARATION NORMALIZED FACTOR  CT IPPMI  XB l-l  0.0 46.4 52.9 139.3 ie5.7 222.1 225.0 371.4 417.8 464.3  ICCC 1C89. 1155. 1209. 1239. 1264. 1278. 1286. .1292. 12-17. 1297.  1006. 686. eoi. 746. 708. 681. 659. 644. 632. 623. 619.  I.CO I.C9 1.15 1.21 1.24 1.26 1.28 1.29 1.29 1.30 1.30  557.1 650.0 747.8 835.7  1295. 1289. 1786. 1786.  605. 602. 596. 591.  1.29 1.29 1.79 1.29  C.1.15  El  l.CC 1. 10 1. 17 1.22 1.26 1.28 1.3C 1.31 1.31 1.31 1.31 1.31 1.31 1.31  CB IFPM)  TABLE  12 IAI  POWER EFFICIENCY  NS l-l  X8 l-l  II IAI  CURRTNT EFFICIENCY  I-)  CT IPPM)  T ISECI  278.6  XT  CURRENT ' ENR. CIAL.  12  111  100.0 l o c o 16.3 26.4 10.1 ICS 7.7 6.8 5.6 4.5 3.6 3.4 2.5 2. I 1.3 1.5 0.6 1.0 0.0 0.9 0.3 0.6 0.0 0.6 -0.3 0.4 -0.6 C.4  100.000 1.470 1.101 0.901 0.761 0.657 0.575 0.5C5 0.448 0.401 0.363 0.331 0.304 0.280  t NUMERICAL EVALUATION OF EXPERIMENT ED1-S2-16/* 9  3  REAL TIME  CCNCFNTRATICN SCPARATION NCRMALI7EC FACTOR  II  XT l - l  9  CURRENT ENR. CIAL.  NS l-l  11 (Al  12 IA)  l.CCC 0.681 0.796 C744 0.704 C.677 0.655 0.640 0.628 0.619 0.615  I.CO 1.24 1.45 1.63 1.76 1.67 1.95 2.01 2.06 7.10 2.11  0.0 0.940 l.CCO 0.970 0.930 0.950 0.950 0.950 0.950 0.950 0.950  CO 0.950 C.980 C980 C.970 C970 C.950 C.950 C950 C.950 0.950  0.601 0.599 0.592 0.587 /  7. 15 2.15 7. 17 7.19  . 0.950 0.950 0.950 0.950  C.950 C.950 C.950 0.950  I NUMERICAL CVHUAI1CN CF EXPERIMENT *UI-5!-l7/tl5  10  11  CURRENT EFFICIENCY El IX)  E2 It)  100.0 t o c o 22.0 29.2 15.1 2C. 1 13.0 12.5 7.5 9.5 6.0 6.5 3.3 5.3 3.8 2.0 1.3 2.8 1.3 7.2 0.0 0.9 -0.3  1.7  -0.7  0.3  - 0 . 3 0 . 0  0.8 0 . 6  12 POWER EFFICIENCY EP (X)  100.000 2.709 2.308 2.003 1.742 1.532 1.359 1.213 1.092 0.993 0.900 0.765 0.654 0.576 0.516  353 1  2  3  *  6  7  8  REAL TIME  NCYC l-l  T ISECI  CP IPPf|  CT (PPM)  XC (-)  0 I 2 3 4 5 6 7 8 9 lb  0.0 46.4 52.9 139.3 185.7 237.1 218.6 325.C 371.4 417.8 464.3  573. 1C57. 1122. 11 35. 1196. 1718. 1234. 1239. 1245. 1245. 1245.  977. 848. 78C. 73C. 694. 666 . 6«e. 632. 622. 613. 609.  I.CO 1.C9 I . 15 1.17 1.23 1.25 1.27 1.27 1.28 1.28 1.28  l.CCO 0.868 0. 799 C.748 C.711 0.682 0.663 C.647 0.637 0.627 0.624  I.CO 1.75 1.44 1.56 1.73 1.H4 1.91 1.97 2.01 2.04 2.05  0.0 . 1.006 0.9P2 0.917 0.91 I 0.948 0.9O5 0.926 0.926 0.894 0.926  12 14 16 18  557.1 65C.C 742. e 835.7  1245. 1239. 1234. 1234.  596. 593. 587. 584.  1.28 1.27 1.27 1.27  0.61C 0.608 0.601 0.598  2. 10 2. 10 2.11 2.12  0.694 0.863 0.894 0.698  TABLE  C.l.16  1  2  CYCLE NO.  REAL TIME  NCYC l-l  0 1 2 3 4 5 6 7 6 9 10 12 14 16 18  CCNCFNIRA IICN PCTTCM TCP  5  CYCLE NC.  CONCENTRAtICN SEPARATION NORMALI ZEC MCIUR  4  CCNCENTRATICN BOTTOM TCP  5  CB (PPM)  CT IPPMI  xe l-l  CO 63.6 127.6 191.3 255.1 318.9 J62.7 446.4 ' 510.2 574.0 637.8  997. 1054; 1C97. 1127. 1152. 1168. 1162. 119C. 1196. 1201. 1207.  toos. 916. 869. 335. 806. 784. 766. 752. 743. 735. 729.  1209. 1207. 1207. 1204.  722. 712. 71C. 704.  C.l.17  II IAI  6  7  8  CCNCENTRATICN SEPARATION NORMALIZED FACTOR  T (SEC)  TABLE  NS l - l  12 IA)  CO C926 C999 C991 C.16'1  C965 C.948 C926 C.948 C.926 C.905  C.905 C.905 C894 C.894  10  tl  CURRENT EFFICUNCY  12 POWER EFFICIFNC Y  El E2 EP I t l It) ( t l  100.0 100.0 19.3 37.7 15.3 15.5 3.4 11.7 14.3 6.6 5.3 6.8 4.2 4.4 1.4 3.9 1.4 2.5 0.0 2.3 0.0 1.0  100.000 7.744 2.213 1.766 1 .646 1.453 1.296 1.158 1.042 0.945 0.859  0.0 -0.7 -0.7 0.0  1.6 0.3 0.8 0.3  0.737 0.634 0.559 0.500  10  11  12  I NUMERICAL EVALUATION CF EXPERIMENT ECI-S3-12/»16  3  765.3 e92.9 1C20.4 1148.C  XT |-|  9  CIRRtNT t NR. CIAL.  9  CURRENT ENR. CIAL.  XT l-l  NS l-l  11 (A)  12 IAI  I.CO 1.C6 1. 10 1.13 t . 16 1.17 1.19 1.19 1.20 1.20 1.21  l.CCO 0.911 0.865 0.631 0.602 C.780 C.764 0.748 0.739 C.732 0.725  I.CO 1.16 1.27 1.36 1.44 1.50 1.55 1.60 1.62 1.65 1.67  0.0 0.560 0.570 0.560 0.520 0.510 0.570 C570 0.520 0.520 0.520  CO C500 C.550 C.560 C.550 0.540 C.540 C540 C540 C.540 0.540  1.21 1.21 1.21 1.21  0.719 C.709 0.706 0.701  1.69 l.Tl 1.71 1.72  0.520 0.520 0.520 0.520  0.540 C.540 0.540 0.540  > NUMERICAL EVALUATION CF EXPERIMCNT EOI-S3-I2/M?  CURRFNT EFFICIENCY El Itl  E2 Itl  100.0 100.0 17.1 29.9 12.8 14.2 9.0 1 C 5 7.9 8.7 5.4 6.8 4.4 5.2 2.7 4.8 1.8 2.8 1.8 2.4 l.B 2.0 0.4 -0.4 0.0 -0.4  1.0 1.6 0.4 C.8  POWER EFFIC1EI EP (t)  100.000 4.782 3.642 3.261 2.9C9 2.607 2.355 2.141 1.940 1.778 1.643 1.399 1.220 1.075 0.961  354 1  2  3  4  Rf AL IIPE  NCYC (-J  T (SEC I  CD (PI'PI  0 1 2 3 4 5 6 7 e 9 io  CC 63.8 127.6 191.3 255.1 318.9 3E2.7 446.4 510.2 574.0 637. e  1081. 1C81. 942. 1185. 855. 1264. 795. 1 322. 749. 1 366. 717. 1397. 697. 1411. 679. 1422. 14 3 C 666. 658. 14 3 3. 649. 142 3.  l.CC 1. 10 1.17 1.22 1.26 1.29 1.3C 1.22 1.22 1.23 1.33  12 14 16 18  765.3 ES2.9 1C20.4 1146.0  64C 633. 63C 624.  1.33 1.32 1.32 1.32  TABLE  Cf NC E-NTRAT ICN HCTICP TCP  5  CYCLE NC.  1433. 1427. 1427. 1425.  C.l.18  CT (PPPI  6  XR l - l  XT l - l  12 <*>  i .ceo ce7i 0.791 C735 C693 C663 0.644 C628 C6I6 0.6C9 C.600  l.CO 1.7b 1.48 1.66 1.S2 1.95 2.03 2. 10 2.15 2.18 2.21  0.0 0.975 0.925 0.878 0.886 0.867 0.870 0.862 0.867 0.855 0.823  CO C. 994 C.941 C.879 C.90t C.P5S C.905 C878 C.878 C.8T8 C.902  0.592 0.586 0.582 0.576  2.24 2.25 2.27 2.28  0.855 o.ei2 0.839 0.828  C.870 C.878 C.87B C.847  10  Jl  CURRENT EFFICIENCY El <*>  F2  1 , 1  12 PnwtR EFFICIENCY EPm  100.0 100.0 18.8 26.2 14.5 15.4 11.1 11.6 8.4 8.3 5.9 6.3 2.T 3.8 2.2 3.5 1.6 2.5 0.5 1.5 0.0 1.7  100.000 2.427 2.019 1.765 1.553 1.383 1.214 l.OBR 0.982 0.888 0.811  0.0 -0.6 0.0 -0.3  0.9 0.6 0.4 O.S  0.687 0.593 0.523 0.469  10  11  12  t NUMERICAL EVALUATION CF EXPERIMENT E0I-S3-12/«18  3  CYCLE NC.  REAL TIME  4  NCYC (-1  T (SEC)  CB (PPM)  CT IPPM)  XB (-)  XT (-)  CO 63.8 127.6 191.3 255.1 318.9 282.7 446.4 510.2 574.0 637.8 7C1.5 765.3 629.1 852.9 556.6 1C20.4  119C. 1270. 1366. 143C. 1475. 1511. 1539. 1556. 1570. 1578. 1507. 1592. 1595. 159B. 1598. 1601. 1601.  1174.  l.CO 1.C7 1.15 1.20 1.24 1.27 1.29 1.31 1.32 1.33 1.23 1.34 1.34 1.24 1.34 1.34 1.34  l.CCC 0.835 C.736 0.665 0.610 0.571 0.542 0.519 0.504 0.495 0.489 0.486 0.481 C47e 0.474 0.473 0.473  CCNCENTRATICN BCT1CM TCP  C.l.19  9  CURRENT ENR. C I A L . II l»l  2  TABLE  8  NS l - l  1  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  7  CPNCKNIHAI ICN SEPARATION NORMALIZED FAC10R  9ec  864. 78C. 716. 671. 636. 609. 592. 581. 574. 57C. 565. 561. 556. 555. 555.  5  C  7  8  CCNCENTRATICN SEPARATION NORMALIZED FACTOR  CURRENT ENR. C I A L .  NS l - l  l.CO  1.28  1.56 1.81 2.03 2.22 2.39 2.52 2.61 2.68 2.73 2.75 2.78 2.81 2.B3 2.05 2.85  9  II (A)  12 (Al  0.0 1.207 1.192 1.149 1.160 1.098 1.098 1.105 1.058 1.058 1.058 1.058 1.058 1.058 1.058 1.058 1.058  CO 1. 105 1.184 1.145 1.093 1.098 1.082 1.058 1.066 1.058 1.058 1.058 1.058 1.058 1.058 1.058 1.058  < NUMERICAL EVALUATICN CF EXPERIMENT EDI-S3-l2/f19  CURRENT EFFICIENCY El IXI  E2 (XI  100.0 10C.0 11.1 29.4 13.6 16.5 9.3 12.3 6.5 9.9 5.6 6.9 5.4 4.3 4.3 2.6 2.6 2.2 1.8 1.3 1.3 1.0 0.9 0.6 0.4 0.8 0.4 0.6 0.8 0.0 0.4 0.2 0.0 0.0  POWER EFFICIENCY EP IXI  100.000 1.503 1.290 1.123 0.994 0.890 0.804 0.729 0.663 0.606 0.556 0.512 0.475 0.442 0.414 0.389 0.365  355  10 CCNCFNTRATICN BCTICM TUP  REAL  NCYC l-l  T ISCCI  CH (PPMI  CI (PPMI  I- I  0.0 53.4 1C6.9 160.3 213.6 267.2 320-7 374. 1 427.6 481. C 534.4  1174. 1764. 1 375. I486. 1596. 17 I C . 1824. 191C. 2C25. 2111. 2213.  1160. 1122. 106P. 1007. 951. 897. 844. 791. 746. 703. 663.  l.CO 1.08 1.17 1.77 1.36 1.46 1.55 1.63 1.72 i.eo 1.89  l.CCC 0.968 C.921 0.669 0.820 C.773 0.777 0.682 0.643 C.6C6 0.572  0 1 7 3 4 5 6 7 a 9 >  c  CURRENT ENR. C I A L .  CONCENTRATION S E P A R A T I O N NORMALIZED FACTOR  CYCLE NC.  XT (-1  NS l-l  II  (Al  17 IAI  1.27 1.46 1.66 1.89 7. 14 2. 19 2.68 2.97 3 . 30  0.0 1.067 1.C10 0.997 0.971 0.964 0.889 0.8E9 0.889 0.851 0.842  CO C T(U. CB70 C061 C.842 C823 C870 C851 C.H23 C814 C 795  t.co  t.u  II  CURRENT EFFICIENCY El (Tl  T7  (tl  100.0 10C.0 1 7.0 9.6 21.9 12.5 22.5 14. 1 73.1 13.5 23.5 13.2 25.6 12.2 19.3 12.5 25.9 11.0 70.4 1C.5 24.2 IC. 1  I7 POWF'R EFFICILNCY EP (tl  100.ooo 0.272 0.291 0.303 0 . 3C8 0.312 0.314 0.3C9 0.311 0.306 0.305  12 14 16 ie 20  641.3 748.2 ess. 1 962.C 1C68.9  2389. 2536. 2679. 2644. 2959.  591. 533. 484. 442. 406.  2.03 2. 16 2.28 2.42 2.52  0.509 C.459 0.417 0.382 C.35C  3.99 4.70 5.47 6.35 7.20  0.814 0.795 0.777 0.748 0.730  0.777 C758 C739 C730 C.711  71.7 18.6 18.5 22.1 15.8  9.3 7.7 6.7 5.7 5.1  0.299 0.290 0.281 0.276 0.267  25 30 35 40 45 50  1336.1 16C3.3 U70.5 2137.8 24C5.C 2672.2  3155. 327e. 3349. 3426. 3467. 3501.  342. 303. 277. 262. 252. 245.  2.69 2.79 2.85 2.92 2.55 2.58  C.295 0.261 0.239 0.226 0.217 0.211  9.12 10.68 11.93 12.93 13.62 14.11  0.711 0.692 0.683 0.603 0.683 0.683  C692 C674 C664 0.664 0.664 C.664  11.0 7.1 4.2 4.6 2.4 2.0  3.7 2.3 1.6 0.9 0.6 0.4  0.242 0.218 0.197 0.180 0.164 0.151  10  u  TABLE  1  2  CYCLE NC. NCYC i-1  0 1 2 3 4  5 6 7 6 9 IC 11 12 13 14 15 16 IT 18 19 20  3  REAL TI"E T (SECT  0.0 73.e 147.6 221.3 295. 1 368.9 442.7 516.4 590.2 664.0 737.8 611.5 685.3 959.1 1C32.9 UC6.6 neo.4 1254.2 1328.0 14C1.T 1475.5  tABIE  » NUMERICAL EVALUATION CF EXPERIMENT ED1-S3-I2/<2C  C.1.2C  4  CCNCENTRATICN BCITOM TCP CB (FPM1  CT (PPMI  1237. 1231. 1024. 1405. 1525. 903. 823. 1606. 1662. 76e. 725. 1696. 697. 1716. 677. 1759. 1764. 664. 1764. 658. 1764. 651. 645. 1761. 1759. 642. 640. 1753. 1750. 637. 1744. 633. 1739. 631. 63C. 17 3 3 . 1 727. 628. 627. 1722. 1716. 626.  C.l.21  5  «  8  .7  CCNCENTRATICN SEPARATION FACTOR NORMALIZED XB <-!  l.CO 1.14 1.23 1.30 1.34 1.37 1.39 1.42 1.43 1.43 1.43 1.42 1.42 1.42 1.42 1.41 1.41 1.40 1.40 1.39 1.39  XT (-1  l.COC 0.632 0.734 0.669 0.624 0.589 C.566 0.55C 0.540 0.535 0.529 0.524 0.522 0.520 0.518 0.515 C513 0.512 0.510 0.509 0.508  CURRENT ENR. C I A L .  NS (-1  l.CO 1.37 1.68 1.94 2.16 2.33 2.45 2.58 2.64 2.67 2.69 2.72 2.72 2.71 2.73 2.74 2.74 2.74 2.74 2. 7) 2.71  9  11 IAI  12 (Al  0.0 0.942 0.922 0.895  0.0 C922 0.949 C.930 C.910 C895 C895 C681 0.881 0.874 C867 C.B61 0.854 C.854 C.847 C.840 C840 C.834 0.834 C.H34 C.827  O.ePl  0.867 0.847 0.849 0.840 0.827 0.834 0.R34 0.827 0.877 0.627 0.H20 0.813 0.813 0.RI3 0.813 0.P06  1 NUMERICAL [VALUATION CF EXPERIMENT E0I-SJ-12/»2I  CURRENT EFFICIENCY El (tl  E7 ( t l  100.0 100.0 26.0 32.6 18.9 IE.6 13.2 12.5 9.3 8.9 5.7 6.9 3.4 4.6 7.3 3.2 1.0 2.1 0.0 1. 1 0.0 1.1 -0.5 1.1 -0.5 0.4 -1.0 0.4 -0.5 0.4 -1.0 0.7 -1.0 0.4 -1.0 C.2 -1.0 0.2 0.7 -1.0 -1.0 0.2  12 POWER EFFICIENCY EP Itl  100.000 3.150 2.570 2.176 1.882 1.650 1.455 1.330 1.191 1.071 0.974 0.893 0.622 0.759 0.707 0.662 0.621 0.5e4 0.551 0.521 0.495  356  to CYCLE KC. NCYC l-l  REAI. TI ft T ISECI  CC e3.e 167.6 251.3 3 35.1 Aia.9 5C2.7 5C6.4 670.2 754.C 827.8 521.5 1CC5.3 ices. 1 1172.9 1256.6 1340.4 1424.2  0 1 2 3 4 5 6 7 8 9  tc  11 17 13 14 15 16 17  TABLE  CCNCENTRAT ICN BCT1CM TCP  cn  ci  (ppM I  |PPf>)  1197. 1201. 974. 1416. 837. 1564. 749. 1657. 669. 1719. 1 753. 651. 1779. 632. 614. 1797. 604. 1796. 597. 1798. 593. 1798. 592. 179B. 591. 1796. 59C 1796. 1 792. 588. 586. 1790. 587. 1787. 586. 1784.  C.1.22  CONCENTRATION SEPARATION NORMAL I7CO MCIOR  XR  XT l-l  NS «-»  II IAI  12 IAI  I.CO 1.18 1.30 1. 38 1.43 1.46 1.48 1.49 1.49 1.50 1.50 1.5C 1.49 1.49 1.49 1.49 1.49 1.49  l.CCC C.ei4 0.699 C626 0.575 0.544 0.528 0.513 0.504 0.499 0.496 C495 0.494 0.492 0.491 0.491 0.490 0.489  1.00 1.45 l.*6 2.20 2.49 2.68 2.30 2.90 2.96 3.00 3.02 3.03 3.03 3.04 3.04 3.03 3.03 3.04  0.0 O.etb 0.878 0.797 0.768 0.764 0.753 0.752 0.757 0-746 0.746 0.740 0.740 0.740 0.740 0.740 0.740 0.740  CO C.794 C834 C.flO) C790 C7H8 C.776 C.764 C.758 C.752 C.752 C.746 C.746 C.746 C.746 C.746 0.746 0.746  l-l  S  2  CYCLE NC.  REAL TIME  NCYC l-l  T ISEC)  CB IFPMI  CT IPPMI  NORMAL 11 EC XB XT (-1 I-)  0.0 93. e 167.6 261.3 375.1 468.9 562.7 656.4 750.2 644.0 937.8 1C21.5 1125.3 1219.1 1312.9 14C6.6 15C0.4  1198. 1452. 1598. 1694. 1750. 1787. 1613. 1621. 163C 1630. 183C.  1196. 955. 809. 716. 662. 622. 602. 588. 575. 571. 569. 568. 565. 564. 562. 561. 561.  I.CO 1.21 1.33 1.41 1.46 1.49 1.51 1.52 1.53 1.53 1.53 1.53 1.52 1.52 1.52 1.52 1.52  a  9 10 11 12 13 14 15 16  TABLE  3  4  CCNCENTRATICN BOTTCM TOP  ieso.  1627. 1624. 1621. 1621. 1818.  C.I.23  CURRENT tFTICICNCY  El Itl  E2 Itl  100.0 1 0 C 0 36.0 30.8 27.9 71.0 14.9 13.9 10.1 9.0 5.7 6. 1 3.2 4.) 3.0 1.5 1.7 1.5 0.5 1. 1 0.7 0.0 0.0 0.2 -0.5 C.2 0.0 C.2 0.2 -0.5 -0.5 CO -0.5 0.2 -0.5 0.2  12 POWtR EFFICIENCY EP Itl  100.000  3.564  2.954 2.495 2.151  1.661  1.628 1.440 1.789 1. 162 1.054 0.964 o.se6 0.822 0.764 0.713 0.670 0.631  t NUMERICAL EVALUATICN CF EXPERIMENT E01-S3-12/I22  1  0 1 2 3 4 5 6 7  CURRCNT CNR. C I A L .  It  6  a  7  CONCENTRATICN SEPARATION FACTOR  l.CCC 0.798 0.676 0.599 0.553 0.520 C.504 0.492 0.481 C478 C.476 0.475 0.477 C.471 0.470 0.469 0.469  9  CURRENT ENR. C I A L .  NS l-l  11 IAI  12 IA)  1.00 1.52 1.97 2.36 2.64 2.87 3.00 3.09 3.17 3.20 3.21 3.22 3.23 3.23 3.23 3.24 3.23  0.0 0.8C0 0.752 0.746 0.704 0.693 0.672 0.677 0.682 0.6e2 0.668  CO C761 C.754 C.704 C.714 C717 C.72S C.714 0.698 C682 C.688 C688 C.688 C.688 C.688 C.688 C.68B  0.668 0.668 0.668 o.6ee 0.668  o.6ea  t NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-12/123  10  11  CURRENT EFFICIENCY El Itl  E2 IX)  100.0 100.0 36.3 36.2 22.1 22.1 14.7 15.1 8.7 9.2 6.1 6.4 4.4 3.1 1.4 2.3 1.4 2.1 CO 0.6 0.4 0.0 0.0 0.2 C.4 -0.5 -0.5 0.2 -0.5 0.2 0.0 0.2 -0.5 0.0  12 POWER EFFICIENCY EP 1X1  100.000 3.874 3.131 2.637 2.237 1.937 1.690 1.487 1.332 1.195 1.082 0.968 0.908 0.839 0.780 0.730 0.684  357 10 CYCLE NC.  RT At I I ME  CCNCENTRAT ICN' BCITC TCP  XT  11 7 9 .  1171.  1 .CO  1 .CCC  I.CO  1032. 98C.  I.C3  n.POl  1.1 7  C O  1  55.0  5 6  2 74.9  1218. 125C. 12 7 8 . 13CC 1314.  325.9  1 325.  7  384.8  1333.  439.8  1 3 39. 1344. 1347.  11  494.8 549.8 6C4.7  12  459.7  1375. 1347.  13  714.7  1344.  8 9 1C  169.7 824.6  14  IS  TABLE  ENR. CIAL.  (-1  0  3 4  CURRTNT  IACTI1R  XP  (FI'K)  1 I C C 144.9 219.9  SEPARATION  (-1  CI  (SCO  2  NCR«ALI/EC  (PPM)  CB  T  NCYC (-1  CONCENTRATION  1344. 1344.  C.1.24  NS (-1  (I  (Al  I 7 IAI  100.0 6.9 5.9 4.9  10C.0 24.9  t . C ' l 1.07}  1 . 128 1. 12H 1.119 1.119  1.5  947. 915.  1.C8 1. 10  C 804 C.781  o«je.  1.11  C.767  88C. 867.  1.12 1.13  0.751  1.50  1.073 1.073  C.74C  1.53  1.C73  1.119  858. 849.  1.14 1.14  841. 835.  1.14 1.17  831. 828. 824.  1.14 1.14 1.14  it)  I.C«1  1.77 1. 35 1.41 1.45  823.  itl  1.110  C.637  1.14  ti  C O  1.C6  •  EFFICIENCY  n.o t.ii'/i  1.091  CYCLE NC. NCYC (-1  0 1 2 3 4 5  T ISECI  0.0 53.1  1245. 1542.  CT  (PPM)  4.0  1.290 1.067 0.918  2.5  2.9  0.793  7.0  3. 1  0.708  2.2  0.636 0.575  1.C73  1.119  1.0  1.6  1.119  0.527  1.59  1.0 0.5  1.6  C.718  1.073 1.073  1.3  C.713 C.709  1.64  1.073  1.61  1.073 1.073 1.073  5.0 -5.0  1.1 0.7  0.484 0.469  1.61  C.7C7 C.704  1.62 1.62  C.703  OF  1.073  1.137 1.119 1.119 1. 1 1 9 1.137 1.119  -0.5  0.0 0.0  CCNCENTRATICN NORMALIZED  XT I-)  xe (-)  CURRENT ENR. C I A L .  SEPARATION FACTOR  NS l-l  II IA)  12 IA)  1238.  I.CO  l.CCC  I.CO  0.0  C O  943.  1.24  0.761  1.63  0.918  C 7 6 4  756.  1.40  C 6 1 C  2.29  0.821  C.773  631.  1.50  0.509  2.94  0.752  C.709  555.  1.57  0.448  3.50  0.735  C.719  507.  1.61  C.409  3.93  0.741  C.698 C.69?  745. 1 828.3 931 . 4  558.9 657.0  477.  1.64  C 3 8 5  4.24  0.746  458.  1.65  0.370  4.47  0.725  446.  1.67  C.360  4.63  0.735  0.676  2085.  444.  1.67  C.358  4.67  0.730  C.687  439.  1.68  C.354  4.74  0.730  C.676  436.  1.68  C.352  4.78  0.725  C 6 7 6  435.  1.69  C.251  4.80  0.775  C.6TI  435.  1.69  0.251  4.00  0.775  C.671  432.  1.69  0.249  4.84  0.775  C.671  428.  1.69  C  346  4.89  0.775  0.671  II  1C24.6  12 13 14 15 16 17 18 19  1117.7  2C91. 2C97. 21CC.  1210.9  21CC.  13C4.0  2103. 2105. 2105. 2108. 2ioe. 2108.  1257.2 1490.3 1583.4 1676.6 1169.7  TABLE  C.I.2S  I  C.687  427.  1.69  0.345  4.90  0.775  C.671  43C.  1.69  0.347  4.68  0.725  C.671  431.  1.69  0.348  4.87  0.725  C.671  432.  1.69  0.249  4.85  0. 775  C.671  NUMERICAL EVALUATION OF EOI-Sl-IJ/» I  0.412  C.4  0.380  O.T  0.356  0.2  0.333  EXPERIMENT  ie67. 1953. 2C04. 2C36. 2C59. 2C76.  7  1.777  1.57  1739.  465.7  100.OCO  1.55  186.3 272.6  TP Itl  C.732  279.4  6  e 9 10  CB IPPMI  CTFICIFNCV  0.725  I NUMERICAL EVALUATION EDl-S3-l2/«24  CCNCENTRATICN BOTTOM TCP  I 7 POWER  9. 1 6.7 4.7  10 REAL TIME  II  CURRENT  EXPERIMENT  11  CURRENT EFFICIENCY El It)  E2 IX)  100.0 32.6 24.2 17.2 11.8 7.0 4.3 3.2 2.4 1.2 0.8 0.8 0.4 0.0 0.4 0.4 0.0 0.4 0.0 0.0  10C.0 39.0 24.4 17.8 1C.7 6.9 4.3 2.8 1.7 0.4 C.8 0.4 C.2 0.0 0.4 0.6 0.2 -C.4 -0.2 -0.2  12  POWER EFFICIENCY EP IXI  100.000 3.709 3.132 2.731 2.366 2.059 1.805 1.605 1.440 1.295 1.180 1.082 0.999 0.925 0.864 0.812 0.764 0.720 0.681 0.645  358 I7  to CYCLE NC. NCYC l-l  REAL 11 »»E  (SEC)  0  0.0 70.6 141.2 2ii. a 282.4 353. 1 473.7 494.3 564.9 635.5 7C6.1 776.7  I 2 3 4 5 6 7 8 9  IC 11 12 13  e47.3 518.0 968.6 1C59.2 1129.8 17C0.4 1211.C  14 15 16 17 16  TABLE  1  CCNCENTRATICN UCTIGM TCP  CP IFPM)  1256. 14 7 5 . 164C. 1761. If 4 7 . 1501. 1541. 1567. 1S84. 1993. 1596. 2C01. 2C1C. 2C13. 2C16. 2C16. 2C13. 2C1C.  2C1C.  C.1.26  CYCLE NC.  PEAL TIME  CT  XT  IPPM)  124C. 993. 839. 731. 654. 606. 068. 542. 526. 516. 51C. 506. 498. 497. 495. 495. 491. 493. 493.  t-l  l.CO 1.1 7 1.31 1.40 1.47 1.51 1.55 1.57 1.58 1.59 1.59 1.59 1.60 1.60 1.61 1.61 1.60 1.60  l.CCO 0.801 0.676 0.591 0.528 0.489 C.458 0.437 0.425 0.416 C.4I 1 0.408 C.4C2 C.401 0.4C0 0.4CC C.396  1.60  0.396  4  CCNCENTRATICN BOTTOM TCP  5  0.0 1.017 0.963 C.975 0.897 0.99? 0.881 0.864 0.861 0.857 0.H50 O.HSO 0.850 0.850 0.850 0.850 0.85C 0.850  CO C946 C984 C.947 C.913 C.892 C.871 C»75 C.H7? C.864 C.850 C.850 C.850 C850 C.850 C.850 C.850 C.850  100.0 ?n.6 72.8 1 7.5 12.7 8.1 6.1 4.0 2.7 1.3 0.5 0.9 1.4 0.5 0.5 0.0  l.'»3 2 . 37 2 . 11 3.09 3 . 38 3.58 3.72 3.81 3 . 87 3.91 3.98 4.00 4.02 4.02 4.04 4.03 4.0)  0.850  C.850  (Tl  -0.5 -0.5 0.0  E? (Tl  toco 14.6 2C9 14.4 1 1.5 7. 1 5.4 3.9  7.4 1.6 1.0  0.6 1.2 C 2 C.2  0.0 0.6 -C.2 0.0  EP  (XI  I0O.0C0 3 . 173 2.822 2.454 2 . I 70 1 .903 1.707 1.533 1.382 1.253 1. 142 1.051 0 .. 9 7 8 0 .. 9 0 0 0 .. 849 .794 0. 0.747  0.7C3 0.665  6  a  7  9  CURRENT ENR. CIAL.  10  11  CURRENT EFFICIENCY El IXI  E2 IXI  12 POWER EFFICIENCY  11 (Al  12 (Al  l.CO 1.13 1.24 1.35 1.44 1.52 1.60 1.66 1.72 1.76 l.ei  l.COC 0.903 0.617 0.739 0.667 0.609 C557 0.517 0.481 0.452 0.425  t.CO 1.25 1.52 1.83 2. 16 2.50 2.R6 3.71 3.57 3.91 4.25  0.0 1.037 0.971 0.927 0.977 0.883 0.872 0.872 0.839 0.839 0.817  CO C936 1.015 1.004 C.949 C.949 C.927 C.883 0.683 C861 C850  471. 432. 406. 387. 377.  i.es 1.93 1.97 2.00 2.02  0.383 0.252 0.331 0.315 0.3C7  4.90 5.49 5.17 6. 14 6.60  0.795 0.764 0.773 0.766 0.761  C.828 C.R17 C.80I C.790 C.784  11.5 8.6 7.1 4.0 4.4  6.5 4.9 3.3 2.5 1.4  0.924 0.849 0.787 0.721 0.668  360. 352. 346. 342.  2.05 2.07 2.07 2.C8  0.293 0.287 0.262 0.278  6.48 1.21 7. 16 7.46  0.761 0.76t 0.761 0.761  C.784 C.784 C.784 C.7B4  1.8 1.8 0.4 0.4  t.l 0.5 0.4 0.3  0.577 0.5C8 0.4SI 0.405  CT (PPM)  XB l-l  0 1 2 3 4 5 6 7 6 9 10  O.C 45.3 90.6 135.9 181.2 226.5 271.8 317.1 262.4 407.8 453.1  1242. 1402. 1542. 1677. 1790. ie9C. 1981. 2C62. 2131. 2192. 2246.  1226. 1109. 1004. 908. 819. 74e. 684. 635. 591. 555. . 522.  12 14 16 18 20  543.7 634.3 724.9 615.5 5C6. 1  2336. 24CC. 24 53. 2483. 2515. 2542. 2569. 2575. 2581.  C.l.27  Fl  NS I-)  CB (PPM)  TABLE  I? (At  POWER  E F F I C IENCY  XT I-)  T (SEC)  10e7.3 1268.6 1449.e 1631.C  l.CO  1.47  CURRENT Efr ICIENCT  tl (Al  NS  (-)  CONCENTRATION SEPARATION FACTOR NORMALIZED  NCYC l-l  24 26 32 36  0.39e  CURRENT ENR. LIAL.  s NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/* 2  3  2  CrNCINTHAIICN SCPARATIUN NOWALIZEO FACTOR  I NUMERICAL EVALUAIICN CF EXPERIMENT EOI-S3-13/0 I  100.0 100.0 32.0 26.3 29.7 21.6 30.2 19.7 25.3 19.4 15.5 23.4 21.8 14.4 11.5 19.2 17.2 1C.3 15.1 8.7 14.1 7.9  EP IX)  100.000 1.586 1.450 1.390 1.332 1.267 t.213 1.156 1.103 1.052 1.007  359 i  1  2  C1CII no.  REAL TIDE  n  CONCFN'fRATICN HOTTON TOP  CONCENTRATION SEPARATION FACTOR NORHALIZED XB (-)  XT <-)  T (SEC)  CD (rrit)  0 2 0 6 8 10  0.0 65. 3 130.6 195.9 261.2 326.5  1260. 1391. 1522. 1657. 180 1. 1930.  1205. 1130. 1099. 1013. 913. 857.  1.00 1. 10 1.20 1. 31 1.02 1.53  1.000 0.951 0.883 0.8 13 0.709 0.688  15 20 25 30 35 no OS SO 55 60 65  089.8 653. 1 816.3 979.6 1102.9 1306. 1 1069.1 1632.7 1795.9 1959.2 2122.5  2216. 2033. 2608. 2702. 2850. 2938. 2996. 3001. 3081. 3099. 3133.  703. 507. 502. 039. 395. 361. 338. 320. 308. 302. 290.  1.75 1.92 2.06 2. 17 2.25 2. 32 2.37 2.41 2.00 2.05 2.08  0.565 0.072 0.003 0. 352 0.317 0.290 0.272 0.257 0.208 0.202 0.236  C.1.28  8  7  6  ICIC  TABLE  CT (PPN)  5  9  CUHBFNT ENR. DIAL. 11 (A)  12 (A)  1.00 1. 16 1.36 1.61 1.90 2.22  0.0 1.087 1.057 1.026 0.980 0.9 19  0.0 1.01 1 i.ooi i.oo i 1.011 0.909  3. 10 o.oa 5. 12 6. 16 7. 11 8.01 8. 73 9. 36 9. 80 10. 11 10.09  0.857 0.851 0.796 0.796 0.790 0.796 0.766 0.766 0.735 0.735 0.7 35  0.903 0.860 0.812 0.812 0.805 0.795 0. 766 0.766 0.735 0.735 0.73S  NS (-)  10  CURRENT EFPICIENCT 11 (*)  REAL TIME  19.2 10.7 12.6 9.7 7.9 6.3 0.3 3.0 3. 1 1.4 2.6  CCNCENTRATICN BOTTOM TCP  T (SECI  CB CT (PPM) ( P P M )  0 1 2 3 4 5 6 7 8 9 10  0.0 95.9 191.8 287.8 383.7 479.6 575.5 671.4 767.3 863.3 959.2  1295; 1517. 1634. 1694. 171C. 1725. 1730. 1727. 1725. 1722. 1716.  C.1.29  9.8 7.7 6.0 0.5 3.1 2.0 1.7 1.0 0.9 0.5 0.6  12 POUER EFFIC tENCT EP  100.000 0. 160 0.371 0. 378 0. 386 0. 388 0.380 0. 358 0. 316 0.312 0.289 0.268 0.209 0.232 0.218 0.203 0.192  I MOHERICAt EVULOATIOU OF EIPERIEEHT B0I-S3-13/S 4  NCYC l-l  TABLE  E2 (*>  100.0 100.0 8.6 16.8 17.8 1 1.8 18.9 1 1.9 21. 2 11.0 20. 1 1 1.5  10 CYCLE NO.  11  1276. 955. 823. 761. 726. 712. 703. 695. 686. 681. 677.  CONCENTRATION SEPARATION NORMALIZED FACTOR  CURRENT ENR. CIAL.  (-)  (-)  NS (-1  It IAI  12 IAI  I.CO 1.17 1.26 1.31 1.22 1.33 t.34 1.33 1.33 1.33 1.33  l.COO C.748 C.645 0.597 0.569 C.558 0.551 0.545 C.538 0.534 0.531  1.00 1.57 1.96 2.19 2.32 2.39 2.43 2.45 2.48 2.49 2.50  0.0 0.975 0.996 0.980 0.959 0.949 0.938 0.933 0.928 0.928 0.917  CO C.964 C959 C.938 C923 C.917 C.912 0.907 C907 C.907 0.897  XB  XT  t NUMERICAL EVALUATICN CF EXPERIMENT EDI-S3-l3/f J  11  CURRENT EFFICIENCY El  E2 (XI  100.0 10C.0 22.3 37.6 11.6 13.4 5.9 6.5 1.7 3.7 1.5 1.5 0.6 1.0 0.8 -0.3 1.0 -0.3 C.6 -0.3 -0.6 0.4  12 POWER EFFICIENCY EP (XI  100.000 4.402 3. 172 2.445 1.953 1.617 1.375 1.191 1.053 0.941 0.849  360 1  2  3  4  CYCLE  REAL  CONCENTRATION  NO.  Tice  UCIICM  NCYC l-l  1 (SECI  O.C 60.6 121.2 181.8 242.4 3C3.1 363 .7 424.3 4E4.9 545.5 6C6.1 666.7 727.3 7E8.C e48.6 9C9.2 969.6 1C30.4  0  1 2 3 <t 5 6 7 8  9 IC 11 12 13 14 IS 16 17  TABLE  1  irp  5  NOHMALI/EC  Ct IPP»I  XP l - l  1306. 1391. 1464. 15 2 2 . 157C. 1606. 16 3 2 . 1654. 1666. 16 7 9 . 1691. 1699. 1705. 1708. 171C. 1713. 1713. 1716.  1291 . 1167. 1086. 1023. 971 . 931. 897. B7I. 85C. 83 7. 619. PIC. 004. 793. 788. 784. 78C. 779.  l.CC 1.C7 1.12 1.17 1.20 1.23 1.25 1.27 1.28 1.29 1. 30 1.30 1.31 1.31 1.31 1.31 1.31 1.31  3  4  CCNCENTRATICN BOTTOM TOP  5  NCYC l-l  T ISEC)  CB IPPM)  CT IPPM)  XB l-l  0.0 60.6  1261. 1438.  1271. 1047.  121.2 iei.8 242.4  157C. 1674.  920. 623. 751.  l.CO 1.12 1.23 1.31 1.37 1.42 1.45  6  363.7  7  424.3  8  484.9  9 10 11 12 13 14 15 16 17  545.5 6C6.1 666.7  727.3 7E6.C  648.6  9C9.2  969.8 1C30.4  I.COC C.904 0.641 C. 792 C.75? C . 721 0.694 C.674 C.65e 0.648 C.634 0.627 0.622 C.614 0.61C 0.607 0.604 C.603  l.CO 1. 18 1 . 31 1.47 1.60 1 . 71 I . HO  0.0 0.61.8 0.660 0.6">3 0.643 0.6'.3 0.677 0.677 0.677 0.610 0.619 0.610 0.610 0.610 0.610 0.610 0.610 0.610  C O C.610 C.652 C.660 C.652 C.652 C.652 C 6 5 7 C.643 C 6 4 3 C.635 C 6 2 7 C.627 C 6 2 7 C.627 C.627 C.627 C.627*  1753. 1813. less. ie87. 1913. 1924. 1938. 1547. 195C 1953. 1953. 1956. 1956. 1953.  695. 658. 626. 606.  1.47 1.49  591.  1.50  574.  1.51  571.  1.52 1.52 1.52 1.52 1.53 1.53 1.52  564. 559.  557. 555. 557. 550.  6  7  8  XT l - l  11 IA)  NS l-l  l.COO  1.00  0.0  0.624  1.36 1.69 2.02  1.130 1. 1 2 2  0.724 0.648  C591 C547 o.sie 0.492 0.477 0.465 0.452  0.450 C.444 0.440  0.439 0.437 0.435 0.4J2  2.32 2.59 2.80 2.99 3.13 3.23  3.35 3.38 3.43  3.47 3.48  3.50 3.51 3.53  C . 1.31  1.114 1.105 t.097 1.072 1.072 1.056 1.039 0.536 1.031 1.023 0.998 1.006 1.006  1.073 1.006  I NUMERICAL EVAIUATICN CF EXPERIMENT  E0t-S)-IJ/f ?  9  CURRENT ENR. C I A L .  _,  TABLE  CURRENT FFFICIENCV  12 «AI  1.94 1.98 2.04 2.07 2.10 2. 13 2.15 2.16 2.17 2 . 18  II  CURRENT  II «»l  1.81)  10  ENR. DIAL.  NS l - l  CONCENTRATION SEPARATION FACTOR NORMALIZED  REAL TIME  3C3.1  XT l - l  FACTOR  9  Fl (XI  E2 IX»  100.0 19.9 17.0 14.1 11.5 a.8 6.3 5.6 1.5 2.9 7.8 2.2 1.4 0.7 0.7 0.7 0.0 0.7  100.0 31.4 19.3 14.8 12.3 9.5 8. 3 6.1 5.0 3. 1 4.4 2.2 1.6 7.6 1.3 1.0 1.0 0.3  I? POWER EFFICIENCY EP <*»  ioo.oco 6.133 5 . IC9 4.494 4.049 3.657 3.330 3.048 2.753 7.565 2 . 396 2.229 2.077 1.951 1.B31 1.724 1.626 1.539  I NUMERICAL EVALUATION OF EXPERIMENT EOI-S3-13/I 6  C.l.30  CYCLE NO.  0 1 2 3 4 5  8  1  CCNCENTRAT ICN S E P A R A T I O N  CC (PPPI  2  6  12 (A)  CO 1. 122 1.163 1.138 1.122 1.122 1.105 1.089 1.072 1.056 1.039 1.023  1.015 1.023 1.C06 1.023 1.006 1.006  10  11  CURRENT EFFICIENCY Fl 1(1  E2 IX)  lao.o l o c o 21.6 30. B 18.1 17.0 14.5 13.2 ICO 11.1 8.4 7.7 6.2 5.2 4.5 4.6 3.8  1.7 4.1 1.3  2.8  0.4  2.3 2.5 0.4 1.2  0.4 0.0 0.4 0.0 -0.4  0.2 0.4 0.4 0.4  0.8  12 POWER EFFICIENCY EP (XI  1no.oco 2.778  2.294 2.008 1.783 1.596 1.434 1.301 1.186  1.083 1.027 0.945 0 . 876 0.817  0.762 0.T15 0.674  0.636  361 |  J  CYCLE KC.  )  4  R ( H CONCENTRATION 1IME UCT1CM TCP  5  NCYC l-l  T ISECI  CP IPPMI  CT IPPfl  XB l - l  0 I 2 3 4 5 6 7 6 9 1C 11 12 13 14 IS  o.c (0.6 121.2 1E1.8 242.4 2C3. 1 36 3.7 424.3 464.9 545.5 6C6.1 666.7 727.3 788.0 848.6 9C9.2  1270. 1466. 1626. 1 756 .  1267. 1019. 875. 764. 684. 626. 581. 557. 537. 522. 513. 506. 501. 497. 493. 49C.  I.CC 1.15 1.2H 1.3P 1.45 1.50 1.54 1.56 1.58 1.59 1.6C 1.61 1.61 1.6 1 1.61 1.61  TABLE  ie44.  1907. 1953. 1984. 2C1C. 2C22. 2C33. 2C39. 2C42. 2C45. 2C45. 2C48.  C.1.32  6  XT l - l  i.crio o.eoe 0.69.1 C.6C5 0.542 0.496 C.46 5 C.442 0.425 C.414 C.407 0.401 C.397 C.294 0.391 0.389  3  4  CCNCENTRATICN TOP ECTTCM  5  6  NCYC l-l  T I SEC I  CB IPP«I  CT IPPMI  XB l-l  XT l-l  9 10 11 12  CO 60.6 121.2 161.6 242.4 3C3.1 263.7 424.3 484.9 545.5 6C6. 1 666.7 127.3  1133. 1355. 1533. 1662. 1761. 1827. ie75.1904. 1933. 1947. 1561. 1973. 1581.  1135. 89C. 730. 617. 539. 484. 451. 424. • 408. 40C 387. 384. 379.  I.CO 1.20 1.35 1.47 1.56 1.61 1.66 1.68 1.71 1.72 1.73 1.74 1.75  l.CCC C.784 0.643 0.543 0.475 C426 0.398 0.374 0.359 0.252 0.341 0.339 0.334  14 16 22  648.6 1C9I.0 1333.5  1587. 1996. 2C01.  377. 377. 374.  1.75 1.76 1.77  0.332 C.22T 0.330  3 4 6 7  TABLE  C.1.33  NS  I.CO 1.41 1.85 2.2R 2.611  3.03 3.31 3.54 3.72 3.84 3.93 4.01 4.05 4.C9 4.12 4.15  9  CURRENT' ENR. CIAL. II •*»  0.0 1.303 1.30) 1.136 1. 370 1.287 1.21) 1.270 1.295 1.271 1.729 1.767 1.270 1.279 1.237 1.204  12 '  , A  CO 1.221 1.754 1.155 1.155 1. 130 1.161 1.130 1.064 1. 122 1. 122 1.081 1.072 1.048 1.204 1.204  10  It  CURRI NT EFTICIENCY '1 E l , 1  F2  1 X 1  100.0 100.0 23.4 ICR 19.0 17.9 15.1 14.9 1C.7 10.) 7.6 8.0 5.9 5.2 3.9 4. 1 3.0 3.1 1.5 2.0 1.5 1.2 0.7 1.1 0.7 0.4 0.6 0.3 0.9 0.5 0.4 0.3  10  7  CONCENTRATION SEPARATION NORMALIZED FACTOR  REAL TIME  2  B  12 POWER FFFIC1CNCY EP  1 1 1  100.OCO 7.C79 1.736 1.539 I. 358 1.210 1 .064 0.976 0.867 0.806 0.738 0.679 0.628 0.584 0.543 O.S09  I NUMERICAL EVALUATICN OF EXPERIMENT EOI-S3-13/I 8  CYCLE NC.  0 1  T  CCNC INT KA T U N SlPARATION NORMALIZED fACTOR  CURRENT ENR. CIAL. II IA)  12 (A)  1.00 1.53 2. 10 2.70 3.27 3.78 4. 16 4.50 4.75 4. 68 5.08 5.14 5.24  0.0 1.369 1.361 1.320 1.287 1.320 1.312 1.303 1.295 1.267 1.270 1.254 1.237  CO 1.779 1.328 1.303 1.320 1.262 1.270 1.246 1.254 1.262 1.287 1.287 1.287  5.29 5.18 5.16  1.279 i.?e7 1.267  1.303 1.279 1.279  NS l-l  I NUMERICAL EVALUATION CF EXPERIMENT EOl-Sl-ll/l 9  11  CURRENT EFFICIENCY El 1*1  E2 IX)  12 POWER EFFICIENCY EP IXI  too .0 t o c o 25 .2 29.7 20 3 16.7 15 .2 13.5 9.1 11 9 7 .7 6.8 5. 7 3.9 3 4 3.4 3 4 2.1 1.7 1.0 I .8 1.6 1 0.3 1 .4 .1 0.6  100.000 1.569 1.146 1.176 1.036 0.916 0.812 0.727 0.657 0.594 0.545 0.501 0.464  0.2 0.2 -0.1  0.400 0.314 0.258  0 .3 0 .3 0 .2  362 to CYCLE NC. NCYC l-t  0 1 7 3 5 6 7 8 9 IC 11 12 13 14 15 16 17 18 15 20 21 22 23  REAL lift  CCNCENTRATICN ec i i c f TCP  T (SEC)  CA IPPf I  CT IPPM)  xe I-)  O.C 51.8 IC3.6 155.4 207.2 25">. 1 310.9 362.7 414.5 466.3 518.1 569.9 621.7 673.6 725.4 777.2 829.C eeo.e 922.6  1C57. 1103. 1149. 119C. 1723. 1748. 1277. 1289. 1303. 1314. 1322. 12 30. 1336. 1341. 1347. 135C. 135C. 135C. 1352. 1352. 1352. 1352. 1352. 1352.  1045. 909. 84 1. 793. 756. 725. 703. 684. 668. 654. 645. 636. 628. 622. 618. 615. 611. 6oe. 606. 604. 601. 597. 597. 596.  l.CC I.C4 1.C9 1.1 1 1. 16 1.18 1.20 1.22 1.23 1.24 1.25 1.26 1.26 1.27 1.27 1.28 1.28 1.28 1.28 1.28 1.28 1.28 1.28 1.28  5E4.4  1C36.2 1088.1 1139.9 1191.7  TABLE  XT  l-l  1.C00  C67C o.eo5 0.759 C. 723 0.694 C.673 0.654 0.640 C.626 0.617 C.6C9 0.601 0.595 0.591 0.589 0.585 0.581 0.580 0.578 0.575 0.572 0.572 0.570  t NUMERICAL EVALUATION CF EDI-S3-13/I10  C.1.34  1  2  CYCLE NC.  REAL TIME  3  4  NCYC l-l  T ISECI  CB IPPMI  CT IPPMI  XB l - l  0 1 2 3 4 5 6 7 e 9 10 11 12 13 14 15 16 IT j iej  0.0 60.6 121.2 181.6 242.4 3C3.1 263.7 424.3 484.9 545.5 6C6.1 666.7 727.3 7E8.0 648.6 9C9.2 969.8 1C30.4 1C91.C  1196. 1339. 1458. 1553. 1679. 1682. 1775. 1756. 1779. I79C. ieoi. 1607. 1813. 1618. 1871. 1621. 1621. 1621. 1821.  1187. 984. 862. 77C 699. 648. 613. 583. 562. 548. 533. 52e. 519. 515. 511. 507. 503. 503. 503.  l.CC 1.12 1.22 1.20 1.36 1.41 1.44 1.47 1.49 1.50 1.51 1.51 1.52 1.52 1.52 1.52 1.52 1.52 1.52  CONCENTRATION BOTTOM TCP  CURRENT ENR. CIAL.  C PNC INTRA!ICN SEPARATION NORMAL 120C TACIOR  5  6  NS l-l  I.CO 1.70 1.35 1.40 1.60 1. 70 1. 79 1.R6 1.93 1.99 7.03 2.07 7.10 2.13 2. 16 2.17 2. 18 2.20 2.21 2.22 2.22 2.24 2.24 2.24  It (Al  0.0  0.965 0.994 1.042 1 .067 1.013 1.013 1.013 1.013 1.023 1.01 3 1.033 0.975 1.013 1.004  0.9P4 1.004 0.965 0.965 0.994 1.004 0.984 0.9C4 0.994  l.COC o.e29 0.726 0.649 0.589 0.546 0.516 0.491 0.474 0.462 0.449 0.445 0.437 0.434 C430 0.427 0.424 0.424 0.424  IA)  CO C946 1.062 1.013 1 .C04 1.03) 1.021 1.052 1 .C04 1.013. C.994 1.C04 1.05? C994 1.C04 1.004 1.013 1.033 1.013 C.994 C.994 C.984 C.994 0.984  CURRTNT EFFICIENCY  El Itl  E2 IX)  100.0 l o c o 8.7 76.0 8.5 11.7 7.1 8.5 5.6 6.8 4.4  4.4 3.0 7.5 7.0 1.5 1.5 1.0 1.0 1.0 0.5 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0  5.4  3.9 3.3 7.8 2.5 1.6 1.6 1.3 1.2 0.7 0.5 C.7 0.7 C.2 0.5 0.5 0.7 0.0 0.2  12 POWER FFFICIENCV EP IX)  100.000 1.952 1.5C1 1.274 1.118 0.999 0.9C6 0.824 0.757 0.700 0.647 0.603 0.564 0.530 0.499 0.470 0.443 0.419 0.399 0.379 0.362 0.347 0.332 0.318  EXPERIMENT  7  8  CCNCENTRATION SEPARATION NORMALIZED FACTOR XT l - l  12  It  9  CURRENT ENR. C I A L .  NS l - l  II IAI  12 (Al  ! . CO 1.35 1.68 2.00 2. 31 2.58 2.79 2.99 3. 14 3.24 3.36 3.40 3.47 3.51 3.54 3.57 3.59 3.59 3.59  0.0 1.056 1.023 1.023 1.015 0.990 0.973 0.957 0.9)2 0.924 0.957 0.949 0.949 0.949 0.957 0.940 0.924 0.957 0.957  CO C.990 1.056 1.073 C.990 C.990 C990 C.973 C.957 C.982 C.940 C.940 C.949 C.93? C.932 C.957 C.957 C.907 C.957  10  11  CURRENT EFFICIENCY El IX)  E2 (XI  100.0 100.0 21.0 31.7 18.I 18.0 14.4 13.9 11.6 t l . l 6.1 8.4 6.8 5.5 5.0 4.7 3.8 3.3 2.2 1.9 1.3 2.6 0.9 0.9 0.9 1.5 0.9 0.6 0.5 0.6 0.0 0.6 0.0 0.6 0.0 0.0 0.0 0.0  12 POWER EFFICIENCY EP IX)  100.000 2.799 2.339 2.054 1.643 1.653 1.489 1.356 1.240 1.131 1.045 0.962 0.895 0.835 - 0.781 0.733 0.691 0.652 0.616 _________  TABLE  C.l.35  I NUMERICAL EVALUATION CF E0I-S3-I3/«ll  EXPERIMENT  363 1  2  CYCLE KC.  REAL TIME  NCYC l-l  T I SEC I  Cfl IPPM)  CT (PPMI  KB XT l - l l - l  0 1 2 3 4 5 6 7 8 9 IC  0.0 70. 6 141.2 211.8 282.4 353.1 423.7 454.3 564.9 635.5 7C6. 1  1314. 1542. 1722. 185C. 1538. 1996. 2C42. 2C68. 2C91. 2103. 2108.  1284. 1032. 868. 747. 66C. 604. 56C. 529. 512. 502. 498.  l.CO 1.17 1.31 1.41 1.48 1.52 1.55 1.57 1.59 1.60 1.60  l.CCO C.604 C.676 0.582 0.515 C.47C C.436 C.412 C.399 C.391 0.388  l.CO 1.46 1.94 , 2.42 2.87 3.23 3.56 3.82 3.99 4.C9 4.14  0.0 1.034 0.977 0.921 0.921 0.921 0.913 0.878 0.864 0.871 0.878  CO C.94? C.963 C.977 C.92I C.906 C.892.  2117. 2117. 2117. 2117. 2114.  486. 476. 472. 477. 477.  1.61 1.61 1.61 1.61 1.61  C.38C 0.371 0.368 0.372 0.372  4.24 4.34 4.38 4.33 4.33  0.857 0.864 0.664 0.871 0.871  C.871 C871 C.864 C.850 C.864 .  12 14 16 18 20  3  847.3 568.6 1129.6 1271.0 1412.2  TABLE  4  CCNCPNTRAIICN HCTTCM ICP  C.l.36  5  6  7  8  CONCENTRATICN SEPARAIICN NCRMALI7CC EACIOR NS <->  1  CURRENT ENR. CIAL. II I*'  12 «*»  cess  C.892 C-892 C.871  10  CURRENT POWER EFFICIENCY EFFICIENCY El £7 <*» '*<» 100.0 100.0 29.3 35.5 24.5 22.6 18.5 16.5 12.8 12.5 8.3 6.3 6.7 6.5 3.9 4.7 3.6 2.5 1.8 1.5 0.9 C.6 0.7 0.0 0.0 0.0 -0.2  10 CCNCENTRATICN BCTTCM TCP  REAL TIME  NCYC l-l  T ISECI  CB IPPM)  0.0 90.6 161.2 271.8 262.4 453.1 543.7 634.3 724.9 815.5 5C6. 1 596.7 ce7.3 178.0 268.6 359.2 449.6 540.4 621.0 721.6  1207. 1206. 1508. 924. 1705. 730. 163 3. 606. 1518. 526. 1973. 476. 2C1C 446. 2C33. 428. 2C45. 413. 2C53. 410. 2C59. 408. 2C62. 401. 2C62. 399. 2C62. 392. 2C62. 397. 2C62. 393. 2C62. 397. 2C62. 396. 2C62. 395. 2C62. 391.  C.l.37  I?  CB C.9 0.3 -0.4 CO  EP  100.OCO 3.527 2.983 2.559 2.291 2.018 1.RC6 1.624 1.469 1.331 1.211 1.031 0.897 0.791 0.704 0.634  t NUMERICAL EVALUATICN CF EXPERIMENT ED!-S3-13/f12  CYCLE NC.  TABLE  II  CT I PPM I  CONCENTRATION SEPARATION NORMAL I/ED FACTOR XB l-l  XT l-l  l.CO 1.25 1.41 1.52 1.59 1.64 1.67 1.69 1.69 1.70 1.71 1.71 1.71 1.71 1.71 1.71 1.71 1.71 1.71 1.71  l.COO 0.766 C.605 0.503 0.437 C.395 0.370 C355 0.342 0.340 0.338 C233 0.330 C.325 0.329 C.326 0.329 C.328 C.327 0.324  11 IAI  12 IAI  0.0 0.817 0.767 0.734 0.695 0.664 0.657 0.690 0.684 0.662 0.662 0.662 0.640 0.673 0.712 0.712 0.712 C.712 0.712 0.712  0.0 C.789 C773 C745 C.723 C717 C.679 C712 C673 C.673 C.668 C706 C.662 C662 C.668 C.651 C651 C.651 C640 C.673  NS l-l  1.00 1.63 2.33 3.02 3.63 4. 14 4.50 4.75 4.95 5.00 5.05 5. 14 5. 17 5.26 5.19 5.24 5. 19 5.20 5.22 5.27  CURRENT ENR. CIAL.  > NUMERICAL EVALUATION CF EXPERIMENT EOI-S3-13/P1J  11  CURRENT EFFICIENCY El Itl  E2 Itl  100.0 100.0 38.3 37.1 26.6 26.0 18.0 17.2 12.8 11.3 8.3 7.5 5.9 4.5 3.5 2.6 1.7 2.4 1.4 C.4 0.9 0.4 0.5 0.9 0.0 0.4 0.0 1.0 0.0 -0.6 0.0 C.6 0.0 -0.6 0.0 C.2 0.0 0.2 0.0 C.6  12 POWER EFFICIENCY EP (II  100.000 3.912 3.336 2.863 2.489 2.176 1.930 1.709 1.534 1.3841.261 1.157 1.070 0.996 0.922 0.865 0.810 0.764 0.723 0.68T  364 3  i  2  CYCLE NC.  REAl 1 IKE  NCYC t- 1  t ISEC)  O.C  0 I 2 3  221.2 331.6  4 5 6  553.1 663.7  11C.6  7 8  774.3  664.9  595.5  9  10  11C6.1  1216.T 1327.3 1438.0  11  12 13  TABLE  4  CONCENTRATION KETICM TCP cn (PP* 1  CT (PPMI  125. 1126. 827. 1455. 1660. 626. 1 787. 511. 436. IE67. 1515. 392. 155C. 373. 1567. 359. 1584. 35C. 199C 343. 344. 1559. 2C01. 342. 2C1C. 342. 339. 2C16. 1  5  C I : N C ' : N 1 R A 1 ION  NORMAL I 2 C O Xl< 1- 1  l.CO 1.29 1.48 1.59 1.66 1.7C  l.CCC  l.CO  C. 387  4.iW  C.318  5.24 5.49 5.68  1. 76 1.77  C.3IC C.305 C.306 C.304 C.204 0.301  1.78 1 . 78 1.79 1.79  1 . 76 2.66 1.50 • 4 . 2 9  0.348  0.331  1.75  Sl.PAMAIIClN FACIEIR NS l-l  0.734 0.556 0.454  a  7  XT (-)  1.71  5.81 5.fll 5.U6 5.P9 5.95  9  CURRENT LNR. CIAL. 11  (Al  0.0 0.617 0.610 0.561 0.54? 0.531 0.5C6 0.53 J 0.S15  0.520 0.515 0.520 0.506 0.497  12 (Al  C O  to  11  CURRENT EFFICIENCY El (X)  100.0  E2 Itl  I0C.0  12 POWER EFFICICNCY EP  It)  mo.ooo  C.610  44.0  41.6  4 . 4 7 6  C.5 7 0 C.542  19.1  28.9 17.1  3. 76) 3. i e 5  C.592  28.5  C.533 C.524  12.5 7. 7 5.8  C.497  2.7  C.515 C.515 C511  C.506 C.506 C.502  2.8 0.9 1.4 0.5 1.4  1.0  1 1.7  7.0  3. 1 2.4 1.5 1.1  -C.2 C.4 CO 0.4  2.746  2. 3 e i 2.091 1.851 1.661 1.499  1.362 1.249 1.157 1.079  I NUMERICAL EVALUATION OF EXPERIMENT EDI-S3-13/U4  C.l.38  5 CCNCENTRATICN BOTTOM TCP  REAL TIME  NCYC l-l  T I SEC)  (PPM)  (PPM)  XE l-l  0 1 2 3 4 5 6 7 8 9 10  0.0 68.3 136.6 2C5.C 273.3 341.6 4C9.S 478.2 546.6 614.9 6E3.2  1281. 1450. 1587. 1725. 1855. 197C. 2C76. 2166. 2254. 2321. 2386;  1267. 1127. 996. 89C. 792. 713. 648. 591. 553. 501. 466.  12 16 20 24 28  619.9 IC93.1 1366.4 1639.7 1913.C  24ec 2602. 2668. 2724. 2736.  414. 352. 324. 311. 303.  CT  CB  C.l.39  4  10  7  CONCENTRATION SEPARATION NORMALIZED FACTOR  CYCLE NC.  TABLE  6  CURRENT ENR. CIAL.  XT (-1  NS l-l  It IAI  12 IAI  l.CO 1.13 1.24 1.25 1.45 1.54 1.62 1.69 1.76 i.ei 1.66  t.coo 0.690 o.7ea C.703 C625 0.563 0.511 C466 0.437 0.395 C.368  l.CO 1.27 1.57 1.92 2.32 2.73 3.17 3.63 4.03 4.59 5.07  0.0 0.820 0.790 0.790 0.776 0.790 0.754 0.739 0.717 0.703 0.661  CO C.776 C.776 C.790 C.790 C.746 C.732 C.732 C.710 C68B C.703  1.94 2.C3 7. 10 2. 13 2.14  0.327 0.278 C.256 0.245 0.239  5.92 7.11 8.71 e.67 6.93  0.673 0.629 0.651 0.637 0.629  C.659 C.651 C.622 C.622 C.615  > NUMERICAL EVALUATION CF EXPERIMENT EOI-SJ-lJ/tlJ  11  CURRENT EFFICIENCY Et Itl  E2 It)  12 POWER EFFICIENCY EP It)  100.0 100.0 28.3 24.7 23.8 22.9 24.0 18.8 23.2 17. 1 19.9 14.5 19.4 12.4 16.7 1C.7 16.7 7.2 13.2 1C6 13.0 6.8  100.OCO 1.425 1.314 1.242 1.190 1.130 1.080 1.028 0.979 0.942 0.901  5.4 3.3 1.6 0.7 0.4  0.823 0.695 0.596 0.515 0.451  9.6 6.6 4.6 1.9 0.7  365 10 CYCLE NC. NCYC (-1  REAL T I ft T ISCCI  PPM  CI I IPPMI  Xl>  l-l  1.74 1.77 l.ei  454. 414. 387. 365.  1.E8 1.93 1.97 2.CO  C.356 0.324 C.303 0.286  342. 326. 321. 317.  2.C4 2.C6 2.07 2.C8  C.266 0.256 0.252 0.248  445.7 52C.C 594.3 668.6  2424. 2486. 2533. 2572.  817.1 965.7 1114.3 1262.8  2628. 2652. 2664. 2670.  12 14 16 18 22 26 30 3*  TABLE  1133.  C.1.4C  l.cn 1.25  1.44  1.5) 1.(0 1.66  1.5)  CtiHRI NT ENR • f I Al . It IAI  12 IAI  0.0 1.212 1.C10 I.050 1.063  CO 1.C10 1.104 1.037  NS l-l  I.R4 2.1-7 2.56 2.9) 3. 31 3.77 4. 13 4.52  1858. 1967. 2C53. 214C. 2236. 228C. 223C.  12P6. 14 50. 1598.  XI  l-l  l.CCC C.90? o.eio C.7)l C.tbl 0.598 C.545 C.502 0.461 0.429 0.401  l.CC 1.13 1.24 1.35  9 to  a  ce I  CCNCt'NTRAI ICN SEPARATION NL'HMALI/EO TACTOR  1277. 1152. 10)5. 934. 844. 764. 697. 641 . 58P. 548. 512.  O.C 37.1 74.3 111.4 I4R.6 If 5.7 222.9 26C.C 257. 1 ?34.3 371.4  0 t 2 3 4 5 6 T  CCNCCN1RATICN flCITCM 1CP  0.9" )  C.9A-)  CURRTNT EFFICIENCY El 111  REAL TIME  CONCENTRATION BCTTCM TCP  EP Itl  100.OCO 1.737 1.683 1.611 1.552 1.490 1.414 1.355 1.313 1.243 1.188  0.979 0.96.9 0.942 0.915 0.867  1.010 1.037 C.979 C.969 C.88R C915  5.30 5.96 6.50 6.99  0.9C? 0.808 0.848 0.835  C.862 C.902 C.875 C.821  13.2 9.7 7.1 5.8  8.5 5.6 3.9 3.4  1.093 1.003 0.921 0.853  7.63 8.07 8.24 8.35  0.821 0.821 0.781 0.781  C.BOB C.808 C.80B C.821  4.4 1.8  1.8 1.2 C.4 0.3  0.740 0.647 0.574 0.514  CONCENTRATION SEPARATION NORMALIZED FACTOR  T ISECI  CB IPPMI  CT IPPMI  XB (-)  0 1 2 3 4 5 6 7 8 9 10  0.0 33.0 65.9 98.9 131.8 164.6 197.8 230.7 263.7 296.6 329.6  1283. 145C 1598. 1733. 1853. 156t. 2C56. 214C 221C 2277. 2333.  1276. 1153. 104C. 933. 849. 765. 697. 641. 59C 546. 517.  I.CO 1.13 1.24 1.35  15 20 25 30 35 40 45  454.4 659.2 824.0 9(8.e 1153.6 1318.4 1483.2  2518. 261 1. 2658. 2682. 2608. 2694. 27C0.  397. 347. 375. 316. 312. 308. 308.  C.l.41  POWER EFFICIENCY  1.0 0.5  « NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/«I6  NCYC l-l  TABLE  F2 HI  12  lor.o 100.0 34. 1 31.3 37.1 26.9 37.6 74.5 29.7 23.6 28.0 2C.0 23.5 16.4 77.6 15.1 25.8 1 3.8 17.1 11.4 14.6 ICO  10 CYCLE KC.  II  XT l-l  CURRFNT ENR. CIAL. II (Al  NS l-l  12  IAI  1.53 1.60 1.67 1.72 1.77 1.82  l.CCO C904 0.815 C731 0.665 0.600 C.546 0.503 0.462 C.428 0.401  I.CO 1.25 1.53 1.85 2.17 2.55 2.9) 3.32 3.7) 4.15 4.53  0.0 1.062 1.138 1.123 1.032 0.925 0.971 0.925 0.971 0.910 0.880  CO 1.107 1.092 1.077 C.971 1.062 1.016 C956 C910 C.880 C.910  1.96 2.C3 2.C7 2.C9 2.C9 2. 10 2.10  0.311 0.272 0.255 0.248 0.245 0.242 0.242  6.30 7.48  0.8H0 0.774 0.804 0.758 0.834 0.769 0.7e9  C.R50 C.8)4 C.789 C.774 C75R C75B C.789  1.44  e.u 8.44  8.56 8.69 8.71  I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-I1/II?  11  CURRENT EFFICIENCY El (tl  E2 IXI  12 POWER EFFICIENCY EP Itl  10C.O 31.5 37.1 29.6 28.3 34.4 33.0 24.6 33.5 27.5 27.9 19.2 25.8 16.5 20.5 16.2 21.0 14.2 18.0 10.5  100.OCO 1.996 1.851 1.769 1.7C1 1.647 1.576 1.512 1.446 1.393 1.333  7.7  1.084 0.902 0.764 0.661 0.576 0.512 0.460  100.0  44.6  12.0 6.8 3.4 1.8 0.4 0.4  0.4  3.4 1.6  0.7 0.3 0.3  0.0  366 10 CYCLE  NC.  REAL  CCNCfNTRAI ICN I'CIICM TCP  XT (-1  NS I.-I  It IAI  I? IAI  l.CCO C.90I 0.815 0.732 C.65 1 0.596 C.541 C498 C.459 0.425 C.396  l.CO 1.25 1.53 1.85 2.21 2.57 2.97 3.36 3.33 4.20 4.61  0.0 1.117  702. 637. 587. 541. 501. 467.  l.CO 1.13 1.24 1.35 1.45 1.53 1.61 1.6P 1.76 1.78 1.83  0.9?9 0.911 0.413 0.846 0.746 0.879 0.796  CO C.946 1.078 1 .04 5 C.974 C.924 C.91 J C.846 C.946 C.780 C.879  361. 317. 297. 288. 284. 283. 283.  1.97 2.C5 2.08 2.C9 2. 11 2.11 2.12  C.307 C.269 0.252 C.244 0.241 0.240 C24C  6.43 7.59 e.27 8.57 8.74 8.80 E.83  0.746 0.647 0.763 0.763 0.730 0.747 0.713  C.TBO C746 C697 C.697 C697. C.697 0.697  l-l  i sec i  CP. (PP")  CT IPPPI  c  CO 3C 1 40.3 50.4 1 20.5 I5C. 7 1E0.6 210.9 241.1 271.2 3CI.4  11 7 5 . 132e. 1466. 15S5. 171C ieo7. If 95. 1976. 2C71. 2103. 2155.  1178. 1062. 96C. 862.  2324. 2412. 2456. 2468. 2483. 2489. 2498.  t  NCYC  1 2 3 4 5 6 7 8  9 IC  452.0 t02.7 753.4 9C4.1 1C54.7 12C5.4 1356.1  15 2C 25 30 35 40 45  TABLE  C.1.42  774 .  XB l - l  2  3  CYCLE NO.  REAL TIME  4  NCYC !->  T I SEC 1  CB IPPMI  CT (PPMI  XB XI l - l l - l  0 1 2 3 4 5 6 7 8 9 10  0.0 26.5 53.C 79.5 1C6.C 132.5 159.0 185.5 212.0 238.6 265.1  1204. 1226. 1242. 1259. 1281. 1297. 1319. 1 339. 1352. 1372. 1386.  1195. 1143. 1075. 1036. 1001. 973. 944. 921. 90C. 880. 867.  l.CO 1.C2 1.C3 1.C5 I.C6  15 20 25 30 35 40 45 50  357.6 530.1 662.7 755.2 927.7 1C60.7 1152.8 1325.3  1433. 1472. 1494. 1503. 1514. 151T. 1517. 1517.  791. 744. 711. 688. 677. 65B. 64e. 645.  CCNCENTRATICN BOTTOM TCP  C.1.43  0.9 74 0.911  CURRENT EFFICIENCY El IXI  F2 III  100.0 100.0 41.6 3R.1 44.2 29.5 41.9 74.2 38.8 27.9 37.9 24.2 30.2 22.0 77.4 18.5 37.2 15.3 11.3 16.0 20.4 11.9 13.2  7.9  3.6 1.0 1.3 0.5 0.8  1?  POWER FEE ICIENCY EP (XI  100.000 2.091 1 .984 1 .444 1 .894 1.816 1.744  1.674 1.630 1 .540 1 .475  8.5 3.4 1.8 0.8 C.3 CI 0.0  1.203 1.0C1 0.848 0.727 0.639 0.568 0.512  11  12  : NUMERICAL EVALUATION OF EXPERIMENT EOI-S3-13/M6  1  TAeiE  CUrt R I. N T CNR. CIAL.  CONCINIRATICN SEPARATION NORMALIZED IACIUR  II  5  6  7  '  8  CRNCENTRATICN SEPARATION NORMALIZED FACTOR  l.CCC 0.957  C.900  0.e67 0.e38 1.08 0.8 14 C79C 1.10 0.771 1.11 1. 12 0.754 0.737 1.14 1.15 0.721 1.19 1.22 1.24 1.25  1.76  1.26 1.26 1.26  0.662 0.623 C.595 0.576 C.563 0.551 0.54? 0.540  I NUMERICAL EVALUATION EOI-SJ-13/II9  CF  9  CURRENT ENR. C I A L .  NS l - l  II (Al  12 IA)  1.49 1.55 1.60  0.0 1.717 1.679 1.754 1.754 1.717 1.754 1.679 1.735 1.717 1.698  CO 1.585 1.792 1.797 1.735 1.735 1.754 1.792 1.792 1.698 1.754  1.80 1.96 2.C9 2.17 2.23 2.79 2.32 2.33  1.735 1.660 1.62? 1.6'.0 1.61.1 1.677 1.622 1.641  1.735 1.698 1.679 1.622 1.622 1 .660 1.585 1.603  l.CO 1.06 1.15 1.71 1.77 1.32 1.39  1.44  EXPERIMENT  10  CURRENT EFFICIENCY Et IX)  E2 IXI  100.0 100.0 4.5 11.5 3.5 13.5 7.7 3.3 4.4 7.1 3.4 5.8 4.5 5.7 4.1 4.6 4.1 2.8 4.0 4.3 2.9 3.6 1.9 1.7 1.0 0.4 0.5 0.1 0.0  0.0  7.9 1.9 1.4 1.0 C.7 0.6 0.5 0.1  POWER EFFICIENCY EP IX)  100.OCO 0.462 0.457 0.4CO 0.375 0.349 0.335 0.320 0.302 0.293 0.281 0.230 0.197 0.171 0.150 0.114 0.120 0 . 108 0.098  367 to CYCLE KC.  urn  NCYC l-l  i sect  TIME t  CO 89.8 179.6 269.5 359.3 444. 1 526.9 628. 1 718.5 8C8.4  C 1 2  3 4 5  6 7 a 9 10  85e.2  CCNCFNTRATICN OCIIOf TCP Cfl IPPM)  Ct IPPM  1182. 1183. 126-4. 1071 . 1325. 982. 1 28 3. 90P. 145C. 85C 1491. 797. 155C. 751. 712. 1598. 1646. 675. 1488. 644. 1725. 614.  CONCENTRATION STPAttATION NORMAL I /EC FACTOR XP l-l  XT l-l  CURRENT ENR • CIAL.  NS  l-l  II IAI  12 IAI  I.CO 1.C7 1.12 1.17 1.23 1.26 1.31 1.35 1.39 1.43 1.46  l.CCC 0.905 C.63C 0. 76e C.719 C.674 C.635 C6C2 0.570 0.544 C519  I.CO 1. 18 1. 35 1.52 1.71 1.R7 2.07 2.25 2.44 2.62 2.81  0.0 0.662 0.668 0.679 0.6FS 0.66B 0.651 0.651 0.646 0.651 0.657  CO C.640 C.679 C.6H5 C.67Q C.679 C.668 C685 C685 C66R C.646  II  CURRTNI EFFICIENCY Et  Itl  T?  Itl  I? POWFR EFFICIENCY EP Itl  100.0 t o c o 13.0 18.3 9.5 13.7 8.4 11.2 10.2 8.9 6.5 8. 1 9.4 7.3 7.7 5.9 7.7 5.7 6.0 4.8 5.9 4.8  100.000 0. 8C9 0.707 0.647 0.609 0.565 0.544 0.517 0.446 0.475 0.456 0.419 0.386 0.360 0.332 0.311  lC77.e 1257.4 1437.1 1616.7 1796.4  569. 534. 507. 486. 468.  1.51 1.56 1.60 1.62 1.64  0.481 0.451 C.429 0.411 C.296  3. 14 3.44 3.72 3.94 4.16  0.657 0.640 0.623 0.623 0.623  C646 C635 C635 C.640 C.612  5.0 4.2 4.1 2.2 2.6  3.7  20  1787. 163e. 1887. 1513. 1544.  25  2245.4 2654.5 3143.6 3592.7  1996. 2C19. 2C33. 2C33.  442. 428. 421. 414. 414.  1.69 1.71 1.72 1.72  C374 0.362 C.356 0.35C  4.51 4.72 4.84  0.618 0.601 0.618 0.562  C.618 C.612 C.596 C.629  1.7 0.8 0.5 0.0 0.0  0.9 0.5 0.3 C.2 0.0  0.264 0.228 0.199 0.176  11  12  12 14 16 18  30 35 40 45  4041.8  TABLE  2C33.  C.1.44  1.72  0.350  4.91 4.91  0.612  C.590  CONCENTRATION BOTTOM TCP  CONCENTRATICN SEPARATION NORMAL IZEO FACTOR  CYCLE NC.  REAL TIME  NCYC l-l  T (SEC I  CB IPPMI  0 5 1C 15 20 25 30  0.0 70.8 141.6 212.4 2e3.2 354.0 424.8  1207. 1206. 1169. 1187. 1 1 6 8 . , 1165. 1155. 1161. 1149. 1156. 1141. 1147. 1133. I14C.  40 50 60 70 80 50 ICO  566.4 7C8.0 849.6 591.2 1132.fi 1274.4 1416.0  1125. 1119. 1114. 1108. 1106. 1103. 1 ICC.  1126. 1116. 1106. 1094. 10B4. 1075. I06e.  0.93 0.93 0.92 C92 0.92 0.91 0.91  0.686  120 14C 160  1659.2 1587.5 22*5.7  1C97. 1C92. IC86.  1054. 1042. 1032.  0.51  0.674  0.90  0.664  C.1.45  0.157  s NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-13/I2C  10  TABLE  2.9 2.2 1.7 1.5  CT IPPMI  XB l-l  XT l-l  CURRENT ENR. C I A L . 11 IAI  NS l-l  12 IAI  CURRENT EFFICIENCY E2 (tl  100.0 3.2 0.3 0.3  100.000 0.041  0.7 0.5  -0.002 -0.003  0.6 0.4 0.4  0.3  -0.000 0.0C1 o.oot 0.002 0.003 0.003 0.003  0.3 0.2 0.2  0.004 0.004 0.004  I.CO  l.COC  I.CO  0.0  CO  0.969 0.966  1.02  1.568 1.695 1.589 1.624 1.624 1.695  1.554 1.660 1.660 1.660  100.0 -1.6 -1.5 -1.1 -0.4 -0.7 -0.6  1.554 1.695 1.695 1.695 1.5B9 1.518 1.695  1.660 1.638 1.624 1.624 1.674 1.624 1.624  -0.3 -0.2 -0.2 -0.2 -0.1 -O.t -0.1  1.481  1.624 1.624 1.624  -0.1 -0.1  0.96 0.45 0.95 0.94  0.90  C963  0.558  I.CO  0.99  C91  0.951 0.945  0.99 0.99  0.934 C925 0.91T 0.507  I.CO l.ro  0.e95 0.891  0.856  1.01 1.01 1.0?  1.03 1.03  1.04 1.05 1.05  1.674 1.765  I NUMERICAL F V H U A I I C N CF EXPERIMENT E0l-Sl-l3/i2l  1.674 1.695  EP (tl  El Itl  0.56 0.97  POWER EFFICIENCY  -0.1  0.4  0.5  0.4 0.4  0.004  -0.005  -0.004  368 II  10 REAL TI»E  CYCLE NC.  CONCENTRATION BCJICM TCP  CONCENTRATION SEPARATION NCR^ALIZEO FACTOR XT l-l  HCYC l-l  T ISECI  CO IFPM  CI IPPM)  xn i-i  0 1 2 3 4 5 6 7 e 9 IC II 12 13 14 IS 16 17 18  O.C 60.6 121.2 lei.s  1237. I4r>c. 15 7 5 . 16 9 6 . 1784. 1E47. 1892. 1924. 1547. 1561. 197C. 1S81. 1987. 1990. 1590. 159C. 159C. 159C. I59C.  1237. 1004. 854. 743. 662. 604. 562. 535. 516. 501. 484. 482. 48C. 477. 470. 467. 466. 464. 464.  l.CCC o.eu 1.27 0.69C 1.37 C.601 1.44 0.535 1.49 0.488 1.53 0.455 1.56 0.433 1.57 0.417 1.54 0.405 t . 5 9 C.391 1.60 C.390 1.61 C.388 1.61 0.382 1.61 0.380 1.61 0.377 1.61 0.376 1.61 0.375 1.61 0.375  242.4  3C3. 1 36 3.7 424.3 484.9  '45.5 6C6. 1 666.7 727.3 76B.0 848.6 9C9.2 569.e 1C30.4 1C51.C  TABLE  1  2  CYCLE NC. NCYC J-l  C.1.46  It IAI  I2 IAI  0.0 1.1PB l.ino 1.1 55 1.155 1.105 1.048 1.081 1.0 11 1.081 1.039 1.072 l.OHl 1.039 1.064 1.039 1.064 1.039 1.056  CO 1.081 1.147 1. 130 1.089 1.089 1 . 138 1.081 1.097 1.064 1.064 1.034 1.039 1.048 1.056 1.064 1.039 1.0B1 1.039  NS l-l  l.CO 1.44 1.B5 7. 78 2.70 3.06 3. 17 3.59 3. 77 1.92 4.07 4.11 4.14 4.22 4.24 4.26 4.27 4.29 4.29  CURRENT EFFICIENCY  fI.2t l  El It)  100.0 1C0.0 27.8 13.2 2C.2 16.5 15.2 16.2 11.6 11.3 8.8 8.3 6.8 5.6 3.9 4.5 2.7 3.4 2.3 2.1 2.4 1.3 1.7 0.2 C.4 O.B 0.4 1.1 0.4 0.0 0.4 0.0 0.2 0.0 0.2 0.0 0.0 0.0  POWER ' EFFICIENCY EP Itl  100.000 2.103 1.848 1.634 1.453 1.299 1.165 1.050 0.953 0.868 0.8C0 0.736 0.680 0.635 0.592 0.555 0.522 0.492 0.466  I NUMERICAL EVALUATION CF EXPERIMENT ED1-S3-13/I22  3 REAL TIME  l.CO  1.17  CURRENT ENR. CIAL.  1?  4  5  CONCENTRATION BOTTOM TOP  6  7  8  CONCENTRATION SEPARATION NORMAL I 2EC FACTOR  9  10  CURRENT ENR. C I A L .  11  CURRENT EFFICIENCY  CB IPPM)  CT IPPM)  XB I-)  XT I-)  NS I-)  11 IA)  12 (A)  0 1 2 3 4 5  0.0 27.1 54.3 El.4 ICS.6 135.7  1295. 1405. 1511. 1603. 1705. 1796.  t2se. 1133. 1032. 942. 86C. 791.  l.CC I.C9 1. 17 1.24 1.32 1.39  l.COO 0.901 0.821 C749 0.6B4 0.629  l.CO 1.21 1.42 1.65 1.93 2.21  0.0 1.4C0 1.529 1.547 1.579 1.474  CO 1.584 1.511 1.455 1.400 1.455  100.0 27.3 23.9 20.7 23.0 21.3  100.0 27.3 23.1 21.5 2C1 16.6  100.000 1.626 1.416 1.307 1.259 1.203  101 15! 20 25 30 35 4C  271.4 ACT.1 542.e 678.5 814.3 95C0 1C65.7  2175. 2400. 2521. 2578. 2611. 2617. 2622.  533. 402. 339. 31C 297. 28B. 286.  1.68 1.85 1.95 1.99 2.C2 2.02 2.C3  C.424 0.32C 0.270 0.246 0.236 0.229 0.228  3.97 5.79 7.22 8.04 8.55 8.84 8.90  1.179 1.29C 1.105 1.197 1.105 1.105 1.105  1.437 1.142 1.179 1.0B7 1.105 1.105 1.105  22.3 12.1 7.6 3.3 2.0 0.4 0.4  12.4 7.9 3.7 1.9 0.8 0.6 0.1  1.046 0.887 0.754 0.641 0.556 0.488 0.433  C.l.47  I NUMERICAL EVALUATION CF EXPERIMENT' £0l-S3-l3/»24  E2 It)  POWER EFFICIENCY  T ISECI  TABLE  El It)  12  EP It)  369  in CYCLE KC.  RIAL 1 l"E  CCNCCNTHAT ICN BOTTOM  rn  1  CTNCINTRATICN  NURMAlIZEU  I ISCCI  CB  CI  xn i-i  1289. 1452. 159P. 1 739. ie5P. 1576.  1254. 11)1. 1014. 913. 82C. 746.  l.CC  5  CO 37. 1 74.3 111.4 148.6 185.7  1C 15 20 25 30 35  371.4 557. 1 742.8 528.5 1114.3 13C0.0  2368. 2566. 2667. 2715. 2736. 2754.  488. 37). 322. 301. 292. 2C6.  NCYC C-l  0 1 2 3  TABLE  C.1.48  XT  I-)  CL'.IRFNI  SEPARATION  FACTOR  ENR.  NS l-l  I.CO 1.25 1.5)  I? IA)  CO C.996 1.07 7 1.021 1.C5D 1.010 C.961 C.929 C.969 C.942 C.BOB C.969  1.24 1.35 1.44 1.51  l.CCC 0.902 0.8C9 C.728 0.654 0.595  2.20 2.53  0.0 1.2 J G 1.111 1.1)1 1.017 1.0)7  1.84 1.59 2.C7 2. 11 2. 12 2. 14  0.3B9 0.297 0.257 C.24C C.233 0.228  4. 72 6.70 8. 05 8.79 9.13 9. 15  0.848 0.821 0.700 0.71) 0.862 0.660  I . I )  I.85  CIAL,  It IAI  El It)  It)  73.4 12.2 7.3  3.4  1.2 1.4  13.5 6.3 2.6 1.2 C.6 0.3 '  12 pnwER EFFICIENCY EP Itl  too.OCO 1.865 1.7C5 1 .621 1.548 1.484 1.228 0.994 0.822 0.692 0.591 0.518  I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/I25  CONCENTRATION ECTTCM TCP  CONCENTRATION SEPARATION NORMAL I ZED FACTOR  CYCLE NC.  REAL TIKE  NCYC l-l  T ISECI  CB IPPMI  CT (PPM)  XB l-l  0 I 2 3 4 5  0.0 37.1 74.3 111.4 148.6 185.7  1292. 1388. 1483. 157C. 1654. 1727.  1264. 1187. 1107. 1036. 968. 909.  l.CC 1.07 1.15 1.22 1.28 1.34  l.COC 0.939 0.e76 0.619 0.765 0.719  10 15 2C 25 30 35 40  371.4 557.1 747.8 528.5 1114.3 13CC.C 1485.7  2C07. 2178. 2768. 2318. 2347. 2365. 2368.  69C. 568. 503. 461. 449. 439. 435.  1.55 1.69 1.76 1.79 1.82 1.63 1.83  0.546 0.449 C398 0.369 0.355 0.347 C.344  C.l.49  E?  loo.o l o c o )).4 31.1 32.5 27.6 31.5 24.9 29. 1 77.4 28.6 18.7  10  TABLE  tl  CURRENT EFFICIENCY  XT I-)  CURRENT ENR. CIAL. It (Al  12 (A)  I.CO 1.14 1.31 1.48 1.67 1.86  0.0 0.608 0.808 0.754 0.6P7 0.673  CO C.727 0.862 C.700 C.673 C.619  2.85 3.76 4.41 4.86 5.12 5.28 5.33  0.536 0.53e 0.512 0.565 0.465 0.512 0.512  0.673 C.619 0.619 C.565 C.619 C.592 C.565  NS l-l  > NUMERICAL (VALUATION CF EXPERIMENT EOI-S3-13/626  11  CURRENT EFFICIENCY El Itl  E2 (XI  12 POWER EFFICIENCY EP It)  100.0 100.0 30.3 26.9 29.6 23.5 29.1 25.6 31.1 25.7 27.6 23.7  100.000 3.754 3.352 3.271 3.255 3.193  16.5 ICO 5.3 3.2 1.5 0.9 0.3  2.812 2.401 2.033 1.737 1.509 1.327 1.179  26.3 16.0 8.9 4.5 3.1 I.7 0.3  370 1  2  3  CYCLE KC. NCYC l-l  4  Hr»l CCN'CrMHAT UN 1I«T: BCTIOM 10P  5  *  CONCENT RAT1TN SFPARATION NORMAL I /CO fAClUR  T ISCCI  CB CI (PI'M IPPMI  XB (-1  XT I-)  0 1 2 3 4 5  CO 32.1 64.3 96.4 178.6 UC?  1709. 1341. 1397. 145C. 1497. 1542.  1767. UH3. 1 122. 10h6. 1013. 968.  I.CO 1.C4 l.CP 1.17 1.16 1.20  l.CCC 0.9 38 C.890 0.645 0.603 0.767  10 15 20 75 30 35 40 45 50  221.4 487.1 642.e 8C3.5 964.3 1125.0 1285.7 1446.4 1607.1  1744. 1661. 1978. 2C42. 2C82. 2105. 212C 2126. 2131.  787. 671. 595. 54 8. 519. 499. 488. 43C 475.  1.35 1.46 1.53 1.58 1.62 1.63 1.64 1.65 1.65  C674 0.532 0.471 C.435 0.411 C396 C287 C.28C C.376  TABLE  C.1.5C  8  t  9  CURRINT CNR. CIAL.  NS l - l  10  CURRTNI EFFICIENCY  II IAI  17 (Al  FI 111  I.CO 1.11 1.72 1. 1) 1.45 1.56  0.0 0.958 0.866 C.9S8 0.847 0.976  CO C646 C.67 1 C.687 C.66 7 C63 )  100.0 18.9 27.1 19.1 19. ) 15.9  2.17 2. 74 3.26 3.65 3.9) 4. 13 4.26 4.34 4.39  C9C3 0.866 0.829 0.879 0.879 0.755 0.755 0.718 0.755  C687 C.606 C.63) C.63) C565 C592 C579 C.592 C565  REAL TIME  NCYC l-l  T ISECI  CB CT (PPM) (PPM)  XB (-)  0 1 2 3 4 5  O.C 49.3 58.6 147.9 197.1 246.4  1237. 1319. 14C0. 1461. 1514. 1556.  I.CO 1.C7 1. 13 1. 18 1.22 1.26  10 IS 20  452.8 739.3 5B5.7  1674. 1705. 1710.  1.35 1.38 1.38  CONCENTRATION. SEPARATION NORMAL I /EC FACTOR  1214. 1069. 983. 913. 855. 815. 699. 66C. 649. — J  XT (-)  CURRENT ENR. CIAL.  POWER EFFICIENCY CP It)  100.000 3.270 2.892 7.658 2.540 7.402 2.0C3 1.731 1.507 1.313 1.161 1.037 0.9)3 0.646 0.773  NS (-)  11 (A)  12 I A)  l.CCC C.681 • 0.610 C752 C.705 0.672  1.00 1.21 1.40 1.57 1.74 1.87  0.0 0.711 0.677 0.745 0.745 0.745  CO C.433 C.663 C589 C571 C.553  0.576 C.544 0.535  2.35 2.53 2.59  0.666 0.677 0.632  C534 C.516 C.553  11  El It)  E2 It)  100.0 100.0 74.6 57.7 25. 1 22.5 17.4 20.4 15.1 17.6 11.9 12.5 7.5 1.9 0.4  7.S 2.6 C.7  12 POWER EFFICIENCY EP It)  100.000 9.507 7.3C4 6.251 5.597 5.026 3.429 2.486 1.912  - •  » NUMERICAL EVALUATION CF EXPERIMENT E0l-S3-l3/#2«  CCNCENTRATICN BOTTOM TCP  CYCLE NC.  REAL TIME  NCYC  T ISEC)  CB IPP")  CT IPPMI  XB (-1  0 1 2 3 4  0.0 54.3 108.6 162.9 217.1  1295. 1438. 1550. 1641. 1713.  1267. 112C. 1009. 92C. 853.  6 8 10 17 14 16;  325.7 434.3 542.8 651.4 740. C 648.5  1601. 1855. 1861. 1898. 1504. 19IC.  761. 712. 6R1. 666. 657. 653.  C.1.52  )0.8 72.8 7C9 19.5 16.0  CURRENT EFFICIENCY  10  TABLE  toco  15.5 13.) 10.9 9. 7 8.1 6.1 5. ) 3.7 3.4 7.7 2.1 t.7 1.3 1.0 0.6 C.7 0.5 CS  10 CONCENTRATION 8CTTCM TCP  C.l.SI  t? Ml  I?  : NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/H27  CYCLE NC.  TABLE  II  CCNCENTRATICN SEPARATION • NORMALIZED FACTOR  CURRENT ENR. CIAL.  XT I-)  (-)  NS  II (A)  12 IAI  I.CO 1. 11 1.20 1.27 1.27  l.CCO C684 0.796 C726 C.473  I.CO 1.76 1.50 1.75 1.97  0.0 0.67? 0.617 0.56? 0.589  CO C.57I C.580 C616 C.553  1.39 1.43 1.45 1.47 1.47 1.48  0.601 0.562 0.536 0.525 0.516 0.515  2.32 2.55 7.70 2.79 2.84 2.86  0.56? 0.56? 0.541 0.514 0.5)4 0.525  C589 C.551 C.54) C.541 C.541 C.553  I NUMERICAL CVALUAMCN OF EXPERIMENT 10I-S1-I1/179 •  11  CURRFNT EFFICIENCY El Itl  E2 Itl  100.0 100.0 37.0 44.6 31.3 33.1 28.5 74.2 70.7 21.0 13.5 8.3 4.1 2.8 0.9 0.9  13.4 7.7 4.9 7.5 1.4 0.6  12 POWER EFFICIENCY EP Itl  100.OCO 4.560 3.947 3.540 3.209 2.622 2. 193 1.868 1.616 1.413 1.253  371 10 CCNCENTRAT ICN SEPARATION NCICAIUED FACTOR  CYCLE NC.  11*6  CCNCENTRATKN BCITCM ICP  NCYC l-l  T (SEC)  CB (f-PM)  CT (PPM)  XB (-)  0 1 2 3 4 5  0.0 25.1 50.3 75.4 ICO.5 125.7  1297. 14 30. 1536. 1651. 1753. U53.  1276. 1153. 104C. 951. 867. 787.  l.CC 1. 10 1.16 1.27 1.35 1.43  IC 15 20 25 30 35  251.4 377.C 5C2.7 628.4 754.1 679.7  2227; 2433. 253C. 2576. 2596. 2611.  526. 395. 335. 306. 297. 290.  run  TABLE  C.1.53  XT (-)  l.CCC C.904 C.82C C.745 0.679 0.617  1.72 0.413 1.68 0.309 1.55 0.263 1 .99 0.242 2.CO 0.233 2.CI 0.228  CURRENT ENR. CIAL.  NS (-1  II IAI  12 IA)  l.CO 1.72 1.44 1. 71 1. 99 2.32  0.0 1.86? 1.96? 1.763 1.540 1.415  CO C.934 C.929 C.962 1.078 1.078  4.16 6.06 7.42 8.22 8.60 8.85  1.763 1.117 1.142 1.018 0.993 1.018  C.614 C.830 C.61 3 C846 C.830 C.830  II  CURRENT EFFICIENCY El Itl  F? It)  100.0 I C C O 33.3 4C.7 25.2 35.9 30.5 3C.9 30.8 24.2 32.8 23.1 19.8 17.1 8.0 4.4 1.7 1.4  76.5 9.9 4.5 2.0 C.9 C.S  17 POWER EFFICIENCY EP Itl  ICO.OCO 1 .B95 1.652 1 .597 1.541 1.512 1 .285 1.114 0.939 0.805 0.698 0.615  I NUMERICAL EVALUATION CF EXPERIMENT EOt-S3-13/#3C  4-  1  2  CYCLE NC.  REAL TIME  NCYC  3  4  CCNCENTRATICN BOTTOM TCP  S  6  T ISEC)  CB (PPM)  CT (PPMI  XB (-)  0 1 2 3 4 5  0.0 30.1 60.3 90.4 120.5 150.7  1322. 1491. 1654. 1796. 1521. 2C39.  1302. 1169. 1045. 942. 847. 762.  l.CO  l.COC  1.13 1.25 1.36 1.45 1.54  10 IS 20 25 30  3CI.4 452.0 602.7 753.4 9C4.1  2439. 2637. 2730. 279C. 2B5C.  49P. 379. 329. 31C 303.  1.64 1.99 2.C6 2.11 2.16  TABLE  C.l.54  8  7  CCNCENTRATICN SEPARATION NORMAL I2EC FACTOR XE l - l  9  CURRENT ENR. CIAL.  NS I-)  II IA)  12 (A)  0.e97 0.«02 C.723 0.647 0.585  1.00 1.26 1.56 1.88 2.25 2.64  0.0 1.195 1.228 1.029 0.896 0.946  0.0 1. 145 1.112 1.095 1. 195 1.128  0.282 C291 0.252 C.238 0.233  4.83 6.85 8.18 e.88 9.27  0.863 0.730 0.830 0.846 0.597  C.996 C962 C.813 C.763 1.012  I NUMERICAL EVALUATION OF EXPERIMENT I01-S3-13/I31  10  11  CURRENT EFFICIENCY El It)  E2 It)  100.0 100.0 44.2 36.5 41.3 34.7 42.9 29.4 43.7 25.9 38.8 22.1 28.9 17.0 7.0 4.4 6.1  16.6 7.7 3.9 1.6 0.4  12 POWER EFFICIENCY EP It)  100.000 2.197 2.071 1.995 1.928 1.849 1.522 1.250 1.034 0.876 0.762  372 to CYCLE NC.  REAL TIME  CCNCENTRATICN 0C11CN TCP  XT l-l  SEPARATION FACTOR  CURRENT ENR. C I A L .  NS (-1  12 IAI  II (A |  NCYC  I ISECI  CP IPPPI  0 1 2 3 4 5 6 7 e 9 IC  CC 33.C 65.9 58.9 131.8 1(4.e 197.8 230. 7 263.7 296.6 329.6  1317. 179C. 1406. 116(. 1637. 1C49. 1 776. 939. 1907. 844. 2C22. 764. 212C 694. 2216. 633. 2295. 582. 2368. 541. 2427. 501.  l.CC 1.11 1.24 1.35 1.45 1.54 1.61 1.68 1.74 1.80 i.e4  l.CCO 0.9C4 o.eu 0.728 0.6 54 C.592 0.538 0.491 0.451 0.419 o.3es  1.00 1.25 1.53 i.es 2.71 2.59 7.99 3.43 3.86 4.79 4.75  0.0 1.214 1.171 1.138 1.047 1.077 0.910 1.001 0.865 0.986 0.804  CO 1.183 1.151 1.016 1 .047 C971 1.173 C956 1.032 C.880 1.032  IS 2C 25 3C  494.4 659.2 824.0 5E6.8  2625. 2727. 2E02. 2e26.  381. 329. 307. 297.  1.99 2.C7 2. 13 2.15  C.295 0.255 0.238 C.230  6.76 8.12 8.94 9.3J  0.834 0.804 0.789 0.834  C.865 C.834 C.834 C.789  TABLE  1  C.I.S5  2  CYCLE NC. NCYC (-)  XB l-l  11  CURRENT EFFICIENCY El Ml  E2 IT)  12 POWER EFFICIENCY EP (Tl  100.0 10C.0 39. 7 29.8 38.4 29.0 34.7 1C.7 35.7 26.0 30.4 71.5 17.7 30.8 ie.i 27.1 26.0 14.1 21.2 13.4 11.0 20.9  100.OCO 1.443 1.D33 1.783 1.733 1 .667 1.554 1.538 1.477 1.418 1. 162  13.6 7.2 5.4 1.6  7.9 3.5 1.5 O.T  1.124 0.936 0.799 0.687  10  II  S NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-13/I32  3 REAL TIME  CT (PP*I  CCNCENTRATIfN NORMALIZED  4  CCNCENTRATICN BCTTCM TCP  5  6  7  8  CONCENTRATION SEPARATION NORMALIZED FACTOR  9  CURRENT ENR. C I A L .  CB IPPM)  CT (PPM)  XB (-)  XT (-)  0 1 2 3 4 5  0.0 33.C 65.9 98.9 121.8 1(4.8  1308. 1394. 1483. 1567. 1(46. 1716.  1278. 1216. 1148. 1081. 1019. 964.  l.CO 1.C7 1.13 1.20 1.76 1.31  l.CCC 0.952 0.898 0.e46 0.797 C754  l.CO 1.12 1.26 1.42 1.58 1.74  0.0 1.168 1.092 1.062 1.107 1.107  CO 1.092 1.138 1. 107 1.016 C956  10 15 20 25 30  229.6 454.4 (59.2 824.C sea.e  2C19. 2227. 2374. 2471. 2542.  729. 57C 464. 396. 352.  1.54 1.70 1.81 i.e9 1.94  0.570 0.446 C363 0.310 0.275  2.71 3.82 4.99 6 . 10 7.05  0.910 0.604 0.789 0.7e9 0.756  C986 C.941 C.865 C.834 C.789  37.9 29.6 21.2 14.1 10.7  27.1 19.2 13.9 9.3 6.3  1.850 1.665 1.495 1.336 1.205  40 50 60  1318.4 1648.0 1977.6  2617. 2658. 2676.  304. 285. 277.  2.CO 2.C3 2.C5  0.238 C223 0.21T  8.40 9.11 9.43  0.713 0.774 0.774  C.619 C.774 C.774  5.9 3.1 1.3  3.3 1.4 0.6  0.989 0.828 0.706  C.1.56  11 (Al  I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-I3/I33  12 IAI  El IXI  E2 (XI  12 POWER EFFICIENCY  T ISECI  TABLE  NS l - l  CURRENT EFFICIENCY  100.0 100.0 41.8 32.3 46.4 34.2 45.0 34.5 34.7 40.5 36.3 33.1  EP IX)  100.000 2.294 2.176 2 . 128 2.079 2.022  373 1  2  3  4  t  REAL TIME  NCYC l-l  1 ISECI  C8 IPPM|  CT I PPM)  X8 I-)  XT l-»  CC 33.0 45.9 58.9 131.8 164. 8  1215. 127C. 1325. 138C 1436. 148C.  1196. 1151. 1096. 1058. 1023. 98C  l.CC 1.C5 1.C9 1.14 1.18 1.22  l.COC 0.962 C917 0.885 0.655 C.620  20 25 30  229.6 494.4 659.2 624. C 566.e  1691. 1653. 1978. 2C75. 2163.  82C 681. 587. 50 7. 446.  1.39 1.52 1.63 1.71 1.78  40 SO to 70  1318.4 1648.C 1977.6 2207.2  2274. 2242. 2286. 2412;  368. 322. 295. 281.  1.67 1.93 1.96 1.99  10  is  TABLE  1  C.I.ST  2  NO. NCYC l-l  T ISECI  0  0.0  1 2 3  33.0  4  S 10 IS 20 25 30 35 40  65.9 56.9  131.8 164.6 229.6 454.4  659.2 824.0 566.8  1153.6 1318.4  TABLE  4  CONCENTRATION BOTTOM TOP  CURRFNT ENR. C I A L .  NS (-1  10  12 IAI  1.00 1.09 I . 19 1.78 I . 18 1.49  0.0 1.138 1.123 1.1C7 1.1?) 1. 153  CO C.B95 C.956 C. 619 C758  0.686 C57C C.491 C.424 C.374  7.03 2.68 3. 32 4.04 4.76  1.0)2 0.834 0.B19 0.819 0.743  C75R C895 C774 C.774 0.789  34.9 33.2 26.3 21.1 19.3  0.307 0.270 0.247 C.235  6.C9 7.15 7.95 8.44  0.698 0.652 0.652 0.60?  C.774 C.789 C.774 C.819  13.6 8.8 5.8 3.7  c.eao  11  12  CURRENT EFFICIENCY  II IAI  5-  6  CT I PPM 1  XB XT l-l l - l  NS l-l  1237. 1297. 1355.  1205. 1086.  1411. 1461.  867. 775. 69e.  I.CO 1.C5 1. 10 1. 14  1.00 1.16 1. 36 1.59  1511. 1696. 1601. 1661.  ie95. 1515; 193C. 1941.  97C  440. 317. 258. 230. 215. 209. 206.  a  7  CCNCENTRATICN SEPARATION NORMALIZED FACTOR  CB IPPMI  C.1.S8  9  El It)  POWER EFFICIENCY  E2 III  100.0 100.0 41 .) 43.1 42.0 46.5 42.7 37.6 47.) 36.3 33.0 46.0  EP I t l  100.000 2.59) 2.460 2.339 7.769 2.221  36.1 26.6 2C.8 17.7 12.9  2.034 1.881 1.734 1.602 1.487  6.8 4.9 3.0 l.S  1.285 1.118 0.983 0.871  * NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/«34  3  REAL TIME  CYCLE  8  7  CCNCENTRAT ICN SE M A M ATICN NORMALIZED TACIOR  CYCLE KC.  0 1 2 3 4 5  CCNCCNIRAIICN DCIICM TCP  S  11 (Al  12 IAI  CO C.986 1.123 C.956 1.062 1.C01 C.743 C.69R C.637 C.637 C.607 C.637 C.667  1.22  l.COO 0.901 o.eos 0.719 0.643 0.579  7. 11  0.0 1.168 1.016 1.047 0.910 0.925  1.37 1.46 1.50 1.53 1.55 1.56 1.57  0.365 0.263 C214 0.191 0.179 C173 C.171  3.76 5.53 7.03 8.04 8.66 9 . CO 9.16  0.634 0.713 0.667 0.652 0.607 0.S76 0.S46  1.18  1.84  9  CURRENT ENR. C I A L .  I NUMERICAL EVALUATION CF EXPERIMENT EDl-SJ-IJ/ilS  10  11  CURRENT EFFICIENCY El Itl  100.0 44.3 48.8 45.3 47.0 46.4 38.0 25.2 15.3 9.0 S.6 4.2 3.6  E2 ( t l  100.0 34.) 29.5 30.8 24.6 27.0 19. 8 ICO 5.3 2.5 1.3 0.6 0.2  12 POWER EFFICIENCY EP (t)  100.OCO 2.492 2.249 2.168 2.085 2.023 1.810 1.561 1.351 1.174 1.037 0.926 0.835  374 10 CYCLE NC.  RP*L 11  CCNCfNIRATICN UCT1CM  TCP  CONCENTRATION SEPARATION NCRMALUEO EAC1E1R  10 IS 2C 25 30  329.6 494 .4 659.2 e24.C 5E8.8  2456. 2602. 303e. 3204. 3246.  857. 74e. ' 646. 581. 53C.  1.90 2. 17 2.35 2.48 2.59  40 50  1318.4 1648.C 1S7T.6  3501. 36C1. 3645.  466. 428. 412.  2.71 2.79 2.82  3  CYCLE NO.  REAL TIME  CONCENTRATION BCTICM TOP  NCYC I-)  T I SEC)  CB CT (PPM) (PPM)  0.0 60.6 121.2 iei.8 242.4 3C3.1 263.7 424.3 484.9 545.5 606.1 6(6.7 727.3 768.0 848.6 5C9.2  TABLE  4  4709. 4868. 4598. 510C. 5187. 5259. 5203. 5332. 5361. 5291. 5405. 5405. 5405. 542C. 542C 542C.  C.I.6C  XT  (-)  I NUMERICAL EVALUATION EOI-S3-13/A36  2  4636. 4263. 4036. 3859. 3711. 3603. 3512. 3444. 3381. 3331. 3291. 3263. 3235. 3212. 319C. 3173.  5  29.1 19.4 15.3 9.6 8.2  0.956 0.941 0.941  1.047 1.062 1.062  4.6 3.0 1.3  5.3 3.0 1.4  0.e30 0.698 0.594  11  12  7.35 8.22 8.66  l.CO 1.13 1.24 1.35 1.46 1.54  1  25.1 19.1 15.0 11.7 8.2  0.369 0.339 C.326  1263. 1218. 1166. 1126. 1081. 1035.  C.1.59  C.986 1.047 1.138 1.168 1.047  2.77 3.66 4.60 5.40 6. 17  1297. 1461. 16C6. 1 147. 1681. 1596.  l.CCC C964 0.923 0.892 C856  5  CC 33.C 65.9 58.9 131.P 164.8  TABLE  1.047 1.C3? 0.895 0.BP4 0.986  0.686 0.592 0.512 C460 C42C  0 1 2 3  to  10C.0 38.0 37.3 31.6 33.9 37.4  cei9  (-1  A  100.0 42.3 41.4 36.3 38.7 32.2  0.0 1.1)0 I.001 1.107 0.9B6 1.016  CI (PPM)  NS l-l  loo.oco 2.454 2.224 2.076 2.019 1.96 7 1 .674 1 .440 1.278 1. 135 1.017  OF EXPERIMENT  6  7  8  CONCENTRATION SEPARATION NORMALIZED FACTOR XB (-)  XT (-)  l.CO 1.03 1.C6 1.08 I . 10 1.12 1.13 1.13 1.14 1.14 1.15 1.15 1.15 1.15 1.15 1.15  l.CCO 0.920 0.871 0.e32 o.eoo C777 C757 C.743 0.729 C7ie C.71C C.704 0.698 0.693 o.6ee 0.684  I NUMERICAL EVALUATION EOI-Sl-l3/«37  EP It)  CO 1.016 1.18) 1.016 1.138 1.062  l.CO 1.17 1. 35 1.52 1. 70 1.89  CB (PPM)  POWER EFFICIENCY  E2 Itl  12 IAI  1 (SEC I  CURRENT EFFICIENCY  12  El IT)  II IAI  HOC l-l  XB  CURRENT ENR. C I A L .  II  CURRENT ENR. C I A L .  NS l - l  l.CO 1. 12 1.22 1.30 1.38 1.44 1.49 1.52 1.56 1.59 1.62 1.63 1.64 1.66 1.67 1.68  9  II IAI  12 IA)  0.0 1.708 1.699 1.650 1.666 1.666 1.666 1.658 1.650 1.650 1.633 1.625 1.617  CO 1.683 1.749 1.782 1.732 1.724 1.716 1.699 1.691 1.691 1.663 1.683 1.683 1.683 I.6B1 1.663  1.611  1.617 1.617  CF EXPERIMENT  10  CURRENT EFFICIENCY  POWER EFFICIENCY  El E2 EP I t l I t l I t l  100.0 100.0 34.4 14.4 20.0 11.9 IS.5 9.5 13.3 8.1 9.7 6.8 8.2 4.1 6.2 2.7 5.7 2.7 4.7 2.7 3.6 1.4 2.6 0.0 2.6 0.0 2.1 1.4 2.1 0.0 1.6 0.0  100.000 5.089 4.014 3.457 3.096 2.787 2.518 2.282 2.100 1 .946 1.803 1.665 1.550 1.458 1.370 1.290  375 10  CYCLE KC. NCYC l-l  RF A l  11 "E  CCKC CNl WAT ICN SEPARATION NCRXAIUEO FACTOR  T I SEC I  CP IFPMI  CT IPPMI  l-l  CC 35.3  45)7. 4666.  4502. 4356. 4246. 4141 .  l.CC l.C) I.C5 I.C6  4043.  I.C8  0.P98  SC42. 51CC. 5158. 5201. 5245.  3951. 3865. 3 791. 3722. 3654. 3597.  1.10 1. 11 1.12 1. 14 1.15 1.16  0.e78 0.e59 0.e42 0.827 0.612 0.759  542C. 5537. S61C. 5654. 5683. 5683.  3353. 3196. 307e. 3000. 2944. 2899.  1.19 1.22 1.24 1.25 1.25 1. 25  C.745 C71C 0.684 0.666 C.654 0.644  let  7 8 9 10  1C5.9 141.2 176.5 211. e 247. 1 282.4 317.8 353. 1  15 70 25 30 35 4C  529.6 7C6.1 ee2.7 1C59.2 1225.7 1412.2  6  CONCENTRATION BCTICH TOP  TABLE  4753. 4825.  4S1 1. 4564.  C.1.61  XB  XT  l-l  l.CCC  0.96e C.943 C57C  t NUMERICAL EVALUATION OF EOI-S3-13/I36  I  2  CYCLE NC.  REAL TIME  NCYC l-l  T ISECI  CB IPPMI  CT IPPMI  XB |-|  CO 37.1 74.3 111.4 148.6 165.7 222.9 260.0 297.1 334.3 271.4  4955. 523C. 5434. 5669. 5660. 6C37. 6215. 6348. 6467. 6602. 6707.  4889. 4646. 4408. 4199. 3997. 3825. 3665. 3517. 3387. 3263. 3162.  I.CO 1.C6 1.10 1.14 1.18 1.22 1.25 1.28 1.31 1.33 1.35  l.COO 0.951 C.902 0.e59 0.818 C.782 0.150 C719 C.693 0.667 0.647  557.1 742.6 528.5 1114.3 13CC.0  7C97. 7255. 7491. 7598. 7628.  2766. 2534. 2366. 2304. 2260.  1.43 1.48 1.51 1.53 1.54  0.566 0.518 0.488 C.471 0.462  C 1 2 3  4 5 6 7 8 9 10 15 20 25 30 35  TABLE  3  4  CONCENTRATION BOTTOM TOP  C.l.62  5  6  CURRFNT ENR • C I A L . II IAI  12 IAI  0.0 1 .946 1.954  CO 1.671 1.791 1 .869 1 .Re4 1.869 1.855 1.841 1.827 1.P27 1.813  NS l-l  I.CO 1.06 1.11 1.16 1.21 1.25 1.29 1.33 1.37 1.41  1.45  1.869 1.R69 1.827  1.869 I.R55 1.841 1.841 1.827  1.87  1.827 1.813 1.784 1.784  1.92 1.95  1.799  1.60 1.72 1.81  1.799  CURRFNT EFFICIENCY El Itl  F? Itl  1C0.0 l o c o 23.2 17.7 16.4 11.8 14.8 10.1 1 1.9 12.3 13.1 8.4 12.3 10.) 8.) 1C.8 ICO 8.4 I C O 6.3 8.4  6.4 5.1  3.4  2.2 1.3  0.9 0.0  7.4 4.8 3.6 7.4 1.8 1.4  12 POWER EFFICIENCY CP 1X1  100.000 2 . IC5 I .690 1.512 1.436 1.349 1 .299 1.240 1 . 142 1.145 1.099 0.930 0.797 0.695 0.611 0.543 0.465  EXPERIMENT.  7  6  CONCENTRATION SEPARATION NORMALIZED FACTOR XT l - l  1.756 1.742 1.728 1.714 1.685 1.685  II  9  CURRENT ENR. C I A L .  NS 1-1  11 IAI  12 IAI  1. 00 1.11 1.22 1.33 i 1.45 1.56 1.67 1.78 1.68 2.CO 2.09  0.0 2.006 1.917 1.912 1.871 1.658 1.831 1.S44 1.865 1.885  0.0 1.723 1.817 i.ees 1.631 1.750 1.750 1.696 1.669 1.615 1.589  2.53 2.86 3.10 3.25 3.33  1.777 1.777 1.723 1.696 1.669  1.615 1.562 1.5)5 1.535 1.521  i.ees  I NUMERICAL EVALUATICN CF EXPERIMENT EUl-SI-ll/«39  10  11  CURRENT EFFICIENCY El (X)  E2 «XI  12 POWER EFFICIENCY EP I t l  100.0 100.0 34.7 35.4 27.0 33.3 31.0 28.0 25.8 27.9 24.1 24.9 24.5 2 3.1 18.3 22.0 16.0 19.7 18.0 19.4 14.1 16.1  100.000 3.583 3.159 2.998 2.861 2.738 2.646 2.535 2.475 2.348 2.255  11.1 7.3  12.4  4.0 3.2  4.9 2.7  0.9  1.5  1.881 1.595 1.371 1.198 1.051  7.5  376 I  ?  CYCLE NC.  REAL TIME  NCYC l-l  3  4  CCNCENTRATICN BCIICH TOP CB IPPM)  CT IPP*I  XO (-1  0.0  5562. 51 32. 474R. 4 39f. 4089. 3814. 3566. 341C. 3156. 300C. 2855.  l.CO 1.C7 1.14 1.20 1.26 1.31 1. 35 1. 39 1.43 1.46  243C. 2173. 2026. 1935. 1881. 1854.  1.58 1.63 1.66 1.69 1.69 « 1.70  IC  371.4  5654. 6C66. 6436. 6766. 7C97. 74CC. 7643. 7e73. 8C72. 6272. 6442.  14 IB 22 26 30 24  520.C 668.6 617.1 965.7 1114.3 1262.6  B555. 9236. 9409. 9535. 9567. 9614.  111.4  5  140.6 ies.7  37.1 74.3  222.9  7 6  26C.C 297.1 334.3  9  6  7  1.49  XT l - l  C.1.63  10  CURRENT ENR. C I A L .  NS l - l  It IA)  12 (Al  n. o 3.015 3.096 3.19C 2.975 2.031 2.827 2.940 2.746 2.665 2.719  C.0 2.827 3. 150 3.177 3.015 3.C02 2.975 2.854 2.867 2.854 2.719  100.0 34.6 30.3 26.1 78.1 26.6 21.8  0.437 0.391 C.364 0.346 0.336 0.233  3.63 4.18 4.57 4.85 5.CO 5.10  2.558 2.396 2.369 2.342 2.356 2.342  2.639 2.585 2.585 2.558 2.531 2.531  12.7 7.4 4.6 3.4 0.6 1.3  ,  _  _  20.4 18.4  19.0 15.8  —  —  NCYC l-l  0 2 4  6 8 10 15 20 25 30 35  REAL TIME  CONCENTRATION BCTTCM TCP CB  CONCENTRATION SEPARATION NORMAL I ZEC FACTOR  CURRENT ENR. C I A L .  (PPM)  (PPM I  CT  XE l-l  XT I-)  NS (-)  II (A)  12 I A)  O.C 74.3 148.6 222.9 297.1 371.4  5376. 6141. 6796. 7294. 775C. 8C87.  5275. 449C. 3854. 3353. 2972. 2677.  l.CO 1.14 1.26 1.36 1.44 1.50  l.CCO 0.851 0.731 0.636 C.563 0.508  1.00 1.34 1.73 2.13 2.56 2.96  0.0 3.581 3.2es 3.096 2.800 2.600  557.1 742.8 528.5 1114.3 13C0.0  8643. 6923. 9C48. 9111. 9127.  220C. 1967. 163e. 1773. 1741.  1.61  0.417 C.373 C.348 C.336 C.230  3.85 4.45 4.83 5.04 5.14  2.773 2.531 2.531 2.504 2.477  TABLE  C.1.64  13.5  IP 0 . 0 C 0 2.391 7.091 1.973 1.843 1.77? 1.692 1 .600 1.557 1.497 1.439  10.7 6.3 3.6 2.3 1.3 0.7  1.242 1.076 0.938 0.829 0.736 0.661  loco 36.5 30.8 27.9  25.8 23.2 2C.8 14. 1 77.4 13.9  t NUMERICAL EVALUATION CF EXPERIMENT EOI-S3-13/I40  ISECI  T  POWER EFFICIENCY  —  10 CYCLE NC.  12  El F2 EP I t l I t l ( t l  1.16 1. 33 1.51 1.71 1.91 2. 11 2.27 2.52 2.71 2.91  1.00  II  CURRENT EEFICIENCY  l.COO C.923 0.854 0.79C 0.735 0.686 0.642 0.613 0.567 0.539 0.513  ,  TABLE  9  8  CONCENTRATION SEPARATION NCHMALIZEU FACIUR  T ISECI  c 1 2 3  6  5  1.66  1.68 1.69 1.7C  I NUMERICAL EVALUATION CF EXPERIMENT E0I-S3-11/I"  11  CURRENT EFFICIENCY El It)  E2 It)  0.0 2.827 2.881 2.827 2.692 2.665  100.0 27.0 25.2 20.3 70.6 15.2  100.0 35.1 27.9  2.531 2.585 2.477 2.423 2.315  10.1 5.6 2.5 1.3 0.3  9.5  22.4  17.9 14.0 4.6  2.6 1.3 0.7  12 POWER EFFICIENCY EP It)  100.000 1.945 1.769 1.614 1.510 1.394 1.148 0.955 0.8C9 0.697 0.611  377 10 Rf/II 1I*E  CYCLE NC. NCYC l-l  CONCENTRATION BCTTCM TCP  CCNCINTHATION SFPARAIICN NORMALIZED FACTOR  CURRFNT ENR. CIAL.  NS l-l  12  T I SEC I  CB (PPPI  CI IPPM  XC (-1  C 1 2 3 4 5  0.0 54.3 ICS.6 162.9 217.1 271.*.  5245. 5772. 6I7C. 6467. 664?. 6e72.  5126. 4414. 3934. 3568. 3291 . 3085.  I.CC 1.10 1.18 1.23 1.28 1.31  1 .ccc 0.861 C.767 C.696 0.642 C.603  l.CO 1.28 1.53 1. 77 1.49 2. 17  0.0 3. 150 3.150 3.C58 3.021 2.984  CO 3.C03 2.855 2. 763 2.640 2.653  7 9 11 13 IS  38C.0 4E8.6 597.1 7C5.7 eiA.3  7C97. 71E8. 7264. 7264. 7279.  2849. 268e. 2611. 2561. 2539.  1.35 1.37 1.38 1.38 1.39  0.556 0.524 0.509 O.SCC 0.495  2.43 2.61 2.72 2.77 2.80  2.874 2.837 2.874 2.817 2.8C0  2.579 2.579 2.542 2.395 2.358  TABLE  C.l.65  XT I-)  t NUMERICAL EVALUATION CF E0l-S3-13/»4l  II I A I  IAI  El It)  6.8 2.8 2.) CO 0.5  CURRENT ENR. C I A L .  REAL TIME  NCYC l-l  T ISECI  CB IPPM)  CT (PPM)  XB (-)  XT (-)  (-)  II IA)  12 I A)  0 1 2 3 4 5  0.0 254.3 588.6 ee2.9 1177.2 1471.5  5332. 5683. 5934. 6C96. 62S9. 6393.  5215. 4636. 428C 4038. 3831. 3665.  l.CO 1.C7 1.11 1.14 1.17 1.20  l.CCO 0.889 0.821 0.774 C.735 0.703  1.00 1.20 1.36 t.48 1.60 1.71  0.0 0.574 0.557 0.557 0.561 0.557  CO C.605 C.646 C637 C.639 C.652  7 9 11 13 15  2C60.0 2648.6 3237.2 3E25.8 4414.4  6542. 6632. 6707. 6751. 6766.  3421. 3269. 3162. 3111. 3055.  1.23 1.24 1.26 1.27 1.27  0.656 C.627 0.606 0.597 0.586  1.87 1.98 2.07 2.12 2.17  0.550 0.554 0.550 0.557 0.564  C.646 C.652 C65B C.646 C.6I5  C.1.66  CCNCENTRATICN SEPARATION NORMALIZED FACTOR  I NUMERICAL EVALUATION CF ECl-S3-l3/»42  8.0 5.4 2.6 1.8 C.8  12 POWER EFF IC IEN'CV EP It)  100.OCO 4.593 3.839 3.373 3.0C9 2.707 2.220 1.856 1.585 1.371 1.210  EXPERIMENT  CYCLE NC.  TABLE  E2 Itl  100.0 10C.0 28.9 41.0 21.9 29.1 16.8 22.9 12.8 17.8 10.4 13.2  10 CCNCENTRATICN BCTTCM TCP  II  CURRFNI EFFICIENCY  NS  EXPERIMENT  11  CURRENT EFFICIENCY El It)  E2 (t)  12 POWER EFFICIENCY EP It)  100.0 100.0 19.5 30.6 14.3 17.6 9.3 12.2 9.3 10.3 7.7 8.1  100.000 10.206 7.994 6.643 5.B76 5.272  6.0 3.7 2.6 1.2 l.S  4.321 3.621 3.122 2.712 2.405  4.3 2.6 2.2 1.3 0.4  APPENDIX C.2  EVALUATION OF EDI I EXPERIMENTS  (i)  Numerical  e v a l u a t i o n of second ED runs.  A short  computer program was w r i t t e n f o r an IBM 360/67 FORTRAN IVG compiler.  The program reads the run number, i n i t i a l c o n d i -  t i o n s , c o n d u c t i v i t y c a l i b r a t i o n data c y c l e p e r i o d , and the mV-readings  from the recorder chart f o r a sequence of c y c l e s .  It p r i n t s a table f o r each run which d i s p l a y s the progress in separation f o r r e p e t i t i v e c y c l i n g . tables (ii)  The program and the  follow. Tables were prepared which contain a record of  current and voltage d i s t r i b u t i o n s  f o r each run.  The e x p e r i -  ments are grouped together according to the parameter which was a l t e r e d in each group (see Table 34 to 39).  The t o t a l  current i s included as well as the a p p l i e d v o l t a g e .  The  average current and voltage in each stage were measured i n cycle ranges given i n columns 4 and 13, r e s p e c t i v e l y .  378  P°Sr  F O R T R A N  I V  31 °i  C  3 £ 0 do vn<sT~e^{. $J  OJACA  C O M P I L E R  R E A D  0 0 0 1 C 0 0 2  (  R E A O 2  5  ,  0 0 0 5  1  )  S E C O N D  (  5  ,  2  )  T  ( F 5 . 1 )  T = T / 6 0 . W R I T E 5  (  6  ,  F O R M A T  5  )  ( 1 H 1 , •  ;  •/  2 ' C Y C L E 3 *  N O .  4 '  N C  .  5 «  6  R E A L  0 0 0 8  C O N C E N T R A T I O N  T I M E  ( - )  7  B R I N E  T  C B  C T  ( M I N )  ( P P M )  ( P P M )  P = 1 . 0 J = 0  0 0 1 1  C B 0 = C B V * ( A 1 * C F ) V  0 0 1 2  C T O = C T V * ( A 2 * C T V + b 2 )  0 0 1 3  W R I T E  0 0 1 4  F O R M A T  0 0 1 5  D O  0 0 1 6  R E A D  0 0 1 7  F O R M A T  0 0 1 8  I F  0 0 1 9  (  6  ,  4  )  +  1 0 0 (  N S ' / ( - ) • /  1 = 1 , N 5  ,  3  ) K , C B V , C T V , L  ( I 2 . 2 F 6 . 2 t 1 2 )  ( L . N E . O )  _ F O R M A T  ( •  W R I T E  (  C T = C T V * ( A 2 * C T V + B 2 ) J = J * K  0 0 2 3  T I M £ = T * J  0 0 2 4  X B = C B / C B O  0 0 2 5  X T = C T / C T O  6  ,  6  )  • )  0 0 2 2  SE=XB/XT  0 0 2 6 0 0 2 7  W R I T E  100  R E A D  105  (  ,  4  )  ( 5 , 1 0 5 )  F O R M A T W R I T E  110  6  J , T I M E , C B , C T , X B , X T , S E  C O N T I N U E N T  ( 1 2 ) ( 6 , 1 1 0 )  F O R M A T  N  T  ,  M  ( / / •  : NUMERICAL EVALUATION OF EXPERIMENT / EDII-Sl-a/«',I2»  T A B L E  2«  3' 0 0 3 3  0 0 3 5  ,  l-l  F A C T O R * / /  J , T I P E , C 8 0 , C T 0 , P , P , P  C B = C B V * I A 1 * C B V + B 1 )  0 0 3 4  t-1  X T  (I4,F7.2,F8.0,F7.0,F9.2,F7.4.F10.2)  0 0 2 1  0 0 3 2  X B  S E P A R A T I O N ' /  Bl)  C 0 2 0  0 0 3 1  N O R M A L I Z E D  T I M E = 0 . 0  0 0 1 0  0 0 3 0  C O N C E N T R A T I O N  D I A L .  •//)  0 0 0 9  0 0 2 9  R U N S  M , N , C B V , C T V , A 1 , C I , A 2 , D 2  1  0 0 2 8  E O  PAGE 0  ( 2 1 2 . F 6 . 2 . 5 F 1 0 . 4 )  F O R M A T  0 0 0 6 C 0 0 7  E V A L U A T E  F O R M A T  1  C 0 0 3 0 0 0 4  T O  12:48:53  12-10-72  M A I N  P R O G R A M  381  W R I T E  120 20  0 0 3 6  ( 6 , 1 2 0 )  F O R M A T  H  ( 1 H 1 . I 3 )  S T O P  END  TOTAL MEMORY REQUIREMENTS 00068E BYTES COMPILE TIME -  1.3  SECONDS  CYCLE NO.  RC AL TIME  NC  T (MINI  l-l  CUNCCNTHATItlN URINE DIAL. CB IPPM)  CONC I: NTR AT I ON NUKMAllZCU  CT IPl'MI  xn l-i  XT (-)  t.cooo  StCAR AT ION FACTIIR NS (-)  0 1 2 3 4 5 6 7 8 9 10  0.0 0.67 1.33 2.00 2.67 3.33 4.00 4.67 5.33 6.00 6.67  5742. 6393. 6)32. 74 76. 7980. 8473. 8955. 9441. 9867. 10297. IC698.  5641. 4842. 4350. 3877. 3438. 302 7. 2650. 2304. 19B9. 1714. 1458.  1.00 1.11 1.21 1.30 1.39 l.4fl 1.56 1.64 1.72 1.79 1.86  0.85B4 0.7712 0.6873 0.6C95 0.5367 0.4698 0.4084 0.3526 0.3039 0.2505  l.OD 1.30 1.57 1.89 2.28 2. 75 3. 32 4.03 4. 87 5.90 7.21  12 14 16 18 20 25 30 35 40  8.00 9.33 10.67 12.00 13.33 16.67 20.00 23.33 26.67  11426. 12064. 12609. 13075. 13443. 13983. 14221. 14357. 14391.  1236. 670. 396. 271. 184. 98. 73. 67. 63.  1.99 2.10 2.20 2.28 2.34 2.44 2.48 2.50 2.51  0.2192 0.1542 0.0701 0.0480 0.0327 0.0174 0.0130 0.0118 0.0112  9. 08 13.62 31.31 47.44 71.61 139.65 191.09 211.95 224.3T  C.2. 1  TABLE  CYCLE NO. NC l-l  T (MINI  0 1 2 3  4 5 6 8 10 12 14 16 18 20 22 24 26 28 30  REAL TIME  * NUMERICAL EVALUATION OF EXPERIMENT EDIl-Sl-8/fl 6  CONCENTRATION BRINE DIAL. CB (PPHI  CONCENTRATION NORMALIZED  CT IPPMI  XB (-)  XT (-1  SEPARATION FACTOR NS (-)  0.0 0.83 1.67 2.50 3.33 4.17 5.00  5698. 5904. 6037. 6155. 6259. 6378. 6497.  5610. 5233. 5120. 5001. 4895. 4777. 4671.  1.00 1.04 1.06 1.08 1.10 1.12 1.14  l.COOO 0.9327 0.9126 0.8914 0.8725 0.8515 0.8326  1.00 1.11 1.16 1.21 1.26 1.31 1.37  6.67 8.33 10.00 11.67 13.33 15.00 16.67 18.33 20.00 21.67  6692. 6872. 7067. 7264. 7415. 7598. 7750. 7888. 8041. 8180. 8318. 8442.  4467. 4269. 4084. 3923. 3756. 3603. 3455. 3314. 3196. 3072. 2955. 2844.  1.17 1.21 1.24 1.27 1.30 1.33 1.36 1.38 1.41 1.44 1.46 1.48  0.7961 0.7609 0.7279 0.6991 0.6695 0.6421 0.6158 0.5906 0.5696 0.5476 0.5267 0.5068  1.48 1.58 1.70 1.82 1.94 2.08 2.21 2.34 2.43 2.62 2.77 2.92  23.33 25.00  TABLE  C.2. 2  S NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-8/*  7  383 CYCLE NO. NC (-1  REAL II ME T (MINI  CONCENTRATION BRINE DIAL. CP. (PPM)  CT <PPM|  CCNCIiNTKAT ION NORMAL 1/CO XB  SEPAR\JION FACTOR  XT  NS  (-1  (-)  (-1  0 2 4 6 8 10  0.0 2.00 4.00 6.00 8.00 10.00  5332. 6066. 6707. 7294. 7842. 8365.  5281. 4414. 3819. 3280. 2788. 2358.  1.00 1.14 1.26 1.37 1.47 1.57  1.0000 0.8359 0.7233 0.6211 0.52B0 0.4466  1.00 1. 16 1.74 2.20 2.79 3.51  14 18 22 26 30  14.00 18.00 22.00 26.00 30.00  9299. 1C090. 10794. 11377. 11834.  1623. 1079. 751. 437. 283.  1.74 1.89 2.02 2.13 2.22  0.3074 0.2043 0.1421 0.0827 0.0537  5.67 9.26 14.24 25.81 41.35  35 40 45  35.00 40.00 4S.00  12245. 12509. 12675.  182. 141. 121.  2.30 0.0344 2.35 0.0268 2.38 0.0229  6 6 . 68 87.65 103.65  TABLE  CYCLE NO. NC  (-)  C.2. 3  REAL TIME T (MINI  t NUMERICAL EVALUATION OF EXPERIMENT EDLI-Sl-8/ff 8  CONCENTRATION BRINE DIAL. CB (PPH)  CT (PPHI  CONCENTRATION NORMALIZED XB  (-)  XT ("I :  SEPARATION FACTOR NS l-l  0 0.0 1 1.33 2 2.67 3 4.00 4 5.33 5 6.67 6 , 8.00 7 9.33 a 10.67 9 12.00 10 13.33  5434. 6542. 7491. 8442. 9299. 10090. 10762. 11377. 11899. 12360. 12708.  5341. 4338. 3563. 2860. 2266. 1763. , 1368. 1047. 776. 570. 416.  1.00 1.20 1.38 1.55 1.71 1.86 1.98 2.09 2.19 2.27 2.34  1.0000 0.8124 0.6671 0.5356 0.4242 0.3310 0.2562 0.1961 0.1454 0.1067 C.0779  I.00 1.48 2.07 2.90 4.03 5.61 7.73 10.68 15.06 21.31 30.01  12 14 16 18 20  16.00 18.67 21.33 24.00 26.67  13275. 13611. 13865. 14000. 14119.  217. 121. 78. 58. 48.  2.44 2.50 2.55 2.58 2.60  0.0407 0.0227 0.0146 0.0109 0.0090  60. 02 110.45 174.35 237.37 289.84  25  33.33  14289.  40.  2.63 0.0075  348.38  TABLE  C.2. 4  r NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-8/H 9  384 CYCLE NO. NC  REAL T IMC T (MINI  CONCENTRATION PR 1 N6 U1AL. CO IPPMI  CT (PPMI  CCNCENTRATION NORMAL 1 ZED XO l-l  XT (-)  Sfc'PARAT ION FACTOR NS  (-»  0 1 2 3 4  0.0 0.83 1.67 2.50 3.33  4781. 5201. 5493. 5757. 6022.  4765. 4251. 3980. 3711. 3455.  1.00 1.09 1.15 1.20 1.26  l.COOO 0.8422 0.8352 0.77P7 0.7250  1.00 1.22 1.18 1.55 1.74  6 6 10 12 14 18 22 26 30 34 38 42 46  5.00 6.67 6.33 10.00 11.67 15.00 18.33 21.67 25.00 28.33 31.67 35.00 38.33  6542. 7007. 7476. 7918. 8318. 9080. 9740. 10233. 10601. 10875. 11036. 11182. 11231.  2972. 2528. 2146. 1795. 1464. 990. 642. 416. 273. 197. 164. 139. 124.  1.37 1.47 1.56 1.66 1.74 1.90 2.04 2.14 2.22 2.27 2.31 2.34 2.35  0.6236 0.5306 0.4503 0.3766 0.3071 0.2C77 0.1347 0.0873 0.0573 0.0414 0.0344 0.0291 0.0259  2.19 2.76 3.47 4.40 5.66 9.14 15.12 24.51 38.66 54.99 67*01 80.28 90.53  TABLE  CYCLE NO. NC (-1  C.2. 5  REAL TIME T (MINI  ? NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-8/I10  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPMI  CONCENTRATION NORMALIZED XB l-l  XT (-1  SEPARATION FACTOR NS  (-)  0 1 2 3 4 5 6 7 8 9 10  0.0 1.13 2.27 3.40 4.53 5.67 6.80 7.93 9.07 10.20 11.33  5376. 5845. 6244. 6587. 6947. 7248. 7552. 7811. 8072. 8303. 8519.  5191. 4484. 4165. 3854. 3563. 3280. 3016. 2788. 2556. 2364. 2157.  1.00 1.09 1.16 1.23 1.29 1.35 1.40 1.45 1.50 1.54 1.58  l.COOO 0.8637 0.8022 0.7423 0.6863 0.6318 0.5810 0.5371 0.4923 0.4553 0.4154  1.00 1.26 1.45 1.65 1.88 2.13 2.42' 2.71 3.05 3.39 3.81  12 14 16 18 20 22 24 26  13.60 15.87 18.13 20.40 22.67 24.93 27.20 29.47  B892. 9221. 9504. 9725. 9B99. 1C042. 10185. 10281.  1865. 1602. 1368. 1184. 1052. 948. 870. 823.  1.65 1.72 1.77 1.81 1.84 1.87 1.89 1.91  0.3592 0.3086 0.2636 0.2280 0.2027 0.1B26 0.1676 0.1586  4.61 5.56 6.71 7.93 9 . 08 10.23 11.31 12.0b  TABLE  C.2. 6  i NUMERICAL EVALUATION OF EXPERIMENT EDIl-Sl-8/»ll  385 CYCLE NO.  REAL TIHE T . CHIN)  NC l-l  CONClNTRAT1 ON BRINE DIAL. CB (PPM)  CI (PPM)  CCNCLNTH AT I ON NUKMAL 1 ZEO XP «-)  XT (-)  SEPARATION FACTOR NS (-)  0 1 2  0.0 0.42 0.83  4380. 4638. 4854.  4290. 4078. 3905.  UOO l.COOO 1.06 0.9527 I.11 0.9124  1.00 1.11 1.21  5  2.08  5434.  3421.  1;24 0.7992  1.55  4.17 6274. 6.25 7112. 8.33 7827. 10.42 8566. 12.50 9315. 14.58 10010. 16.67 10698. 18. 75 11344. 20.83 11981. 22.92 12559. 25.00 13142. 27.08 13662. 29.17 14102. 31.25 14459. 33.33 14801. 35.42 15059. 37.50 15317.  2672. 2043. 1527. 1110. 792. 544. 345. 225. 144. 93. 63. 48. 35. 29. 23. 18. 17.  1.43 1.62 1.79 1.96 2.13 2.29 2.44 2.59 2.74 2.87 3.00 3.12 3.22 3.30 3.38 3.44 3.50  10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90  TABLE  CYCLE NO. NC l-l  C.2. 7  REAL TIME T (MINI  0.6242 0.4772 0. 3568 0.2593 0.1850 0.1271 0.0805 0.0526 0.0336 0.0218 0.0147 0.0112 0.0082 0.0068 0.0053 0.0042 0.0040  2.30 3.40 5.01 7.54 11.49 17.48 30.34 49.28 81.39 131.56 203.85 278.93 390.83 483.70 638.26 811.73 874.31  > NUMERICAL EVALUATION OF EXPERIMENT E0U-Sl-8/#l2  CONCENTRATION BRINE DIAL. CB IPPHI  CT (PPM)  CONCENTRATION NORMALIZED XB  (-)  XT l-l  SEPARATION FACTOI NS l-l  0 2 4 6 8 10  0.0 1.67 3.33 5.00 6.67 8.33  5129. 5493. 5816. 6126. 6423. 6662.  5007. 4630. 4321. 4043. 3779. 3540.  I.00 1.07 1.13 1.19 1.25 1.30  l.COOO 0.9247 0.8629 0.8075 0.7548 0.7070  1.00 1.16 1.31 1.48 1.66 1.84  15 20 25 30 35 40 45 50 55  12.50 16.67 20.63 25.00 29.17 33.33 37.50 41.67 45.83  7264. 7796. '8210. 8566. 8861. 9080. 9315. 9488. 9598.  3016. 2584. 2216. 1929. 1688. 1485. 1331. 1199. 1094.  1.42 0.6024 1.52 0.5159 1.60 0.4426 1.67 0.3853 1.73 0.3370 1.77. 0.2965 1.82 0.2659 1.85 0.2395 1.87 0.2186  2.35 2.95 3.62 4.33 5.13 5.97 6.83 7.72 8.56  TABLE  C.2. 8  » NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-fl/»I3  386 CYCLE NO.  REAL TIME T  NC l-»  OVlCI NIRATION HKINC DIAL. CB (PPM)  CT (P>>M»  CIHC NfRAT ION NORMAL 1ZEU XH (-1  XT (-)  SFPAKATION F AC IfTR NS (-1  0 1 2  0.0 1.17 2.33  5071. 5259. 5391.  4948. 4350. 4251.  1.00 l.COOO 1.04 0.R791 1.06 0.H592  I.00 1.18 1.24  4 6 8 10  4.67 7.00 9.33 11.67  5610. 51110. 6037. 6244.  4020. 3796. 3563. 3421.  1.11 1.15 1.19 1,23  0.8125 0.7672 0.72C0 0.6914  1.36 1.50 1.65 1.78  15 20 25 30 35 AO  17.50 23.33 29.17 35.00 40.83 46.67  6692. 7082. 7430. 7735. 7980. 8133.  2927. 2567. 2255. 1999. 1773. 1602.  1.32 1.4C 1.47 1.53 1.57 1.60  0.5915 0.5188 0.4556 0.4041 0.3584 0.3238  2.23 2.69 3.22 3.73 4.39 4.95  TABLE  CYCLE NO. NC l-l  C.2. 9  REAL TIME T (MINI  t NUMERICAL EVALUATION OF EXPERIMENT EOll-Sl-B/f14  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPM I  CONCENTRATION NORMALIZED XB (-1  XT l-l  SEPARATION FACTOR NS (-1  0 1 2 3 4  0.0 2.15 4.30 6.45 8.60  5405. 5816. 6111. 6393. 6662.  5293. 4194. 3934. 3654. 3376.  1.00 1.08 1.13 1.18 1.23  l.COOO 0.7923 0.7433 0.6903 0.6378  1.00 1.36 1.52 1.71 1.93  6 8 10  12.90 17.20 21.50  7143. 7446. .8010.  2883. 2446. 2054.  1.32 0.5446 1.38 0.4622 1.48 0.3880  2.43 2.93 3.82  14 18  30.10 38. ro  8690. 9221.  1432. 1000.  1.61 0.2705 1.71 0.1890  5.94 9.03  20  43.00  9472.  818.  1.75 0.1545  11.34  TABLE  C.2.10  % NUMERICAL EVALUATION OF EXPERIMENT  EOIl-Sl-8/m  387 CYCLE  NO.  RF. AL CUNClNIRA1ION 11 ML' UK IMF. DIAL.  cn  T  NC  IM1NI  1-1  CT  IPPM)  Cl.'NCI 'ItRAI 1 (IN NU'IF'ALIZCC X"  (PPMI  I-)  1  SCI'ARAT ( U N  FACIOR  XT  NS  (-1  l-l  0 I 2 3 4 5 6 7 e 9 10  0.0 0.83 1.67 2.50 3.33 4.17 5.00 5.83 6.67 7.50 8.33  5508. 6126. 6632. 7128. 7598. 0057. 8504. 8955. 9378. 9788. 10185.  5490. 4601. 41 30. 3682. 3263. 2871. 2517. 2173. 1865. 1581. 1321.  1.00 1.11 1.20 1.29 1.38 1.46 1.54 1.63 1.7C 1.78 1.85  l.COOO 0 . a 180 0.7522 0.67C7 0.5443 0.5230 0.4585 0.3958 0.3396 0.2879 0.24C5  12 14 16 18 20  10.00 11.67 13.33 15.00 16.67  10955. 11639. 12261. 12791. 13192.  896. 5 70. 416. 233. 151.  1.99 2.11 2.23 2.32 2.40  0.1632 0.1038 0.0758 0.0424 0.0276  12.19 20.35 29.38 54.82 86.82  25 30  20.83 25.00  13780. 14034.  81. 60.  2.5C 0.0147 2.55 0.0110  170.28 231.10  TABLE  CYCLE NO. NC l-l  0 1 2  C.2.11  REAL TIME T (MINI  o.o  1.00 1.33 l.oO 1.«I3 2. 32 2.H0 3.37 4. 11 5.01 6.17 7.69  < NUMERICAL EVALUATION OF EXPERIMENT E 0 U - S l - 8 / f 16  CONCENTRATION BRINE DIAL. CB (PPM)  CT I PPM)  CONCENTRATION NORMALIZED XB l - l  XT l - l  SEPARATION FACTOR NS (-1  4 5 6 7 8 9 10  0.83 1.67 2.50 3.33 4.17 5.00 5.83 6.67 7.50 8.33  5143. 5727. 6244. 6722. 7173. 7628. 8057. 8488. 8861. 9221. 9567.  5061. 4414. 3963. 3534. 3128. 2755. 2419. 2108. 1838. 1586. 1379.  1.00 1.11 1.21 1.31 1.39 1.48 1.57 1.65 1.72 1.79 1.86  l.COOO 0.8722 0.7830 0.6984 0.6181 0.5444 0.4779 0.4165 0.3631 0.3134 0.2725  1.00 1.28 1.55 1.87 2.26 2.72 3.28 3.96 4.74 5.72 6.83  12 14 16 18 20  10.00 11.67 13.33 15.00 16.67  10201. 10714. 11133. 11458. 11703.  1021. 751. 560. 421. 324.  1.98 2.08 2.16 2.23 2.28  0.2018 0.1483 0.1106 0.0832 0.0641  9.83 14.05 19.57 26.77 35.52  25 30  20.83 25.00  12113. 12278.  207. 167.  2.36 0.04C9 2.39 0.0329  57.52 72.49  33  27.50  12327.  151.  2.40 0.0299  80.08  3  TABLE  C.2.12  t NUMERICAL EVALUATION OF EXPERIMENT CI»ll-Sl-8/«l7  388 CVCIE NO. NC I-)  ML' AL TI ML I (M|N)  CONC I N IRA F I ON RRINt UIAL. CO (PPMI  CT (PPMI  CC'ICKITR A t I FIN NJKMAtl/EO Xn  l - l  XT (-)  SEPARATION FACWR NS (-1  0 1 2  0.0 0.65 1.30  5361. 5M60. 62H9.  5251. 4718. 4338.  1.00 l.COOO 1.04 0.fl4<36 1.17 6~'.t>262  1.00 1.72 1.42  4 6 8 10  2.60 3.90 5.20 6.50  7128. 7903. 8597. 9268.  3541. 2944. 2419. 1972.  1.33 1.47 1.60 1.73  6".6H19 0.56C6 0.46C6 0.3756  1.94 7.63 3.4H 4.60  15 20 25 30  9.75 13.00 16.25 19.50  10553. 11377. 11883. 12195.  1184. 740. 503. 375.  1.97 2.12 2.22 2.27  0.2254 0.1410 0.0958 0.0715  8.73 15.05 23.13 31.B3  TABLE  CYCLE NO. NC I-)  C.2.13  REAL TIME T (MINI  i NUMERICAL EVALUATION OF EOIl-Sl-8/flB  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPMI  CONCENTRATION NORMALIZED XB (-1  XT (-1  EXPERIMENT  SEPARATION FACTOR NS (-)  0 1 2  0.0 0.48 0.97  4926. 4007. 5216. 4583. 5508. 4333.  1.00 l.COOO 1.06 0.9536 1.12 0.9014  1.00 1.11 1.24  4 6 8 10  1.93 2.90 3.87 4.83  6126. 6707. 7218. 7674.  3837. 3659. 2960. 2595.  1.24 1.36 1.47 1.56  0.7982 0.7613 0.6159 0.5398  1.56 1.79 2.38 2.89  15 20 25 30 35 40  7.25 9.67 12.08 14.50 16.92 19.33  86431 9299. 9772. 1C090. 1C329. 10489.  IRB6. 1421. 1089. 870. 720. 627.  1.75 1.89 1.98 2.05 2.10 2.13  0.3924 0.2957 0.2266 0.1810 0.1497 0.1304  4.47 6.38 8.7b 11.32 14.01 16.33  TABLE  C.2.14  t NUMERICAL EVALUATION OF EDU-Sl-8/«19  EXPERIMENT  389 REAL I IMF  CYCLE  NO.  CONCI NTRAI IUN UK INC 01AL.  T  NC  I f IN)  C\\  (PPMI  crwtt NTRM ION NORMAL 1/CO  CT  xn  IPPM)  I-)  XT I-)  SCPAKATIOM EACIDH  NS l-l  0 1 2  0.0 0.50 1.00  5508. 5830. 6244.  5400. 5126. 4U65.  1.00 I.COCO 1.0b 0.4412 1.13 0.9010  4 6 8 10  2.00 3.00 4. CO 5.00  6<H7. 7548. 8026. 8365.  4309. 37H5. 33 36. 2955.  1.26 1.38 1.46 1.52  0.7980 0. 7C09 0.61/fl 0.5472  1.57 1.47 2.36 2.78  15 20 25 30 35 40 45  7.50 10.00 12.50 15.00 17.50 20.00 22.50  9693. 10425. IC939. 11296. 11540. 11736. 11883.  2173. 1655. 1305. 1079. 896. 797. 714.  1.76 1.09 1.49 7.05 2.10 2.13 2.16  0.4024 0.3065 0.2416 0.1997 0.1659 0.1476 0.1323  4.37 6.17 8.22 10.27 12.63 14.43 16.31  TABLE  CYCLE NO. NC l-l  C.2.15  REAL TIME T IMIN)  1.00 1.12 l.?b  i NUMERICAL EVALUATION OF EXPERIMENT EDlI-Sl-8/*20  CONCENTRATION BRINE OIAL. CB IPPM)  CT (PPMI  CONCENTRATION NORMAL IZEO XB XT l - l I-)  SEPARATION FACTOR NS l - l  0 0.0 1 0.98 2 1.97 3 2.95 4 3.93 5 4.92 6 5.90 7 ' 6.88 B 7.87 9 8.85 10 9.83  5216. 6244. 7188. 8007. 8986. 9772. 104B9. 11150. 11703. 12113. 12493.  5102. 3969. 2124. 3654. 1940. 1448. 1037. 725. 493. 329. 222.  1.00 1.20 1.38 1.55 1.72 1.87 2.01 2.14 2.24 2.32 2.40  1.0000 0.7778 0.4163 0.7161 0.3802 0.?e37 0.2032 0.1420 0.0966 0.0645 0.0436  1.00 1.54 3.31 2.17 4.53 6.60 9.90 15.05 23.23 35.98 54.94  12 14 16 18 20  11.80 13.77 15.73 17.70 19.67  12941. 13125. 13275. 13393. 13494.  106. 60. 40. 32. 28.  2.48 2.52 2.55 2.57 2.59  0.02C8 0.0119 0.0079 0.0062 0.0054  119.50 212.28 322.19 412.«2 476.46  25 30  24.50 29.50  13696. 13881.  24. 22.  2.61 0.0047 2.66 0.0043  554.16 612.76  34  33.43  14017.  21.  2.69 0.0041  648.22  TABLE  C.2.16  I NUMERICAL EVALUATION OF EXPERIMENT E0ll-Sl-8/«?l  390 CYCLE NO.  HEAL TIME  CONCENTRATION UK 1NE DIAL.  CONCENTRATION NORMALIZED  SEPARATION FACTOR  ! 1  NC (-)  0 1 2 3 4 5 6 7 a 9 10 12 14 16 18 20 25  T (MINI  0.0 1.33 2.67 4.00 5.33 6.67 8.00  NC <->  CT (PPM|  xn (-1  XT l-l  10.67 12.00 13.33  2654. 3614. 4394. 5013. 5508. 5919. 6229. 6467. 6662. 6781. 6887.  2501. 1854. 1379. 979. 678. 462. 311. 205. 139. 93. 66.  1.00 1.36 1.66 1.89 2.08 2.23 2.35 2.44 2.51 2.56 2.59  l.COOO , 0.7412 0.5513 0.3916 0.2712 0.1848 0. 1245 0.0818 0.0555 0.0373 0.0262  16.00 18.67 21.33 24.00 26.67 33.33  7067. 7173. 7264. 7370. 7446. 7598.  37. 26. 16. 14. 11. 10.  2.66 2.70 2.74 2.78 2.81 2.86  0.0147 0.0103 0.0062 0.0056 0.0044 0.0040  4.33  TABLE  CYCLE NO.  cn (PPMI  C.2.17  REAL TIME T IHINI  NS (-)  1.00 l.«4 1.00 4.82 7.65 12.07 18.85 29.77 4S. 22 68.49 99.03 181.08 263.13 438.45 492.53 633.35 710.93  .» NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/*22  CONCENTRATION BRINE) DIAL. CB (PPMI  CT (PPM)  CONCENTRATION NORMALIZED XB (-)  XT (-)  SEPARATION FACTOR NS (-1  0 I 2 3 4 5 6 7 8 9 10  0.0 1.02 2.03 3.05 4.07 5.08 6.10 7.12 8.13 9.15 10.17  2668. 3222. 3713. 4180. 4609. 4984. 5187. 5639. 5904. 6126. 6319.  2611. 2092. 1725. 1395. 1110. 870. 668. 508. 391. 296. 228.  1.00 1.21 1.39 1.57 1.73 1.87 1.94 2.11 2.21 2.30 2.37  l.COOO 0.8010 0.6606 0.5341 0.4251 0.3332 0.2558 0.1947 0.1496 0.1134 0.0871  1.00 1.51 2.11 2.93 4.06 5.61 7.60 10.86 14.80 20.24 27.18  12 14 16 18 20  12.20 14.23 16.27 18.30 20.33  6557. 6707. 6826. 6872. 6932.  146. 101. 78. 66. 58.  2.46 2.51 2.56 2.58 2.60  0.0561 0.0386 0.0297 0.0251 0.0222  43.83 65.07 86.05 102.63 117.05  25 30  25.42 30.50  7082. 7143.  51. 49.  2.65 0.0197 2.68 0.0187  134.86 143.02  TABLE  C.2.18  S NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-B/I23  I  391 CYCLE NO.  RFAL 11 ME  NC  CUNLeNlRATIUN URINE DIAL.  cn  T  (M|N|  l-l  IPPM)  XT  1.00 1.29 1.55 1.79 1.99 2.17 2.31  l.COOO 0.7218 0.5393 0.3859 0.2662 0.1813 0.1205  1.00 1.79 2.88 4.64 7.49 11.99 19.19 74.42  10  10.00  6917.  91.  2.59 0.0348  15 20 25 30  15.00 20.00 25.CO 30.00  7233. 7400. 7598. 7750.  47. 36. 33. 30.  2.71 2.77 2.85 2.91  CYCLE NO. NC <-)  REAL TIME T (MINI  0.0180 0.0137 0.0128 0.0116  CONCENTRATION BRINE OIAL. CB (PPMI  CT IPPMI  CONCENTRATION NORMALIZED  150.76 202.06 223.19 250.45  SEPARATION FACTOR  XD (-»  XT (-1  1.00 1.08 1.15 1.21 1.27  l.COOO 0.8534 0.7942 0.7360 0.6809  1.00 1.27 1.44 1.64 1.87 2.39 3.01 3.80  0.0 0.67 1.33 2.00 2.67  1257. 1358. 1442. 1522. 1597.  1241. 1059. 986. 913. 845.  6 8 10  4.00 5.33 6.67  1752. 1886. 2021.  724. 618. 525.  1.39 0.5832 1.50 0.4979 1.61 0.4231  15 20 25 30 35 40 45  10.00 13.33 16.67 20.00 23.33 26.67 30.00  2304. 2517. 2666. 2771. 2838. 2877. 2916.  348. 235. 165. 126. 103. 90. 84.  1.83 2.00 2.12 2.20 2.26 2.29 2.32  C.2.20  (-)  t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/124 .  0 1 2 3 ,4  TABLE  NS  I-)  0.0 1.00 2.00 3.00 4.00 5.00 6.00  C.2.19  2606. 1H81. 1-.05. 1005. 694. 472. 314.  xn  SEPARATION FACIOR  (-1  0 1 2 3 4 5 6  TABLE  266S. 34 46. 4137. 4781. 5318. 5801. 6170.  CT  (PPMI  CllNCf NIRATION NORMALIZED  0.2807 0.1892 0.1331 0. 1019 0.0832 0.0728 0.0676  NS (-1  6 . S3 10.58 15.94 21.64 27.14 31.45 34.32  t NUMERICAL EVALUATION OF EXPERIMENT 1 EOII-Sl-8/»25  392 CYCLC NO.  RL" AL 1 IMC  NC -)  T IMIN)  CONCI NTR A TI UN URINE DIAL. CR I PPM I  CT IPPMI  CIINCLNIR AT ION  SEPARATION P AC till  NORMAL 1110 XP XT l-l I-)  NS l-»  3 4  0.0 1.00 2.00 3.00 4.00  1294. 1650. 1940. 2706. 2452.  1290. 991. 784. 606. 458.  1.00 l.COOO 1.2 7 0. 7680 l.OC| 0.60H0 1.70, 0.4700 1.89 0.3550  1.00 1.7,6 2.47 3.63 5.34  6 8 10  6.00 8.00 10.00  2832. 308**. 3252.  254. 139. 81.  2.19 0.1970 2.39 0.1080 2.51 0.0630  11.11 22.10 39. P3  14 18 22 26 30  14.00 18.00 22.00 26.00 30.00  3415. 3500. 3563. 3625. 3671.  34. 24. 21. 19. 18.  0 1 ?  TABLE  C.2.21  CYCLE NO.  REAL TIME  NC  T IMIN)  I-)  2.64 2.70 2.75 2.80 2.84  0.0266 0.0185 0.0159 0.0144 0.0140  99.21 146.19 173.1) 194.52 202.59  ! NUMERICAL EVALUATION OF EXPERIMENT E0II-SI-8/I26  CONCENTRATION BRINE 01 AL. CB IPPM)  CT IPPMI  CONCENTRATION NORMALIZED XT  XB l-l  (-)  SEPARATION FACTOI NS l-l  0 1 2 3 4 5 6  0.0 1.33 2.67 4.00 5.33 6.67 8.00  1257. 1741. 2119. 2430. 2699. 2916. 3067.  1251. 915. 660. 464. 319. 215. 144.  1.00 1.38 1.69 1.93 2.15 2.32 2.44  l.COOO 0.7309 0.5278 0.3711 0.2546 0.1722 0.1155  1.00 1.89 3.19 5.21 8.43 13.47 21.12  8 10 12 14  10.67 13.33 16.00 18.67  3280. 3404. 3489. 3557.  71. 35. 23. 18.  2.61 2.71 2.77 2.83  0.0567 0.0284 0.0184 0.0143  46.01 95.50 151.22 197.43  18 22 26 30  24.00 29.33 34.67 40.00  3688. 3808. 3905. 3992.  14. 12. 11. 11.  2.93 3.03 3.11 3.17  0.0110 0.0096 0.0092 0.0088  265.91 315.89 338.53 362.28  TABLE  C.2.22 < NUMERICAL FVALUATION OF EXPERIMENT EOII-S1-8/I27 !  CYCLE NO.  REAL TIMET (MINI  NC  t->  C C N U N . IT R A 1 ION BRINE* DIAL. CD (PPMI  CT IP^MI  0 L 2 3 4 5 6  0.0 0.83 1.67 2.50 3.33 4.17 5.00  12U4. 1511. 1698. 1865. 2026. 2178. 2309.  1277. 1045. 913. 709. 676. 575. 486.  8 10 12 14 16 18 20  6.67 8.33 10.00 11.67 13.33 15.00 16.67  2561. 2760. 2921. 3039. 3128. 3229. 3291.  341. 233. 156. 107. 75. 53. 37.  25 30 35  20.83 25.00 2<».17  3376. 3427. 3466.  22. 17. 15.  TABLE  CYCLE NO. NC l-l  C.2.23  REAL TIME T IMINI  SCl'ARMlON N ' W A L 1 /El) M c r r m  CCNCr.NTWAT I U N  XI)  l-l  (-1  1.00 l.COCO l . i n 0.8182 1.32 0 . 7 1 5 2 1.45 0 . 6 1 8 2 1.58 0 . 5 2 9 3 1.70 0 . 4 5 0 5 l.BC 0.3908  1.00 1.44 1.H5 2.35 2.18 3.7 7 4 . 72  0.2667 0.1828 0.1222 0.0638 0.0586 0.0411 0.0292  7.48 11.76 18.62 28.23 41.60 6 1 . 19 87.83  2.00 2.15 2.28 2.37 2.44 2.52 7.56  2.63 0 . 0 1 6 9 2.67 0 . 0 1 3 3 2.70 0 . 0 1 2 1  t NUMERICAL E V A L U A T I O N OF E011-S1-8/928  CONCENTRATION BRINE DIAL. CB (PPM)  CT (PPM)  NS I-I  XT  COMCENTRATION NORMALIZED  ^  155.90 200.21 222.77  EXPERIMENT  SEPARATION FACTOR  XB (-)  XT (-)  NS (-)  1.00 1.32 1.57 1.76 1.90 1.98 2.05 2.09  l.COOO 0.6636 0.4681 0.3086 0.2006 0.1296 0.0854 0.0617  1.00 1.99 3.36 5.70 9.46 15.28 23.96 33.79  0 1 2 3 4 5 6 7  0.0 1.32 2.63 3.95 5.27 6.58 7.90 9.22  1263. 1666. 1983. 2222. 2397. 2501. 2584. 2633.  1254. 832. 587. 387. 252. 163. 107. 77.  10  13.17  2694.  43.  2.13 0 . 0 3 4 5  61.91  12 14 16  15.80 18.43 21.07  2705. 2738. 2760.  39. 37. 37.  2.14 0 . 0 3 1 4 2.17 0 . 0 2 9 8 2.19 0 . 0 2 9 3  68.29 72.69 74.56  TAOLe  C.2.24  I NUMERICAL EVALUATION OF E0ll-Sl-8/«29  EXPERIMENT  394 Rf AL CONCIN1RAIION T 1 MG DRINF- U I A L .  CYCLE NO.  T  NC l-l  (MINI  0 t 2 3 4  0.0 1.00 2.00 3.00 4.00  6 8 10 15 20 25  NC l-l  CT  (PPMI  FACTOR  XII l-l  XT  (-1  NS (-1  1.00 1.12 1.23 1.33 1.41  l.COOO 0.7536 0.6517 0.5652 0.4888  1.00 1.47 l.RB 2.15 2.89  6.00 8.00 10.00  2010. 2157. 2266.  462. 347. 264.  1.56 0.3646 1.67 0.2739 1.76 0.2088  4.28 6.11 8.42  15.00 20.00 25.00  2419. 2474. 2501.  159. 129. 116.  1.88 0.1253 1.92 0.1018 1.94 0.0916  C.2.23  REAL TIME T (MINI  CONCENTRATION BRINE DIAL. CB IPPMI  CT IPPMI  0.0 0.68 1.37 2.05 2.73  1226. 1379. 1506. 1629. 1757.  1210. 916. 707. 677. 583.  6 8 10  4.10 5.47 6.83  1983. 2184. 2369.  14 18 22 26 30 34  9.57 12.30 15.03 17.77 20.50 23.23  2650. 2821. 2927. 2988. 3027. 3055.  TABLE  C.2.26  14.98 10.14 21.17  3 NUMERICAL EVALUATION OF EXPERIMENT EDll-Sl-a/t30  0 1 2 3 4  11  SLI'ARAI ION  NORMAL 1 ZED  1209. 1267. 1448. 955. 15BI. 826. 1 709. 716. 1822. 619.  TAOLE  CYCLE NO.  cn  (PPMI  Co'tci - n f A i u i ' i  CONCENTRATION NORMALIZED XB XT l - l (-)  1.00 1.12 1.23 1.33 1.43  SEPARATION FACTOR NS l - l  L.COOO 0.7569 0.6503 0.5597 0.4819  1.00 1.49 1.89 2.37 2.97  430. 315. 228.  1.62 0.3550 1.78 0.2601 1.93 0.1887  4.56 6.85 10.24  119. 68. 45. 35. 32. 29.  2.16 2.30 2.39 2.44 2.47 2.49  22.04 41.13 63.64 83.16 94.56 103.92  0.0981 0.0560 0.0375 0.0293 0.0261 0.0240  J NUMERICAL EVALUATION OF EXPCRIMCNT 1 E0II-S1-B/831  I I  I I  395 CYCLE NO.  HF AL Tilt  NC -1  T (MINI  0 I 2 3 A 5 6  0.0 0.83 1.67 2.50 3.33 4. 17 5.00  CUNCf NTRATI ON UR1ND OIAL. CB ( PCM I  CT (PPMI  1247. 15'17. 1902. 2184. 2435. 2644. 2827.  1238. 071. 655. 484. 350. 248. 173.  CCNCtNTRAT II1N NORMALIZED XII l-l  XT l-l  1.00 1.C0C0 1.2H 0.70)1 1.53 0.5292 1.75 0.31C6 1 . -750.2823 2.12 0.2000 2.27 0.1396  STMAUAf ION FACtllf N5 l-l  1.00 1.H2 2.88 4.48 6.92 10.1.0 16.24  8 10 12 14  6.67 8.33 10.00 11.67  3078. 3224. 3308. 3370.  84. 42. 24. 16.  2.47 2.59 2.65 2.70  0.0675 0.0)41 0.0197 0.0127  36.57 75.91 134.77 212. 70  18 22 26  15.00 18.33 21.67  3466. 3546. 3620.  10. 8. 7.  2.78 0.0078 2.84 0.0062 2.90 0.0053  355.87 455.02 546.48  TABLE  CYCLE NO. NC l-l  C.2.27  REAL TIME T (PIN)  r NUMERICAL EVALUATION OF EXPERIMENT EDlI-Sl-8/»32  CONCENTRATION BRINE OIAL. CB (PPMI  CT IPPM!  CCNCENTRATION NORMAL IZEO XB (-)  XT I-)  SEPARATION FACTOR NS I-)  i;  0 1 2 3 4 5 6 7 9 10  0.0 0.98 1.97 2.95 3.93 4.92 5.90 6.88 7.87 8.85 9.83  1205. 1666. 2064. 2408. 2677. 2871. 3027. 3128. 3201. 3263. 3314.  1191. 787. 529. 342. 217. 134. 83. 52. 33. 22. 15.  1.00 1.38 1.71 2.00 2.22 2.38 2.51 2.60 2.66 2.71 2.75  l.COOO 0.6609 0.4442 0.2871 0. 1820 0.1127 0.0693 0.0433 0.0276 0.0181 0.0125  1.00 2.09 3.86 6.96 12.21 21.15 36.24 59.92 96.19 149.71 220.78  12 14 16 18 20  11.80 13.77 15.73 17.70 19.67  3410. 3478. 3551. 3620. 3677.  8. 5. 3. 2. 2.  2.83 2.89 2.95 3.00 3.05  0.0065 0.0038 0.0027 0.0021 0.0015  435.42 761.30 1088.42 1459.64 2012.11  25  24.58  3R19.  1.  3.17 O.C009  3657.97  e  TABLE  C.2.28  t NUMERICAL EVALUATION OF EXPERIMENT EUII-S1-8/I33  396 CYCLE  REAL  NO.  11 M L  NC  T  (-)  (H1N>  CONClNTHA TI ON BRINE  PIAL.  CB (PPMI  CT (PPMI  CONCI:NTRAT ION N O R M A L 1 ZF XI  0 XT  (-1  (-1  SEPARAT  NS (-1  0  0.0  1234.  1276.  1.00  l.COOO  1.00  1  1.30  1918.  806.  1.49  0.6320  2.36  2  2.60  2419.  494.  1.8H  0.3873  4.87  3  3.90  2816.  294.  2.19  0.2305  9.51  4  5.20  3111.  170.  2.42  0.1335  1 8 . 16  5 6  6.50  3331 . 3472.  98.  2.59  0.0768  33.76  85.  2.70  0.0667  7  3580.  37.  2.79  0.0288  40.53 96.77  8  9 . 10 10.40  3682.  24.  2.87  0.0190  150.90  9  11.70  3762.  17.  2.93  0.0133  219.58  10  13.00  3831.  13.  2.98  0.0100  298.12  7.80  15  19.50  4176.  5.  3.25  0.0040  804.36  20  26.00  4484.  2.  3.49  0.0015  2303.13  25  32.50  4748.  1.  3.70  0.C006  6096.32  TABLE  CYCLE NO. NC t-l  C.2.29  REAL TIME T (KIN)  i NUMERICAL EVALUATION OF EDII-S1-8/I34  CONCENTRATION BRINE DIAL. CB (PPMI  CT IPPHI  CONCENTRATION NORMALIZED XB l-l  i  XT (-1  EXPERIMENT  SEPARATION FACTOR NS l - l  0  0.0  1.00  l.COOO  0.83  1215. 1342.  1200.  I  1013.  1.10  0.8441  1.31  2  1.67  1448.  942.  1.19  0.7849  1.52  3  2.50  1549.  871.  1.27  0.7258  1.76  4  3.33  1639.  80S.  1.35  0.6710  2.01  6  5.00  1811.  684.  1.49  0.5699  2.61  8  6.67  1962.  577.  1.61  0.4806  3.36  10  8.33  2097.  485.  1.73  0.4043  4 . 2 7  1.00  15  12.50  2369.  303.  1.95  0.2527  7.72  20  16.67  2567.  186.  2.11  0.1548  13.64  25  20.83  2699.  119.  2.22  0.0989  22.46  30  25.00  2788.  81.  2.29  0.0677  33.B7  35  29.17  2844.  65.  2.34  0.0538  43.53  TABLE  C.2.30  t NUMERICAL EVALUATION OF E O I L - S l - 8 / f 35  ION  FACIOR  EXPERIMENT  397 CYCLE NO.  HT AL CIINCI N1HAI HIN 11 Ml. UK INI- DIAL. T ("INI  NC C-l  cn  CI iPPM i  (prM)  CU^Ci NTrfAl ION NOW PAL 1 / El) XII l-l  XT l - l  SKPAHAT ION FACinB NS l-l  0 1 2 3 4 5 6 7 8  0.0 1.00 2.00 3.00 4.00 5.00 6.00 7.00 B.OO  1220. 1575. 1465. 212'). 2 304 . 2561 . 2727. 2U60. 2966.  12 1«. 429. 7 )4. 562. 421. .310. 227. 165. 119.  1.00 1.29 1.5 3 1.74 1.44 2. i c 2.23 2.34 2.43  l.COOO 0.7627 0.6028 0.4619 0.345) 0.7542 0.1864 0.1)56 0.0975  I . 00 1.69 2.53 ) . 78 5.61 0.76 11.99 17.20 24.94  10 12 14 16 18 20  10.00 12.00 14.00 16.00 18.00 20.00  3111. 3201. 3257. 3302. 3342. 3370.  65. 39. 27. 21. 18. 17.  2.55 2.62 2.67 2.71 2.74 2.76  0.0531 0.0321 0.C225 0.0169 0.0151 0.0138  48.04 8 1 . 72 t18.85 154.65 100.77 200.52  25 30  25.00 30.00  3444. 3506.  15. 14.  2.82 0.0122 2.87 0.0117  231.6*2 246.53  TABLE  CYCLE NO. NC (-)  C.2.31  REAL TIME T IMIN)  » NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/*35eL  CONCENTRATION BRINE DIAL. CD (PPM)  CT (PPMI  CCNCENTRATION NORMALIZED XB I-)  XT (-)  1252. 1251. 1448. 1099. 1607. 984. 1757.. 869. 1902. 765.  1.00 1.16 1.28 1.40 1.52  l.COOO 0.8784 0.7866 0.6948 0.6113  1.00 1.32 1.63 2.02 2.49 3.73 5.57 8.27  0 1 2 3 4  0.0 1.00 2.00 3.00 4.00  6 8 10  6.00 8.00 10.00  2157. 2380. 2572.  578. 427. 311.  1.72 0.4619 1.90 0.3412 2.05 0.2485  15 20 25 30 35 40  15.00 20.00 25.00 30.00 35.00 40.00  2888. 3039. 3123. 3167. 3201. 3224.  137. 68. 52. 37. 34. 32.  2.31 2.43 2.49 2.53 2.56 2.57  TABLE  SEPARATION FACTOR  C.2.32  0.1093 0.0546 0.0412 0.0297 0.0269 0.0258  NS (-1  21.11 44.42 60.48 85.21 95.02 99.90  t NUMERICAL EVALUATION OF EXPERIMENT EUll-Sl-8/«36  398 CYCLE NU.  HE AL 1IMC T (MINI  NC (-)  CEINCTN 1R A1 1 (IN CCNCl N1HAI ION l\«INF. DIAL. NORMAL 1/CO ClI (PPMI  CI (PPMI  XP l-l  XT (-1  1.00 1.3? 1.56 1.79 2.00 2.19 2.34  l.COOO 0 . 61,' lb 0.4)48 0.3010 0.2029 0.1149 ,0.0892  STPAKATION MCIOR NS (-1  11.25 13.50  1147. 1511. 1745. 2054. 2298. 2512. 2683.  1157. 70 3. 50). 348. 235. 156. 103.  8 10  18.00 22.50  2916. 3055.  52. 31.  2.54 0.0446 2.66 0.C270  57.02 93.75  15 20 25 30  33.75 45.00 56.25 67.50  3201. 32BO. 3365. 3427.  18. 14. 13. 12.  2.79 2.86 2.93 2.99  0.0154 0.U123 0.0110 0.0105  181.44 2 ) ) . 22 265.82 285.13  0 1 2 3 4 5 6  0.0 2.25 4.50 6.75 q.oo  TABLE  CYCLE NO. NC (-»  C.2.33  REAL TIME T (MINI  t NUMERICAL EVALUATION OF EXPERIMENT E0I1-S1-8/K3T  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPM)  0 1 2 3 4 5 6  0.0 1.18 2.37 3.55 4.73 5.92 7.10  1252. 1432. 1575. 1714. 1838. 1962. 2081.  1242. 948. 819. 710. 606. 516. 436.  8 10  9.47 11.83  2287. 2463.  310. 213.  15 20 25 30 35 40  17.75 23.67 29.58 35.50 41.42 47.33  2783. 2933. 3000. 3039. 3067. 3083.  84. 44. 32. 28. 27. 26.  TABLE  C.2.34  1.00 2.17 3.60 5.95 9. B8 16.24 26.7)  CONCENTRATION NORMALIZED XB (-)  1.00 1.14 1.26 1.37 1.47 1.57 1.66  XT (-)  SEPARATION FACTOR NS (-1  t.COCO 0.7632 0.6594 0.5711 6.4881 0.4154 0.3510  I.00 1.50 1.91 2.40 3.01 3.77 4.73  1.83 0.2492 1.97 0.1713  7.33 11.48  2.22 7.34 2.40 2.43 2.45 2.46  32.93 66.73 94.17 108.20 114.50 118.58  0.0675 0.0351 0.0254 0.0224 0.0214 0.0208  I N'JMFRICAL E V A L U A T I O N EOII-SI-B/HS  OF  EXPERIMENT  CYCLE NO. NC -)  RIAL TIME  CONCENTRATION HHINE DIAL.  T (PIN)  CT cn 1 PPMI IPPMI  XII I-)  XT (-)  1.00 1.4? 1.79 2. 12 2.37 2.55 2.68  l.COOO 0.5801 0.3665 0.2228 0.12U3 0.0758 0.0467  SCPAKAIION I AC ItlR NS (-)  1.00 2.44 4.48 9.50 18.47 33.67 5 7. 18  0 1 2 3 4 5 6  0.0 2.42 4.83 T.75 9.67 12.08 14.50  1268. 1795. 2266. 2683. 3005. 32 35. 3398.  8 10  19.33 24.17  3591. 3716.  29. 20.  2.83 0.0227 2.93 0.0156  124.83 187.83  15 20 25 30  36.25 48.33 60.42 72.50  3946. 4107. 4222. 4309.  13. 10. 9. 8.  3.11 3.24 3.33 3.40  303.10 389.50 450.52 551.77  TABLE  CYCLE NO. NC t->  C.2.35  REAL TIME T (MINI  1256. 729. 461. 2B0. 161. 95. 59.  CCNCI NIHAI II.1N NORMALI ZfcU  O.U103 0.0083 0.0074 0.0062  t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/139  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPMI  CONCENTRATION NORMALIZED  SEPARATION FACTOR  XB (-)  XT (-)  NS J-l  1.00 1.37 1.66 1.92 2.14 2.32 2.45  1.0000 0.6871 0.5115 0.3561 0.2407 0.1565 0.1013  I.00 2.00 3.24 5.40 8.90 14.84 24.21  0 1 2 3 4 5 6  0.0 1.53 3.07 4.60 6.13 7.67 9.20  1289. 1768. 2135. 2479. 2760. 2994. 3162.  1286. 884. 658. 458. 310. 201. 130.  8 10  12.27 15.33  3381. 3500.  58. 30.  2.62 0.0451 2.72 0.0236  58.12 115.21  15 20 25  23.00 30.67 38.33  3648. 3762. 3865.  15. 12. 10.  2.83 0.0115 2.92 0.C090 3.0C 0.0060  245.37 3 2 3 . 33 373. 71  TABLE  C.2.36  < NUMERICAL EVALUATION OF EXPERIMENT E0ll-SI-8/«40  400 RIAL CONCENTRATION T I Hi. URINE OIAL.  CYCLE NO.  cn  T  NC  (-1  CT (PPMI  (PPMI  (MINI  CUNCLNTRATION NORMALIZCD 1  XP (-»  XT (-1  SEI'ARAT ION TACIOR NS (-1  0 1 2  0.0 0.27 0.53  1305. 1342. 1374.  1300. 1258. 12)7.  1.00  1.03 0.9673 1.05 0.9514  1.00 1.06 I.11  4 6 10  1.07 1.60 2.13 2.67  1448. 1501. 1554. 1607.  1197. 1158. 1122. 1086.  1.11 1.15 1.19 1.23  0.9206 0.89C9 0.8631 0.8353  1.21 1.29 1 . IB 1.47  15 20 25 30 35 40 45 50  4.00 5.33 6.67 8.00 9.33 10.67 12.00 13.33  1725. 1848. 1956. 2064. 2178. 2271. 2369. 2463.  1006. 934. 864. 800. 742. 686. 633. 587.  1.32 1.42 1.50 1.53 1.67 1.74 1.82 1.89  0.7738 0.7183 0.6647 0.6151 0.57C4 0.5278 0.4871 0.4514  1.71 1.97 2.26 2.57 2.93 3.30 3.73 4.18  60 70 80 90 100 110  16.00 18.67 21.33 24.00 26.67 29.33  2639. 2805. 2949. 3100. 3235. 3336.  501. 426. 361. 306. 258. 219.  2.02 2.15 2.26 2.38 2.48 2.56  0.3849 0.3274 0.2778 0.2351 0.1984 0.1687  5.25 6.57 8.14 10.11 12.50 15.16  e  TABLE  CYCLE NO. NC  s NUMERICAL EVALUATION OF EXPERIMENT E0U-Sl-8/*4l  C.2.37  REAL TIHE T (MINI  l.COOO  CONCENTRATION BRINE DIAL. CT (PPMI  CB (PPMJ  CONCENTRATION NORMALIZED XB l-l  XT (-)  1.00 1.20 1.37 1.53 1.68  l.COOO 0.8921 0.7919 0.7026 0.6145  1.00 1.35 , 1.73 2.18 2.73 4.22 6.35 9. 38  0 1 2 3 4  0.0 0.58 1.17 1.75 2.33  1184. 1421. 1618. 1811. 1983.  1171. 1045. 928. 823. 720.  6 8 10  3.50 4.67 5.83  2364. 2716. 3055.  555. 423. 322.  2.00 0.4736 2.29 0.3612 2.58 0.2753  14 18 22 26 30 34 38 42 46 50 54  8.17 10.50 12.83 15.17 17.50 19.83 22.17 24.50 26.83 29.17 31.50  3688. 4234. 4689. 5013. 5317. 5454. 5671. 5822. 5882. 6004. 6126.  182. 108. 65. 42. 29. 21. 16. 13. 10. 9. 7.  3.12 3.58 3.96 4.24 4.49 4.61 4.79 4.92 4.97 5.07 5.18  i, I,, TABLE  C.2.38  SEPARATION FACTOR  0.1553 0.0920 0.0557 0.0358 0.0246 0.0180 0.0138 0.0110 0.0089 0.0073 0.0064  NS (-1  20.07 38.90 71.09 118*34 182.40 256.70 348.02 446.62 557.12 697.85 810.23  .. ., ._ _ 8 NUMERICAL EVALUATION OF EXPERIMENT EUll-Sl-8/142  CYCLE NO. NC l-l  RIAL TIME  CONCENTR AT I ON BKINIi OIAL.  T  CO  (MINI  1 PPM 1  CT IPPMI  CC'iXENTR AT I ON NORMALIZED xn I-I  XT l-l  1226. 1310. 1374. 1442. 1453.  1204. 1064. 1005. 942. 865.  l . 00 l.COOO  2 3 4  0.0 0.52 1.03 1.55 2.07  6 8 10  3.10 4.13 5.17  1623. 1730. 1838.  780. 818. 738.  1.32 0.6484 1.41 0.6795 1.50 0.6131  15 20 25 30 35 40 45 50 55 60  7.75 10.33 12.92 15.50 18.08 20.67 23.25 25.83 28.42 31.00  2059. 2233. 2364. 2463. 2528. 2572. 2622. 2644. 2672. 2694.  449. 335. 257. 204. 170. 148. 133. 125. 117. 115.  1.68 1.82 1.93 2.01 2.06 2.10 2.14 2.16 2.18 2.20  0 I  TABLE  CYCLE NO. NC I-)  C.2.39  REAL TIME T IMIN)  CONCENTRATION BRINE DIAL. CB IPPM)  CT (PPMI  0.0 0.83 1.67 2.50 3.33 4.17 5.00  1231. 1549. 1805. 2037. 2238. 2413. 2572.  1224. 987. 805. 648. 517. 406. 321.  8 10  6.67 8.33  2799. 2955.  196. 124.  14 18 22 26  11.67 15.00 18.33 21.67  3139. 3241. 3314. 3376.  58. 38. 30. 27.  C.2.40  1 •  0.3730 0.2787 0.2133 0.1693 0. 1415 0.1233 0.1104 0.1040 0.0975 0.0954  NS l-l  1.00 1.21 I . 34 1.50 1.61 2.04 2.08 2.45 4.50 6.54 9.04 11.R6 14.58 17.03 19.38 20.75 22.35 23.04  I NUMERICAL EVALUATION OF EXPERIMENT EDM.-SI-8/S43  0 1 2 3 4 5 6  TABLE  1.07 0.8842 1.12 0.8349 l . , l f l 0.7824 1.19 0.7353  SEPARATION FACTOR  CONCENTRATION NORMAL IZEO  SEPARATION FACTOR  XB !-)  XT I-)  1.00 1.26 1.47 1.66 1.82 1.9,6 2.09  l.COOO 0.8061 0.6575 0.5290 0.4225 0.3319 0.2624  1.00 1.56 2.23 3.13 4.30 5.91 7.96  2.27 0.1602 2.40 0.1012  14.20 23.73  2.55 2.63 2.69 2.74  0.0472 0.0307 0.0248 0.0223  NS (-)  54.02 85.85 108.71 122.76  r NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/f44  402 CYCLC NO.  REAL  t  IMF  CONCI  cn  T  NC  l-l  NIRA  !1KINF  (MINI  1 1 ON  DIAL. CT  IPPM)  (PPM)  ClTiCI NT R AT I O N NORMAL 1 Z E D I <  SF P A R A T  X(j (-)  XT  NS  (-)  (-)  1.00 l.in l . 32 1.4 7 1.60  l.COOO 0.8645 0.7583 0.66C3 0.5723  1.00 1.36 1.75 2.23 2.80  0.0 0.67 1.33 2.00 2.67  127R. 1506. 1693. 1881. 2040.  1276. 1103. 96 d. 842. 730.  10  4.00 5.33 6.67  2331. 2561. 2738.  542. 396. 293.  1.82 0.4247 2.00 0.3104 2.14 0.2295  4.79 6.45 9.33  14 18 22 26 30 34  9.33 12.00 14.67 17.33 20.00 22.67  2977. 3123. 3218. 3302. 3353. 3410.  165. 103. 74. 61. 54. 51.  2.33 2.44 2.52 2.58 2.62 2.67  0.1294 0.08C9 0.0576 0.0480 0.0425 0.0403  17.99 30.70 41.68 53.79 61.76 66.11  0 1  ^  3 <v 6 a  TAOLE  CYCLE NO. NC l-l  C.2.41  REAL TIME T (MINI  0 1 2 3 4  I NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/»45  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPMI  CONCENTRATION NORMALIZED XB (-)i  XT (-)  SEPARATION FACTOR NS l - l  0.0 0.35 0.70 1.05 1.40  1242. 1273. 1300. 1331. 1358.  1233. 1158. 1118. 1080. 1045.  1.00 l.COOO 1.03 0.9393 1.05 0.9069 1.07 0.8755 1.0910.8473  1.00 1.09 1.15 1.22 1.29  6 2.10 8 ' 2.80 10 ; 3.50  1416. 1464. 1517.  982. 929. 878.  1.14 0.7960 1.18 0.7531 1.22 0.7123  1.43 1.57 1.72  15 20 25 30 35 40  5.25 7.00 8.75 10.50 12.25 14.00  1634. 1730. 1816. 1886. 1940. 1978.  775. 691. 627. 575. 531. 501.  1.32 1.39 1.46 1.52 1.56 1.59  0.6287 0.5607 0.5084 0.4665 0.4310 0.4059  2.09 2.49 2.88 3.26 3.63 3.93  50 60 70 80  17.50 21.00 24.50 28.00  2059. 2113. 2146. 2173.  451. 421. 404. 395.  1.66 1.70 1.73 1.75  0.3661 0.3410 0.3274 0.32C1  4.53 4.99 5.78 5.47  TABLE  C.2.42  ION  FACTOR  I NUMERICAL EVALUATION OF EXPERIMENT EDII-S1-8/H46  "I  403 CYCLE NO.  REAL TIMC  NC  T (MINI  CONCENIRAT lll'l BRINI: DIAL. CU (PPM)  CT (PPHI  CUMCENTRAT ION NORMAL I ZED XT I-I  1.00 1.09 1.21 1.32 1.41  1.0000 0.9410 0.6851 0.8261 0.7703  1.00 1.16 1.37 1.60 1.83 2.38 2.99 3.75  0.0 0.35 0.70 1.05 1.40  1226. 1342. 1465. 1618. 1730.  1224. 1152. 1084. 1011. 943.  6 e 10  2.10 2.80 3.50  1945. 2119. 2276.  815. 707. 606.  1.59 0.6660 1.73 0.5774 1.86 0.4953  15 20 25 30 35 40 45 50  5.25 7.00 8.75 10.50 12.25 14.00 15.75 17.50  2419. 2694. 2855. 2949. 3039. 3089. 3151. 3196.  426. 308. 232. 187. 155. 137. 125. 116.  1.97 2.20 2.33 2.41 2.48 2.52 2.57 2.61  CYCLE NO. NC I-)  C.2.43  REAL TIME T I MINI  NS (-1  XP (-)  0 1 2 3 A  TABLE  SEPARATION FACIOR  0.3477 0.2518 0.1897 0.1528 0.1264 0.1117 0.1022 0.0948  5.67 8.73 12.28 15.75 19.61 22.56 25.15 27.49  * NUMERICAL EVALUATION OF EXPERIMENT ED1I-S1-8/947  CONCENTRATION BRINE DIAL. CB IPPMI  CT (PPM)  CONCENTRATION NORMALIZED XB («|  XT (-)  SEPARATION FACTOR NS 1-)  0 5 10 15 20  0.0 0.92 1.83 2.75 3.67  1270. 1297. 1333. 1369. 1402.  1246. 1184. 1126. 1081. 1055.  1.00 1.02 1.05 1.08 l.lO  l.COOO 0.9503 0.9037 0.8675 0.8468  1.00 1.08 1.16 1.24 1.30  30 40 50 60 70 60 90 100  5.50 7.33 9.17 11.00 12.83 14.67 16.50 18.33  1461. 1508. 1544. 1575. 1603. 1620. 1632. 1646.  984. 938. 903. 877. 855. 841. 829. 819.  1.15 1.19 1.22 1.24 1.26 1.28 1.28 1.30  0.7899 0.7526 0.7246 0.7039 0.6863 0.6749 0.6656 0.6573  1.46 1.58 1.68 1.76 1.B4 1.B9 1.93 1.97  TABLE  C.2.44  7 NUMERICAL EVALUATION OF EXPERIMENT ED1I-S1-8/D48  404 CYCLE NO. NC I-)  RC AL  I |Mh T (MINI  CONCtNTRAI I ON I'.R 1 NC D I A L . CD 1 PPM)  C r f l C f N T K A r ION NORMAL 1/.CO  cr  xn  XT  (PPM)  (-)  (-)  StPARAT ION FACTOR NS l-l  1 !  5 6 7 8 9 10  0.0 1.33 2.67 4.00 5.33 6.67 8.00 9.33 10.67 12.00 13.33  1289. 191 1. 2200. 2528. 2788. 2994. 3145. 3263. 3348. 3427. 3495.  1264. 897. 640. 441. 301. 203. 133. 94. 65. 47. 35.  12 14 16  16.00 18.67 21.33  3603. 3682. 3762.  23. 18. 15.  2.79 2.86 2.92  0.0184 0.0143 0.0122  152.17 199.97 238.36  20  26.67  3911.  13.  3.03  0.0105  288.70  25 30 35 40  33.33 40.00 46.67 53.33  4078. 4251. 4368. 4461.  12. 11. 10. 10.  3.16 0 . C 0 9 2 3.30 0 . 0 0 9 5 3.39 0 . 0 0 8 1 3.46 O.0077  344.49 389.44 420.34 452.20  0 1 2 3  4  TARLB  C.2.45  1.00 l.COCO 1.40 0 . 7 0 9 2 1.71 0 . 5 C 6 1 1.96 0 . 3 4 9 0 2.16 0 . 2 3 7 8 2.32 0 . 16C2 2.44 0 . 1 0 5 1 2.53 0 . 0 7 4 0 2.60 0 . 0 5 1 0 2.66 0 . 0 3 7 2 2.71 0 . 0 2 8 1  1.00 1.98 3.37 5.62 9 . 10 14.50 23.22 34.22 50.90 71.38 96.62  » NUMERICAL EVALUATION OF E X P E R I M E N T E D l l - S l - 8 / f j.9  —  CYCLE NO.  REAL TIME T (MINI  NC l-l  CONCENTRATION BRINE DIAL. CB (PPMI  CT (PPMI  CONCENTRATION NORMAL 17.E0  —  —  XB I-1  XT (-)  1.00 1.36 1.63 1.89 2.13 2.32 2.46  1.0000 0.7208 0.4889 0.3579 0.2298 0.1442 0.0927  1.00 1.B8 3.33 5.29 9.28 16.11 26.56  0.0 1.52 3.03 4.55 6.07 7.58 9.10  1315. 1784. 2140. 2490. 2805. 3055. 3241.  1280. 922. 626. 458. 294. 184. 119.  8 10  12.13 15.17  3472. 3597.  54. 32.  2.64 0 . 0 4 2 3 2.73 0 . 0 2 5 2  62.34 108.50  15 20 25 30  22.75 30.33 37.92 4 5 . 50  3796. 3934. • 4020. 4055.  21. 16. 14. 12.  2t.;89 2.99 3.06 3.08  178.95 237.35 200.74 328.82  TABLE  C.2.46  .  NS (-)  0 1 2 3 4 5 6  0.0161 0.0126 0.0109 0.0094  ^  SEPARATION FACTOR  .  : NUMERICAL EVALUATION OF E X P E R I M E N T EDLI-S1-8/I50  •• •  •  405 CVCIE NO. NC l-l  RCAL TIME T (MINI  CONCENTRATION OR INC OIAL. CB (PPMI  CT IPPM)  CLNCTNIKUION NORPALIZEO XD . (-)  XT (-)  SEPARATION FACTOR NS (-1  0 1 1  0.0 1294. 0.67 1337. 0.67 102907.  1271. 1264. 1251.  1.00 l.COOO 1.03 0.9949 79.51 0.4848  1.00 1.04 80.74  3 5  2.00 3.33  1501. 1650.  1206. 1148.  1.16 0.9492 1.27| [0.9036  1.22 1.41  9  6.00  1956.  1018.  1.51 0.8010  1.89  14 19 24 29  9.33 12.67 16.00 19.33  2298. 2572. 2799. 2968.  864. 733. 613. 522.  1.78 1.99 2.16 2.31  0.6802 0.5766 0.4822 0.4112  2.61 3-45 4.48 5.62  39 49 59 69 79 69 99 109  26.00 32.67 39.33 46.00 52.67 59.33 66.00 72.67  3269. 3466. 3620. 3762. 3877. 3974. 4055. 4124.  377. 275. 201. 155. 116. 97. 77. 65.  2.53 2.68 7.80 2.91 3.00 3.07 3.13 3.19  !o.2964 0.2162 0.1584 0.1218 0.0914 0.0761 0.0609 0.0508  8.52 12.39 17.66 23.86 32.78 40.33 51.43 62.77  TABLE  CYCLE NO. NC l-l  C.2.47  : NUMERICAL EVALUATION OF EXPERIMENT EDII-SI-8/S51  REAL TIME  CONCENTRATION BRINE DIAL.  T (MINI  CB . CT (PPM) (PPMI  CONCENTRATION NORMALIZED XB (-) •  XT' (-)  SEPARATION FACTO*. NS (-1  0 1 2 3 4 5  0.0 0.67 1.33 2.00 2.67 3.33  1321. 1395. 1501. 1597. 1671. 1779.  1206. 1138. 1058. 983. 909. 839.  1.00 1.06 1.14 1.21 1.27 1.35  l.COOO 0.9433 0.8770 0.8150 0.7540 0.6952  1.00 1.12 1.30 1.48 1.68 1.94  10 15 20 25 30  6.67 10.00 13.33 16.67 20.00  2146. 2457. 2S84. 2705. 2794.  555. 362. 236. 144. 115.  1.62 1.86 1.96 2.05 2.12  0.4599 0.3005 0.1957 0.1198 0.0952  3.53 6.19 10.00 17.10 22.22  40 50 60  26.67 33.33 40.00  2899. 2977. 3039.  68. 53. 48.  2.20 0.0567 2.25 0.0439 2.30 0.0390  38.73 51.41 58.14  TABLE  C.2.46  : NUMERICAL EVALUATION OF EXPERIMENT EDM-SlrB/f52 I  CYCLE fJO. NC (-)  REAL T1MF T IMIN)  C0NCENTRA1ION BRINE DIAL. CB (PPM)  CT (PPM)  CONCENTRATION NORMAL 12 ED XB l - l  XT (-)  1.00 l.COOO 1.24 0.7771 1.36 0.6339 1.42 0.5112 1.49 0.4090 1.55,6.3476 1.61 0.3067  SEPARATION FACTOR NS (-»  I.00 1.59 2.15 2.79 3.64 4.46 5.26  0 1 2 3 4 5 6  0.0 0.67 1.33 2.00 2.67 3.33 4.00  1278. 1581. 1741. 1822. 1902. 1983. 2064.  1262. 980. 800. 645. 516. 439. 387.  8 10 12 14 16  5.33 6.67 8.00 9.33 10.67  2227. 2364. 2446. 2484. 2578.  310. 271. 232. 210. 193.  1.74 1.B5 1.91 1.94 2.02  0.2454 0.2147 0.1840 0.1667 0.1534  7.10 8.61 10.40 11.66 13.15  21 26 31 36 41 46 SI 56  14.00 17.33 20.67 24.00 27.33 30.67 34.00 37.33  2749. 2944. 3083. 3196. 3297. 3365. 3421. 3449.  168. 142. 132. 116. 110. 103. 97. 90.  2.15 2.30 2.41 2.50 2.58 2.63 2.68 2.70  0.1329 0.1125 0.1043 0.0920 0.0869 0.0818 6.0767 0.0716  16.18 20.47 23.13 27.16 29.67 32.17 34.90 37.70  TABLE  C.2.49  t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/»53  Table C-2-50 Average Current and Voltage D i s t r i b u t i o n s 1  2  5  H  RUtl NO.  CURRENT Lamp erej  CYCLE NO.  C-]  INITIAL FINAL  [-]  6 7  5  8  9  10 11 12 13  AVERAGE CURRENT [ampere] TO STAGE NO 1  2  1n Second ED Experiments  3  4  5  6  7  IU  CYCLE NO. 8  C-]  15 16 17 18 19 20 21 " 22 AVERAGE PROBE VOLTAGE [ v o l t ] IN STAGE NO.  VOLTAGE APPLIED  1  2  3  4  5  6  7  8  [volt] 10 10 10 10  12 10 8 11  5.4 5.1 5.6 5.5  2.6 4.1 3.8 4.6  70-85 20-40 25-35 10-20  .02 .3 .15 .36  .03 .31 .22 .45  .04 .35 .34 .51  .1 .40 .46 .59  .26 .52 .65 .64  .55 .69 .82 .70  .83 .71 .78 .70  .85 70-85 .76 20-40 .89 .69 10-20  8.5 5.8  8.5 6.2  8.2 5.9  7.3 5.5  6.5 5.3  6.0 4.9  3.9 3.6  4.2 4.0  5.5  5.2  5.0  4.5  4.5  4.5  3.8  4.0  15 14 7  5.6 5.5 5.6  5.5 5.7 5.6  10-20 .30 25-35 .520-30 .6  .45 .58 .62  .55 .63 .64  .68 .73 .70 .74 .70 .71  .86 .84 .79  .72 .73 .75  .73 5-12 .71 23-35 .74  4.7 4.6  4.6 4.5  4.4  4.4 4.4  4.2  4.4 4.3  3.6 3.5  4.1 3.8  47 45 44 35a  0.70 1.32 1.88 2.60  0.36 0.68 1.04 1.40  _ _ 45-46 _ 8-12 - .04 13-19 16-24 .020 .025 .05  _ .25 .10 .25 .2 .31 .275 .36  47-49 .36 16-20 .38 22-27 .41 5-12  _  _  9.0 8.4  9.0 8.0  9.0 8.5 9.0 7.9  8.5 8.7 9.0 7.5  7~9 7.1 6.9  7.2 7.0 7.0  19 20 18 17 6  1.45 0.88 1.75 1.00 3.00 " 1.72 4.70 2.60 5.60 3.20  37-38 36-37 . 22-25 19-25 30-40 .05  -  .61 34-35 - 42-43 .75 27-31 .80 31-33 .95  6.2  .15 .16  .29 . 71 _ _ .33 .56 .52 .67 .62 .72  7.6  .08  - .39 .20" .20 .34 .30 .'45  7.6 8.1 7.5  6.1 7.6  5.8 4.9  5.2 4.8  27 22 9  2.2 4.0 5.5  1.1 1.5 2.0  18-24 .01 18-25 .02 15-25 .05  .02 .03 .08  .04 .05 .10  .07 .12 .08 .17 .19 .31  .22 .25 .45  .28 .38 .55  .31 .5 .74  6-14 5-12  35a 23 6  2.6 4.2 5.6  1.4 2.1 3.2  16-24 .02 19-27 .02 30-40 .05  .025 .05 .04 .09 .08 .16  .08 .16 .15 .26 .30 .45  .275 .36 .39 .48 .62 .72  .41 .59 .95  5-12 7-15  33 24 21  3.5 5.8 8.8  2.0 3.0 3.4  16-24 .01 16-24 .02 16-24 .03  .025 .05 .04 .07 .05 .09  .1 .25 .13 .22 .16 .26  41 25 30  3.6 3.0 3.0  3.4 2.4 2.6  50-58 .26 18-26 .13 17-25 .10  .30 .15 .13  .38 .42 .25 .35 .26 .37  _  _  -  .34 .20 .20  _  .1 - .06 .06 .11 .08 .16 _  _  _  8.2  8.3  _  —  _ _  10 10 10 10 10 10 10 10 10 10 10  _  8.3  8.7 8.2  8.8 8.2  8.9 8.3  8.7 8.3  8.3 8.0  8.2 7.6  7.6 7.0  7.6 6.3  10 10 10  8.2 7.3  8.3 7.6  8.4 7.7  8.0 7.5  7.9 7.0  7.5 6.8  6.9 5.6  7.0 5.6  10 10 10  .44 .58 .71  .58 .70 6-14 13.8 13.8 13.6 13.6 13.2 12.8 10.8 10.8 .80 .94 25-34 13.2 13.3 13.0 12.4 12.5 11.6 9.7 9.4 .96 1.2 25-34 13.5 13.3 12.9 12.4 11.5 11.1 8.8 8.8  15 15 15  .50 .45 .45  .56 .50 .52  10 10 10  .55 73-85 .53 25-35 .51 6-14  7.5 7.5 7.6 8.25 8.25 8.1 7.0 7.0 6.8  7.3 7.5 6.8  7.1 7.2 6.8  7.1 6.4 6.5  6.0 5.4 5.5  6.1 5.75 5.7  CONTINUED  o  Table C-2-50  i RUN  2 NO.  C-3 42 35a 29  4 CYCLE NO.  INITIAL FINAL  [-3  5 -.6-7  8  9  10  11  12  AVERAGE CURRENT [ampere]. TO STAGE NO 1  2  3  4  5  6  7  13  IU  CYCLE NO. 8  [-3  15  16  17  18  19 ,20  21  AVERAGE PROBE VOLTAG E [ v o l t ] IN STAGE NO.  22 VOLTAGE APPLIED  1  2  3  4  5  6  7  8  [volt]  9.3 8.2  9.3 8.3 8.5  9.2 8.4  9.3 8.0 7.8  9.2 7.9  9.0 7.5 7.3  8.6 6.9  7.2 7.0 6.3  10 10 10  2.56 2.6 2.65  .93 1.4 1.8  18-26 .04 16-24 .02 12-15  .05 .05 .025 .05 .07  .08 .12 .08 .16 .16  .15 .28 . 27E .36 .32  .42 38-46 .41 5-12 .39 7-11  1.3 2.7 4.2  1.05 1.8 2.75  19-27 .05 .06 .08 24-32 .024 .038 .06 17-25 .016 .03 .06  .10 .13 .12 .24 .13 .28  .18 .36 .46  .23 28-36 4.3 4.3 4.2 4.0 3.8 3.6 3.0 2.9 .51 13-22 8.4 8.5 8.3 8.0 7.75 7.45 6.25 6.25 .82 7-15 13.4 13.4 13.2 13.0 12.5 12.0 10.0 10.0  36 35a 33  1.4 2.6 3.5  .8 15-23 .03 1.4 16-24 .02 2.0: . 16-24 .01-  .05 .06 .025 .05 .025 .0.5  .08 .10 .08 .16 .1 .25  .13 .18 .27' .36 .44 .58  13 8 16  2.2 5.6 9.5  2.0 3.8 6.9  40-50 .19 25-35 .15 20-30 .11  .21 .22 .19  .22 .34 .31  .24 .28 .34 .29 .28 .46 .65 .82 .78 .89 .50' .78 1.15 1.3 1.4  40-50 2.4  2.5  2.2  2.0  2.1  2.0  1.6  1.5  11-19 9.2  9.3  9.2  8.8  8.5  8.2  6.0  6.5  5 10 15  37 38 25  2.0 2.65 3.0  1.55 2.2 2.4  17-25 .01 17-25 .04 18-26 .13  .02 .06 .15  .03 .11 .20  .06 .18 .18 .29 .25 .35  .31 .43 .45  .42 .52 .50  .49 .51 .53  6-14 8.2 8.3 8.1 29-37 8.8 8.5 8.3 25-35 8.25 8.25 8.1  7.9 7.8 7.5  7.4 7.3 7.2  6.9 6.9 6.4  5.4 5.2 5.4  5.7 5.5 5.75  10 10 10  39 40 35a  2.08 2.32 2.6  1.44 1.6 1.4  17-25 .01 • .02 .03 15-23 .01 .02 .03 16-24 .02 .025 .05  .06 .15 .06 .16 .08 .16  .20 .31 .275  .39 .40 .36  .46 .47 .41  8.3 8.2 8.0  7.6 7.9 7.9  7.0 7.8 7.5  5.8 6.8 6.9  5.7 6.5 7.0  10 10 10  35 28 " 32  :  3  CURRENT [ampere]  (Continued)  .21 .50 .70  .21 23-31 4.5 4.4 4.3 4.2 4.0 3.8 3.3 3.0 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 -.70 6-14 13.8 13.8: 13-.6 13.6 13.2 12.8 ,10.8 10.8  5-13 8.6 4-12 8.0 5-12 8.2  8.7 8.3 8.3  8.5 8.2 8.4  5 10 15 5 10 15  APPENDIX C.3  COMPUTER PROGRAM FOR SPACER MODEL i  i  The input data a r e :  (in text)  M  = number of mixing c e l l s  m  N  = number of s l i c e s in s o r p t i o n membrane  n  PE  = Fourier number  Fo  R  = width r a t i o  P  CHALE  = channel length  i/b  COMLE  = C e l l length  !  EPSILO = l a y e r thickness W  d'/b 6/b v/b / v/l  = velocity i  PODRO XSI  = p o t e n t i a l drop  Ai|>  = membrane r e s i s t a n c e  DTAU ERROR  = s t a r t i n g i n t e g r a t i o n step length = maximum t o l e r a b l e i n t e g r a t i o n e r r o r  TAU1  = duration of f i r s t h a l f c y c l e  TAU2  = duration of second h a l f c y c l e  OMEG  = a c c e l e r a t i o n f a c t o r f o r Gauss-Seidel iteration  408  5 At  . 4 0 8 r\  ERRIT  = maximum t o l e r a b l e i t e r a t i o n  error  DTAUP  = p r i n t i n g step  ICYC  = number of c y c l e s  INIT  = c o n t r o l d i g i t to read i n i n i t i a l matically i n i t i a l i z e .  length  !i  \  data or t o auto  409 C C c c c c  1 7  3 4 5 6 7 8 <J 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 SI 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 81 84 85 86  SPACER MODEL  < I'ACKViAKfl OIFFFRLNCE SCHEME CAUSS - SEIOFL 1 IE RAH ION AUTOMATIC A|)IUSI»ENT OF TIME STEP S U E J 1 VERSION FOR PLOT 1 INC 1  OIMFNSION CI 1C0,20),CH(1C0,2()),CI'( 100