UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A Cyclic electrodialysis process : investigation of closed systems 1972

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1973_A1 B38.pdf [ 26.68MB ]
Metadata
JSON: 1.0059007.json
JSON-LD: 1.0059007+ld.json
RDF/XML (Pretty): 1.0059007.xml
RDF/JSON: 1.0059007+rdf.json
Turtle: 1.0059007+rdf-turtle.txt
N-Triples: 1.0059007+rdf-ntriples.txt
Citation
1.0059007.ris

Full Text

^ 0 % A CYCLIC ELECTRODIALYSIS PROCESS I n v e s t i g a t i o n of C l o s e d Systems by DIETER BASS D i p l . I n g . , U n i v e r s i t a e t 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 i n the Department of CHEMICAL ENGINEERING We ac c e p t t h i s t h e s i s as con f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA Decembe r , 19 72 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^ < O f C The University of British 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 demineraliza- tion 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. Ten system parameters were analysed on a simple bench scale c e l l . 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 electrically. Final separation factors ranged between 2 and ~6000. Large separation factors were achieved for long channels, long pause times, and high applied potentials. The initial rate of i i separation appeared to be a maximum for a channel length of approxi- mately one meter and pause times of about ten seconds. During the fir 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. i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES x LIST OF FIGURES x i i i ACKNOWLEDGEMENTS x x i i i Chapter 1 INTRODUCTION AND SCOPE 1 2 PROCESS PRINCIPLES . . . . 4 2.1 E l e c t r o d i a l y s i s 4 2.1.1 Origin of separation 5 2.1.2 Membrane s e l e c t i v i t y 8 2.1.3 Transport processes through ion sele c t i v e membranes 12 2.1.4 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 i t s applications 14 2.1.5 Concentration p o l a r i z a t i o n and other problems in steady-state e l e c t r o d i a l y s i s 16 2.1.6 Current reversal techniques 21 2.2 Parametric pumping, heatless adsorption and s i m i l a r c y c l i c separation processes . . 24 i v Chapter Page 2.2.1 Parametric pumping 25 2.2.2 Other c y c l i c operations 33 3 EFFECT OF FINITE MASS TRANSFER RATES ON PARAMETRIC PUMPING AND PURE PAUSE OPERATION. . . . 37 3.1 General 37 3.2 Constant, Uniformly Distributed Rates of Mass Transfer 39 3.2.1 Parametric pumping operation 41 3.2.2 Pure pause operation 51 3.3 Concentration Dependent Rates of Mass Transfer 52 3.3.1 Pure pause operation 54 3.3.2 Parametric pumping operation 56 3.3.3 Comparison of pause and parametric pumping operations . . . . . . . . . . 56 3.4 Summary 60 3.5 Comment on an Equilibrium Model with Instantaneous Displacement 61 4 THE CYCLIC ELECTRODIALYSIS PROCESS - OPERATION AND APPARATUS 65 4.1 Description of the Batch Operation 65 4.2 The F i r s t Bench Module 68 4.2.1 El 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 flow 83 4.2.4 Timing and switch boxes 84 4.2.5 Rinse loop 88 4.2.6 Measuring and recording 88 v Chapter - Page 4.3 The Mini P i l o t Plant Module 90 4.3.1 Electrodi alyser No. 2 (ED 11) 90 4.3.2 Rinse d i s t r i b u t i o n system 98 4.3.3 Current and voltage measurements . . . 98 5 EXPERIMENTAL RESULTS AND DISCUSSION. . . . . . . . 101 5.1 Data Co 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 Cell (EDI). . . . . 108 5.3.1 Parameters 108 5.3.2 Effect of applied voltage. . . . . . . 109 5.3.3 Effect of pause time 120 5.3.4 Effect of s u p e r f i c i a l velocity . . . . 128 5.3.5 Effect of displaced volume 135 5.3.6 Effect of dead volumes 141 5.3.7 Effect of i n i t i a l concentration. . . . 147 5.3.8 Effect of internal flow d i s t r i b u t i o n and axial dispersion . . . 151 5.3.9 Effect of external mixing in brine reservoir 159 5.3.10 Effect of capacity c e l l thickness. . . 164 5.3.11 Effect of thickness and hydro- dynamic properties of spacer screens 165 5.3.12 Comment on pH-changes 167 5.3.13 Comment on current e f f i c i e n c i e s . . . . 167 5.3.14 Comment on true limits and on re p r o d u c i b i l i t y of batch runs 170 vi Chapter Page 5.4 Summary of Experience Gained on F i r s t E l e c t r o d i a l y s i s Cell 173 5.5 The Second E l e c t r o d i a l y s i s Cell (EDI I) . . . . 175 5.5.1 Data reduction and presentation. . . . 176 5.5.2 Effect of channel length 178 5.5.3 Effect of pause time 194 5.5.4 Effect of applied voltage 205 5.5.5 Effect of i n i t i a l concentration. . . . 205 5.5.6 Effect of displaced volume 211 5.5.7 Effect of dead volumes 221 5.5.8 Effect of s u p e r f i c i a l v e l o c i t y . . . . 221 5.5.9 Reproducibility 226 5.5.10 Comment on the material balance for the solute 229 5.5.11 Comment on the performance of individual stages . 231 5.5.12 Experimental test of the constant rate model . 239 5.5.13 Comment on the e f f e c t of end mixing 241 5.5.14 Production of 90% demineralized solution 243 5.6 Summary of Results and Experience on the Second ED Module 247 6 MATHEMATICAL MODELS 250 6 .1 Spacer Model 250 6.1.1 Model equations 252 6.1.2 Considerations related to c y c l i c process operations 261 vi i Chapter Page 6.1.3 Solutions 262 6.1.4 Backward Difference scheme with Gauss-Seidel i t e r a t i o n 264 6.1.5 Results of computer simulations. . . . 269 6.1.5.1 Accuracy and convergence. . . 269 6.1.5.2 Effect of operating parameters 270 6.1.5.3 Comparison with experimental resul ts . . . 271 6.1.6 Concluding comments on the spacer model 278 6.2 Rate Model 279 7 CONCLUSIONS 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 MEMBRANE- SPACER FRAME 305 B MATHEMATICAL DERIVATIONS 308 •B.l DERIVATION OF CONCENTRATION TRANSIENTS FOR CON- STANT, UNIFORMLY DISTRIBUTED RATES OF MASS TRANSFER. PARAMETRIC PUMPING OPERATION 309 B. 2 DERIVATION OF CONCENTRATION TRANSIENTS FOR CON- CENTRATION DEPENDENT RATES OF MASS TRANSFER - PURE PAUSE OPERATION 313 B.3 RATE THEORY OF PARAMETRIC PUMPING 318 v i i i APPENDICES Page B.4 MULTIPLE STEP DISPLACEMENT MODEL (STOP-GO ALGORITHM) 325 B. 5 DERIVATION OF CONCENTRATION TRANSIENTS FOR EQUILIBRIUM CONTROLLED PURE PAUSE OPERATION. . . . 330 C COMPUTER PROGRAMS 336 C. l EVALUATION OF EDI EXPERIMENTS 337 C.2 EVALUATION OF EDII EXPERIMENTS 378 C.3 SPACER MODEL 408 i x LIST OF TABLES Tab 1 e Page 1. Computer S i m u l a t i o n s of 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 Dependent 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 (EDI) 75 3 P r o p e r t i e s of Neosepta Membranes 76 4 S t a c k Pack V e r s i o n s Used i n F i r s t ED C e l l . . . . 79 5 P i s t o n Pump S p e c i f i c a t i o n s 84 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 of 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 from a Beckman Sol 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 C o m p i l a t i o n of Experiments on EDI-S1-8 107 9 C o m p i l a t i o n of Experiments on EDI-S2-15 10 C o m p i l a t i o n of Experiments on EDI-S2-16 11 C o m p i l a t i o n of Experiments on EDI-S3-12 12 C o m p i l a t i o n of Experiments on EDI-S3-13 13 C o m p i l a t i o n of Experiments on ED 11-S1-8 x Tab 1 e Page 14 E f f e c t of A p p l i e d V o l t a g e (A$) on EDI-SI-8 116 15 E f f e c t o f A p p l i e d V o l t a g e (A$) on EDI-S2-15 16 E f f e c t of A p p l i e d V o l t a g e (A$) on EDI-S3-12 and EDI-S3-13 17 E f f e c t of Pause Time (x) on EDI-S2-15 and EDI-S2-16 122 18 E f f e c t on Pause Time (T) on EDI-S3-12 19 E f f e c t o f Pause Time (x) on EDI-S3-13 20 E f f e c t of S u p e r f i c i a l V e l o c i t y (v) on EDI-SI-8 131 21 E f f e c t o f S u p e r f i c i a l V e l o c i t y (v) on EDI-S2-16, EDI-S3-12 22 E f f e c t of S u p e r f i c i a l V e l o c i t y (v) on EDI-S3-13 23 E f f e c t of D i s p l a c e d Volume (s) on EDI-S1-8, EDI-S2-15 and EDI-S3-13 . . 137 24 E f f e c t of Dead Volumes (<S R /6 T ) on EDI-S2-15, EDI-S3-12 and EDI-S3-13 . .  1  142 25 E f f e c t o f I n i t i a l C o n c e n t r a t i o n ( c 0 ) on EDI-S3-12 and EDI-S3-13 148 26 Step Response Experiments on EDI-S1-8 157 27 Step Response Experiments on EDI-S3-12 Runs #1-14 157 28 Step Response Ex p e r i m e n t s on EDI-S3-12 Runs #15-24 158 x i Table Page 29 Step Response Experiments on EDI-S3-13 158 30 Effect of End Mixing on EDI-S3-12 . 162 31 Effect of Capacity Cell Thickness on E1 ectrodi alyzer No. 1 166 32 pH-Changes in Some EDI-S3-12 Runs 167 33 Results of Step-Response Tests on Second ED Cells 180 34 Effect of Channel Length (MS) on Second E1 ectrodi alyzer 184 35 Ef f e c t of Pause Time (x) on Second Electrodi alyzer 196 36 Effect of Applied Voltage (A$) on Second Electrodi alyzer 206 37 Effect of I n i t i a l Concentration (c 0 ) on Second E l e c t r o d i a l y z e r . . . . . . . . . . . . 212 38 Effect of Displaced Volume (6) on Second Electrodi alyzer 217 39 Effect of S u p e r f i c i a l Velocity (v) on Second El ectrodi alyzer 223 40 Spacer Model No. I, Effect of Layer Thickness 272 41 Spacer Model No. I, Effect of Fourier Number 273 42 Spacer Model No.I, Effect of Applied Potential 274 X I i LIST OF FIGURES Fi gure Page 1 The e l e c t r o d i a l y s i s p r i n c i p l e . . . . . 6 2 Transport processes across an anion- s e l e c t i v e membrane 13 3 M u l t i c e l l e l e c t r o d i a l y s i s stack (schemati c) 13 4 Concentration po l a r i z a t i o n of an ion- se l e c t i v e membrane 18 5 Thermal parametric pumping . 18 6 Characteristics of batch separation via equilibrium theory of parametric pumping . . . . 30 7 Concentration transients for equilibrium theory of parametric pumping (according to P i g f o r d , 1969a) 32 8 Heatless adsorption a i r drying system, used by Skarstrom ( 1959) 34 9 C y c l i c zone adsorption (proposed by P i g f o r d , 1969b) 35 10 E l e c t r o d i a l y s i s systems with constant, uniformly dis t r i b u t e d rates of mass transfer . . 40 11 Concentration p r o f i l e s during the f i r s t cycle 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 conditions of equal, constant, and uniformly dis t r i b u t e d rates of mass transfer 43 xi i i Fi gure Page 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 para- metric pumping mode under conditions of equal , constant, and uniformly d i s t r i b u t e d rates of mass transfer 44 13 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 parametric pumping mode under conditions of unequal , constant, and uniformly dis t r i b u t e d rates of mass transfer 45 14 Development of standing waves in a parametric pumping operation under conditions of equal, constant and uniformly d i s t r i b u t e d rates of mass transfer when variables are switched one-quarter cycle out of phase 47 15 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 parametric pumping mode under conditions of equal, con- stant and uniformly d i s t r i b u t e d rates of mass t r a n s f e r , when periodic variables are switched one-quarter cycle out of phase 48 16 Average top and bottom product transients for phase s h i f t operation of a constant rate controlled parametric pump 50 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. . . 50 18 Effect of the number of segments (N) on the product concentration transients for con- centration dependent rates of mass transfer (ai=a 2 =0.01 sec _1 ,T=20 sec, p=1.0, 6=1.0). . . 58 19 Product concentration transients for equi- librium controlled pure pause operation 63 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 66 xi v Fi qure Page 21 Time variation of applied potential (a) and flow rate (b) for c y c l i c e l e c t r o - d i a l y s i s process 66 22 Block diagram of experimental testing s t a t i o n . . . 69 23 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) 72 24 Electrodi alyser No. 1 80,81,82 25 Glass f i b r e spacer screen 78 26 Floating l i d expansion tank 85 27 Automatic switching arrangement for c y c l i c el ectrodi alys i s process 85 28 Piston Pump Drive. E l e c t r i c c i r c u i t for motor reversal 87 29 Clamping arrangement of eight stages in mini p i l o t plant module 91 30 Schematic assembly of one stage of the second e l e c t r o d i a l y z e r 87 31 ' Integrated membrane-spacer frame for e l e c t r o d i a l y z e r No. 2. Parts and assembly . . . . 93 32 E l e c t r o d i a l y s e r No. 2. Electrode end frames of a single stage 94 33 Process flows through second ele c t r o - d i a l y s i s c e l l (schematic) 96 34 Current monitoring c i r c u i t 99 35 EDI-S2-15/#l5. Traces of current and probe voltage recording during the f i r s t f i v e cycles I l l xv Fi gure Page 36 S t a c k v o l t a g e v s . e l e c t r o d e v o l t a g e f o r f i r s t ED c e l l 112 37 EDI-S1-8/#36. 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 s t a n t 113 38 EDI-S2-15/#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 i s c o n c e n t r a t i o n dependent. . . 113 39 E f f e c t of a p p l i e d v o l t a g e on f i n a l concen- 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 o p e r a t i o n . EDI-S2-1 5/#7 ,8 ,9 ,10 ,1 7 . . . . . . . . .117 40 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 c e n t r a t i o n s 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-S3-13/ #6,7,11 ,8,22,9 118 41 E f f e c t of 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 of pause time (x) on s e p a r a t i o n f a c t o r f o r second and t h i r d s t a c k e x p e r i m e n t s 123 43 E f f e c t of pause time on f i n a l r e s e r v o i r con- c e n t r a t i o n s f o r t h i r d s t a c k e x p e r i m e n t s . ED I - S3-12/#24 ,18,21 ,22 ,23 and EDI-S3-13/#10 ,11 ,7, 12,2,13,1 ,14 124 44 E f f e c t of pause time (x) 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/ #24 ,18 ,21 ,22 ,23 and EDI-S3-1 3/#10 ,11 ,7 ,12 ,2 , 13,1 ,14 124 45 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 46 E f f e c t of pause time (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 126 x v i Fi gure Page 47 Contrasting pause and no-pause operation for t h i r d stack experiments. EDI-S3-13/ #21 ,32 127 48 Effect 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 reservoir concentrations for pause and no- pause operation. EDI-S3-13/#l5 ,3 ,16,25,17, 32,18,31 and EDI-S3-13/#20 ,19 ,21 132 49 Effect 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 separation factors for 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 50 Effect of s u p e r f i c i a l v e l o c i t y (v) on con- centration transients for no-pause operation. EDI-S3-13 133 51 Effect of s u p e r f i c i a l v e l o c i t y (v) on con- centration transients for pause operation. EDI-S3-13 134 52 Effect of displaced volume (6) on f i n a l reservoir concentrations for pause operation. EDI-S3-13/#4,3 S 2,12,5 138 53 Effect of displaced volume (6) on f i n a l separation factor for pause operation. EDI-S3-13/#4 ,3 , 2,12,5 138 54 Effect of displaced volume (6) on concentra- tion transients for pause operation. EDI-S3-13 139 55 Effect of displaced volume (6) on real time transients for no-pause operation 140 56 Effect of dead volumes (Sg/S T ) on concentra- tion t r a n s i e n t s . EDI-S2-15 143 57 Effect of dead volumes (S B /<5 T ) on concentra- tion t r a n s i e n t s . EDI-S3-1 3 144 x v i i Fi gure Page 58 Effect of dead volumes (Sg/6 T ) on s a l t i n g factor t r a n s i e n t s . EDI-S2-15 146 59 Effect of i n i t i a l concentration (c 0 ) on dialysate concentration t r a n s i e n t s . EDI-S3-1 2 149 60 Effect of i n i t i a l concentration (c 0 ) on concentration t r a n s i e n t s . EDI-S3-13 150 61 Effect of i n i t i a l concentration (c 0 ) on concentration t r a n s i e n t s . EDI-S3-13 150 62 Internal mixing. Effect of number of e f f e c t i v e mixing stages (m) on response to step change in feed coricentrati on: . _ (a) response function x ( t ) ; (b)'slope (x(t)) of response curve (di mensi on!ess ) 155 63 Maximum slope (x) vs. number of mixing stages (m) 156 64 Step response of second stack versions (schemati c) 156 65 Effect of internal dispersion. Transients of separation factor and dialysate product concentration for second stack versions 160 66 Qualitative model of the concentration 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 operation with internal dispersion and well mixed end reservoirs 163 67 Uniqueness and r e p r o d u c i b i l i t y of f i n a l separation factor for second stack experiments 171 68 Uniqueness of f i n a l separation factor for second stack experiments 172 69 Dimensionless slope of step response curves for second ED c e l l as function of the number of e l e c t r o d i a l y s i s stages 179 x v i i i Fi gure Page 70 Effect of channel length (MS) on separation factor transients 185 71 Effect of channel length (MS) on concentration transients . . . . . 186 72 Effect of channel length (MS) on current d i s t r i b u t i o n 187 73 Effect of channel length (MS) on separation factor transients . . . 188 74 Effect of channel length (MS) on current d i s t r i b u t i o n 189 75 Effect of channel length (MS) on separation factor transients 190 76 Effect of channel length (MS) on concentration transients 191 77 Effect of channel length (MS) on current d i s t r i b u t i o n 192 78 Effect of channel length (MS) on i n i t i a l rate of separation (a) 193 79 Effect of pause time (x) on separation factor transients 197 80 Effect of pause time (x) on concentra- tion transients 198 81 Effect of pause time (x) on current d i s t r i b u t i o n .199 82 Effect of pause time (x) on separation factor transients 200 83 Effect of pause time (x) on current d i s t r i b u t i o n 201 xi x Fi gure Page 84 Effect of pause time (x) on separation factor t r a n s i e n t s . 202 85 Effect of pause time (x) on concentra- tion transients 203 86 Effect of pause time (x) on i n i t i a l rate of separation (a) 204 87 Effect of applied voltage (A$) on separation factor transients 207 88 Effect of applied voltage (A$) on separation factor transients 208 89 Effect of applied voltage (A$) on separation factor transients 209 90 Effect of applied voltage (A$) on i n i t i a l rate of separation (a) 210 91 Effect of i n i t i a l concentration (c 0 ) on separation factor transients 213 92 Effect of i n i t i a l concentration (c 0 ) on separation factor transients 214 93 Effect of i n i t i a l concentration (co) on separation factor transients 215 94 Effect of displaced volume (6) on separation factor transients 218 95 Effect of displaced volume (6) on separation factor transients 219 96 Effect of displaced volume (6) on separation factor transients 220 97 Effect of dead volumes (6g/6 T ) on concentration transients 222 xx Fi gure Page 98 Effect of s u p e r f i c i a l velocity (v) on separation factor transients 224 99 Effect of s u p e r f i c i a l v e l o c i t y (v) on separation factor transients 225 100 Reproducibility of second stack experiments. . . . 227 101 Reproducibility of second stack experiments. . . . 228 102 Overvoltage-current curves of the electro- d i a l y s i s stages 232 103 Time-space d i s t r i b u t i o n of current at l i m i t i n g conditions 236 104 Time-space d i s t r i b u t i o n of probe voltage at l i m i t i n g conditions 237 105 Influence of phase s h i f t (y) on transients for constant rate operation 240 106 Effect of end mixing on concentration transients 242 107 Concentration transients of top and bottom reservoir concentrations during production run #3 compared to batch run #26 (low concentration) 245 108 Concentration transients of top and bottom reservoir concentrations during production run #5 compared to batch run #6 (high concentration) 246 109 Derivation of the spacer model equations 253 110 Effect of width r a t i o (6) on separation factor transients predicted by Spacer Model . . . . . . . 275 xx i Fi gure Page 111 Comparison of computer simulation with experimental results on runs #22,23,24 ( f i rst stack) 276 112 Comparison of computer simulation with experimental run #36 ( f i r s t stack) 277 x x i i ACKNOWLEDGEMENT I wish to thank Dr. D.W. Thompson, under whose direction this work was conducted, for his helpful guidance and encouragement throughout this i n v e s t i g a t i o n . I also wish to thank the faculty and s t a f f of the Chemical Engineering Department of the University of B r i t i s h Columbi a. I am indebted to the University of B r i t i s h Columbia, the National Research Council, and Environment Canada for fi n a n c i a l support. I would l i k e to express my gratitude to my wife Jacqueline for her continual support and forebearance throughout these years. x x i i i Chapter 1 INTRODUCTION AND SCOPE E l e c t r o d i a l y s i s has achieved only p a r t i a l success in brackish water demineralization despite many theoretical advantages i t offers over other desalting processes. The problem areas in e l e c t r o d i a l y s i s practise are fouling and scale formation on the membranes and the rather complex design of the multicompartment e l e c t r o d i a l y s i s c e l l . Periodic current interruptions and/or reversals have been employed in standard e l e c t r o d i a l y s i s stacks to reduce p o l a r i z a t i o n effects and deposition of particulates on the membranes. Lacey (1965) invented an electrosorption stack of much simpler construction than conventional e l e c t r o - d i a l y s i s stacks. In this apparatus s a l t is absorbed by, or desorbed from, the stack depending on the d i r e c t i o n of the e l e c t r i c current. The process resembles packed bed adsorption/ desorption or ion exchange systems. Wilhelm et al. (1966) investigated a temperature cycled adsorption-desorption process in which the di r e c t i o n of the f l u i d flow was reversed synchronously with the temperature 1 2 switching. This process, known as parametric pumping, has recently attracted a great deal of attention because very large separations were experimentally obtained for one system. The concept of this work is to combine c y c l i c e lectro- sorption-desorption with the flow reversal employed in the temperature cycled parametric pump. The purpose of this study is to analyze the potential of a c y c l i c e l e c t r o d i a l y s i s process for large separations, to develop suitable modules for experimental t e s t s , and to investigate systematically the e f f e c t of process variables on the performance of . closed systems. The material of this thesis has been arranged in three main parts: The s e c o n d c h a p t e r r e v i e w s t h e p r i n c i p l e s w h i c h a r e c o m b i n e d i n t h e 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 , and t h e t h i r d c h a p t e r p r e s e n t s some b a s i c c o n s i d e r a t i o n s o f t h e c o n t r o l l i n g s t e p s and c o n t r a s t s t h e s t a n d a r d c y c l i c p r o c e s s ( p a r a m e t r i c pump- i n g ) w i t h a new c y c l i c o p e r a t i o n ( p u r e p a u s e m o d e ) . In t h e . f o u r t h c h a p t e r d e t a i l s o f t h e l a b o r a t o r y a p p a r a t u s a r e g i v e n , and t h e f i f t h c h a p t e r p r e s e n t s and d i s c u s s e s e x p e r i m e n t a l r e s u l t s . 3 A m a t h e m a t i c a l model o f t h e s t a n d a r d c y c l i c o p e r a t i o n o f t h e e l e c t r o d i a l y s i s s t a c k s i s d e v e l o p e d i n t h e s i x t h c h a p t e r , w h i c h a l s o i n c l u d e s a n u m e r i c a l s o l u t i o n o f t h e model e q u a t i o n s , and c o m p a r e s c o m p u t e r s i m u l a t i o n s w i t h e x p e r i m e n t a l r e s u l t s . Conclus i ons results of this work, and are recommendati ons , contained in the based on the seventh chapter. Chapter 2 PROCESS PRINCIPLES This section reviews the basic process p r i n c i p l e s which are combined in the c y c l i c e l e c t r o d i a l y s i s process. 2.1 Electrodi a l y s i s E l e c t r o d i a l y s i s is a unit operation for separations in an ionic s o l u t i o n . Along with other membrane processes e l e c t r o d i a l y s i s belongs to the class of "selective transport methods" (Shaffer and Mintz, 1966). Since e l e c t r o d i a l y s i s gained commercial status some f i f t e e n years ago, a large number of publications have appeared on fundamental aspects, membrane phenomena, potential a p p l i - c a tions, process technology, and process economics. Wilson's monograph (1960) is 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 are included in books dealing with desalination processes, e.g. Spiegler (1962,1966), Sporn (1966), Popkin (1968); or with membrane processes, e.g. Rickles (1967), Lacey (1972). 4 5 In this work the term e l e c t r o d i a l y s i s is used in the conventional sense, i . e . related to solute-solvent separa- t i o n s , although i t is not r e s t r i c t e d to such processes as discussed below. 2.1.1 Origin of separation. Consider the system in Figure 1 in which an elec- t r o l y t i c c e l l is divided into two compartments by an ion- selective membrane. Anode and cathode are connected to a power source (not shown in Figure 1) which maintains a constant e l e c t r i c potential difference between the electrodes. Suppose the applied potential difference (or voltage) is large enough so that current flows through the c e l l , which is f i l l e d with e l e c t r o l y t e solution of a simple s a l t such as sodium chloride (NaCl). The current is transported by anions and cations according to th e i r transport numbers. The sum of these tran- sport numbers is unity in the solution and in the membrane, v +  + v_ = v +  + v_ = 1 (1) solution membrane but the transport numbers of the ionic species is not neces- s a r i l y equal in the two phases. Membrane F i g u r e I. The e l e c t r o d i a l y s i s p r i n c i p l e 7 If v_ > v_ the membrane is said to be anion s e l e c t i v e . This means that the number of anions which carry current is larger in the membrane than in the s o l u t i o n . The number of moles of anions (n_) which are selec- t i v e l y transferred through an anionic membrane by e l e c t r o l y s i s is proportional to the number of Coulombs and the difference in transport numbers (v_ - v _ ) . The number of Coulombs is given by the time integral of the current (I) l tl I(t)dt "'o Thus V - v f 1 1 n_ = ~  F  ' I(t) d t , (2) 0 where z_ is the valence of the anions, and F is Faraday's constant. Because of the condition of e l e c t r o n e u t r a l i t y , the number of moles of cations (n + ) which are rejected by the membrane is id e n t i c a l for equivalent ions ( z _ = z +  = z ) . The molar concentration change (Ac) of the solution with volume (V) is given as 8 I ( t ) d t (3 o The two solution-membrane interfaces experience concentration changes which are of id e n t i c a l magnitude but of opposite si g n . The side facing the cathode is depleted and the side facing the anode is enriched. Enrichment and depletion are inverted at a cation s e l e c t i v e membrane, which is characterized by the inequality v +  > v +  . The concentration changes are carried into the membrane and solution bodies by d i f f u s i o n a l and/or convective mass transport. Demineralized solvent (dialysate) and enriched solution (brine) may, therefore, be withdrawn from opposite sides of the membrane. The separation of solute and solvent o r i g i n a t e s , therefore, from a difference in transport number of ionic species in membrane and s o l u t i o n . This difference is ca l l e d s e l e c t i v i t y , and is the subject of the following s e c t i o n . 2.1.2 Membrane s e l e c t i v i t y . Commercially available membranes are almost exclu- s i v e l y of the resinous ion-exchange type. The s e l e c t i v i t y is v - v Ac =  -TTT 9 achieved by incorporating a large number of fixed ionic groups * in a matrix of inert material. The presence of a high concentration of fixed ionic groups has an exclusion e f f e c t on ions with the same sign as these groups. According to the Gibbs-Donnan p r i n c i p l e , equilibrium between solution and membrane phase means equality of the chemical potentials of the solute. For a f u l l y ionized s a l t and neglecting osmotic pressure terms, one has a + a _ _ a + a +  • a_ = a +  • a_ (4) where the a's denote ion a c t i v i t i e s and the a's stoichiometric c o e f f i ci ents. In s i m p l i f i e d form, when a c t i v i t i e s are replaced by concentrations and assuming equivalent ions equation (4) reduces to c +  • c = c +  • c (5) * An excellent summary of preparative methods found in the patent l i t e r a t u r e is given by Placek (1970). 10 In an anion sele c t i v e membrane in which anionic groups of concentration X are present, the electroneutra1ity condition has the form c = X + c, (6) The ionic concentrations in the solution are id e n t i c a l to the solute concentration (c) because of the assumption of equivalent anions and cations: c = c +  = c (7) Combining ( 5 ) , (6) and (7) one finds c +  • (X + c + ) = c : (8) Dividing both sides by the fixed ion concentration y i e l d s equation (9) 1 + + T (9) which may be approximated for d i l u t e solutions ( c +  << X) by (io) Equation (10) shows that the cation concentration in an anion sele c t i v e membrane varies as the square of the 11 solution concentration and may be kept very small by increas- ing the number of fixed ionic groups (X) in the membrane. The contribution of cations to the current flow is accordingly small, since the flux of cations ( j + ) along an e l e c t r i c potential gradient (grad(O)) is ->• j +  = - u +  • c +  • z +  • grad($) (11) where u~ +  is the mobility of the cations in the membrane. It must be kept in mind that equation (11) is written as the isolated ion flux due to a potential gradient. The presence of concentration and pressure gradients as well as the migration of other species results in very complicated actual dependences. It is beyond the scope of this work to account for the various treatments of these aspects. Guides to the published l i t e r a t u r e may be found in Wilson's (1960) or in He l f f e r i c h ' s (1962) books. Also, most of the results reported are limited to steady-state conditions and i t is d i f f i c u l t or impossible to project those results to unsteady-state situations which dominate the present process. The s e l e c t i v i t y of the membranes is often charac- terized by a quantity called permselectivity (P) which is defined (Wilson, 1960), as 12 v - v P = ~ (12) 1 - v  + where positive subscripts refer to cation s e l e c t i v e membranes and negative signs to anion s e l e c t i v e ones. The permselectivity therefore expresses the increase in transport number over the value in free solution as a fraction of the maximum possible increase 3  i.e. the increase that would be observed in the case of an ideally selective membrane (Wilson, 1960). 2.1.3 Transport processes through ion-selective membranes. The various transport processes which occur simul- taneously through ion-selective membranes are b r i e f l y catalogued in this s e c t i o n . Figure 2 i l l u s t r a t e s these processes for an anion s e l e c t i v e membrane during e l e c t r o d i - a l y t i c separation. It also shows the l a t e r a l concentration profi1e. a) G e g e n - i o n t r a n s p o r t : The membrane exhibits a preference for some ions (gegen-ions) and discriminates against others (co-ions). Ideally the total current is carried by gegen-ions alone. b) C o - i o n t r a n s p o r t : Any co-ion p a r t i c i p a t i o n in the current flow uses energy but yields no separation. Membrane 13 Co-ion Transport Solute Diffusion 1- I Electric Field *~ f Gegen-ion Transport Osmosis + Electro- osmosis Distance F i g u r e 2. T r a n s p o r t p r o c e s s e s a c r o s s an a n i o n - s e l e c t i v e membrane. Brine - F T O i a l y s a t e Rinse \ \ \ \ \ \ \ \ \ \ \ \ Cathode Rinse Feed F i g u r e 3. M u l t l c e l l e l e c t r o d i a l y s i s s t a c k ( s c h e m a t i c ) . 14 c) So I u t e d i f f u s i o n : A concentration gradient develops inside the membrane as a result of the concentration changes. Solute diffuses back along this gradient. d) S o l v e n t t r a n s f e r due t o i o n s o l v a t i o n usually dilutes the enriched i n t e r f a c e , but this depends upon the e f f e c t i v e number of solvent molecules attached to each ionic species and the actual degree of s e l e c t i v i t y of the membrane. e) E I e c t r o - o s m o s i s : Solvent in the membrane experiences f r i c t i o n a l forces imparted by the moving ions. f ) Osmos i s : The difference in solvent a c t i v i t i e s in the adjoining solutions forces solvent through the mem- brane. Osmotic effects reduce the extent of separation. Wilson (1960) presented a detailed discussion of these effects and Schlbgel (1964) wrote an excellent monograph on membrane transport phenomena in general ( i . e . not r e s t r i c t e d to ion-selective membranes). 2.1.4 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 i t s a p p l i c a t i o n s . The m u l t i c e l l e l e c t r o d i a l y z e r which is presently used was proposed by Meyer and Strauss (1940). Figure 3 is a _ In this discussion the electrode reactions have been disregarded because they provide merely a link between el e c t r o n i c and e l e c t r o l y t i c current transport in e l e c t r o d i a l y s i s systems. The energy requirements to maintain the electrode reactions are only a small f r a c t i o n of the total 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 arrangement. A number of p a r a l l e l channels (1 ,2,3,••• ,n) is formed by an array of interleaved cation (c) and anion (a) se l e c t i v e membranes. This stack is placed between f l a t electrodes. Feed solution flows up- ward through the stack, becomes depleted in one set of channels (1 ,3 ,5 , ••• ,Figure 3), and enriched in another set ( 2 , 4 , 6 , » « « , Figure 3). Dialysate and brine have to be collected and drawn off separately. Electrode reaction products are removed by independent rinse streams (Figure 3). It is not essential to have both anion and cation sele c t i v e membranes in the stack. In the transport depletion process n e u t r a l , or non- s e l e c t i v e , membranes replace the anionic ones in the stack, see e.g. Kollsman (1959), Lacey (1962), Lang et aZ.(1968), Huffman (1969). Only one kind of selec t i v e membranes form the stack of the electrodecantation process. Feed is introduced at an intermediate location to the flow channels. Separation is achieved by density induced convection, see F r i l e t t e (1957), Kollsman (1958), Bier (1959), Friedlander and Rickles (1965). E l e c t r o d i a l y s i s is conventionally applied to separate solutes from solvent. The membranes discriminate also between ions of d i f f e r e n t charge and size but of the same sign. Based on this membrane property, p u r i f i c a t i o n processes have 16 been proposed for mixed e l e c t r o l y t e solutions by Dewey and G i l l 11 and ( 1956), and several others (Wilson, 1960). On a commercial scale,table s a l t is produced from sea water in Japan by a process in which monovalent ions (above a l l NaCl) are s e l e c t i v e l y extracted and concentrated by e l e c t r o d i a l y s i s (Tsunoda, 1965; Yamane, 1969). Exchange reactions in the e l e c t r o l y t i c state is another f i e l d of application (Wilson, 1960: Cohan, 1965). E l e c t r o d i a l y s i s competes with other membrane pro- cesses and conventional separation techniques in water d e s a l i - nation and po l l u t i o n c o n t r o l . It is a t t r a c t i v e whenever problems with minor impurities (less than 10,000 ppm) arise (Friedlander, 1966). 2.1.5 Concentration p o l a r i z a t i o n and other problems in steady-state e l e c t r o d i a l y s i s . The difference in transport numbers between membranes and solution causes local depletion and enrichment of solute at the i n t e r f a c e s , and l a t e r a l concentration gradients develop in the v i c i n i t y of the membranes. S t i r r i n g of the bulk solution may l i m i t these concentration gradients to d i f f u s i o n controlled layers. If the concept of a Nernst layer is adopted,the steady-state condition for the solute flux at an 17 anion s e l e c t i v e membrane corresponds to ^ ^ - i r r  1  -JK -  c °> =f ( c « -  c ;>  ( 1 3 » see Figure 4 and compare with equation (3) where i current density [ampere/cm 2 ] D d i f f u s i o n c o e f f i c i e n t [cm 2 /sec] 6 Nernst f i l m thickness [cm] Co bulk concentration [g-moles/1itre] c',c" solution concentrations at the membrane surface [g-moles/1itre] If the layer thickness is controlled by the flow conditions alone, a l i m i t i n g case exists when c^ becomes zero. The corresponding l i m i t i n g current density ^ ^ n m is Wltm-. " , • C° ( 1 4 ) In aqueous solutions, no true l i m i t exists because hydroxyl or hydrogen ions w i l l take part in the ionic transfer at very low concentrations of solu t e . This is usually referred to as water s p l i t t i n g . Effects of concentration p o l a r i z a t i o n of the mem- branes on the e l e c t r o d i a l y s i s process are always undesirable: 18 F i g u r e 4. C o n c e n t r a t i o n p o l a r i z a t i o n o f an i o n - s e l e c t i v e membrane. F i g u r e 5. T h e r m a l p a r a m e t r i c p u m p i n g . 19 a) The mass t r a n s f e r r a t e s a re l i m i t e d . T h i s r e q u i r e s l a r g e r membrane a r e a s . b) If t he c u r r e n t d e n s i t y i s c l o s e t o t he l i m i t i n g o n e , w a t e r s p l i t t i n g reduces t he c u r r e n t e f f i c i e n c y and p o s - s i b l y t he pH of t h e p r o d u c t . c) The s t a c k r e s i s t a n c e i s i n c r e a s e d . d) The Donnan p o t e n t i a I , (He I f f e r i c h , 1962) i s i n c r e a s e d and the e f f e c t i v e s t a c k v o l t a g e i s t h e r e f o r e + r e d u c e d . The early work on this phenomenon was summarized by Wilson (1960). The more recent l i t e r a t u r e may be divided in the following three classes: 1. Fundamenta l a s p e c t s of t he 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 phenomena, Cook ( 1 9 6 1 , 1 9 6 5 ) ; M a n d e r s l o o t ( 1 9 6 5 ) ; S p i e g l e r ( 1 9 7 1 ) ; 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 t he 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 based upon s o l u t i o n s of t he f l ow f i e l d i n the c h a n n e l s , B e l f o r t ( 1 9 6 8 ) ; S o n i n ( 1 9 6 8 ) ; 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 of the hyd rodynamic 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 horizontal concentration p r o f i l e s across the f i l m s . See equation (24), page 53 for 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 c o r r e l a t i o n s t o c h a r a c t e r i z e i n d i v i d u a l s t a c k p e r f o r m a n c e s , e.g. Rosenberg ( 1 9 5 7 ) ; Cowan (1959); Weiner ( 1 9 6 4 ) ; M a n d e r s l o o t (1965); K i t a m o t o (1970,1971); Sata ( 1 9 6 9 ) ; Yamane ( I 969a ) . Concentration polarization is often linked with other problems in actual e l e c t r o d i a l y s i s p r a c t i s e . S c a l e f o r m a t i o n . Supersaturation and local pH changes may cause some components of the feed water to p r e c i p i t a t e at the membrane surface. In p a r t i c u l a r Calcium and Magnesium Bicarbonates and Sulphatesmay form deposits in the concentrate channels of the stack (Matz, 1965). F o u l i n g is caused by suspended solids present in many waters. These p a r t i c l e s deposit and accumulate on the membrane surface, thus increasing the stack resistance. Korngold (1970) pre- sented a comprehensive experimental study of the fouling behaviour of ten commercial anion sele c t i v e membranes. It has been observed that fouling is apparently r e s t r i c t e d to anionic membranes, mainly because p r e c i p i t a t i o n of organic matter occurs often under a c i d i c conditions (Kressman, 1969; Cook, 1965; S o l t , 1965). Po i son i ng is defined as a reaction of ionic species with the fixed ionic groups of the membrane matrix. There seems to be 21 a close r e l a t i o n to the fouling mechanism and i t is experi- mentally d i f f i c u l t to distinguish between both. Kobus (1972) reported cases of soap poisoning in which anionic membranes eventually became cation s e l e c t i v e after complete poisoning. These membranes did not only lose t h e i r s e l e c t i v e properties but also showed an increase in r e s i s t i v i t y . Other problems in p r a c t i c a l ED operation may be summarized as follows (Matz, 1965; Wilson, 1960; Furukawa, 1968; Tsunoda, 1965; C a l v i t , 1965): ( i ) E l e c t r i c a l l eakage t h r o u g h m a n i f o l d d i s t r i b u t o r s . ( i i ) H y d r a u l i c and e l e c t r i c a l l eakage due t o g a s k e t t i n g d i f f i c u l t i e s . ( i i i ) I r r e g u l a r f l ow 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 of s t a g n a t i o n in i n d i v i d u a l c h a n n e l s . ( i v ) 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 of sealant as w e l l as of the 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 related to the complicated construction of conventional e l e c t r o d i a l y s i s equipment. 2.1.6 Current reversal techniques. Current reversal has been proposed as a measure to reduce scale formation, fouling and poisoning and is employed in two forms (Matz, 1965). 22 Reve rsed p o l a r i t y . At periodic i n t e r v a l s . ( u s u a l l y several hours) the electrode p o l a r i t y is reversed, either for a short time during which the effluents are usually discarded, or in a regular cycle with continuous production. The l a t t e r operating method requires interchange piping for brine and di a l y s a t e . Matz states that many plants are p a r t i a l l y success- ful in extending the periods between dismantling of the stacks when operated in this mode. P u l s e d c u r r e n t . The usual current direction is p e r i o d i c a l l y interrupted by short current pulses with inverted p o l a r i t y . The cycle periods are in the order of several seconds, with counterpulses l a s t i n g fractions of a second only (Matz, 1962). The basic idea of this technique is to frequently disturb the concentration l a y e r s , since i t has been found that scale forming precipitates as well as fouling c o l l o i d s require some induction period before permanent deposition occurs (Spiegler, 1961; Korngold, 1970). Tests of this method in Webster, South Dakota, showed some success in scale reduction at the price of a moderate reduction in current e f f i c i e n c y ( C a l v i t , 1965). E l e c t r o s o r p t i o n - d e s o r p t i o n . Lacey (1965,1968) conceived and investigated a process which is based on the reversed p o l a r i t y technique. The standard e l e c t r o d i a l y s i s stack was converted 23 into an absorption stack, which contained only one set of flow channels. The channels were separated by three-layer sheets which consisted of an anion and a cation s e l e c t i v e membrane and a non-selective inner layer or core. These composite sheets were sealed along the four edges. They served as temporary storage compartments for solute during one p o l a r i t y of the applied e l e c t r i c p o t e n t i a l . Feed s o l u t i o n , which flowed continuously through the channels, became demineralized and was drawn off as dialysate product for the duration of this absorption part of the c y c l i c operati on. The p o l a r i t y was reversed before the compartments reached a state of sa t u r a t i o n , i . e . before th e i r storage capacity was f i l l e d . Subsequent regeneration of the membrane compartments enriched the feed s o l u t i o n , and the result i n g brine e f f l u x was usually rejected. Cycle times ranged between 15 minutes and one hour. This stack modification has some int e r e s t i n g consequences: F i r s t , the process is no longer continuous in nature but resembles more a fixed bed adsorption system operating with an electrochemical potential driving f orce. Dialysate and brine are produced successively in a single set of channels instead of simultaneously in adjacent channels as in a conventional m u l t i c e l l e l e c t r o d i a l y z e r . 24 Second, the stack is much simpler in design. It has less leakprone d i s t r i b u t i o n manifolds, a smaller number of channels, and improved membrane u t i l i z a t i o n factors since the membranes are not used to separate brine and dialysate and may therefore be as small as the active i n t e r i o r of the stack. T h i r d , the regeneration step usually requires - additional energy, the cost of which must be balanced against savings resulting from the s i m p l i f i e d c e l l design. 2.2 Parametric Pumping, Heatless Adsorption and Similar Cyclic Separation Processes The term parametric pumping was introduced by Wilhelm (1966) for a temperature cycled adsorption-desorption process with reversing flow d i r e c t i o n . Skarstrom (1959) had used a simi l a r process, before, to dry a i r in a pressure cycled operation which Alexis (1967) called heatless adsorption and employed to upgrade hydrogen. Wilhelm and his co-workers investigated temperature cycled adsorption of li q u i d s both t h e o r e t i c a l l y and experimentally: Wilhelm and Sweed (1968), Wilhelm et al. (1968), Sweed and Wilhelm (1969), Rolke and Wilhelm (1969). This system has also been studied by Wakao et al. (1968), Pigford et al. (1969), Aris (1969), Horn and Lin (1969), Harris (1970), Baker III (1970), Gregory and 25 Sweed (1970), Rhee and Amundson (1970), Sweed and Gregory (1971) , Chen and H i l l (1971), Chen et al. (1972), Butts et al. (1972) . Temperature cycled gas adsorption has been i n v e s t i - gated by Jenczewski and Myers (1968,1971) and Patrick et al. (1972). Sabadell and Sweed (1970) showed the a p p l i c a b i l i t y of the parametric pumping p r i n c i p l e to pH cycled packed bed adsorption. Heatless adsorption was revived by Eluard (1970), Batta (1971), and Shendelman and Mitchell (1972). Although Sweed (1971) presented an excellent review on parametric pumping up to the year 1970 i n c l u s i v e , the basic concept and Pigford et al.'s (1969) equilibrium model are b r i e f l y introduced in the next s e c t i o n . Heatlass adsorp- tion and some other c y c l i c separation processes are subse- quently related to parametric pumping. 2.2.1 Parametric pumping. Consider the closed system in Figure 5. It consists of a jacketed tubular column and two end r e s e r v o i r s . The column is packed with a bed of adsorbent, the temperature of which is controlled by the temperature of the jacket f l u i d . The mixture to be separated is contained in the bottom reservoir No. 2 and in the void spaces of the column. The system is a closed one, i . e . there is neither feed of fresh solution nor removal of products. This s i t u a t i o n is 26 analoguous to the f a m i l i a r t o t a l reflux operation of a d i s t i l - l a t i o n column, and i t w i l l , therefore, be referred to as to t a l reflux mode. Most workers describe a parapump cycle of the t o t a l reflux system, shown in Figure 5 , as a sequence of these steps: ( i ) D i s p l a c e upward through a heated bed. ( i i ) D i s p l a c e downward through a c o o l e d bed. I n i t i a l l y the bed i s usually hot, the concentration is uniform, and solution and adsorbent are everywhere in equilibrium. If the coupled cycling of bed temperature and f l u i d displacement is carried out,the average concentration of the effluents from top and bottom reservoirs w i l l change as function of the number of cycles (transients). During the f i r s t upward displacement,the concentra- tions remain at t h e i r i n i t i a l equilibrium values. After this displacement is complete, the temperature is lowered and the flow moves downward. Solute redistributes between the phases and solution which is depleted in adsorbate emerges from the bottom end of the column. The second cycle begins by reversing the flow direc- tionand r a i s i n g the temperature to the i n i t i a l l e v e l . I f conditions are properly chosen,the top effluent w i l l be en- riched in adsorbate, and the bottom effluent w i l l be even further depleted during this second cycle. 27 Very large concentration differences between top and bottom effluents have been experimentally achieved for repetetive cycling by Wilhelm (1968a) for a toluene-heptane- s i l i c a gel system. The separation factor (ns) which has been defined as the r a t i o of the average effluent concentrations, top compared to bottom, increased beyond 10 s  in this system. Favourable conditions for temperature cycled para- metric pumping of l i q u i d s in packed bed adsorption columns are: 1 . La rge t e m p e r a t u r e changes and t e m p e r a t u r e s e n s i t i v e a d s o r p t i o n i s o t h e r m s . 2. P a c k i n g w i t h l a r g e a d s o r p t i o n c a p a c i t y . 3. No b r e a k t h r o u g h of c o n c e n t r a t i o n f r o n t s . 4 . E q u i l i b r i u m between s o l u t i o n and a d s o r b e n t . 5. La rge hea t t r a n s f e r c o e f f i c i e n t s . 6. M i n i m a l a x i a l d i s p e r s i o n . 7 . Synch ronous s w i t c h i n g of bed t e m p e r a t u r e and f l u i d d i s p l a c e m e n t . Pigford et al. (1969a) developed a simple model which must be regarded as l i m i t i n g case for parametric pumping separations. This "equilibrium model" has the advantage that i t describes the concentration transients in closed mathematical form. It has, therefore, been used extensively to simulate batch, semicontinuous and continuous systems (Gregory, 1970; Chen, 1970,1972; Butts, 1972; Shendelman, 1972). However, Gregory (1970) showed that this model is usually inadequate to describe experimental results q u a n t i t a t i v e l y . 28 The following assumptions characterize the e q u i l i b - rium theory: (a) i n s t a n t a n e o u s i n t e r p h a s e 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) l i n e a r e q u i l i b r i u m i s o t h e r m s , ( c ) no a x i a l d i s p e r s i o n , (d) i n s t a n t a n e o u s t e m p e r a t u r e c h a n g e s . Upon close inspection of these assumptions, one sees that they account for conditions 4, 5, and 6 above. The remaining conditions may be externally set by the experimenter. For square wave displacement of one void volume combined with a synchronous temperature square wave, the mass conservation equation (for a s l i c e of thickness dz) dc£ 8 c r /-. \ 3 c „ I  +  f  +  (1 -e) . s dz 3t e 9t = 0 (15) where v constant i n t e r s t i t i a l v e l o c i t y [cm/sec] Cp f l u i d concentration c„ s o l i d concentration s z direction of flow t time e f r a c t i o n a l void volume of the packing [g-moles solute/ cm 3  solution] [g-moles solute/ cm 3  s o l i d ] [cm] [sec] 29 becomes 9c f 9c f Here c s  = M • c f  (17) and M = l i n e a r equilibrium constant m = — M The hyperbolic d i f f e r e n t i a l equation (16) may be solved by the method of c h a r a c t e r i s t i c s for each half cycle (Acrivos, 1956). The c h a r a c t e r i s t i c s in the (z,t) plane are straight l i n e s . Since c f  remains constant along any characteri s t i c, ^ = T - T — (18) dt 1 + m The movement of concentration waves in the bed may be displayed g r a p h i c a l l y . The analytical solutions are thus based on keeping track of concentration bands as they travel through the bed. Figure 6 is a hypothetical example of a closed system. The bed length is shown as ordinate against the number of c y c l e s . The lines have slopes F i g u r e 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 t h e o r y of p a r a m e t r i c pumping. o 31 f i rst half cycles , second half c y c l e s . Since  m H 0 T  < m c o L D '  t h e n e t m o t l ' o n  °f the bands is upward. The top or bottom effluen t concentration is a mixture of bands which originate in known concentrations of preceding cycles. A band which travels from bottom to top emerges with the same concentration i t had when i t entered. After an i n i t i a l start-up period the bands no longer depend on the i n i t i a l concentration. Aris (1969) has shown that a pair of difference equations always e x i s t s , which completely describe average top and bottom product concentrations as functions of the number of cyc l e s . Gregory (1970) extended the analysis to allow for dead volumes in the top and bottom reservoirs and displacements of less than one void volume. The common result of these analy t i c a l solutions is the prediction that the concentration at the bottom of the column tends to that of pure solvent as the number of cycles increases. Figure 7 is a plot of the normalized top and bottom concentration transients according to Pigford et al. 's equations for m = 0.227 and m _ = 0.5. and T T i  d u r i n 9 HOT ~ v  — during 1 + m COLD 32 F i g u r e 7 . 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 t h e o r y of 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 dispersive effects and f i n i t e mass and heat transfer rates l i m i t the separation, as also may non- li n e a r equilibrium isotherms (Rhee and Amundson, 1970). Wilhelm and his co-workers developed models which take some or a l l of those non-idealities into account (Wilhelm, 1966; Wilhelm and Sweed, 1968; Wilhelm et al. , 1968; Sweed and Wilhelm, 1969; Rolke and Wilhelm, 1969; Sweed and Gregory, 1971). Their numerical solutions agreed quite well with experimental r e s u l t s . 2.2.2 Other c y c l i c operations. Heatless adsorption, the or i g i n a l c y c l i c adsorption system, works on the pressure dependence of the gas adsorption equilibrium. The system is much more a t t r a c t i v e from a pra c t i c a l point of view because pressure changes may be i n i t i a t e d almost instan t l y compared to the slow heating and cooling in thermally forced systems. Skarstrom's (1959) double column arrangement is i l l u s t r a t e d in Figure 8. When column A adsorbs under high pressure, column B is 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 volumetric purge flow rate exceeds the feed flow r a t e . Shendelman (1972) obtained s i m i l a r results for a system 34 C0 2  in He, as did Alexis (1967) with the system H 2  in hydro- carbons, and Batta (1971) with O2 in a i r . Dry A i r Valve I _ T T Va lve 2 1—t=*<J 1 > < — , P u r g e Val ve Wet Air 4 4 Way Va lve Wet A i r F i g u r e 8 : H e a t l e s s a d s o r p t i o n a i r d r y i n g s y s t e m , used by S k a r s t r o m ( 1 9 5 9 ) . Heatless adsorption must be considered a one-cycle operation which resembles more a conventional chromatographic separation or a fixed bed ion exchange than a parametric pump. The regeneration step for each column is a counter 35 current backwashing with a purge stream from the other column's product. This is the only reflux in the system. Cyclic zone adsorption — Cyc l i c zone adsorption was devised by Pigford et al. (1969b). The system, which is shown in Figure 9, consists of two temperature cycled adsorp- tion columns. The temperature cycles of the columns are one- half cycle out of phase, i . e . one adsorbs (cold) while the other one desorbs (hot) and vice versa. A four-way valve is switched synchronously with the temperature of the beds. Pur i f ied Feed F i g u r e 9 . C y c l i c zone a d s o r p t i o n ( p r o p o s e d by P i g f o r d , I 9 6 9 b ) . 36 Obviously, the twin columns may be considered as two independent separators which have been synchronized in such a way as to achieve 'continuous production of two streams of d i f f e r e n t concentrations, one higher and one lower than that of the feed' ( P i g f o r d , et al. 3  1969b). There is no reflux between the columns, which are regenerated using feed solution in co-current flow. Electrosorption-desorpt-Con (Lacey, 1965 ,1968) — The e1ectrosorption process, described in Section 2.1.6, i s also a one-cycle separation process without r e f l u x . It is analoguous to a single column c y c l i c zone adsorber, which alternately produces enriched and depleted s o l u t i o n . Chapter 3 EFFECT OF FINITE MASS TRANSFER RATES ON PARAMETRIC PUMPING AND PURE PAUSE OPERATION 3.1 General The equilibrium theory of parametric pumping i l l u - strates the process p r i n c i p l e with great s i m p l i c i t y . Although the analy t i c a l solutions provided by this theory agree qu a l i - t a t i v e l y with experimental results on some adsorption separa- tion systems, the equations are not suitable for designing real systems (Gregory and Sweed, 1970). In p a r t i c u l a r the equilibrium theory neglects a l l rate processes. Rolke and Wilhelm (1969) attributed the small separations obtained on a NaCl/mixed ion exchange resin system for water deminerali- zation to slow rates of i n t r a p a r t i c l e mass t r a n s f e r . An e l e c t r o d i a l y s i s process may be operated with comparatively high mass transfer rates at concentrations far removed from equilibrium and may therefore be better represented by a rate model than by the equilibrium theory. Two very simple but physically reasonable rate models w i l l be investigated t h e o r e t i c a l l y . The basic assumpti 37 38 of these models is that the equilibrium condition may be neglected. In other words, i f the two phases were in stationary contact for an i n d e f i n i t e period of time, the adsorbate would be transferred completely into one of the phases. It is further assumed that axial dispersion is n e g l i g i b l e , that the f l u i d is incompressible and has constant density, that no l a t e r a l concentration gradients exist or develop, and that the f l u i d v e l o c i t y changes in a stepwise manner and remains constant during the time intervals between steps. Using the same notation as in Section 2.1, the mass balance equation for a horizontal s l i c e of thickness dz is again 3c f  dcf 3c TT + v Tz + p TT ~ 0 <'5> 1 - £ where p = = volume r a t i o . e Two simple rate laws w i l l be considered: 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 wh ich a re p r o - p o r t i o n a l t o the c o n c e n t r a t i o n in one of the p h a s e s . These rate laws are investigated for two operational modes I. C o n t i n u o u s d i s p l a c e m e n t o r p a r a m e t r i c pump ing : both 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 p o t e n t i a l ) a re c o n t i n u o u s l y " o n " a t a l l t i mes. 39 ( i ) p o t e n t i a l " o n 1 1 — upward d i s p l a c e m e n t , ( i i ) 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 . 2. E x c h a n g e - d i s p l a c e o r pure p a u s e : when one v a r i a b l e i s " o n " the 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 the s i m p l e s t p e r i o d i c form of t h i s mode, i s c o n s i d e r e d h e r e , wh ich c o n s i s t s of f o u r s t e p s . ( i ) p o t e n t i a l " o n " — no f l o w , ( i i ) p o t e n t i a l " o f f " — upward d i s p l a c e m e n t , ( i i i ) 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 — no f I o w , ( i v ) p o t e n t i a l " o f f " — downw.ard d i s p l a c e m e n t . A closed system in which one void volume is displaced w i l l be the basis of the subsequent ana l y s i s . 3.2 Constant, Uniformly Distributed Rates of Mass Transfer There are two e l e c t r o d i a l y s i s systems which would obey such rate laws. Figure 10 is a sketch of the physical arrangements. The stacks are supposed to be sorption stacks composed of perfect ion-selective membranes. In the meandering flow version (Figure 10.a) the f l u i d is introduced into one of the outer channels. The effluent from this f i r s t channel flows to the adjacent channel, etc. u n t i l i t has reached the l a s t channel in the stack. The electrodes are connected to a regulated constant current power supply. The channels should be short to eliminate 40 unequal potential d i s t r i b u t i o n s due to resistance changes in the s o l u t i o n . Out t t Flow In El. Held Flow I r T ' Out CONSTANT CURRENT OPERATION (a) MEANDERING FLOW (b) MEANDERING CURRENT F i g u r e 10: E l e c t r o d i a l y s i s sys tems w i t h 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 t r a n s f e r . The meandering current version is 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 e l e c t r i c a l l y as well as h y d r a u l i c a l l y . Again, the D.C. power supply is operated in constant current mode, and the stages should be short. 41 Both devices allow an external control of the mass transfer rates , or dc f  dc = - p  d t  = K = constant (19) Obviously equation (19) w i l l break down as one of the con- centrations approaches zero, since the applied potential must then increase beyond a l l bounds. Since the equation can predict negative concentrations i t must be used with caution. 3.2.1 Parametric pumping operation. If the rate constants are of equal magnitude but of opposite sign during the two half cycles of a parametric pumping operation, one has dt dt o d C s = - P dt -K for d i l u t i o n K for enrichment (20) The solution of this system of d i f f e r e n t i a l equations is t r i v i a l . Suppose the i n i t i a l condition is c f (t=0) = c 0  , c s (t=0) = c 0 . The effluent concentration during the f i r s t (demineralization) half cycle is 42 Cf(t) = c 0  - Kt The average product concentration C T  -j becomes T/2 r 'T , 1 T/2 c f ( t ) d t - K 'o where T = cycle period (T < 2c 0 /K , for non-negative values of c f (t)). If the p o l a r i t y of the e l e c t r i c potential and the direc t i o n of the f l u i d displacement are simultaneously switched i t is straightforward to show that the average bottom product concentration during the next part cycle is C B,1 ~  C o During the next demineralization the top product concentration is C T,2  _ C o  "  K  ' 4 which is i d e n t i c a l to c T,l Final conditions are therefore reached within the f i r s t c y c l e . Figure 11 i l l u s t r a t e s the internal and product concentration p r o f i l e s i n i t i a l l y (Figure 11.a), after the f i r s t half cycle (Figure 11.b), and after the second half cycle (Figure 11.c). 43 - v z o \-< or i-z UJ o z o o Co Co Reservoir 1 ED .stack Reservoir 2 > -f o i it -e (a) (b) F i g u r e I I : C o n c e n t r a t i o n p r o f i l e s d u r i n g 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 p r o c e s s o p e r a t e d i n p a r a m e t r i c 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 r a t e s of mass t r a n s f e r . For s i m p l i c i t y i t is assumed that the end reservoirs are packed with inert material having the same void volume as the separator. A plot of the average top and bottom product con- centration transients is shown in Figure 12. The i n i t i a l decrease in top product concentration is c l e a r l y a result of the s t a r t i n g conditions. If the more general case of unequal rate constants is considered, the resulting product concentrations are 44 O < or » - z LxJ O Z o o TIME F i g u r e 12: P r o d u c t 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 p r o c e s s o p e r a t e d in p a r a m e t r i c pumping mode under c o n d i t i o n s of equa 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 . shown in Figure 13. Here i t is assumed, that K x  applies for demineralization and K 2  for enrichment, see also equation (20). Although the concentrations show further changes after the f i r s t c y c l e , these changes cannot be con- sidered as true separation because top and bottom product transients remain p a r a l l e l . Concentrations continue to change due to r e d i s t r i b u t i o n of solute between solution and sorption 45 < z  c - K- - o z: o o K,<K2 ^ C L - 7/2 2T 3T T IME F i g u r e 13: P r o d u c t c o n c e n t r a t i o n t r a n s i e n t s e l e c t r o d i a l y s i s p r o c e s s o p e r a t e d pumping mode under c o n d i t i o n s of 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 t r a n s f e r . f o r c y c l i c i n p a r a m e t r i c uneq ua I , c o n - r a t e s of mass membranes. Obviously, the model w i l l break down i f one of the concentrations reaches zero. These physical r e s t r i c t i o n s of the model are discussed above. Up to this point standard parametric pumping seems to have no separation potential when used in a system con- t r o l l e d by a constant transfer rate. This is in contrast to 46 experimental results on a thermal parapump system which is operated close to equilibrium, see Wilhelm and Sweed (1968). It was found that maximum separation was achieved when the two control variables were switched simultaneously. The equilibrium theory substantiated this finding t h e o r e t i c a l l y , see Pigford et al. (1969a). In t h e i r work no separation occurred i f temperature and displacement were switched one quarter cycle out of phase. This behaviour is inverted when the system is con- t r o l l e d by constant transfer rates. In this case maximum separation is obtained when the e l e c t r i c p o l a r i t y is switched one quarter cycle out of phase to the flow r e v e r s a l . Figure 14 i l l u s t r a t e s the consecutive action for two cycles in steps of one-half cycle from the s t a r t . It is assumed that the rate constants are equal (Ki = K 2 ) , and that the e f f l u e n t remain unmixed in the end r e s e r v o i r s . For convenience i t i s , again, assumed that the reservoirs are packed with inert material having the same void volume as the separator. The abscissa in Figure 14 i s , therefore, divided into three sections: - £ < z < 0 for the bottom reservoir 0 < z < % for the separator % < z < 2£ for the top reservoir * This assumption does not affect the values of the average top and bottom effluent concentrations. z o cc t- z UJ o o o t=0 •4 A t = T VI -e 21 -t 3T -e e zt t=2T V F i g u re 14: Deve lopment of s t a n d i n g waves in a p a r a m e t r i c 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 , 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 i f v a r i a b l e s are s w i t c h e d 1/4 c y c l e ou t of p h a s e . 48 A symmetric standing wave of increasing amplitude is generated as a result of the periodic f o r c i n g . The average product transients (see Figure 15) are straight l i n e s . F i g u r e 15: P r o d u c t 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 p r o c e s s o p e r a t e d in p a r a m e t r i c 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 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 re 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 case of unequal rate constants and any phase s h i f t y is summarized in the following equations for the average top and bottom product transients (0 < y < j) which are derived in Appendix B . l . C j = c o - KiJ+ (K 2+ K j X i + where and Cg - Co where 2 T T 3T 5T 2 ' 2 ' 2 • • • + fK2-Ki  +  K 2 +Kx  Y 2— T t = T , 2T , 3T , o • • (21) The transients are straight l i n e s . Figure 16 is a plot for three values of y = 0» T/8, T/4, assuming K 2  > K x  . The important results of this section are summarized as 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 of 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 in 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 of the phase 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 the 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 pump ing . K , < K 2 l 1 1 1 1 1 r — 0 T/2 T 2T 3T TIME F i g u r e 16. Ave rage top and bot tom 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. F i g u r e 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. e n O 51 3. A n a l y t i c a l s o l u t i o n s f o r the ave rage p r o d u c t 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 the c y c l e t ime have been d e r i v e d . These t r a n s i e n t s a re s t r a i g h t l i n e s . 4. The b reak in the top p r o d u c t t r a n s i e n t r e f l e c t s the i n f l u e n c e of the i n i t i a l c o n c e n t r a t i o n d i s t r i b u t i o n . 3.2.2 Pure pause operation. The mass transfer rates in the model systems of Figure 10 do not depend on flow conditions, rather they are externally c o n t r o l l e d . It may, therefore, be assumed that the rate constants Ki and K 2  are equal for pure pause and parametric pumping operation, although this w i l l not be v a l i d for other systems. The solutions of the model equations (13) are very simple in this case. The transients of the product concen- trations obey the relations c T  — c o Ki £ - (K 2 +K x )| ( *41 for t T 3T 5T 2 ' 2 ' 2 ' and (22) c D  = c 0  + K 2 - (K 2 +Ki)^ t for t = T , 2T , 3T , where again the phase s h i f t is defined in the i n t e r v a l 52 0 < Y < J i . e . the switching of the potential leads the flow switching by Y • One can recognize that maximum separation is obtained by simultaneously switching the two v a r i a b l e s . In this case the product transients have twice the slope of a parametric pump with one-quarter cycle phase s h i f t (see Figure 15, and equation 21). 3.3 Concentration Dependent Rates of Mass Transfer While i t might be possible to operate a constant rate e l e c t r o d i a l y s i s process, this is not very p r a c t i c a l . In conventional e l e c t r o d i a l y s i s a constant e l e c t r i c potential is usually applied to the electrodes. The local current density ( i ) is then a function of the concentrations along the current path. For perfectly s e l e c t i v e membranes in steady state the concept of the Donnan potential may be adopted, see H e l f f e r i c h (1962). The current density ( i ) is then the r a t i o of the e f f e c t i v e stack voltage and the total resistance per unit membrane area 53 Figure 17 i l l u s t r a t e s the co-ordinate system and the l a t e r a l concentration p r o f i l e in the smallest unit of an electrosorption stack: a flow channel and an adjacent three- layer membrane, see also Section 2.1.6. The applied potential (A$) is diminished by the Donnan potential ( A $ D o n ) . A$ = 2RT Don zF in (24) at membranes The total resistance of the unit is the sum of the integral solution resistances, Rf and R s . Rf = RT 2z z F z D RT S  2z 2 F 2 D r b -7?yT dy' c,(y') (25) and the resistance of both membranes (R_) x  m Substituting (24) and (25) into (23) gives 54 2RT zF at membranes (26) RT 2z 2 F 2 D dy ra dy' c s T T J + R m The Donnan potential w i l l usually be small compared to the applied p o t e n t i a l . The current density is therefore mainly controlled by the lowest concentration in the current path. The concentration is low in the flow channels during depletion, and in the membrane core during enrichment. The rate laws subsequently assumed are based on these approxima- tions: 9t 9t + a i C f during d i l u t i o n = -a 2 c during enrichment (27) 3.3.1 Pure pause operation. The exchange-displace type of process operation is considered f i r s t , because i t may be solved a n a l y t i c a l l y . The d e t a i l s of this step-by-step c a l c u l a t i o n are referred to in Appendix B.2. 55 For one void volume displacement, without phase s h i f t , the product concentration transients are Co v '1 Co ^ = 2+p n- l pq" - qp"" (1-p) I 1=0 (28) where p = exp (- aiT/2) q = exp (- a 2 T/2) p = is as defined before . In equation (28) the bottom product concentration decreases exponentially, whereas the top product concentra- tion is limited by the overall mass balance. The separation factor (ns) is here defined as the ra t i o of bottom and top product concentrations. This separa- tion factor increases without l i m i t as the number of cycles approaches i n f i n i t y . Although the product transients are of s i m i l a r form to those for parametric pumping under equilibrium c o n t r o l , a fundamental difference e x i s t s . Equations (28) are functions of real time, whereas the equilibrium theory e s s e n t i a l l y excludes time from the mathematical s o l u t i o n . 56 3.3.2 Parametric pumping operation. If equations (27) are substituted into the mass balance (15) the resulting p a r t i a l d i f f e r e n t i a l equations may, in p r i n c i p l e , be solved for any half c y c l e , see Appendix B. 3. A numerical solution to the problem was preferred here, however, since the number of terms in the f i n i t e series solution grows geometrically with the number of c y c l e s . The numerical cal c u l a t i o n scheme was i d e n t i c a l to the STOP-GO algorithm, developed by Sweed and Wilhelm (1969). In this scheme the continuous p a r t i a l d i f f e r e n t i a l equations are approximated by a set of N ordinary d i f f e r - e n t i a l equations (ODE) which are solved N times for a d i s - placement of one void volume. A conceptual model of the algorithm and a FORTRAN IV program for computer simulations are described in Appendix B.4. I n c i d e n t a l l y , the case N=l is equivalent to a pure pause operation, and the results of computer simulations are i d e n t i c a l to numerical evaluations of equations (28). 3.3.3 Comparison of pause and parametric pumping operations. In this section the results of a number of computer simulations for three values of N(N = 1,4,50) are compared. 57 Figure 18 shows the normalized concentration tran- sients for a x  = a 2  = 0.01 [ s e c - 1 ] , T = 20 [sec] , and p = 1.0 for one void volume displacement: ( i ) N = I o r pure pause 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 . ( i i ) N = 4 r e p r e s e n t s an o p e r a t i o n wh ich c o n s i s t s of f o u r pauses and f o u r o n e - q u a r t e r d i s p l a c e m e n t s . 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 f rom 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 b reak in the top p r o d u c t t r a n s i e n t a f t e r t he f i r s t c y c l e may be r e c o g n i z e d . ( i i i ) N = 50 o r p a r a m e t r i c pumping shows ve ry l i t t l e a d d i t i o n a l s e p a r a t i o n a f t e r t he f i r s t c y c I e . NOTE: The r e s u l t s f o r N = 100 a re v i r t u a l l y i d e n t i c a l . Table 1 l i s t s normalized top and bottom concentra- tions and the corresponding separation factor after 50 cycles for various parameter values. The results may be summarized as follows: 1. B e s t s e p a r a t i o n i s a lways a c h i e v e d w i t h 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 the s e p a r a t i o n . T h i s i s e q u i v a l e n t t o i n c r e a s i n g the r a t e c o n s t a n t s a i and a 2 by equa l f a c t o r s . 3 . I f t he 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 t o l o n g e r second h a l f c y c l e ) the s e p a r a t i o n i s i m p r o v e d . 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 PURE PAUSE 4 A 50 • PARAPUMP ,05 F i g u r e 18: E f f e c t of the number of segments on the p r o d u c t 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 o n c 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 ( a i = a 2 = 0 .0 T = 20 s e c , p = 1 .0 , 6 = 1 . 0 ) . I sec" Table 1 Computer Simulat ions of Pure Pause, Parametric Pumping, and Mul t ip le Step Displacement Operations for Concentration Dependent Mass Transfer Rates SIMULATION RUN NO. RATE CONSTANTS CYCLE PERIOD VOLUME RATIO DISPLACED VOLUME NO. OF SEGMENTS NO. OF CYCLES CONCENTRATIONS SEPARATION FACTOR BOTTOM TOP [ - ] ai [sec - 1 3 a 2 [sec- 1 ] T [sec] P [-] <5 [-] N [-] nc [- ] X B [- ] X T [- 3 ns [- 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 .01 .01 .01 .01 ,02 .01 20 40 80 20 20 1 1 1 1 1 1/2 1/4 1/2 1 1 1 1 1 1 1 1/2 1/4 1 4 50 1 4 50 4 50 1 4 50 1 4 50 1 4 50 2 8 100 4 16 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 2.9 5 1 .66 1.11 3.00 1 .87 1.21 2.04 1 .38 2.99 2.01 1 .36 2.46 1 .38 .92 2.21 1 .24 .83 3.64 1 .56 .92 4.56 1.58 .0067 .450 .894 .0000 .303 .806 .207 .661 .0067 .488 1 .04 .0067 .378 .747 .0067 .342 .672 .0067 .328 .710 .0067 .328 438. 3.70 1 .24 66067. 6.17 1 .50 9.85 2.08 443. 4.11 1 .30 365. 3.66 1 .24 328. 3.63 1 .24 540. 4.77 1.29 677 . 4.83 60 4. A d e c r e a s e in 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 ) reduces top and bot tom p r o d u c t c o n c e n t r a t i o n s and may lead to a s t e a d y d e c l i n e of bot tom p r o d u c t c o n - c e n t r a t i o n in p a r a m e t r i c pumping o p e r a t i o n (N=50). 5. If l e s s than one v o i d volume i s d i s p l a c e d w i t h the same c y c l e p e r i o d the s e p a r a t i o n i s i mp rove d . N o t e t h a t 5 = i r e q u i r e s N = 2 f o r p u r e p a u s e o p e r a t i o n , 6 = £ r e q o i r e s N = k e t c . 3.4 Summary In this chapter two simple laws for the rate of mass transfer in c y c l i c separation processes have been analyzed to determine t h e i r effect on the transient response of closed systems with continuous or pulse li k e displacement. The rate laws are physically well founded for 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 conditions complementary to the local equilibrium concept. It is shown that the standard parametric pumping operation is generally very i n e f f i c i e n t for f i n i t e mass transfer rates i f the influence of an equilibrium relationship is n e g l i g i b l e . A pure pause operation overcomes much of these limitations and leads to unlimited separations. It is also demonstrated that for constant and uniformly distributed mass transfer rates, the phase re l a t i o n between the forced variables is contrary to that for the equilibrium theory of parametric pumping. The maximum 61 separation e f f e c t w i l l be obtained i f the phase s h i f t amounts to one quarter of a total c y c l e . The separation in this case i s , however, s t i l l small compared to a pure pause operation. 3.5 Comment on an Equilibrium Model with Instantaneous Displacement At this point the question may be asked, what is the e f f e c t of a pure pause operation on an equilibrium con- t r o l l e d system? Is the instantaneous solute r e d i s t r i b u t i o n at the beginning of the half cycles the true separating mechanism? Or is i t , a l s o , necessary to displace the solu- tion slowly enough that equi1ibriurn is always maintained? The derivation of the model equations is contained in Appendix B.5. The product concentrations as functions of the number of cycles are described by the following equati ons: CASE 1: The stationary phase is i n i t i a l l y unloaded or in the low equilibrium state. The f i r s t dis- placement is up without changing the equilibrium 62 _ i = 1 +  K  ~  x C n KA-1 and I I Co p - 1 n-1 A K 1 K K - A KA-1 n-1 (29) where K = 1 + mi , and A = 1 + m 2  ; mi & m 2  are defined i n Secti on 2.2.1. CASE 2: The stationary phase is i n i t i a l l y loaded. F i r s t displacement is down without changing the equi 1 i bri urn _B_ c 0 * + I - A A K A - f-Ll K A n-1 and (30) Co KA-1 1 - f 1 1 K A n-1 Figure 19 i l l u s t r a t e s the transients for K = 1.5 and A = 1.25. 63 A" 1,25 F i g u r e 19: P r o d u c t 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 ( 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 conditions are reached within a few cycles. The l i m i t i n g separation factor for both cases is f i n i t e and i d e n t i c a l : £-tm(ns) = llm _P_ = K-1  =  mx X-l m 2 (31) 64 The solute merely redistributes according to the two equilibrium states in such a manner that the adsorbent concentration asymptotically approaches a constant value. The time interval of active separation is comparatively short. In answer to the above questions one can therefore deduce that, in the standard parametric pumping operation, f i n i t e flow rates are essential for successful separation when the system is controlled by equilibrium. Another aspect of this model emerges i f a combina- tion of rate and equilibrium control is considered for a pure pause operation. Obviously the transient equations (29) or (30) constitute the maximum separation which can be obtained in such a system. For e l e c t r o d i a l y s i s , however, where the ratio mi/m 2  is usually extremely l a r g e , this l i m i t a t i o n does not arise in p r a c t i s e . Chapter 4 THE CYCLIC ELECTRODIALYSIS PROCESS - OPERATION AND APPARATUS 4.1 Description of Batch Operation Figure 20 i l l u s t r a t e s the four basic steps which constitute a single c y c l e . The e l e c t r o d i a l y s i s (ED) c e l l is shown schematically as a rectangular box with a diagonal d i v i s i o n indicating the membranes (a symbol which is found frequently for membrane separators). The composite sorption membranes are represented by a double-layer. Two reservoirs ( c i r c l e s in Figure 20) are connected to the ends of the ED c e l l . P a r t i a l shading of the c i r c l e s indicates the l i q u i d content of these reservoirs at d i f f e r e n t stages during the cycl e . The f i r s t half cycle is characterized by positive direction of the e l e c t r i c f i e l d (n) (sign convention: anode l e f t - cathode r i g h t ) . This w i l l be referred to as positive po l a r i t y of the applied potential (A<J>). The membranes are positioned in such a way that positive p o l a r i t y is equivalent 65 T, First Hnlf Cycle PG use Displacement Second Half Cycle 21 66 F i g u r e 20. B a t c h o p e r a t i o n of c y c l i c e l e c t r o d i a l y s i s p r o c e s s (a) UJ < ? o _ i Li- Tl ME (b) F i g u r e 21. 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 f l ow 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 p r o c e s s . 67 to solute uptake, i . e . the cationic membranes face the anode. The intrachannel solution becomes depleted during the entire f i r s t half cycle which consists of a "PAUSE" or no-flow interval ( T J followed by a "DISPLACEMENT" interval ( T 2 ) . The f l u i d flows with rate (Q) from the lower to the upper reservoi r . The second half cycle begins with a p o l a r i t y reversal (- n) and simultaneously the flow stops for another "PAUSE" interval ( T 3 ) . The intrachannel solution receives solute for the duration of this second half c y c l e , which is concluded by a "DISPLACEMENT" interval (x.J. Solution is thus returned from the upper to the lower reservoir with flow rate (- Q) . In this study the parameters A<j> , Q , x.. (i = 1 , 2, 3, 4) are subject to the following conditions: ( i ) The a p p l i e d p o t e n t i a l (A<|)) c h a n g e s i n a s q u a r e wave m a n n e r . A t t h e b e g i n n i n g o f e v e r y h a l f c y c l e t h e s i g n i s r e v e r s e d b u t t h e m a g n i t u d e i s r e g u l a t e d t o r e m a i n c o n s t a n t d u r i n g t h e e n t i r e o p e r a t i o n , F i g u r e 21a. ( i i ) The f l o w r a t e (Q) v a r i e s i n a p u l s e l i k e f a s h i o n . P o s i t i v e p u l s e s a l t e r n a t e w i t h n e g a t i v e o nes o f t h e same m a g n i t u d e and d u r a t i o n (x 2  = T i * ) , see F i g u r e 21b. ( i i i ) In most e x p e r i m e n t s t h e pau s e t i m e s a r e e q u a l (xi = X 3 ) and b e c a u s e o f ( i i ) t h i s means s y m m e t r i c h a l f c y c l e s . 68 ( i v ) Flow r a t e ( Q ) and d i s p l a c e m e n t t i m e s (x 2 = T i» ) are a d j u s t e d so t h a t the t o t a l volume d i s p l a c e d (Q • T 2 ) i s equa l o r l e s s than the s o l u t i o n volume i n i t i a l l y c o n t a i n e d in t he lower r e s e r v o i r . The ED c e l l rema ins c o m p l e t e l y f i l l e d w i t h s o l u t i o n , t h e r e f o r e , but the d i s p l a c e d volume and any e x c e s s vo lumes in the r e s e r v o i r s may va ry from run t o r u n . In F i g u r e 20 no e x c e s s vo lumes (or dead volumes) are shown. (v) The b a s i c c y c l e i s r e p e a t e d in the same o r d e r f o r a f i n i t e number of t i m e s . Starting conditions are always (a) u n i f o r m l y d i s t r i b u t e d c o n c e n t r a t i o n s . (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 . 4.2 The F i r s t Bench Module The experimental part of this work was performed on two ED c e l l versions, the f i r s t of which w i l l be described in this s e c t i o n . Most of the auxilary equipment was i d e n t i c a l for both modules. In order to avoid unnecessary r e p e t i t i o n s , but at the same time retain the c l a r i t y of the presentation, the equipment w i l l be shown as a block diagram. This block diagram is i d e n t i c a l for both ED c e l l versions, see Figure 22. The e l e c t r o d i a l y s i s c e l l (ED) is connected to the process l i n e , the rinse loop and the e l e c t r i c power. 0 CM F i g u r e 22. B l o c k diagram of e x p e r i m e n t a l t e s t i n g s t a t i o n . 70 The rinse loop consists of tank 12, valve V3 and pump P2. The process lin e is open-ended and terminates in the top reservoir T above ED and in the bottom reservoir B below ED. In the same line are found the conductivity c e l l s CI and C2, pump PI, and valve VI, and a branch leading through valve V2 to tank Tl which contains the stock solution (NaCl/H 2 0). The DC power input may be traced from the e l e c t r i c binding posts EP1 and EP2, through the switch box SB1 to the regulated DC r e c t i f i e r . A second e l e c t r i c c i r c u i t indicates that the flow rate and the dir e c t i o n of flow delivered by the positiv e displacement pump PI may be controlled by means of a motor c o n t r o l l e r and a switch box SB2. A timer, which is triggered by PI, i n i t i a t e s the switching of SB1 and SB2. Four signals are recorded simultaneously and con- tinuously: The solution concentrations in the conductivity c e l l s , the current input to the ED c e l l measured by shunt A, and the actual potential drop across the stack pack measured by reversible probe electrodes. The current signal was integrated during some of the experiments to determine the average current consumption. 71 4.2.1 E l e c t r o d i a l y s e r No. 1 (EDI) The primary objective of this f i r s t unit was to i d e n t i f y important parameters of the c y c l i c process and to study t h e i r effects q u a l i t a t i v e l y . Figure 23 shows an exploded view of EDI, reduced machine drawings are contained in Appendi x A.1. A constant thickness centre frame design was chosen for the following reasons: 1. S i m p l e c o n s t r u c t i o n wh ich i s easy t o m a n u f a c t u r e . 2. No l i q u i d d i s t r i b u t i o n m a n i f o l d s because f l ow i s d i s p e r s e d i n t e r n a l l y . 3. On ly two s e a l s r e q u i r e d . 4. Membrane -space r s t a c k i s a s e p a r a t e b l o c k , t he o v e r a l l s i z e of wh ich i s d e t e r m i n e d by the c e n t r e f rame o p e n - i n g . T h i c k n e s s of s o r p t i o n membranes a n d / o r s p a c e r s c r e e n s may be v a r i e d w i t h i n t h e s e l i m i t s . The centre frame is made from a 1" Perspex p l a t e . The opening in the centre is recessed at top and bottom to form two l i q u i d d i s t r i b u t i o n chambers in which d i s t r i b u t o r p l a t e s , each containing 32 x 0.032"* holes, are mounted. The process solution which flows through the centre frame is physically separated by two single membranes from the 72 End Frame Nut Cent re F r a m e S t a c k - P a c k End F r a m e G a s k e t Bo l t — i - E lec t rode S p a c e r G a s k e t Bo l t Nut : 31 E l e c t r o d e S p a c e r Membrane Membrane F i gu re 2 3 . 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 ( e x p l o d e d v i e w , s c h e m a t i c ) . 73 electrode assemblies. Each of these assemblies consists of a 1" polyethylene p l a t e , a f l a t graphite electrode, a graphite bolt with a nylon nut, a spacer screen, and a r e s i l e n t s i l i c o n rubber gasket. Two rinse ports provide i n l e t and outlet of the wash s o l u t i o n . Detail drawings of the electrode end frame (see Appendix A.l) show how the rinse stream is dis- tributed and c o l l e c t e d . Electrodes were cut from a graphite block of unknown origin and f i t t e d in the resets provided in the polyethylene plates. Some unsuccessful experimenting with brass connectors led f i n a l l y to the threaded graphite bolts shown in Figure 23. These had a conical head to provide a larger contact area with the counter-sunk electrode plates. Bolts and electrodes were sanded f l a t a f t e r assembly. Special Nylon nuts were made to tighten the b o l t s . The electrodes were permanently set into the end blocks with a bed of s i l i c o n rubber. The separating membranes were of the same kind as used in the stack (see below). The whole assembly was held together by a clamping device which consisted of two rectangular frames (manufactured from 1" square pipes) and four t i e rods (see det a i l drawing, Appendi x A.1). 74 The probe electrodes were made from 1 [£2/ft] s i l v e r wire. Four threads twisted into a single wire (10" long) were protected by a sleeve of SCOTCH tape except the ends. One end was soft soldered to a 1 x 2 [mm 2 ] s i l v e r plate (0.020" thick) and the point of contact was covered with con- tact cement. This probe was always inserted into the rinse compartment with the unprotected side of the plate facing the electrode and the covered side touching the separating membrane. The probes measured, therefore, the potential drop across the stack and the two separating membranes. The main features of the f i r s t ED c e l l are summarized in the following Table 2. 4.2.2 Membrane-spacer stacks. Three stack versions were tested in the course of this work by combining two types of spacer screens with two di f f e r e n t sorption membranes. The Sorption Membranes Resinous ion exchange membranes were purchased from Tokuyama Soda, Japan. These were commercially used membranes. The manufacturer's s p e c i f i c a t i o n s are given in Table 3. 75 Tab l e 2 E I e c t r o d i a I y s e r No. I ( E D I ) Des i gn R i g i d C e n t r e Frame S i n g l e S t a g e E 1 e c t r o d e A r e a 230 [ c m 2 ] A c t i ve Volume 630 [ c m 3 ] #x I n h e r e n t Dead Volume 40 [ c m 3 ] #** Membrane U t i l i z a t i o n 83 m R i n s e S y s t e m S i n g l e P a s s G a s k e t s One on Each E l e c t r o d e Frame Mate r i a l s C e n t r e Frame P l e x i g l a s s E l e c t r o d e Frame L.D. P.E. E l e c t r o d e G r a p h i t e Te rm i n a 1 Graph i t e G a s k e t s S i l i c o n R u b b e r * r e f e r s t o t h e s p a c e w h i c h w i l l be f i I l e d w i t h t h e membrane s p a c e r s t a c k c a l c u l a t e d f r o m t h e d i m e n s i o n s o f t h e two f l o w d i s t r i b u t i o n c h a m b e r s **# f r a c t i o n o f t o t a l membrane a r e a e x p o s e d t o c i r c u l a t i n g s o l u t i o n . 76 T a b l e 3 P r o p e r t i e s of NEOSEPTA Membranes, f rom Yamane (1969) Type CL c a t i o n 25T s e 1 e c t i ve AV4-4T a n i o n s e l e c t i v e Back i ng PVC PVC Th i c k n e s s 1 ) 0 . 1 5 - 0 . 1 7 0 .15 - 0 .17 B u r s t s t r e n g t h 2) 3 - 4 5 - 7 Ion exchange c a p a c i t y 3) 1 .8 - 2 . 0 1.5 - 2 .0 Water c o n t e n t 4) . 30 - .40 .20 - .25 E l e c t r i c r e s i s t a n c e 5) 2 .7 - 3 .2 3 .5 - 4 . 5 T r a n s p o r t number 6) > .98 > .98 1) [mm] 2) [ k g / c m 2 ! ] 3) Cmeg/gram dry membrane in N a - f o r m , o r C l - f o r m ] 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 2 0 / g r a m dry membrane in N a - f o r m , o r C I - f o r m ] 5) 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 a t 25 [ ° C ] [ft c m 2 ] 6) measured by e l e c t r o d i a l y s i s in 0 . 5 N NaCI s o l u t i o n , c u r r e n t d e n s i t y 10 [m A/cm 23 a t 25 [ ° C ] The sorption membranes, or "capacity c e l l s , " were made in two versions with a large core and with zero core. In the f i r s t case the core was 1/32" th i c k , consisting of a sturdy SPURLDITE frame, and a double layer of p l a s t i c coated 7 7 glass f i b r e screen (14/18 strands per inch, approx. 1/64" thick) f i t t e d into the central opening of the frame. An anion and a cation sel e c t i v e membrane of the same size as the frame were placed on opposite sides and sealed around the four edges with SCOTCH tape. Care had to be taken to keep the membranes always moist because they not only shrink upon drying but may develop cracks. A l s o , i t was desired to produce capacity c e l l s in 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 surfaces had been s l i g h t l y sanded. Since the strengthening fabric of the membranes is PVC, the sanding procedure probably exposed the PVC filaments. This method was not used in the experimental c e l l s since i t seemed desirable to be able to inspect the capacity c e l l i n t e r i o r and to modify the core. In the "zero" core version, the capacity c e l l s con- sisted of the two membranes and the sealing tape. Again, the a i r pockets were completely removed before s e a l i n g . The Spacers Belfort and Guter (1968) investigated the flow pattern produced by various screens, and found that multiple 78 layers of net-like fabrics showed the least tendency to develop areas of stagnation. The f i r s t spacer was made of four layers of the same glass f i b r e screen used for the f i r s t capacity c e l l core. The sketch below indicates the f o l d i n g . SPURLDITE str i p s (10" x 1/4" x 1/32") strengthened the structure along the sides. Figure 25: Glass fibre spacer screen. The second spacer material was a conventional VEXAR p l a s t i c net: L 12 (12/12 strands/inch, clear polypropylene) which was kindly supplied by DuPont DeNemours of Canada. 79 It was cut p a r a l l e l to one strand d i r e c t i o n and used as a single layer only. Thickness approx. 0.81 [mm]. The spacers are also shown in Figure 24a. The following membrane spacer stacks were combined and investigated in this work: Table 4 Stack Pack V e r s i o n s Used i n F i r s t ED C e l l S t a c k ^ ^ v . V e r s i o n P r o p e r t y ^ - v . 1 2 3 No. of u n i t s Space r mate r i a l Channe1 t h i ck- ness [cmU 8 g l a s s f i b re 0.205 15 o r 16 VEXAR® LI2 0. 127 or 0.116 12 o r 13 g l a s s f i b re 0.165 o r 0.155 Membrane m a t e r i a l NEOSEPTA CL 25T & AV4T Cap ac i t y ce 1 1 type Free f1ow vo1ume [cm 2 ] w i t h c o r e 282 no c o r e 387 o r 373 no c o r e 389 o r 370 The stacks were assembled to form packs using two PVC clamps as shown in Figure 24b. These packs f i t t e d into the centre frame opening and were inserted as one block according to Figure 24c. 80 F i g u r e 2 4 . L I e c t r o d i a I y z e r N o . I. ( a ) S p a c e r s c r e e n s and c a p a c i t y c e l l c o r e ( s c a l e : i n c h e s ) . F i g u r e 2 4. E I e c t r o d i a I y z e r No. I . (b) S t a c k - p a c k a n d r i g i d c e n t r e f r a m e ( s c a l e : i n c h e s ) . F i g u r e 2 4 . E I e c t r o d i a I y z e r No . I. ( c ) C e l l r e a d y f o r a s s e m b l i n q ( s c a l e : i n c h e s ) . 83 4.2.3 Process flow. It was planned that the volume of each displacement pulse would be of the same magnitude as the free flow volume of the e l e c t r o d i a l y s e r . Since this was r e l a t i v e l y small, a piston pump driven by a variable speed D.C. motor was f e a s i b l e . The features of this combination are: 1. P o s i t i v e d i s p l a c e m e n t . 2. Pump body and end r e s e r v o i r a re one p a r t . , 3. R e v e r s i b l e w i t h m in ima l t ime l a g . 4. S h o r t s t a r t - u p t ime ( i . e . squa re p u l s e s ) . 5. No dead v o l u m e . 6. A c c u r a t e f l ow r a t e s e t t i n g . ' 7. P i s t o n d i s p l a c e m e n t i s n a t u r a l t r i g g e r f o r t i m i n g . 8 . May be m o d i f i e d t o p roduce o t h e r than s q u a r e 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 a c c o r d i n g t o s p e c i f i c a t i o n s in w o r k s h o p . 10. R e l i a b l e because ve ry l i t t l e w e a r . The reciprocating piston acted as an infusion-with- drawal pump. The pump was manufactured according to the spe c i f i c a t i o n s given in Table 5. The cylinder of the piston pump formed the storage tank at one end of the process l i n e . The opposite end of the 84 T a b l e 5 P i s t o n Pump S p e c i f i c a t i o n s PUMP P1STON FACE AREA Ccm 2 ] MAXIMUM PISTON MOVEMENT [cm] DISPLACED VOLUME [cm 3 ] FLOW RATE [cmVsec] 22 . 88 2 7 . 5 0 to 630 2 . 5 to 75 DRI VE 1/4 hp DC MOTOR SCR MOTOR CONTROL REDUCTION GEAR RATIO PINION^and RACK BOSTON RAD 1OTROL E25 1 / 4 8 l i n e was connected to a f l o a t i n g l i d expansion tank which is shown in Figure 26. 4.2.4 Timing and switch boxes. As mentioned in the previous s e c t i o n , the l i n e a r dis- placement of the piston is used to trigger timing and switch- ing c i r c u i t s . In the c y c l i c operation described in d e t a i l under 4.1 the natural control variable for switching is d i s - placed volume and not time. However, the pause times are independent variables and separate timing devices have to be provided for these. ! / / / / 6.5 " -7' 00 ro \ \ V A V V 9> -Sj- ro F i g u r e 26. F l o a t i n g l i d e x p a n s i o n tank 117 V 60 ~ G L N 4 • • ft — • n— • Q  m 1  & R3 " 7 S W I <S 9 DI Rl R2 my R j l / \ ^ —e + 1 — D2 D2 I 4 R4 SW2 R4 PUMP DISPLACEMENT 00 F i gure 27. 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 p r o c e s s S = s w i t c h , R = r e l a y , D = time d e l a y r e l a y C = e l e c t r o m e c h a n i c a l c o u n t e r , SW = m i c r o sw i t c h . 86 Figure 27 shows how displaced volume and pause times are c o n t r o l l e d : A cam is attached to the reciprocating rack which drives the piston. This cam operates microswitches SW1 and SW2 which are adjustably mounted. Relays Rl and R2 are used to reverse the po l a r i t y of the motor armature (see Figure 28). Both are, however, delayed by s o l i d state delayed relays DI and D2 (Potter and Brumfield CDB38-70004, adjustable from 0.6 to 60 seconds). Relays R3 and R4 control the p o l a r i t y of the e l e c t r i c potential which is applied to the e l e c t r o d i a l y s i s c e l l from a S0RENS0N DCRA 40-10A power supply. The relay c i r c u i t is id e n t i c a l to the one shown in Figure 28 except that the input comes from the DC power supply and the output goes to the c e l l . When the piston is moving the c i r c u i t s are self-holding using contacts R3/1 or R4/1. An electromechanical counter C receives one inpulse every cycle by means of contact Rl/1. The switch boxes SB1 and SB2 in Figure 22 consist of the following components which are combined in one network: 0 m z m 3 9 9 0 a a &- OUT D.C. M O T O R R2 3 R2 2 <>6 ? o -9 S P E E D C O N T . 87 IN - + + - ' B O S T O N R A D I O T R O L F i g u r e 28. 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 reve rs a I . E L E C T R O D E E N D F R A M E A N I O N I C M E M B R A N E C A T I O N I C M E M B R A N E E L E C T R O D E E N D F R A M E E L E C T R O D E I. S P A C E R 8 C E N T R A L F R A M E S A N I O N I C M E M B R A N E E L E C T R O D E V S P A C E R F i g u r e 30. Schematic assembly of one stage of the second e I e c t r o d i a I y z e r . 88 SB1 : relays R3 and R4 SB2 : relays Rl , R2 , DI , D2 4.2.5 Rinse loop. The electrode wash liquor was pumped by a p e r i s t a l t i c pump from a p l a s t i c tank through a flow s p l i t t e r to the elec- trode end frames. It returned to the holding tank where the streams were remixed. P l a s t i c tubing allowed the flow rates to each electrode to be balanced. 4.2.6 Measuring and recording. Concentrations: Sodium chloride concentration was continuously measured conductometrically. Flow type conduc- t i v i t y c e l l s (Beckman Instr. , CEL-VDJ series) used with d i r e c t reading conductivity meters (Beckman I n s t r . , Solu-Meter RA5) monitored the concentrations of the solution flows at both ends of the ED c e l l . Automatic temperature compensation was provided. A 0 to 10 [mV] D.C. output signal from the Solu- Meter allowed potentiometric recording of the concentration in the following ranges (see Table 6). 89 T a b l e 6 C o n d u c t i v i t y and NaCI C o n c e n t r a t i o n Ranges of BECKMAN C o n d u c t i v i t y C e l l s CEL-VDJ C o r r e s p o n d i n g t o a 0-IOCm V]D.C. s i g n a l from a BECKMAN So Iu-Meter RA5 Ce11 C o n s t a n t K [ c m - 1 ] Con d uct i v i t y Cm i cromhos/cm] NaCI s o l u t i o n c o n c e n t r a t i o n CppmD 5 0 -- 2,500 0 - 1,300 20 0 -- 10,000 0 - 5,480 50 0 -- 25,000 0 - 15,370 The accuracy of the output signal is ±0.5% of f u l l s c a l e . Current: The current was recorded as the potential drop across a Nichrome resistance wire (16 gauge). The shunt resistance varied according to the length of the wire. Prior to every experiment a D.C. current signal of known magnitude was calibrated to f u l l scale of the recorder pen using the s l i d i n g scale vernier of the recorder (see below). Current was therefore measured d i r e c t l y and continuously. Voltage: The preparation of probe electrodes has been described in detail in Section 4.2.1. The signal which was picked up by these probes represented the voltage drop across the stack. Continuous recording of this probe voltage 90 allowed the average stack potential to be determined. The local changes could be used to i d e n t i f y p o larization e f f e c t s . Recorder: The above signals were traced by a WATANABE 4 pen recorder, model MC6-11S4H. A l l four pens u t i l i z e d the f u l l chart width of 25[cm]. pH: Samples for pH-checks were taken for some runs just prior to the experiment and immediately thereafter from both process and rinse stream and measured in the usual way. 4.3 The Mini P i l o t Plant Module The p r i n c i p l e modification of this module compared to the f i r s t one consisted of a complete redesign of the e l e c t r o d i a l y s i s c e l l . This necessitated modifications to the rinse loop as well as additions to current 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 consisted of eight equal stages, each composed of eight membrane-spacer frames and two electrode end frames. The eight stages were mounted in a two level clamp- ing device as i l l u s t r a t e d in Figure 29. The stages were 91 F i gu re 29 . Clamping a r r a n g e m e n t o f e i g h t s t a g e s i n m i n i p i l o t p l a n t m o d u l e ( 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 dialysate end. The stages were always connected in series h y d r a u l i c a l l y and usually in p a r a l l e l e l e c t r i c a l l y . Less than eight stages could be operated on line by changing tube connections and disconnecting 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 , in i t s e l f . Apart from the location of rinse and process flow ports in the electrode end frames the stages were i d e n t i c a l . In contrast 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 stack, the new design fea- tures a multiple-frame centre part. A schematic picture of the assembly is given in Figure 30, (page 87). Each central frame consisted of three components which were permanently joined together, see Figure 31: ( i ) An o u t e r s e a l i n g f rame ( 8 - 7 / 8 " x 3" x 1 /16" ) w i t h keyshaped l i q u i d d i s t r i b u t i o n s l o t s , made o f low d e n s i t y p o l y e t h y l e n e . ( i i ) A t r i p l e membrane 6 - 3 / 8 " x 1 - 3 / 4 " , composed of two ion exchange membranes (CI00 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 , Amer i can Mach ine and Foundry C r o p . ) and a l a y e r of Whatman f i I t e r paper No. I. ( i i i ) A s p a c e r s c r e e n 6 - 1 4 / 1 6 " x 1 - 7 / 8 " x 0 . 0 3 8 " Vexar® T P 2 3 , 10 x 10 s t r a n d s pe r i n c h , c u t d i a g o n a l l y , made of c l e a r p o l y p r o p y l e n e . The membranes were heat sealed along both short sides. The long sides remained open to insert and to remove the f i l t e r paper. 93 p o l y p r o p y l e n e s p a c e r s c r e e n w e l d e d s p a c e r f r a m e t r i p l e membra ne p o I y e t h y I e n e f rame a s s e m b I y F i g u re 31 . I n t e g r a t e d m e m b r a n e - s p a c e r f r a m e f o r e l e c t r o - d i a l y z e r N o . 2 . P a r t s and a s s e m b l y ( s c a l e : i n c h e s ) 94 F i g u r e 3 2 . E i e c t r o d i a I y z e r N o . 2 . E l e c t r o d e end f r a m e s o f a s i n g l e s t a g e ( s c a l e : i n c h e s ) . 95 The polypropylene spacer screen was pressed into the frame by means of a heated j i g . Then the t r i p l e membrane was tagged at three corners to the frame using a heated bar. A more detailed description of the manufacturing procedure may be found in Appendix A.3. It should be noted that although approximately 20 d i f f e r e n t operations were necessary to produce one u n i t , a l l 64 membrane-spacer frames showed excellent s i mi 1ari t y . The electrode end frames had to f u l f i l l the follow- ing tasks: 1. Ho ld the e l e c t r o d e s w i t h t h e i r t e r m i n a l s . 2. P r o v i d e a r i n s e chamber . 3. D i s t r i b u t e ( o r c o l l e c t ) t he p r o c e s s f l ow i n t o ( o r f rom) the membrane s t a c k . 4. P r o v i d e a s e a l i n g f a c e . Appendix A.2 shows how the end frame was designed to meet these demands, see also Figure 32. The double pass rinse was an important c h a r a c t e r i s t i c of the construction. The external pipe connections for the process solu- tion were located in the electrode end frames. Figure 33 i l l u s t r a t e s the internal flow d i s t r i b u t i o n . Hydraulic leaks between rinse and process stream could be avoided by 0-ring seals as indicated in Figure 33. 96 These were the only gaskets in addition to the separating membranes, see also Figure 30» (page 87). OUT F i g u r e 33: P r o c e s s f l ow t h rough second e I e c t r o d i a I y s e r s t a g e . Table 7 summarizes the s p e c i f i c a t i o n s of the second electrodi alyser: 97 T a b l e 7 E l e c t r o d i a l y s e r No. 2 ( E D M ) Des i gn M u l t i p l e Frame S t a c k E i g h t S t a g e s w i t h E i g h t Frames Each M e m b r a n e - S p a c e r F rame C o m p o s i t e P o p - I n U n i t , 3 P a r t s P e r m a n e n t l y J o i n e d E 1 e c t r o d e A r e a 60 [ c m 2 ] * A c t i ve V o i d Vo1ume 50 [ c m 3 ] I n h e r e n t Dead Volume 10 [ c m 3 ] ** Membrane U t i l i z a t i o n 97 [*] R i n s e S y s t e m Doub1e P a s s * Gas k e t s 2 S e p a r a t i n g Membranes 4 0 - R i n g s f o r P r o c e s s F l o w s M a t e r i a 1s S t a c k Frame P o l y e t h y l e n e E l e c t r o d e Frame P l e x i g l a s s E l e c t r o d e G r a p h i t e Te rm i na1 G r a p h i t e p e r s t a g e ** f r a c t i o n o f t o t a l membrane a r e a a v a i l a b l e f o r i o n i c t r a n s f e r . 98 4.3.2 Rinse d i s t r i b u t i o n system. The wash liquor (10,000 [ppm] aqueous NaCl solution) was pumped by a centrifugal pump (Cole Parmer, model MDX-3) from a two-gallon p l a s t i c tank through a d i s t r i b u t i o n mani- fold and the 16 rinse compartments and returned to the holding tank. The flow rate was measured at 0.90  + Q"O8 [ l i t r e / m i n ] per compartment and did not require special c o n t r o l . 4.3.3 Current and voltage measurements. Current consumption and stack voltage were measured i n d i v i d u a l l y for each sta.ge.. However, because of the limited number of pens, only one current and one voltage signal were recorded simultaneously. Current Shunts were prepared from NICHR0ME resistance wire (14 gauge), and integrated into the e l e c t r i c a l manifold which distributed the D.C. power from switch box SB1 (see Figure 22) to the stages. The wiring i s shown in Figure 34. The shunt resistances were 50.0[mft] ± 1.5% for the currents to the individual stages and 25.0 mfi for the total current. 99 SELECTOR SWITCH TO RECORDER F i g u r e 34. C u r r e n t m o n i t o r i n g c i r c u i t . 100 Voltage Probe electrodes were prepared from s i l v e r wire cable (8 leads of l [ f i / f t j resistance wire) which was hammered into s t r i p s approximately 1/8" wide and 5/1000" th i c k . The s t r i p s were dip coated with waterproof contact cement (Canadian Industries Limited) and the coating was removed from one side of the t i p which was located inside the stack. The probes were inserted between the separating membranes and the stack pack and sealed with s e l f - s e t t i n g s i l i c o n rubber g e l . A second selector switch was connected to the probes and to one recorder pen. The c i r c u i t is analoguous to the one shown in Figure 34. Chapter 5 EXPERIMENTAL RESULTS AND DISCUSSION In this chapter the experiments are compiled and correlated in three ways: a . Su rvey t a b l e s f o r each s t a c k c o n t a i n the o p e r a t i n g c o n d i t i o n s and the l i m i t i n g , s t e a d y - p e r i o d i c s t a t e reached a f t e r a c e r t a i n number of cy I c e s . b. Group t a b l e s and d iag rams i I l u s t r a t e the e f f e c t o f s i n g l e v a r i a b l e s under o t h e r w i s e f i x e d c o n d i t i o n s . c . I n d i v i d u a l t a b l e s and d iag rams p r e s e n t a r e c o r d of t he t r a n s i e n t s f o r s i n g l e t e s t r u n s . The c o l l e c t i o n of raw data during the course of a complete batch run w i l l be described f i r s t , followed by de t a i l s about the processing of these data into table form. Subsequently, a discussion of the variables w i l l i l l u s t r a t e the main features of the process phenomena. In the concluding section of this chapter the application of these batch system results to the operation of a continuous system w i l l be di cussed. 101 5.1 Data Collection A complete batch run consisted of the followi consecutive steps: 1. F i l l r i n s e t ank w i t h 6 t o 8- l i t e r s of f r e s h r i n s e l i q u o r (NaCI in d i s t i l l e d w a t e r , v a r y i n g c o n c e n t r a t i o n ) . 2 . F i l l sys tem w i t h p r o c e s s s o l u t i o n o f d e s i r e d c o n c e n t r a t i o n (NaCI i n d i s t i l l e d wate r ) . 3 . S t a r t r i n s e pump. 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 of c o n d u c t i v i t y m e t e r s . 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 s h u n t 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 ranges and c h a r t s p e e d . 8. Take pH samp les of p r o c e s s and r i n s e s o l u t i o n . 9 . Se 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 - ment , dead v o l u m e s , pump s p e e d , pause t i m e s , a p p l i e d D . C . v o l t a g e ) . 10. Note down d a t e , o p e r a t i n g c o n d i t i o n s , v a r i a b l e r e c o r d e d by each pen and a p p r o p r i a t e r a n g e , c h a r t s p e e d . 11. Check t o t a l c y c l e p e r i o d w i t h s t op w a t c h . 12. Turn c o u n t e r back t o z e r o , and 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 com- p l e t i o n of nex t f o r e w a r d s t r o k e of p i s t o n pump ( t he membrane a r rangement and t he e l e c t r o d e p o l a r i t y i s s e t t o d e m i n e r a l i z e the s o l u t i o n d u r i n g t h i s f i r s t h a l f eye Ie ) . 103 14. Record c u r r e n t and v o l t a g e s i g n a l s f o r d i f f e r e n t s t a t i o n s by m a n i p u l a t - ing s e l e c t o r s w i t c h e s , and mark pen t r a c e s a c c o r d i n g l y ( second ED c e l l o n l y ) . 15. W r i t e down any o b s e r v a t i o n r e l a t e d t o e x p e r i m e n t . 16. Change r e c o r d e r pen ranges in 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 reached 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 in t h i s o r d e r . 18. Read t o t a l number of c y c l e s and note down . 19. Take pH samp les of p r o c e s s and r i n s e s t r e a m s , o r e q u i l i b r a t e c o n c e n t r a t i o n of p r o c e s s s o l u t i o n t o check mass ba I ance f o r s o l u t e . 2 0 . T e s t pH samp les and note down r e s u l t s . The recorder chart thus contained a l l the o r i g i n a l information related to the test run. The following d e t a i l s were extracted from the chart. a . Mean p r o d u c t c o n c e n t r a t i o n s in 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 consump t i on f o r any h a l f c y c l e . The l o c a l c u r r e n t t r a n s i e n t s were ave raged 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 consumpt i on of the second 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 the f i r s t c y c l e s , and in a r o t a t i n g sequence w i t h the i n d i v i d u a l s t a g e s t h e r e a f t e r . 104 c . Mean s t a c k v o l t a g e f o r each 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 Iy . A g a i n , t he s t a g e s were read in r o t a t i o n f o r the second 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 mechanisms and i n t e r n a l c o n c e n - t r a t i o n d i s t r i b u t i o n s . 5.2 Main Survey Tables Current and concentration data were converted into proper units by means of c a l i b r a t i o n curves. The columns of the main survey tables are (see Tables 8 to 13): 1. Run number (#): The experiments on each stack were numbered chronologically and they are l i s t e d in this order. Two numbers separated by a dash (-) indicate a change in operating conditions during the run. 2. I n i t i a l c o n c e n t r a t i o n ( c 0 ) in parts per m i l l i o n NaCI in d i s t i l l e d water. 3. D i s p l a c e d volume (6) as f r a c t i o n of the free solution volume V 0  contained in the system between the conduc- t i v i t y c e l l s . 4. S u p e r f i c i a l v e l o c i t y (v) in centimeters per second. This is based on the active void volume ( V ) of the a 105 stack and the total length {&) of the electrodes in flow di r e c t i on. where Q = volumetric flow rate delivered by piston pump. 5. Pause t ime (x) in s e c o n d s . A single number is given when the pause times for f i r s t and second half cycle were equal . For unequal pause times the notation 10/5 stands for 10 sec during demineralization , 5 sec during enrichment. 6. C y c l e p e r i o d (T) in s e c o n d s . Since the flow rates Q were equal for both half cycles T is calculated as T = ?  V ° '  8  + T + T 1  *• Q  T T  T B where t T  and Tg are the pause times for demineralization and enrichment res p e c t i v e l y . 7. A p p l i e d p o t e n t i a l i n v o l t s ( A $ ) . The electrode voltage is given because this is the true independent v a r i a b l e . 8. Number of eye Ies ( n c ) . The subsequent columns refer to conditions which exist after nc cycles from start-up. 106 9. T o t a l c u r r e n t ( I ) in amperes . This base current is the arithmetic mean of the average current consumption for demineralizing and enriching half c y c l e s . 10. B r i n e c o n c e n t r a t i o n (x D ) and D — 11. D i a l y s a t e c o n c e n t r a t i o n (x^-) both normalized with respect to the i n i t i a l concentration c 0 . 12. S e p a r a t i o n f a c t o r (ns ) defined as the r a t i o of brine (bottom product) to dialysate (top product) concentration 13. T h i s column c o n t a i n s comments o n : The presence of dead volumes* 6g and 6 T  in brine and dialysate r e s e r v o i r , respectively (6g and 8j are given as fractions of the free solution volume V 0  (see item 3 ) ) , whether l i m i t i n g conditions are reached or not, and the number of stages for the second ED c e l l . The main survey tables of a l l successful experiments are presented on the following pages. Successful means not interrupted by mechanical, e l e c t r i c a l , or human f a i l u r e . * Or excess volumes. Table 8 Compilation of Experiments on EDI-S1-8 J 2 2 JL _5 6 Z 8 9 in n 12 11 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS % [-] Co [ppm] 6 [-] ' • V [cm/sec] T [sec] T [sec] AO [ vo l t ] nc [ - ] I [ampere] BRINE DIALYSATE L = l i m i t reached NL = l i m i t not reached 6g/5y = dead volumes X B [ - J X T [ - ] n s [ - ] 1 1090 1.10 1.21 _ 53.3 4 10 _ 1 .020 1 .020 1 .00 NL 2 1050 1.10 1.21 - 53.3 6 7 0.37 0.995 0.999 1 .00 NL 3 1040 1.10 1.77 - 36.4 6 8 0.385 0.999 0.996 1 .00 NL 4 1050 1.10 2.33 - 27.6 6 9 0.40 0.998 1 .000 1 .00 NL 5 1090 1.10 1.21 - 53.3 6 8 0.35 1 .005 1 .000 1 .01 NL 6 1080 1 .73 1 .21 - 84.3 4 6 0.23 1 .030 0.974 1 .06 L 7 1090 1 .73 1.21 . - 84.3 6 9 0.37 1 .020 0.938 1 .09 L 8 1090 1 .73 1.66- - 61 .4 6 12 0.39 1 .010 0.955 1 .06 L 9 1080 1 .73 2.62 - 39.0 6 10 0.41 1 .010 0.972 1 .04 L 10-0 1110 1 .73 0.65 - 157.4 8 9 0.52 1.110 0.900 1 .23 L -1 1 .21 - 84.3 8 16 0.57 1 .020 0.928 1.10 NL 14 1020 1.00 1 .21 - 50.2 6 7 0.32 0.969 0.983 0.99 NL 15-0 1020 1.00 1.21 - 50.2 6 9 0.32 0.970 0.997 0.97 L -1 0.65 - • - ' 93.8 13 0.30 0.965 0.972 0.99 L 21 770 1 .00 0.65 93.8 4* 7 - 0.950 1 .000 0.95 NL 22 775 1 .00 1.21 50.2 5* 10 • - 0.955 1 .010 0.95 L 23 760 1.00 1 .21 - 50.2 10 - 0.956 1 .010 0.95 L 24 765 1.00 1.21 - 50.2 5* 10 . - 0.962 1 .020 0.95 L 29 850 0.42 2.33 - 8.7 11 40 1 .00 1 .10 0 .969 1.13 L 30 700 1.75 1 .77 - 57.1 7.55 10 - 1 .03 0.973 1 .06 L 31 710 1 .00 1 .77 - 34.3 7.55 13 0.35 0.99 1 .00 0.99 L 32 720 1 .00 1.77 - 34.3 12.5 6 0.55 0.95 0.97 0.98 L 33 710 1 .00 2.33 . - 26.1 12.5 10 0.60 0.965 0.985 0.98 L 34 700 1 .00 2.89 21 .0 12.5 9 0.65 0.975 0.99 0.985 L 35 700 1 .00 1 .21 - 50.2 12.5 9 0.55 0.96 0.96 1 .00 L 36 700 1 .00 0.65 - 93.8 12.5 8 0.50 1 .04 0.935 1.11 L 37 720 1.00 - 0.65 - 93.8 5.0 5 0.20 1 .02 0.98 1 .05 L 38 725 1 .80 1.21 _ 87.3 15.0 6 0.60 1 .02 0.862 1.19 L 39 710 1.80 1 .21 - 87.3 20.0 5 0.75 1 .07 0.86 1 .25 L 40 760 1 .00 1.21 - 50.2 6.0 8 0.28 0.986 0.995 0.991 L 41 760 1 .00 1.21 - 50.2 10.0 7 0.44 0.956 0.975 0.980 L 42 760 1 .00 1.21 - 50.2 20.0 7 0.78 0.972 0.954 1 .02 L * Probe vo l tage, hand regulated. Table 9 Compilation of Experiments on EDI-S2-15 1 7 3 n 5 6 7 8 9 i n 11 1? 13 RUN NO. CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT CONCENTRATION SEPARATION REMARKS INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL FACTOR BRINE DIALYSATE L = limit reached # c 0 6 V T T A<t> nc I XB XT n s NL = limit not reached [-] [ppm] [-] [cm/sec] [sec] [sec] [volt] [ - ] [ampere] [ - ] [ - ] [ - ] = dead volumes 1 930 0.95 1.29 0 35 4 10 0.23 1 .00 0.990 1 .01 L 2 890 0.95 0.47 20 137 10 8 0.30 1 .45 0.580 2.50 NL 3 910 0.47 1.41 10 36 16 15 0.60 1 .37 0.566 2.42 L, « B  - 4 910 0.47 ' 1.41 10 36 16 14 0.60 1 .50 0.582 2.59 I 5-0 930 0.47 2.11 5 21 16 14 ' 0.74 1 .25 0.722 1.73 NL -1 10 31 25 0.62 1 .50 0.563 2.67 NL 6 990 1.00 2.23 10 42 20 14 0.75 1 .23 0.641 1.92 • L 7 940 1.00 0.88 0 '55 8 10 0.40- 1 .01 0.935 1 .08 L 8 950 1.00 0.88 0 55 16 10 • 0.70 1 .01 0.858 1.18 L 9 970 1.00 • 0.88 0 55 24 10 0.85 1.07 0.801 1.33 L 10 960 1.00 ' 0.88 0 55 32 10 1 .00 1.14 0.750 1 .52 L 11 960 1.00 ' • 2.23 5 32 32 14 1 .25 1 .29 0.631 2.05 L 12-0 940 1.00 2.23 5 32 32 10 • 1 .25 1 .31 0.623 2.10 L -1 10 42 16 0.90 1 .41 0.548 2.58 NL 13 930 1.00 2.23 10 42 16 10 0.65 1.28 0.671 1 .91 L 14 980 1.00 2.23 ' 15 52 16 10 0.60 1 .32 0.607 2.17 NL 15 960 1.00 0.47 15 132 16 7 0.43 1 .42 0.585 2.43 L 16 975 0.59 0.47 25 111 16 15 0.30 •1 .60 0.397 4.03 NL, 5 B = .35 17 1025 1.0 0.88 0 • 55 40 • 10 1 .30 1.14 0.747 1 .52 L 18 1010 1.0 1 .70 14 56 40 7 1.15 1 .54 0.561 2.75 L 19 1020 0.5 1.70 7 28 40 14 • 1.40 1.72 0.529 3.24 L 20 1040 0.5 1 .70 7 28 40 15 1 .28 1 .50 0.463 3.24 NL, 6 B = .5 21 980 0.5 1.70 7 '28 40 22 1 .32 1 .54 0.568 2.72 NL, SB=<5T = 1.0 22 1050 0.5 0.88 0 28 40 10 1 .25 0.98 0.950 1 .03 L, «B = 1-5 23 1020 1.0 1.70 0 29 32 10 1 .44 1 .00 0.888 1.13 NL 24 1020 0.25 1.70 3.5 14 40 65 1.72 1 .42 0.468 3.02 NL, 6 B  = -75 26 1020 1.0 0.47 15 132 24 8 0.48 1.51 0.582 2.60 L 27 1090 1.0 2.23 15 52 32 10 0.96 1.46 0.537 2.72 L 28-0 1070 1.0 2.23 5 32 32 4 1.38 1 .25 0.719 1 .74 NL -1 10 42 7 1.18 1 .37 0.615 2.23 NL -2 15 52 11 1 .00 1 .45 0.540 2.69 NL -3 :  5 32 18 1 .30 1.28 0.644 1 .99 L 29 1070 1.54 0.88 0 84 40 6 1.05 1.20 0.670 1 .80 L 30-0 1010 0.5 1.77 7 28 16 21 0.80 1 .27 0.621 2.05 L, <5B = -5 -1 14 42 34 0.52 1 .41 0.486 2.91 L 31 1030 0.59 0.47 25 111 16 . 13 0.36 1 .55 0.449 3.45 L, «B.» 32 1120 0.25 1.70 3.6 14 40 60 1 .70 1 .63 0.494 3.31 NL 33 1150 1.0 2.23 15 52 32 11 0.90 1 .39 0.517 2.70 L Table 10 Compilation of Experiments on EDI-S2-16 1 2 3 4 5 6 7 8 9 10 11 1? 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE DIALYSATE L = limit reached NL = limit not reached # Co 6 V T T AO nC I XB XT ns [-] [ppm] [-] [cm/sec] [sec] [sec] [volt] [ -] [ampere] [ - ] [ " ] [- ] 6g/6y = dead volumes 1 1100 1.00 2.32 15 52 32 10 0.84 1.47 0.484 3.04 L 2 1070 1.00 0.92 15 85 32 9 0.71 1 .55 0.476 3.25 L 3-0 1175 0.61 0.92 15 52 32 14 0.70 1 .88 0.341 5.52 NL -1 25 72 20 0.60 2.04 0.274 7.46 L 4 1220 0.61 0.92 25 72 32 14 0.70 2.11 0.278 7.58 L 5-0 1250 0.61 0.92 15 52 32 13 0.70 1 .36 0.238 5.71 NL, 6 B  = 1.84 -1 25 72 21 0.50 1 .41 0.179 7.88 L, 6 B  - 1.8*. -2 0.49 25 111 32 40 0.40 1 .46 0.158 9.24 L, 6 B  = 1.84 -3 1 .77 25 67 32 50 0.45 1 .44 0.176 8.18 NL, 6 B  = 1.84 -4 0.92 25 72 16 60 0.30 1 .40 0.222 6.32 NL, 6 Q  = 1.84 6-0 1225 0.61 0.92 15 52 16 . 16 0.50 1 .29 0.308 4.18 L, 6B = 1.84 -1 25 72 16 22 0.40 1 .32 0.250 5.28 L, 6B = 1.84 -2 15 52 40 38 0.63 1 .43 0.196 7.05 L, 6R - 1.84 -3 25 72 40 45 0.52 1 .41 '0.142 10.10 L, 6B - K84 7 1250 0.61 0.92 0 22 40 50 1 .50 1.11 0.585 1 .88 L, 6B = 1.84 8-0 1240 0.61 0.92 0 22 32 30 1 .41 1.10 0.714 1 .54 L -1 0 22 40 50 " 1 .60 1 .22 0.630 1 .94 L 9-0 1200 1.00 0.92 0 53 40 15 1 .26 1 .31 0.589 2.22 L -1 0.49 99 40 19 0.84 1 .48 0.447 3.31 NL o cr Table 11 Compilation of Experiments on EDI-S3-12 1 2 3 4 5 fi 7 8 q in IT 17 13 RUN NO. CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT CONCENTRATION SEPARATION REMARKS INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL FACTOR BRINE D1ALYSATE L = NL = l i m i t r e a c h e d l i m i t no t r e a c h e d Co 6 V T T AG nc I X B X T ns [-] [ppm] [-] [cm/sec] [sec] [sec] [ v o l t ] [ - ] [ampere] [- ] [ - ] [ - ] V 6 T = dead vo 1 umes 1-0 1225 1 .00 1.33 0 36 32 10 1.50 1 .07 0.821 1 .31 L -1 0.92 0 52 18 1 .35 1.18 0.705 1 .67 L -2 5 62 25 1.20 1 .41 0.526 2.69 L -3 15 82 30 1.00 1 .56 0.411 3.81 L -4 0.49 15 129 35 0.70 1 .72 0.316 5.46 L 2-0 1220 0.59 0.92 15 62 32 20 0.90 2.04 0.265 7.72 L -1 25 82 25 0.70 2.21 0.217 10.20 L -2 0.49 25 111 31 0.62 2.32 0.175 13.28 L 3-0 1230 0.59 0.92 15 62 32 16 0.80 1.37 0.194 7.06 L, 6B - 1.75 -1 25 82 24 0.60 1 .43 0.136 10.52 L,. 6B = 1.75 -2 0.49 25 111 30 0.50 1 .47 0.110 13.40 L, ! 6 B 1 . 7 5 4-0 1245 0.59 0.92 15 62 32 16 0.90 2.03 0.259 7.85 L -1 25 82 23 0.70 2.17 0.218 9.97 L 5-0 1280 0.59 0.92 25 82 32 16 0.75 2.12 0.237 8.98 NL -1 0.49 25 111 20 0.70 2.21 0.217 10.19 NL -2 0.47 0.49 25 96 28 0.65 2.33 0.091 25.70 L, 5B = 0.12 -3 0.29 0.49 25 80 36 0.56 2.38 0.055 43.00 L, 6B = 0.30 6-0 1280 0.29 1 .33 10 31 32 50 0.65 1 .36 0.131 10.41 L, 6B = 2.06 -1 0.92 10 36 60 0.60 1 .38 0.111 12.48 NL, 6B = 2.06 -2 0.49 10 50 70 0.55 1 .39 0.106 13.17 L, 6B = 2.06 -3 20 70 80 0.45 1 .43 0.083 17.14 L, 6B = 2.06 -4 0.12 0.49 20 52 145 0.35 1 .47 0.048 30.50 L, 6B = 2.18 ' 7 1280 0.59 0.49 20 .100 32 15 0.85 2.09 0.222 9 . 38 NL 7a 8 1280 0.59 0.49 20 100 32 15 0.75 2.29 0.191 12.00 L, b r i n e u n m i x e d 1270 1 .00 0.92 20 93 32 10 0.95 1 .64 0.376 4.36 L b r i n e unmi x e d 8a 1270 1 .00 0.92 20 93 32 12 0.75 1 .83 0.255 7.18 NL, 9-0 4800 1 .00 0.92 0 53 16 5 3.10 — 0.922 — L -1 5 63 10 3.00 — 0.898 — NL -2 10 73 20 2.70 — 0.636 — NL -3 15 83 35 2.30 — 0.545 — NL 10-0 4680 0.59 0.92 15 62 32 15 3.20 — 0.273 — L -1 • 25 82 20 2.80 2.00 0.205 10.00 L 11 4560 1 .00 0.92 15 83 32 11 3.60 1 .52 0.386 3.94 L b r i n e u n m i x e d 11a 4600 1 .00 0.92 15 . 83 32 15 3.10 1 .76 0.267 6.60 L, 12-0 4690 0.59 0.92 15 62 16 20 2.00 — 0.341 — NL, 6B = 1.75 -1 0.49 30 120 16 29 1.30 — 0.216 — NL, 6B = 1.75 -2 24 33 1.40 — 0.157 — L, 6B = 1.75 13 4830 1 .00 0.92 15 83 16 10 2.20 . 1 .30 0.533 2.44 ' L 6 CONTINUED Table 11 (Continued) 1 2 3 4 5 6 7 8 9 10 11 12 13 O H M M rt CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT rnwrpMTD/iTTnw SEPARATION D F M U D I c ' C KUN NU • INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL FACTOR r\ L nMK NO f_ A \f T A d> T BRINE DIALYSATE n c I —- l i m i t " r * o 3 / * h o * H if Co 0 V T 1 Li * r II V* 1 11 o U — l i m i t , I C d t l l c U A NL » limit not reached [-] [ppm] [-] [cm/sec] [sec] [sec] [volt] [ - ] [ampere] [ - ] [ - ] [ - ] 60/6_ = dead volumes D 1 14 5000 1 .00 0.92 25 103 16 .8 2.10 1 .42 0.496 2.86 L 15 1000 1.00 1.32 5 46 20 18 0.95 1.29 0.588 2.19 L 15 980 1 .00 1.32 5 46 20 18 0.90 1.27 0.598 2.12 L 17 1130 1 .00 0.90 5 64 10 18 0.53 1 .20 0.700 1 .72 L 18 1080 1 .00 0.90 5 64 20 18 0.84 1 .32 0.578 2.28 L 19 1175 1 .00 0.90 5 64 30 16 1.06 1 .34 0.473 2.85 L 20 1160 0.25 0.90 . 20 54 30 50 0.75 2.67 0.211 12.64 L 21 1230 1.00 0.90 10 74 20 ]0 0.81 1 .39 0.508 2.73 L 22 1200 1.00 0.90 15 84 20 17 0.74 1 .49 0.486 3.04 L 23 1200 1.00 0.90 20 94 20 16 0.69 1 .52 0.469 3.23 L 24 1170 1.00 0.90 0.6 55 20 15 1.09 1.14 0.703 1:62 L o CL Table 12 Compilation of Experiments on EDI-S3-13 1 2 3 H 5 6 7 8 • 9 . . . 10 11 12 13 RUN NO. CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT CONCENTRATION SEPARATION REMARKS INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL FACTOR B R I N E D I A L Y S A T E L = l i m i t r e a c h e d # C 0 6 V T T nc I X B [ - ] XT ns [ - ] [ppm] [ - ] [cm/sec] [sec] [sec] [volt] [ - ] [ampere] T [ - ] [ - ] NL V 6 T = l i m i t no t r e a c h e d = dead v o l u m e s 1 1240 1 .90 20 93 22 19 .70 1 .69 .349 4.85 L 2 1250 1 .95 10 71 22 18 .85 1 .60 .398 4.03 L 3 1228 0.5 .95 10 45 22 36 .77 2.08 .278 7.46 NL 4 1240 0.25 .95 10 34 22 65 .73 2.34 .236 9.90 NL 5 1270 1.5 .95 10 96 22 10 .91 1 .33 .531 2. 50 L 6 1300 1 .95 5 61 10 17 .62 1 .31 .603 2.18 L 7 1270 1 .95 5 61 22 17 1 .00 1 .52 .432 3.53 L 8 1260 1 .95 5 61 30 15 1 .20 1.61 .389 4.15 L 9 1135 1 .95 5 61 40 22 1 .28 1 .77 .330 5.36 L 10 1045 1 .95 0.6 52 22 23 .99 1 .28 .570 2.24 L 11 1250 1 .95 5 61 22 18 .96 1 .52 .424 3.59 L 12 1282 1 .95 10 71 22 20 .87 1 .61 .372 4.33 L 13 1205 1 .95 20 91 22 19 .69 1 .71 .324 5.27 L 14 1125 0.5 .95 30 111 22 13 .50 1 .79 .301 5.95 L 15 1265 0.5 .50 10 68 22 28 .62 2.14 .239 8.93 NL 15 1275 0.5 1 .40 10 37 22 34 .80 2.08 .248 8.35 NL 17 1270 0.5 1 .85 10 33 22 45 .79 2.10 .242 8.71 L 18 1180 0.5 2.36 10 30 22 45 .70 2.12 .240 8.83 L 19 1195 0.5 .50 0.6 50 22 50 .87 1 .26 . 540 2.33 L 20 1185 0.5 .27 0.6 90 22 45 .60 1 .72 .350 4.91 L 21 1205 0.5 1 .85 0.6 14 22 160 1.69 0.90 .856 1 .05 NL 22 1205 1 .95 . 5 61 30 18 1 .05 1.61 .375 4.29 L 24 1260 0.5 1 .40 10/5 32 22 40 .91 2.03 .228 8.90 L 25 1250 0.5 1 .40 10/10 37 22 35 .81 2.14 .228 9.35 NL 25 1260 0.5 1 .40 10/10 37 10 40 .54 1 .83 .344 5.33 L 27 1260 0.5 1 .40 10/5 32 10 50 • .65 1 .65 .376 • 4.39 L 28 1210 1 1 .40 10/5 49 10 20 .59 1 .38 .535 2.59 NL 29- 1270 1 1 .40 10/10 54 10 16 .54 1 .48 .•515 2.86 - L 30 1280 0.5 2.36 10/5 25 22 35 .92 2.01 .228 8.85 NL 31 1300 0.5 2.36 10/10 30 22 30 .80 2.16 .233 9.27 L 32 1290 0.5 1.85 10 33 22 30 .81 2.15 .230 9.33 L 33 1280 0.5 1 .85 10 33 22 60 .77 2.05 .217 9.43 L. 6B = <ST=0.5 34 1200 0.5 1 .85 10 33 22 70 .71 1 .99 .235 8.44 NL, SB=<5T = 1 -0 35 1200 0.5 1.85 10 33 22 40 .60 1 .57 .171 9.16 L, 6b = ST"=0 .0 6 B =6 T  = 1 .0 36 1260 0.5 1.85 10 33 22 60 1.00 2.82 .326 8.66 NL, 37 4640 1 0.95 5 61 10 15 1 .65 1.15 .684 1 .68 L 38 4500 0.5 0.95 5 35 10 40 1.73 1 .25 .644 1 .95 NL 39 4890 0.5 1 .40 10 37 10 35 1 .54 1 .54 .462 3.33 NL 40 5560 0.5 1 .40 10 37 15 34 2.44 1 .70 .333 5.10 L 40a 5275 0.5 1.40 10 74 15 35 2.35 1 .70 .330 5.14 L 41 5125 1 1 .40 10 54 15 15 2.58 1 .57 .495 3.18 L 42 5215 1 .16 0.6 285 5 15 0.60 1 .27 .586 2.17 NL Table 13 Compilation of Experiments on EDII-S1-8 1 2 3 4 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS [-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] A* [volt] nc [ - ] I [ampere] BRINE DIALYSATE ns [- ] MS L NL = N o . o f s t a g e s = l i m i t r e a c h e d = l i m i t no t r e a c h e d = dead v o l u m e s [ - ] [ X - 1 - ] 6 5700 2/3 5 .4 10 40 10 40 5.6 2 .51 0 .011 224 NL 7 5700 2/3 5 .4 0.6 50 10 30 3.8 1 .48 0 .507 3 L 8 5300 2/3 5 .4 5 60 10 45 3.2 2 .38 0 .023 104 NL 9 5400 2/3 5 .4 20 80 10 25 2.0 2 .63 0 .008 348 L 10 4800 2/3 5 .4 5 50 10 46 4.1 2 .35 0 .026 91 NL 11 5300 1 5 .4 5 68 10 26 4.6 1 .91 0 .159 12 L 12 4300 1/4 5 .4 5 25 10 90 2.6 3 .50 0 .004 874 L 13 5100 2/3 5 .4 5 50 5 55 2.0 1 .87 0 .219 9 L 14 5050 2/3 3 .0 0.6 70 10 40 5.7 1 .60 0 .324 5 L 15 5400 2/3 1 .6 0.6 129 10 20 5.5 1 .75 0 .155 11 L 16 5500 2/3 5 .4 5 50 15 30 6.9 2 .55 0 .011 231 NL 17 5100 2/3 5 .4 10 50 10 33 2.6 2 .40 0 .0 30 80 L , MS = 6 18 5300 2/3 5 .4 10 39 10 30 1.7 2 .27 0 .072 32 NL, MS = 4 19 4900 2/3 5 .4 10 29 10 40 0.9 2 .13 0 .130 16 L, MS = 2 20 5500 2/3 5 .4 10 30 10 45 1.0 2 .16 0 .132 16 . L, MS = 2 21 5200 2/3 5 .4 10 59 15 34 3.4 2 .69 0 .004 648 L 22 2600 2/3 5 .4 20 80 10 25 1 .5 2 .86 0 .004 710 L 23 2650 2/3 5 .4 10 61 10 30 2.1 2 .68 0 .019 143 L 24 2650 2/3 5 .4 10 60 15 30 3.0 2 .91 0 .012 250 L 25 1250 2/3 5 .4 0.6 40 10 45 2.4 2 .32 0 .068 34 L 26 1290 2/3 5 .4 10 60 10 30 1 .4 2 .84 0 .014 202 L 27 1250 2/3 5 .4 20 80 10 30 1.1 3 .18 0 .009 362 L 28 1280 2/3 5 .4 5 50 10 35 1.8 2 .70 0 .012 222 L 29 1260 1 5 .4 10 79 10 16 1 .8 2 .19 0 .029 74 L 30 1270 1 5 .4 0.6 60 10 25 2.6 1 .94 0 .092 21 L 31 1220 2/3 5 .4 0.6 41 15 34 3.4 2 .49 0 .024 103 L 32 1240 2/3 5 .4 5 50 15 26 2.8 2 .90 0 .005 546 L 33 1200 2/3 5 .4 10 59 15 25 2.0 3 .17 0 .001 3600 NL 34 1280 2/3 5 .4 20 78 15 25 1 .8 3 .70 0 .001 6100 NL 35 1220 2/3 5 .4 5 50 5 35 1.1 2 .34 0 .054 43 NL 35a 1220 2/3 5 .4 10 60 10 30 1 .4 2 .87 0 .012 247 L 36 1250 2/3 5 .4 10 60 5 40 0.8 2 .57 0 .0.26 99 L 37 1150 2/3 1 .4 0.6 135 10 30 1.6 2 .99 0 .011 285 L 38 1250 2/3 3 .0 0.6 71 10 40 2.2 2 .46 0 .021 118 L 39 1260 2/3 1 .4 10 145 10 30 1.5 3 .40 0 .006 552 NL 40 1290 2/3 2 .2 10 92 10 25 1.6 3 .00 0 .008 373 ' NL CONTINUED Table 13 (Continued) 1 2 3 4 5 6 7 : 8 .9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE DIALYSATE MS = No. of s tages # i-1 Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] [volt] nc [ - ] I [ampere] X B [- ] X T [- ] ns [- ] L = NL = V 5 T - limit reached limit not reached dead volumes 41 1300 1/4 5.4 0.6 16 10 no 3.4 2.56 0.169 15 NL 42 1175 1/4 5.4 10 35 10 54 0.9 5.18 0.006 810 NL 43 1210 2/3 5.4 0.6 31 10 60 2.2 2.20 0.095 23 L, MS = 6 44 1225 2/3 5.4 10 50 10 26 1.0 2.74 0.022 122 NL, MS = 6 45 1275 2/3 5.4 10 40 10 34 0.7 2.67 0.040 66 L, MS = 4 46 1240 2/3 5.4 0.6 21 10 80 1.5 1.75 0.320 5 L, MS = 4 47 1225 2/3 5.4 10 21 10 50 0.4 2.61 0.095 28 L, MS = 2 48 1250 2/3 5.4 0.6 11 10 100 1.2 1.30 0.657 2 L , MS = 2 49 1270 2/3 5.4 20 80 10 40 1.2 3.46 0.008 452 NL 50 1290 2/3 2.2 10 91 10 20 1.5 3.31 0.013 262 NL 51 1280 2/3 5.4 10 40 10 no 0.6 3.19 0.051 * 63 NL, MS = 4  6 B  "  6 T - i ' unmixed 52 1250 2/3 5.4 10 40 10 60 0.6 2.30 0.040 58 NL, MS = 4, 6B = 6y = i 53 1280 - 2/3 5.4 10 40 10 55 0.6 2.70 0.072 ** 38 NL, MS = 4, * B " « T  =  * unmi xed CONCENTRATIONS MEASURED IN WELL MIXED END RESERVOIRS, TWO STAGES ON EACH END INACTIVE. CONCENTRATIONS MEASURED BETWEEN ACTIVE AND INACTIVE STAGES. 108 Tables 8 to 12 contain experimental results obtained with the f i r s t ED c e l l , Table 13 shows results from the second ED c e l l in batch mode. This stands for the f i r s t e l e c t r o d i a l y s e r (EDI), used with the second stack (S2) version, which contained f i f t e e n (15) spacer-membrane u n i t s , and refers to run number fi v e (#5). 5.3 The F i r s t E l e c t r o d i a l y s i s Cell (EDI) 5.3.1 Parameters. The parameters which were studied on this f i r s t ED c e l l (EDI) may be divided into the following two groups: The following type of abbreviation w i l l be used subsequently: EDI - S2 - 15/#5 O p e r a t i n g p a r a m e t e r s : 1 . Applied voltage A$ 2. Pause time T 3. S u p e r f i c i a l v e l o c i t y v 4. Displaced volume 6 6. 5. Dead volume ^ B ^ T I n i t i a l concentration c 0 109 Design parameters: 7. Internal flow d i s t r i b u t i o n and axial dispersion 8. External mixing in brine reservoir 9. Thickness of capacity c e l l core 10. Thickness and hydrodynamic properties of spacer screen. A l l except two of these parameters are defined in preceding sections. Items 7. and 8. are discussed in f u l l d e t a i l under 5.3.8 and 5.3.9, re s p e c t i v e l y . Each of these ten parameters is analysed separately by forming groups of experiments in which the other parameters are constant. These groups are presented in tables which display the operating parameters and the f i n a l conditions at the end of each experiment in the same order as the main survey ta b l e s . The transient response of the ED c e l l was evaluated for a series of systematic runs on the second and t h i r d stack versions. Appendix C.l describes the computer calculations which were performed on the raw data for each cycle and l i s t s tables of printout. 5.3.2 Effect of applied voltage. The main survey tables l i s t values of the constant voltage supplied by the regulated D.C. power source, since 110 this is the true independent v a r i a b l e . The voltage drop across the stack is primarily a function of this applied voltage but i t varies systematically during the c y c l i c operation. A typical example of these fluctuations is shown in Figure 35, which is a copy of the traces of probe voltage (potentiogram) and current (electrogram) recorded during the f i r s t f i v e cycles of EDI - S2 - 15/#15. The p o l a r i t y reversal of the e l e c t r i c potential is suppressed in the potentiogram but is indicated by positive and negative signs in the time f i e l d s below the curve. The following trends characterize the potentiogram: a . P robe v o l t a g e i s g e n e r a l l y w e l l below the e l e c t r o d e v o l t a g e due t o the s o l u t i o n r e s i s t a n c e of t he 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 - t a n c e s in t h e c o n n e c t o r s . b. Peaks r e s u l t f rom each p o l a r i t y r e v e r s a l . The peaks r e f l e c t the b a t t e r y e f f e c t o f the membrane s t a c k , and appea r t o be s h a r p e r when s w i t c h i n g f rom 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 t han v i c e v e r s a . T h i s b a t t e r y e f f e c t i s most p ronounced f o r c a p a c i t y c e l l s w i t h " z e r o " c o r e because o f the ve ry l a r g e c o n c e n t r a t i o n changes in t h o s e c e l l s (DONNAN e f f e c t ) . However , the peaks a re of moderate magn i tude com- pa red t o the l e v e l of t he 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 he 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 peaks decay w i t h i n a few s e c o n d s . Subsequen t changes of the probe v o l t a g e a re a n t a g o n i s t i c t o the c u r r e n t c h a n g e s , 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 he e l e c t r o d e r e a c t i o n s . A P P L I E D V O L T A G E * ! 6 [ v ] 11 POTENT IOG RAM ELECTROGRAM NO. of CYCLES [-] F i g u r e 35. EDI-S2-I5/#I 5. T r a c e s 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 d u r i n g the f i r s t f i v e c y c l e s . 112 F i gu re 36 . P r o b e v o l t a g e v s . e l e c t r o d e v o l t a g e f o r f i r s t ED c e l l . I.I o IT H 2 UJ o z o o 1.0 0 .9- BRINE DIALYSATE 113 F i g u r e 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 in 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 re c o n s t a n t . O DC UJ O z o o F i g u r e 38 . EDI - S 2 — I5 /#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 in 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 dependen t . 114 A plot of the mean probe voltage vs. applied voltage for a l l three membrane packs may be f i t t e d by straight lines as i l l u s t r a t e d in Figure 36. The points f a l l below the diagonal l i n e and are divided in low concentration and high concentration * runs. The scatter of the points is caused by variations in process concentration, positioning of the probes, and by i n - accuracies of the averaging method. Tables 14, 15 and 16 show the effect of the applied voltage (A$) on final conditions for experiments with f i r s t , second, and third stack versions, respectively. The separation is generally improved for larger values of A$ , and the current consumption increases simultaneously. The improvements in separation with increasing potential depend on the values of the other parameters. The following trends may be i d e n t i f i e d . 1. L i t t l e or no improvement occurred for zero pause time, fast displacement, and large sorption capacity of the mem- branes (see Table 14). An inspection of the concentration transients shows a l l the c h a r a c t e r i s t i c s of the model discussed in Section 3.2.1. Figure 37 is a typical example of the real time transients of the reservoir concentrations. The top reservoir concentration (dialysate) drops sharply for the f i r s t c y c l e , and both concentrations remain p a r a l l e l and d r i f t upward for subsequent cycles. Separation is thus completed * See page 147. 115 after one cycle. The improvements which may be achieved by an increased potential are r e s t r i c t e d to the f i r s t c y c l e , and therefore remain small. The current consumption increased almost proportionally to the applied p o t e n t i a l . In these experiments the concentrations changed very l i t t l e compared to the i n i t i a l concentration, 1. e. the e l e c t r i c resistance of the stack stayed almost constant. 2. Small improvements were observed for zero pause time, slow displacement, and small sorption capacity of the mem- branes (see the f i r s t group in Table 15). Typical concentra- tion transients of these experiments are shown in Figure 38. A break of the dialysate transient after the f i r s t cycle is c l e a r l y v i s i b l e , but the separation is further increased dur- ing the next cycles. The shape of these curves agrees well with the model presented in Section 3.3.2. Figure 39 i l l u s t r a t e s d i r e c t l y the influence of the applied potential (A<1>) on f i n a l separation factor ( n s ) , f i n a l reser- voir concentrations (Xg and x ^ ) , and f i n a l current ( I ) . The current consumption is seen to r i s e less than proportional to the applied potential up to approximately 32 [V]. This behaviour is attributed to the simultaneous increase in bottom Table 14 Effect of Applied Voltage (A4>) on EDI-S1-8 1 2 3 f} 5 6 7 8 9 10 11 12 13 CONCENTR. VOLUME . VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT r n M r r w T O A T T n w SEPARATION n r II ri t/ r I\ U It tx u - INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL LUINUtN 1 KA 1 I UN FACTOR REMARKS BRINE DIALYSATE • # Co 6 V T T nc I X T ns L — l i m i t r e a c h e d [-] [ppm] [-] B 1 NL = l i m i t no t r e a c h e d [cm/sec] [sec] [sec] [volt] [- ] [ampere] [" ] [ - ] c - \ 6g/6-j- = dead v o l u m e s 14 1020 1.00 1.21 _ 50.2 6.0 7 0.32 0.969 0.983 0.99 NL 1-5-0 1020 6.0 9 0. 32 0.970 0.997 0.97 L 40 760 6.0 8 0.28 0.986 0.995 0.99 L 41 760 10.0 7 0.44 0.956 0.975 0.98 L 35 700 12.5 9 0.55 0.960 0.960 1 .00 L 42 750 20.0 7 0.78 0.972 0.954 - 1 .02 L 6 1080 1.73 1.21 _ 84.3 4.0 6 0.23 1 .03 0.974 1 .06 L 7 1090 1.73 84.3 6.0 9 0.37 1 .02 0.938 1 .09 L 38 725 1 .80 87.3 15.0 6 0.60 1 .02 0.862 1 .19 L 39 710 1.80 87.3 20.0 5 0.75 1 .07 0 .860 1.25. L 37 720 1.00 0.65 _ 93.8 5.0 5 0.20 1 .02 0 .980 1 .05 L 15-1 1020 6.0 13 0.30 0.965 0.972 , 0.99 L 36 700 12.5 8 0.50 1.04 0.935 1.11 L 3 1040 1.10 1.77 _ 36.4 6.0 8 0.39 0.999 0.996 1 .00 NL 31 710 1 .00 34.3 7.55 13 0.35 0.99 1 .00 0.99 L 32 720 1 .00 34.3 12.5 6 0.55 0.95 0.97 0.98 L Table 15 Effect of Applied Voltage (A$) on EDI-S2-15 1 2 3 H 5 6 7 8 9 10 11 12 13 D 1! v wn CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT P f i M P r M T r j f l T T r i M SEPARATION r\ U11 IX u . INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL UUNLcIN 1 KA 1 I UN FACTOR REMARKS BRINE D1ALYSATE # 1 _ Co 6 V T T nc I ns L — l i m i t reached [-3 [ppm] [-] [cm/sec] B T NL = l i m i t not reached [sec] [sec] [volt] [ - ] [ampere] [ - ] [ - J [- ] dead vo1umes 7 940 1.00 0.88 0.0 55 8 10 0.40 1.01 0.935 1.08 L 8 950 16 10 0.70 1 .01 0.858 1.18 L 9 970 24 10 0.85 1 .07 0.801 1 .33 L 10 960 32 10 1.00 1.14 0.750 1 .52 L 17 1025 40 10 1.30 1.14 0.747 1 .52 L • 13 930 1.00 2.23 10 42 15 10 0.65 1 .28 0.671 1 .91 L 6 990 20 14 0.75 1 .23 0.541 1 .92 L 12-1 940 32 16 0.90 1.41 0. 548 2.58 NL 14 980 1.00 2.23 15 52 15 10 0.60 1 .32 0.607 2.17 NL 27 1090 32 10 0.96 1 .46 0.537 2.72 L 28-2 1070 32 11 1.00 1 .45 0. 540 2.69 NL 33 1150 32 11 0.90 1 .39 0.517 2.70 L EDI -S2-16 5-4 1250 0.61 0.92 25 72 16 60 0.30 1.40 0.222 6.32 NL, 6B = 1.84 6-1 1225 16 22 0.40 1.32 0.250 5.28 L, 6B = 1.84 5-1 1250 32 21 0.50 1 .41 0.179 7.88 L, 6B = 1.84 6-3 1225 40 45 0.52 1.41 0.142 10.10 L , 6B = 1-84 CT. CD Table 16 Effect of Applied Voltage (A*) on EDI-S3-12 and EDI-S3-13 1 2 3 4 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS [-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] AO [volt] nc [- ] I [ampere] BRINE D1ALYSATE ns [ - ] L = limit reached NL = limit not reached Sg/Sy = dead volumes XB [- ] XT [- ] 17 18 19 1-2 1130 1080 1175 1225 1.00 .90 .90 .90 .92 5 64 64 64 62 10 20 30 32 18 18 16 25 0.53 0.84 1 .06 1.20 1.20 1 .32 1 .34 1.41 0.700 0.578 0.473 0.526 1 .72 2.28 2.85 2.69 L L L L 6 7 11 • 8 22 9 1300 1270 1250 1260 1205 1135 1.00 .95 5 61 10 22 22 30 30 40 17 17 18 15 18 22 .62 1.00 .96 1.20 1.05 1.28 1 .31 1 .52 1 .52 1 .61 1 .61 1 .77 0.603 0.432 0.424 0.389 0.375 0.330 2.18 3.53 3.59 4.15 4.29 5.36 EDI-S3-13 L L L L L • L en CONCENTRATION [ - ] b ro !>> b) zu SEPARATION FACTOR [-] 118 0) = 1200 [ppm], 6 = 1.0 [-], v = 0.95 [cm/sec], x = 5.0 [sec] ure 4 0 . E f f e c t of 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 - c e n t r a t i o n s 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- I2 /# 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 [ - ] , v = 0.95 [cm/sec], T = 5.0 [sec] F i g u r e 4 1 . E f f e c t of a p p l i e d v o l t a g e on f i n a l s e P ^ a + < 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 . E D l - i o - . z / #17 1 8 , 1 9 , 1 - 2 and ED I-S3-I3/#6,7,I I , 8 ,22 , 9 . 120 reservoir concentration, and r e f l e c t s the changes in stack resistance due to p a r t i a l removal of solute from the ED c e l l . The r i s e of the current with A$ is accelerated as the brine concentration stagnates between 32 and 40 [V]. 3. Large improvements were recorded for pause time operations on the second and t h i r d stack version of the f i r s t ED c e l l (see Tables 15 and 16). The influence of the applied poten- t i a l (A$) on f i n a l reservoir concentrations and f i n a l separa- tion factor of the groups in Table 16 are shown in Figures * 40 and 41 r e s p e c t i v e l y . The f i n a l current consumption i n - creased less than proportional to the applied p o t e n t i a l . This confirms the concept of an overall resistance increase within the stack for enhanced separation. 5.3.3 Effect of pause time. The influence of equal pause times (T) at the beginning of each half cycle was studied on the second and t h i r d stack versions. Table 17, 18, and 19 summarize the operating parameters and the f i n a l conditions reached in these experi- ments, and Figures 42 , 43 and 44 d i r e c t l y display the e f f e c t of the pause time on f i n a l separation factors and f i n a l reservoir concentrations for several groups of experiments. * The abscissa is the applied potential per number of flow channels. This reduced potential allows comparison between stacks containing d i f f e r e n t numbers of flow channels. 121 The results show that the separation is improved for prolonged pause times, and that better separation is always accompanied by reduced current consumption. There is some indication that the f i n a l separations w i l l eventually reach l i m i t i n g levels set by the amount of internal mixing, - and the combined influences of molecular d i f f u s i o n , DONNAN equili b r i u m , and capacity of the sorption membranes. Figure 45 shows the transient of the top reservoir concentration for EDI - S3 - 12/#6-0. The i n i t i a l part of the curve is a fine example of the exponential decay predicted by the model in * Section 3.3.1. However, after twenty cycles the curve begins to asymptotically approach a f i n i t e l i m i t set by dispersive effects which are discussed in Section 5.3.8. The real time transients of the reservoir concentra- tions for the EDI - S3 - 13 group (see Table 19) are shown in Figure 46. Final conditions are reached after approximately 15 [min] in a l l experiments. The break in the transients of the top reservoir concentration disappears as the pause time is lengthened and the solution in the bottom reservoir accumu- lates more and more of the total solute. This model does not account for the mass transfer during displacement, which happened in the experiment due to the continuous application of the e l e c t r i c potential (A$). Since the displaced volume (6) was small and the velo c i t y of displacement was larg e , the ra t i o of pause time to residence time was also large. Sections 5.3.4 and 5.3.5 demonstrate that the material transferred during displacement contributes very l i t t l e to the separation under such conditions. Table 17 Effect of Pause Time (x) on EDI-S2-15 and EDI-S2-16 1 2 3 4 5 6 7 8 5 10 U 12 13 D U N w n CONCENTR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT M r* T f l l T Pi ( I T T A M SEPARATION REMARKS K U H li U • INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED NO. TOTAL CONCENTRATION FACTOR # BRINE DIALYSATE Co 6 • V T T A * nc I X T ns L = l i m i t r e a c h e d [-] [ppm] [-] B r NL = l i m i t no t r e a c h e d [cm/sec] [sec] [sec] [volt] [ -] [ampere] [ -] [- ] [ - ] 6g/6y =• dead v o l u m e s 11 960 1 .00 2.33 5 32 32 14 1.25 1 .29 0.631 2.05 L 12-0 940 - 5 32 10 1.25 1 .31 0.623 2.10 L 28-3 1070 5 32 18 • 1.30 1 .28 0.644 1 .99 L 27 1090 15 52 10 0.96 1 .46 0.537 2.72 L 28-2 1070 15 52 11 1.00 1.45 0.540 2.69 NL 33 1150 15 52 11 0.90 1.33 0.517 2.70 L EDI-S2-16 8-0 1240 0.61 0.92 0 22 32 30 1.41 1.10 0.714 1 .54 L 3-0 1175 15 52 14 0.70 1 .88 0.341 5.52 NL 3-1 1175 25 72 20 0.60 2.04 0.274 7.46 L 4 1220 25 72 14 0.70 2.11 0.278 7.58 L 7 1250 0.61 0.92 0 22 40 50 1 .50 1.11 0.567 1 .96 L, 6 B  - 1.84 6-2 1225 15 52 38 0.63 1 .43 0.196 7.05 L, <S B  = 1 .84 6-3 1225 25 72 45 0.52 1.41 0.142 10.10 L, 6 B  = 1.84 ro ro Table 18 Effect of Pause Time (T) on EDI-S3-12 1 2 3 n 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE DIALYSATE L = NL = 6 B /6 T  = l i m i t r e a c h e d l i m i t n o t r e a c h e d dead vo 1 times # C-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] [volt] nc [- ] I [ampere] [ - ] X T [- ] ns [- ] 1-1 1-2 1-3 8 1225 1225 1225 1270 1.00 0.92 0 5 15 20 52 62 82 93 32 18 25 30 10 1.35 1.20 1.00 0.95 1.18 1.41 1 .56 1.64 0.705 . 0.526 0.411 0.376 1 .67 2.69 3.89 4.36 L L L L 24 18 21 22 23 1170 1080 1230 1200 1200 1.00 0.90 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 0.703 0.578 0.508 0.486 0.469 1 .62 2.28 2.73 3.04 3.23 L L L L L 9-0 9-1 9-2 9-3 4800 . 1.00 0.92 0 5 10 15 53 63 73 83 16 5 10 20 35 3.10 3.00 2.70 2.30 — 0.922 0.89 8 0.636 0.545 — L NL NL NL ro ro Table 19 Effect of Pause Time (T) on EDI-S3-13 1 2 3 4 5 6 7 8 : 9 10 11 12 13 RUM NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS # C-] BRINE DIALYSATE L = limit reached NL = limit not reached 6g/5-p = dead volumes Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] AO [volt] nc [ -] I [ampere] X B [ -] X T [ "] ns [- ] 14 11 7 12 2 13 1 14 1045 1250 1270 1285 1250 1205 1240 1125 1.00 0.95 0.6 5 5 10 10 20 20 30 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 L L L L L L L L 24 16 25 1260 1275 1250 0.50 1.40 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 27 26 1260 1260 0.50 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 30 31 18 1280 1300 1180 0.50 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 F i g u r e 4 2 . E f f e c t of pause t ime (x) on s e p a r a t i o n f a c t o r f o r second and t h i r d s t a c k e x p e r i m e n t s . UJ N> -) -+» » \ Q) -+> — =*fc -+ CD — N> — O — J> O -+ J> >• 3 • — CO o 00 -t> M O "O — -ID) - c ro -4 co ro 3- CD N T 4 UJ CL — 3 D) CO CD 3 -4 Q. 0) O O 3 m TT 0 -+> — CD — 1 X 3 W D 01 UJ CD — I I • -J UJ 3 CD \ CD CO =* 3 ro h -i o co < - • O <• m — l o o v — O — I 3 ro co o - Ul CD ro i 3 i — =**: -(•> m « . M O ) - * — 4-, n -t, J> - -4 CD • — O O 00-1-4 ro -+. o — o -h * i ro "o M 4 0) ZT cz ro — co UJ -i CD CL DJ -4 3 CO —• O. -4 3 0) CD m n — H i ro ^ CO x Ul "d o I CD 3 — -I UJ — • -+> \ 3 — % CD 3 — 3D) O H - — — 1/1 — . co — CD v. XJ ~ j m oj — O I D) ro i -4 •• co — ro UJ o — | 3 UJ ro 125 F i g u r e 45. D ia 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 of ED I-S3-I2/#6-0. 126 F i g u r e 46 . E f f e c t of pause t ime (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 [sec] 400 1 1200 __l 1600 _ J _ _ Q r » BRINE 6= ^8 DIALYSATE L E G E N D RUN S Y M B O L Z [ s e c ] 21 O 0.6 32 A 1 0 Co - 1250 [ppm], 6 = 0.5 [ - ] , v =1.85 [cm/sec], A $ = 2 2 [V] F i g u r e 4 7 . 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 f o r t h i r d s t a c k e x p e r i m e n t s . E D I — S 3 — I 3 / # 2 I , 3 2 . 128 Figure 47 contrasts the concentration transients of standard parametric pumping operation (no-pause) with pause operation (x = 10 [sec]) under otherwise i d e n t i c a l con- d i t i o n s . The l a t t e r are p a r t i c u l a r l y favourable for the pause operation because they combine small displaced volume (6 = 0.5), fast displacement (v = 1.85 [cm/sec]), and moderate applied potential (A* = 12.5 [V]). The l a s t group of Table 19 contains experiments with unequal pause times. In particular,, the brine producing half cycle was shortened, since the current consumption during these periods became usually very small (see the electrogram in Figure 35). The pause times for these part cycles were halved without s i g n i f i c a n t effects on the f i n a l conditions. 5.3.4 Effect of s u p e r f i c i a l v e l o c i t y . The s u p e r f i c i a l v e l o c i t y (v) was varied for groups of experiments on a l l three stack versions. Operating par- ameters and f i n a l conditions are compiled in Table 20, 21 and 22 for f i r s t , second and t h i r d stack, respectively. The effect 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 reservoir concen- trations and f i n a l separation factors i s graphically displayed in Figure 48 and 49, respectively, for the groups of Table 22. Figures 50 and 51 show the real time transients of the reser- voir concentrations of these groups. 129 The results are quite d i f f e r e n t depending on the value of the pause time, and may be summarized as follows. 1. No-pause operation. Final separation is consider- ably improved for slow v e l o c i t i e s of displace- ment. The improvement in separation is accompanied by reduced current consumption. This agrees with the models presented in Chapter 3. If the cycle period is prolonged by reducing the flow r a t e , the residence time w i l l be propor- t i o n a l l y increased, but at the same time the rate of mass transfer w i l l be decreased accord- ing to some power function of v. Generally, in packed beds and in flow channels with turbu- lence promoters, the steady state transfer c o e f f i c i e n t s have been found to be proportional to v n , where n = 0.5 to 0.8 (see e.g. Hicks, 1968; Yamane, 1969b; and Kitamoto et al. , 1971). It may be expected that the influence of the residence time is prevailing in the case of unsteady-state mass transfer in the el e c t r o - d i a l y s i s system, too. The experiments with no-pause time confirm this t r a i n of thoughts, and Figure 50 i l l u s t r a t e s 130 that a reduction in velo c i t y leads to concen- tration transients which resemble those of pause operations. 2. Operations with moderate pause time. Final separation is v i r t u a l l y independent of s u p e r f i c i a l v e l o c i t y . The rate at which this l i m i t is approached may be improved by i n - creasing the v e l o c i t y . The increase in rate is at the expense of a higher current con- sumpti on. The improved rate of separation is in complete accord with the concept that the pause time is the true cause of a successful c y c l i c operation of the e l e c t r o d i a l y s i s process, at least in the parameter regime investigated. The pause periods of the c y c l i c operation seem to be responsible for a certain amount of separation which is inde- pendent of the v e l o c i t y . The displacement may, therefore, be implemented as fast as mechanically feas i b l e or economically • des i r a ble. Table 20 Effect of Superficial Velocity (v) on EDI-S1-8 1 2 3 4 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE DIALYSATE L = NL = V 5 T = -• l i m i t r e a c h e d = l i m i t no t r e a c h e d = dead v o l u m e s # [-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] AO [volt] nc [ - ] I [ampere] X B [ - ] X T [- ] ns [- ] 2 5 3 4 1050 1090 1040 1050 1.10 1.21 1.21 1.77 2.33 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 7 8 9 1090 1090 1080 1 .73 1.21 1.66 2.62 - 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 36 35 32 33 34 700 700 720 710 700 1.00 0.65 1.21 1.77 2.33 2.89 — 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 Effect of Superficial Velocity (v) on EDI-S2-16, EDI-S3-12 2 1 4 5 6 7 8 9 IG 11 12 13 RU;i NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS 9 C-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] A* [ v o l t ] nc [-] I [ampere] BRINE DIALYSATE ns [- ] L = l i m i t reached NL » l i m i t not reached 5g/6T >» dead volumes X B [ -] X T [- ] 5-2 5-1 5-3 1250 0.61 0.49 0.92 1 .77 25 111 72 67 32 40 21 50 0.40 0.50 0.45 1 .46 1 .41 1 .44 0.158 0.179 0.176 9.24 7.88 8.18 L, 6 B = 1.84 L, 6 B = 1.84 NL, 6 B = 1.84 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 EDI-S3-12 L, 6 B = 2.06 NL, 6 B = 2.06 L, 6 B = 2.06 CO CD Table 22 Effect of Superficial Velocity (v) on EDI-S3-13 1 2 3 k 5 6 7 S O 10 11 n 13 C0(ICEi'<TR. VOLUME VELOCITY PAUSE CYCLE VOLTAGE CYCLE CURRENT SEPARATION REMARKS INITIAL DISPLACED SUPERFICIAL TIME PERIOD APPLIED no. TOTAL CONCENTRATION FACTOR 6 P. 1 !J £ DIALYSATE i S Co 6 V T T A* nc I ns L  m  11 ra 11 rc&cncd [-3 C-] [co/sec] 6 r NL " limit rot reached [PP=I] [sec] [sec] [volt] C-3 [ampere] [ -3 [- 3 [-•] fig/Sy " dead vo1urr.es 15 1265 0.50 0.50 10 68 22 28 0.62 2.14 0.239 8.93 NL 3 1228 0.95 45 36 0.77 2.08 0.278 7.46 NL 15 1275 1 .40 37 34 0.80 2.08 0.248 8.35 NL 25 1250 1 .40 37 35 0.81 2.14 0.228 9 .35 NL 17 1270 1 .85 33 45 0.79 2.10 0.242 8.71 L 32 1290 1 .85 33 30 0.81 2.15 0.230 9.33 L 18 1180 2.36 30 45 0.70 2.12 0.240 8.83 L 31 1300 2.36 30 30 0.80 2.16 0.233 9.27 L 20 1185 0.50 0.27 0.6 90 22 45 0.60 1 .72 0.350 4.91 L '19 1195 0.50 50 50 0.87 1 .26 0.540 2.33 L 21 1205 1.85 14 160 1.69 0.90 0.856 1 .05 NL F i g u r e 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 pause and no -pause o p e r a t i o n . 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 . F i g u r e 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 o p e r a - t i o n . 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 . F i g u r e 5 0 . 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 f o r no -pause o p e r a t i o n . EDI —S3—I 3. 134 F i g u r e 5 1 . 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 f o r pause o p e r a t i o n . E D I - S 3 - I 3 . 135 5.3.5 Effect of displaced volume. The displaced volume ( 6 ) was varied in three groups of experiments. Table 23 summarizes operating parameters and f i n a l conditions. Figures 52 and 53 show, r e s p e c t i v e l y , the eff e c t of displaced volume on f i n a l reservoir concentrations and f i n a l separation factor for the group of experiments with 10 seconds pause time. The real time transients of top and bottom reservoir concentrations are i l l u s t r a t e d in Figure 54 for the same group of experiments. Figure 55 shows analoguous real time transients for two experiments with no pause time. Reducing the displaced volume ( 6 ) has the following e f f e c t s . 1. No -pause o p e r a t i o n : The f i n a l s e p a r a t i o n i s r e d u c e d . Most of t he r e d u c t i o n o c c u r s d u r i n g the f i r s t c y c l e . The f i n a l c u r r e n t i s u n a f f e c t e d . 2 . Pause o p e r a t i o n (x -~ 10 L~sec]): The f i n a l s e p a r a t i o n i s i m p r o v e d . The r a t e of s e p a r a t i o n i s s l owed down. The f i n a l c u r r e n t i s r e d u c e d . These results agree with a model in which f i n i t e mass transfer rates are c o n t r o l l i n g , and may be explained as follows using this model. I . For no -pause o p e r a t i o n : Most of t he s e p a r a t i o n o c c u r s d u r i n g t he f i r s t c y c l e as shown in C h a p t e r 3. The 136 l o c a l e f f l u e n t c o n c e n t r a t i o n d u r i n g t he f i r s t h a l f c y c l e d e - c r e a s e s mono ton i ca I Iy w i t h t i m e . The ave rage e f f l u e n t c o n - c e n t r a t i o n t h e r e f o r e a l s o d e c r e a s e s mono ton i ca I Iy w i t h t i m e . R e d u c i n g t he d i s p l a c e d volume s h o r t e n s t he d u r a t i o n of each h a l f c y c l e . T h u s , the mean v a l u e of the e f f l u e n t c o n c e n t r a - t i o n d u r i n g the f i r s t h a l f c y c l e i s r e d u c e d . S i n c e t he o v e r - a l l c o n c e n t r a t i o n changes are g e n e r a l l y s m a l l , t he c u r r e n t consump t i on i s u n a f f e c t e d . 2. For pause o p e r a t i o n : Two l i m i t i n g s i t u a t i o n s may be c o n s i d e r e d . When the d i s p l a c e m e n t i s v e r y l a r g e the c y c l e t ime i n c r e a s e s and t he r a t i o of pause t ime t o c y c l e t i m e app roaches z e r o . The i n i t i a l i n f l u e n c e of the pause t ime on the e f f l u e n t c o n c e n t r a t i o n , t h e r e f o r e , g r a d u a l l y d i s a p p e a r s . The o t h e r l i m i t i s o b t a i n e d as the d i s p l a c e d volume a p p r o a c h e s z e r o . In t h i s case the sys tem would be e x p e c t e d t o respond more and more as t o a pure pause o p e r a t i o n , i . e . e x p o n e n t i a l decay of the d i a l y s a t e c o n c e n t r a t i o n . The r e s u l t s c o n f i r m t h i s t r e n d . The l i m i t e d f i n a l c o n c e n t r a t i o n s f o r f i n i t e d i s - p l a c e m e n t a re caused by d i s p e r s i o n e f f e c t s : When the d i s p l a c e d volume i s l a r g e t he c o n c e n t r a t i o n f r o n t emerges f rom the s t a c k . The p a r t of t he f r o n t t h a t emerges becomes c o m p l e t e l y d i s p e r s e d in t he w e l l mixed d i a l y s a t e r e s e r v o i r . S i m i l a r l y , d u r i n g r e v e r s e d f l o w , low c o n c e n t r a t e d s o l u t i o n b r e a k s t h rough i n t o the w e l l mixed b r i n e r e s e r v o i r and becomes c o m p l e t e l y d i s p e r s e d Table 23 Effect of Displaced Volume {&) on EDI-S1-8, EDI-S2-15 and EDI-S3-13 1 / 3 l\ 5 6 7 8 3 10 11 "P 33 RUN i"iO. COi'lCil iiTR. Iii IT IAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE HO. ClTxP.EiYT TOTAL CO liCEKT RATIO!! SEPARATION FACTOR REMARKS 6RWJE CtALYSATE L • lJr.lt reached UL " l i c i t not reached Sg/S-j. •> deed votu.-r.es t [-] Co 6 C-] V [cm/sec] T [sec] T [sec] AO [volt] nc [-3 I [ampere] [-3 *T C- 3 ns [-3 14 15-0 40 2 5 7 1020 1020 760 1050 1090 1090 1.00 1 .00 1.00 1.10 1.10 1 .73 1.21 50.2 50.2 50.2 53.3 53.3 84.3 6 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 0.983 0.997 0.995 0.999 1 .000 0.938 0.99 0.97 0.99 1 .00 1 .01 1 .09 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 C o = 1250 [ppm], v = 0.95 [cm/sec], T - 10 [ s e c ] , A4> = 22 [V] F i g u re 52 . 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 . E D I - S 3 - I 3 / # 4 , 3 , 2 , 1 2 , 5 . 0-1 , , . 0 . 5 . 1 15 DISPLACED VOLUME [-] CO CO F i gure 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 . E D I - S 3 - I 3 / # 4 , 3 , 2 , 1 2 , 5 . .2 F i g u r e 54. E f f e c t of 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 EDI-S2-I5/#29 , <f = l.54 M = 1050 [ppm], v = 0.88 [cm/sec] , x = 0.0 [ s e c ] , 40 F i g u r e 55. E f f e c t of d i s p l a c e d volume (6) on r e a l t i m e t r a n s i e n t s f o r no -pause o p e r a t i o n . 141 t h e r e i n . When the d i s p l a c e d volume i s s m a l l enough t o p r e - ven t b r e a k t h r o u g h , d i s p e r s i o n i s r e s t r i c t e d t o m i x i n g , b y - p a s s i n g and c h a n n e l i n g in t he s t a c k . These i n t e r n a l d i s p e r - s i o n e f f e c t s a re a lways p r e s e n t and w i l l be d i s c u s s e d in d e t a i I under 5 . 3 . 7 . 5.3.6 Effect of dead volumes. The experiments with variable dead volumes*in the end reservoirs are grouped in Table 24. These r e s u l t s , together with the real time transients of the product con- centrations for the f i r s t group (see Figure 56) and the t h i r d group (see Figure 57) of Table 24 may be summarized as follows: 1. The p r e s e n c e of dead vo lumes does not i n f l u e n c e the f i n a l s e p a r a t i o n f a c t o r . 2. If t he dead vo lumes a re equa l the f i n a l p r o - duc t c o n c e n t r a t i o n s a re unchanged . The r a t e of s e p a r a t i o n i s s l owed down, howeve r , as the dead vo lumes in each r e s e r v o i r a re i n c r e a s e d . 3. E x p e r i m e n t s w i t h equa l t o t a l dead volume but unequa l dead vo lumes in the r e s e r v o i r s show t h a t the f i n a l c o n c e n t r a t i o n s a re lower and the c u r r e n t consump t i on much s m a l l e r when 6 D > 6-,-, and v i c e v e r s a when 6 D < 6 T . T h i s D I b I c o n f i r m s the c o n c e p t of a d e v e l o p i n g c o n c e n t r a t i o n wave , wh ich - Or excess volumes. Table 24 Effect of Dead Volumes (« R/« T) on EDI-S2-15, EDI-S3-12 and EDI-S3-13 1 2 3 Q. , 5 6 7 8 9 10 11 12 : 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE D1ALYSATE L NL V 6 T = limit reached = limit not reached = dead volumes # [-] Co [ppm] <5 [-] V [cm/sec] T [sec] T [sec] [volt] nc [ - ] I [ampere] X B [- ] X T [- ] ns C - ] . 19 1020 0.5 1.70 7 28 40 14 1.40 1 .72 0.529 3.24- L, 6 B L, 6 B NL, 6 B = 0.0, 6 T  = 0.0 20 1040 15 1.30 1 .50 0.463 3.24 = 0.5, 6 T  = 0.0 21 9 80 22 1.35 1 .54 0.568 2.72 = 1.0, 6T = 1.0 • EDI-S3-12 2-0 1220 0.59 0.92 15 62 32 20 0.90 2.04 0.265 7.72 L -1 25 82 25 0.70 2.21 0.217 10.20 L -2 0.49 25 111 31 0.62 2.32 0.175 13.28 L 3-0 1230 0.92 15 62 16 0.80 1.37 0.194 7.06 L. 6 B = 1 .75, 5 T  " 0.0 -1 25 82 24 0.60 1 .43 0.136 10.52 L, 6 B = 1 .75, 5 T  = 0.0 -2 0.49 25 111 30 0.50 1.47 0.110 13.40 L, 6 8 - 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 [-], v = 1.70 [cm/sec], T = 7.0 [ s e c ] , A$ = 40 F i g u r e 56 . E f f e c t of dead vo lumes ( 6 g / 6 y ) on c o n c e n t r a t i o n t r a n s i e n t s . E D I - S 2 - I 5 . 144 F i g u r e 5 7 . E f f e c t of dead vo lumes (<5 R /6 T ) on c o n c e n t r a t i o n t r a n s i e n t s . ED I -S3- I 3. 145 i s pushed out i n t o the b r i n e r e s e r v o i r . A l a r g e r e s e r v o i r volume means a s m a l l c o n c e n t r a t i o n c h a n g e . S i n c e t he f r o n t r e e n t e r s the e I e c t r o d i a I y z e r d u r i n g e v e r y odd h a l f c y c l e , the c u r r e n t consumpt i on i s s m a l l e r i f t he f r o n t has a low c o n c e n t r a t i o n . 4 . A " s a l t i n g f a c t o r " may be d e f i n e d as the amount of s o l u t e added to t he b r i n e p r o d u c t and a " d e s a l t i n g f a c t o r " as the amount removed from the d i a l y s a t e p r o d u c t . The f a c t o r s a re n o r m a l i z e d w i t h r e s p e c t t o the i n i t i a l s o l u t e c o n c e n t r a - t i o n and the d i s p l a c e d v o l u m e : ( c T - c 0 ) ( 5 v 0 + Vj) c„ <5v0 * f " ,1 x T - 1 = [ x T - 1 i 1 + - J ( c B - c 0 ) ( 6 v 0 + v B ) c 0 <5v0 r <5 ^ x_ - 1 1 + B-GO 1 5 J A p l o t of t h e s e f a c t o r s as f u n c t i o n s of r e a l t ime shows t h a t the d e v i c e c o u l d be used as a c o n t i n u o u s s o l u t e pump. If t he r e s e r v o i r vo lumes were i n f i n i t e and we I I m i x e d , a c o n s t a n t amount of s a l t would be removed f rom one r e s e r v o i r and added to the o p p o s i t e one d u r i n g each c y c l e (see F i g u r e 5 8 ) . 146 F i g u r e 5 8 . E f f e c t of dead vo lumes ( 6 R / 6 T ) on s a l t i n g f a c t o r t r a n s i e n t s . E D I - S 2 - I 5 . 147 5.3.7 Effect of i n i t i a l concentration. The i n i t i a l concentration (c 0 ) was changed from ~ 1250 ppm to ~ 5000 ppm NaCl/H 2 0 in three groups of experi- ments (see Table 25). At the same time the concentration of the rinse solution was increased from 2,000 to 10,000 ppm in order to maintain the same r a t i o between the resistances of the two s o l u t i o n s . In a l l cases the higher c 0  had a retarding e f f e c t on the transients (see Figure 59,60,61). The l i m i t i n g separation factor was reduced for the EDI-S3-13 runs which had shorter pause times and a smaller applied voltage than the EDI-S2-12 group. The reasons for this behaviour are: 1. The h i g h e r c o n c e n t r a t i o n r e q u i r e s p r o p o r t i o n a l l y l a r g e r mass t r a n s f e r r a t e s t o a c h i e v e t he same s e p a r a t i o n . The o v e r p o t e n t i a Is wh ich a re n e c e s s a r y t o m a i n t a i n the i n - c r e a s e d e l e c t r o d e c u r r e n t d e n s i t i e s reduce t he e f f e c t i v e s t a c k v o l t a g e (see a l s o F i g u r e 3 6 ) . 2 . The s p e c i f i c c o n d u c t i v i t y of ion exchange mem- b ranes i s more o r l e s s i ndependen t of t he s o l u t i o n c o n c e n t r a - t i o n in the range i n v e s t i g a t e d (D 'A I e s s a n d r o , 1971) . T h i s c o n s t a n t r e s i s t a n c e te rm reduces the c u r r e n t d e n s i t y (compare w i t h e q u a t i o n ( 2 3 ) , S e c t i o n 3 . 3 . If the pause times are long or the voltage high, these effects are less pronounced (Figure 59). Table 25 Effect of I n i t i a l Concentration (c 0 ) on EDI-S3-12 and EDI-S3-13 1 2 5 ' H 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE DIALYSATE L - NL " V 5 x " limit reached limit not reached dead volumes # C-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] AS [volt] nc C-3 I [ampere] X B [- ] X T [-3 ns [- ] 4-0 -1 10-0 -1 1245 4680 0.59 0.92 15 25 15 25 62 82 62 82 32 16 23 15 20 0.90 0.70 3.20 2.80 2.03 2.17 2.00 0.259 0.218 0.273 0.205 7.85 9.97 10.00 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 i g 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 (co ) on 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 s . EDI—S3—12. S - 1.0 [-], v - 0.95 [ c m / s e c ] ' , T - 5.0 [ s e c ] . At - 10 [V] Figure 60. Effect of In i t ia l concentration ( C o ) on concentration t rans ien ts . EOI-S3-I3. 151 5.3.8 Effect of internal flow d i s t r i b u t i o n and axial dispersion. The flow d i s t r i b u t i o n and longitudinal mixing were measured using a step response method. Flow systems with axial dispersion have often been simulated by models based on d i s t r i b u t i o n s of residence times. The concept has been discussed by Danckwerts (1953) who also measured the axial d i f f u s i o n c o e f f i c i e n t by a method which involved the response function of a system to a step change in concentration at the i n l e t . Kramers and Alberda (1953) proposed a mixing c e l l model and measured the axial mixing by a frequency response method, which was also employed by McHenry and Wilhelm (1957). Aris (1957) showed that the mixing c e l l model and the con- tinuous model using an axial d i f f u s i o n c o e f f i c i e n t coincide for more than about 25 mixing c e l l s . The mixing c e l l concept was further advanced by Young (1957), Epstein (1958), and many others. Young (1957), in p a r t i c u l a r , gives an a n a l y t i c a l expression for the ef f l u e n t response of m equal mixing tanks to a step change of the i n l e t concentration. The equation may be modified to account for the inherent dead volumes of the f i r s t ED c e l l design. If these dead volumes are assumed to be well mixed, the normalized effluent concentration is a function of time according to equation (32). 1 52 x = - L T + - m r r - l m exp (32) + e x p ( - mt) I ^ f / - j=o  J ' 1 + ( m - j ) m+l-j (m+ 1 - j ) r — m where v„ - v. 2 v. v„ - v. inherent dead volume v, = active stack void volume a T  _. t Q v a t = time Q = flow rate x =  c  "  C l c o ~  c  1 i n i t i a l concentration C j = f i n a l concentration This function was evaluated using a d i g i t a l computer. The results for r = 0.04 are shown in Figure 62. The upper part of the diagram i l l u s t r a t e s the function (32), the lower part is the f i r s t derivative of (32) w.r.t. time t . Figure 63 shows the dependence of the maximum slope (x) on m for two values of r . The curves go through a minimum at m = 2, 153 increase monotonically for larger m, and approach a f i n i t e l i m i t which is given by Hm\(k)\ = ^ m - H » According to equation (32) the response should be independent of the flow r a t e , the di r e c t i o n of flow, and whether the step is an increase or a decrease in concentration. + The results for tests on the f i r s t and t h i r d stack versions are presented in Table 26 to 29. The sign of the slopes indicates response to an increasing (+) or a decreasing & (-) step, t is the time at which the maximum slope occurred, _* and x the corresponding concentration. The response curves of the second stack versions could not be evaluated in the same way, since pronounced by- passing was observed. Typical response curves are sketched in Figure 64. The concentration in experiments with EDI-S2-15 decreased very soon after the step had entered the stack, passed through a plateau, and descended f i n a l l y toward the i n l e t concentration. Another spacer plus sorption membrane added to the same pack almost eliminated the plateau, but the shape of the curve was not of the F type predicted by a + The step response method may be u t i l i z e d to measure the void volume between the conductivity detectors. 154 mixing c e l l model. This may be due to a nonuniform flow d i s t r i b u t i o n . The spacer screens consisted of a single layer of p l a s t i c netting cut p a r a l l e l to one strand. The solution flowed therefore in many p a r a l l e l groves rather than through a random packing. The flow rates through the groves varied because the spacing was not controlled accurately. The response curves of EDI-S1-8 stack most closely resembled those predicted by a mixing c e l l model (see Table 26). The mean value of the maximum slopes was k = 1.27 and _* occurred after t = 0.965. This corresponded to 10 e f f e c t i v e mixing stages (see Figure 63). The t h i r d stack was tested with 12 and 13 spacers plus sorption membranes. By-passing (or channelling) was noticed for the former and is manifested in the high value _* of t = 1.11. The addition of another unit increased the value of the slope from x = 1.26 to x = 1.42 and shortened — * + the time lapse to t = 1.01. The e f f e c t i v e number of mixing stages is m = 12 or 13, see Figure 63. The t h i r d stack comprised the same spacer screens as the f i r s t one. The increased m is a result of the more f l e x i b l e capacity c e l l s . They d i s t r i b u t e the areal compres- sion from the electrode end frames more evenly than the A l l values averaged. 155 F i g u r e 6 2 . 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 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_ in f eed 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 ) ) of 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 15 20 NUMBER OF MIXING STAGES m [-} r 25 T 30 F i g u r e 63. Maximum s l o p e (x) v s . number of m i x i n g s t a g e s (m) EDI-S2-I5 EDI-S2-I6 F i g u r e 64. Step response of second s t a c k v e r s i o n s ( s c h e m a t i c ) . 157 T a b l e 26 Step Response E x p e r i m e n t s on E D I - S I - 8 Flow Rate 0 Hem 3 / s ee l D i sp 1 acement Up/Down L-I Maximum S I ope • X T i me t * Concen t r a t i on —* X L-l 14. 1 14. 1 14.1 20 . 8 2 0 . 8 Dow n Up Down Up Down - 1 .27 - 1 .26 + 1.21 - 1 . 38 -1 .24 0 . 856 0 .960 1 . 1 1 1 .03 1 .02 0 . 5 17 0 .564 0 . 423 0 .549 0 .570 T a b l e 27 S tep Response E x p e r i m e n t s on E D I - S 3 - I 2 Runs #1-14 Flow Rate Q C c m V s e c H D i sp1aceme nt Up/Down L-l Max i mum S 1 ope • x L-l T i me t * L-l Concen t r a t i on X * L-l 14.1 14.1 20 . 8 2 0 . 8 Up Down Up Down - 1 . 1 2 + 1.07 - 1 .09 + 1.14 1.19 1.21 1 . 20 1.17 - 1 58 T a b l e 28 S t e p R e s p o n s e E x p e r i m e n t s on E D I - S 3 - I 2 Runs #15-24 Flo w R a t e D i s p 1 a c e m e n t Maximum S l o p e • X C - ] T i me C o n c e n t r a t i on Q Up/Dow n T * X* [ c m 3 / s e c ] L>: c-: n-D 7.03 Dow n -1.174 1 . 1 8 1 0 .592 7.03 Up +1.210 1 .031 0 .469 7.03 Dow n + 1 .057 1 . 1 59 0 . 426 7.03 Up -1.210 1 .054 0.570 14.1 Dow n - 1 . 148 1 .204 0.497 14.1 Up +1.275 1 .024 0.518 14.1 Down +1.123 1 . 1 48 0.5 12 14.1 Up -1.131 1.125 0.5 12 28.3 Down - 1 .349 1.155 0.520 28.3 Up +1.336 1 .058 0.568 2 8 . 3 Dow n +1.227 1 .005 0 .600 2 8 . 3 Up - 1 .249 1.155 0.506 T a b l e 29 S t e p R e s p o n s e E x p e r i m e n t s on E D I - S 3 - I 3 Flow R a t e Q Ccm V s e c ] D i s p 1 a c e m e n t Up/Down L> ] Maximum S 1 ope • X [-3 T i me t * L>: C o n c e n t r a t i on X* C - D 7.03 Down -1.259 1 .049 .604 7.03 Up +1.416 0 .940 .336 7.03 Down +1.326 1 .005 .393 7.03 Up -1 .351 1 .020 . 596 14.1 Down -1.468 1 .086 .59 1 14.1 Up +1.598 0.978 . 388 14.1 Down +1.327 1 .032 . 340 14. 1 Up - 1 .427 1 .032 .639 2 8 . 3 Dow n -1.429 0 .974 .623 28.3 Up +1.743 0 .967 .45 1 28.3 Dow n +1.374 1 .029 .371 28.3 Up - 1 .324 1 .008 .640 1 59 combination of sturdy frames and strengthened spacers present in the f i r s t stack. A comparison of the separation runs on the stacks shows that the versions with less axial d i s p e r s i o n , by-passing, channelling, etc. achieved much better separation f a c t o r s , see Figures 40,41; 44,45; 65. The internal dispersion effects are, therefore, mainly responsible for the f i n i t e separation l i m i t of pause operations. Figure 51 presents further evidence in favour of this interpretation of the r e s u l t s , since the l i m i t i n g conditions are shown to be independent of the flow rate. 5.3.9 Effect of external mixing in brine r e s e r v o i r . Three pairs of experiments were performed on the EDI-S3-12 stack to study the ef f e c t of mixing of the effl u x concentration on the performance. The f i r s t run of each pair had the usual complete mixing of both reservoirs but in the second run the brinereservoir was replaced by a c o i l of 5/16" I.D. TYGON tubing (8 m long). Consequently, the mixing was reduced. The improvement in separation as well as in power requirement is evident from the results l i s t e d in Table 30. The pair #7-#7a shows the least improvement. This is due to the small displaced volume as explained subsequently. A q u a l i t a t i v e picture of the concentration p r o f i l e s in the reservoirs and in the ED c e l l at l i m i t i n g conditions 160 F i g u r e 6 5 . 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 is presented in Figure 66, which is s i m i l a r l y constructed to Figures 11 and 14 , Section 3.2.1. It is assumed that the end reservoirs are well mixed after each displacement, and that the total void volume of the stack is displaced. The lines are followed through one cycle according to the operat- i ng sequence : (0) t = 0 The ED ee l I and the b r i n e tank 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 i s empty . D i a l y z a t i o n s t a r t s , f l ow i s s t o p p e d . (1) t = T At the end of the f i r s t pause t ime the 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 i s lowered ( i i ) t = ^- The w e l l mixed b r i n e volume i s f l ow ed t h r o u g h the ED c e l l p r o d u c i n g t he d i a l y s a t e p r o f i l e ( i i ) wh ich i s then w e l l m i x e d , i . e . t he d i a g o n a l l y shaded a r e a s above and below ( i i i ) a re e q u a l . ( i i i ) + = 5 " + T T n e • n i"e r n a I p r o f i l e i s r a i s e d f rom ( i i ) t o ( i i i ) d u r i n g the e n r i c h i n g pause t i m e . ( i v ) t = T The e f f l u e n t p r o f i l e ( i v ) in the b r i n e tank i s w e l l mixed t o y i e l d ( v ) . S i n c e 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 the ED c e l l , and the loop i s t h u s c l o s e d . The cross shaded areas indicate the current requirements to maintain the steady periodic concentration f r o n t s . The dotted lines (with arrows) show the concentration changes of some volume elements as they reciprocate in the module. Several effects may be explained by this model: Table 30 Effect of End Mixing on EDI-S3-12 1 2 3 4 5 6 7 8 9 10 11 12 73 RUIi iiO. COi.'CtfiTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE fin. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS § C-3 Co [ppm3 S C-3 V [cm/sec] T £sec] T [sec] AO [volt] nc C - l I [ 2 t i p e r e 3 8 R1; J E DIALYSATE ns [ - 3 L a limit reached NL « limit not reached a dead volumes x 3 C - 3 X T C - 3 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 F i g u r e 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 i n 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 p a u s e 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 m i x e d end r e s e r v o i r s . 164 1. A p r e s e r v a t i o n of the e f f l u x p r o f i l e r e n d e r s the i n t e r n a l d i s p e r s i o n l e s s e f f e c t i v e because the g r a d i e n t s a re s m o o t h e r , and t he b r e a k t h r o u g h o c c u r s l a t e r . 2. S m a l l e r d i s p l a c e d vo lumes a l s o p r e v e n t a break- t h rough of the f r o n t s . 3. C u r r e n t consump t i on i s reduced i f t he h i g h con- c e n t r a t i o n peaks r e s i d e o n l y f o r s h o r t t ime p e r i o d s i n the a c t i v e ED c e l l , i . e . i f t he e f f l u x peaks a re p r e s e r v e d . 5.3.10 Effect of capacity c e l l thickness. F i r s t and t h i r d stacks only d i f f e r in the construc- tion of the capacity c e l l s . However, a comparison of experi- ments under s i m i l a r operating conditions 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 f l ow c h a n n e l s changed when the f rames were removed f rom the c a p a c i t y c e l l s . T h i s i s p r o b a b l y a r e s u l t of t he i n c r e a s e d f l e x i b i l i t y of t he ceI I s . 2. The i n t e r n a l m i x i n g of t he s t a c k s was found t o be d i f f e r e n t ( see S e c t i o n 5.3.8). The basis of comparison is therefore open to di s - cussion. Only two pairs of experiments were selected from 165 the data, see Table 31. (Note, the applied voltage is reduced to the potential per spacer plus sorption membrane.) The runs were no-pause operations and were therefore rate l i m i t e d . The actual value of the concentrations and of the separation factors should not be stressed because of the reasons given above. One fact emerges nevertheless quite c l e a r l y : A reduction in the thickness of the capacity c e l l core increases the current consumption. This is quite important for a pause operation. The high rates of mass transfer increase the separation. Unfortunately, the importance of the pause times was not realized at the time experiments on the f i r s t stack were performed. 5.3.11 Effect of thickness and hydrodynamic properties of spacer screens. The second and t h i r d stack versions were designed to study the e f f e c t of the spacer screen. The channel thickness was believed to have a s i m i l a r e f f e c t to the thickness of the capacity c e l l . The step response measurements, Section 5.3.9, revealed however, that the internal dispersion is caused by d i f f e r e n t mechanisms for the two stacks, and i t becomes very d i f f i c u l t to define a common basis for the runs. Table 31 Effect of Capacity Cell Thickness on Electrodlalyzer No. 1 1 2 3 4 5 6 7 8 9 10 11 12 13 RUN NO. CONCENTR. INITIAL VOLUME DISPLACED VELOCITY SUPERFICIAL PAUSE TIME CYCLE PERIOD VOLTAGE APPLIED CYCLE NO. CURRENT TOTAL CONCENTRATION SEPARATION FACTOR REMARKS BRINE 01ALYSATE L = 1 tmi t reached NL <* limit not reached 6Q/6J = dead volumes C-] Co [ppm] 6 [-] V [cm/sec] T [sec] T [sec] [volt] nc [ -] I [ampere] X B [ - ] X T [- ] ns '[- 3 42 1-0 750 1225 1.00 1.00 1.21 1.33 - 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 36 24 700 1170 1.00 1 .00 0.65 0.90 - 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 the pH of process and rinse solutions was checked before and after each run. However, no s i g n i f i c a n t changes occurred. The systematic pH sampling was, therefore, discontinued. Occasional l a t e r checks, e s p e c i a l l y for experi- ments with long pause times and high voltages, disclosed that the pH of the process solution becomes more a c i d i c , but the rinse stream remains e s s e n t i a l l y unchanged. Typical results are l i s t e d below in Table 32. Table 32 pH-Changes for some EDI-S3-I2 Runs \ . pH PROCESS RINSE Run before after before after 1 1 6.3 5.6 7.6 7.7 1 3 6.4 6.35 7.5 7.6 1 4 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 current e f f i c i e n c y . The change in current e f f i c i e n c y during the course of a number of experiments are l i s t e d in Table C . l . l to C.1 .66 168 (see Appendix C . l ) . Depending on the v a l u e s o f the o p e r a t i n g parameters (see T a b l e s 9 t o 13), the c u r r e n t e f f i c i e n c i e s s t a r t between 25 and 50% f o r the f i r s t c y c l e , d e c r e a s e q u i t e r a p i d l y f o r subsequent c y c l e s , and tend t o ze r o as the s e p a r a - t i o n approaches s t e a d y , p e r i o d i c s t a t e . When t h e s e r e s u l t s are compared to c o n v e n t i o n a l , s t e a d y - s t a t e e l e c t r o d i a l y s i s , b a t c h 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 ) Most c o n t i n u o u s systems r e q u i r e s e v e r a l s t a g e s f o r d e m i n e r a I i z i n g the feed water t o the s p e c i f i e d p r o d u c t c o n c e n t r a t i o n . The e l e c t r o d i a l y s i s t e s t bed i n Webster, South D a k o t a , o p e r a t e d w i t h f o u r s t a g e s , and d e m i n e r a I i z e d 1600 ppm b r a c k i s h water t o 350 ppm p r o d u c t ( C a l v i t and S l o a n , 1965). The average c u r r e n t e f f i c i e n c y per s t a g e d ecreased from 92 t o 83$ as the stream became p r o g r e s s i v e l y d e p l e t e d . The o v e r a l l c u r r e n t e f f i c i e n c y f o r removing 19% iota I d i s - s o l v e d s o l i d s was 90$. ( i i ) The c u r r e n t e f f i c i e n c y i n a bat c h r e c i r c u l a - t i o n system d e c r e a s e s in time s i m i l a r t o the p r e s e n t c y c l i c e l e c t r o d i a l y s i s p r o c e s s . M a n d e r s l o o t (1964) reporte'd c u r r e n t e f f i c i e n c i e s of 85% f o r 94$ d e m i n e r a I i z a t i o n of 0.05N aqueous sodium c h l o r i d e s o l u t i o n . The reasons f o r much s m a l l e r c u r r e n t e f f i c i e n c i e s f o r ex p e r i m e n t s on the f i r s t ED c e l l are as f o l l o w s : 169 N a t u r e of the c y c l i c o p e r a t i o n : Suppose the current density is uniform and constant, one void volume is d i s p l a c e d , the membranes are perfectly s e l e c t i v e , and the pause time is zero. In this case, the effluent concentration during the f i r s t half cycle decreases l i n e a r l y in time. The current e f f i c i e n c y is exactly 50% since only one-half of the demin- eral i z e d solution volume is recovered, the other half remains in the e l e c t r o d i a l y z e r . According to this model the current e f f i c i e n c i e s of subsequent cycles are zero, since the efflue n t concentrations remain unchanged. In r e a l i t y , when operating with pause times, the current e f f i c i e n c i e s decreased gradually as functions of the number of cycles. The displaced volume in most of these experiments was less than a void volume. This reduced the e f f i c i e n c y , as did the presence of dead volumes. It was also found that the current consumption of the stack during displacement contributed very l i t t l e to the separation. It may be more e f f i c i e n t to disconnect the e l e c t r i c power during displacements, or displace at very high flow rates. I n te rnaI m i x i n g results in dispersion of the con- centration f r o n t . These dispersive effects must be balanced by e l e c t r i c energy input at steady periodic conditions, i . e . a larger and larger amount of the current is consumed to main- tain the concentration wave as the separation progresses. 170 C h a n n e l i n g a n d / o r unequal f l ow d i s t r i b u t i o n causes nearly stagnant volume elements which become p e r i o d i c a l l y demineralized and enriched but never emerge as products. 5.3.14 Comment on true l i m i t s and r e p r o d u c i b i l i t y of batch runs. The operating conditions were changed during the course of some experiments in such a manner as to test the uniqueness of the f i n a l concentrations, see the tables in Appendix C.l for runs: #28 (EDI-S2-I6) #5,6,8,9 (EDI-S2-I6) Figure 67 shows the separation factor (ns) as a function of the number of cycles (nc) for runs #27 and #28 on EDI-S2-15, and Figure 68 is a s i m i l a r plot for runs #8 and #9 on ED I- S2-16. Both figures demonstrate the r e p r o d u c i b i l i t y and the uniqueness of the f i n a l separation f a c t o r . The r e p r o d u c i b i l i t y of the results was tested f r e - quently throughout the experimental program and was found to be excellent in most cases. Tables 14, 15, 16, 17, 19, 22, 23 and Figures 40, 41, 43, 44, 46 may be referred to for a comparison of replicate experiments. However, the flow dis- t r i b u t i o n and consequently the internal dispersion appeared to be d i f f e r e n t when the same stack was dismantled and reassembled. This influenced the r e p r o d u c i b i l i t y of separation runs. F i g u r e 6 7 . 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 . F i g u r e 68. Un iqueness 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 . ro 173 5.4 Summary of Experience Gained on F i r s t ED Cell The experimental work on the f i r s t ED c e l l had to meet several objectives: a) Se rve 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 the 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 to an e I e c t r o s o r p t i o n s t a c k . b) T e s t p r e d i c t i o n s of s e v e r a l s i m p l e t h e o r e t i c a l m o d e l s . c) S c r e e n o p e r a t i n g and d e s i g n p a r a m e t e r s t o d e t e r m i n e t h e i r r e l a t i v e i m p o r t a n c e f o r such c y c l i c o p e r a t i o n s . d) P r o v i d e a b a s i s f o r u n d e r s t a n d i n g the phenomena i n v o l v e d in o r d e r t o d e s i g n an improved s t a c k and ED modu le . This program was successfully completed and produced the following r e s u l t s : 1. 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 c o n - t r o l l e d by the r a t e s of mass t r a n s f e r a c r o s s the membranes. E q u i l i b r i u m p l a y s o n l y a s u b o r d i n a t e r o l e . 2. The s t a n d a r d p a r a m e t r i c pumping o p e r a t i o n i s u s u a l l y ve ry i n e f f i c i e n t under t h e s e c i r c u m s t a n c e s . The con c e n t r a t i o n t r a n s i e n t s show t h a t t he main s e p a r a t i o n o c c u r s d u r i n g the f i r s t c y c l e , e x c e p t f o r l a r g e a p p l i e d v o l t a g e s an o r long r e s i d e n c e t i m e s . 174 3. The a d d i t i o n of a f l ow pause a f t e r each p o l a r i t y r e v e r s a l improves the s e p a r a t i o n f a c t o r s by more than an o r d e r of m a g n i t u d e . 4. I n t e r n a l d i s p e r s i o n e f f e c t s wh ich i n c l u d e c h a n n e l l i n g and b y - p a s s i n g a re t he main cause f o r l i m i t e d s e p a r a t i o n in a pause o p e r a t i o n . 5. The a p p l i e d v o l t a g e i s the second i m p o r t a n t p a r a m e t e r . 6. The c u r r e n t c o n s u m p t i o n i n c r e a s e s a p p r o x i m a t e l y p r o p o r t i o n a l w i t h the i n i t i a l c o n c e n t r a t i o n a t o t h e r w i s e i d e n t i c a l c o n d i t i o n s . However , t he s e p a r a t i o n f a c t o r i s found t o be s lowed down and a p p r o a c h e s lower l i m i t i n g v a l u e s . 7. Dead vo lumes in t he end r e s e r v o i r s d e l a y the s e p a r a t i o n but do not a l t e r the l i m i t . 8. The d i s p l a c e d volume may be reduced t o o b t a i n b e t t e r f i n a l s e p a r a t i o n . 9. E x t e r n a l m i x i n g reduces s e p a r a t i o n when i n t e r n a l m i x i n g i s a l s o p r e s e n t . 10. The s u p e r f i c i a l v e l o c i t y has a m inor e f f e c t on s e p a r a t i o n in pause o p e r a t i o n s and may be i n c r e a s e d to a l e v e l s e t by pumps o r m e c h a n i c a l l i m i t a t i o n s . 175 5.5 The Second E l e c t r o d i a l y s i s Cell (EDII) The results on the f i r s t ED c e l l were used to design a second module. The following objectives were pursued: 1. D e s i g n and p roduce new s t a c k pack wh ich - i s s i m p l e i n 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 a c c u r a t e l y , - i s r e l i a b l e in p e r f o r m a n c e , - i s r e a d i l y assemb led and d i s a s s e m b l e d , - a l l o w s the pack s i z e t o be i n c r e a s e d o r d e c r e a s e d , - may be used w i t h t h e same a u x i l a r y equ ipment as the p r e v i o u s c e l l , - might be eas i l y scaled up. 2. D e s i g n and p roduce new e l e c t r o d e end f rames f o r t h i s s t a c k p a c k . 3. I n v e s t i g a t e e f f e c t of c h a n n e l l e n g t h . 4. S tudy e f f e c t of o p e r a t i o n p a r a m e t e r s : - pause t i me - i n i t i a l c o n c e n t r a t i o n - d i s p I a c e d voIume - a p p l i e d v o I t a g e - f Iow r a t e 176 5. T e s t t h e o r e t i c a l model based on c o n s t a n t u n i f o r m r a t e of mass t r a n s f e r . The equipment and i t s features are described in Chapter 4.3, and the manufacturing procedures for stack units and electrode end frames are contained in Appendix A.3. The length of the flow channels was adjustable since the new ED module consisted of eight i d e n t i c a l stages. The stages were always connected in series h y d r a u l i c a l l y and usually in p a r a l l e l e l e c t r i c a l l y . In four runs an e l e c t r i c series connection was used to analyze uniform rates of mass tr a n s f e r . In the l a t t e r case the D.C. power supply was oper- ated in constant current mode, whereas the regular test series c a l l e d for the more r e a l i s t i c constant voltage mode. These tests were performed on the f u l l number of stages. 5.5.1 Data reduction and presentation. The data obtained on the second ED module d i f f e r e d from those on the f i r s t one as explained in Section 5.2. This required d i f f e r e n t processing and modified presentation of the r e s u l t s . The form of the main survey table is retained to allow easier comparison with the results on the f i r s t ED c e l l . Table 13 l i s t s operating parameters and conditions at the end of experiments #6 to #53 in chronological order. It can be 177 seen that the f i n a l dialysate concentrations are often well below 1% of the i n i t i a l concentration. The conductometric measuring system is not very accurate in this regime, see Section 4.2.6, and the table should, therefore, be used with caution. Consequently, i t is more meaningful to compare rates of separation instead of f i n a l conditions. For this purpose the concentration changes and the separation factors were evaluated as functions of time. The corresponding tables are described and contained in Appendix C.2. From these evaluation tables transients of the separation factors are plotted in semi-1ogarithmic diagrams for groups of experiments in which a single parameter was varied. The i n i t i a l rates of separation were determined from the graphs by drawing a straight li n e through the i n i t i a l points. The i n i t i a l rate of separation was approximated by d log(ns) _  a  _  c p n s t j ( 3 3 ) Equation (33) is also the d e f i n i t i o n of the rate constant(a) which w i l l be reported subsequently. Complementary to the t r a n s i e n t s , additional i n f o r - mation was compiled and grouped in tables for i n i t i a l and f i n a l total current consumption, applied electrode voltage, mean current, and mean probe voltage in each stage (see 178 Appendix C.2). Operating conditions, i n i t i a l rate of separa- tion ( a ) , i n i t i a l and f i n a l total current, and the pH changes in process and rinse streams of the same groups of experiments are presented in tables 35 to ^9 • 5.5.2 Effect of channel length. The e f f e c t of the channel length on internal dis- persion was analyzed using the step response method previously described. The result i n g F-diagrams did not suggest channell- ing or by-passing, and the fronts were much sharper than for the previous ED c e l l . The results of these response tests are l i s t e d in Table 33, and the dimensionless slope x of the curves is graphically displayed in Figure 69 as a function of the number of stages ( L ) . One can see that the shape of the curve is s i m i l a r to the theoretical one shown in Figure 63. However, the graphical determination of the slopes i s not only rather i n - accurate but also subject to a certain personal touch. The f i n i t e l i m i t of the slope for increasing number of stages is caused by mixing in the interconnecting pipes and in the l i q u i d d i s t r i b u t i o n systems in the stack. For more than 6 stages this l i m i t is nearly reached. In other words, the flow in the channels may be considered to be piston flow, although there is s t i l l internal mixing in the system. (A 179 F i gu re 69 . D imens ion 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 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 s t a g e s . 180 Table 33 Results of Step-Response Tests on Second ED Ce l l s Stages i n Series C - 3 F1ow Rate 0 C c m 3 / s e c 3 T i me La£_se t * C s e c 3 Maximum Slope X C - 3 Concent rat i on — * X C - 3 #i 2.81 3.60 37. 1 29.3 -1.95 -2.03 0 .62 0.66 #5 & #6 7.40 21.7 -2.56 0.58 #7 & #8 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 to #8 6.4 14.1 84.0 37.7 -3.50 -4.07 0.62 0.55 value of x ~ 4.0 corresponds to at least 50 e f f e c t i v e mixing stages.) The e f f e c t of the channel length on separation was studied in three sets of experiments with 2, 4, 6, and 8 stages connected in series (see Table 34). The separation factor transients of the three groups are displayed in Figure 70, 73, and 75; the concentration transients of two groups are i l l u s t r a t e d in Figure 71 and 76, and the local current consumptions at steady periodic conditions are plotted in 181 Figures 72, 74 and 77. F i n a l l y , in Figure 78, the rate con- stant (a) is plotted against the number of stages (MS). The results are: 1. A f o u r f o l d i n c r e a s e in channe l l e n g t h ( f r om 31 cm t o 124 cm) r a i s e s t h e f i n a l s e p a r a t i o n by a t l e a s t one o r d e r of m a g n i t u d e . 2 . The i n i t i a l t r a n s i e n t of t he s e p a r a t i o n f a c t o r may be a p p r o x i m a t e d by an e x p o n e n t i a l f u n c t i o n 3 . The r a t e c o n s t a n t (a) i n c r e a s e s w i t h the channe l l e n g t h but appea rs t o go t h r o u g h a maximum. Fo r t h e h igh c o n c e n t r a t i o n group t h i s maximum i s a t abou t MS = 5 . The maxima f o r t h e o t h e r g roups l i e between MS = 6 and MS = 8. 4 . If t h e pause t i m e i s i n c r e a s e d ( f rom T = 0.6 t o 10 CsecH) t he r a t e c o n s t a n t v s . MS c u r v e seems t o be d i s p l a c e d t o a h i g h e r l e v e l w i t h no change in s h a p e . 5 . The 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 t he no -pause group show an improvement in s e p a r a t i o n w i t h MS, wh ich has some s i m i l a r i t y t o the e f f e c t of t he pause t i m e on the f i r s t ED ceI I. :e. IS 2. dc^s not" e*i<s t~ 183 6 . For t h e l a s t group in T a b l e 34 the r a t e c o n s t a n t appea rs t o be l e s s a f f e c t e d by MS. T h i s group has a h i g h c o n c e n t r a t i o n and a pause t ime of T = 10 U s e e ] . The d i a l y s a t e t r a n s i e n t s in F i g u r e 76 show p o i n t s of i n f l e c t i o n , i . e . t he amount o f s o l u t e wh ich i s removed f rom t h i s p r o d u c t s t r eam i s a l m o s t c o n s t a n t per c y c l e and does not d e c r e a s e a t a c o n - s t a n t r a t e as p r e d i c t e d by t he model in S e c t i o n 3 . 3 . I t i s b e l i e v e d t h a t t h i s b e h a v i o u r r e f l e c t s a s a t u r a t i o n e f f e c t of t he s o r p t i o n membranes wh ich i s o n l y n o t i c e a b l e a t h i g h e r c o n - c e n t r a t i o n s ( f o r f u r t h e r d e t a i l s see S e c t i o n 5 . 5 . 3 ) . 7 . The i n i t i a l t o t a l c u r r e n t i s a p p r o x i m a t e l y p r o p o r t i o n a l t o the channe l l e n g t h , as e x p e c t e d . The r a t i o of f i n a l t o i n i t i a l c u r r e n t does not depend on MS f o r t he g roups w i t h x = 10 U s e e ] , but d e c r e a s e s in the no -pause c a s e . 8 . The l o c a l c u r r e n t d i s t r i b u t i o n s r e f l e c t the i n - t e r n a l mass t r a n s f e r r a t e s ave raged o v e r one c y c l e a t s t e a d y p e r i o d i c c o n d i t i o n s . They i l l u s t r a t e t h e c o n c e n t r a t i o n g r a d i e n t s wh ich have d e v e l o p e d . A l a r g e d i f f e r e n c e i n c u r r e n t c o n s u m p t i o n between f i r s t and l a s t s t a g e i s i d e n t i c a l t o I a rge sepa r a t i o n . 9 . Most of the c u r r e n t d i s t r i b u t i o n c u r v e s l e v e l o f f t oward t he bot tom end ( s t a g e No. 8 ) . T h i s r e f l e c t s the Table 34 Effect of Channel Length (MS) on Second Electrodialyzer » NO. OF PAUSE INITIAL APPLIED DISPL. SUPERF. INITIAL TOTAL CURRENT RINSE pH RUN NO. STAGES TIME CONC. VOLTAGE VOLUME VELOCITY RATE PROCESS pH INITIAL FI NAL INITIAL FINAL INITIAL FI NAL # MS x C n AO $ y [-] [-] [sec] [ppm] [volt] [-] [cm/sec] [min~ l ] [ampere] [ampere] [-1 [-] [-] [-] 48 2 0.6 1250 10 2/3 5.4 .028 0.88 1.16 5.2 6.3 5.7 5.8 46 4 1240 .064 1.44 1 .48 5.7 6.0 5.2 5.1 43 6 1210 .077 2.60 2.16 5.9 5.5 5.1 5.1 25 8 1250 .077 3.00 2.40 6.1 5.3 6.0 5.8 47 2 10 1225 10 2/3 5.4 .109 0.70 0.36 6.5 6.3 5.4 5.6 45 4 1275 .140 1 .32 0.68 6.4 6.0 5.4 5.2 44 6 1225 .170 1 .88 1 .04 • 6.5 5.0 5.2 5.6 26 8 1290 .170 2.70 1.40 6.1 5.5 5.8 5.7 35a 8 1220 .170 2.60 1 .40 7.2 6.3 5.2 5.6 19 2 10 4900 10 2/3 5.4 .087 1.45 0.88 _ _ _ 20 2 5500 .087 1.75 . 1 .00 5.3 5.2 5.9 6.1 18 4 5300 .096 3.00 1 .72 _ _ 17 6 5100 .096 4.70 2.60 - _ 6 8 5700 .086 5.60 3.20 - - - - , CO F i g u r e 7 0 . E f f e c t of c h a n n e l l e n g t h f a c t o r t r a n s i e n t s . (MS) on s e p a r a t i o n F i g u r e 7 1 . E f f e c t of channe l l e n g t h (MS) on c o n c e n t r a t i o n t r a n s i e n t s . 187 F i g u r e 7 2 . E f f e c t of channe l l eng th (MS) on c u r r e n t d i s t r i b ut i o n . F i g u r e 73. E f f e c t of channe l l eng th (MS) 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 . 189 F i g u r e 7 4 . E f f e c t of channe l l eng th (MS) on c u r r e n t d i s t r i b u t i o n . F i g u r e 75. E f f e c t of channe l l e n g t h (MS) 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 . F i g u r e 7 6 . E f f e c t of channe l l e n g t h (MS) on c o n c e n t r a t i o n t r a n s i e n t s . 192 F i g u r e 77. E f f e c t of channe l l eng th (MS) on c u r r e n t d i s t r i b u t i o n . 0.2 F i g u r e 7 8 . E f f e c t of channe l l e n g t h (MS) on i n i t i a l r a t e of sepa r a t i on ( a ) . 194 p e n e t r a t i o n of t h e c o n c e n t r a t i o n f r o n t i n t o the ED s t a c k d u r i n g a comp le te c y c l e . A l s o , one can see t h a t the more s u c c e s s f u l s e p a r a t i o n r e s u l t s in l a r g e r c u r r e n t s a t the bot tom end of t he c h a n n e l , a l t h o u g h some of t h i s e f f e c t i s o b s c u r e d by the f a c t t h a t the runs w i t h s h o r t e r c h a n n e l s have l e s s s e g m e n t s . 5.3.3 Effect of pause time. The pause time (T) was varied for three sets of experiments from 0.6 to 20 seconds, see Table 35. The separ- ation factor transients are displayed in Figure 79, 82, 84; concentration transients in Figure 80, 85; current d i s t r i b u - tions in Figure 81, 82; and the e f f e c t of pause time on the rate constant (a) is plotted in Figure 86. The results are summarized as follows: 1. An i n c r e a s e in the pause t ime f rom 0 . 6 t o 10 C s e c 3 enhances the r a t e of s e p a r a t i o n as w e l l as t he f i n a l s e p a r a t i o n . The f i n a l d i a l y s a t e c o n c e n t r a t i o n i s a t l e a s t an o r d e r of magn i tude s m a l l e r t han in no -pause o p e r a t i o n . 2 . I n c r e a s i n g of t he pause t ime beyond 10 CsecH improves the s e p a r a t i o n f o r h i g h c o n c e n t r a t i o n ( c 0 ) bu t not f o r a low o n e . T h i s c o i n c i d e s w i t h a s a t u r a t i o n e f f e c t , see F i g u r e 8 0 , wh ich i s s i m i l a r t o t he one o b s e r v e d i n the p r e - v i o u s s e c t i o n (see a l s o b e l o w ) . 195 3. The c u r r e n t d i s t r i b u t i o n s i l l u s t r a t e t he t r a n - s i t i o n f rom no -pause t o pause o p e r a t i o n . The c o n c e n t r a t i o n f r o n t i s g r a d u a l l y b u i l t - u p and pushed ou t of the e l e c t r o - d i a l y z e r as x i n c r e a s e s . 4. The i n i t i a l , t o t a l c u r r e n t d e c r e a s e s w i t h i n - c r e a s i n g x f o r t he groups w i t h low c o n c e n t r a t i o n s , bu t rema ins f a i r l y c o n s t a n t f o r h i g h c o n c e n t r a t i o n r u n s . The f i n a l c u r r e n t a lways d e c r e a s e s w i t h x . Note on the saturation e f f e c t : If the concentration is la r g e , the capacity c e l l core experiences drastic concentration changes. During absorption the increase may reach the level where the membranes become flooded with solute from within and gradually loose t h e i r ion s e l e c t i v i t y . At the same time, the membrane pol a r i z a t i o n is much larger and the rate of absorption further reduced. A certain amount of solute has to be accumulated in the capacity c e l l s before the e f f e c t becomes apparent. At low i n i t i a l concentrations the mass transfer rates are probably more controlled by high solution resistance than by po l a r i z a t i o n e f f e c t s . Therefore the transients of the dialysate products decrease exponentially. Table 35 Effect of Pause Time (T) on Second Electrodialyzer D 11; I K. A MO. OF PAUSE INITIAL APPLIED DISPL. SUPERF. INITIAL TOTAL CURRENT RINSE pH RUN NO. STAGES TIME COKC. VOLTAGE VOLUME VELOCITY RATE PROCESS pH # MS x Cn A* SL INITIAL FINAL INITIAL Fl NAL INITIAL Fl NAL [-] C-3 [sec] v rj [ppm] [volt] [-] [cm/sec] [mln- 1 ] [ampere] [ampere] [-] j [-] [-] [-3 7 8 0.6 5700 10 2/3 5.4 .018 5.6 5.6 _ _ _ _ 8 5 5300 .063 5.6 3.8 - - - - 10 5 4800 .063 5.1 4.1 5.7 5.7 5.6 6.5 6 10 5700 .086 5.6 3.2 - - - - 9 20 5400 .108 5.5 2.0 - - - - 25 8 0.6 1250 10 2/3 5.4 .077 '3.0 2.4 6.1 5.3 6.0 5.8 28 5 1280 .120 2.7 1 .8 - - - - 26 10 1290 .170 2.6 1.4 6.1 5.5 5.8 5.7 35a 10 1220 .170 2.7 1 .4 7.2 6.3 5.2 5.6 27 20 1250 .170 2.2 1 .1 6.2 5.6 5.4 5.3 31 8 0.6 1220 15 2/3 5.4 .148 4.4 3.4 6.1 4.7 5.7 6.1 32 5 1240 .229 4.2 2.8 6.2 5.3 6.0 6.0 33 10 1200 .255 3.5 2.0 6.4 5.7 5.7 5.6 34 20 1280 .229 3.0 1.8 6.9 6.0 6.3 6.8 F i g u re 7 9 . E f f e c t of pause t r a n s i e n t s . t i me (T) on s e p a r a t i o n f a c t o r F i g u r e 80 . E f f e c t of pause t ime (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 . 199 F i g u r e 8 1 . E f f e c t of pause t ime (T ) on c u r r e n t d i s t r i b u t i o n . F i g u re 82 . E f f e c t of pause t ime (x) on s e p a r a t i o n f a c t o r t rans i e n t s . 201 F i g u r e 8 3 . E f f e c t of pause t ime (x) on c u r r e n t d i s t r i b u t i o n . 202 F i g u r e 84 . E f f e c t of pause t ime (T ) 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 . 203 F i g u re 8 5 . E f f e c t of pause t ime ( T ) on c o n c e n t r a t i o n t r a n s i e n t s . 204 F i g u r e 86. E f f e c t of pause t ime (x) on i n i t i a l r a t e of sepa r a t ion ( a ) . 205 5.5.4 Effect of applied voltage. The applied electrode voltage (A$) was increased in 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 in Table 36, and the transients of the separation factors are shown in Figures 87, 88, 89. The results are: 1. I n i t i a l r a t e and f i n a l s e p a r a t i o n a re much improved by an i n c r e a s e of t h e a p p l i e d p o t e n t i a l . 2 . The r a t e c o n s t a n t i s a p p r o x i m a t e l y a l i n e a r f u n c t i o n of A $ , see F i g u r e 9 0 . From t h e o r e t i c a l c o n s i d e r a t i o n s t he f u n c t i o n has t o pass t h rough the p o i n t o f o r i g i n . 3 . The c u r r e n t consump t i on (bo th i n i t i a l and f i n a l ) i s p r o p o r t i o n a l t o A $ . 4 . The h igh c o n c e n t r a t i o n runs show the same s a t u - r a t i o n e f f e c t wh ich was n o t i c e d p r e v i o u s l y . 5.5.5 Effect of i n i t i a l concentration. The i n i t i a l concentration (c 0 ) was increased for three groups of experiments from 1200 to 2500 to 5700 ppm NaCI. The rinse solution remained at 10,000 ppm NaCI. Table Table 36 Effect of Applied Voltage (A*) on Second Electrodialyzer RUN NO. NO. OF STAGES PAUSE TIKE INITIAL CONC. APPLIED VOLTAGE DISPL. VOLUME SUPERF. VELOCITY INITIAL RATE TOTAL CURRENT PROCESS pK RINSE pH a MS Co AO 6 • • a INITIAL FINAL IH 1T1 AL FINAL INITIAL FINAL V T V [-3 C-3 [sec3 [ppm] [volt3 C-3 [cm/sec] [rain-1} [ampere3 [arcpere3 C-3 [-3 C-3 C-3 35 28 32 8 5 1220 1280 1240 5 10 15 2/3 5.4 .072 .120 .229 1 .3 2.7 4.2 1.1 1.8 2.8 7.2 6.2 7.0 5.3 6.5 6.0 5.2 6.0 36 26 35a 33 8 10 1250 1290 1220 1200 5 10 10 15 2/3 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 13 8 10 16 8 5 5100 5300 4800 5500 5 10 10 15 2/3 5.4 .030 .063 .063 .116 2.2 5.6 5.1 9.5 2.0 3.8 4.1 6.9 5.7 5.7 6.0 5.9 5.7 5.5 5.7 5.6 5.4 6.5 6.5 5.4 r o o c n 207 F i g u r e 8 7 . E f f e c t of a p p l i e d v o l t a g e (A$) on s e p a r a t i o n f a c t o r t r a n s i e n t s . 208 Fi gure 8 8 . E f f e c t of a p p l i e d v o l t a g e (A$) 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 . 209 F i g u r e 8 9 . E f f e c t of a p p l i e d v o l t a g e (AO) 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 . 210 F i g u r e 9 0 . 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 r a t e of sep a r a t ion ( a ) . 211 37 summarizes the operating conditions and Figure 91, 92 and 93 display the separation factor t r a n s i e n t s . The results are: 1. The i n i t i a l r a t e of s e p a r a t i o n i s reduced by h i g h e r i n i t i a l c o n c e n t r a t i o n s (see a l s o F i g u r e 96 and f o o t - note on page 2 2 1 ) • 2. The f i n a l s e p a r a t i o n f a c t o r shows no c o n s i s t e n t r e s u l t s . In F i g u r e 91 the f i n a l ns seems t o be independent of c 0 ; the same a p p l i e s f o r h i g h e s t and lowest c o n c e n t r a t i o n s in F i g u r e 92. The c 0  = 2500 ppm curve r i s e s t o a much h i g h e r l e v e l than the o t h e r two i n F i g u r e 92 but reaches a lower l i m i t i n g v a l u e i n F i g u r e 93. The c 0  = 1200 ppm t r a n s i e n t i n c r e a s e s w e l l beyond I O 3 . I t was s t r e s s e d e a r l i e r t h a t the c o n d u c t i v i t y meter i s not a c t u a l l y c a p a b l e of m o n i t o r i n g such l a r g e c o n c e n t r a t i o n changes. I t i s b e l i e v e d , however, t h a t the a c c u r a c y of the meters i s not the p r i m a r y cause of t h i s s c a t t e r . 3. Both i n i t i a l and f i n a l c u r r e n t i n c r e a s e w i t h c 0  , but at a d e c r e a s i n g r a t e . 5.5.6 Effect of displaced volume. The displaced volume (6) was varied for three sets of experiments and increased from 1/4 to 2/3 to 1 total void Table 37 Effect of I n i t i a l Concentration (c 0 ) on Second Electrodialyzer F.Ui. ?«G. iiO. OF STAGES PAUSE TIHE INITIAL CQKC. APPLIED VOLTAGE CISPL. VOLUME SUPERF. VELOCITY INITIAL RATE TOTAL CURRENT PROCESS r>; RINSE pK i [-3 MS C-3 T [sec] C 9 [ppn] [ v o l t ] <5 C - ] V [cm/sec] a [ m l n - 1 ] INITIAL F111 At. INITIAL Ft HAL INITIAL FINAL [atapore] [srcpere] C - ] C - ] C - ] C - ] 27 22 9 8 20 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 26 35a 23 6 8 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 33 24 21 8 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 6.8 213 F i g u r e 9 1 . 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 . 214 F i g u r e 9 2 . 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 20 30 TIME [min] Fi gure 93. E f f e c t o f i n i t i a , c o n c e n t r a t i o n ( = . ) 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 . 216 volume, see Table 38. The separation factor transients are plotted in Figure 94, 95 and 96. The following findings have been extracted: 1. In a no -pause o p e r a t i o n , a t low c o n c e n t r a t i o n s , t he i n i t i a l r a t e i s l a r g e s t f o r 6 = I and d e c r e a s e s s l i g h t l y w i t h 6 , see F i g u r e 9 4 . The f i n a l s e p a r a t i o n i s s m a l l e r f o r l a r g e 6 ' s because of the b r e a k t h r o u g h of t he c o n c e n t r a t i o n f r o n t ( o r p a r t of i t ) . 2 . In pause o p e r a t i o n a t the same c o n d i t i o n s t h i s i n i t i a l e f f e c t d i s a p p e a r s more o r l e s s , see F i g u r e 9 5 . What rema ins i s the c o n t i n u e d r i s e of t h e t r a n s i e n t f o r 6 = 1 /4 , beyond the bounds of a c c u r a c y of the p r e s e n t m e a s u r i n g s y s t e m . 3 . For h i g h c o n c e n t r a t i o n s ( c 0 = 5500 ppm) the s a t u r a t i o n e f f e c t causes the t r a n s i e n t s t o r i s e f a s t e r f o r s m a l l 6 ' s than f o r l a r g e o n e s . The amount of s a l t t h a t i s r e d i s t r i b u t e d between s o l u t i o n and s o r p t i o n membranes i s a l m o s t c o n s t a n t per c y c l e . The c y c l e p e r i o d i s s m a l l i f 6 i s s m a l l . The r e a l t ime t r a n s i e n t s a r e , t h e r e f o r e , a c c e l e r a t e d . The f i n a l s e p a r a t i o n i s a l s o much s m a l l e r i f 6 i s l a r g e , b e c a u s e , a l t h o u g h the f r o n t does not b reak t h r o u g h , t h e sys tem has a c e r t a i n amount of i n t e r n a l d i s p e r s i o n . Table 38 Effect of Displaced Volume (6) on Second Electrodialyzer D I I M M f\ NO. OF PAUSE INITIAL APPLIED DISPL. SUPERF. INITIAL TOTAL CURRENT RUN NO. STAGES TIME CONC. VOLTAGE VOLUME VELOCITY RATE PROCESS pH RINSE pH # MS T Co v a IN IT IAL FINAL I N I T I A L F 1 NAL I N I T I A L F INAL [-] [-] [sec] [ppm] [volt] [-] [cm/sec] [mi n~*] [ampere] . [ampere] [-] [-] [-] [-] 41 8 0.6 1300 10 1/4 5.4 .057 3.6 3.4 6.1 5.8 5.3 5.3 25 1250 2/3 .077 3.0 2.4 6.1 5.3 6.0 5.8 30 1270 1 .091 3.0 2.6 - - 42 8 10 1175 10 1/4 5.4 .159 2.6 0.9 6.2 5.9 5.1 5.3 26 1290 2/3 .170 2.7 1.4 6.1 5.5 5.8 5.7 35a 1220 2/3 .170 2.6 • 1.4 7.2 6.3 5.2 5.6 29 1260 1 .170 2.7 1.8 - - - - 12 8 5 4300 10 1/4 5.4 .091 5.4 2.6 5.4 5.7 5.5 6.5 8 5300 2/3 .063 5.6 3.8 _ _ _ 10 4800 2/3 .063 5.1 4.1 5.7 5.7 5.6 6.5 11 5300 1 .046 5.5 4.6 6.2 6.3 6.8 6.7 218 219 F i g u r e 9 5 . E f f e c t of d i s p l a c e d volume ( 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 . 220 0 10 20 30 40 TIME [min] F i g u r e 96 . E f f e c t of d i s p l a c e d volume (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 . 221 4. The i n i t i a l c u r r e n t consumpt ion i s i n d e p e n d e n t of 6 e x c e p t f o r the no -pause g r o u p . The f i n a l c u r r e n t r e f l e c t s t h e amount of s e p a r a t i o n a t t he end of each r u n . 5.5.7 Effect of dead volumes. The dead volumes + were increased for a single pair of runs (#45 & #52, on 4 stages) to check findings from the f i r s t ED c e l l . The result is shown in Figure 97 in terms of the product concentration t r a n s i e n t s . One can see that the f i n a l separation is the same for both experiments, although the presence of 1/2 void volume in each end reservoirs slows down the rate at which the l i m i t is approached. 5.5.8 Effect of s u p e r f i c i a l v e l o c i t y . The flow rate of the process solution was altered in three groups of experiments, which are l i s t e d in Table 39 together with t h e i r operating conditions. Again, separation factor transients are diagrammatically shown in Figure 98 and * 99. The results are si m i l a r to those obtained on the f i r s t ED c e l l : Figure 98 contains results on no-pause experiments for high and low concentrations. The retarding influence of the i n i t i a l concentration is very clear from this graph. + 0r excess volumes in the end reservoirs. 222 F i g u r e 9 7 . E f f e c t of dead vo lumes ( 6 / 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 . Table 39 Effect of Superficial Velocity (v) on Second Electrodialyzer RUN NO. NO. OF STAGES PAUSE TIHE INITIAL CONC. APPLIED VOLTAGE DISPL. VOLUME SUPERF. VELOCITY INITIAL RATE TOTAL CURRENT PROCESS pH RINSE pH # [-3 MS C-3 T [sec3 Co [ppm] A* [volt] <5 [-] V [cm/sec] a [m1n- 1 ] INITIAL FINAL INITIAL FINAL INITIAL Fl NAL [ampere] [ampere] [-] [-] [-] [-3 37 38 25 8 0.6 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 39 40 26 35a 8 10 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 15 14 7 8 0.6 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 ro ro co 224 x = 0.60 [sec] 0 10 20 30 40 50 60 TIME [min] F i g u r e 9 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 (v) 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 . 225 F i g u r e 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 (v) 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 . 226 1. In c o n t i n u o u s d i s p l a c e m e n t mode ( n o - p a u s e ) s low d i s p l a c e m e n t improves t he r a t e as w e l l as the f i n a l s e p a r a t i o n f o r low c o n c e n t r a t i o n , and the c u r r e n t consump t i on i s s m a l l e r . At h i gh c o n c e n t r a t i o n s the i n i t i a l r a t e becomes e s s e n t i a l l y i ndependen t of t he v e l o c i t y v , bu t i s a l s o ve ry s m a l l . The c u r r e n t i s a l s o i ndependen t o f v . 2 . In pause o p e r a t i o n an i n c r e a s e of v r e s u l t s in a b e t t e r i n i t i a l p e r f o r m a n c e . The f i n a l s e p a r a t i o n f a c t o r does not depend on v . The i n i t i a l c u r r e n t c o n s u m p t i o n i s s m a l l e r f o r t he s low d i s p l a c e m e n t r u n . 5.5.9 Reproducibi1i ty. Several of the runs were repeated to test the re- p r o d u c i b i l i t y of the r e s u l t s . The following pairs may be compared (see Table 34, 35; Figure 82, 100, 101): #8 & #10 , #26 & #35a , #27 & #49 , #40 & #50 The i n i t i a l dialysate transient and a l l of the brine transient are generally extremely well reproduced. The f i n a l branch of the top product transient is subject to the limited accuracy of the conductometric measuring system. The f i n a l values of the dialysate concentrations are for most runs less than 3% F i g u r e 100. R e p r o d u c i b i l i t y of second s t a c k e x p e r i m e n t s . 228 F i g u re 10 1. R e p r o d u c i b i l i t y of second s t a c k e x p e r i m e n t s . 229 "of the i n i t i a l concentration. Small variations of the operat- ing conditions may influence the actual l i m i t reached. The following accuracies are estimated to apply to these parameters: F l o w r a t e Q : ±2 $ A p p l i e d v o l t a g e A$ : ±1 $ P a u s e t i m e s T : ±0.5% D i s p l a c e d v o l u m e <5 : ±0.5$ C o n c e n t r a t i o n s c T  , c R  : ±0.5$ 5.5.10 Comment on the material balance for the solute. A closed system requires conservation of the total mass in the system. The e l e c t r o d i a l y s i s process involves two l i q u i d streams which are separated by ion sel e c t i v e membranes. Solute or solvent w i l l permeate through the membranes, and solution may seep from one stream into the other through mechan- i c a l leaks. Any exchange of material would be detected either as volume or as concentration change of the two streams. Three situations have been considered to check the changes in the process stream. I. The s y s t e m was f i l l e d w i t h r i n s e and p r o c e s s s o l u t i o n s o f known v o l u m e s . The c o n c e n t r a t i o n o f t h e p r o c e s s s t r e a m was a l w a y s s m a I l e r t h a n t h e c o n c e n t r a t i o n o f t h e r i n s e 230 s t r e a m . The volume of t he p r o c e s s s o l u t i o n d e c r e a s e d s l i g h t l y when t h e sys tem was a l lowed t o s t a n d f o r s e v e r a l days w i t h no c i r c u l a t i o n o r a p p l i e d p o t e n t i a l . E v a p o r a t i o n may have caused some volume change and o s m o t i c wa te r t r a n s f e r was r e s p o n s i b l e f o r the r e m a i n d e r . The o s m o t i c wa te r t r a n s p o r t t h rough the • s e p a r a t i n g membranes f rom low t o h i gh c o n c e n t r a t i o n was accom- p a n i e d by s o l u t e f l u x in the o p p o s i t e d i r e c t i o n , s i n c e the p r o c e s s s t r e a m c o n c e n t r a t i o n i n c r e a s e d more than the wa te r removal a l o n e would e x p l a i n . 2. The sys tem was f i I led w i t h measured vo lumes of r i n s e and p r o c e s s s o l u t i o n a t d i f f e r e n t c o n c e n t r a t i o n s , and c i r c u l a t e d w h i l e d i s c o n n e c t e d from the power s u p p l y . A f t e r e q u i l i b r a t i o n of t h e p r o c e s s s o l u t i o n w i t h the s o r p t i o n mem- b r a n e s , n e i t h e r volume nor c o n c e n t r a t i o n of t h e s t r eam changed o v e r a p e r i o d of one h o u r . 3. The p r o c e s s s o l u t i o n was e q u i l i b r a t e d b e f o r e and a f t e r some s e p a r a t i o n runs in which no pH samp les were t a k e n . The vo lumes were found t o be unchanged but the c o n - c e n t r a t i o n was usua l ly out of b a l a n c e by up t o +5% f o r the f i r s t runs of t h e day . A f t e r two o r t h r e e e x p e r i m e n t s , the c o n c e n t r a t i o n s b e f o r e and a f t e r t he runs were e q u a l , howeve r . From these results i t is concluded that no mechanical leaks e x i s t e d , but that the membranes are quite permeable to solute. 231 The increase in solute concentration in the f i r s t daily runs may be an ef f e c t of a change in the d i s t r i b u t i o n of solute between solution and sorption membranes. Since the experi- ments were always stopped after the completion of a f u l l c y c l e , the i n i t i a l d i s t r i b u t i o n in the stack after some 12 hours of rest is l i k e l y to be d i f f e r e n t for that at the end of a run. 5.5.11 Comment on the performance of individual stages. The following tests were performed to detect whether differences between individual 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 differences affected the separating performance. a) O v e r p o t e n t i a l - c u r r e n t i n f o r m a t i o n . The mean probe voltage and the mean current in each stage were evaluated and are tabulated in Appendix C.2. From these tables overpotential-current diagrams were pre- pared for each stage, see Figure 102. The scatter of the points, which are plotted for runs with constant applied voltage (A$ =10 v ) , is considerable. A l s o , the bulk of the points s h i f t s from small currents for the f i r s t stage to large currents for the eighth stage, because these constitute the dialysate and the brine end of the assembly, r e s p e c t i v e l y . 232 0 .2 .4 .6 .8 I [A] 0 .2 .4 .6 .8 I [A] F i g u r e 102.. O v e r v o I t a g e - c u r r e n t c u r v e s of t h e e l e c t r o d i a l y s i s s t a g e s . F i g u r e 102. O v e r v o I t a g e - c u r r e n t c u r v e s of the e l e c t r o - d i a l y s i s s t a g e s . 234 The experimental points may be approximated by.straight lines in the range of currents investigated here. The slopes of the lines show a variation of 0.80 i .16 fi ( ± 20%). These slopes represent mainly the resistances of the s o l i d connectors, the s o l u t i o n , and the dividing membrane in the rinse chambers. The flow rate to the various rinse chambers was almost equal, so that the hydrodynamic conditions may be assumed i d e n t i c a l . Any difference in slope should, therefore, indicate unequal * contact resistances. Figure 102 shows that stages 1, 2, 7, 8 have larger resistances than the others. b) Compar i son of l o c a l c u r r e n t and probe v o l t a g e t r a n s i e n t s d u r i n g a s i n g l e c y c l e . The shape of the current and voltage curves traced by the multipen recorder during a complete cycle at l i m i t i n g conditions is copied in Figure 103 and 104, r e s p e c t i v e l y , for a typ i c a l run (#49). The numbers refer to the stage number. Each half cycle consists of a pause time followed by displace- ment. The f i r s t half cycle is an absorption half c y c l e . The general course of the transients w i l l be described f i r s t : * The graphite connectors constituted some problems in the present c e l l s . They broke frequently and were too porous. Small amounts of rinse solution seeped through the graphite, causing corrosion of the metallic parts of the e l e c t r i c manifold. 235 The c u r r e n t s are r e l a t i v e l y small during the demin- e r a l i z i n g pause time. When the flow s t a r t s , solution of high concentration enters the eighth stage. The current through this stage increases sharply, goes through a maximum, and remains at a f a i r l y high l e v e l . When the concentration front reaches the seventh sta^e the current here shows a peak, e t c . Although the displacement is 2/3 void volumes, the concen- t r a t i o n front just reaches the fourth stage by the end of the displacement period, which shows the retarded v e l o c i t y of the concentration wave in the absorption stack. The highest current peak is observed in the sixth stage. The currents increase in a step-wise manner at the start of the enriching pause time followed by rapid decays which indicate the depletion of the sorption membranes. Again the sixth stage shows a very high peak. During the displacement part of this half cycle the currents decrease further and show l i t t l e influence of the hydrodynamic conditions in the f1ow channel. The probe v o l t a g e s are set in re l a t i o n to the measured electrode voltage while the output voltage of the power supply is constant. The electrode voltage varies in time because there are several relay contacts as well as the resistances of the measuring shunts in series with the ED c e l l . 2 3 6 I.CH UJ rr or . z> o o UJ rr 3 < UJ 2 0 4 0 6 0 8 0 T IME [sec] Pause j-Displ. Pause |oispl.-| 1st, hal f 2 n d , half C Y C L E F i gure 103. T i m e - s p a c e d i s t r i b u t i o n of c u r r e n t a t l i m i t i n g con d i t i o n s . 237 12- UJ CD < o > a Ul or 3 CO < Ul 2j 8- i 20 40 60 ELECTRODE VOLTAGE •PauseJ-Displ.- Pausejoispl. Ist. half 80 TIME [sec] 2nd. half C Y C L E F i g u r e 104. Time-space d i s t r i b u t i o n of probe v o l t a g e at l i m i t i n g c o n d i t i o n s . 238 The probe voltages are higher than the applied electrode voltage during most of the f i r s t pause time. This is attributed to the membrane battery e f f e c t in unsteady-state operation. During the displacement the current increases and the probe voltage f a l l s therefore below the applied one. When the p o l a r i t y is switched the probe voltages increase. This indicates the reversed battery e f f e c t . The stack vol- tages pass through a minimum as the helpful concentration polarization disappears and increase subsequently toward a level d i s t i n c t l y below the electrode voltage. Again, stage No. 6 seems to perform much better than No. 7 and No. 8. Its voltage level is higher despite the fact that i t consumes almost as much current. The performance of No. 7 seems to be p a r t i c u l a r l y poor and i t shows the lowest minimum during the second part c y c l e . c) Runs w i t h s e l e c t e d s t a g e s . The previous discussion shows differences between stages No. 5 & 6, and No. 7 & 8. A real l i f e test was per- formed on the two pairs (see runs #19 & #20, Table 34). The separation transients coincide almost p e r f e c t l y . The higher current consumption of run #20 is probably caused by the 10% higher concentration. It is concluded that the differences between stages which are a result of the manufacturing procedure do not 239 seriously influence the performance of the stages with respect to t h e i r separating task. They may, however, influence the f i n a l l i m i t of separation. 5.5.12 Experimental test of the constant rate model. Four experiments were performed to test the constant rate model proposed in Chapter 3. The eight stages were connected in series h y d r a u l i c a l l y and e l e c t r i c a l l y . The D.C. power supply was operated in constant current mode. These currents had to be f a i r l y small, as the maximum output voltage of the D.C. supply was limited to 40 V. In two runs the e l e c t r i c potential was switched in phase with the flow (y = 0, see equations (21)). The phase s h i f t in the other runs amounted to one quarter cycle (y = . The results are shown in form of concentration transients (see Figure 105), and confirm that: ( i ) t he s e p a r a t i o n i s v i r t u a l l y c o m p l e t e d a f t e r the f i r s t c y c l e f o r i n - p h a s e s w i t c h i n g , ( i i ) t he c o n c e n t r a t i o n t r a n s i e n t s a re s t r a i g h t l i n e s w i t h equa l a b s o l u t e v a l u e s of the s l o p e s f o r equa l r a t e s when the 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 . T h i s h o l d s e x p e r i m e n t a l l y o n l y f o r the f i r s t c y c l e s , because the power s u p p l y c o u l d not 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 v o l t a g e , ( i i i ) t he d e c r e a s e i n d i a l y s a t e c o n c e n t r a t i o n d u r i n g the f i r s t c y c l e i s l a r g e r f o r i n - p h a s e o p e r a - t i o n than f o r o u t - o f - p h a s e o n e . C o = 1250 [ppm], 6 = 1 [ - ] , v - 4.3 [cm/sec], T = 0.6 [sec] F i g u r e 105. 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 c o n s t a n t r a t e o p e r a t i o n . ro o 241 5.5.13 Comment on the e f f e c t of end mixing. End mixing may be suppressed in the multiple stage ED module as follows. If less than eight stages are connected e l e c t r i c a l l y the others may remain in the process flow l i n e as inert (or i d l e ) beds with small dispersion. The following combination was chosen: four active stages bracketted by two i d l e ones on either s i d e . Runs #51 and #53, see Table 13, were i d e n t i c a l experiments except for the location of the conductivity c e l l s : between the reservoirs and the l a s t i d l e stages for run #51, and between the l a s t active and the f i r s t i d l e stage on each side for run #53. A comparison run (#52) was performed with the same four centre stages but no i d l e stages. The dead volumes in the reservoirs (Sg = 6 T  = 1/2) were the same in this run as the volume of two i d l e stages in runs #51 and #53. The results of the three tests are shown in Figure 106. The comparison run (#52) separates i n i t i a l l y at a rate intermediate to those of the other experiments (#51 and #53), but reaches i t s f i n a l conditions before the other transients taper o f f . This indicates that p a r t i a l suppression of the end mixing does not improve the f i n a l separation. There are two reasons that f i n a l conditions are much slower approached in runs #51 and #53 than in run #52. I . S o l u t e i s s t o r e d i n the s o r p t i o n membranes when the ED s t a g e s are used as dead volumes. The b r i n e 242 F i g u r e 106. E f f e c t of end m i x i n g on c o n c e n t r a t i o n t r a n s i e n t s . 243 c o n c e n t r a t i o n t e n d s toward a h i g h e r l i m i t , t h e r e f o r e , and the d i a l y s a t e t r a n s i e n t i s damped. 2. Suppose the i n t e r n a l d i s p e r s i o n in t he ED s t a g e s may be n e g l e c t e d . In t h i s case the r e s e r v o i r c o n c e n t r a t i o n s w i l l not e x p e r i e n c e any change w h a t s o e v e r i f t he d i s p l a c e d volume i s e q u a l t o t h e volume in the i d l e s t a g e s . The d i s - p l a c e d volume in e x p e r i m e n t s #5 1 and #53 exceeded t h o s e of t h e i d l e s t a g e s by 1/6 v o i d , o n l y , and the i n t e r n a l d i s p e r s i o n i s c o m p a r a t i v e l y s m a l l . H e n c e , the c o n c e n t r a t i o n s of t h e r e s e r v o i r s o l u t i o n s changed a t a s low r a t e , and t h e 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 he i d l e s t a g e s a re damped. 5.5.14 Production of 90% demineralized s o l u t i o n . The l i n e a r decay of the dialysate transients i n d i - cates the potential of the process for a continuous system. To demonstrate this,two production runs (#3 and #5) were performed in which a 90% demineralized product was i n t e r - mittently replaced by fresh feed. The brine side remained closed during these expriments. Salt accumulated continuously in the brine r e s e r v o i r , therefore. Operating conditions were i d e n t i c a l to those for batch runs #6 and #26. The concentration changes in dialysate and brine reservoirs are shown in Figures 107 and 108, 244 respectively for low (c 0  = 1250 ppm) and high ( c 0  = 5500 ppm) concentrati ons. In Figure 107 the product was removed seven times. Each demineralization lasted eight c y c l e s . The eighth de- mineralization was continued u n t i l steady periodic conditions were reached. The f i n a l separation factor of ns = 322 was obtained with a f i n a l brine product concentration of close 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 factor appears to be improved at the higher brine concentration. This is in l i n e with the previous findings on the e f f e c t of the i n i t i a l concentration, see Section 5.5.5. In Figure 108 a s i m i l a r pair of experiments, #5 and #6, is shown. The dialysate product was removed four times after every 15th cycle in run #5. The product concentration begins to increase after the second production c y c l e , and the f i n a l separation factor is only ns = 76, against a f i n a l brine product of almost 25,000 ppm. The i n i t i a l transients of run #5 are perfectly reproduced in run #6, which reaches a f i n a l separation factor of ns = 185 against a f i n a l brine concentration of 14,000 ppm. The mean current consumption increases during the production runs by a small amount due to the larger brine concentration. The currents are recorded in Figures 107 and 108 for each production c y c l e . 245 F i g u r e 107. 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 bot tom r e s e r v o i r c o n c e n t r a t i o n s d u r i n g p r o d u c t i o n run #3 compared to ba t ch run #26 ( low c o n c e n t r a t i o n ) . 100 NUMBER OF CYCLES C-3 PRODUCTION EXPERi o o to CD o > tn c-i o o •o •o ro o 3 CD n F i 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 r e s e r v o i r c o n c e n t r a t i o n s r u n #5 compared t o b a t c h c o n c e n t r a t i o n ) . of t o p and b o t t o m d u r i n g p r o d u c t i o n run #6 ( h i g h ro 247 The results of the production runs confirm that c y c l i c e l e c t r o d i a l y s i s has potential for a continuous system over a large concentration range (up to at least 10,000 ppm). The high concentrations require more recycle or longer r e s i - dence times. It should be pointed out that no attempt was made to optimize the production process. The pause time and the applied voltage were rather small, and the feed was introduced in large batches at the low concentration end, instead of in smaller portions during each cycle at a location where the averaged concentration of the t r a v e l l i n g front coincides with the feed concentration. S i m i l a r l y , one would withdraw the product intermittently during each cycle in any r e a l i s t i c open system. 5.6 Summary of Results and Experience on the Second ED Module 1. It was demonstrated that simple stacks may be produced on a laboratory s c a l e . The stacks consisted of inte- grated frames which held the spacer screens and the absorption membranes and which distributed the flow into the channels. 2. A segmented module was b u i l t which consisted of eight individual stages. The stages seem to a l l perform approximately equally in separating 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 internal mixing characterized the stack hydrodynamics. 4. The influence of the channel length was investigated by operating up to eight stages in series h y d r a u l i c a l l y . The results show improvements of the l i m i t of separation s i m i l a r to the influence of the pause time, as the residence time is increased. A l s o , there is less i n - ternal dispersion for longer channels. The i n i t i a l rate of separation appears to be a maximum for a channel length of approximately one meter. 5. Systematic perturbations of four and of the i n i t i a l concentration eight stage module: Pause time ( t ) : A p p I i e d v o l t a g e (A*) D i s p l a c e d volume (6.) S u p e r f i c i a l v e l o c i t y (v) I n i t i a l c o n c e n t r . (co) 6. The separation factors range from i n s i g n i f i c a n t (ns = 3, for run #7) to very large (ns > 10 3  for runs #33, #34). 7. The pause times remain an essential feature of the c y c l i c e l e c t r o d i a l y s i s process operation even for long channels, but they may be kept short (approximately 10 seconds or less) i f the other conditions are favourable. 8. The i n i t i a l rate of separation increases almost l i n e a r l y with the applied voltage. The production may therefore be accelerated but only at the expense of additional energy because the current consumption rises in pro- portion to the voltage. 9. In a pause operation the ve l o c i t y of displacement has l i t t l e e f f e c t on the separation and may be kept as large as possible. operating parameters were performed on the in  + l ° r -i _l_0 _ !  0  L s e c J \0_  + J 5  [ v o l t ] 2/3  + l / 3  r - i ± L ± -5/12  L J . +0.0  r  , -, 5 .4 _ 4  j Lcm/secJ _ K A  +4450  r  -, 250 _  | 0 0  LppmJ 249 10. If the pause time is omitted, slow displacement is neces- sary to keep the residence time long, which in turn slows down the rate of separation. Usually such an operation is i n e f f i c i e n t . 11. The displaced volume should be small enough to prevent breakthrough of the concentration f r o n t . If i t is re- duced the f i n a l separation increases almost without 1 i mi t . 12. The i n i t i a l concentration has a retarding e f f e c t on the i n i t i a l rate of separation. The influence on the f i n a l separation could not be established for the conditions tested. 13. The presence of dead volumes in the end reservoirs slows down the rate of change of the concentrations. There is no e f f e c t on the l i m i t s which are eventually reached. 14. Two preliminary production runs on the module showed the potential 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 solutions up to at least 10,000 ppm. No attempt was made to optimize operating conditions. 15. A theoretical model which assumes constant and uniform rate of mass transfer through the membranes was con- firmed experimentally. 16. pH changes in process and rinse solution were generally small, but there is a trend toward higher a c i d i t y of the product stream for high voltages and long pause times. Chapter 6 MATHEMATICAL MODELS 6.1 Spacer Model Sonin and Probstein (1968) derived general mass balance equations for mass transfer in electrodialysis channels. They made the following assumptions and s i m p l i f i - cati ons: 1. The f l u i d c o n s i s t s of u n - i o n i z e d ( n o n p o l a r ) s o l v e n t and an i n f i n i t e l y d i l u t e , f u l l y i o n i z e d s a l t wh ich i s not so I v a t e d . 2. The f l u i d i s i n c o m p r e s s i b l e and a t c o n s t a n t t e m p e r a t u r e . 3. The membranes a re p e r f e c t l y s e l e c t i v e , have c o n s t a n t e l e c t r i c a l c o n d u c t i v i t y w i t h r e s p e c t t o the g e g e n - i o n s , and are impermeable w i t h r e s p e c t t o s o l v e n t m o l e c u l e s . 4. No c h e m i c a l r e a c t i o n t a k e s p l a c e . 5. N e r n s t - E i n s t e i n e q u a t i o n f o r the ion m o b i l i t i e s h o l d s . 250 251 6. T w o - d i m e n s i o n a l g e o m e t r y . 7. No i n t e r p h a s e mass t r a n s f e r r e s i s t a n c e . 8 . D i f f u s i o n c o e f f i c i e n t s and v a l e n c e s of p o s i t i v e and n e g a t i v e ion a re e q u a l . Under these assumptions the mass conservation equa- tions for any volume element may be reduced to |c_L + v . vc' = D • V 2 c' (35) and V(c' . v *) - 0 (36) where c' = solution concentration [g-mole/cm 3 ] t' = time [sec] -> V = f l u i d v e l o c i t y vector [cm/sec] V = gradient [cm- 1 ] D = solute d i f f u s i o n c o e f f i c i e n t [cm 2 /sec] $ = e l e c t r i c potential [ v o l t ] Equations (35) and (36) and appropriate boundary and i n i t i a l conditions have been used by Sonin and Probstein to calculate the steady-state concentration and current 252 d i s t r i b u t i o n s in channel flow assuming laminar and/or turbu- lent velocity p r o f i l e s . In this work d i f f e r e n t hydrodynamic conditions w i l l be assumed based on the modified stack design. In p a r t i c u l a r , the presence of a spacer material in the flow channels sug- gests that the channels be divided into a series of well mixed c e l l s . The e f f e c t i v e number of c e l l s is not necessarily i d e n t i c a l to the number of spacer holes but must be determined experimentally. It w i l l be further assumed that each mixing c e l l consists of a turbulent core and two stagnant sublayers across which only d i f f u s i o n and e l e c t r o l y t i c migration take pi ace. 6.1.1 Model equations. Figure 109 i l l u s t r a t e s the co-ordinate systems and the dimensions of the j t h  mixing c e l l and the adjacent j t h section in the stagnant sorption membrane. Some of the. channel volume is occupied by s o l i d spacer material. This is indicated by shaded bars across the channel which reduce the free flow length of the mixing c e l l by the r a t i o d %l m where I length of flow channel d e f f e c t i v e length of mixing c e l l m number of mixing c e l l s . 253 Figure 109. Derivation of the spacer model equations. 254 The two p a r t i a l d i f f e r e n t i a l equations (35) and (36) w i l l be replaced by a system of difference equations and PDEs accord- ing to the following procedure. The notation was chosen, where and c j , k k = 1 for turbulent ocre = 2 for stagnant sublayer == 3 for stagnant inner layer j = 1 , 2 , • • • , m For turbulent core: del dt' d p j - 1 b^26 *  V C j , 2 (37) y =6 with the i n i t i a l condition @ t ' = 0 c j , l  = c ° For stagnant sublayers: (v = 0) 255 with i n i t i a l condition @ t' = 0 >  c \ o ~  co boundary conditions 9 c 0 , D j,2 Ti— 9y"^ 2zF anion s e l e c t i v e membrane r ' -  s  '  C j , 2  = c j , i For stagnant inner layer: (v = 0) ' C j,3 9 t" = D 9 2  c' j,3 9y' (39) with i n i t i a l condition boundary conditions 0 , c. , = c 0 'j ,3 0 , D 3c .;.3 ^1 2zF l ' a  8 C J , 3 2 ' 9y' N.B. The flux of s a l t due to the e l e c t r i c current must be corrected according to the difference i n free volume between flow channel and inner l a y e r . c a t i on s e l e c t i v e membrane The current densities ( i . ) couple equations (37), (38) and (39) over t h e i r boundary conditions. The potential drop across a flow channel and an adjacent sorption membrane has a constant value A $ . Due to assumption 8 there is no 256 charge polarization at the membranes and the equation for the current density is simply A $ - 2 A3> 1 - 5 — (40) J R tot where A $ D 0 n Donnan potential R,. ̂  total resistance tot The Donnan potential and the total resistance are given by equation (26) in Section 3.3. The following dimension 1 ess quantities were intro- duced: 257 c . j , k co k = 1 ,2,3 ; j = 1 , 2 , 3 , - . . , m = and v = K— Jl/v (41) P - TT B  ~ b Fo = b P gy v  (Fourier Number) V b j 2 z F D c, K = 2 R . • 2 z 2  F 2  D c, membrane b RT 258 The resu l t i n g dimensionless equations and t h e i r i n i t i a l and boundary conditions are d c dt m b - 1 , 1 •j.ij F o ( i - B) '  V C J,2 (42) y=3 9 C .i,2 3t _1_ Fo a 2  c. LA 9 y' (43) 3 c 3t J Fo 3 2  c (44) @ t = 0 , c. , = c . 9 = c. - = 1.0 3 c y = 0 3 , 2 9y 3 c 1^3 = ay l . • ir y - 3 , c j j 2 - C j J 3C. ~ = P. J >3 2 » 3y 0 (45) 259 where c . A^ - 2 In - J - ^ C j , 2 y=0 i . = J (46) 1 - 2 6 + 2 dy_ + 2 + 5 0 0 At this point an additional assumption regarding the concentration p r o f i l e in the stagnant sublayer is i n t r o - duced. The concentration p r o f i l e is l i n e a r i z e d . This sim- p l i f i e s equations (42), (43), (46) and some boundary condi- tions in (45). The f i n a l set of equations for the spacer model is for j = 1 ,2 ,3 , • • • , m. • (47) 260 d c dt = - m •j.ij (48) 2(1 - 3) Fo • 3 2 (1 - 23) m C J J "  C J,2J 3 • Fo 3 c JL1 _ at j _ Fo a 2 c 3 y" (49) wi th t > 0 , c Q 1  = 1 .0 t =  ° '  C j , l  = C J 5 2 =  c j 5 3 =  1 - 0 (50) 9 C i 3 2 3 c J\3 9y 261 and m Aip - 2 In m C j , 2 2B In 1 - 23  +  _ C j , l c m (51) P / 2 j , l c m C j , 2 + 2 dy  C j , 3 + K where the superscript (m) denotes the concentration of the solution at the i n t e r f a c e , and c n  -j is the feed to the f i r s t mi xi ng eel 1 . The set 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 con- ditions with m independent linear second order partial differential equations. Looking at the ODE's alone, this is an i n i t i a l value problem, whereas the PDE's are of the parabolic type and constitute an initial-boundary problem. 6.1.2 Considerations related to c y c l i c process operations. The system of equations (47) to (51) describes a period s t a r t i n g with uniformly d i s t r i b u t e d i n i t i a l concentra- t i o n s . In general, any concentration d i s t r i b u t i o n at t = 0 262 may replace the i n i t i a l condition in (50). This is important for c y c l i c operations of the e l e c t r o d i a l y s i s stack. When operating parameters are changed in steps, the time axis may be transposed mathematically, because i t is generally more convenient to sta r t calculations at t = 0 for constant- parameter values than to define the step changes of the parameters as functions of time. The thickness of the stagnant sublayers (6) is generally a function of the flow conditions and may be evalu- ated from mass transfer c o r r e l a t i o n data i f these are a v a i l - able (see also Section 5.3.4). However, very l i t t l e informa- tion is available on the unsteady-state mass transfer which must be considered in a c y c l i c operation. The thickness (6) i s , therefore, treated as an independent v a r i a b l e . The concept of stagnant sublayers w i l l break down as the velocity approaches zero, i . e . as the flow becomes more and more laminar. The model equations must, therefore, be used with caution under those conditions. In the present form they cannot be applied to pause operations. 6.1.3 Soluti ons. The nonlinear form of the coupling condition (51) makes an a l y t i c a l solutions of the model equations very un- l i k e l y . A semi-analytical approach i s , in p r i n c i p l e , possible 263 i f the current densities are assumed to remain stepwise constant. However, the resulting series solutions would have to be evaluated numerically in any case. It was preferred to find direct numerical solutions based on approximations of the system equations (47) to (51). A number of standard numerical integration schemes have been considered, see e.g. McCracken and Dorn (1964), Hamming ( 1962) : - F o u r t h o r d e r R u n g e - K u t t a (RKS) - M i l n e f i f t h o r d e r p r e d i c t o r c o r r e c t o r 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 scheme - Backward 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 f i r s t two integration schemes are suitable for f i r s t order PDEs and are offered by most computing centres as l i b r a r y subroutines with fixed and/or variable step length. In the present system of equations the second order space derivative was replaced by the conventional central difference expression to test the RKS. An a n a l y t i c a l solution of the unsteady state d i f f u s i o n equation (49) was used as test case. Carslaw and Jaeger (1959) give such a solution a f i n i t e slab with constant heat i n f l u x through both boundaries. 264 It was found that RKS diverges in some cases when integrating with fixed step s i z e s , although a reduction in time step size usually led to s a t i s f a c t o r y convergence. The s t a b i l i t y of the difference methods was tested using e-schemes. It was found that the common difference scheme is unstable for the unsteady state d i f f u s i o n equation. The Crank-Nicholson scheme showed i n s t a b i l i t y for equation (47). The backward difference scheme was stable in a l l cases. Since RKS, as well as Milne, require difference approximations of some p a r t i a l d e r i v a t i v e s , i t was f i n a l l y decided to use the stable backward difference scheme in the present model. This is an i m p l i c i t method which requires an i t e r a t i o n method as the following derivation shows. 6.1.4 Backward Difference scheme with Gauss Seidel i t e r a t i o n . The backward difference scheme approximates the f i r s t time derivative by - c At (52) and the second position derivative by 265 3 2 c lay' y ,t C y+Ay,t ~  2 c y , t  + C .y-Ay,t Ay 2 (53) Suppose the inner layer of the sorption membrane is divided into 2n p a r a l l e l s l i c e s of thickness A * = 2n" (54) This is equivalent to expanding the second subscript (k) of the concentrations to k = l ^ , " - , n + 3. It is s u f f i c - ient to consider half of the layer thickness only because the concentration p r o f i l e is symmetric. In addition to the two-dimensional space grid ( s u b s c ripts, j,k) a time grid has been introduced by equation (52). This w i l l be labeled by superscripts (1) and (0) for the new time value and the old one r e s p e c t i v e l y . The following abbreviations are used: _ 2 • At Z l  Fo • 3 266 zk = m • At =  2 • At z s Fo • 3 • (1 - 23) The system of equations (47) to (51) is transformed into the following i m p l i c i t algorithm to calculate the new c'. K'S. J » K For j 1 ,2 , ••• , m C j , l "  C j , l  = Z * * ( C j - l , l ~  C j j ) "  2 5  * ( C J J C j , 2 o C j , 2 ( C j - 1 , 1 " C j , l I 1 - c j,2 i c .  0 0.3 o C J,3 + z, • 1 C j , 4 - c. . = z 'j,4 - 2 c ' + c' 'j,5  C j , 4  C j , 3 267 l o _ C j ,n+2 "  c j ,n+2 ~ z 3 l C J,n+3 2 C J,n+2  + c j,n+l c' - c° = 2 J,n+3  c j,n+3  L • c j,n+2 "  c j ,n+3 where S * A i | ; - .2 • In J 1 - 26 c'. , J ,1 In + 2Q -T flLl) h , 2 i C j , l "  C j , 2 + £ + S 3 " K 4 2 1 - + — 7 — + — 7 — + ... + — r — 3  C j,4  c j,5  c j,n+3 SIMPSON'S rule If i . were constant a lin e a r matrix equation could 3 be established and solved by standard methods. The Gauss- Seidel i t e r a t i o n was employed in the following way: 1. Calculate i . for c. - values 0 J > K 2. Calculate c'. . values and find D - Max|c^ k  - c ° j k | k = 1 ,2 , n+3 3. If D > i t e r a t i o n error go to 1 268 A computer program was written which consisted of a main program and three subroutines. The main program read parameter values, i n i t i a l i z e d the concentration matrix, organized the i n t e g r a t i o n , adjusted time step size and kept track of the averaged current consumption as well as of the effluent concentrations and the material balance. The periodic switching of e l e c t r i c p o l a r i t y and di r e c t i o n of f l u i d flow was also performed automatically by the program for a given number of cyc l e s . The printout varied according to the information that was desired. 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 current density, the values of z^(£.=l • • ,6) according to increasing or decreasing time step s i z e , and performed the Gauss-Seidel i t e r a t i o n . A l i s t i n g of the FORTRAN IV program is presented in Appendix C.3, which also d e t a i l s the required input data. The integration step size was controlled by the following c r i t e r i o n : Each integration was performed twice with the current time step (At) and with At/2. If DD = Max c* j k ( A t ) - c ^ k ( A t / 2 ) > ERROR j = 1 , 2 , « - ' , m k = 1,2, — , n + 3 269 the current step size was halved and the same integration step was repeated. If DD < 0.05 * ERROR the current step size was doubled. The two values of the new concentrations were also used to correct the actual concentrations on the basis of the estimated truncation e r r o r . 6.1.5 Results of computer simulations. The objectives of simulation runs were: a) To t e s t a c c u r a c y and convergence of 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 e f f e c t s of o p e r a t i n g pa r a m e t e r s . c) To compare the model w i t h e x p e r i - mental res uIts . 6.1.5.1 Accuracy and convergence. The integration was tested by - v a r y i n g the number of s l i c e s i n the s o r p t i o n membrane (n) - a d j u s t i n g the t o l e r a b l e i t e r a t i o n and i n t e g r a t i o n e r r o r s - m o d i f y i n g the program from a b s o l u t e t o r e l a t i v e e r r o r c o n t r o l 270 The results are: 1. Between f o u r and s i x s l i c e s per h a l f s o r p t i o n membrane are u s u a l l y s u f f i c i e n t i f p < I . 2. For a b s o l u t e e r r o r c o n t r o l both i n t e g r a t i o n e r r o r and i t e r a t i o n e r r o r s h o u l d be s m a l l e r than 5 * I O - 3 . If the i t e r a t i o n e r r o r i s one o r d e r of magnitude s m a l l e r than the i n t e g r a t i o n e r r o r , e.g. I 0 - I +  v s . I 0 ~ 3 , the number of i t e r a t i o n s l i e s between 3 and 5 and the time s t e p s i z e i s between 1/64 and 1/256, whereas the time s t e p s i z e d e c r e a s e s and the number of i t e r a t i o n s becomes very s m a l l (I t o 2) i n the case of comparable e r r o r l i m i t s , e.g. i f both are s e t t o I O - 3 . 3. The m a t e r i a l b a l a n c e i s g e n e r a l l y i n t h e o r d e r of ± 0.1$, but t h e r e are i n d i c a t i o n s of s y s t e m a t i c d r i f t s as the number of c y c l e s i s i n c r e a s e d . 4. R e l a t i v e e r r o r c o n t r o l i s very time consuming e s p e c i a l l y when the d i a l y s a t e c o n c e n t r a t i o n becomes s m a l l . The r e s u l t s compare g e n e r a l l y very w e l l w i t h r e s u l t s o b t a i n e d under a b s o l u t e e r r o r c o n t r o l ( a t l e a s t 3 s i g n i f i c a n t f i g u r e s ) . 6.1.5.2 Effect of operating parameters. It was found that small Fourier numbers, small layer thickness, high potentials and small thickness ratios lead to 271 good separation- Tables 40, 41 and 42, and Figure 110 show typ i c a l results of systematic computer simulations. 6.1.5.3 Comparison with experimental r e s u l t s . Figure 111 i l l u s t r a t e s the experimental concentra- tion transients for EDI-SI-8/#22, #23, #24 runs and computer simulations for a set of parameters which were partly calcu- lated from the operating conditions (M, Fo, AIJJ, 6, p, c 0 ) , partly estimated and adjusted for a reasonable f i t ( 6 , £ ) . The experiments were s p e c i f i c a l l y performed for a test of the simulation program. As explained in Section 5.3.2 the probe voltage was subject to c h a r a c t e r i s t i c f l u c - t uations, whereas the model assumed constant A<£>. The D.C. power supply voltage was, therefore, hand regulated in such a way as to maintain a constant probe voltage signal for the runs l i s t e d above. Figure 112 shows a comparison of calculated (solid line) and. experimental (points) concentration transients for EDI-SI-8/#36. The previously f i t t e d parameters 8 and £ were adjusted again. Although the model predicts the dialysate transient reasonably w e l l , i t f a i l s to do so for the brine. It was also found that the model breaks down for small membrane core thickness in combination with large applied voltages. Negative concentrations occur at some stages during Table 40 Spacer Model No. I, Effect of Layer Thickness Parameters RUN NO. M Fo B P 5 6 3 20 2 0.05 0.1 1 16 1 3.2 1 8 CURRENT CYCLE NO. TOP CONCENTRATION BOTTOM CONCENTRATION SEPARATION FACTOR DEPLETING ENRICHING C T C B ns - 1 E 3 8 3 8 3 8 3 8 3 8 1 2 3 4 5 6 7 8 9 10 11 12 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 1 .47 2.01 2.04 2.03 1 .98 1 .94 1.92 1 .91 1 .90 1 .90 1 .42 2.08 2.04 2.00 1 .95 1 .92 1 .89 1 .88 1 .87 1 .86 1 .86 1 .86 2 .29 2.12 2.08 2.02 1 .97 1.94 1 .92 1 .91 1 .91 1.91 2.25 2.12 2.12 2.05 1 .99 1.95 1 .92 1 .89 1 .88 1 .87 1 .86 1 .86 Table 41 Spacer Model No. I, Effect of Fourier Number Parameters RUN NO. M Fo 3 P Af TT ? 6 2 20 20 0.05 1 16 1 3.2 1 3 2 CYCLE NO. TOP CONCENTRATION BOTTOM CONCENTRATION SEPARATION FACTOR CUR RENT DEPLETING ENRICHING C T c : B ns i D - i E 2 -3 2 3 2 3 2 3 2 3 1 1 .00 1.66 .87 .23 1.16 7.1 2 1.01 1.98 .87 .16 1.16 12.4 3 1 .02 2.17 .87 .089 1.17 24.4 4 1.02 2.28 .87 .049 1.17 45.7 5 1.03 2.34 .88 .032 1.17 72.6 6 1.03 2. 37 .88 .024 1.17 97.9 7 1.03 2. 38 .88 .020 1.17 116.8 8 1 .04 2.39 .89 .019 1.17 127.5 9 1 .04 2.40 .89 .018 1.17 133.2 10 2.40 .018 136.1 ro —i co Table 42 Spacer Model No. I, Effect of Applied Potential Parameters RUN NO. M Fo B P TT K 6 3 20 2 0.05 0.1 1 16 8 1 3.2 1 4 Compari son CYCLE NO. TOP CONCENTRATION BOTTOM CONCENTRATION SEPARATION FACTOR CURRENT DEPLETING ENRICHING c T c B. ns 1 D - 1 E 3 4 3 4 3 4 3 4 3 4 1 1 .66 1 .28 .234 .487 7.1 2.6 1 .47 2.29 2 1 .98 1 .44 .160 .507 12.4 2.9 2.01 - 2.12 3 2.17 1 .55 .089 .485 45.7 3.2 2.04 - 2.08 - 4 2.28 1.62 .049 .455 72.6 3.6 2.03 - 2.02 - 5 2.34 1.67 .032 .429 97.8 3.9 1 .98 - 1.97 - 6 2. 37 1 .72 .024 .408 116.8 4.2 1.94 - 1 .94 - 7 2.38 .020 127.5 1 .92 1 .92 8 2.39 .019 133.0 1 .91 1.91 9 2.40 .018 136.0 1 .90 1 .91 10 2.40 .018 138.0 1 .90 1 .91 SIMULATION PARAMETERS 275 M = 20 , Fo= 2 , 16 , S* 10 , /3= 0.1 , £ = 3.2 F i g u r e 110. E f f e c t of w i d t h r a t i o (? ) on concentrat ion factor 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 . 276 .04- 1.04 O EXPERIMENT — SIMULATION NUMBER OF CYCLES o o M = 8 Fo = 135 AV= 24.3 6= 1.00 0.6 /3= 0.1 ^ = 0.6 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 runs #22,23,24 (f i r s t s t a c k ) . 277 < cc f- Z Ul o z o o 2 t— O CD 1.00 .95- NUMBER OF CYCLES ui o z o o Q. O I- 1.05- z o H 1.00- < CC .95- .90- M = 8 Fo = 72.2 *f= 44.3 6 = 1.00 5 * 0.6 /3= 0.08 5= 1.0 A EXPERIMENT SIMULATION l 4 T " 8 NUMBER OF CYCLES .85 75- Fi gu re 112. Comparison of computer simulation with experimental run #36 ( f i r s t s tack). 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 in i t s present form predicts the ef f e c t of system parameters on the separation of no-pause operations q u a l i t a t i v e l y . It may be used to f i t singular experiments q u a n t i t a t i v e l y , but these f i t s do not have much pract i c a l s i g n i f i c a n c e . In p a r t i c u l a r , the model breaks down for very large rates of mass tra n s f e r ; this is probably due to the l i n e r i z a t i o n of the concentration p r o f i l e s in the stagnant sublayers. Modifications of the model may include: 1. N o n l i n e a r c o n c e n t r a t i o n p r o f i l e s in t he s u b - l a y e r s , i . e . e x p a n d i n g the l a t e r a l c o n c e n t r a t i o n g r i d ( s u b - s c r i p t k) in the f l ow c h a n n e l s . 2. I n c l u d e wa te r t r a n s f e r due t o s o l v a t i o n o f t h e i o n s . 3. Accoun t f o r d e n s i t y i nduced f r e e c o n v e c t i o n i n s o r p t i o n membranes. 279 4. I n c l u d e s o r p t i o n c a p a c i t y o f ion exchange membranes. 5 . R e p l a c e c o n c e n t r a t i o n s by a c t i v i t i e s . 6 . M o d i f y e q u a t i o n s t o a l l o w f o r f l ow pauses a t the b e g i n n i n g of each h a l f c y c l e . 6 . 2 Rate Model The rate model presented in Section 3.3 may be improved along the following l i n e s . 1. Combine pure pause and p a r a m e t r i c pumping o p e r a t i o n s t o a pa rapause o p e r a t i o n in wh ich t he e l e c t r i c p o t e n t i a l i s c o n t i n u o u s l y a p p l i e d w h i l e t he f l o w pauses a t t he b e g i n n i n g of each h a l f c y c l e . 2 . A l l o w f o r i n t e r n a l d i s p e r s i o n e f f e c t s by i n t r o - d u c i n g t h e m i x i n g c e l l c o n c e p t . 3 . Mod i f y t he r a t e law by i n c l u d i n g more te rms of t he c u r r e n t d e n s i t y a p p r o x i m a t i o n ( e q u a t i o n ( 2 7 ) . 4 . Measure r a t e s o f mass t r a n s f e r e x p e r i m e n t a l l y as f u n c t i o n of o p e r a t i n g and sys tem p a r a m e t e r s and use t h e s e c o r r e - l a t i o n d a t a i n form of s e m i - e m p i r i c a I t r a n s f e r e q u a t i o n s . Chapter 7 CONCLUSIONS AND RECOMMENDATIONS The purpose of this work was to investigate and to develop a c y c l i c e l e c t r o d i a l y s i s process, both experimentally and t h e o r e t i c a l l y . The results of this study lead to the following conclusions. 1. C y c l i c e l e c t r o d i a l y s i s can a c h i e v e ve ry l a r g e s e p a r a t i o n s (ns > IO 3 ) in a c l o s e d s y s t e m . 2. The r e s p o n s e of e I e c t r o s o r p t i o n s t a c k s t o p e r i o d i c a l t e r n a t i o n s of the p o l a r i t y of the e l e c t r i c f i e l d and of t h e d i r e c t i o n of t he f l u i d d i s p l a c e m e n t i s gove rned by t he r a t e of mass t r a n s f e r . E q u i l i b r i u m c o n d i t i o n s have g e n e r a l l y l i t t l e i n f l u e n c e . 3 . Flow pauses at t he b e g i n n i n g of each h a l f c y c l e r e p r e s e n t i m p o r t a n t f e a t u r e s of the c y c l i c p r o c e s s o p e r a t i o n . Modera te pause t i m e s (up t o 10 CsecU) c o n s i d e r a b l y improve both the r a t e of s e p a r a t i o n and the l i m i t i n g s e p a r a t i o n com- pared t o no -pause o p e r a t i o n . 280 281 4 . The e f f e c t of t e n sys tem p a r a m e t e r s c o u l d be s t u d i e d on a s i m p l e bench s c a l e e l e c t r o d i a l y s i s c e l l , wh ich f e a t u r e d a r i g i d c e n t r e f rame d e s i g n . F i n a l s e p a r a t i o n f a c t o r s between I and 40 were o b t a i n e d e x p e r i m e n t a l l y . The c y c l i c o p e r a t i o n gave b e s t s e p a r a t i o n f o r moderate pause t i m e s , h igh a p p l i e d v o l t a g e , smal l d i s p l a c e d vo lume, smal l i n t e r n a l m i x i n g , un i form f low d i s t r i b u t i o n , smal l s o r p t i o n c a p a c i t y of the s t a c k , l a rge f1ow r a t e . 5. S imple s t a c k s were des igned f o r a m i n i - p i l o t p l a n t module and m a n u f a c t u r e d u s i n g a s t a n d a r d i z e d p r o c e d u r e . T h i s r e s u l t e d in u n i f o r m f l ow d i s t r i b u t i o n in the c h a n n e l s . Sma l l d i s p e r s i o n c o e f f i c i e n t s w e r e , t h u s , a c h i e v e d . 6 . A h i g h f i n a l s e p a r a t i o n i s o b t a i n e d by i n c r e a s - ing t he channe l l e n g t h o r the pause t i m e . The i n i t i a l r a t e of s e p a r a t i o n appea rs t o be a maximum f o r a channe l l e n g t h of a p p r o x i m a t e l y I meter and pause t i m e s of abou t 10 s e c o n d s . 7. The s e p a r a t i o n f a c t o r (ns ) d u r i n g t he f i r s t few c y c l e s can be a p p r o x i m a t e d by an e x p o n e n t i a l f u n c t i o n ns = 10 a • t whe re and a i s t h e r a t e c o n s t a n t i n C m i n - 1 ] ] t i s t h e r e a l t i m e i n C m i n 3 282 A x i a l d i s p e r s i o n l i m i t s the s e p a r a t i o n as s t e e p c o n c e n t r a t i o n f r o n t s deveI o p . 8. The p o t e n t i a l o f t he 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 f o r l a r g e s e p a r a t i o n s in an open sys tem o v e r t he c o n c e n t r a t i o n range f rom 1,000 t o a t l e a s t 10,000 CpprnJ NaCI was d e m o n s t r a t e d . 9. M o d e l l i n g of t he c l o s e d sys tem has met o n l y p a r t i a l s u c c e s s . A q u a l i t a t i v e model wh ich assumes c o n c e n - t r a t i o n dependent mass t r a n s f e r r a t e s e x p l a i n s most of t he e x p e r i m e n t a l r e s u l t s . A more r i g o r o u s m o d e l , wh ich r e q u i r e s n u m e r i c a l t e c h n i q u e s , may be f i t t e d t o some d a t a bu t canno t p r e d i c t e x p e r i m e n t a l r e s u l t s a p r i o r i . 10. The e x p e r i m e n t a l r e s u l t s a re g e n e r a l l y h i g h l y r e p r o d u c i b l e i f a s t a n d a r d i z e d t e s t i n g p r o c e d u r e i s f o l l o w e d . The c o n d u c t o m e t r i c c o n c e n t r a t i o n measu r i ng sys tem becomes i n a c c u r a t e , h o w e v e r , f o r ve ry s m a l l c o n c e n t r a t i o n s . On the basis of the results of this study the follow- ing recommendations can be made. I. The d e s i g n o f e l e c t r i c c o n n e c t o r s t o the e l e c - t r o d e s s h o u l d be i m p r o v e d . 283 2. P r o v i s i o n s h o u l d be made t o measure d i f f e r e n t c o n c e n t r a t i o n r a n g e s , e . g . by p a r a l l e l c o n d u c t i v i t y c e l l s . 3. O t h e r s o l u t e s s h o u l d be i n v e s t i g a t e d , both in b i n a r y and in mu I t i componen t m i x t u r e s . 4. D i f f e r e n t s p a c e r s c r e e n s may be used t o a n a l y z e the i n f l u e n c e of the hyd rodynam ic c o n d i t i o n s . 5. O t h e r o p e r a t i n g p r o c e d u r e s s h o u l d be i n v e s t i - g a t e d . In p a r t i c u l a r i t i s p roposed t o d i s c o n n e c t the e l e c t r i c power from the ED s t a c k s d u r i n g d i s p l a c e m e n t . T h i s c o u l d lead t o l a r g e power s a v i n g s a t m o d e r a t e l y reduced s e p a r a t i o n . A l s o , t he e f f e c t of a phase s h i f t between e l e c t r i p o l a r i t y and pump r e v e r s a l s s h o u l d be a n a l y z e d . 6. The 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 on f i n a l s e p a r a t i o n f a c t o r s s h o u l d be c h e c k e d . I t may be d e s i r a b l e t o c l o s e the s o r p t i o n membranes a l o n g a l l f o u r s i d e s f o r ve ry l a r g e c o n c e n t r a t i o n s (> 10,000 ppm). 7. An open sys tem s h o u l d be d e s i g n e d i n wh ich feed i s i n t e r m i t t e n t l y i n t r o d u c e d and p r o d u c t s a re drawn o f f . NOMENCLATURE Typical Unit a = thickness of inner layer of adsorp- rcml tion membrane  L J 3 ± = Inion (-) i V i t y ° f C a t i ° n ( + ) ° r [g-mole/litre] ai = rate constant during d i l u t i o n half R -I-, cycle  L s e c J a 2  = rate constant during enrichment  r  - i - , half cycle  L s e c J b = thickness of spacer screen or width r . m i of flow channel  L c m j c = concentration [g-mole/litre] d = e f f e c t i v e length of mixing c e l l s [cm] D = d i f f u s i o n c o e f f i c i e n t [cm. 2 /sec] F = Faradays constant = 96 .5 x 10 3  [A sec/g-equiv.] Fo = Fourier number i = current density [A/cm 2 ] I = current [A] j = integer j = flux vector ["fl-mole ~ (_ cm 2  sec_ 284 285 Typical Unit k = integer number K = rate constant f 9 : m o 1 e — \J l tre-sec_ I = channel length or integer [cm] m = M(l- e )/e , or number of mixing cells M = l i n e a r equilibrium constant cm 3  of s o l u t i [cm 3  of s o l i d n = number of gram moles or  r  ,  n integer number [g-mole] nc = number of cycles ns = separation factor N = number of segments of STOP-GO algori thm p = e x p ( - a i j ) P = permselectivity of ion exchange membrane Ps or Salting or Pd = Desalting factor q = expC-az^-) Q = flow rate [cm 3 /sec] r = dimension 1 ess volume ratio R = areal resistance [fi cm 2 ] t = real time [sec] 286 = cycle time = 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 in packing or channels = ve l o c i t y vector = volume = dimensionless concentration concentration of fixed ionic charge in membrane matrix l a t e r a l distance co-ordinate valence of charged species or d i r e c t i o n of flow Typical Unit [sec] t ern 2  g-mole 1 V sec g-equivj [cm/sec] [cm/sec] [cm 3 ] g-mole g-dry membrane [cm] [g-equiv/g-mole] [cm] z i = c a l c u l a t i o n constants (i = l,2,*--,6) Greek Symbols a = stoichiometric c o e f f i c i e n t 6 = dimensionless layer thickness Y = phase lag 6 = thickness of Nernst layer or fr a c t i o n of void volume displaced e = f r a c t i o n a l void volume of packing r\ = e l e c t r i c f i e l d vector G = absolute temperature [cm] [ - ] [°K] 287 Typical Units 1 + m i X 1 + m 2 v = transport number £ = dimensionless membrane resistance TT = length f r a c t i o n P = (l-e)/ e = r a t i o of volume of packing to void volume T' =  a^/2 T = pause time [sec] V = f i n i t e difference symbol or divergence operator or [cm - 1 ] gradient vector [cm - 1 ] A$ = applied e l e c t r i c potential [V] A<J> Don = Donnan potential [V] Aip = dimensionless potential Subscri pts + for p o s i t i v e l y charged species (cations) for negatively charged species (anions) 0 refers to i n i t i a l state Lim at l i m i t i n g , steady-periodic state s s o l i d or adsorbent phase f f l u i d phase T top reservoir B bottom reservoir Supers c r i pts = refers to property in membrane m = refers to membrane solution 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., Chem. Eng. Progr., 63, No. 5, p. 69 (1967); A r i s , R., I&EC fund., 8, 603 (1969). A r i s , R. , N.R. Amundson, A. I. Ch. E. J . , _3 , 280 (1957). Baker I I I , B., I&EC fund., 9, 686 (1970). Batta, L.B., U.S. patent 3,564,816 (1971). B e l f o r t , 6., G.A. Guter, Desalination, 5, 267 (1968). , Desalination, 1_0 , 221 ( 1972). B i e r , M., "Electrophoresis: Theory, Method, and Applications," Acad. Press, N.Y. (1959). Butts, T.J., R. Gupta, N.H. Sweed, Chem.Eng. S c i . , 27, 855 (1972). ~ ~ C a l v i t , B.W., J . J . Sloan, in Proc. F i r s t Intern. Symp. Water Desalination, Washington, D.C, Oct. 3-9, 1965, Vol. 2, p. 11. Carslaw, H.S., J.C. Jaeger, "Conduction of Heat in Solids," 2nd ed., Clarendon Press, Oxford (1959). Chen, H.T., F.B. H i l l , Separation S c i . , 6, 411 (1971). Chen, H.T., J.L. Rak, J.D. Stokes, F.B. H i l l , A. I. Ch. E. J . , 1_8 , 356 (1972). 289 290 Cohan, H.J., R.W. Kennedey, i n : Proc. 1st Intern. Symp. Water Desalination, Washington, D.C., Oct. 3-9, 1965, Vol. 3, p. 389. Cook, B.A., Electrochim. Acta.., 3 , 307 ; 4, 179; 5, 216 (1961). , i n : Proc. 1st Intern. Symp. Water Desalination, Washington, D.C., Oct. 3-9, 1965, Vol. 2, p. 219. Cowan, D.A., J . Brown, I&EC, 5J_, 1 445 ( 1959). Danckwerts, P.V., Chem.Eng S c i . , 2, 1 (1953). Dewey, D.R., E.R. G i l l i l a n d , U.S. Patent 2,741,591 (1956). Eluard, R. , French patent 1 ,601 ,126 (1970). Epstein, N. , Can. J . Chem. Eng., 3/5 , 210 (1958). Forgacs, C , N. I s h i b a s h i , J . L e i b o v i t z , J . Sinkovic, K.S. S p i e g l e r , Desalination, 1_0 , 181 (1972). Friedlander, H.F., R.N. R i c k l e s , Anal. Chem., 3_7 ( 8 ) , 27 A (1965). , Chem-Eng., 73, 111 ( 1966). F r i l e t t e , V.J., J . Phys. Chem., 61_, 168 (1957). Furukawa, D.H., Chem. Eng. Progr. Symp. Ser., No. 90, Vol. 64, (1968),p. 171. Gregory, R.A., N.H. Sweed, Chem. Eng. J . , 1_, 207 ( 1970). Hamming, R.W., "Numerical Methods for S c i e n t i s t s and Engi- neers," McGraw-Hill (1962). H a r r i s , P.R., I&EC fund., 9, 684 (1970). 291 H e l f f e r i c h , F., "Ion Exchange," McGraw-Hill, N.Y. (1962). Hicks, R.E., W.G.B. Manders 1 oot, Chem. Eng. S c i . , 23_, 1201 (1968) . Horn, F.J.M., C.H. L i n , Berichte Bunsengesellschaft Physikalische Chemie, 7_3 , 575 ( 1969). Huffman, E.L., U.S. Off. Saline Water Res. Dev. Rep. 439 (1969) . Jenczewski, T.J., A.L. Myers, A. I. Ch. E. J . , 1_4 , 509 (1968). , I&EC fund., 9 , 216 (1970). Kitamoto, A., Y. Takashima, J . Chem. Eng. Japan, 3_, 182 (1970). , Desalination, 9, 51 (1971). Kobus, E.J.M., P.M. Heertjes, Desalination, 1_0, 383 (1972). Kollsman, P., U.S. Patent 2,854,393 (1958). , U.S. Patent 2 ,872 ,407 (1959). Korngold, E. , et at., Desalination, 8 , 195 (1970). Kramers, H., G. Alberda, Chem. Eng. S c i . , 2 , 173 (1953). Kressman, T.R.E., F.L. Tye, J . Electrochem. S o c , 116, 25 (1969). Lacey, R.E., S. Loeb, "Industrial Membrane Technology," W i l e y - I n t e r s c i . , N.Y. (1972). Lacey, R.E., "Electrosorption and Desorption, Process for Demineralization," U.S. Off. Saline Water Res. Dev. Rep. No. 398 (1968). , "Desalination by Electrosorption and Desorption," U.S. Off. Saline Water Res. Dev. Rep. No. 135 (1965). 292 Lacey, R.E., "Demineralization by transport depletion," u S Off. Saline Water Res. Dev. Rep. No. 80 (1962). Lang, E.W., E.L. Huffman, R.E. Lacey, J . Electrochem. S o c , 115, 88c (1968). McCracken, D.D., W.S. Dorn, "Numerical Methods and FORTRAN programming," Wiley, N.Y. (1964). McHenry, K.W. J r . , R.H. Wilhelm, A. I. Ch. E. J . , 3, 83 (1957). Mandersloot, W.G.B., R.E. Hicks, IE&C proc. des. dev., 4, 304 (1965). Mas, L.J. et al. , Desalination, 7_, 285 (1970). Matz, R. in "Proc. Interregional Seminar Economic Appl . Water Desal.," N.Y., 22 Sept. to 2 Oct., 1965, p. 79. Matz, R. et al. , U.S. patent 3,029,196 (1962). Meyer, K.H., W. Strauss, Helv, chim-acta, 2_3, 795 (1940). P a t r i c k , R.R., J.T. Schrodt, R.I. Kermore, Separation S c i . , 7, 331 (1972). P i g f o r d , R.I., E. Baker I I I , D.E. Blum, I&EC fund., 8, 144 (1969a). , I&EC fund., 8, 848 (1969b). Placek, C , "Ion Exchange Resins," Noyes Data Corp., 1970. Pn u e l i , D., G. Grossman, Desalination, 7_, 297 ( 1970). Popkin, R., "Desalination," F.A. Praeger, N.Y. (1968). Rhee, H.K., N.R. Amundson, I&EC fund., 9_, 303 ( 1970). R i c k l e s , R.N., "Membranes, Technology and Economics," Noyes Develop. Corp. (1967). 293 Rolke, R.W., R.H. Wilhelm, I&EC fund., 8, 235 (1969). Rosenberg, N.W., C.E. T i r r e l l , I&EC, 49_, 780 ( 1957). Sata, R. et al. , B u l l . Chem. Soc. Japan, 4_2, 279 ( 1969). Sabadell, J.E., N.H. Sweed, Separation S c i . , 5_, 1 71 ( 1970). Schlb'gel, R. , "Stofftransport durch Membranen," Steinkopf, Darmstadt (1964). Shaffer, L.H., M.S. Mintz, " E l e c t r o d i a l y s i s , " i n : "Principles of Desalination," ed. K.S. Sp i e g l e r , Acad. Press, 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). Solan, A., Y. Winograd, The Phys. of F l u i d s , U_, 1372 (1969). Solan, A., Y. Winograd, U. Katz, Desalination, 9, 89 (1971). S o l t , G.S. i n : "Proc. F i r s t Intern. Symp. Water Desal., Washington, D.C. , Oct. 3-9 , 1965 , Vol. 2, p. 219. Sonin, A.A., R.F. Probstein, U.S. Off. Saline Water Res. Dev. Rep. No. 375, 1968. Spiegler, K.S. (ed), "Salt-Water P u r i f i c a t i o n , " John Wiley & Son, N.Y. , 1962; :  , "Principles of Desalination," Acad. Press, N.Y. , 1966 . , Desalination, 9, 367 (1971). , Adv. Chem. Ser., 38 , 179 (1961 ) . Sporn, P., "Fresh Water from Saline Waters," Pergamon Press, Oxford, 1966. 294 Sweed, N.H., R.H. Wilhelm, I&EC fund., 8, 221 (1969). Sweed, N.H., R.A. Gregory, Aichey, 1_7, 171 (1971b). Sweed, N.H., F.B. H i l l , "Parametric Pumping," i n : "Progress in Separation and P u r i f i c a t i o n , " (E.S. Perry, ed.), Wiley, N.Y. (1971), Vol. 3, p. 171-240. Tsunoda, Y. i n : "Proc. 1st Intern. Symp. Water Desalination, Washington, D.C., Oct. 3-9, 1965, Vol. 2, p. 325. Wakao, N., H. Matsumoto, K. Juzuki , A. Kawahara, Kagaku Kogaku, 32, 169 (1968). Weiner, S.A., P.M. Rapier, W.K. Baker, I&EC proc. des. dev., 3, 126 (1964). Wilhelm, R.H., A.W. Rice, A.R. Bendelius, I&EC fund., 5, 141 (1966). Wilhelm, R.H., N.H. Sweed, Science, 195, 522 (1968a). Wilhelm, R.H., A.W. Rice, R.W. Rolke, N.E. Sweed, I&EC fund., 7, 337 (1968b). Wilson, J.R. (ed.), "Demineralization by E l e c t r o d i a l y s i s , " Butterworth, London, 1960. Yamane, R. et al. , I&EC proc. des. dev., 8, 159 (1969a). , B u l l . Chem. Soc. Japan, 42̂ , 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  F i g u r e A. I . 2 . E I e c t r o d i a I y z e r N o . I <?n s i t u > . 299 F i g u r e A . I . 3 . Dimensions of EDI e l e c t r o d e end frame. 300 1 i I - 7 ' j«P.rJ- F i gure A.I.4. Dimensions of EDI centre frame. F i g u r e A . 1 . 5 . D i m e n s i o n s of EDI c l a m p i n g f r a m e . APPENDIX A.2 ELECTRODIALYZER NO. 2 302 F i g u r e A . 2 . I L a b o r a t o r y t e s t i n g s t a t i o n . o Figure A.2.2 Dimensions of EDM electrode end frame. APPENDIX A.3 MANUFACTURING PROCEDURE FOR MEMBRANE-SPACER FRAME Each membrane spacer frame consisted of 5 parts which were permanently joined together. Figure A-3-1 shows an exploded view of the assembly. Anionic _ Membrane Filter Paper Cationic — Membrane i 23 Polyethylene Frame Polypropylene Spacer Figure A-3-1: Exploded view of membrane-spacer assembly. 305 306 CUTTING; The supporting frame was punched out of low density polyethylene sheets (1/16" thickness) with a double-knife- edge. The outer edge cut measured 3" x 8-7/8", the inner one was 1-1/2" x 6-11/16". The frames were unsymmetric, and were therefore marked at one corner for future reference. Flow 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 stream holes on the electrode end p l a t e s , see Appendix A.2. Resets (1/8" wide x 0.035" deep) were milled out along both inside lengths of the frames. Spacer screens were punched out using a single- knife-edge (1-7/8" x 6-11/16"). Spacers were then i n d i v i d u a l l y f i t t e d to the resets of the frames. Membranes were pre-cut and soaked for 24 hours in 0.5N aqueous NaCI solution and punched out using a single- knife-edge (1-3/4" x 6-3/8"). F i l t e r paper (Whatman No. 1) was cut into 1-1/2" x 6-1/16" pieces. ASSEMBLING: Each membrane pair was sealed along both widths with a heated bar (seal approximately 1/8" wide). A piece of f i l t e r paper was inserted between the sealed membranes. 307 The spacers were welded to the frames by means of a heated j i g which was mounted on a crank shaft punch. The temperature of the j i g was controlled by a rheostat to approximately 240 ° F . Spacer, frame, and a sheet of thin paper were positioned under the hot j i g . The paper was used to aid separation of the j i g after completion of the jo i n i n g process of frame and spacer. i "LT 33 / / / / / \ \ \ \ \ J i g w i t h Hea t ing Cab le - P a p e r - F r a me S p a c e r F i g u r e A - 3 - 2 : W e l d i n g of s p a c e r and f r a m e . The hot j i g was lowered and pressed down with gradually i n - creasing pressure for approximately 1 minute. The joined spacer frame was then quickly removed and quenched in a cold water bath. The paper was removed. A sorption membrane was tagged to the frame by means of a heated bar. 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 is neglected i t is s u f f i c i e n t to consider what happens to the uniform concentration of one- end reservoir during any complete c y c l e , which starts with feeding the reservoir solution to the separator. The brine cycle is i l l u s t r a t e d in Figure B - l . The concentration p r o f i l e s in brine tank and separator are shown at d i f f e r e n t instants during the (k+1) cycle: 0 - r e f e r s t o t h e i n i t i a l c o n c e n t r a t i o n i n t h e b r i n e t a n k . 1 - a f t e r t i m e t = T/2 - y ( p o l a r i t y s w i t c h e d t o n e g a t i v e ) . 2 - a f t e r o n e - h a l f c y c l e t = T / 2 . 3 - a f t e r t i m e t = T/2 + y. 4 - a f t e r t i m e t = T - y ( p o l a r i t y b a c k t o pos i t i ve ) . 5 - a t end o f c y c l e t = T. 309 3 09 A F i g u r e B . I . C o n c e n t r a t i o n changes in 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 in p a r a m e t r i c pump- ing o p e r a t i o n . 310 The shaded area is the effluent concentration p r o f i l e at the end of the cycle indicates the r i s e in concentration. The calculation of the lines 5 is straightforward. 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 • °] [CB,k + ( K 2 " K i ) J + 2 K i Y » \ ~ v\ 'B,k 5 2 The t o t a l area is simply A = K 2 Y 2  + h (K2-KOJ+ 2(K 1  + K 2 ) Y (y- 2 Y ) + ̂  (K 2 -Ki)T + 2K lY Thus the concentration change is given by c B , k + l "  C B , k = f A  = ( K 2 - K l >! + + By s i m i l a r i t y , the dialysate change during the (£ + 1) cycle (see also Figure 3.1 .b) i s : C T,* + 1 "  C T,* = (Ka-K,) 7 , - (K 1 + K 2 ) J The f i r s t dialysate producing half cycle must calculated separately. A s i m i l a r area analysis gives c - c C T,1  C T,0 T (T 2-Y \ K: { 2Ki - K 2 Y T Y  + r Kx+2Ki 2  Y - K 2 Y : (I 2 - K 2 r Hence c. •• - c t,l T,0 312 In general, for n £ 1 T,n = c T,0 K i | + (K 2 + K K 2 -Ki Ki+K 2  x 4 " 2 1 (n-l)T and c B,n  C B,0  + K 2 - K i . Ki+K2 x 4 2 T n T 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 stationary and moving parts of the systems may be considered as blocks. One void volume displacement is assumed. For the n t h  d i l u t i o n half cycle one has, according to the assumed rate law C T e s C B T and n 3t = - a x r 1 c n n 3t at subject to the i n i t i a l conditions for t = 0 ( • C T V. J n N n - l ( c i ) » - ( c s ] » - l 313 314 Hence Hn " ( C T]n-l  e X P ( "  3 l t ) ( B . 2 . 1 ) n " ( C s)n-1  +  K ^ J n - l C 1  " « P ( - » l t > ] .th S i m i l a r l y for the n enrichment half cycle C T 1 3t n and n 9t a 2 - P 3t n subject to the i n i t i a l conditions for t = 0 ( 1 f 1 C B n C B • r i c = c! I  S J n n - l n 315 Hence 1 - exp(-a 2 1 ) n n f i l ' n [ C B J n-1 *> J (B.2.2) 1 - exp(-a 2  t) The systems of difference equations (B.2.1) and (B.2.2) may be solved stepwise as follows. The global start- ing condition is chosen to be for t = 0 • H. - hi - ( and the abbreviations h i ) and p = exp q = exp - a 2 are used. n= 1 1 + l ( l - p ) (c s ) = q + f ( l - P ) ( c g j ^ - 1 + P(l-q) + ( l - q ) ( l - p ) 316 n = 2 (  t c n = 3 P 2 k) = q • l ( l - p ) • I p ( l - p ) ( c s) "  q 2 +  ^ ( 1 " P } +  F pq ( 1 " p ) ( c B j = 1 + p(l-q) + ( l - q ) ( l - p ) + p ( l - q ) [ q + ^ 0 - p f | + ( l - q ) ( l - p ) p - 1 + p(l-q)(l+q) + (l-q)(l-p)(l+p+q) - P 3 [ C ;] = q 2  + q(l-p)l(p+q) + \ p 2 (l-q) [ c l = q 3  + q 2 ( l - p ) l ( p + q ) + q(l-p) 1 p 2 ^ ' 3 = q[q 2  + £ ( 1 - P ) ( P 2  + q 2  + pq)] ( c B j = l + (l-q)[p(l+q) + (l-p)(l+P+qf|+p(l-q)[q 2  + q(l-p)l(p+q)] + ( l - p ) ( l - q ) q 2  - = 1 + (1-q) pp(l+q+q 2 ) + ( 1-p) (1+q + p+q  2  + pq + p 2  )J 317 n = 4 C B V. . J = 1 + p(l-q)(l+q+q 2 ) + (1-q)(1-p)(1+p+q+q 2 +pq+p 2 ) + p ( l - q ) [ q 3 + ( l - p ) £ ( p 2 q + q 3  + pq 2 )] + ( l - q ) ( l - p ) p : 2  +  p ( l . q * ) - p * - q * +  I pk-* q*  +  \ p 5 "* q* £=1 H=l 2 + p ( l V ) - p* - q(l-p) I p3"* q* i = 0 The general recurrence scheme is clear now and the result becomes c T  I = p n T n ( 1 c = 2 + P(l-q n) - pn - q ( l - p ) p n - 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 half cycle followed by an enrichment half c y c l e . After substitution of the rate laws (19) into the mass balance equation ( 6 ) , one has for the f i r s t part cycle 3c f  3c f _ t  + V _ L + a i C f = 0 f 3C. 3t ~  3 1 C f * (B.3.1) and for the second part cycle 3t = - a 2  c, 3c f Tt 3c _ L _ 1 2 . C = 0 3 z p s (B.3.2) 318 319 The method of c h a r a c t e r i s t i c s (Acrivos, 1956), is applied and the following sets of ordinary d i f f e r e n t i a l equa- tions are obtained: The f i r s t equation of ( i ) is rewritten as dc. dt dz = - a! • c. or dz dt and d In c 1 dt - ai (B.3.3) The p a r t i a l d i f f e r e n t i a l of the second equation in (B.3.1) is i d e n t i c a l to the total derivative dc 3c 3c . ac s  =  s , s_ dẑ  =  s_ dt 3t 3z * dt at since there is no flow in the stationary phase (dz/dt = 0) Hence dc s _ ai c . (B.3.4) d t p " f S i m i l a r l y , for the set of equations (B.3.2) one f i nds 320 ^ 1 dt a 2  c s  , (B.3.5) and dz dt = v , and dc f ~dT P 92 c( (B.3.6) Because of (B.3.5) i t is not possible to eliminate the concentration in the stationary phase, c s , from the set of equations. The local concentration p r o f i l e s in both phases have to be calculated step by step. The following equations take into account that the frames of reference for equations (B.3.3) and (B.3.6) are t r a v e l l i n g with the f l u i d velocity v, whereas equations (B.3.4) and (B.3.5) are written for a stationary frame of reference. If the (z,t) plane is considered one can calculate the necessary local and average concentration p r o f i l e s . For the f i r s t part cycle: 321 c4u=e ,t) Cf(z, t=T/2) T /2) T /2 c f (A,t) = c f (£-vt,0) exp(-ait) t,n T T/2 c f U , t ) dt z '2 : B,n-l  e x P a z f z I 1 z/v f c c ( z 0) + * i s ' p c^(z-vt,0) exp(-ait) dt + p f i 2 c B,n-l  e x P a i z 322 For the second part cycle c 5 (z, t ) c^(z,t) c s (z ,T) = c s c^(z =̂0,t) f Tl exp - a 2  j \ 4 c f (z,T) = c T n  + pa B,n T T/2 r z/v z + I - v t , j exp(-a 2 t) dt ( r) /" Tl c f (0,t) - c f  vt , j  +  pa 2  c s  v t _ v s , j exp(-a 2 s) ds T/2 T f T/2 c f (0,t) dt 323 In Table B-l the concentration d i s t r i b u t i o n s in time and space are presented for four successive half cycles and under the r e s t r i c t i o n s , ĉ - = c g  = 1.0 at t = 0, ai = a 2  = a, p = 1. The time and space average concentrations are included as w e l l . The abbreviations x' = aT/2 and £ = az/v are used. Table B.l : Average and local Concentrations During the First Two Cycles of a Parametric Pumping Operation for Concentration Dependent Rates of Mass Transfer. — •- 1/2 / 3/Z 2 AVERAGE EFFLUENT • AVERAGE SOLUTIOA/ AVERAGE ADSORBED LOCAL SOLUTIOA' 2 e . p H ) + £ ^ - Z L expM ')j| exp(- j ) LOCAL AD-SOR&EA/T 2-(/*j- Z) axf>6-J) 2 < * f ( - z ) - APPENDIX B.4 MULTIPLE STEP DISPLACEMENT MODEL (STOP-GO ALGORITHM) In the conceptual model of this scheme the two phases may be represented by two-dimensional pl a t e s . The areas of the plates indicate the volumes of each of the phases. Since the frame of reference may be attached to either of the phases, i t w i l l be assumed that the adsorbent (or adsorp- tion membrane) is displaced r e l a t i v e to the s o l u t i o n . The displacement occurs stepwise. The plates are divided into segments of i d e n t i c a l length Az = £/N according to the number of steps (see Figure B-2). If one void volume is displaced, there w i l l be N segments on the moving plate and 2N segments on the stationary one. Each segment repre- sents a separate well mixed c e l l . During the STOP periods mass is transferred between adjacent c e l l s for time interv a l s At = T/2N. During each GO step the segments are displaced by one increment without mass transfer taking place. At the end of each half cycle the 325 326 segments on the stationary p l a t e , which have no neighbours on the moving p l a t e , may be intermixed to satisfy- the end mixing condition. CM N 4 Direction of Displacement 2N F i g u r e 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 s t e p 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 IV program was prepared for an IBM 360/67 d i g i t a l computer to simulate concentration dependent mass transfer rates according to equations (27), see Section 3.3. The program is written in double precision because round-off errors affected the overall mass balance for large N's. The FORTRAN program is l i s t e d on the next page followed by the computer printout of a simulation run for 327 N = 100 , 6 = \ , a 2 = O.OlCsec" 1] , a 2 = O.OUsec- 1] , p = 0.5 , T = 10[sec] 328 1 c 2 C MULTIPLE STFP I) I SI'LACF MFNT MODEL 3 C C0NCEN1 *ftT t UN nt?LNl>FNT RATES DF H\SS TRANSFE* 4 C 5 OOUniE PRCCISION P. 0, P 1 , 01 ,.:F FF , S? , S I . DE XP, X I 203 ) , Y ( 200 » 6 REAL A I , A 2 ,.'4 , F A U » P A , B S , S F P 7 READ 15,1) M . N O.U.Al,A?,K,TAJ 8 1 FORMAT ( 3 I 3 , 4 r f > . 4 ) 9 C 10 M l = H f l 11 N 0 1 = N D » 1 12 M2=M«ND 13 P=-Al*rAU/ND 14 P=DEXP(P| 15 Q=-A2*TAU/ND 16 ; = Dfi X P O ) 17 P l = ( l . D O - P I / R 18 Q l = ( l . D U - t f l * R 19 BA=100./(MH',*R*N0> 20 DO 2 1=1,M2 21 X ( I ) = 1 . 0 0 22 2 Y U M 1 . 0 0 23 C 24 WRITE ( 6 , 3 ) M ,N,N0,M,Al,A2,.*,TAJ 25 3 FORMAT ( 1H I / / / • DISPERSION MODEL 3F RATE THEORY •// 26 110X,' ENDS WELL MIXED, EXCHANGE' - DISPLACE 27 2« NUMBER OF COMPARTMENTS = 13/ 28 3' NUMBER OF CYCLES = •• • 1 3 / 29 4 ' DISPLACED VOLUME = ' ,\it'/' t l i f 30 5« INITIAL CONCENTRATION = 1.0 •/ 31 6« DESALINATION KATE COEFFICIENT = • , F 6 . 4 , ' ! l / S E C J • / 32 7< CONCENTRATION RATE COEFFICIENT = • , F 6 . 4, • t 1 / SEC ) ' / 33 8' VOLUME RATIO = S F 6 . 3 / 34 9» CYCLE TIME = '.F6.1 , ' ( S E C I ' / / / » 35 WRITE ( 6 , 4 ) 3 6 4 FORMAT Ii' CYCLE NO. B*IN6 DIALYSATB S E P A R A T I 3 N BALANCE ( ? ) 37 !•> 38 C 39 C F I R S T HALF C Y C L E 40 C 41 DO 100 J=1,N 42 DC 10 L=1,N0 43 l = F + L 44 OC 5 K=1,V 45 1=1-1 46 Y ( I * l ) = Y ( 1 ) * X ( I ) « P 1 47 5 X ( I ) = X ( I ) » P 48 1C CCNTINUE \ 49 C E F F = 0 . 0 50 OG 11 1=1,NO 51 11 C E F F = C 6 F F * X ( I I 52 CEFF=CEFF/ND 53 00 12 1=1,NO 54 12 X ( I ) = C E F F 55 C 56 C SECCNC HALF CYCLE 57 C 58 00 2 0 1=1,NO 59 !=ND1-L 60 OC 15 K=1,K 61 1=1*1 62 X { I ) = X ( I ) » Y ( I ) * C 1 63 15 Y ( I - 1 ) = Y ( I ) * C 64 2C CCNTINUE 65 S1=0.0 66 S2=0.0 67 S3=0.0 68 OC 21 1=1.f 69 S 1 = S 1 * X ( I ) 70 21 S 3 = S 3 * Y ( l l 71 DC 22 I = H t H 2 72 22 S 2 = S 2 * X ( I I 73 B S = « S H S 7 » S 3 « K ) * E A 74 S2=S2/ND 75 SEP=S2/CEFF 76 CC 23 I'fl,f>2 77 23 X U ) = S2 78 C 79 C P R I M C U T 8C C 81 WRITf (6,25) J,S2,CEFF,SEP,8S 82 25 FCR^AI ( I 7 . 4 F I 2 . 4 ) 63 ICO C C M I N U E 84 S I C P 85 ENC FKC CF FILE 329 DISPERSICN PCCEL OF RATE THEORY ENDS KELL M X E O , EXCHANGE - DISPLACE NLCeER CF CCKPARTPENTS NIPSER CF CYCLES DISPLACEC VCLL"E INITIAL CCNCEMRATICN DESALINM1CK RATE CCEFFICIENT CCNCENTRATICN RATE CCEFFICIENT VCLL'PE RAT1C CYCLE TICE ICO 60 50/1C0 1.0 0 . 0 1 C C I l / S E C l 0.01CCI1/SECI C.5CC 10.01 SEC) CYCLE NC. BRINE DIALYSATE SEPARATION BALANCE 1 0.9821 0.95C7 1.C330 99.9998 2 0.S668 0.9293 1.C404 99.9998 3 0.9539 0.9105 1.C477 99.9998 4 0.9430 0.8939 1.0549 99.9998 5 0.9338 0.8793 1.0620 99.9998 6 0.9260 0.8663 1.0689 99.9998 7 0.9195 0.e548 1.0757 99.9998 8 0.9140 0.8445 1.0823 99.9998 9 0.9C94 0.8352 i.oe a 8 99.9998 10 0.9C55 0.8269 1.C951 99.9998 11 0.9024 0.8194 1.1C13 99.9998 12 0.8SS8 0.8126 1.1073 99.9998 13 0.8976 0.8063 1.1132 99.9998 14 0.8959 0.8CC6 1.119C 99.9998 15 0.8946 0.7954 1.1247 99.9998 16 0.8936 0.7905 1.1303 99.9998 17 0.6928 0.7861 1.1358 99.9998 18 0.8923 0 . 7 e i 9 1.1412 99.9998 19 0.8920 0.778C 1.1465 99.9998 20 0.8918 0.7743 1.1518 99.9998 21 0.8918. 0.7708 1.1569 99.9998 22 0.8920 0.7676 1.1620 99.9998 23 0.8922 0.7645 1.1671 99.9998 24 0.8926 0.7615 1.1721 99.9998 25 0.8930 0.7587 1.1770 99.9998 26 0.8935 0.756C 1.1818 99.9998 27 0.8941 0.7535 1.1867 99.9998 28 0.8947 0.751C 1.1914 99.«»998 29 0.8954 0.7486 1.1962 99.9998 30 0.8962 0.7463 1.2C09 99.9998 31 0.8970 0.744C 1.2C55 99.9998 32 0.8978 0.7419 1.2102 99.9998 33 0.8966 0.7398 1.2147 99.9998 34 0.8995 0.7377 1.2193 99.9998 35 0.9CC4 0.7357 1.2238 99.9998 36 0.9013 0.7338 1.2283 99.9998 37 0.9022 0.7319 1.2328 99.9998 38 0.9032 0.73CC 1.2372 99.9998 39 0.9C42 0.7282 1.2416 99.9998 40 0.9052 0.7264 1.2460 99.9998 41 0.9C62 0.7247 1.2504 99.9998 42 0.9072 0.723C 1.2547 99.9998 43 C.9C82 0.7213 1.2590 99.9998 44 0.9C92 0.7197 1.2633 99.9998 45 0.9102 0.7181 1.2676 99.9998 46 0.9113 0.7165 1.2719 99.9998 47 0.9123 0.7149 1.2761 99.9998 48 0.9133 0.7134 1.2803 99.9998 49 0.9144 0.7119 1.2e45 99.9998 50 0.9154 0.7104 1.2887 99.9998 51 0.9165 0.7089 1.2928 99.9998 52 0.9175 0.7075 1.297C 99.9998 53 0.9ie6 0.706C 1.3011 99.9998 54 0.9197 0.7C46 1.3C52 99.9998 55 0.92C7 0.7032 1.3C97 99.9998 56 0.9218 0.7019 1.2133 99.9998 57 0.9228 0.7CC5 1.3173 99.999H 58 0.9239 0.6992 1. 2214 99.9998 59 0.9249 0.6979 1.3254 99.9998 60 0.9260 0.6966 1.3293 99.9998 STCP e x c c u n c N 0 I CHP I K M EC APPENDIX B.5 DERIVATION OF CONCENTRATION TRANSIENTS FOR EQUILIBRIUM CONTROLLED PURE PAUSE OPERATION CASE A: I n i t i a l equilibrium constant K 2 . F i r s t displacement downward. It is s u f f i c i e n t to consider the overall concentra- tions of the adsorbent (c ) and of the solution in the end s reservoirs and inside the separator (c^ and C g ) . The mass balances during the n t h  cycle are: for the f i r s t half cycle c c B c B n + P C c B > n-1 S and the second half cycle 330 331 C B ( C T]  + p ( c s )  =  ( C T) .  + p ( c s Substitute equilibrium relations r 0 c s v. J = K 2 f< n and Ki and l e t and use X = 1 + pK 2  and K = 1 + pKx n- 1 J  n One has to solve the system of difference equations 332 ( C B) , + 1 " - 1 ) ! ' n - 1 n - 1 + X - 1 K subject to the i n i t i a l conditions ( C B] " (CT E.g. n = 1 c- Cp + ( x - i )c 0  „ x — Co — K K n = 2 = c, 1 + ( < - ! ) • £ C o l + -r 1 1 X K • for n > 1 l C Tj X/ + X - 1 f,  +  1 11 X K Co- - c, x _ i f i _ r " 333 n = 3 Co. X 1 +  X i + (K ' K 1 K Co 1 + M x l + j _ KX = £0- J  3 K K ̂ X K_ + ( X - 1) + ( X - 1) (1 1 K 1 + ̂ x = c, M X 11 K 1 +  7x The form of the equation is now obvious, so that in general 3 3 4 = 1 + [X K n - 2 I £=0 ( 1 = 1 + fl U 1 KX KX n - 1 or h) ' n = 1 + K-X KX - 1 (KX) n - 1 X K 1 K K-X KX - 1 (KX) n - 1 CASE B: I n i t i a l equilibrium constant K i . F i r s t displace- ment up. By analogy with case A, the mass balances lead to the system of difference equations 335 (c T ) + U - l ) ( c B . V. ' n - 1 V J > n. for n > 1 f 1 c, + (K - 1) c n-1 Subject to the i n i t i a l conditions H. - K = c, The solution i s c 0 * + 1 K -X KX - 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 is shown in Figure C . l . The pr in tout columns involve the fo l lowing c a l c u l a t i o n s . 1 : Cycle number (ncyc) i s part of the input d a t a 2 : Real time (t) in seconds t - 2 * + ^ - • ncyc ( C - l - 1 ) 3 & 4 : Average bottom (c B ) and top (Cj) reservo i r concen- t ra t ions in parts per m i l l i o n NaCI in H20 converted from [mV] reading using c a l i b r a t i o n data fo r con- duc t i v i t y c e l l . 5 & 6 : Concentrations ( x g and Xy) normalized w . r . t . the i n i t i a l concentrat ions. 7 : Separation factor (ns) as ra t i o of average bottom and top product concentrat ions 337 3 3 8 8 & 9 : Average current consumptions during enr ich ing and d ia l yz ing ( I 2 ) ha l f cycle in amperes. Converted from [mV] reading using res is tance c a l i - brat ion data. 1 0 & 11 : Current e f f i c i e n c i e s of d ia l yz ing (E x ) and en r i ch - ing (E 2 ) ha l f cycle in per cent according to the usual d e f i n i t i o n (see e .g . Wi lson, 1 9 6 0 ) . a c t u a l c o n c e n t r a t i o n change ^ 1 0 0 ( C - l - 2 ) t h e o r e t i c a l c o n c e n t r a t i o n change The theore t i ca l concentrat ion change i s ca lcu la ted assuming perfect membranes and neglect ing water t rans fer as wel l as the volume changes due to the s a l t t r ans fe r . Consider a flow channel of volume V / n , where V a a i s the act ive void volume of the stack and n is the number of spacer screens. The theore t i ca l concen- t ra t i on change, in [ppm], of the so lu t ion 1n t h i s channel is given by A n " I • t • 1 0 6 * M (r i o\ A c t h e o r . zF • V , /n ( C " 1 " 3 ) a [sec] where I mean current [A] t duration the current I i s passed z valence [g-equiv . /g-mole] F  9 F ^ 5 0 0 a y ' S C ° n S t a n t = [A sec /g -equ iv . ] M molecular weight of r„,„ solute = 5 8 . 4 5 [g/g-mole] I t i s assumed that the displaced volume ( 6 • Vo) of concentrat ion Co + c i s mixed with the dead volume in the reservo i r which receives the e f f l u x . The theore t i ca l concentrat ion change i s therefore for the enr ich ing ha l f cycle 1 339 Ac t h e o r , I I, • U - n .  6  '  V o/ V a *  1 0  •  M zF « • v0 + vB for the dialyzing half cycle AC t h e o r , 2 I 2  • t 2  • n zF 6 • V 0 /V a  • 10 6  • M 6 • V 0  + V T F i n a l l y for the coulombic e f f i c i e n c i e s in [%] E, = C B,ncyc'~  C B,ncyc - l 6 V ° + V Ii • t i • n ' 6 V 0 /V a B c T  - c T  6 Vo + V T T , ncyc- I T, ncyc T I 2  • t 2  • n * 6 V 0 /V a 0.165 • 0.165 (C-l-4) Equations (C-l-4) are reasonably accurate for di l u t e solutions provided water transfer is n e g l i g i b l e . Power e f f i c i e n c y E^ in per cent is defined as theoretical minimum, reversible work of separation ,  n f ) actual work performed * For ideal dilute solutions the numerator is given as the reversible work of mixing per g-mole of solution 340 •Aw r e v = R0 i = 1 i = 1 where .Q and ( 2 ) refer to the state before and after mixing, and the y. are the mole fractions of the the components j in the state Q or ( 2 ) R universal gas constant = 8.317 Wsec K g-mole 0 absolute temperature = 298 [°K] The actual work performed is Aw act j ncyc where l,k 2,k • average current during k enriching half cycle average current during k dialyzing half cycle th th The reversible work has to be calculated for each reservoir separately, multiplied by the number of moles in the r e s e r v o i r , and the dialyzing work sub' tracted from the enriching work. 341 Thus E = P [ - A w r e v ] • [6V 0 + VB] - (• v ; e n r . ^ ' K Aw rev dial («sv0+vT A<{) c  k=l ^  1 k  + ! 2,k 13770.0 [%] 342 READ: Calibration constants for concen- t r a t i o n s , flow rate, current 1 READ : Run no., i n i t i a l concentration, operating conditions, no. of cards 1 CALCULATE : operating parameters In proper units PRINT : table heading T i = 1, no. of cards READ : Cycle no., concentrations, currents, k yes n o READ : set of new operating conditions RECALCULATE : operating parameters CALCULATE : Concentrations, separation factor (+ PRINT) currents, e f f i c i e n c i e s • PRINT : stack detalIs , operating parameters Figure C.I.: Flow chart of evaluation program for EDI runs 343 1 c 2 C PROGRAM TC EVALUATE FIRST ED CELL EXPERIMENTS 3 C 4 READ (5,1) NS,NC,VOL,VA 5 1 FORMAT (2I3.2F6 . 4 ) 6 RE AC (5,2) AC,A1,B1,A2,B2 7 2 FORMAT (5FIC.2) 8 REAC (5,3) NC,NCARD,SPE,CISP,PHI,DVB,OVT,DTF,DTS,CBV,CTV 9 3 FORMAT (21 3,F4.1,8F6.4 ) 10 IF (SPC-.GT;4C.01 GO TO 4 11 A3=0.689 12 03=0.686 13 GO TO 5 14 4 A3=C.79l 15 B3=-3.43 16 5 V={A3*SPE*B3)*24.1/VA 17 CBG=CBV*(Al*Cev*Bl) 18 J CTC=CTV*(A2*Crv*e2) 19 1 YC=(CB0+CTG)/6494444.4 20 X1M=Y0*AL0G(YO) 21 VC=2.288*DISP 22 VB=2.288*DVB 23 VT=2.288*CVT 24 HT1=DTS+VC/V*24.1/VA 25 HT2=0TF+V0/V«24.1/VA 26 T=HT1+;HT2 27 I HE1=0.165*(VC+VB)/V0«VA/NC/HTI 28 HE2= 0.165*(V0+VT)/V0*VA/NC/HT2 29 HEP=2754C.00/PHl/T 30 C 31 C SUMMATION CONTROL VARIABLES 32 C 33 L=0 :\ 34 Zl=1.0 35 Z2=100.0 36 CU=0.0 37 CB1=CB0 38 CT1=CT0 39 TIME=0.0 40 C 41 C PRINT TABLE HEAD 42 C 43 WRITE (6,6) (1,1=1,12) 44 6 FORMAT (1H1, • • 46 214,17,18,17,18,17,19,ie,17,18,17,18// 47 3'CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT 48 "4 CURRENT POKER'/ 49 5* NO. TIME BOTTOM TOP NORMALIZED FACTOR ENR. OIA 50 6L.- EFFICIENCY EFFICIENCY'// 51 7'NCYC T CB CT XB XT NS II 12 52 8 El E2 EP •/• I-) (SEC) (PPM) (PPM) (-) ( 53 9-) (-) (A) (A) It) m ( * ) • / » 54 WRITE (6,7) 56 l—i : '. « / ) 57 C 58 C PRINT INITIAL CCNOITICNS 59 C 60 WRITE (6,8) l,CU,CR0,CTC,Zl,Zl,2l,CU,CU,Z7,Z2,22 f>l 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 62 C  3 4 4 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 103 CU=CU+(CL'KCL I 2)*INCYC-L) 104 Yl=CB/3247222.2 1C5 Y2=CT/3247222.2 1C6 EP=( (V0+VB)*(X1M-Y1*ALCG(Yl))•(VO*VT)*(Y2*ALCG(Y2)-XlM))/CU»HEP 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 1 2 3 4 5 6 ? n 9 1 0 11 1 2 CYCIE RC A l crscr-MRAi I C N C O N C I NTWAI I C N SfCARATIO* 1 CUHHTN f ClWRCNf P O W I R K C . l i f t U C I 1 C M ( C P NURMAl Ur.O • F A C T O R r . N H . L' 1 Al . EFFICIENCY trr icitNCY NCYC T CP CI XI ! X T NS 1 1 1 2 El C? F P l - l ( S E C ) ( T P * ) (PPM) l-» l-> l - l IA) I A ) I t ) I t l I D 0 o.c 1 0 3 2 . K i l l . I.CO 1 .ceo I.CO 0 . 0 C O 1 0 0 . 0 1 0 0 . 0 1 0 0 . o c o 1 5 5 . 5 1 2 7 R . 7 7 4 . 1 . 2 4 0 . 1 6 4 1 . 6 2 1 . 1 ( . 0 1 . 1 2 0 3 7 . 5 3 7 . 7 7 . 3 7 1 7 1 1 1 . 1 1 4 1 6 . 6 7 1 . 1 . 3 7 0 . 6 6 2 2 . 0 7 1 . 1 6 0 1 . 7 0 0 IP.O 1 3 . 2 1 . 6 7 8 3 l ( k . 6 1 4 9 7 . 6 2 2 . 1 . 4 5 0 . 6 1 4 2 . 1 6 1 . 2 C 0 1 . 1 8 0 1 0 . ) 6 . 4 1 . 3 C I 4 2 2 2 . 2 1 5 4 2 . 5 9 3 . 1 . 4 9 C . « 8 6 7 . 5 5 1 . 2 C 0 1 . 1 6 0 5 . 7 3 . 0 1 . 0 5 7 5 2 1 7 . 7 1 5 7 C . 5 8 2 . 1 . 5 2 0 . 5 7 6 2 . 6 4 1 . 7 0 0 1 . 1 2 0 1 . 6 1 . 4 0.661 6 3 3 3 . 2 1 5 6 4 . 5 7 0 . 1 . 5 3 U . 5 6 3 2 . 7 3 1 . 7 C 0 1 . 1 0 0 1 . 8 1 . 8 0. 7 5 7 7 lee.e 1 5 6 9 . 56e. 1 . 5 4 0 . 5 6 1 2.75 1 . 2 C 0 1.100 0.7 0 . 4 0.655 TABLE C . l . 1 « NU»ERICAl EVALUATICN OF EXPERICENT E 0 1 - S 2 - 1 5 / 4 1 8 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NO. TI"E BCTTCM TCP N 0 R M A L I 2 E 0 FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT xe XT NS 1 1 ' 1 2 E l E? EP l - l ISEC) IPPMI IPPMI «-) l - l «-> ( A l IAI IT! I t ) I t ) 0 0.0 1C13. 1019. I.CO l.CCC I.CO 0.0 C O 100.0 100.0 1 0 0 . 0 0 0 1 27.6 1122. 929. 1.11 0.911 1.21 1.440 1.300 23.1 21.3 0.739 2 55.5 1212. 851. 1.20 0.e35 1.43 1.4C0 1.400 1 9 . 8 1 6 . 9 0.682 3 83.3 1303. 787. 1.29 0.777 1.67 1.4C0 1.400 1 9 . 9 14.1 0.648 4 111.1 1377. 735. 1.36 0.722 l . R B 1.400 1.390 1 6 . 1 1 1 . 4 0.604 5 138.9 1447. 697. 1.43 C.684 2.09 1.400 1.380 15.2 8 . 6 0.564 6 166.6 15CC. 664. 1.48 C.652 2 . 7 7 1.4CC 1.360 11.6 7.3 0.523 7 1V4 . 4 1564. 639. 1.54 0.627 2.46 1.400 1.360 14.1 5.8 0.497 8 222.2 1584. 626. 1.56 0.614 2.55 1.4C0 1.360 4 . 3 2 . 9 0.450 9 249.9 1626. 606. 1.60 0.595 2.70 1.400 1.360 9 . 2 4 . 4 0.426 1C 277.7 1654. 587. 1.63 C.576 2.R3 1.4C0 1.360 6 . 2 4 . 4 0.401 11 3C5.5 1679. 570. 1 . 6 6 0.559 2.96 1.4C0 1.360 5 . 6 3 . 8 0.379 12 333.2 1702. 559. 1.68 C.548 3.06 1.4C0 1.360 4 . 9 2 . 6 0.358 13 361.0 1722. 546. 1.70 0.536 3.16 1.4C0 1.360 4 . 3 2.3 0.339 14 3E8.6 1739. 539. 1.72 0.529 3.24 1.400 1.360 3.7 2.0 0.322 TABLE C . l . 2 : NUMERICAL EVALUATICN OF EXPERIMENT E D I - S 2 - 1 3 / I 1 9 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER KG. TIME BCTTCP TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP l - l ISEC) (PPM) (PPM) l - l l - l l - l IA) IA) (II I t ) I t l 0 0.0 1036. 1042. I.CO l.CCO 1.00 0.0 C O 100.0 100.0 100.000 1 27.8 1100. 942. 1.C6 C.903 1.17 1.360 1.220 27.8 2 5 . 3 0.880 2 55.5 1155. 676. 1.11 0.640 1.32 1.320 1.400 2 5 . 3 14.4 0.774 4 111.1 1261. 738. 1.22 0.708 1.72 1.320 1.360 24.8 15.6 0.731 6 166.6 1347. 656. 1.30 C.63I 7.06 1.370 1.320 19.9 9.3 0.651 8 222.2 1416. 599. 1.36 0.574 2.38 1.370 1.300 16.1 7.0 0.568 10 277.7 1475. 5 5 5 . 1.42 0.532 2.67 1.3C0 1.280 13.8 5 . 3 0.536 12 333.2 1517. 521. 1.46 C.5C0 2.92 1 .2 80 1.260 10.0 4.1 0.488 14 3(8.8 1547. 494. 1.49 C.474 3.15 1.2P0 1.760 7.4 3 . 3 0.446 IS 416.6 1558. 462. 1.50 0.463 1.74 1.280 1.760 5.4 2.B 0.426 tARLF C . l . 1 I NUMERICAL FVALL'AIICN CF EXPERIMENT IOI-S2-15/I2C 346 , | ? J 4 5 6 7 II 4 10 I I I ? . C Y C L E R E H CCNCFN1HM ICN CPNCfNT R A T ICN St I'ARAT I C N CURRFNT CUKHfNT POWCR N O . T i e r I ' d i c K irp K C H ^ A L I / I L ' i«cinn I N K . C I A I . rrricirNCY t m c i i N C v N C Y C T Cn C l XI! XT NS I I 12 F l F2 CP ( - » (SEC) IPI 'M |PP»> (-1 l - l l - l I A I I A I l t » 1*1 H I c O.C 978. 9HC • 1.C0 I.CCO I.CO 0.0 CO 100.0 10C.0 100.000 2 55.5 1C59. H4C. i.ce C.90H I. 19 1.360 1.160 27.5 30.5 0.985 4 111.1 1133. 839. 1.16 0.65S I. 35 1.340 1.340 25.2 17.7 0.862 6 1(6.6 1196. 73C. 1.22 0. 796 1.54 1.320 1.320 21.9 20.2 0.817 fl 222.? 125C. 739. 1.28 C.754 1. 70 1.320 1.32C 19.1 14.4 0.757 IC 277.7 1306. 699. 1.33 C.713 1.87 1.320 1.320 19.2 13.9 0.720 12 333.2 135C. 675. 1.38 0.688 2.01 I. 120 1.320 15.4 e.5 0.668 1* 3E8.8 1388. 645. 1.42 0.658 2. 16 1.320 1.320 13.5 10.3 0.631 16 444.3 142S. 619. 1.46 C.632 2.31 1.320 1.320 12.6 9.0 0.599 ie 459.9 1458. 596. 1.49 C.608 2.45 1.320 1.320 11.6 8.1 0.570 20 555.4 14 86. 575. 1.52 0.587 2.59 1.320 1.320 9.7 7.2 0.542 22 610.9 1511. 557. 1.54 0.568 2.72 1.370 1.320 P.8 6.3 0.516 TABLE C . l . 4 t NUMERICAL EVALUATION OF EXPERIMENT EDI-S2-15/I21 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT CURRENT POWER TI'E 8CTTC»« TCP NCRKALWEO FACTOR ENR. C1AL. EFFICIENCY EFFICIE NCYC T C8 CT xe XT NS t l 12 El E2 EP l - l (SEC) (PPP) (PPM (-i (-1 l - l (Al IAI m 1X1 IX) 0 0.0 1C29. 1038. l.CO I.CCC l.CO 0.0 CO 100.0 100.0 100.000 1 50.2 1237. eo5. 1.20 0.7 75 1.55 1.120 1.000 31.4 39.6 2.957 2 ICO.4 1358. 70C. 1.32 0.675 1.96 1.120 1.040 18.4 17.0 2.231 3 150.6 1416. 663. 1.38 C.639 2. 15 I.ICO l.COO 9.0 6.3 1.713 4 2C0.e 143C. 613. 1.39 0.590 2.35 1.060 1.000 2.2 A.5 1.410 5 251.0 1466. 596. 1.42 0.574 2.48 1.C20 0.980 6.0 2.9 1.213 6 301.3 1483. 584. 1.44 0.563 2.56 l.ccn C.960 2.8 2.1 1.054 7 351.5 1489. 573. 1.45 0.552 2.62 0.960 C.960 , 1.0 2.1 0.931 a 4C1.T 1494. 569. 1.45 0.548 2.65 0.960 0.960 1.0 0.7 0.829 9 451.9 15C0. 564. 1.46 C.543 2.68 0.960 C.960 1.0 0.9 0.750 10 502.1 1503. 557. 1.46 C.537 2.72 0.960 C.960 o.s 1.1 0.666 TABLE C . l . S * NUMERICAL EVALUATION OF EXPERIMENT E01-S2-I3/I2T 347 ' 1 f 3 4 5 6 7 fl 9 10 II 12 CYCLE P.FH CCNCFNTHAI ICN CONCENTRATICN SEPARATION CURRCNT CURRENT POWER ,NC. t If fc UCITCM TCP NORMAL IUU MCIOR I N K . CI At.. EFFICIENCY EFFICIENCY NCYC r CB CT xe XT NS 11 12 El E2 EP (-1 ISEC) 1PPMI |PPM| I-) l - l (-1 I.M IAI IXI IX) IXI 0 0.0 1C 11. I02e. l.CO l.CCO 1.00 0.0 CO 100.0 too.o 100.000 1 30.2 1127. 885. 1.11 U.861 1.29 1.520 1.300 20.1 31.0 2.077 2 60.4 1196. 819. 1.17 0.797 1.47 1.4P0 1.360 13.0 13 .6 1.6CR 3 9C6 124B. 765. 1.22 0.744 1.65 1.440 1.320 10.2 11 .6 1.387 4 120.8 1272. 739. 1.25 C.719 1. 74 1.4 40 1.320 4.R 5.5 1.154 5 151.0 1339. 6B4. 1.31 C.665 1.98' 1.240 1.140 22.5 IC.3 1. 169 6 161.3 1372. 655. 1.35 0.637 2. 11 1.240 1.160 11.3 5.2 1.087 7 211.5 1397. 632. 1.37 0.615 2.23 1.2C0 1.120 8.8 4 . 4 1.013 8 246.7 1441.' 9 2ei.9 1464.' 10 317.1 1477. 11 352.3 1480. 593. 1.41 C.577 571. 1.44 0.556 560. 1.45 0.545 555. 1.45 0.540 2.45 l.OCO l.COO 2.58 1.040 1.000 2.66 1.C20 I.000 2.69 l.OCO C.960 17.3 6.6 0.866 9.0 3.7 0.828 5.8 2.0 0.781 1.2 0.9 0.730 12 377.5 1419. 13 4C2.7 1377. 14 427.9 1344. 15 453.1 1330. 16 478.3 1317. IT 5C3.6 1314. IB 528. e 1303. 60C 1.39 C.5B3 618. 1.35 0.601 642. 1.32 0.625 654. 1.31 0.636 655. 1.29 0.637 660. 1.29 0.642 662. 1.28 0 . 6 4 4 2.39 1.2P0 1.200 2.25 1.320 1.160 2.11 1.4C0 1.240 2.05 1.360 1.260 2.03 1.320 1.280 2.01 1.320 1.280 1.99' 1.320 1.2B0 -20.2 -10.6 0.825 -13.3 - 4.4 0.705 -10.0 -5.6 0.601 - 4.3 - 2.6 0.538 -4 . 4 - 0.3 0.491 - 0 . 9 - I . 1 0.455 - 3 . S - 0 . 3 0 . 4 2 0 T A B L E C . l . 6 < N U M E R I C A L E V A L U A T I O N C F E X P E R I M E N T E O l - S 2 - 1 3 / # 2 B 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 CYCLE REAL CCNCENTRATICK CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TI"E BOTTOM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS II 12 El E2 EP l - l ISEC) I PPM) IPPM) <-) (-) |-| |A) IA) (X) IX) IX) 0 CO 11C0. 1096. l.CO l.CCO l.CO 0.0 CO 100.0 100.0 100.000 1 50.2 1347. 851. 1.22 0.776 1.58 l.OCO C.900 37.8 41.T 3.748 2 ICO.4 148C. 722. 1.35 C659 2.04 0.960 0.920 21.3 21.5 2.885 .3 150.6 1544. 639. 1.40 0.5B2 2.41 0.920 C900 10 .7 14.3 2.334 4 2C0.E 1587. 600. 1.44 0.547 2.64 0.880 C.880 7.3 6.7 1.936 5 251.0 1603. 574. 1.46 0.524 2.78 0.860 C.860 3.0 4.6 1.639 6 2C1.3 1617. 555. 1.47 0.506 2.91 0.840 C840 2.6 3.5 1.429 7 351.5 1620. 548. 1.47 0.500 2.95 0.840 C.830 O.S 1.2 1.248 8 401.7 1617. 542. 1.47 0.494 2 . 9 8 0.840 0.830 -0.5 1.2 1.105 9 451.9 1617. 535. 1.47 0.488 3.01 0.840 C.R30 0 . 0 1.2 0.994 1 0 5C2.I 1615. 530. 1 . 4 7 0 . 4 8 4 3 . 0 4 0.840 0.830 - 0.5 1 . 0 0.902 T A B L E C . l . 7 I N U M E R I C A L E V A L U A T I O N O F E X P E R I M E N T E D I - S 2 - 1 6 / * 1 348 l 2 3 4 5 6 7 8 <» CYCLE REAL CCNCENTRATICN Cl'NClNIRAI ICN SFPARATION CURRENT NC. TIME 8CIICM 1CP NCHMAl l/EC fAC10H CNR. CIAL. NCYC T cn CI XC XT NS II 17 l - l (SEC) IPI'M) (PPM) (-) l - l l - l 1 A I IA) 0 0.0 1C67. 1067. I.CO l.CCC I.CO 0.0 CO 1 83.6 1355. 784. 1.27 C.735 I.7J O.RHC C.740 7 167.6 1517. 645. 1.47 0.605 2.35 0.620 C760 3 251.3 1623. 577. 1.52 0.541 2.61 o.nco 0.740 4 335.1 1643. 544. 1.54 0.51C 3.C2 C.7RO C.720 5 418. "J 1662. 526. 1.56 C.493 3. lb 0.760 C. 700 6 5C2.7 1671. 516. 1.57 0.484 3.24 0.760 C.700 7 566.4 1665. 513. 1.56 0.481 3.24 0.720 C700 8 670.2 1662. SIC. 1.56 0.478 3.76 0.770 C.700 9 754.0 1654. 506. 1.55 0.476 3.25 0.770 C.700 10 11 CURRENT EFFICIENCY El 111 E2 I t l 12 POWFR ETF ICIENCV EP IX) 100.0 100 30.0 35 16. I 12.2 2.3 2.4 1.0 -0.7 -0.4 - l . l 0 1 16.8 8.5 4.1 2.4 1.4 0.3 0.5 0.2 100.000 3.049 2.358 1.910 1 .575 1.279 1.093 0.945 0.834 0.742 TABLE C . l . 8 « NUMERICAL EVALUATICN CF EXPERIMENT E0I-S2-16/* 2 ' 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POKER NC. TIME 8CTTCM TCP NORMAL 12EC FACTOR ENR. OIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 El E2 EP l - l (SEC) IPPM) (PPM) l - l (-) l - l IA) IA) l«) (XI (SI 0 0.0 1237. 1 81.6 1598. 2 163.3 1867. 3 244.9 2C68. 4 326.5 2227. 5 4C8.2 2344. 6 469.8 2418. 7 571.4 2477. 8 653.1 2507. 9 734.7 2551. 10 816.3 2566. 11 898.0 2561. 12 979.6 2590. 13 1C61.2 2599. 14 1142.9 2608. 1219. I.CO l.COO 955. 1.29 0.783 755. 1.51 0.619 619. 1.67 0.508 529. 1.60 0.434 464. 1.90 0.281 426. 1.96 0.349 393. 2.CO C.223 381. 2.C3 0.312 366. 2.C6 0.302 355. 2.C7 0.291 346. 2.C9 C.286 346. 2.C9 0.2e4 342. 2.10 0.280 339. 2.11 0.278 1.00 0.0 CO 1.65 0.760 C.720 2.44 0.750 C.700 3.29 0.730 C.700 4.15 0.720 C.700 4.9R 0.710 C.700 5.60 0.700 C.700 6.21 0.7C0 C.700 6.49 0.7C0 C.700 6.84 0.7C0 C.700 7.13 0.700 C.700 7.30 0.7C0 C.700 7.38 0.700 C.700 7.49 0.700 0.700 7.58 0.700 0.700 100.0 100.0 100.000 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 TABLE C . l . 9 I NUMERICAL EVALUATION OF EXPERIMENT EOI-S2-I6/I 4 349 1 2 3 4 } 7 8 9 10 11 17 CYCLE REAL CCNCFNTRATICN CONCCNT RATICN SEPARATION CURRENT CURRFN1 POWFR NO. TI»E BCTIC" TCP NCRMAll/EO FACTOR LNR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS II 17 E l E? EP l - l ( SEC I CFPf 1 IPPMI l - l l - l l - l IA) 1 A) I t l I t ) I t l 0 o.c 1264. 1749. I.CO I.CCC I.CO C O C O 100.0 100.0 100.oco I 61.6 1344. l o i s . 1.C6 0.816 I. 30 0.960 0.900 41.6 31.R 2. 140 2 123.3 1408. 845. 1.11 0.677 1.65 0.950 C 9 2 0 31.5 73.6 1.851 3 i e i . 9 1466. 7IC. 1.16 0.568 2.04 0.940 C.900 31.0 18.8 1.69? 4 246.5 1514. 606. 1.20 0.4R6 2.47 0.970 C.900 25.7 14.3 1.543 5 3C8.2 1564. 529. 1.24 0.424 2.92 0.9CO C.860 27.9 11.2 1.458 T 431.4 1676. 419. 1.29 C. 336 3.R3 0.820 C.800 IB.8 8.6 1.775 9 554.7 1665. 361. 1.32 0.289 4.55 o.7ec C.760 12.6 4.8 1.117 It 678.C 1696. 322. 1.34 0.258 5.20 0.740 C 7 0 0 10.5 3.5 1.007 13 e c i . 2 1716. 297. 1.36 0.238 5.71 0.700 C.680 7.1 2.4 0.905 14 e57.9 1730. 284. 1.37 C.227 6.C2 0.5C0 C 4 8 0 27.5 2.5 0.964 IS 514.5 1742. 27C. 1.38 0.216 6.38 0.5C0 C.480 22.0 2.8 0.943 17 lC27.e 1759. 239. 1.39 0.191 7.28 0.5C0 0.480 16.5 3.0 0.899 19 1141.0 1173. 228. 1.40 C. 183 7.67 0.5C0 C 4 8 0 13.R 1.0 0.852 21 1254.3 1781. 223. 1.41 0. 179 7.88 0.5C0 C.480 8.3 0.5 0.804 23 27 29 1347.6 1534.1 1627.3 1773. 1767. 1767. 243. 252. 259. 1.40 C 1 9 4 1.40 0.201 1.40 0.208 7.22 6.94 6.73 0.580 C.560 0.570 C.560 0.570 0.560 -7.1 -2.4 0.0 -2.2 -0.5 -0.9 0.889 0.769 0.721 30 1684.0 1776. 245. 1.40 0.196 7.16 0.490 C.440 16.9 3.0 0.5e9 32 1797.2 1793. 231. 1.42 0.185 7.67 0.460 C 4 4 0 18.0 1.5 0.577 36 2C23.8 1798. 218. 1.42 0.175 8.15 0.450 C.440 3.1 0.7 0.537 37 21C9.2 1813. 213. 1.43 0.170 8.41 0.4C0 C.4G0 18.1 0.9 0.357 39 22eC.O 1827. 201. 1.45 0.161 8.97 0.4CC C.400 9.1 1.0 0.351 41 2450.6 i e 4 7 . 197. 1.46 0.158 9.24 0.400 C.400 12.7 0.3 0.348 43 2533.2 1824. 45 2615.6 1618. 47 2658.C 1815. 51 2662.8 1815. 205. 1.44 0.164 215. 1.44 0.173 217. 1.44 0.174 219. 1.44 0.176 6.78 0.460 C.450 8.34 0.460 C.440 8.27 0.450 0.440 6.18 0.450 C.440 -45.1 -1.0 0.675 -11.8 -1.4 0.645 -6.0 -0.2 0.621 0.0 -0.2 0.582 ,52 2919.4 i e i c 154 3C32.7 179C.- 56 3146.C 1781. 58 3259.2 1776. to 3372.5 1776. 230. 1.43 0.184 252. 1.42 0.201 264. 1.41 0.212 275. 1.40 0.22C 277. 1.40 0.222 7.79 0.300 C.320 7.03 0.260 C.300 6.65 0.280 C.300 6.38 0.260 C.300 6.32 0.2R0 C.300 -18.5 -3.0 0.415 -34.6 -3.4 0.394 -14.8 -2.0 0.360 -9.9 -1.6 0.369 0.0 -0.4 0.362 TABLE C . l . l C J NUMERICAL EVALUATION OF EXPERIMENT E01-S2-16/* 5 350 1 2 3 4 0 6 1 R 9 10 11 12 CYCLE RIAL CCNCl:N 1RAT ICN CONCENTRATION SEPARATION CURRENT CUKHTNT POWER NC. Jiff. OCHCM It P NUHMAL 1 1(0 FACIHH ENR. C I A L . E F F I C I E N C Y E F F I C I E N C Y NCYC T CR CT XO XT NS 11 12 E l F2 EP (-1 (SEC) (PPM) IPPMI (-1 l - l I-) (A) (A) ( t l IT) IXI 0 0.0 2 4 3 5 . 1725. l.CO I.COO 1.00 0.0 C O 100.0 100.0 IOO.OCO 1 61.6 1263. 1045. 0.52 0.85 1 C M 0.760 C.680 - 7 7 0 . 1 33.2 -13.473 2 123. 3 1 307. 90"). 0.54 C.742 0. 72 0. 7.'0 C.700 31.1 24.2 -5.757 3 184.9 1347. 793. 0.55 C.647 C. 85 0.720 C.680 27.5 21.3 -7.639 4 246. 5 1337. 716. 0.57 0.584 C .9f 0.7C0 C 6 6 0 28.3 14.6 -1.425 6 369.8 1448. 574. 0.59 0.468 1.27 0.6C0 C.600 25.4 14.8 -0.333 e 493.1 14<»C 51C. 0.61 0.416 1.47 0.670 C 5 6 0 1 7.1 7.2 0.053 10 616.3 1519. 4 5 1 . 0.62 C.360 1.69 0.520 C 5 2 0 14.0 7.0 0.239 12 739.6 1515. 4 1 3 . 0.63 C.337 1.87 0.5C0 C S O O 8.0 4.8 0.305 .14 662.9 1554. 39C. 0.64 C.318 2.01 0.490 C 4 9 0 9.5 3.0 0.351 16 986.1 1562. 377. 0.64 0.307 2.09 0.490 C 4 8 0 4.1 1.7 0.347 17 1C42.8 1575. 3 5 5 . 0.65 C 2 8 9 2.23 0.38C C 4 0 0 34.1 5.2 0.422 18 IC99.4 1581. 339. 0.65 0.277 2.34 O . ' i C O C. 380 13.0 3.8 0.434 2C 1212.7 1599. 32C. 0.66 0.261 2.52 0.400 0.370 22.7 2.5 0.468 22 1325.9 1 ( 0 5 . 306. 0.66 0.249 2.64 0.4C0 C.370 6.5 1.8 0.461 23 1272.6 1605. 313. 0.66 0.256 2.58 0.420 0.420 0.0 -2.3 0.533 24 1419.2 1602. 322. 0.66 C.263 2.50 0.440 0.440 -5.9 -2.6 0.499 26 1512.4 1597. 332. 0.66 0.271 2.42 0.460 C.450 -5.6 -1.3 0.444 28 16C5.7 1594. 337. 0.65 0.275 2.38 0.460 C 4 5 0 -2.8 -0.7 0.405 30 1699.0 1591. 3 3 9 . 0.65 C 2 7 7 2.36 0.460 C.450 -2.8 -0.4 0.373 37 2C25.4 1674. 24C. 0.69 0.196 3.51 0.650 0.600 17.7 3.0 0.490 45 2478.5 1741. 174. 0.71 0.142 5.03 0.560 0.500 14.5 1.6 0.436 51 2758.3 1720. 217. 0.71 0.177 3.99 0.6C0 .0.540 -5.8 -1.6 0.418 TABLE C.l.11 : NUMERICAL EVALUATION OF EXPERIMENT E0I-S2-16/* 6 1 2 3 4 5 6 7 B 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TIME BCTTCM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XR XT NS 11 12 E l E2 EP l - l ISEC) IPPM) (PPM) I-) (-) l - l (A) (A) I t ) (X) IXI 0 0.0 1242. 1 31.6 1257. 2 63.3 1263. 3 54.9 1273. 4 126.5 127e. 8 253.1 1305. 12 379.6 1376. 16 5C6.1 1337. 20 637.7 1347. 24 759.2 1352. 28 e e 5 . 7 1 358. 32 1CI2.2 1358. 36 m e . e 1358. 40 1265.3 1258. 47 1486.7 1363. 1251. l.CO l.COC 1148. l.CI C.918 1099. 1.C2 0.8 78 1060. 1.03 C.e47 1027. 1.C3 0.821 933. 1.05 0.745 873. 1.C7 0.698 832. 1.08 C.665 804. 1.C8 C.642 784. 1.C9 0.627 77C. 1.C9 0.615 761. I.C9 C.608 753. I.C9 0.602 743. 1.C9 0.594 T 3 I . 1.10 0.589 l.CO 0.0 0.0 1.10 1.520 1.380 1.16 1.520 1.480 1.21 1.560 1.520 1.25 1.580 1.500 1.41 1.540 1.500 I.53 1.520 1.500 1.62 1.5C0 1.500 1.68 1.500 1.500 1.74 I.SCO 1.500 1.78 1.5C0 1.500 I.BO I.SCO 1.500 1.8.2 I.SCO 1.500 1.14 1.500 I.5CU I.en i.5co i.soo 100.0 l o c o 100.000 6.7 18.2 0.441 6.7 8. 1 0.381 6.6 6.2 0.346 3.2 5.4 0.306 4.2 3.8 0.240 3.4 2.4 0.203 1.7 1.7 0.171 0.4 . 1.2 0. 146 1.7 0.8 0.131 0.9 0.6 0.117 0.0 0.4 0 . 103 0.0 0. 3 0.093 0.0 0.4 0.0B4 0.9 0.) 0.074 TABLE C . l . ( 2 I NUMERICAL EVALUATION CF EXPERIMENT t l l l - S i - l t / t f 351 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POKER KC. TIME 8GT1CM TCP NCRPALUEO FACTOR CNR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT X8 XT NS II 12 E l E2 EP l - l ISECI IPPM IPPP) l - l (-1 1-1 IA) IAI I t l IXI IXI c CO 1226. 1238. l.CO 1.000 1.00 0.0 CO 100.0 100.0 IOO.OCO 1 31.6 1247. 1142. 1.C2 C922 I. 10 1.320 1.280 3.9 18.4 0.535 2 63.3 1263. 1104. I.C3 0.892 1. 16 1.340 1.340 2.9 6.8 0.398 3 54.9 1278. 1076. I.C4 0.e69 1.20 1.360 1.350 2.8 5.1 0.336 4 126.5 1254. 105C. 1.C6 0.648 1.25 1.380 1.360 2.8 4.6 0.302 5 158.2 1305. 1C31. 1.C6 0.832 1.28 1.390 1.37.0 1.8 3.4 0.270 1C 316.3 1347. 965. I.10 0.779 1.41 1.420 1.400 1.4 2.3 0. 184 15 474.5 1360. 931. l.ll 0.752 1.48 1.420 1.400 0.5 1.2 0.137 2C 632.7 1366. 909. 1.11 C.734 1.52 l;420 1.400 0.2 0.8 0.109 25 790.8 1368. 897. 1.12 0.724 1.54 1.420 1.400 0.1 0.4 0.090 3C 549.0 1344. 884. 1.10 0.714 1.54 .1.420 1.400 -0.8 0.4 0.073 32 1C12.2 1405. 862. 1.15 0.696 1.65 1.620 1.580 4.6 1.7 0.080 35 11C7.1 1440. 835. 1.17 .0.674 1.74 1.640 1.600 1.7 1.4 0.081 4C 1265.3 1472. 806. 1.20 0.651 1.84 1.640 1.600 0.9 0.9 0.076 45 1423.5 1485. 791. 1.21 0.639 1.90 1.640 1.600 0.4 0.5 0.070 50 1561.6 1496. T8C 1.22 0.630 1.94 1.640 1.600 0.3 0.3 0.064 52 17C2.4 1645. 56 1S44.C 1795. 60 2185.6 1SIC. 65 2487.7 1962. 686. 1.34 0.554 581. 1.46 0.469 537. 1.56 0.433 519. 1.60 0.419 2.42 1.080 1.160 3.12 l.COO 1.130 3.60 0.960 1.100 3.82 0.96C 1.100 8.8 5.2 0.044 4.8 3.0 0.052 3.3 1.3 0.056 1.4 0.4 0.056 67 2550.9 1822. 70 2645.8 1696. 75 2eC4.C 1594. 60 2962.1 1546. 581. 1.49 0.469 658. 1.28 0.531 722. 1.30 0.583 742. 1.26 0.599 3.17 1.6C0 1.520 2.60 1.620 1.560 2.23 1.620 1.560 2.11 1.620 1.560 -10.6 -5.0 0.089 -6.1 -4.0 0.071 -3.0 -2.0 0.055 -1.4 -C.6 0.047 TABLE C.l.13 t NUMERICAL EVALUATION OF EXPERIMENT ECl-52-U/t 6 352 1 0 II 12 CYCLE NC. NCYC l - l HEAL 1I*E T I SEC I CCNCFNTRATICN BCITCM TCP cn IFPMI CT IPPM) CCNCFNTRATICN SCPARATION NCRMALI7EC FACTOR X8 l - l XT I-) NS l - l CURRENT ' ENR. CIAL. II IAI 12 IAI CURRTNT EFFICIENCY El 1 1 1 t2 ITI POWER EFFICIENCY EP I t l 0 0.0 1184. I20C. l.CC l.CCC I.CO 0.0 C O 100.0 l o c o 100.000 1 51.9 1202. 993. 1. 10 0.828 1.33 1.0«0 1 . 160 16.3 26.4 1.470 2 103.8 1381. 903. 1. 17 C.753 1.55 1.160 1.240 10.1 I C S 1.101 3 155.6 14'.2. 845. 1.22 C.704 1. 73 1.180 1.260 7.7 6.8 0.901 2C7.5 1466. 806. 1.26 C.672 I.FT 1 .2C0 1.280 5.6 4.5 0.761 5 259. 4 1517. 77 7. 1.28 0.647 I .98 1.2C0 1.2*0 3.6 3.4 0.657 6 311.3 1 5 35. 755. 1.3C C.629 2.06 1.2C0 1.230 2. I 2.5 0.575 T 363. 1 1546. 742. 1.31 o.6ie 2. It 1.240 1.280 1.3 1.5 0.5C5 8 415.C 1551. 733. 1.31 0.611 2. 15 1.240 1.280 0.6 1.0 0.448 9 466.9 1551. 725. 1.31 C.604 2.17 1.240 1.280 0.0 0.9 0.401 ic 518.8 1554. 72C. 1.31 0.6CC 2.19 1.240 1.280 0.3 0.6 0.363 i i 570.7 1554. 715. 1.31 0.596 2.20 1.240 1.280 0.0 0.6 0.331 12 622.5 1551. 711. 1.31 C.592 2.21 1.240 1.280 -0.3 0.4 0.304 13 674.4 1546. 707. 1.31 0.589 2.22 1.240 1.280 -0.6 C.4 0.280 14 773.5 16 34. 636. 1.38 C53C 2.60 0.760 C.900 9.0 6.1 0.166 15 872.5 1688. 593. 1.43 0.495 2.88 0.780 C.9C0 5.3 3.7 0. 173 16 571.6 1714. 56e. 1.45 0.473 3.06 0.8C0 C.880 2.6 2.3 0.173 17 1C70.6 1741. 553. 1.47 0.461 3.19 0.8C0 C.880 2.6 1.3 0.172 18 1169.7 1752. 542. 1.48 0.452 3.28 0.8C0 C.880 1.0 1.0 0.168 19 1268.8 1754. 537. 1.48 0.447 3.31 O.BCO C.BBO 0.3 0.5 0. 162 20 v 1320.6 1674. 587. 1.41 0.4B9 2.89 1.160 1.200 -10.3 -6.2 0.262 21 1272.5 1621. 626. 1.37 0.522 2.63 1.180 1.220 -6.T -4.7 0.228 22 1424.4 1566. 645. 1.34 C.538 2.49 1.2C0 1.240 -4.3 -2.3 0.205 23 1476.3 1562. 662. 1.32 0.552 2.39 1.2C0 1.240 -3.0 -2.0 0.167 24 1528.1 1541. 670. 1.30 0.556 2.33 1.2C0 1.240 -2.6 -C.9 0.173 25 158C.C 153C. 673. 1.29 0.561 2.30 1.2G0 1.240 -1.3 -0.5 0. 162 26 1621.9 1522. 675. 1.29 0.562 2.79 1.2C0 1.240 -1.0 -0.2 0.154 27 1663.8 1517. 675. 1.28 0.562 2.28 1.2C0 1.240 -0.7 0.0 0.147 28 1735.7 1511. 676. 1.28 0.563 2.27 1.200 1.240 -0.7 -0.2 0.140 29 1787.5 15C6. 677. 1.27 C.S65 2.25 1.200 1.240 -0.7 -0.2 0.134 TABLE C.l.14 t NUMERICAL EVALUATION OF EXPERIMENT ED1-S2-16/* 9 1' 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TIME 8CTT0M TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 El E2 EP l - l ISECI IFPM) IPPMI l - l l - l l - l (Al IA) IX) It) (X) 0.0 ICCC 1006. I.CO l.CCC I.CO 0.0 CO 100.0 t o c o 100.000 46.4 1C89. 686. I.C9 0.681 1.24 0.940 0.950 22.0 29.2 2.709 52.9 1155. e o i . 1.15 0.796 1.45 l.CCO C.980 15.1 2C. 1 2.308 139.3 1209. 746. 1.21 C744 1.63 0.970 C980 13.0 12.5 2.003 ie5.7 1239. 708. 1.24 0.704 1.76 0.930 C.970 7.5 9.5 1.742 222.1 1264. 681. 1.26 C.677 1.67 0.950 C970 6.0 6.5 1.532 278 .6 1278. 659. 1.28 0.655 1.95 0.950 C.950 3.3 5 . 3 1.359 225.0 1286. 644. 1.29 0.640 2.01 0.950 C.950 2.0 3.8 1.213 371.4 .1292. 632. 1.29 0.628 2.06 0.950 C950 1.3 2.8 1.092 417.8 12-17. 623. 1.30 0.619 7.10 0.950 C.950 1.3 7.2 0.993 464.3 1297. 619. 1.30 0.615 2.11 0.950 0.950 0 . 0 0.9 0.900 557.1 1295. 605. 1.29 0.601 7. 15 . 0.950 C.950 - 0 . 3 1.7 0.765 650.0 1289. 602. 1.29 0.599 2.15 0.950 C.950 -0.7 0 . 3 0.654 747.8 1786. 596. 1.79 0.592 7. 17 0.950 C.950 - 0 . 3 0.8 0.576 835.7 1786. 591. 1.29 0.587 / 7.19 0.950 0.950 0 . 0 0 . 6 0.516 TABLE C.1.15 I NUMERICAL CVHUAI1CN CF EXPERIMENT *UI-5!-l7/tl5 353 1 2 3 * 5 6 7 8 9 10 t l 12 CYCLE REAL CCNCFNIRA IICN CONCENTRAtICN SEPARATION CIRRtNT CURRENT POWER NC. TIME PCTTCM TCP NORMALI ZEC MCIUR t NR. CIAL. EFFICUNCY EFFICIFNC Y NCYC T CP CT XC XT NS II 12 El E2 EP l - l ISECI IPPf| (PPM) (-) |-| l - l IAI IA) I t l It) ( t l 0 0.0 573. 977. I.CO l.CCO I.CO 0.0 . CO 100.0 100.0 100.000 I 46.4 1C57. 848. 1.C9 0.868 1.75 1.006 C926 19.3 37.7 7.744 2 52.9 1122. 78C. I. 15 0. 799 1.44 0.9P2 C999 15.3 15.5 2.213 3 139.3 11 35. 73C. 1.17 C.748 1.56 0.917 C991 3.4 11.7 1.766 4 185.7 1196. 694. 1.23 C.711 1.73 0.91 I C .16'1 14.3 6.6 1 .646 5 237.1 1718. 666 . 1.25 0.682 1.H4 0.948 C965 5.3 6.8 1.453 6 218.6 1234. 6«e. 1.27 0.663 1.91 0.9O5 C.948 4.2 4.4 1.296 7 325.C 1239. 632. 1.27 C.647 1.97 0.926 C926 1.4 3.9 1.158 8 371.4 1245. 622. 1.28 0.637 2.01 0.926 C.948 1.4 2.5 1.042 9 417.8 1245. 613. 1.28 0.627 2.04 0.894 C.926 0.0 2.3 0.945 lb 464.3 1245. 609. 1.28 0.624 2.05 0.926 C.905 0.0 1.0 0.859 12 557.1 1245. 596. 1.28 0.61C 2. 10 0.694 C.905 0.0 1.6 0.737 14 65C.C 1239. 593. 1.27 0.608 2. 10 0.863 C.905 -0.7 0.3 0.634 16 742. e 1234. 587. 1.27 0.601 2.11 0.894 C894 -0.7 0.8 0.559 18 835.7 1234. 584. 1.27 0.598 2.12 0.698 C.894 0.0 0.3 0.500 TABLE C.l.16 I NUMERICAL EVALUATION CF EXPERIMENT ECI-S3-12/»16 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRFNT POWER NO. TIME BOTTOM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFIC1EI NCYC T CB CT xe XT NS 11 12 El E2 EP l - l (SEC) (PPM) IPPMI l - l l - l l - l (A) IAI I t l I t l ( t ) 0 CO 997. toos. I.CO l.CCO I.CO 0.0 CO 100.0 100.0 100.000 1 63.6 1054; 916. 1.C6 0.911 1.16 0.560 C500 17.1 29.9 4.782 2 127.6 1C97. 869. 1. 10 0.865 1.27 0.570 C.550 12.8 14.2 3.642 3 191.3 1127. 335. 1.13 0.631 1.36 0.560 C.560 9.0 1C5 3.261 4 255.1 1152. 806. t . 16 0.602 1.44 0.520 C.550 7.9 8.7 2.9C9 5 318.9 1168. 784. 1.17 C.780 1.50 0.510 0.540 5.4 6.8 2.607 6 J62.7 1162. 766. 1.19 C.764 1.55 0.570 C.540 4.4 5.2 2.355 7 446.4 ' 119C. 752. 1.19 0.748 1.60 C570 C540 2.7 4.8 2.141 6 510.2 1196. 743. 1.20 0.739 1.62 0.520 C540 1.8 2.8 1.940 9 574.0 1201. 735. 1.20 C.732 1.65 0.520 C.540 1.8 2.4 1.778 10 637.8 1207. 729. 1.21 0.725 1.67 0.520 0.540 l.B 2.0 1.643 12 765.3 1209. 722. 1.21 0.719 1.69 0.520 0.540 0.4 1.0 1.399 14 e92.9 1207. 712. 1.21 C.709 l . T l 0.520 C.540 -0.4 1.6 1.220 16 1C20.4 1207. 71C. 1.21 0.706 1.71 0.520 0.540 0.0 0.4 1.075 18 1148.C 1204. 704. 1.21 0.701 1.72 0.520 0.540 -0.4 C.8 0.961 TABLE C.l.17 > NUMERICAL EVALUATION CF EXPERIMCNT EOI-S3-I2/M? 354 1 2 3 4 5 6 7 8 9 10 J l 12 CYCLE Rf AL Cf NC E-NTRAT ICN CPNCKNIHAI ICN SEPARATION CURRENT CURRENT PnwtR NC. IIPE HCTICP TCP NORMALIZED FAC10R ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CD CT XR XT NS II 12 E l F2 EP (-J (SEC I (PI'PI (PPPI l - l l - l l - l l»l <*> <*>  1 , 1 m 0 C C 1C81. 1081. l.CC i .ceo l.CO 0.0 C O 100.0 100.0 100.000 1 63.8 1185. 942. 1. 10 c e 7 i 1.7b 0.975 C. 994 18.8 26.2 2.427 2 127.6 1264. 855. 1.17 0.791 1.48 0.925 C.941 14.5 15.4 2.019 3 191.3 1 322. 795. 1.22 C 7 3 5 1.66 0.878 C.879 11.1 11.6 1.765 4 255.1 1 366. 749. 1.26 C 6 9 3 1.S2 0.886 C.90t 8.4 8.3 1.553 5 318.9 1397. 717. 1.29 C 6 6 3 1.95 0.867 C.P5S 5.9 6.3 1.383 6 3E2.7 1411. 697. 1.3C 0.644 2.03 0.870 C.905 2.T 3.8 1.214 7 446.4 1422. 679. 1.22 C 6 2 8 2. 10 0.862 C 8 7 8 2.2 3.5 l.OBR e 510.2 14 3 C 666. 1.22 C 6 I 6 2.15 0.867 C.878 1.6 2.5 0.982 9 574.0 14 3 3. 658. 1.23 0.6C9 2.18 0.855 C.8T8 0.5 1.5 0.888 io 637. e 142 3. 649. 1.33 C.600 2.21 0.823 C.902 0.0 1.7 0.811 12 765.3 1433. 6 4 C 1.33 0.592 2.24 0.855 C.870 0.0 0.9 0.687 14 ES2.9 1427. 633. 1.32 0.586 2.25 o . e i 2 C.878 -0.6 0.6 0.593 16 1C20.4 1427. 6 3 C 1.32 0.582 2.27 0.839 C.87B 0.0 0.4 0.523 18 1146.0 1425. 624. 1.32 0.576 2.28 0.828 C.847 -0.3 O.S 0.469 TABLE C.l.18 t NUMERICAL EVALUATION CF EXPERIMENT E0I-S3-12/«18 1 2 3 4 5 C 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TIME BCT1CM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS II 12 E l E2 EP (-1 (SEC) (PPM) IPPM) (-) (-) l - l (A) ( A l IXI (XI IXI 0 C O 119C. 1174. l.CO l.CCC l.CO 0.0 C O 100.0 10C.0 100.000 1 63.8 1270. 9 e c 1.C7 0.835 1.28 1.207 1. 105 11.1 29.4 1.503 2 127.6 1366. 864. 1.15 C.736 1.56 1.192 1.184 13.6 16.5 1.290 3 191.3 143C. 78C. 1.20 0.665 1.81 1.149 1.145 9.3 12.3 1.123 4 255.1 1475. 716. 1.24 0.610 2.03 1.160 1.093 6.5 9.9 0.994 5 318.9 1511. 671. 1.27 0.571 2.22 1.098 1.098 5.6 6.9 0.890 6 282.7 1539. 636. 1.29 0.542 2.39 1.098 1.082 4.3 5.4 0.804 7 446.4 1556. 609. 1.31 0.519 2.52 1.105 1.058 2.6 4.3 0.729 8 510.2 1570. 592. 1.32 0.504 2.61 1.058 1.066 2.2 2.6 0.663 9 574.0 1578. 581. 1.33 0.495 2.68 1.058 1.058 1.3 1.8 0.606 10 637.8 1507. 574. 1.23 0.489 2.73 1.058 1.058 1.3 1.0 0.556 11 7C1.5 1592. 57C. 1.34 0.486 2.75 1.058 1.058 0.9 0.6 0.512 12 765.3 1595. 565. 1.34 0.481 2.78 1.058 1.058 0.4 0.8 0.475 13 629.1 159B. 561. 1.24 C 4 7 e 2.81 1.058 1.058 0.4 0.6 0.442 14 852.9 1598. 556. 1.34 0.474 2.B3 1.058 1.058 0.0 0.8 0.414 15 556.6 1601. 555. 1.34 0.473 2.05 1.058 1.058 0.4 0.2 0.389 16 1C20.4 1601. 555. 1.34 0.473 2.85 1.058 1.058 0.0 0.0 0.365 TABLE C.l.19 < NUMERICAL EVALUATICN CF EXPERIMENT EDI-S3-l2/f19 355 10 II I 7 CYCLE NC. NCYC l - l REAL T ISCCI CCNCFNTRATICN BCTICM TUP CH C I (PPMI (PPMI CONCENTRATION SEPARATION NORMALIZED FACTOR I- I XT (-1 NS l - l CURRENT ENR. C I A L . I I (Al 17 IAI CURRENT EFFICIENCY E l ( T l T7 ( t l POWF'R E F F I C I L N C Y EP ( t l 0 0.0 1174. 1160. l.CO l.CCC t.co 0.0 C O 100.0 10C.0 100.ooo 1 53.4 1764. 1122. 1.08 0.968 t . u 1.067 C T(U. 1 7.0 9.6 0.272 7 1C6.9 1 375. 106P. 1.17 C.921 1.27 1.C10 C B 7 0 21.9 12.5 0.291 3 160.3 I486. 1007. 1.77 0.669 1.46 0.997 C 0 6 1 22.5 14. 1 0.303 4 213.6 1596. 951. 1.36 0.820 1.66 0.971 C.842 73.1 13.5 0. 3C8 5 267.2 17 IC. 897. 1.46 C.773 1.89 0.964 C 8 2 3 23.5 13.2 0.312 6 320-7 1824. 844. 1.55 0.777 7. 14 0.889 C 8 7 0 25.6 12.2 0.314 7 374. 1 191C. 791. 1.63 0.682 2. 19 0.8E9 C 8 5 1 19.3 12.5 0.3C9 a 427.6 2C25. 746. 1.72 0.643 2.68 0.889 C.H23 25.9 11.0 0.311 9 481. C 2111. 703. i.eo C.6C6 2.97 0.851 C 8 1 4 70.4 1C.5 0.306 > c 534.4 2213. 663. 1.89 0.572 3. 30 0.842 C 795 24.2 I C . 1 0.305 12 641.3 2389. 591. 2.03 0.509 3.99 0.814 0.777 71.7 9.3 0.299 14 748.2 2536. 533. 2. 16 C.459 4.70 0.795 C 7 5 8 18.6 7.7 0.290 16 e s s . 1 2679. 484. 2.28 0.417 5.47 0.777 C 7 3 9 18.5 6.7 0.281 i e 962.C 2644. 442. 2.42 0.382 6.35 0.748 C 7 3 0 22.1 5.7 0.276 20 1C68.9 2959. 406. 2.52 C.35C 7.20 0.730 C.711 15.8 5.1 0.267 25 1336.1 3155. 342. 2.69 C.295 9.12 0.711 C 6 9 2 11.0 3.7 0.242 30 16C3.3 327e. 303. 2.79 0.261 10.68 0.692 C 6 7 4 7.1 2.3 0.218 35 U70.5 3349. 277. 2.85 0.239 11.93 0.683 C 6 6 4 4.2 1.6 0.197 40 2137.8 3426. 262. 2.92 0.226 12.93 0.603 0.664 4.6 0.9 0.180 45 24C5.C 3467. 252. 2.55 0.217 13.62 0.683 0.664 2.4 0.6 0.164 50 2672.2 3501. 245. 2.58 0.211 14.11 0.683 C.664 2.0 0.4 0.151 TABLE C.1.2C » NUMERICAL EVALUATION CF EXPERIMENT ED1-S3-I2/<2C 1 2 3 4 5 « . 7 8 9 10 u 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TI"E BCITOM TCP NORMALIZED FACTOR ENR. C I A L . EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E7 EP i-1 (SECT (FPM1 (PPMI <-! (-1 (-1 IAI ( A l ( t l ( t l I t l 0 0.0 1237. 1231. l.CO l.COC l.CO 0.0 0.0 100.0 100.0 100.000 1 73.e 1405. 1024. 1.14 0.632 1.37 0.942 C 9 2 2 26.0 32.6 3.150 2 147.6 1525. 903. 1.23 0.734 1.68 0.922 0.949 18.9 IE.6 2.570 3 221.3 1606. 823. 1.30 0.669 1.94 0.895 C.930 13.2 12.5 2.176 4 295. 1 1662. 76e. 1.34 0.624 2.16 O.ePl C.910 9.3 8.9 1.882 5 368.9 1696. 725. 1.37 0.589 2.33 0.867 C 8 9 5 5.7 6.9 1.650 6 442.7 1716. 697. 1.39 C.566 2.45 0.847 C 8 9 5 3.4 4.6 1.455 7 516.4 1759. 677. 1.42 0.55C 2.58 0.849 C 6 8 1 7.3 3.2 1.330 6 590.2 1764. 664. 1.43 0.540 2.64 0.840 0.881 1.0 2.1 1.191 9 664.0 1764. 658. 1.43 0.535 2.67 0.827 0.874 0.0 1. 1 1.071 IC 737.8 1764. 651. 1.43 0.529 2.69 0.834 C 8 6 7 0.0 1.1 0.974 11 611.5 1761. 645. 1.42 0.524 2.72 0.R34 C.B61 -0.5 1.1 0.893 12 685.3 1759. 642. 1.42 0.522 2.72 0.827 0.854 -0.5 0 . 4 0.622 13 959.1 1753. 640. 1.42 0.520 2.71 0.877 C.854 -1.0 0 . 4 0.759 14 1C32.9 1750. 637. 1.42 0.518 2.73 0.627 C.847 -0.5 0 . 4 0.707 15 UC6.6 1744. 633. 1.41 0.515 2.74 0.H20 C.840 -1.0 0.7 0.662 16 n e o . 4 1739. 631. 1.41 C 5 1 3 2.74 0.813 C 8 4 0 -1.0 0 . 4 0.621 IT 1254.2 17 33. 63C. 1.40 0.512 2.74 0.813 C.834 -1.0 C.2 0.5e4 18 1328.0 1 727. 628. 1.40 0.510 2.74 0.RI3 0.834 -1.0 0.2 0.551 19 14C1.T 1722. 627. 1.39 0.509 2. 7) 0.813 C.H34 -1.0 0.7 0.521 20 1475.5 1716. 626. 1.39 0.508 2.71 0.P06 C.827 -1.0 0.2 0.495 tABIE C.l.21 1 NUMERICAL [VALUATION CF EXPERIMENT E0I-SJ-12/»2I 356 to It 12 CYCLE KC. REAI. CCNCENTRAT ICN CONCENTRATION SEPARATION CURRCNT TI ft BCT1CM TCP NORMAL I7CO MCIOR CNR. CIAL. CURRENT POWtR tFTICICNCY EFFICIENCY NCYC l - l T ISECI cn ci ( p p M I |PPf>) XR l - l XT l - l NS «-» II I A I 12 IAI El I t l E2 I t l EP I t l 0 C C 1201. 1 e3.e 1416. 2 167.6 1564. 3 251.3 1657. 4 3 35.1 1719. 5 Aia.9 1 753. 6 5C2.7 1779. 7 5C6.4 1797. 8 670.2 1796. 9 754.C 1798. tc 827.8 1798. 11 521.5 179B. 17 1CC5.3 1796. 13 i c e s . 1 1796. 14 1172.9 1 792. 15 1256.6 1790. 16 1340.4 1787. 17 1424.2 1784. 1197. I.CO l.CCC 974. 1.18 C.ei4 837. 1.30 0.699 749. 1. 38 C 6 2 6 669. 1.43 0.575 651. 1.46 0.544 632. 1.48 0.528 614. 1.49 0.513 604. 1.49 0.504 597. 1.50 0.499 593. 1.50 0.496 592. 1.5C C 4 9 5 591. 1.49 0.494 5 9 C 1.49 0.492 588. 1.49 0.491 586. 1.49 0.491 587. 1.49 0.490 586. 1.49 0.489 1.00 0.0 C O 1.45 O.etb C.794 l . * 6 0.878 C 8 3 4 2.20 0.797 C.flO) 2.49 0.768 C 7 9 0 2.68 0.764 C 7 H 8 2.30 0.753 C.776 2.90 0.752 C.764 2.96 0.757 C.758 3.00 0-746 C.752 3.02 0.746 C.752 3.03 0.740 C.746 3.03 0.740 C.746 3.04 0.740 C.746 3.04 0.740 C.746 3.03 0.740 C.746 3.03 0.740 0.746 3.04 0.740 0.746 100.0 1 0 C 0 100.000 30.8 36.0 3.564 27.9 71.0 2.954 14.9 13.9 2.495 10.1 9.0 2.151 5.7 6. 1 1.661 4.) 3.2 1.628 1.5 3.0 1.440 1.5 1.7 1.789 0.5 1. 1 1. 162 0.0 0.7 1.054 0.0 0.2 0.964 -0.5 C.2 o.se6 0.0 C.2 0.822 -0.5 0.2 0.764 -0.5 C O 0.713 -0.5 0.2 0.670 -0.5 0.2 0.631 TABLE C.1.22 t NUMERICAL EVALUATICN CF EXPERIMENT E01-S3-12/I22 1 2 3 4 S 6 7 a 9 10 11 12 CYCLE REAL CCNCENTRATICN CONCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TIME BOTTCM TOP NORMAL 11 EC FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP l - l ISEC) IFPMI IPPMI (-1 I-) l - l IAI IA) I t l IX) 1X1 0 0.0 1198. 1196. I.CO l.CCC 1.00 0.0 C O 100.0 100.0 100.000 1 9 3 . e 1452. 955. 1.21 0.798 1.52 0.8C0 C 7 6 1 36.3 36.2 3.874 2 167.6 1598. 809. 1.33 0.676 1.97 0.752 C.754 22.1 22.1 3.131 3 261.3 1694. 716. 1.41 0.599 2.36 0.746 C.704 14.7 15.1 2.637 4 375.1 1750. 662. 1.46 0.553 2.64 0.704 C.714 9.2 8.7 2.237 5 468.9 1787. 622. 1.49 0.520 2.87 0.693 C 7 1 7 6.1 6.4 1.937 6 562.7 1613. 602. 1.51 C.504 3.00 0.672 C.72S 4.4 3.1 1.690 7 656.4 1621. 588. 1.52 0.492 3.09 0.677 C.714 1.4 2.3 1.487 a 750.2 163C 575. 1.53 0.481 3.17 0.682 0.698 1.4 2.1 1.332 9 644.0 1630. 571. 1.53 C 4 7 8 3.20 0.6e2 C 6 8 2 C O 0.6 1.195 10 937.8 183C. 569. 1.53 C.476 3.21 0.668 C.688 0.0 0.4 1.082 11 1C21.5 i e s o . 568. 1.53 0.475 3.22 0.668 C 6 8 8 0.0 0.2 0.968 12 1125.3 1627. 565. 1.52 0.477 3.23 0.668 C.688 -0.5 C.4 0.908 13 1219.1 1624. 564. 1.52 C.471 3.23 0.668 C.688 -0.5 0.2 0.839 14 1312.9 1621. 562. 1.52 0.470 3.23 o . 6 e e C.688 -0.5 0.2 0.780 15 14C6.6 1621. 561. 1.52 0.469 3.24 0.668 C.688 0.0 0.2 0.730 16 15C0.4 1818. 561. 1.52 0.469 3.23 o.6ea C.68B -0.5 0.0 0.684 TABLE C.I.23 t NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-12/123 357 10 II I 7 CYCLE NC. NCYC (-1 RT At I I ME T (SCO CCNCENTRAT ICN' B C I T C TCP CB (FI 'K ) CI (PPM) C O N C E N T R A T I O N S E P A R A T I O N C U R R T N T N C R « A L I / E C IACT I1R E N R . C I A L . XP ( - 1 XT ( - 1 NS (-1 ( I ( A l I 7 I A I C U R R E N T E F F I C I E N C Y t i i t l i t ) P O W E R C T F I C I F N C V TP I t l 0 C O 11 7 9 . 1 1 7 1 . 1 . C O 1 . C C C I . C O n.o C O 1 0 0 . 0 1 0 C . 0 1 0 0 . O C O 1 5 5 . 0 1 2 1 8 . 1 0 3 2 . I . C 3 n . P O l 1.1 7 t . i i ' / i 1 . 0 9 1 6 . 9 2 4 . 9 1 . 7 7 7 2 1 I C C 1 2 5 C . 9 8 C . 1 . C 6 C . 6 3 7 1 . 7 7 I . C « 1 1 . 1 1 0 5 . 9 9 . 1 1 . 2 9 0 3 1 4 4 . 9 12 7 8 . 9 4 7 . 1 . C 8 C 8 0 4 1 . 35 t . C ' l 1 . 1 2 8 4 . 9 6 . 7 1 . 0 6 7 4 2 1 9 . 9 1 3 C C 9 1 5 . 1 . 10 C . 7 8 1 • 1 . 4 1 1 . 0 7 } 1 . 1 2 H 4 . 0 4 . 7 0 . 9 1 8 5 2 7 4 . 9 1 3 1 4 . o«je. 1 . 1 1 C . 7 6 7 1 . 4 5 1 . 0 7 3 1 . 1 1 9 2 . 5 2 . 9 0 . 7 9 3 6 3 2 5 . 9 1 3 2 5 . 8 8 C . 1 . 1 2 0 . 7 5 1 1 . 5 0 1 . 0 7 3 1 . 1 1 9 7 . 0 3 . 1 0 . 7 0 8 7 3 8 4 . 8 1 3 3 3 . 8 6 7 . 1 . 1 3 C . 7 4 C 1 . 5 3 1 . C 7 3 1 . 1 1 9 1 . 5 2 . 2 0 . 6 3 6 8 4 3 9 . 8 1 3 3 9 . 8 5 8 . 1 . 1 4 C . 7 3 2 1 . 5 5 1 . C 7 3 1 . 1 1 9 1 . 0 1 . 6 0 . 5 7 5 9 4 9 4 . 8 1 3 4 4 . 8 4 9 . 1 . 1 4 0 . 7 2 5 1 . 5 7 1 . 0 7 3 1 . 1 1 9 1 . 0 1 . 6 0 . 5 2 7 1C 5 4 9 . 8 1 3 4 7 . 8 4 1 . 1 . 1 4 C . 7 1 8 1 . 5 9 1 . 0 7 3 1 . 1 3 7 0 . 5 1 . 3 0 . 4 8 4 11 6 C 4 . 7 1 3 7 5 . 8 3 5 . 1 . 1 7 C . 7 1 3 1 . 6 4 1 . 0 7 3 1 . 1 1 9 5 . 0 1 . 1 0 . 4 6 9 12 4 5 9 . 7 1 3 4 7 . 8 3 1 . 1 . 1 4 C . 7 0 9 1 . 6 1 1 . 0 7 3 1 . 1 1 9 - 5 . 0 0 . 7 0 . 4 1 2 13 7 1 4 . 7 1 3 4 4 . 8 2 8 . 1 . 1 4 C . 7 C 7 1 . 6 1 1 . 0 7 3 1 . 1 1 9 - 0 . 5 C . 4 0 . 3 8 0 14 1 6 9 . 7 1 3 4 4 . 8 2 4 . 1 . 1 4 C . 7 0 4 1 . 6 2 1 . 0 7 3 1 . 1 3 7 0.0 O.T 0 . 3 5 6 IS 8 2 4 . 6 1 3 4 4 . 8 2 3 . 1 . 1 4 C . 7 0 3 1 . 6 2 1 . 0 7 3 1 . 1 1 9 0.0 0 . 2 0 . 3 3 3 TABLE C.1.24 I NUMERICAL EVALUATION OF EXPERIMENT E D l - S 3 - l 2 / « 2 4 10 1 1 1 2 CYCLE NC. REAL TIME CCNCENTRATICN BOTTOM TCP C C N C E N T R A T I C N S E P A R A T I O N N O R M A L I Z E D F A C T O R CURRENT ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC T (-1 ISECI CB IPPMI CT (PPM) xe (-) XT I-) NS l - l I I IA) 12 IA) E l I t ) E2 IX) EP IXI 0 1 2 3 4 5 6 7 e 9 10 I I 12 13 14 15 16 17 18 19 0 . 0 5 3 . 1 1 8 6 . 3 2 7 9 . 4 2 7 2 . 6 4 6 5 . 7 5 5 8 . 9 6 5 7 . 0 7 4 5 . 1 8 2 8 . 3 9 3 1 . 4 1 C 2 4 . 6 1 1 1 7 . 7 1 2 1 0 . 9 1 3 C 4 . 0 1 2 5 7 . 2 1 4 9 0 . 3 1 5 8 3 . 4 1 6 7 6 . 6 1 1 6 9 . 7 1245. 1542. 1 7 3 9 . i e 6 7 . 1953. 2C04. 2C36. 2C59. 2C76. 2 0 8 5 . 2C91. 2C97. 21CC. 2 1 C C . 2103. 2105. 2105. 2108. 2 i o e . 2108. 1 2 3 8 . 9 4 3 . 7 5 6 . 6 3 1 . 5 5 5 . 5 0 7 . 4 7 7 . 4 5 8 . 4 4 6 . 4 4 4 . 4 3 9 . 4 3 6 . 4 3 5 . 4 3 5 . 4 3 2 . 4 2 8 . 4 2 7 . 4 3 C . 4 3 1 . 4 3 2 . I . C O 1 . 2 4 1 . 4 0 1 . 5 0 1 . 5 7 1 . 6 1 1 . 6 4 1 . 6 5 1 . 6 7 1 . 6 7 1 . 6 8 1 . 6 8 1 . 6 9 1 . 6 9 1 . 6 9 1 . 6 9 1 . 6 9 1 . 6 9 1 . 6 9 1 . 6 9 l . C C C 0 . 7 6 1 C 6 1 C 0 . 5 0 9 0 . 4 4 8 C . 4 0 9 C 3 8 5 0 . 3 7 0 C . 3 6 0 C . 3 5 8 C . 3 5 4 C . 3 5 2 C . 2 5 1 0 . 2 5 1 0 . 2 4 9 C 3 4 6 0 . 3 4 5 0 . 3 4 7 0 . 3 4 8 0 . 2 4 9 I.CO 1 . 6 3 2 . 2 9 2 . 9 4 3 . 5 0 3 . 9 3 4 . 2 4 4 . 4 7 4 . 6 3 4 . 6 7 4 . 7 4 4 . 7 8 4 . 8 0 4 . 0 0 4 . 8 4 4 . 8 9 4 . 9 0 4 . 6 8 4 . 8 7 4 . 8 5 0 . 0 0 . 9 1 8 0 . 8 2 1 0 . 7 5 2 0 . 7 3 5 0 . 7 4 1 0 . 7 4 6 0 . 7 2 5 0 . 7 3 5 0 . 7 3 0 0 . 7 3 0 0 . 7 2 5 0 . 7 7 5 0 . 7 7 5 0 . 7 7 5 0 . 7 7 5 0 . 7 7 5 0 . 7 2 5 0 . 7 2 5 0 . 7 7 5 C O C 7 6 4 C . 7 7 3 C . 7 0 9 C . 7 1 9 C . 6 9 8 C . 6 9 ? C . 6 8 7 0 . 6 7 6 C . 6 8 7 C . 6 7 6 C 6 7 6 C . 6 T I C . 6 7 1 C . 6 7 1 0 . 6 7 1 C . 6 7 1 C . 6 7 1 C . 6 7 1 C . 6 7 1 100.0 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 -0.2 100.000 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 TABLE C.I.2S I NUMERICAL EVALUATION OF EXPERIMENT E O I - S l - I J / » I 358 to I 7 CYCLE NC. NCYC l - l R E A L 11 »»E (SEC) C C N C E N T R A T I C N U C T I G M T C P CP IFPM) CT IPPM) CrNCINTHAIICN SCPARATIUN NOWALIZEO FACTOR XT t - l NS (-) C U R R E N T E N R . L I A L . t l (Al I? (At CURRENT Efr ICIENCT Fl ( T l E? (Tl POWER E F FIC IENCY E P (XI 0 0.0 1256. 124C. l . C O l .CCO l . C O 0.0 C O 100.0 t o c o I 70.6 14 75. 993 . 1.1 7 0.801 1.47 1.017 C 9 4 6 ? n . 6 1 4 . 6 2 141.2 164C. 839 . 1.31 0.676 l . ' »3 0 .963 C 9 8 4 72 .8 2 C 9 3 2 i i . a 1761. 731. 1.40 0.591 2. 37 C.975 C .947 1 7.5 14 .4 4 282.4 If 4 7 . 654. 1.47 0.528 2 . 11 0.897 C .913 12.7 1 1.5 5 353. 1 1501. 606 . 1.51 0.489 3.09 0 . 9 9 ? C.892 8.1 7. 1 6 473 .7 1541. 068. 1.55 C.458 3 . 38 0.881 C.871 6.1 5.4 7 494 .3 1567. 542 . 1.57 0.437 3.58 0 .864 C » 7 5 4 . 0 3.9 8 564.9 1S84. 526 . 1.58 0.425 3.72 0.861 C .H7? 2 .7 7.4 9 635 .5 1993. 516. 1.59 0.416 3.81 0 .857 C.864 1.3 1.6 IC 7C6.1 1596. 51C. 1.59 C.4I 1 3. 87 0.H50 C . 8 5 0 0 .5 1.0 11 776.7 2C01 . 506 . 1.59 0.408 3.91 O.HSO C .850 0 .9 0.6 12 e47.3 2C1C. 498 . 1.60 C.4C2 3.98 0 .850 C .850 1.4 1.2 13 518 .0 2C13 . 497 . 1.60 C.401 4 .00 0 .850 C 8 5 0 0 . 5 C 2 14 968.6 2C16. 495 . 1.61 0 .4C0 4.02 0 .850 C .850 0 .5 C.2 15 1C59.2 2C16. 495 . 1.61 0.4CC 4.02 0 .850 C . 8 5 0 0 .0 0.0 16 1129.8 2C13 . 491 . 1.60 C.396 4.04 0 .85C C.850 -0.5 0.6 17 17C0.4 2C1C. 4 9 3 . 1.60 0.39e 4 .03 0 .850 C .850 -0.5 -C.2 16 1211.C 2C1C. 4 9 3 . 1.60 0 .396 4 . 0 ) 0.850 C.850 0.0 0.0 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 .978 .900 . 849 .794 0 . 7 4 7 0.7C3 0.665 0 . 0 . 0 . 0. TABLE C.1.26 s NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/* 2 1 2 3 4 5 6 7 a 9 10 11 12 CYCLE PEAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BOTTOM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 El E2 EP l - l (SEC) (PPM) (PPM) l - l I-) I-) (Al (Al IXI IXI IX) 0 O.C 1242. 1226. l.CO l.COC t.CO 0.0 CO 100.0 100.0 100.000 1 45.3 1402. 1109. 1.13 0.903 1.25 1.037 C936 32.0 26.3 1.586 2 90.6 1542. 1004. 1.24 0.617 1.52 0.971 1.015 29.7 21.6 1.450 3 135.9 1677. 908. 1.35 0.739 1.83 0.927 1.004 30.2 19.7 1.390 4 181.2 1790. 819. 1.44 0.667 2. 16 0.977 C.949 25.3 19.4 1.332 5 226.5 ie9C. 74e. 1.52 0.609 2.50 0.883 C.949 23.4 15.5 1.267 6 271.8 1981. 684. 1.60 C557 2.R6 0.872 C.927 21.8 14.4 t.213 7 317.1 2C62. 635. 1.66 0.517 3.71 0.872 C.883 19.2 11.5 1.156 6 262.4 2131. 591. 1.72 0.481 3.57 0.839 0.683 17.2 1C.3 1.103 9 407.8 2192. 555. . 1.76 0.452 3.91 0.839 C861 15.1 8.7 1.052 10 453.1 2246. 522. l . e i 0.425 4.25 0.817 C850 14.1 7.9 1.007 12 543.7 2336. 471. i.es 0.383 4.90 0.795 C.828 11.5 6.5 0.924 14 634.3 24CC. 432. 1.93 0.252 5.49 0.764 C.R17 8.6 4.9 0.849 16 724.9 24 53. 406. 1.97 0.331 5.17 0.773 C.80I 7.1 3.3 0.787 18 615.5 2483. 387. 2.00 0.315 6. 14 0.766 C.790 4.0 2.5 0.721 20 5C6. 1 2515. 377. 2.02 0.3C7 6.60 0.761 C.784 4.4 1.4 0.668 24 10e7.3 2542. 360. 2.05 0.293 6.48 0.761 C.784 1.8 t . l 0.577 26 1268.6 2569. 352. 2.07 0.287 1.21 0.76t C.784 1.8 0.5 0.5C8 32 1449.e 2575. 346. 2.07 0.262 7. 16 0.761 C.784 0.4 0.4 0.4SI 36 1631.C 2581. 342. 2.C8 0.278 7.46 0.761 C.7B4 0.4 0.3 0.405 TABLE C.l.27 I NUMERICAL EVALUAIICN CF EXPERIMENT EOI-S3-13/0 I 359 1 2 i n 5 6 7 8 9 10 11 12 C1CII no. REAL TIDE CONCFN'fRATICN HOTTON TOP CONCENTRATION NORHALIZED SEPARATION FACTOR CUHBFNT ENR. DIAL. CURRENT EFPICIENCT POUER EFFIC tENCT ICIC T (SEC) CD CT (rrit) (PPN) XB XT (-) <-) NS (-) 11 12 (A) (A) 11 E2 (*) (*> EP 0 0.0 1260. 1205. 1.00 1.000 2 65. 3 1391. 1130. 1. 10 0.951 0 130.6 1522. 1099. 1.20 0.883 6 195.9 1657. 1013. 1. 31 0.8 13 8 261.2 180 1. 913. 1.02 0.709 10 326.5 1930. 857. 1.53 0.688 15 089.8 2216. 703. 1.75 0.565 20 653. 1 2033. 507. 1.92 0.072 25 816.3 2608. 502. 2.06 0.003 30 979.6 2702. 039. 2. 17 0. 352 35 1102.9 2850. 395. 2.25 0.317 no 1306. 1 2938. 361. 2. 32 0.290 OS 1069.1 2996. 338. 2.37 0.272 SO 1632.7 3001. 320. 2.41 0.257 55 1795.9 3081. 308. 2.00 0.208 60 1959.2 3099. 302. 2.05 0.202 65 2122.5 3133. 290. 2.08 0.236 1.00 0.0 0.0 100.0 100.0 100.000 1. 16 1.087 1.01 1 16.8 8.6 0. 160 1.36 1.057 i.ooi 17.8 1 1.8 0.371 1.61 1.026 i.oo i 18.9 1 1.9 0. 378 1.90 0.980 1.011 21. 2 11.0 0. 386 2.22 0.9 19 0.909 20. 1 1 1.5 0. 388 3. 10 0.857 0.903 19.2 9.8 0.380 o.oa 0.851 0.860 10.7 7.7 0. 358 5. 12 0.796 0.812 12.6 6.0 0. 316 6. 16 0.796 0.812 9.7 0.5 0.312 7. 11 0.790 0.805 7.9 3.1 0.289 8.01 0.796 0.795 6.3 2.0 0.268 8. 73 0.766 0. 766 0.3 1.7 0.209 9. 36 0.766 0.766 3.0 1.0 0.232 9. 80 0.735 0.735 3. 1 0.9 0.218 10. 11 0.735 0.735 1.4 0.5 0.203 10.09 0.7 35 0.73S 2.6 0.6 0.192 TABLE C.1.28 I MOHERICAt EVULOATIOU OF EIPERIEEHT B0I-S3-13/S 4 10 11 12 CYCLE NO. REAL TIME CCNCENTRATICN BOTTOM TCP CONCENTRATION SEPARATION CURRENT NORMALIZED FACTOR ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC l - l T (SECI CB CT (PPM) (PPM) XB (-) XT (-) NS (-1 It IAI 12 IAI E l E2 (XI EP (XI 0 0.0 1295; 1276. I.CO l.COO 1.00 0.0 CO 100.0 10C.0 100.000 1 95.9 1517. 955. 1.17 C.748 1.57 0.975 C.964 22.3 37.6 4.402 2 191.8 1634. 823. 1.26 C.645 1.96 0.996 C959 11.6 13.4 3. 172 3 287.8 1694. 761. 1.31 0.597 2.19 0.980 C.938 5.9 6.5 2.445 4 383.7 171C. 726. 1.22 0.569 2.32 0.959 C923 1.7 3.7 1.953 5 479.6 1725. 712. 1.33 C.558 2.39 0.949 C.917 1.5 1.5 1.617 6 575.5 1730. 703. t.34 0.551 2.43 0.938 C.912 0.6 1.0 1.375 7 671.4 1727. 695. 1.33 0.545 2.45 0.933 0.907 -0.3 0.8 1.191 8 767.3 1725. 686. 1.33 C.538 2.48 0.928 C907 -0.3 1.0 1.053 9 863.3 1722. 681. 1.33 0.534 2.49 0.928 C.907 -0.3 C.6 0.941 10 959.2 1716. 677. 1.33 0.531 2.50 0.917 0.897 -0.6 0.4 0.849 TABLE C.1.29 t NUMERICAL EVALUATICN CF EXPERIMENT EDI-S3-l3/f J 360 1 2 3 4 5 6 1 8 9 1 0 II I? C Y C L E R E A L C O N C E N T R A T I O N C C N C E N T R A T I C N S E P A R A T I O N C U R R E N T C U R R E N T POWER N O . T i c e U C I I C M i r p N O H M A L I / E C F A C T O R E N R . D I A L . F F F I C I E N C V E F F I C I E N C Y NCYC 1 CC Ct X P XT N S I I 12 F l E2 E P l - l ( S E C I ( P P P I I P P » I l - l l - l l - l «»l « A I ( X I I X » <*» 0 O.C 1306. 1291 . l.CC I.COC 1 60.6 1391. 1167. 1.C7 C.904 2 121.2 1464. 1086. 1.12 0.641 3 181.8 15 2 2. 1023. 1.17 C. 792 <t 242.4 157C. 971 . 1.20 C.75? 5 3C3.1 1606. 931. 1.23 C . 721 6 363 .7 16 32. 897. 1.25 0.694 7 424.3 1654. B 7 I . 1.27 C.674 8 4E4.9 1666. 85C. 1.28 C.65e 9 545.5 16 79. 83 7. 1.29 0.648 IC 6C6.1 1691. 619. 1. 30 C.634 11 666.7 1699. P I C . 1.30 0.627 12 727.3 1705. 004. 1.31 0.622 13 7E8.C 1708. 793. 1.31 C.614 14 e48.6 171C. 788. 1.31 0.61C IS 9C9.2 1713. 784. 1.31 0.607 16 969.6 1713. 78C. 1.31 0.604 17 1C30.4 1716. 779. 1.31 C.603 l . C O 0 . 0 C O 1 0 0 . 0 1 0 0 . 0 i o o . o c o 1 . 1 8 0 . 6 1 . 8 C . 6 1 0 1 9 . 9 3 1 . 4 6 . 1 3 3 1 . 3 1 0 . 6 6 0 C . 6 5 2 1 7 . 0 1 9 . 3 5 . I C 9 1 . 4 7 0 . 6 " > 3 C . 6 6 0 1 4 . 1 1 4 . 8 4 . 4 9 4 1 . 6 0 0 . 6 4 3 C . 6 5 2 1 1 . 5 1 2 . 3 4 . 0 4 9 1 . 71 0 . 6 ' . 3 C . 6 5 2 a . 8 9 . 5 3 . 6 5 7 I . HO 0 . 6 7 7 C . 6 5 2 6 . 3 8 . 3 3 . 3 3 0 1 . 8 1 ) 0 . 6 7 7 C 6 5 7 5 . 6 6 . 1 3 . 0 4 8 1 . 9 4 0 . 6 7 7 C . 6 4 3 1 . 5 5 . 0 2 . 7 5 3 1 . 9 8 0 . 6 1 0 C 6 4 3 2 . 9 3 . 1 7 . 5 6 5 2 . 0 4 0 . 6 1 9 C . 6 3 5 7 . 8 4 . 4 2 . 3 9 6 2 . 0 7 0 . 6 1 0 C 6 2 7 2 . 2 2 . 2 2 . 2 2 9 2 . 1 0 0 . 6 1 0 C . 6 2 7 1 . 4 1 . 6 2 . 0 7 7 2 . 1 3 0 . 6 1 0 C 6 2 7 0 . 7 7 . 6 1 . 9 5 1 2 . 1 5 0 . 6 1 0 C . 6 2 7 0 . 7 1 . 3 1 . B 3 1 2 . 1 6 0 . 6 1 0 C . 6 2 7 0 . 7 1 . 0 1 . 7 2 4 2 . 1 7 0 . 6 1 0 C . 6 2 7 0 . 0 1 . 0 1 . 6 2 6 2 . 1 8 0 . 6 1 0 C . 6 2 7 * 0 . 7 0 . 3 1 . 5 3 9 TABLE C.l.30 I NUMERICAL EVALUATION OF EXPERIMENT EOI-S3-13/I 6 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POWER NO. TIME BOTTOM TOP NORMALIZED FACTOR ENR. C I A L . EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 F l E2 EP l - l ISEC) IPPM) IPPM) l - l l - l l - l IA) (A) 1(1 IX) (XI 0 0 . 0 1261. 1271. l.CO l.COO 1.00 0 . 0 C O l a o . o l o c o 1no.oco 1 6 0 . 6 1438. 1047. 1.12 0 . 6 2 4 1 . 3 6 1.130 1. 122 2 1 . 6 30. B 2 . 7 7 8 2 121.2 1 5 7 C . 9 2 0 . 1.23 0.724 1 . 6 9 1. 1 2 2 1.163 18.1 17.0 2.294 3 i e i . 8 1 6 7 4 . 6 2 3 . 1.31 0 . 6 4 8 2 . 0 2 1 . 1 1 4 1.138 1 4 . 5 13.2 2.008 4 242 . 4 1753. 7 5 1 . 1.37 C 5 9 1 2.32 1 . 1 0 5 1.122 1 1 . 1 I C O 1 . 7 8 3 5 3 C 3 . 1 1813. 695. 1.42 C 5 4 7 2 . 5 9 t . 0 9 7 1.122 8.4 7.7 1 . 5 9 6 6 363.7 l e s s . 6 5 8 . 1.45 o . s i e 2 . 8 0 1 . 0 7 2 1.105 6 . 2 5.2 1 . 4 3 4 7 4 2 4 . 3 i e 8 7 . 6 2 6 . 1 . 4 7 0 . 4 9 2 2 . 9 9 1 . 0 7 2 1 . 0 8 9 4.5 4 . 6 1 . 3 0 1 8 4 8 4 . 9 1913. 6 0 6 . 1 . 4 9 0 . 4 7 7 3 . 1 3 1 . 0 5 6 1 . 0 7 2 3 . 8 2 . 8 1 . 1 8 6 9 545.5 1924. 591. 1.50 0 . 4 6 5 3 . 2 3 1 . 0 3 9 1 . 0 5 6 1.7 2.3 1.083 10 6 C 6 . 1 1938. 5 7 4 . 1 . 5 1 0 . 4 5 2 3.35 0 . 5 3 6 1 . 0 3 9 4.1 2.5 1.027 11 6 6 6 . 7 1547. 571. 1.52 0.450 3 . 3 8 1 . 0 3 1 1 . 0 2 3 1.3 0.4 0 . 9 4 5 12 7 2 7 . 3 195C 5 6 4 . 1.52 C . 4 4 4 3 . 4 3 1 . 0 2 3 1.015 0 . 4 1.2 0 . 8 7 6 13 7 E 6 . C 1953. 5 5 9 . 1.52 0 . 4 4 0 3.47 0 . 9 9 8 1.023 0.4 0 . 8 0 . 8 1 7 14 648 . 6 1953. 557. 1.52 0.439 3 . 4 8 1 . 0 0 6 1.C06 0.0 0.2 0.762 15 9 C 9 . 2 1956. 555. 1.53 0.437 3.50 1 . 0 0 6 1.023 0.4 0.4 0.T15 16 969 . 8 1956. 557. 1.53 0.435 3.51 1.073 1.006 0.0 0.4 0 . 6 7 4 17 1C30.4 1953. 550. 1.52 0.4J2 3.53 1.006 1.006 -0.4 0.4 0.636 _, TABLE C. 1.31 I NUMERICAL EVAIUATICN CF EXPERIMENT E 0 t - S ) - I J / f ? 361 | J ) 4 5 6 T B 9 10 It 12 CYCLE R ( H CONCENTRATION CCNC INT KA T UN SlPARATION CURRENT' CURRI NT POWER KC. 1IME UCT1CM TCP NORMALIZED fACTOR ENR. CIAL. EFTICIENCY FFFIC1CNCY NCYC T CP CT XB XT NS II 12 ' El F2 EP l - l ISECI IPPMI IPPfl l - l l - l •*»  , A '  1 , 1 1 X 1 1 1 1 0 o.c 1270. 1267. I.CC i.crio I (0.6 1466. 1019. 1.15 o.eoe 2 121.2 1626. 875. 1.2H 0.69.1 3 1E1.8 1 756 . 764. 1.3P C.6C5 4 242.4 i e 4 4 . 684. 1.45 0.542 5 2C3. 1 1907. 626. 1.50 0.496 6 36 3.7 1953. 581. 1.54 C.46 5 7 424.3 1984. 557. 1.56 C.442 6 464.9 2C1C. 537. 1.58 0.425 9 545.5 2C22. 522. 1.59 C.414 1C 6C6.1 2C33. 513. 1.6C C.407 11 666.7 2C39. 506. 1.61 0.401 12 727.3 2C42. 501. 1.61 C.397 13 788.0 2C45. 497. 1.6 1 C.294 14 848.6 2C45. 493. 1.61 0.391 IS 9C9.2 2C48. 49C. 1.61 0.389 I.CO 0.0 CO 100.0 100.0 100.OCO 1.41 1.303 1.221 23.4 ICR 7.C79 1.85 1.30) 1.754 19.0 17.9 1.736 2.2R 1.136 1.155 15.1 14.9 1.539 2 . 6 1 1 1. 370 1.155 10.) 1C.7 I. 358 3.03 1.287 1. 130 7.6 8.0 1.210 3.31 1.21) 1.161 5.9 5.2 1 .064 3.54 1.270 1.130 3.9 4. 1 0.976 3.72 1.295 1.064 3.1 3.0 0.867 3.84 1.271 1. 122 1.5 2.0 0.806 3.93 1.729 1. 122 1.5 1.2 0.738 4.01 1.767 1.081 0.7 1.1 0.679 4.05 1.270 1.072 0.4 0.7 0.628 4.C9 1.279 1.048 0.3 0.6 0.584 4.12 1.237 1.204 0.9 0.5 0.543 4.15 1.204 1.204 0.4 0.3 O.S09 TABLE C.1.32 I NUMERICAL EVALUATICN OF EXPERIMENT EOI-S3-13/I 8 CYCLE NC. NCYC l - l REAL TIME T I SEC I 3 4 5 6 7 CCNCENTRATICN CONCENTRATION SEPARATION ECTTCM TOP CB CT IPP«I IPPMI NORMALIZED XB l - l XT l - l FACTOR NS l - l CURRENT ENR. CIAL. II IA) 12 (A) 10 11 12 CURRENT POWER EFFICIENCY EFFICIENCY El 1*1 E2 IX) EP IXI 0 CO 1133. 1135. I.CO l.CCC 1.00 0.0 C O too .0 t o c o 100.000 1 60.6 1355. 89C. 1.20 C.784 1.53 1.369 1.779 25 .2 29.7 1.569 2 121.2 1533. 730. 1.35 0.643 2. 10 1.361 1.328 20 3 16.7 1.146 3 161.6 1662. 617. 1.47 0.543 2.70 1.320 1.303 15 .2 13.5 1.176 4 242.4 1761. 539. 1.56 0.475 3.27 1.287 1.320 11 9 9.1 1.036 3C3.1 1827. 484. 1.61 C426 3.78 1.320 1.262 7 .7 6.8 0.916 6 263.7 ie75.- 451. 1.66 0.398 4. 16 1.312 1.270 5. 7 3.9 0.812 7 424.3 1904. 424. • 1.68 0.374 4.50 1 .303 1.246 3 4 3.4 0.727 484.9 1933. 408. 1.71 0.359 4.75 1.295 1.254 3 4 2.1 0.657 9 545.5 1947. 40C 1.72 0.252 4. 68 1.267 1.262 1 .7 1.0 0.594 10 6C6. 1 1561. 387. 1.73 0.341 5.08 1.270 1.287 I .8 1.6 0.545 11 666.7 1973. 384. 1.74 0.339 5.14 1.254 1.287 1 .4 0.3 0.501 12 127.3 1581. 379. 1.75 0.334 5.24 1.237 1.287 1 .1 0.6 0.464 14 648.6 1587. 377. 1.75 0.332 5.29 1.279 1.303 0 .3 0.2 0.400 16 1C9I.0 1996. 377. 1.76 C.22T 5.18 i.?e7 1.279 0 .3 0.2 0.314 22 1333.5 2C01. 374. 1.77 0.330 5.16 1.267 1.279 0 .2 -0.1 0.258 TABLE C.1.33 I NUMERICAL EVALUATION CF EXPERIMENT E O l - S l - l l / l 9 362 to It 12 CYCLE NC. NCYC l-t REAL l i f t T ( S E C ) C C N C E N T R A T I C N ec i i c f TCP CA IPPf I CT I P P M ) C PNC INTRA!ICN SEPARATION NORMAL 120C TACIOR xe I-) XT l - l NS l - l CURRENT ENR. CIAL. It ( A l 12 I A ) CURRTNT E F F I C I E N C Y El I t l E2 I X ) POWER FFFICIENCV EP IX) 0 O.C 1C57. 1045. l.CC 1 . C 0 0 I.CO 0 . 0 C O 100.0 l o c o 1 51.8 1103. 909. I.C4 C67C 1.70 0.965 C 9 4 6 8.7 76.0 7 IC3.6 1149. 84 1. 1.C9 o.eo5 1.35 0.994 1.062 8.5 11.7 3 155.4 119C. 793. 1.1 1 0.759 1.40 1.042 1.013 7.1 8.5 207.2 1723. 756. 1. 16 C. 723 1.60 1 .067 1 .C04 5.6 6.8 5 25">. 1 1748. 725. 1.18 0.694 1. 70 1.013 1.03) 4 . 4 5 . 4 6 310.9 1277. 703. 1.20 C.673 1. 79 1.013 1.021 4.4 3.9 7 362.7 1289. 684. 1.22 0.654 1.R6 1.013 1.052 3.0 3.3 8 414.5 1303. 668. 1.23 0.640 1.93 1.013 1 .C04 7.5 7.8 9 466.3 1314. 654. 1.24 C.626 1.99 1.023 1.013. 7.0 2.5 IC 518.1 1322. 645. 1.25 0.617 7.03 1.01 3 C.994 1.5 1.6 11 569.9 12 30. 636. 1.26 C.6C9 2.07 1.033 1.C04 1.5 1.6 12 621.7 1336. 628. 1.26 0.601 7.10 0.975 1.05? 1.0 1.3 13 673.6 1341. 622. 1.27 0.595 2.13 1.013 C 9 9 4 1.0 1.2 14 725.4 1347. 618. 1.27 0.591 2. 16 1 . 0 0 4 1.C04 1.0 0.7 15 777.2 135C. 615. 1.28 0.589 2.17 0.9P4 1.004 0.5 0.5 16 829.C 135C. 611. 1.28 0.585 2. 18 1.004 1.013 0.0 C.7 17 eeo.e 135C. 6oe. 1.28 0.581 2.20 0.965 1.033 0.0 0.7 18 922.6 1352. 606. 1.28 0.580 2.21 0.965 1.013 0.5 C.2 15 5E4 . 4 1352. 604. 1.28 0.578 2.22 0.994 C.994 0.0 0.5 20 1C36.2 1352. 601. 1.28 0.575 2.22 1.004 C.994 0.0 0.5 21 1088.1 1352. 597. 1.28 0.572 2.24 0.984 C.984 0.0 0.7 22 1139.9 1352. 597. 1.28 0.572 2.24 0.9C4 C.994 0.0 0.0 23 1191.7 1352. 596. 1.28 0.570 2.24 0.994 0.984 0.0 0.2 100.000 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 TABLE C.1.34 t NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/I10 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CONCENTRATION CCNCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BOTTOM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS I I 12 E l E2 EP l - l ISECI IPPMI IPPMI l - l l - l l - l IAI ( A l IX) (XI IX) 0 0.0 1196. 1187. l.CC l.COC ! . CO 0.0 C O 100.0 100.0 100.000 1 60.6 1339. 984. 1.12 o.e29 1.35 1.056 C.990 21.0 31.7 2.799 2 121.2 1458. 862. 1.22 0.726 1.68 1.023 1.056 18.I 18.0 2.339 3 181.6 1553. 7 7 C 1.20 0.649 2.00 1.023 1.073 14.4 13.9 2.054 4 242.4 1679. 699. 1.36 0.589 2. 31 1.015 C.990 11.6 t l . l 1.643 5 3C3.1 1682. 648. 1.41 0.546 2.58 0.990 C.990 8.4 6.1 1.653 6 263.7 1775. 613. 1.44 0.516 2.79 0.973 C 9 9 0 6.8 5.5 1.489 7 424.3 1756. 583. 1.47 0.491 2.99 0.957 C.973 5.0 4.7 1.356 e 484.9 1779. 562. 1.49 0.474 3. 14 0.9)2 C.957 3.8 3.3 1.240 9 545.5 I79C. 548. 1.50 0.462 3.24 0.924 C.982 1.9 2.2 1.131 10 6C6.1 i e o i . 533. 1.51 0.449 3.36 0.957 C.940 1.3 2.6 1.045 11 666.7 1607. 52e. 1.51 0.445 3.40 0.949 C.940 0.9 0.9 0.962 12 727.3 1813. 519. 1.52 0.437 3.47 0.949 C.949 0.9 1.5 0.895 13 7E8.0 1618. 515. 1.52 0.434 3.51 0.949 C.93? 0.9 0.6 0.835 14 648.6 1871. 511. 1.52 C 4 3 0 3.54 0.957 C.932 0.5 0.6 0.781 15 9C9.2 1621. 507. 1.52 0.427 3.57 0.940 C.957 0.0 0.6 -  0.733 16 969.8 1621. 503. 1.52 0.424 3.59 0.924 C.957 0.0 0.6 0.691 IT j 1C30.4 1621. 503. 1.52 0.424 3.59 0.957 C.907 0.0 0.0 0.652 i e j 1C91.C 1821. 503. 1.52 0.424 3.59 0.957 C.957 0.0 0.0 0.616 _________ TABLE C.l.35 I NUMERICAL EVALUATION CF EXPERIMENT E0I-S3-I3/«ll 363 1 2 3 4 5 6 7 8 1 10 II I? CYCLE REAL CCNCPNTRAIICN CONCENTRATICN SEPARAIICN CURRENT CURRENT POWER KC. TIME HCTTCM ICP NCRMALI7CC EACIOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T Cfl CT KB XT NS II 12 El £7 EP l - l I SEC I IPPM) (PPMI l - l l - l <-> I * ' «*» <*» '*<» 0 0.0 1314. 1284. l.CO l.CCO 1 70. 6 1542. 1032. 1.17 C.604 2 141.2 1722. 868. 1.31 C.676 3 211.8 185C. 747. 1.41 0.582 4 282.4 1538. 66C. 1.48 0.515 5 353.1 1996. 604. 1.52 C.47C 6 423.7 2C42. 56C. 1.55 C.436 7 454.3 2C68. 529. 1.57 C.412 8 564.9 2C91. 512. 1.59 C.399 9 635.5 2103. 502. 1.60 C.391 IC 7C6. 1 2108. 498. 1.60 0.388 12 847.3 2117. 486. 1.61 C.38C 14 568.6 2117. 476. 1.61 0.371 16 1129.6 2117. 472. 1.61 0.368 18 1271.0 2117. 477. 1.61 0.372 20 1412.2 2114. 477. 1.61 0.372 l.CO 0.0 CO 100.0 100.0 100.OCO 1.46 1.034 C.94? 29.3 35.5 3.527 1.94 , 0.977 C.963 24.5 22.6 2.983 2.42 0.921 C.977 18.5 16.5 2.559 2.87 0.921 C.92I 12.8 12.5 2.291 3.23 0.921 C.906 8.3 6.3 2.018 3.56 0.913 C.892. 6.7 6.5 1.RC6 3.82 0.878 c e s s 3.9 4.7 1.624 3.99 0.864 C.892 3.6 2.5 1.469 4.C9 0.871 C-892 1.8 1.5 1.331 4.14 0.878 C.871 0.9 C.6 1.211 4.24 0.857 C.871 0.7 C B 1.031 4.34 0.864 C871 0.0 C.9 0.897 4.38 0.664 C.864 0.0 0.3 0.791 4.33 0.871 C.850 0.0 -0.4 0.704 4.33 0.871 C.864 . -0.2 CO 0.634 TABLE C.l.36 t NUMERICAL EVALUATICN CF EXPERIMENT ED!-S3-13/f12 10 11 12 CYCLE NC. REAL TIME CCNCENTRATICN BCTTCM TCP CONCENTRATION SEPARATION NORMAL I/ED FACTOR CURRENT ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC T l - l ISECI CB IPPM) CT I PPM I XB l - l XT l - l NS l - l 11 IAI 12 IAI E l I t l E2 I t l EP (II 0.0 1207. 1206. l.CO l.COO 1.00 0.0 0.0 100.0 100.0 100.000 90.6 1508. 924. 1.25 0.766 1.63 0.817 C.789 38.3 37.1 3.912 161.2 1705. 730. 1.41 C.605 2.33 0.767 C773 26.6 26.0 3.336 271.8 163 3. 606. 1.52 0.503 3.02 0.734 C745 18.0 17.2 2.863 262.4 1518. 526. 1.59 0.437 3.63 0.695 C.723 12.8 11.3 2.489 453.1 1973. 476. 1.64 C.395 4. 14 0.664 C717 8.3 7.5 2.176 543.7 2C1C 446. 1.67 0.370 4.50 0.657 C.679 5.9 4.5 1.930 634.3 2C33. 428. 1.69 C355 4.75 0.690 C712 3.5 2.6 1.709 724.9 2C45. 413. 1.69 0.342 4.95 0.684 C673 1.7 2.4 1.534 815.5 2C53. 410. 1.70 0.340 5.00 0.662 C.673 1.4 C.4 1.384- 5C6. 1 2C59. 408. 1.71 0.338 5.05 0.662 C.668 0.9 0.4 1.261 596.7 2C62. 401. 1.71 C233 5. 14 0.662 C706 0.5 0.9 1.157 ce7.3 2C62. 399. 1.71 0.330 5. 17 0.640 C.662 0.0 0.4 1.070 178.0 2C62. 392. 1.71 C.325 5.26 0.673 C662 0.0 1.0 0.996 268.6 2C62. 397. 1.71 0.329 5.19 0.712 C.668 0.0 -0.6 0.922 359.2 2C62. 393. 1.71 C.326 5.24 0.712 C.651 0.0 C.6 0.865 449.6 2C62. 397. 1.71 0.329 5. 19 0.712 C651 0.0 -0.6 0.810 540.4 2C62. 396. 1.71 C.328 5.20 C.712 C.651 0.0 C.2 0.764 621.0 2C62. 395. 1.71 C.327 5.22 0.712 C640 0.0 0.2 0.723 721.6 2C62. 391. 1.71 0.324 5.27 0.712 C.673 0.0 C.6 0.68T TABLE C.l.37 > NUMERICAL EVALUATION CF EXPERIMENT EOI-S3-13/P1J 364 i 2 3 4 5 6 7 a 9 to 1 1 12 CYCLE REAl CONCENTRATION C I : N C ' : N 1 R A 1 ION Sl.PAMAIIClN CURRENT CURRENT POWER N C . 1 IKE KETICM TCP NORMAL I 2 C O FACIEIR LNR. CIAL. EFFICIENCY EFFICICNCY NCYC t cn CT Xl< XT NS 1 1 12 El E2 E P t- 1 ISEC) (PP* 1 (PPMI 1 - 1 (-) l - l (Al (Al (X) I t l I t ) 0 O.C 1 125. 1126. l.CO l . C C C l . C O 0.0 C O 100.0 I0C.0 mo.ooo I 11C .6 1455. 827. 1 . 2 9 0.734 1 . 76 0 . 6 1 7 C.610 4 4 . 0 4 1 . 6 4 . 4 7 6 2 221.2 1 6 6 0 . 626. 1 . 4 8 0.556 2 . 6 6 0 . 6 1 0 C . 5 9 2 28.5 28 .9 3. 76) 3 331.6 1 787. 511. 1 . 5 9 0.454 1 . 5 0 0 . 5 6 1 C.5 7 0 19 .1 17.1 3. ie5 4 IE67. 4 3 6 . 1 . 6 6 C . 3 8 7 • 4 . 2 9 0 . 5 4 ? C . 5 4 2 12.5 1 1 . 7 2 . 7 4 6 5 553.1 1515. 392. 1 . 7 C 0 . 3 4 8 4 . i W 0 . 5 3 1 C.533 7 . 7 7.0 2. 3ei 6 663.7 1 5 5 C . 373. 1 . 7 1 0.331 5 . 2 4 0 . 5 C 6 C . 5 2 4 5.8 3. 1 2.091 7 774.3 1567. 359. 1.75 C . 3 1 8 5 . 4 9 0 . 5 3 J C . 4 9 7 2 . 7 2 . 4 1.851 8 6 6 4 . 9 1584. 35C. 1 . 7 6 C.3IC 5 . 6 8 0 . S 1 5 C.515 2.8 1 . 5 1.661 9 595.5 199C 343. 1 . 7 7 C.305 5.81 0.520 C.515 0 . 9 1 . 1 1 . 4 9 9 10 11C6.1 1559. 3 4 4 . 1.78 C.306 5 . f l l 0.515 C 5 1 1 1 . 4 -C.2 1.362 1 1 1216.T 2C01. 342. 1 . 78 C.304 5 . U 6 0.520 C.506 0 . 5 C.4 1.249 12 1327.3 2C1C. 342. 1.79 C.204 5 . P 9 0.506 C.506 1 . 4 CO 1.157 1 3 1438.0 2C16. 3 3 9 . 1 . 7 9 0.301 5 . 9 5 0.497 C.502 1.0 0.4 1.079 TABLE C.l.38 I NUMERICAL EVALUATION OF EXPERIMENT EDI-S3-13/U4 CYCLE NC. REAL TIME NCYC T l - l I SEC) CCNCENTRATICN BOTTOM TCP 5 4 7 CONCENTRATION SEPARATION CB ( P P M ) CT ( P P M ) NORMALIZED XE l - l XT (-1 FACTOR NS l - l CURRENT ENR. CIAL. It IAI 12 IAI 10 11 CURRENT EFFICIENCY Et I t l E2 It) 12 POWER EFFICIENCY EP I t ) 0 0.0 1281. 1267. l.CO t.coo l.CO 0.0 CO 100.0 100.0 100.OCO 1 68.3 1450. 1127. 1.13 0.690 1.27 0.820 C.776 28.3 24.7 1.425 2 136.6 1587. 996. 1.24 o.7ea 1.57 0.790 C.776 23.8 22.9 1.314 3 2C5.C 1725. 89C. 1.25 C.703 1.92 0.790 C.790 24.0 18.8 1.242 4 273.3 1855. 792. 1.45 C625 2.32 0.776 C.790 23.2 17. 1 1.190 5 341.6 197C. 713. 1.54 0.563 2.73 0.790 C.746 19.9 14.5 1.130 6 4C9.S 2C76. 648. 1.62 0.511 3.17 0.754 C.732 19.4 12.4 1.080 7 478.2 2166. 591. 1.69 C466 3.63 0.739 C.732 16.7 1C.7 1.028 8 546.6 2254. 553. 1.76 0.437 4.03 0.717 C.710 16.7 7.2 0.979 9 614.9 2321. 501. i . e i 0.395 4.59 0.703 C68B 13.2 1C6 0.942 10 6E3.2 2386; 466. 1.66 C.368 5.07 0.661 C.703 13.0 6.8 0.901 12 619.9 24ec 414. 1.94 0.327 5.92 0.673 C.659 9.6 5.4 0.823 16 IC93.1 2602. 352. 2.C3 0.278 7.11 0.629 C.651 6.6 3.3 0.695 20 1366.4 2668. 324. 7. 10 C.256 8.71 0.651 C.622 4.6 1.6 0.596 24 1639.7 2724. 311. 2. 13 0.245 e.67 0.637 C.622 1.9 0.7 0.515 28 1913.C 2736. 303. 2.14 0.239 6.93 0.629 C.615 0.7 0.4 0.451 TABLE C.l.39 > NUMERICAL EVALUATION CF EXPERIMENT EOI - S J - l J / t l J 365 10 II 12 CYCLE NC. NCYC (-1 REAL T I ft T ISCCI CCNCCN1RATICN flCITCM 1CP ce I PPM I CI IPPMI CCNCt'NTRAI ICN SEPARATION NL'HMALI/EO TACTOR Xl> l - l XI l - l NS l - l CtiHRI NT ENR • f I Al . It IAI 12 IAI CURRTNT EFFICIENCY El 111 F2 HI POWER EFFICIENCY EP I t l 0 O.C 12P6. 1277. l.CC l.CCC l.cn 0.0 CO 100.0 lor.o 100.OCO t 37.1 14 50. 1152. 1.13 C.90? 1.25 1.212 1.C10 34. 1 31.3 1.737 2 74.3 1598. 10)5. 1.24 o.eio 1.5) 1.C10 1.104 37.1 26.9 1.683 3 111.4 1133. 934. 1.35 C.7)l I.R4 I.050 1.037 37.6 74.5 1.611 4 I4R.6 1858. 844. 1.44 C.tbl 2.1-7 1.063 C.9A-) 29.7 23.6 1.552 5 If 5.7 1967. 764. 1.5) 0.598 2.56 0.9" ) 1.010 28.0 2C.0 1.490 6 222.9 2C53. 697. 1.(0 C.545 2.9) 0.979 1.037 23.5 16.4 1.414 T 26C.C 214C. 641 . 1.66 C.502 3. 31 0.96.9 C.979 77.6 15.1 1.355 a 257. 1 2236. 58P. 1.74 0.461 3.77 0.942 C.969 25.8 1 3.8 1.313 9 ?34.3 228C. 548. 1.77 0.429 4. 13 0.915 C.88R 17.1 11.4 1.243 to 371.4 223C. 512. l . e i 0.401 4.52 0.867 C915 14.6 ICO 1.188 12 445.7 2424. 454. 1.E8 C.356 5.30 0.9C? C.862 13.2 8.5 1.093 14 52C.C 2486. 414. 1.93 0.324 5.96 0.808 C.902 9.7 5.6 1.003 16 594.3 2533. 387. 1.97 C.303 6.50 0.848 C.875 7.1 3.9 0.921 18 668.6 2572. 365. 2.CO 0.286 6 .99 0.835 C.821 5.8 3.4 0.853 22 817.1 2628. 342. 2.C4 C.266 7.63 0.821 C.BOB 4.4 1.8 0.740 26 965.7 2652. 326. 2.C6 0.256 8.07 0.821 C.808 1.8 1.2 0.647 30 1114.3 2664. 321. 2.07 0.252 8.24 0.781 C.80B 1.0 C.4 0.574 3* 1262.8 2670. 317. 2.C8 0.248 8.35 0.781 C.821 0.5 0.3 0.514 TABLE C.1.4C « NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/«I6 10 11 12 CYCLE KC. REAL TIME NCYC T l - l ISECI CONCENTRATION BCTTCM TCP CB IPPMI CT IPPMI CONCENTRATION SEPARATION CURRFNT NORMALIZED FACTOR ENR. CIAL. XB (-) XT l - l NS l - l II (Al 12 IAI CURRENT EFFICIENCY El ( t l E2 IXI POWER EFFICIENCY EP I t l 0 0.0 1283. 1276. I.CO l.CCO I.CO 0.0 CO 100.0 10C.O 100.OCO 1 33.0 145C 1153. 1.13 C904 1.25 1.062 1.107 44.6 31.5 1.996 2 65.9 1598. 104C. 1.24 0.815 1.53 1.138 1.092 37.1 29.6 1.851 3 98.9 1733. 933. 1.35 C731 1.85 1.123 1.077 34.4 28.3 1.769 4 131.8 1853. 849. 1.44 0.665 2.17 1.032 C.971 33.0 24.6 1.7C1 5 164.6 156t. 765. 1.53 0.600 2.55 0.925 1.062 33.5 27.5 1.647 6 197.8 2C56. 697. 1.60 C.546 2.9) 0.971 1.016 27.9 19.2 1.576 7 230.7 214C 641. 1.67 0.503 3.32 0.925 C956 25.8 16.5 1.512 8 263.7 221C 59C 1.72 0.462 3.7) 0.971 C910 20.5 16.2 1.446 9 296.6 2277. 546. 1.77 C.428 4.15 0.910 C.880 21.0 14.2 1.393 10 329.6 2333. 517. 1.82 0.401 4.53 0.880 C.910 18.0 10.5 1.333 15 454.4 2518. 397. 1.96 0.311 6.30 0.8H0 C.R50 12.0 7.7 1.084 20 659.2 261 1. 347. 2.C3 0.272 7.48 0.774 C.8)4 6.8 3.4 0.902 25 824.0 2658. 375. 2.C7 0.255 e.u 0.804 C.789 3.4 1.6 0.764 30 9(8.e 2682. 316. 2.C9 0.248 8.44 0.758 C.774 1.8 0.7 0.661 35 1153.6 2608. 312. 2.C9 0.245 8.56 0.834 C75R 0.4 0.3 0.576 40 1318.4 2694. 308. 2. 10 0.242 8.69 0.769 C75B 0.4 0.3 0.512 45 1483.2 27C0. 308. 2.10 0.242 8.71 0.7e9 C.789 0.4 0.0 0.460 TABLE C.l.41 I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-I1/II? 366 10 II 1? C Y C L E NC. NCYC l - l REAL t i s e c i CCNCfNTRAI ICN I'CIICM TCP CP. (PP") CT IPPPI CONCINIRATICN SEPARATION NORMALIZED IACIUR XB l - l XT (-1 NS I.-I CUrt R I. N T CNR. CIAL. It IAI I? IAI CURRENT EFFICIENCY El IXI F2 I I I POWER FEE ICIENCY EP (XI c C O 11 75. 1178. l.CO l.CCO l.CO 0.0 C O 100.0 100.0 100.000 1 3 C 1 132e. 1062. 1.13 C.90I 1.25 1.117 C.946 41.6 3R.1 2.091 2 40.3 1466. 96C. 1.24 0.815 1.53 0.9 74 1.078 44.2 29.5 1 .984 3 50.4 15S5. 862. 1.35 0.732 1.85 0.911 1 .04 5 41.9 74.2 1 .444 4 1 20.5 171C 774 . 1.45 C.65 1 2.21 0.9?9 C.974 38.8 27.9 1 .894 5 I5C. 7 i e o 7 . 702. 1.53 0.596 2.57 0.911 C.924 37.9 24.2 1.816 6 1E0.6 If 95. 637. 1.61 C.541 2.97 0.413 C.91 J 30.2 22.0 1.744 7 210.9 1976. 587. 1.6P C 4 9 8 3.36 0.846 C.846 77.4 18.5 1.674 8 241.1 2C71. 541. 1.76 C.459 3.33 0.746 C.946 37.2 15.3 1.630 9 271.2 2103. 501. 1.78 0.425 4.20 0.879 C.780 11.3 16.0 1 .540 IC 3CI.4 2155. 467. 1.83 C.396 4.61 0.796 C.879 20.4 11.9 1 .475 15 452.0 2324. 361. 1.97 C.307 6.43 0.746 C.TBO 13.2 8.5 1.203 2C t02.7 2412. 317. 2.C5 C.269 7.59 0.647 C 7 4 6 7.9 3.4 1.0C1 25 753.4 2456. 297. 2.08 0.252 e.27 0.763 C 6 9 7 3.6 1.8 0.848 30 9C4.1 2468. 288. 2.C9 C.244 8.57 0.763 C.697 1.0 0.8 0.727 35 1C54.7 2483. 284. 2. 11 0.241 8.74 0.730 C 6 9 7 . 1.3 C.3 0.639 40 12C5.4 2489. 283. 2.11 0.240 8.80 0.747 C.697 0.5 C I 0.568 45 1356.1 2498. 283. 2.12 C 2 4 C E.83 0.713 0.697 0.8 0.0 0.512 TABLE C.1.42 : NUMERICAL EVALUATION OF EXPERIMENT EOI-S3-13/M6 1 2 3 4 5 6 7 ' 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CRNCENTRATICN SEPARATION CURRENT CURRENT POWER NO. TIME BOTTOM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XI NS I I 12 Et E2 EP !-> I SEC 1 IPPMI (PPMI l - l l - l l - l ( A l IA) IX) IXI IX) 0 0.0 1204. 1195. l.CO l.CCC l.CO 0.0 C O 100.0 100.0 100.OCO 1 26.5 1226. 1143. 1.C2 0.957 1.06 1.717 1.585 4.5 11.5 0.462 2 53.C 1242. 1075. 1.C3 C.900 1.15 1.679 1.792 3.5 13.5 0.457 3 79.5 1259. 1036. 1.C5 0.e67 1.71 1.754 1.797 3.3 7.7 0.4CO 4 1C6.C 1281. 1001. I.C6 0.e38 1.77 1.754 1.735 4.4 7.1 0.375 5 132.5 1297. 973. 1.08 0.8 14 1.32 1.717 1.735 3.4 5.8 0.349 6 159.0 1319. 944. 1.10 C 7 9 C 1.39 1.754 1.754 4.5 5.7 0.335 7 185.5 1 339. 921. 1.11 0.771 1.44 1.679 1.792 4.1 4.6 0.320 8 212.0 1352. 90C. 1. 12 0.754 1.49 1.735 1.792 2.8 4.1 0.302 9 238.6 1372. 880. 1.14 0.737 1.55 1.717 1.698 4.0 4.3 0.293 10 265.1 1386. 867. 1.15 0.721 1.60 1.698 1.754 2.9 3.6 0.281 15 357.6 1433. 791. 1.19 0.662 1.80 1.735 1.735 1.9 7.9 0.230 20 530.1 1472. 744. 1.22 0.623 1.96 1.660 1.698 1.7 1.9 0.197 25 662.7 1494. 711. 1.24 C.595 2.C9 1.62? 1.679 1.0 1.4 0.171 30 755.2 1503. 688. 1.25 0.576 2.17 1.6'.0 1.622 0.4 1.0 0.150 35 927.7 1514. 677. 1.76 C.563 2.23 1.61.1 1.622 0.5 C.7 0.114 40 1C60.7 151T. 65B. 1.26 0.551 2.79 1.677 1 .660 0.1 0.6 0.120 45 1152.8 1517. 64e. 1.26 0.54? 2.32 1.622 1.585 0.0 0.5 0. 108 50 1325.3 1517. 645. 1.26 0.540 2.33 1.641 1.603 0.0 0.1 0.098 TAeiE C.1.43 I NUMERICAL E V A L U A T I O N CF E X P E R I M E N T E O I - S J - 1 3 / I I 9 367 to II I ? CYCLE KC. NCYC l - l urn TIME t i sect CCNCFNTRATICN OCIIOf TCP Cfl Ct IPPM) IPPM CONCENTRATION STPAttATION CURRENT NORMAL I /EC FACTOR ENR • CIAL. XP l - l XT l - l NS l - l II IAI 12 IAI CURRTNI EFFICIENCY Et I t l T? I t l POWFR EFFICIENCY EP I t l C CO 1182. 1183. I.CO l.CCC I.CO 0.0 CO 100.0 t o c o 100.000 1 89.8 126-4. 1071 . 1.C7 0.905 1. 18 0.662 C.640 13.0 18.3 0. 8C9 2 179.6 1325. 982. 1.12 C.63C 1. 35 0.668 C.679 9.5 13.7 0.707 3 269.5 1 28 3. 90P. 1.17 0. 76e 1.52 0.679 C.6H5 8.4 11.2 0.647 4 359.3 145C. 85C 1.23 C.719 1.71 0.6FS C.67Q 10.2 8.9 0.609 5 4 4 4 . 1 1491. 797. 1.26 C.674 1.R7 0.66B C.679 6.5 8. 1 0.565 6 526.9 155C. 751. 1.31 C.635 2.07 0.651 C.668 9.4 7.3 0.544 7 628. 1 1598. 712. 1.35 C6C2 2.25 0.651 C685 7.7 5.9 0.517 a 718.5 1646. 675. 1.39 0.570 2.44 0.646 C685 7.7 5.7 0.446 9 8C8.4 1488. 644. 1.43 0.544 2.62 0.651 C66R 6.0 4.8 0.475 10 85e.2 1725. 614. 1.46 C519 2.81 0.657 C.646 5.9 4.8 0.456 12 lC77.e 1787. 569. 1.51 0.481 3. 14 0.657 C646 5.0 3.7 0.419 14 1257.4 163e. 534. 1.56 0.451 3.44 0.640 C635 4.2 2.9 0.386 16 1437.1 1887. 507. 1.60 C.429 3.72 0.623 C635 4.1 2.2 0.360 18 1616.7 1513. 486. 1.62 0.411 3.94 0.623 C.640 2.2 1.7 0.332 20 1796.4 1544. 468. 1.64 C.296 4.16 0.623 C.612 2.6 1.5 0.311 25 2245.4 1996. 442. 1.69 C374 4.51 0.618 C.618 1.7 0.9 0.264 30 2654.5 2C19. 428. 1.71 0.362 4.72 0.601 C.612 0.8 0.5 0.228 35 3143.6 2C33. 421. 1.72 C.356 4.84 0.618 C.596 0.5 0.3 0.199 40 3592.7 2C33. 414. 1.72 0.35C 4.91 0.562 C.629 0.0 C.2 0.176 45 4041.8 2C33. 414. 1.72 0.350 4.91 0.612 C.590 0.0 0.0 0.157 TABLE C.1.44 s NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-13/I2C 10 11 12 CYCLE NC. REAL TIME CONCENTRATION BOTTOM TCP CONCENTRATICN SEPARATION CURRENT NORMAL IZEO FACTOR ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP l - l (SEC I IPPMI IPPMI l - l l - l l - l IAI IAI I t l ( t l ( t l 0 0.0 1207. 1206. I.CO l.COC I.CO 0.0 C O 100.0 100.0 100.000 5 70.8 1187. 1169. 0.56 0.969 1.02 1.568 1.554 -1.6 3.2 0.041 1C 141.6 1168. , 1165. 0.97 0.966 I.CO 1.695 1.660 -1.5 0.3 0.004 15 212.4 1155. 1161. 0.96 C 9 6 3 0.99 1.589 1.660 -1.1 0.3 -0.005 20 2e3.2 1149. 1156. 0.45 0.558 C 9 1 1.624 1.674 -0.4 0.4 -0.004 25 354.0 1141. 1147. 0.95 0.951 0.99 1.624 1.695 -0.7 0.7 -0.002 30 424.8 1133. I14C. 0.94 0.945 0.99 1.695 1.660 -0.6 0.5 -0.003 40 566.4 1125. 1126. 0.93 0.934 I.CO 1.554 1.660 -0.3 0.6 -0.000 50 7C8.0 1119. 1116. 0.93 C 9 2 5 l . r o 1.695 1.638 -0.2 0.4 0.0C1 60 849.6 1114. 1106. 0.92 0.91T 1.01 1.695 1.624 -0.2 0.4 o.oot 70 591.2 1108. 1094. C 9 2 0.507 1.01 1.695 1.624 -0.2 0.5 0.002 80 1132.fi 1106. 10B4. 0.92 0.e95 1.0? 1.5B9 1.674 -0.1 0.4 0.003 50 1274.4 1103. 1075. 0.91 0.891 1.03 1.518 1.624 -O.t 0.4 0.003 ICO 1416.0 1 ICC. I06e. 0.91 0.686 1.03 1.695 1.624 -0.1 0.3 0.003 120 1659.2 1C97. 1054. 0.51 0.674 1.04 1.481 1.624 -0.1 0.3 0.004 14C 1587.5 1C92. 1042. 0.90 0.664 1.05 1.674 1.624 -0.1 0.2 0.004 160 22*5.7 IC86. 1032. 0.90 0.856 1.05 1.765 1.624 - 0 . 1 0.2 0.004 TABLE C.1.45 I NUMERICAL FVHUAIICN CF EXPERIMENT E 0 l - S l - l 3 / i 2 l 368 10 II 1? CYCLE NC. HCYC l - l REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT TI»E BCJICM TCP NCR^ALIZEO FACTOR ENR. CIAL. CURRENT POWER ' EFFICIENCY EFFICIENCY T ISECI CO IFPM CI IPPM) xn i - i XT l - l NS l - l I t IAI I 2 IAI E l I t ) f.2 I t l EP I t l 0 O.C 1237. 1 60.6 I4r>c. 2 121.2 15 75. 3 l e i . s 16 96. 4 242 . 4 1784. 5 3C3. 1 1E47. 6 36 3.7 1892. 7 424.3 1924. e 484 . 9 1547. 9 '45.5 1561. IC 6C6. 1 197C. II 666.7 1S81. 12 727.3 1987. 13 76B.0 1990. 14 848.6 1590. IS 9C9.2 159C. 16 569.e 159C. 17 1C30.4 159C. 18 1C51.C I59C. 1237. l.CO l.CCC 1004. 1 . 1 7 o.eu 854. 1.27 0.69C 743. 1.37 C.601 662. 1.44 0.535 604. 1.49 0.488 562. 1.53 0.455 535. 1.56 0.433 516. 1.57 0.417 501. 1.54 0.405 484. t.59 C.391 482. 1.60 C.390 48C. 1.61 C.388 477. 1.61 0.382 470. 1.61 0.380 467. 1.61 0.377 466. 1.61 0.376 464. 1.61 0.375 4 6 4 . 1.61 0.375 l.CO 0.0 C O 1.44 1.1PB 1.081 1.B5 l . i n o 1.147 7. 78 1.1 55 1. 130 2.70 1.155 1.089 3.06 1.105 1.089 3. 17 1.048 1 . 138 3.59 1.081 1.081 3. 77 1.0 11 1.097 1.92 1.081 1.064 4.07 1.039 1.064 4.11 1.072 1.034 4.14 l.OHl 1.039 4.22 1.039 1.048 4.24 1.064 1.056 4.26 1.039 1.064 4.27 1.064 1.039 4.29 1.039 1.0B1 4.29 1.056 1.039 100.0 1C0.0 100.000 27.8 13.2 2.103 16.5 2C.2 1.848 16.2 15.2 1.634 11.3 11.6 1.453 8.8 8.3 1.299 6.8 5.6 1.165 4.5 3.9 1.050 3.4 2.7 0.953 2.1 2.3 0.868 1.3 2.4 0.8C0 1.7 0.2 0.736 O.B C.4 0.680 0.4 1.1 0.635 0.0 0.4 0.592 0.0 0.4 0.555 0.0 0.2 0.522 0.0 0.2 0.492 0.0 0.0 0.466 TABLE C.1.46 I NUMERICAL EVALUATION CF EXPERIMENT ED1-S3-13/I22 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BOTTOM TOP NORMAL I 2EC FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP J - l ISECI IPPM) IPPM) I-) I-) I-) IA) (A) I t ) I t ) I t ) 0 0.0 1295. t 2 s e . l.CC l.COO l.CO 0.0 C O 100.0 100.0 100.000 1 27.1 1405. 1133. I.C9 0.901 1.21 1.4C0 1.584 27.3 27.3 1.626 2 54.3 1511. 1032. 1. 17 0.821 1.42 1.529 1.511 23.9 23.1 1.416 3 E l . 4 1603. 942. 1.24 C 7 4 9 1.65 1.547 1.455 20.7 21.5 1.307 4 ICS.6 1705. 86C. 1.32 0.6B4 1.93 1.579 1.400 23.0 2 C 1 1.259 5 135.7 1796. 791. 1.39 0.629 2.21 1.474 1.455 21.3 16.6 1.203 101 271.4 2175. 533. 1.68 C.424 3.97 1.179 1.437 22.3 12.4 1.046 15! ACT.1 2400. 402. 1.85 0.32C 5.79 1.29C 1.142 12.1 7.9 0.887 20 542.e 2521. 339. 1.95 0.270 7.22 1.105 1.179 7.6 3.7 0.754 25 678.5 2578. 3 1 C 1.99 0.246 8.04 1.197 1.0B7 3.3 1.9 0.641 30 814.3 2611. 297. 2.C2 0.236 8.55 1.105 1.105 2.0 0.8 0.556 35 9 5 C 0 2617. 28B. 2.02 0.229 8.84 1.105 1.105 0.4 0.6 0.488 4C 1C65.7 2622. 286. 2.C3 0.228 8.90 1.105 1.105 0.4 0.1 0.433 TABLE C . l . 4 7 I NUMERICAL EVALUATION CF EXPERIMENT' £0l-S3-l3/»24 369 i n t l 12 CYCLE KC. NCYC C-l RIAL 1 l"E I ISCCI C C N C C N T H A T I C N B O T T O M rn1 CB CI C T N C I N T R A T I C N S E P A R A T I O N NURMAlIZEU F A C T O R xn i - i X T I-) NS l - l C L ' . I R F N I E N R . C I A L , It IAI I? IA) CURRENT EFFICIENCY El It) E ? I t ) pnwER EFFICIENCY EP I t l 0 CO 1289. 1254. l.CC l.CCC I.CO 0.0 CO loo.o l o c o too.OCO 1 37. 1 1452. 11)1. I . I ) 0.902 1.25 1.2 J G C.996 )).4 31.1 1.865 2 74.3 159P. 1014. 1.24 0.8C9 1.5) 1.111 1.07 7 32.5 27.6 1.7C5 3 111.4 1 739. 913. 1.35 C.728 I.85 1.1)1 1.021 31.5 24.9 1 .621 148.6 i e 5 P . 82C. 1.44 0.654 2.20 1.017 1.C5D 29. 1 77.4 1.548 5 185.7 1576. 746. 1.51 0.595 2.53 1.0)7 1.010 28.6 18.7 1.484 1C 371.4 2368. 488. 1.84 0.3B9 4. 72 0.848 C.961 73.4 13.5 1.228 15 557. 1 2566. 37). 1.59 0.297 6.70 0.821 C.929 12.2 6.3 0.994 20 742.8 2667. 322. 2.C7 0.257 8. 05 0.700 C.969 7.3 2.6 0.822 25 528.5 2715. 301. 2. 11 C.24C 8.79 0.71) C.942 3.4 1.2 0.692 30 1114.3 2736. 292. 2. 12 C.233 9.13 0.862 C.BOB 1.2 C.6 0.591 35 13C0.0 2754. 2C6. 2. 14 0.228 9. 15 0.660 C.969 1.4 0.3 ' 0.518 TABLE C.1.48 I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/I25 1 0 1 1 12 CYCLE NC. NCYC l - l REAL TIKE T ISECI CONCENTRATION ECTTCM TCP CB CT IPPMI (PPM) CONCENTRATION SEPARATION CURRENT NORMAL I ZED FACTOR ENR. CIAL. XB l - l XT I-) NS l - l It (Al 12 (A) CURRENT EFFICIENCY E l I t l E2 (XI POWER EFFICIENCY EP It) 0 I 2 3 4 5 10 15 2C 25 30 35 40 0.0 37.1 74.3 111.4 148.6 185.7 371.4 557.1 747.8 528.5 1114.3 13CC.C 1485.7 1292. 1388. 1483. 157C. 1654. 1727. 2C07. 2178. 2768. 2318. 2347. 2365. 2368. 1264. 1187. 1107. 1036. 968. 909. 69C. 568. 503. 461. 449. 439. 435. l.CC 1.07 1.15 1.22 1.28 1.34 1.55 1.69 1.76 1.79 1.82 1.63 1.83 l.COC 0.939 0.e76 0.619 0.765 0.719 0.546 0.449 C398 0.369 0.355 0.347 C.344 I.CO 1.14 1.31 1.48 1.67 1.86 2.85 3.76 4.41 4.86 5.12 5.28 5.33 0.0 0.608 0.808 0.754 0.6P7 0.673 0.536 0.53e 0.512 0.565 0.465 0.512 0.512 C O C.727 0.862 C.700 C.673 C.619 0.673 C.619 0.619 C.565 C.619 C.592 C.565 100.0 100.0 30.3 26.9 29.6 29.1 31.1 27.6 26.3 16.0 8.9 4.5 3.1 I.7 0.3 23.5 25.6 25.7 23.7 16.5 ICO 5.3 3.2 1.5 0.9 0.3 100.000 3.754 3.352 3.271 3.255 3.193 2.812 2.401 2.033 1.737 1.509 1.327 1.179 TABLE C.l.49 > NUMERICAL (VALUATION CF EXPERIMENT EOI-S3-13/626 370 1 2 3 4 5 * t 8 9 10 II I? CYCLE Hr»l CCN'CrMHAT UN CONCENT RAT1TN SFPARATION CURRINT CURRTNI POWER KC. 1I«T: BCTIOM 10P NORMAL I /CO fAClUR CNR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CI XB XT NS II 17 FI t? CP l - l ISCCI (PI'M IPPMI (-1 I-) l - l IAI (Al 111 M l It) 0 CO 1709. 1767. I.CO l.CCC I.CO 0.0 CO 100.0 t o c o 100.000 1 32.1 1341. UH3. 1.C4 0.9 38 1.11 0.958 C646 18.9 )0.8 3.270 2 64.3 1397. 1 122. l.CP C.890 1.72 0.866 C.67 1 27.1 72.8 2.892 3 96.4 145C. 10h6. 1.17 0.645 1. 1) C.9S8 C.687 19.1 7 C 9 7.658 4 178.6 1497. 1013. 1.16 0.603 1.45 0.847 C.66 7 19. ) 19.5 2.540 5 U C ? 1542. 968. 1.20 0.767 1.56 0.976 C63 ) 15.9 16.0 7.402 10 221.4 1744. 787. 1.35 C674 2.17 C9C3 C687 15.5 13.) 2.0C3 15 487.1 1661. 671. 1.46 0.532 2. 74 0.866 C.606 10.9 9. 7 1.731 20 642.e 1978. 595. 1.53 0.471 3.26 0.829 C.63) 8.1 6.1 1.507 75 8C3.5 2C42. 54 8. 1.58 C.435 3.65 0.879 C.63) 5. ) 3.7 1.313 30 964.3 2C82. 519. 1.62 0.411 3.9) 0.879 C565 3.4 7.7 1.161 35 1125.0 2105. 499. 1.63 C396 4. 13 0.755 C592 2.1 t.7 1.037 40 1285.7 212C 488. 1.64 C287 4.26 0.755 C579 1.3 1.0 0.9)3 45 1446.4 2126. 43C 1.65 C.28C 4.34 0.718 C.592 0.6 C.7 0.646 50 1607.1 2131. 475. 1.65 C.376 4.39 0.755 C565 0.5 C S 0.773 TABLE C.1.5C : NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/H27 10 11 12 CYCLE NC. REAL TIME CONCENTRATION CONCENTRATION. SEPARATION CURRENT 8CTTCM TCP NORMAL I /EC FACTOR ENR. CIAL. CURRENT POWER EFFICIENCY EFFICIENCY NCYC l - l T ISECI CB CT (PPM) (PPM) XB (-) XT (-) NS (-) 11 (A) 12 I A) El It) E2 It) EP It) 0 O.C 1237. 1214. I.CO l.CCC 1.00 0.0 CO 100.0 100.0 100.000 1 49.3 1319. 1069. 1.C7 C.681 • 1.21 0.711 C.433 74.6 57.7 9.507 2 58.6 14C0. 983. 1. 13 0.610 1.40 0.677 C.663 25. 1 22.5 7.3C4 3 147.9 1461. 913. 1. 18 C752 1.57 0.745 C589 17.4 20.4 6.251 4 197.1 1514. 855. 1.22 C.705 1.74 0.745 C571 15.1 17.6 5.597 5 246.4 1556. 815. 1.26 0.672 1.87 0.745 C.553 11.9 12.5 5.026 10 452.8 1674. 699. 1.35 0.576 2.35 0.666 C534 7.5 7.S 3.429 IS 739.3 1705. 66C. 1.38 C.544 2.53 0.677 C.516 1.9 2.6 2.486 20 5B5.7 1710. 649. 1.38 0.535 2.59 0.632 C.553 0.4 C.7 1.912 — J - • TABLE C.l.SI » NUMERICAL EVALUATION CF EXPERIMENT E0l-S3-l3/#2« 10 11 12 CYCLE NC. REAL TIME CCNCENTRATICN BOTTOM TCP CCNCENTRATICN SEPARATION • NORMALIZED FACTOR CURRENT ENR. CIAL. CURRFNT EFFICIENCY POWER EFFICIENCY NCYC T ISEC) CB IPP") CT IPPMI XB (-1 XT I-) NS (-) II (A) 12 IAI El I t l E2 I t l EP I t l 0 0.0 1295. 1267. I.CO l.CCO I.CO 0.0 CO 100.0 100.0 100.OCO 1 54.3 1438. 112C. 1. 11 C684 1.76 0.67? C.57I 37.0 44.6 4.560 2 108.6 1550. 1009. 1.20 0.796 1.50 0.617 C.580 31.3 33.1 3.947 3 162.9 1641. 92C. 1.27 C726 1.75 0.56? C616 28.5 74.2 3.540 4 217.1 1713. 853. 1.27 C.473 1.97 0.589 C.553 70.7 21.0 3.209 6 325.7 1601. 761. 1.39 0.601 2.32 0.56? C589 13.5 13.4 2.622 8 434.3 1855. 712. 1.43 0.562 2.55 0.56? C.551 8.3 7.7 2. 193 10 542.8 1861. 6R1. 1.45 0.536 7.70 0.541 C.54) 4.1 4.9 1.868 17 651.4 1898. 666. 1.47 0.525 2.79 0.514 C.541 2.8 7.5 1.616 14 740. C 1504. 657. 1.47 0.516 2.84 0.5)4 C.541 0.9 1.4 1.413 16; 648.5 19IC. 653. 1.48 0.515 2.86 0.525 C.553 0.9 0.6 1.253 TABLE C.1.52 I NUMERICAL CVALUAMCN OF EXPERIMENT 10I-S1-I1/179 • 371 10 II 17 C Y C L E r u n N C . 11*6 C C N C E N T R A T K N B C I T C M I C P CCNCENTRAT ICN SEPARATION CURRENT NCICAIUED FACTOR ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC l - l T ( S E C ) CB (f-PM) CT ( P P M ) XB ( - ) XT (-) NS (-1 II IAI 12 IA) El I t l F? It) EP I t l 0 0.0 1297. 1276. l.CC l.CCC l.CO 0.0 C O 100.0 ICCO ICO.OCO 1 25.1 14 30. 1153. 1. 10 C.904 1.72 1.86? C.934 33.3 4C.7 1 .B95 2 50.3 1536. 104C. 1.16 C.82C 1.44 1.96? C.929 25.2 35.9 1.652 3 75.4 1651. 951. 1.27 C.745 1. 71 1.763 C.962 30.5 3C.9 1 .597 4 ICO.5 1753. 867. 1.35 0.679 1. 99 1.540 1.078 30.8 24.2 1.541 5 125.7 U53. 787. 1.43 0.617 2.32 1.415 1.078 32.8 23.1 1.512 IC 251.4 2227; 526. 1.72 0.413 4.16 1.763 C.614 19.8 76.5 1 .285 15 377.C 2433. 395. 1.68 0.309 6.06 1.117 C.830 17.1 9.9 1.114 20 5C2.7 253C. 335. 1.55 0.263 7.42 1.142 C.61 3 8.0 4.5 0.939 25 628.4 2576. 306. 1 .99 0.242 8.22 1.018 C846 4.4 2.0 0.805 30 754.1 2596. 297. 2.CO 0.233 8.60 0.993 C.830 1.7 C.9 0.698 35 679.7 2611. 290. 2.CI 0.228 8.85 1.018 C.830 1.4 C.S 0.615 TABLE C.1.53 I NUMERICAL EVALUATION CF EXPERIMENT EOt-S3-13/#3C 4 - 1 2 3 4 S 6 7 8 9 10 11 12 CYCLE REAL CCNCENTRATICN CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NC. TIME BOTTOM TCP NORMAL I2EC FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XE NS II 12 El E2 EP ISEC) (PPM) (PPMI (-) l - l I-) IA) (A) It) It) It) 0 0.0 1322. 1302. l . C O l . C O C 1.00 0.0 0.0 100.0 100.0 100.000 1 30.1 1491. 1169. 1.13 0.e97 1.26 1.195 1. 145 44.2 36.5 2.197 2 60.3 1654. 1045. 1.25 0.«02 1.56 1.228 1.112 41.3 34.7 2.071 3 90.4 1796. 942. 1.36 C.723 1.88 1.029 1.095 42.9 29.4 1.995 4 120.5 1521. 847. 1.45 0.647 2.25 0.896 1. 195 43.7 25.9 1.928 5 150.7 2C39. 762. 1.54 0.585 2.64 0.946 1.128 38.8 22.1 1.849 10 3CI.4 2439. 49P. 1.64 0.282 4.83 0.863 C.996 28.9 16.6 1.522 IS 452.0 2637. 379. 1.99 C291 6.85 0.730 C962 17.0 7.7 1.250 20 602.7 2730. 329. 2.C6 0.252 8.18 0.830 C.813 7.0 3.9 1.034 25 753.4 279C. 31C 2.11 C.238 e.88 0.846 C.763 4.4 1.6 0.876 30 9C4.1 2B5C. 303. 2.16 0.233 9.27 0.597 1.012 6.1 0.4 0.762 TABLE C.l.54 I NUMERICAL EVALUATION OF EXPERIMENT I01-S3-13/I31 372 to 11 12 CYCLE NC. NCYC REAL TIME I ISECI CCNCENTRATICN 0C11CN TCP CP CT IPPPI (PP*I CCNCENTRATIfN SEPARATION NORMALIZED FACTOR XB l - l XT l - l NS (-1 CURRENT ENR. CIAL. I I (A | 12 IAI CURRENT EFFICIENCY E l M l E2 IT) POWER EFFICIENCY EP ( T l 0 CC 1317. 179C. l.CC l.CCO 1.00 0.0 CO 100.0 10C.0 100.OCO 1 33.C 1406. 116(. 1.11 0.9C4 1.25 1.214 1.183 39. 7 29.8 1.443 2 65.9 1637. 1C49. 1.24 o . e u 1.53 1.171 1.151 38.4 29.0 1.D33 3 58.9 1 776. 939. 1.35 0.728 i.es 1.138 1.016 34.7 1C.7 1.783 4 131.8 1907. 844. 1.45 0.6 54 2.71 1.047 1 .047 35.7 26.0 1.733 5 1(4.e 2C22. 764. 1.54 C.592 2.59 1.077 C971 30.4 71.5 1 .667 6 197.8 212C 694. 1.61 0.538 7.99 0.910 1.173 30.8 17.7 1.554 7 230. 7 2216. 633. 1.68 0.491 3.43 1.001 C956 27.1 i e . i 1.538 e 263.7 2295. 582. 1.74 0.451 3.86 0.865 1.032 26.0 14.1 1.477 9 296.6 2368. 541. 1.80 0.419 4.79 0.986 C.880 21.2 13.4 1.418 IC 329.6 2427. 501. i.e4 o.3es 4.75 0.804 1.032 20.9 11.0 1. 162 IS 494.4 2625. 381. 1.99 C.295 6.76 0.834 C.865 13.6 7.9 1.124 2C 659.2 2727. 329. 2.C7 0.255 8.12 0.804 C.834 7.2 3.5 0.936 25 824.0 2E02. 307. 2. 13 0.238 8.94 0.789 C.834 5.4 1.5 0.799 3C 5E6.8 2e26. 297. 2.15 C.230 9.3J 0.834 C.789 1.6 O.T 0.687 TABLE C.I.S5 S NUMERICAL EVALUATION OF EXPERIMENT E0I-S3-13/I32 1 2 3 4 5 6 7 8 9 10 I I 12 CYCLE REAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BCTTCM TCP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP (-) ISECI IPPM) (PPM) (-) (-) l - l ( A l IAI IXI (XI IX) 0 0.0 1308. 1278. l.CO l.CCC l.CO - 0.0 C O 100.0 100.0 100.000 1 33.C 1394. 1216. 1.C7 0.952 1.12 1.168 1.092 41.8 32.3 2.294 2 65.9 1483. 1148. 1.13 0.898 1.26 1.092 1.138 46.4 34.2 2.176 3 98.9 1567. 1081. 1.20 0.e46 1.42 1.062 1. 107 45.0 34.5 2. 128 4 121.8 1(46. 1019. 1.76 0.797 1.58 1.107 1.016 40.5 34.7 2.079 5 1(4.8 1716. 964. 1.31 C 7 5 4 1.74 1.107 C 9 5 6 36.3 33.1 2.022 10 229.6 2C19. 729. 1.54 0.570 2.71 0.910 C 9 8 6 37.9 27.1 1.850 15 454.4 2227. 5 7 C 1.70 0.446 3.82 0.604 C.941 29.6 19.2 1.665 20 (59.2 2374. 464. 1.81 C 3 6 3 4.99 0.789 C.865 21.2 13.9 1.495 25 824.C 2471. 396. i.e9 0.310 6. 10 0.7e9 C.834 14.1 9.3 1.336 30 sea.e 2542. 352. 1.94 0.275 7.05 0.756 C.789 10.7 6.3 1.205 40 1318.4 2617. 304. 2.CO 0.238 8.40 0.713 C.619 5.9 3.3 0.989 50 1648.0 2658. 285. 2.C3 C 2 2 3 9.11 0.774 C.774 3.1 1.4 0.828 60 1977.6 2676. 277. 2.C5 0.21T 9.43 0.774 C.774 1.3 0.6 0.706 TABLE C.1.56 I NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-I3/I33 373 1 2 3 4 S t 7 8 9 10 11 12 CYCLE REAL CCNCCNIRAIICN CCNCENTRAT ICN SE M A M ATICN CURRFNT CURRENT POWER KC. TIME DCIICM TCP NORMALIZED TACIOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC 1 C8 CT X8 XT NS II 12 E l E2 EP l - l ISECI IPPM| I PPM) I-) l-» (-1 IAI IAI I t ) I I I I t l 0 C C 1215. 1196. l.CC l.COC 1.00 0.0 C O 100.0 100.0 100.000 1 33.0 127C. 1151. 1.C5 0.962 1.09 1.138 C.B95 41 .) 43.1 2.59) 2 45.9 1325. 1096. 1.C9 C 9 1 7 I . 19 1.123 C.956 42.0 46.5 2.460 3 58.9 138C 1058. 1.14 0.885 1.78 1.1C7 c.eao 42.7 37.6 2.339 4 131.8 1436. 1023. 1.18 0.655 I . 18 1.1?) C. 619 47.) 36.3 7.769 5 164. 8 148C. 9 8 C 1.22 C.620 1.49 1. 153 C 7 5 8 33.0 46.0 2.221 10 229.6 1691. 8 2 C 1.39 0.686 7.03 1.0)2 C 7 5 R 34.9 36.1 2.034 is 494.4 1653. 681. 1.52 C 5 7 C 2.68 0.834 C 8 9 5 33.2 26.6 1.881 20 659.2 1978. 587. 1.63 C.491 3. 32 0.B19 C 7 7 4 26.3 2C.8 1.734 25 624. C 2C75. 50 7. 1.71 C.424 4.04 0.819 C.774 21.1 17.7 1.602 30 566.e 2163. 446. 1.78 C.374 4.76 0.743 0.789 19.3 12.9 1.487 40 1318.4 2274. 368. 1.67 0.307 6.C9 0.698 C.774 13.6 6.8 1.285 SO 1648.C 2242. 322. 1.93 0.270 7.15 0.652 C.789 8.8 4.9 1.118 t o 1977.6 2286. 295. 1.96 0.247 7.95 0.652 C.774 5.8 3.0 0.983 70 2207.2 2412; 281. 1.99 C.235 8.44 0.60? C.819 3.7 l . S 0.871 TABLE C.I.ST * NUMERICAL EVALUATION CF EXPERIMENT EDI-S3-13/«34 1 2 3 4 5- 6 7 a 9 10 11 12 CYCLE REAL CONCENTRATION CCNCENTRATICN SEPARATION CURRENT CURRENT POWER NO. TIME BOTTOM TOP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP l - l ISECI IPPMI I PPM 1 l - l l - l l - l ( A l IAI I t l ( t l ( t ) 0 0.0 1237. 1205. I.CO l.COO 1.00 0.0 C O 100.0 100.0 100.OCO 1 33.0 1297. 1086. 1.C5 0.901 1.16 1.168 C.986 44.3 34.) 2.492 2 65.9 1355. 9 7 C 1. 10 o.eos 1. 36 1.016 1.123 48.8 29.5 2.249 3 56.9 1411. 867. 1. 14 0.719 1.59 1.047 C.956 45.3 30.8 2.168 4 131.8 1461. 775. 1.18 0.643 1.84 0.910 1.062 47.0 24.6 2.085 S 164.6 1511. 69e. 1.22 0.579 7. 11 0.925 1.C01 46.4 27.0 2.023 10 229.6 1696. 440. 1.37 0.365 3.76 0.634 C.743 38.0 19. 8 1.810 IS 454.4 1601. 317. 1.46 0.263 5.53 0.713 C.69R 25.2 I C O 1.561 20 659.2 1661. 258. 1.50 C 2 1 4 7.03 0.667 C.637 15.3 5.3 1.351 25 824.0 i e 9 5 . 230. 1.53 0.191 8.04 0.652 C.637 9.0 2.5 1.174 30 566.8 1515; 215. 1.55 0.179 8.66 0.607 C.607 S.6 1.3 1.037 35 1153.6 193C. 209. 1.56 C 1 7 3 9. CO 0.S76 C.637 4.2 0.6 0.926 40 1318.4 1941. 206. 1.57 C.171 9.16 0.S46 C.667 3.6 0.2 0.835 TABLE C.1.S8 I NUMERICAL EVALUATION CF EXPERIMENT E D l - S J - I J / i l S 374 10 II 12 CYCLE NC. HOC l - l RP*L 11 1 (SEC I CCNCfNIRATICN U C T 1 C M TCP CB (PPM) CI (PPM) CONCENTRATION SEPARATION CURRENT NCRMALUEO EAC1E1R ENR. CIAL. XB (-1 XT (-) NS l - l I I IAI 12 IAI CURRENT EFFICIENCY E l IT) E2 I t l POWER EFFICIENCY EP I t ) 0 C C 1297. 1263. l.CO l.CCC l.CO 0.0 C O 100.0 10C.0 l o o . o c o 1 33. C 1461. 1218. 1.13 C 9 6 4 1.17 1.1)0 1.016 42.3 38.0 2.454 2 65.9 16C6. 1166. 1.24 0.923 1. 35 I.001 1.18) 41.4 37.3 2.224 3 58.9 1 147. 1126. 1.35 0.892 1.52 1.107 1.016 36.3 31.6 2.076 A 131.P 1681. 1081. 1.46 C 8 5 6 1. 70 0.9B6 1.138 38.7 33.9 2.019 5 164.8 1596. 1035. 1.54 c e i 9 1.89 1.016 1.062 32.2 37.4 1.96 7 10 329.6 2456. 857. 1.90 0.686 2.77 1.047 C.986 25.1 29.1 1 .674 IS 494 .4 2602. 74e. 2. 17 0.592 3.66 1.C3? 1.047 19.1 19.4 1 .440 2C 659.2 303e. ' 646. 2.35 0.512 4.60 0.895 1.138 15.0 15.3 1.278 25 e24.C 3204. 581. 2.48 C 4 6 0 5.40 0.BP4 1.168 11.7 9.6 1. 135 30 5E8.8 3246. 53C. 2.59 C 4 2 C 6. 17 0.986 1.047 8.2 8.2 1.017 40 1318.4 3501. 466. 2.71 0.369 7.35 0.956 1.047 4.6 5.3 0.e30 50 1648.C 36C1. 428. 2.79 0.339 8.22 0.941 1.062 3.0 3.0 0.698 to 1S7T.6 3645. 412. 2.82 C.326 8.66 0.941 1.062 1.3 1.4 0.594 TABLE C.1.59 I NUMERICAL EVALUATION OF EXPERIMENT EOI-S3-13/A36 1 2 3 4 5 6 7 8 9 10 11 12 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT CURRENT POWER NO. TIME BCTICM TOP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS I I 12 E l E2 EP I-) I SEC) (PPM) (PPM) (-) (-) l - l IAI IA) I t l I t l I t l 0.0 60.6 121.2 i e i . 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 4709. 4868. 4598. 510C. 5187. 5259. 5203. 5332. 5361. 5291. 5405. 5405. 5405. 542C. 5 4 2 C 542C. 4636. 4263. 4036. 3859. 3711. 3603. 3512. 3444. 3381. 3331. 3291. 3263. 3235. 3212. 319C. 3173. 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 C 7 7 7 C 7 5 7 C.743 0.729 C 7 i e C.71C C.704 0.698 0.693 o.6ee 0.684 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 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 1.611 1.617 1.617 C O 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 1.663 100.0 14.4 11.9 9.5 8.1 6.8 4.1 2.7 2.7 2.7 1.4 0.0 0.0 1.4 0.0 0.0 100.0 34.4 20.0 IS.5 13.3 9.7 8.2 6.2 5.7 4.7 3.6 2.6 2.6 2.1 2.1 1.6 100.000 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 TABLE C.I.6C I NUMERICAL EVALUATION CF EXPERIMENT EOI-Sl-l3/«37 375 10 II 12 CYCLE KC. NCYC l - l RF A l 11 "E T I SEC I CONCENTRATION CCKC CNl WAT ICN SEPARATION CURRFNT BCTICH TOP NCRXAIUEO FACTOR ENR • CIAL. CURRFNT EFFICIENCY CP CT IFPMI IPPMI XB l - l XT l - l NS l - l I I IAI 12 IAI E l I t l F? I t l POWER EFFICIENCY CP 1X1 6 7 8 9 10 15 70 25 30 35 4C C C 4 5 ) 7 . 4502. l.CC l.CCC I.CO 0.0 C O 1C0.0 35.3 4 6 6 6 . 4356. l.C) 0.96e 1.06 1 .946 1.671 17.7 let 4753. 4246. I.C5 C.943 1.11 1.954 1.791 11.8 1C5.9 4825. 4141 . I.C6 C 5 7 C 1.16 1.869 1 .869 10.1 141.2 4S1 1. 4 0 4 3 . I.C8 0.P98 1.21 1.R69 1 .Re4 12.3 176.5 4 5 6 4 . 3951. 1.10 0.e78 1.25 1.827 1.869 8.4 211. e SC42. 3865. 1. 11 0.e59 1.29 1.869 1.855 1 0 . ) 247. 1 51CC. 3 7 9 1 . 1.12 0.e42 1.33 I.R55 1.841 8.) 282.4 5158. 3722. 1. 14 0.827 1.37 1.841 1.827 8.4 317.8 5201. 3654. 1.15 0.612 1.41 1.841 1.P27 6.3 353. 1 5245. 3597. 1.16 0.759 1.45 1.827 1.813 6.4 529.6 542C. 3353. 1.19 C.745 1.60 1.827 1.756 5.1 7C6.1 5537. 3196. 1.22 C 7 1 C 1.72 1.813 1.742 3.4 ee2.7 S61C. 307e. 1.24 0.684 1.81 1.784 1.728 2.2 1C59.2 5654. 3000. 1.25 0.666 1.87 1.784 1.714 1.3 1225.7 5683. 2944. 1.25 C.654 1.92 1.799 1.685 0.9 1412.2 5683. 2899. 1. 25 0.644 1.95 1.799 1.685 0.0 l o c o 23.2 16.4 14.8 1 1.9 13.1 12.3 1C.8 I C O I C O 8.4 7.4 4.8 3.6 7.4 1.8 1.4 100.000 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 TABLE C.1.61 t NUMERICAL EVALUATION OF EXPERIMENT. EOI-S3-13/I36 I 2 3 4 5 6 7 6 9 10 11 12 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BOTTOM TOP NORMALIZED FACTOR ENR. CIAL. EFFICIENCY EFFICIENCY NCYC T CB CT XB XT NS 11 12 E l E2 EP l - l ISECI IPPMI IPPMI |-| l - l 1-1 IAI IAI (X) «XI I t l C C O 4955. 4889. I.CO l.COO 1. 00 0.0 0.0 100.0 100.0 100.000 1 37.1 523C. 4646. 1.C6 0.951 1.11 2.006 1.723 34.7 35.4 3.583 2 74.3 5434. 4408. 1.10 C.902 1.22 1.917 1.817 27.0 33.3 3.159 3 111.4 5669. 4199. 1.14 0.e59 1.33 i 1.912 i.ees 31.0 28.0 2.998 4 148.6 5660. 3997. 1.18 0.818 1.45 1.871 1.631 25.8 27.9 2.861 5 165.7 6C37. 3825. 1.22 C.782 1.56 1.658 1.750 24.1 24.9 2.738 6 222.9 6215. 3665. 1.25 0.150 1.67 1.831 1.750 24.5 2 3.1 2.646 7 260.0 6348. 3517. 1.28 C 7 1 9 1.78 1.S44 1.696 18.3 22.0 2.535 8 297.1 6467. 3387. 1.31 C.693 1.68 1.865 1.669 16.0 19.7 2.475 9 334.3 6602. 3263. 1.33 0.667 2.CO i.ees 1.615 18.0 19.4 2.348 10 271.4 6707. 3162. 1.35 0.647 2.09 1.885 1.589 14.1 16.1 2.255 15 557.1 7C97. 2766. 1.43 0.566 2.53 1.777 1.615 11.1 12.4 1.881 20 742.6 7255. 2534. 1.48 0.518 2.86 1.777 1.562 7.3 7 . 5 1.595 25 528.5 7491. 2366. 1.51 0.488 3.10 1.723 1.5)5 4.0 4.9 1.371 30 1114.3 7598. 2304. 1.53 C.471 3.25 1.696 1.535 3.2 2.7 1.198 3 5 13CC.0 7628. 2260. 1.54 0.462 3.33 1.669 1.521 0.9 1 . 5 1.051 TABLE C.l.62 I NUMERICAL EVALUATICN CF EXPERIMENT E U l - S I - l l / « 3 9 376 I ? 3 4 5 6 7 8 9 10 II 12 CYCLE REAL CCNCENTRATICN CONCENTRATION SEPARATION CURRENT CURRENT POWER NC. TIME BCIICH TOP NCHMALIZEU FACIUR ENR. CIAL. EEFICIENCY EFFICIENCY NCYC T CB CT XO XT NS I t 12 E l F2 EP l - l ISECI IPPM) IPP*I (-1 l - l l - l IA) ( A l I t l I t l ( t l c 0.0 5654. 5562. l.CO l.COO 1.00 n . o C . 0 100.0 l o c o IP 0 . 0 C 0 1 37.1 6C66. 51 32. 1.C7 C.923 1.16 3.015 2.827 34.6 36.5 2.391 2 74.3 6436. 474R. 1.14 0.854 1. 33 3.096 3. 150 30.3 30.8 7.091 3 111 .4 6766. 4 3 9 f . 1.20 0.79C 1.51 3.19C 3.177 26.1 2 7 . 9 1.973 140.6 7C97. 4089. 1.26 0.735 1.71 2.975 3.015 78.1 25.8 1.843 5 i e s . 7 74CC. 3814. 1.31 0.686 1.91 2.031 3.C02 26.6 23.2 1.77? 6 222 . 9 7643. 3566. 1. 35 0.642 2. 11 2.827 2.975 21.8 2C.8 1.692 7 26C.C 7e73. 341C. 1. 39 0.613 2.27 2.940 2.854 20 . 4 14. 1 1 .600 6 297.1 8C72. 3156. 1.43 0.567 2.52 2.746 2.867 18 . 4 7 7 . 4 1.557 9 334.3 6272. 300C. 1.46 0.539 2.71 2.665 2.854 19.0 13 . 9 1.497 IC 371 . 4 6442. 2855. 1 . 4 9 0.513 2.91 2.719 2.719 15.8 13.5 1.439 14 520.C B555. 243C. 1.58 0.437 3.63 2.558 2.639 12.7 10.7 1.242 IB 668.6 9236. 2173. 1.63 0.391 4.18 2.396 2.585 7.4 6.3 1.076 22 617.1 9409. 2026. 1.66 C.364 4.57 2.369 2.585 4.6 3.6 0.938 26 965.7 9535. 1935. 1.69 0.346 4.85 2.342 2.558 3.4 2.3 0.829 30 1114.3 9567. 1881. 1.69 0.336 5.CO 2.356 2.531 0.6 1.3 0.736 24 1262.6 9614. 1854. « 1.70 0.233 5.10 2.342 2.531 1.3 0.7 0.661 , , _ _ — — — TABLE C.1.63 t NUMERICAL EVALUATION CF EXPERIMENT EOI-S3-13/I40 10 11 12 CYCLE REAL NC. TIME CONCENTRATION BCTTCM TCP CONCENTRATION SEPARATION CURRENT NORMAL I ZEC FACTOR ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC l - l T ISECI CB CT (PPM) (PPM I XE l - l XT I-) NS (-) I I (A) 12 I A) E l I t ) E2 I t ) EP I t ) 0 O.C 5376. 5275. l.CO l.CCO 1.00 0.0 0.0 100.0 100.0 100.000 2 74.3 6141. 449C. 1.14 0.851 1.34 3.581 2.827 27.0 35.1 1.945 4 148.6 6796. 3854. 1.26 0.731 1.73 3.2es 2.881 25.2 27.9 1.769 6 222.9 7294. 3353. 1.36 0.636 2.13 3.096 2.827 20.3 2 2 . 4 1.614 8 297.1 775C. 2972. 1.44 C.563 2.56 2.800 2.692 70.6 17.9 1.510 10 371 . 4 8C87. 2677. 1.50 0.508 2.96 2.600 2.665 15.2 14.0 1.394 15 557.1 8643. 220C. 1.61 0.417 3.85 2.773 2.531 10.1 9.5 1.148 20 742.8 6923. 1967. 1.66 C.373 4.45 2.531 2.585 5.6 4.6 0.955 25 528.5 9C48. 163e. 1.68 C.348 4.83 2.531 2.477 2.5 2.6 0.8C9 30 1114.3 9111. 1773. 1.69 C.336 5.04 2.504 2.423 1.3 1.3 0.697 35 13C0.0 9127. 1741. 1.7C C.230 5.14 2.477 2.315 0.3 0.7 0.611 TABLE C.1.64 I NUMERICAL EVALUATION CF EXPERIMENT E 0 I - S 3 - 1 1 / I " 377 10 II 12 CYCLE NC. Rf/II 1I*E CONCENTRATION CCNCINTHATION SFPARAIICN CURRFNT BCTTCM TCP NORMALIZED FACTOR ENR. CIAL. CURRFNI EFFICIENCY POWER EFF IC IEN'CV NCYC l - l T I SEC I CB (PPPI CI IPPM XC (-1 XT I - ) NS l - l I I I A I 12 I A I E l I t ) E2 I t l EP I t ) C 0.0 5245. 5126. I.CC 1 .ccc l.CO 0.0 CO 100.0 10C.0 100.OCO 1 54.3 5772. 4414. 1.10 0.861 1.28 3. 150 3.C03 28.9 41.0 4.593 2 ICS.6 6I7C. 3934. 1.18 C.767 1.53 3.150 2.855 21.9 29.1 3.839 3 162.9 6467. 3568. 1.23 C.696 1. 77 3.C58 2. 763 16.8 22.9 3.373 4 217.1 664?. 3291 . 1.28 0.642 1.49 3.021 2.640 12.8 17.8 3.0C9 5 271.*. 6e72. 3085. 1.31 C.603 2. 17 2.984 2.653 10.4 13.2 2.707 7 38C.0 7C97. 2849. 1.35 0.556 2.43 2.874 2.579 6.8 8.0 2.220 9 4E8.6 71E8. 268e. 1.37 0.524 2.61 2.837 2.579 2.8 5.4 1.856 11 597.1 7264. 2611. 1.38 0.509 2.72 2.874 2.542 2.) 2.6 1.585 13 7C5.7 7264. 2561. 1.38 O.SCC 2.77 2.817 2.395 CO 1.8 1.371 IS e i A . 3 7279. 2539. 1.39 0.495 2.80 2.8C0 2.358 0.5 C.8 1.210 TABLE C . l . 6 5 t NUMERICAL EVALUATION CF EXPERIMENT E0l-S3-13/»4l 10 11 12 CYCLE NC. REAL TIME CCNCENTRATICN BCTTCM TCP CCNCENTRATICN SEPARATION NORMALIZED FACTOR CURRENT ENR. CIAL. CURRENT EFFICIENCY POWER EFFICIENCY NCYC T l - l ISECI CB CT IPPM) (PPM) XB (-) XT (-) NS (-) I I IA) 12 I A) E l I t ) E2 ( t ) EP I t ) 0 0.0 5332. 5215. l.CO l.CCO 1.00 0.0 C O 100.0 100.0 100.000 1 254.3 5683. 4636. 1.C7 0.889 1.20 0.574 C.605 19.5 30.6 10.206 2 588.6 5934. 4 2 8 C 1.11 0.821 1.36 0.557 C.646 14.3 17.6 7.994 3 ee2.9 6C96. 4038. 1.14 0.774 t.48 0.557 C 6 3 7 9.3 12.2 6.643 4 1177.2 62S9. 3831. 1.17 C.735 1.60 0.561 C.639 9.3 10.3 5.B76 5 1471.5 6393. 3665. 1.20 0.703 1.71 0.557 C.652 7.7 8.1 5.272 7 2C60.0 6542. 3421. 1.23 0.656 1.87 0.550 C.646 4.3 6.0 4.321 9 2648.6 6632. 3269. 1.24 C.627 1.98 0.554 C.652 2.6 3.7 3.621 11 3237.2 6707. 3162. 1.26 0.606 2.07 0.550 C 6 5 B 2.2 2.6 3.122 13 3E25.8 6751. 3111. 1.27 0.597 2.12 0.557 C.646 1.3 1.2 2.712 15 4414.4 6766. 3055. 1.27 0.586 2.17 0.564 C.6I5 0.4 l . S 2.405 TABLE C.1.66 I NUMERICAL EVALUATION CF EXPERIMENT ECl-S3-l3/»42 APPENDIX C.2 EVALUATION OF EDI I EXPERIMENTS ( i ) Numerical evaluat ion of second ED runs. A short computer program was wr i t ten for an IBM 360/67 FORTRAN IVG compiler. The program reads the run number, i n i t i a l cond i - t i o n s , conduct iv i ty ca l i b ra t i on data cyc le pe r iod , and the mV-readings from the recorder chart for a sequence of c y c l e s . It p r in ts a table for each run which d isp lays the progress in separat ion for r epe t i t i ve c y c l i n g . The program and the tables f o l l ow . ( i i ) Tables were prepared which contain a record of current and voltage d i s t r i bu t i ons for each run. The expe r i - ments are grouped together according to the parameter which was a l tered in each group (see Table 34 to 39). The to ta l current i s included as wel l as the appl ied vo l tage. The average current and voltage in each stage were measured in cycle ranges given in columns 4 and 13, r espec t i ve l y . 378 31 °i OJACA 3 £ 0 do vn<sT~e {̂. $J P°Sr 381 F O R T R A N I V C C O M P I L E R M A I N 12-10-72 12:48:53 PAGE 0 0 0 0 1 C 0 0 2 C 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 C 0 0 7 0 0 0 8 0 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 1 4 0 0 1 5 0 0 1 6 0 0 1 7 0 0 1 8 0 0 1 9 C 0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0 2 5 0 0 2 6 0 0 2 7 0 0 2 8 0 0 2 9 0 0 3 0 0 0 3 1 0 0 3 2 0 0 3 3 0 0 3 4 0 0 3 5 0 0 3 6 P R O G R A M T O E V A L U A T E S E C O N D E O R U N S R E A D ( 5 , 1 ) M , N , C B V , C T V , A 1 , C I , A 2 , D 2 1 F O R M A T ( 2 1 2 . F 6 . 2 . 5 F 1 0 . 4 ) R E A O ( 5 , 2 ) T 2 F O R M A T ( F 5 . 1 ) T = T / 6 0 . W R I T E ( 6 , 5 ) 5 F O R M A T ( 1 H 1 , • ; 1 •/ 2 ' C Y C L E R E A L C O N C E N T R A T I O N C O N C E N T R A T I O N T I M E B R I N E D I A L . N O R M A L I Z E D T C B C T X B X T ( M I N ) ( P P M ) ( P P M ) t-1 l-l 100 105 110 120 20 N O . N C ( - ) 3 * 4 ' 5 « 6 . , 7 •//) T I M E = 0 . 0 P = 1 . 0 J = 0 C B 0 = C B V * ( A 1 * C F ) V + Bl) C T O = C T V * ( A 2 * C T V + b 2 ) W R I T E ( 6 , 4 ) J , T I P E , C 8 0 , C T 0 , P , P , P F O R M A T ( I 4 , F 7 . 2 , F 8 . 0 , F 7 . 0 , F 9 . 2 , F 7 . 4 . F 1 0 . 2 ) D O 1 0 0 1 = 1 , N R E A D ( 5 , 3 ) K , C B V , C T V , L F O R M A T ( I 2 . 2 F 6 . 2 t 1 2 ) I F ( L . N E . O ) W R I T E ( 6 , 6 ) _ F O R M A T ( • • ) C B = C B V * I A 1 * C B V + B 1 ) C T = C T V * ( A 2 * C T V + B 2 ) J = J * K T I M £ = T * J X B = C B / C B O X T = C T / C T O S E = X B / X T W R I T E ( 6 , 4 ) J , T I M E , C B , C T , X B , X T , S E C O N T I N U E R E A D ( 5 , 1 0 5 ) N T F O R M A T ( 1 2 ) W R I T E ( 6 , 1 1 0 ) N T , M F O R M A T ( / / • 2« T A B L E 3' W R I T E ( 6 , 1 2 0 ) H F O R M A T ( 1 H 1 . I 3 ) S T O P END S E P A R A T I O N ' / F A C T O R * / / N S ' / ( - ) • / : NUMERICAL EVALUATION OF EXPERIMENT / EDII-Sl-a/«',I2» TOTAL MEMORY REQUIREMENTS 00068E BYTES COMPILE TIME - 1.3 SECONDS CYCLE RC AL NO. TIME CUNCCNTHATItlN URINE DIAL. CONC I: NTR AT I ON NUKMAllZCU StCAR AT ION FACTIIR NC T CB CT xn XT NS l - l (MINI IPPM) IPl'MI l - i (-) (-) 0 0.0 5742. 5641. 1.00 t.cooo l.OD 1 0.67 6393. 4842. 1.11 0.85B4 1.30 2 1.33 6)32. 4350. 1.21 0.7712 1.57 3 2.00 74 76. 3877. 1.30 0.6873 1.89 4 2.67 7980. 3438. 1.39 0.6C95 2.28 5 3.33 8473. 302 7. l.4fl 0.5367 2. 75 6 4.00 8955. 2650. 1.56 0.4698 3. 32 7 4.67 9441. 2304. 1.64 0.4084 4.03 8 5.33 9867. 19B9. 1.72 0.3526 4. 87 9 6.00 10297. 1714. 1.79 0.3039 5.90 10 6.67 IC698. 1458. 1.86 0.2505 7.21 12 8.00 11426. 1236. 1.99 0.2192 9. 08 14 9.33 12064. 670. 2.10 0.1542 13.62 16 10.67 12609. 396. 2.20 0.0701 31.31 18 12.00 13075. 271. 2.28 0.0480 47.44 20 13.33 13443. 184. 2.34 0.0327 71.61 25 16.67 13983. 98. 2.44 0.0174 139.65 30 20.00 14221. 73. 2.48 0.0130 191.09 35 23.33 14357. 67. 2.50 0.0118 211.95 40 26.67 14391. 63. 2.51 0.0112 224.3T TABLE C . 2 . 1 * NUMERICAL EVALUATION OF EXPERIMENT E D I l - S l - 8 / f l 6 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS l - l (MINI (PPHI IPPMI (-) (-1 (-) 0 0.0 5698. 5610. 1 0.83 5904. 5233. 2 1.67 6037. 5120. 3 2.50 6155. 5001. 4 3.33 6259. 4895. 5 4.17 6378. 4777. 6 5.00 6497. 4671. 8 6.67 6692. 4467. 10 8.33 6872. 4269. 12 10.00 7067. 4084. 14 11.67 7264. 3923. 16 13.33 7415. 3756. 18 15.00 7598. 3603. 20 16.67 7750. 3455. 22 18.33 7888. 3314. 24 20.00 8041. 3196. 26 21.67 8180. 3072. 28 2 3 . 3 3 8318. 2955. 3 0 2 5 . 0 0 8442. 2844. 1.00 l.COOO 1.00 1.04 0.9327 1.11 1.06 0.9126 1.16 1.08 0.8914 1.21 1.10 0.8725 1.26 1.12 0.8515 1.31 1.14 0.8326 1.37 1.17 0.7961 1.48 1.21 0.7609 1.58 1.24 0.7279 1.70 1.27 0.6991 1.82 1.30 0.6695 1.94 1.33 0.6421 2.08 1.36 0.6158 2.21 1.38 0.5906 2 . 3 4 1.41 0.5696 2 . 4 3 1.44 0.5476 2.62 1.46 0.5267 2.77 1 . 4 8 0.5068 2.92 TABLE C . 2 . 2 S NUMERICAL EVALUATION OF EXPERIMENT E 0 I I - S 1 - 8 / * 7 383 CYCLE REAL CONCENTRATION CCNCIiNTKAT ION SEPAR\JION NO. II ME BRINE DIAL. NORMAL 1/CO FACTOR NC T CP. CT XB XT NS (-1 (MINI (PPM) <PPM| (-1 (-) (-1 0 0.0 5332. 5281. 1.00 1.0000 1.00 2 2.00 6066. 4414. 1.14 0.8359 1. 16 4 4.00 6707. 3819. 1.26 0.7233 1.74 6 6.00 7294. 3280. 1.37 0.6211 2.20 8 8.00 7842. 2788. 1.47 0.52B0 2.79 10 10.00 8365. 2358. 1.57 0.4466 3.51 14 14.00 9299. 1623. 1.74 0.3074 5.67 18 18.00 1C090. 1079. 1.89 0.2043 9.26 22 22.00 10794. 751. 2.02 0.1421 14.24 26 26.00 11377. 437. 2.13 0.0827 25.81 30 30.00 11834. 283. 2.22 0.0537 41.35 35 35.00 12245. 182. 2.30 0.0344 66. 68 40 40.00 12509. 141. 2.35 0.0268 87.65 45 4S.00 12675. 121. 2.38 0.0229 103.65 TABLE C.2. 3 t NUMERICAL EVALUATION OF EXPERIMENT EDLI-Sl-8/ff 8 CYCLE REAL CONCENTRATION NO. TIME BRINE DIAL. NC (-) T (MINI CB CT (PPH) (PPHI CONCENTRATION NORMALIZED XB (-) XT ("I : SEPARATION FACTOR NS l - l 0 0.0 5434. 5341. 1.00 1.0000 I.00 1 1.33 6542. 4338. 1.20 0.8124 1.48 2 2.67 7491. 3563. 1.38 0.6671 2.07 3 4.00 8442. 2860. 1.55 0.5356 2.90 4 5.33 9299. 2266. 1.71 0.4242 4.03 5 6.67 10090. 1763. , 1.86 0.3310 5.61 6 , 8.00 10762. 1368. 1.98 0.2562 7.73 7 9.33 11377. 1047. 2.09 0.1961 10.68 a 10.67 11899. 776. 2.19 0.1454 15.06 9 12.00 12360. 570. 2.27 0.1067 21.31 10 13.33 12708. 416. 2.34 C.0779 30.01 12 16.00 13275. 217. 2.44 0.0407 60. 02 14 18.67 13611. 121. 2.50 0.0227 110.45 16 21.33 13865. 78. 2.55 0.0146 174.35 18 24.00 14000. 58. 2.58 0.0109 237.37 20 26.67 14119. 48. 2.60 0.0090 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 REAL CONCENTRATION CCNCENTRATION Sfc'PARAT ION NO. T IMC PR 1 N6 U1AL. NORMAL 1 ZED FACTOR NC T CO CT XO XT NS (MINI IPPMI (PPMI l - l (-) (-» 0 0.0 4781. 4765. 1 0.83 5201. 4251. 2 1.67 5493. 3980. 3 2.50 5757. 3711. 4 3.33 6022. 3455. 6 5.00 6542. 2972. 6 6.67 7007. 2528. 10 6.33 7476. 2146. 12 10.00 7918. 1795. 14 11.67 8318. 1464. 18 15.00 9080. 990. 22 18.33 9740. 642. 26 21.67 10233. 416. 30 25.00 10601. 273. 34 28.33 10875. 197. 38 31.67 11036. 164. 42 35.00 11182. 139. 46 38.33 11231. 124. 1.00 l.COOO 1.00 1.09 0.8422 1.22 1.15 0.8352 1.18 1.20 0.77P7 1.55 1.26 0.7250 1.74 1.37 0.6236 2.19 1.47 0.5306 2.76 1.56 0.4503 3.47 1.66 0.3766 4.40 1.74 0.3071 5.66 1.90 0.2C77 9.14 2.04 0.1347 15.12 2.14 0.0873 24.51 2.22 0.0573 38.66 2.27 0.0414 54.99 2.31 0.0344 67*01 2.34 0.0291 80.28 2.35 0.0259 90.53 TABLE C.2. 5 ? NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-8/I10 CYCLE REAL CONCENTRATION NO. TIME BRINE DIAL. CONCENTRATION NORMALIZED SEPARATION FACTOR NC (-1 T (MINI CB CT (PPMI (PPMI XB l - l XT (-1 NS (-) 0 0.0 5376. 5191. 1.00 l.COOO 1.00 1 1.13 5845. 4484. 1.09 0.8637 1.26 2 2.27 6244. 4165. 1.16 0.8022 1.45 3 3.40 6587. 3854. 1.23 0.7423 1.65 4 4.53 6947. 3563. 1.29 0.6863 1.88 5 5.67 7248. 3280. 1.35 0.6318 2.13 6 6.80 7552. 3016. 1.40 0.5810 2.42' 7 7.93 7811. 2788. 1.45 0.5371 2.71 8 9.07 8072. 2556. 1.50 0.4923 3.05 9 10.20 8303. 2364. 1.54 0.4553 3.39 10 11.33 8519. 2157. 1.58 0.4154 3.81 12 13.60 B892. 1865. 1.65 0.3592 4.61 14 15.87 9221. 1602. 1.72 0.3086 5.56 16 18.13 9504. 1368. 1.77 0.2636 6.71 18 20.40 9725. 1184. 1.81 0.2280 7.93 20 22.67 9B99. 1052. 1.84 0.2027 9. 08 22 24.93 1C042. 948. 1.87 0.1B26 10.23 24 27.20 10185. 870. 1.89 0.1676 11.31 26 29.47 10281. 823. 1.91 0.1586 12.0b TABLE C.2. 6 i NUMERICAL EVALUATION OF EXPERIMENT EDIl-Sl-8/»ll 385 CYCLE REAL CONClNTRAT1 ON CCNCLNTH AT I ON SEPARATION NO. TIHE BRINE DIAL. NUKMAL 1 ZEO FACTOR NC T . CB CI XP XT NS l - l CHIN) (PPM) (PPM) «-) (-) (-) 0 0.0 4380. 4290. UOO l.COOO 1.00 1 0.42 4638. 4078. 1.06 0.9527 1.11 2 0.83 4854. 3905. I.11 0.9124 1.21 5 2.08 5434. 3421. 1;24 0.7992 1.55 10 4.17 6274. 2672. 1.43 0.6242 2.30 15 6.25 7112. 2043. 1.62 0.4772 3.40 20 8.33 7827. 1527. 1.79 0. 3568 5.01 25 10.42 8566. 1110. 1.96 0.2593 7.54 30 12.50 9315. 792. 2.13 0.1850 11.49 35 14.58 10010. 544. 2.29 0.1271 17.48 40 16.67 10698. 345. 2.44 0.0805 30.34 45 18. 75 11344. 225. 2.59 0.0526 49.28 50 20.83 11981. 144. 2.74 0.0336 81.39 55 22.92 12559. 93. 2.87 0.0218 131.56 60 25.00 13142. 63. 3.00 0.0147 203.85 65 27.08 13662. 48. 3.12 0.0112 278.93 70 29.17 14102. 35. 3.22 0.0082 390.83 75 31.25 14459. 29. 3.30 0.0068 483.70 80 33.33 14801. 23. 3.38 0.0053 638.26 85 35.42 15059. 18. 3.44 0.0042 811.73 90 37.50 15317. 17. 3.50 0.0040 874.31 TABLE C.2. 7 > NUMERICAL EVALUATION OF EXPERIMENT E0U-Sl-8/#l2 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOI NC T CB CT XB XT NS l - l (MINI IPPHI (PPM) (-) l - l l - l 0 0.0 5129. 5007. I.00 l.COOO 1.00 2 1.67 5493. 4630. 1.07 0.9247 1.16 4 3.33 5816. 4321. 1.13 0.8629 1.31 6 5.00 6126. 4043. 1.19 0.8075 1.48 8 6.67 6423. 3779. 1.25 0.7548 1.66 10 8.33 6662. 3540. 1.30 0.7070 1.84 15 12.50 7264. 3016. 1.42 0.6024 2.35 20 16.67 7796. 2584. 1.52 0.5159 2.95 25 20.63 '8210. 2216. 1.60 0.4426 3.62 30 25.00 8566. 1929. 1.67 0.3853 4.33 35 29.17 8861. 1688. 1.73 0.3370 5.13 40 33.33 9080. 1485. 1.77. 0.2965 5.97 45 37.50 9315. 1331. 1.82 0.2659 6.83 50 41.67 9488. 1199. 1.85 0.2395 7.72 55 45.83 9598. 1094. 1.87 0.2186 8.56 TABLE C.2. 8 » NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-fl/»I3 386 CYCLE REAL OVlCI NIRATION CIHC NfRAT ION SFPAKATION NO. TIME HKINC DIAL. NORMAL 1ZEU F AC IfTR NC T CB CT XH XT NS l-» (PPM) (P>>M» (-1 (-) (-1 0 0.0 5071. 4948. 1 1.17 5259. 4350. 2 2.33 5391. 4251. 4 4.67 5610. 4020. 6 7.00 51110. 3796. 8 9.33 6037. 3563. 10 11.67 6244. 3421. 15 17.50 6692. 2927. 20 23.33 7082. 2567. 25 29.17 7430. 2255. 30 35.00 7735. 1999. 35 40.83 7980. 1773. AO 46.67 8133. 1602. 1.00 l.COOO I.00 1.04 0.R791 1.18 1.06 0.H592 1.24 1.11 0.8125 1.36 1.15 0.7672 1.50 1.19 0.72C0 1.65 1,23 0.6914 1.78 1.32 0.5915 2.23 1.4C 0.5188 2.69 1.47 0.4556 3.22 1.53 0.4041 3.73 1.57 0.3584 4.39 1.60 0.3238 4.95 TABLE C.2. 9 t NUMERICAL EVALUATION OF EXPERIMENT EOll-Sl-B / f14 CYCLE REAL CONCENTRATION NO. TIME BRINE DIAL. CONCENTRATION SEPARATION NORMALIZED FACTOR NC l - l T (MINI CB (PPMI CT (PPM I XB (-1 XT l - l NS (-1 0 0.0 5405. 5293. 1.00 l.COOO 1.00 1 2.15 5816. 4194. 1.08 0.7923 1.36 2 4.30 6111. 3934. 1.13 0.7433 1.52 3 6.45 6393. 3654. 1.18 0.6903 1.71 4 8.60 6662. 3376. 1.23 0.6378 1.93 6 12.90 7143. 2883. 1.32 0.5446 2.43 8 17.20 7446. 2446. 1.38 0.4622 2.93 10 21.50 .8010. 2054. 1.48 0.3880 3.82 14 30.10 8690. 1432. 1.61 0.2705 5.94 18 38. ro 9221. 1000. 1.71 0.1890 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 C Y C L E RF. AL CUNClNIRA1ION Cl.'NCI 'ItRAI 1 (IN S C I ' A R A T ( U N NO. 11 ML' UK IMF. DIAL. NU'IF'ALIZCC FACIOR N C T cn C T X " XT N S 1-1 IM1NI IPPM) (PPMI I-) (-1 1 l - l 0 0.0 5508. 5490. I 0.83 6126. 4601. 2 1.67 6632. 41 30. 3 2.50 7128. 3682. 4 3.33 7598. 3263. 5 4.17 0057. 2871. 6 5.00 8504. 2517. 7 5.83 8955. 2173. e 6.67 9378. 1865. 9 7.50 9788. 1581. 10 8.33 10185. 1321. 12 10.00 10955. 896. 14 11.67 11639. 5 70. 16 13.33 12261. 416. 18 15.00 12791. 233. 20 16.67 13192. 151. 25 20.83 13780. 81. 30 25.00 14034. 60. 1.00 l.COOO 1.00 1.11 0. a 180 1.33 1.20 0.7522 l.oO 1.29 0.67C7 1.«I3 1.38 0.5443 2. 32 1.46 0.5230 2.H0 1.54 0.4585 3.37 1.63 0.3958 4. 11 1.7C 0.3396 5.01 1.78 0.2879 6.17 1.85 0.24C5 7.69 1.99 0.1632 12.19 2.11 0.1038 20.35 2.23 0.0758 29.38 2.32 0.0424 54.82 2.40 0.0276 86.82 2.5C 0.0147 170.28 2.55 0.0110 231.10 TABLE C.2.11 < NUMERICAL EVALUATION OF EXPERIMENT E0 U - S l - 8 / f 16 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS l - l (MINI (PPM) I PPM) l - l l - l (-1 0 o.o 5143. 5061. 1.00 l.COOO 1.00 1 0.83 5727. 4414. 1.11 0.8722 1.28 2 1.67 6244. 3963. 1.21 0.7830 1.55 3 2.50 6722. 3534. 1.31 0.6984 1.87 4 3.33 7173. 3128. 1.39 0.6181 2.26 5 4.17 7628. 2755. 1.48 0.5444 2.72 6 5.00 8057. 2419. 1.57 0.4779 3.28 7 5.83 8488. 2108. 1.65 0.4165 3.96 8 6.67 8861. 1838. 1.72 0.3631 4.74 9 7.50 9221. 1586. 1.79 0.3134 5.72 10 8.33 9567. 1379. 1.86 0.2725 6.83 12 10.00 10201. 1021. 1.98 0.2018 9.83 14 11.67 10714. 751. 2.08 0.1483 14.05 16 13.33 11133. 560. 2.16 0.1106 19.57 18 15.00 11458. 421. 2.23 0.0832 26.77 20 16.67 11703. 324. 2.28 0.0641 35.52 25 20.83 12113. 207. 2.36 0.04C9 57.52 30 25.00 12278. 167. 2.39 0.0329 72.49 33 27.50 12327. 151. 2.40 0.0299 80.08 TABLE C.2.12 t NUMERICAL EVALUATION OF EXPERIMENT CI»ll-Sl-8/«l7 388 CVCIE ML' AL CONC I N IRA F I ON CC'ICKITR A t I FIN SEPARATION NO. TI ML RRINt UIAL. NJKMAtl/EO FACWR NC I CO CT Xn XT NS I-) (M|N) (PPMI (PPMI l - l (-) (-1 0 0.0 5361. 5251. 1 0.65 5M60. 4718. 2 1.30 62H9. 4338. 4 2.60 7128. 3541. 6 3.90 7903. 2944. 8 5.20 8597. 2419. 10 6.50 9268. 1972. 15 9.75 10553. 1184. 20 13.00 11377. 740. 25 16.25 11883. 503. 30 19.50 12195. 375. 1.00 l.COOO 1.00 1.04 0.fl4<36 1.72 1.17 6~'.t>262 1.42 1.33 6".6H19 1.94 1.47 0.56C6 7.63 1.60 0.46C6 3.4H 1.73 0.3756 4.60 1.97 0.2254 8.73 2.12 0.1410 15.05 2.22 0.0958 23.13 2.27 0.0715 31.B3 TABLE C.2.13 i NUMERICAL EVALUATION OF EXPERIMENT E O I l - S l - 8 / f l B CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS I-) (MINI (PPMI (PPMI (-1 (-1 (-) 0 0.0 4926. 1 0.48 5216. 2 0.97 5508. 4007. 1.00 4583. 1.06 4333. 1.12 l.COOO 1.00 0.9536 1.11 0.9014 1.24 4 1.93 6126. 3837. 6 2.90 6707. 3659. 8 3.87 7218. 2960. 10 4.83 7674. 2595. 15 7.25 86431 IRB6. 20 9.67 9299. 1421. 25 12.08 9772. 1089. 30 14.50 1C090. 870. 35 16.92 1C329. 720. 40 19.33 10489. 627. 1.24 0.7982 1.56 1.36 0.7613 1.79 1.47 0.6159 2.38 1.56 0.5398 2.89 1.75 0.3924 4.47 1.89 0.2957 6.38 1.98 0.2266 8.7b 2.05 0.1810 11.32 2.10 0.1497 14.01 2.13 0.1304 16.33 TABLE C.2.14 t NUMERICAL EVALUATION OF EXPERIMENT EDU-Sl-8/«19 389 CYCLE REAL CONCI NTRAI IUN crwtt NTRM ION SCPAKATIOM NO. I IMF UK INC 01AL. NORMAL 1/CO EACIDH NC T C\\ CT xn XT NS If IN) (PPMI IPPM) I-) I-) l - l 0 0.0 5508. 5400. 1 0.50 5830. 5126. 2 1.00 6244. 4U65. 4 2.00 6<H7. 4309. 6 3.00 7548. 37H5. 8 4. CO 8026. 33 36. 10 5.00 8365. 2955. 15 7.50 9693. 2173. 20 10.00 10425. 1655. 25 12.50 IC939. 1305. 30 15.00 11296. 1079. 35 17.50 11540. 896. 40 20.00 11736. 797. 45 22.50 11883. 714. 1.00 I.COCO 1.00 1.0b 0.4412 1.12 1.13 0.9010 l.?b 1.26 0.7980 1.57 1.38 0. 7C09 1.47 1.46 0.61/fl 2.36 1.52 0.5472 2.78 1.76 0.4024 4.37 1.09 0.3065 6.17 1.49 0.2416 8.22 7.05 0.1997 10.27 2.10 0.1659 12.63 2.13 0.1476 14.43 2.16 0.1323 16.31 TABLE C.2.15 i NUMERICAL EVALUATION OF EXPERIMENT EDlI-Sl-8/*20 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE OIAL. NORMAL IZEO FACTOR NC T CB CT XB XT NS l - l IMIN) IPPM) (PPMI l - l I-) l - l 0 0.0 5216. 5102. 1.00 1.0000 1.00 1 0.98 6244. 3969. 1.20 0.7778 1.54 2 1.97 7188. 2124. 1.38 0.4163 3.31 3 2.95 8007. 3654. 1.55 0.7161 2.17 4 3.93 8986. 1940. 1.72 0.3802 4.53 5 4.92 9772. 1448. 1.87 0.?e37 6.60 6 5.90 104B9. 1037. 2.01 0.2032 9.90 7 ' 6.88 11150. 725. 2.14 0.1420 15.05 B 7.87 11703. 493. 2.24 0.0966 23.23 9 8.85 12113. 329. 2.32 0.0645 35.98 10 9.83 12493. 222. 2.40 0.0436 54.94 12 11.80 12941. 106. 2.48 0.02C8 119.50 14 13.77 13125. 60. 2.52 0.0119 212.28 16 15.73 13275. 40. 2.55 0.0079 322.19 18 17.70 13393. 32. 2.57 0.0062 412.«2 20 19.67 13494. 28. 2.59 0.0054 476.46 25 24.50 13696. 24. 2.61 0.0047 554.16 30 29.50 13881. 22. 2.66 0.0043 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 HEAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME UK 1NE DIAL. NORMALIZED FACTOR ! 1 NC T cn CT xn XT NS (-) (MINI (PPMI (PPM| (-1 l - l (-) 0 0.0 2654. 2501. 1.00 l.COOO , 1.00 1 1.33 3614. 1854. 1.36 0.7412 l.«4 2 2.67 4394. 1379. 1.66 0.5513 1.00 3 4.00 5013. 979. 1.89 0.3916 4.82 4 5.33 5508. 678. 2.08 0.2712 7.65 5 6.67 5919. 462. 2.23 0.1848 12.07 6 8.00 6229. 311. 2.35 0. 1245 18.85 7 4.33 6467. 205. 2.44 0.0818 29.77 a 10.67 6662. 139. 2.51 0.0555 4S. 22 9 12.00 6781. 93. 2.56 0.0373 68.49 10 13.33 6887. 66. 2.59 0.0262 99.03 12 16.00 7067. 37. 2.66 0.0147 181.08 14 18.67 7173. 26. 2.70 0.0103 263.13 16 21.33 7264. 16. 2.74 0.0062 438.45 18 24.00 7370. 14. 2.78 0.0056 492.53 20 26.67 7446. 11. 2.81 0.0044 633.35 25 33.33 7598. 10. 2.86 0.0040 710.93 TABLE C.2.17 .» NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/*22 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE) DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS <-> IHINI (PPMI (PPM) (-) (-) (-1 0 0.0 2668. 2611. I 1.02 3222. 2092. 2 2.03 3713. 1725. 3 3.05 4180. 1395. 4 4.07 4609. 1110. 5 5.08 4984. 870. 6 6.10 5187. 668. 7 7.12 5639. 508. 8 8.13 5904. 391. 9 9.15 6126. 296. 10 10.17 6319. 228. 1.00 l.COOO 1.00 1.21 0.8010 1.51 1.39 0.6606 2.11 1.57 0.5341 2.93 1.73 0.4251 4.06 1.87 0.3332 5.61 1.94 0.2558 7.60 2.11 0.1947 10.86 2.21 0.1496 14.80 2.30 0.1134 20.24 2.37 0.0871 27.18 12 12.20 6557. 146. 14 14.23 6707. 101. 16 16.27 6826. 78. 18 18.30 6872. 66. 20 20.33 6932. 58. 25 25.42 7082. 51. 30 30.50 7143. 49. 2.46 0.0561 43.83 2.51 0.0386 65.07 2.56 0.0297 86.05 2.58 0.0251 102.63 2.60 0.0222 117.05 2.65 0.0197 134.86 2.68 0.0187 143.02 TABLE C.2.18 S NUMERICAL EVALUATION OF EXPERIMENT E0II-S1-B/I23 I 391 CYCLE RFAL CUNLeNlRATIUN CllNCf NIRATION SEPARATION NO. 11 ME URINE DIAL. NORMALIZED FACIOR NC T cn CT xn XT NS l - l ( M | N | IPPM) (PPMI (-1 I-) (-) 0 0.0 266S. 2606. 1 1.00 34 46. 1H81. 2 2.00 4137. 1-.05. 3 3.00 4781. 1005. 4 4.00 5318. 694. 5 5.00 5801. 472. 6 6.00 6170. 314. 10 10.00 6917. 91. 15 15.00 7233. 47. 20 20.00 7400. 36. 25 25.CO 7598. 33. 30 30.00 7750. 30. 1.00 l.COOO 1.00 1.29 0.7218 1.79 1.55 0.5393 2.88 1.79 0.3859 4.64 1.99 0.2662 7.49 2.17 0.1813 11.99 2.31 0.1205 19.19 2.59 0.0348 74.42 2.71 0.0180 150.76 2.77 0.0137 202.06 2.85 0.0128 223.19 2.91 0.0116 250.45 TABLE C.2.19 t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/124 . CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE OIAL. NORMALIZED FACTOR NC T CB CT XD XT NS <-) (MINI (PPMI IPPMI (-» (-1 (-1 0 0.0 1257. 1241. 1.00 l.COOO 1.00 1 0.67 1358. 1059. 1.08 0.8534 1.27 2 1.33 1442. 986. 1.15 0.7942 1.44 3 2.00 1522. 913. 1.21 0.7360 1.64 ,4 2.67 1597. 845. 1.27 0.6809 1.87 6 4.00 1752. 724. 1.39 0.5832 2.39 8 5.33 1886. 618. 1.50 0.4979 3.01 10 6.67 2021. 525. 1.61 0.4231 3.80 15 10.00 2304. 348. 1.83 0.2807 6. S3 20 13.33 2517. 235. 2.00 0.1892 10.58 25 16.67 2666. 165. 2.12 0.1331 15.94 30 20.00 2771. 126. 2.20 0. 1019 21.64 35 23.33 2838. 103. 2.26 0.0832 27.14 40 26.67 2877. 90. 2.29 0.0728 31.45 45 30.00 2916. 84. 2.32 0.0676 34.32 TABLE C.2.20 t NUMERICAL EVALUATION OF EXPERIMENT EOII-Sl-8/»25  1 392 CYCLC RL" AL CONCI NTR A TI UN CIINCLNIR AT ION SEPARATION NO. 1 IMC URINE DIAL. NORMAL 1110 P AC till NC T CR CT XP XT NS -) IMIN) I PPM I IPPMI l - l I-) l-» 0 0.0 1294. 1290. 1.00 l.COOO 1.00 1 1.00 1650. 991. 1.2 7 0. 7680 1.7,6 ? 2.00 1940. 784. l.OC| 0.60H0 2.47 3 3.00 2706. 606. 1.70, 0.4700 3.63 4 4.00 2452. 458. 1.89 0.3550 5.34 6 6.00 2832. 254. 2.19 0.1970 11.11 8 8.00 308**. 139. 2.39 0.1080 22.10 10 10.00 3252. 81. 2.51 0.0630 39. P3 14 14.00 3415. 34. 2.64 0.0266 99.21 18 18.00 3500. 24. 2.70 0.0185 146.19 22 22.00 3563. 21. 2.75 0.0159 173.1) 26 26.00 3625. 19. 2.80 0.0144 194.52 30 30.00 3671. 18. 2.84 0.0140 202.59 TABLE C.2.21 ! NUMERICAL EVALUATION OF EXPERIMENT E0II-SI-8/I26 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE 01 AL. NORMALIZED FACTOI NC T CB CT XB XT NS I-) IMIN) IPPM) IPPMI l - l (-) l - l 0 0.0 1257. 1251. 1.00 l.COOO 1.00 1 1.33 1741. 915. 1.38 0.7309 1.89 2 2.67 2119. 660. 1.69 0.5278 3.19 3 4.00 2430. 464. 1.93 0.3711 5.21 4 5.33 2699. 319. 2.15 0.2546 8.43 5 6.67 2916. 215. 2.32 0.1722 13.47 6 8.00 3067. 144. 2.44 0.1155 21.12 8 10.67 3280. 71. 2.61 0.0567 46.01 10 13.33 3404. 35. 2.71 0.0284 95.50 12 16.00 3489. 23. 2.77 0.0184 151.22 14 18.67 3557. 18. 2.83 0.0143 197.43 18 24.00 3688. 14. 2.93 0.0110 265.91 22 29.33 3808. 12. 3.03 0.0096 315.89 26 34.67 3905. 11. 3.11 0.0092 338.53 30 40.00 3992. 11. 3.17 0.0088 362.28 TABLE C.2.22 < NUMERICAL FVALUATION OF EXPERIMENT EOII-S1-8/I27 ! C Y C L E R E A L CCNUI.NTRA1 I O N CCNCr .NTWAT I U N SCl'ARMlON N O . T IME - B R I N E * D I A L . N'WAL 1 /El) M c r r m N C T C D C T XI) XT N S t-> ( M I N I ( P P M I I P ^ M I l - l (-1 I - I 0 0.0 12U4. 1277. 1.00 l.COCO 1.00 L 0.83 1511. 1045. l . i n 0.8182 1.44 2 1.67 1698. 9 1 3 . 1.32 0.7152 1.H5 3 2.50 1865. 7 0 9 . 1.45 0.6182 2.35 4 3.33 2026. 676. 1.58 0.5293 2.18 5 4.17 2178. 5 7 5 . 1.70 0.4505 3.7 7 6 5.00 2309. 4 8 6 . l.BC 0.3908 4. 72 8 6.67 2 5 6 1 . 3 4 1 . 2.00 0.2667 7.48 10 8.33 2760. 2 3 3 . 2.15 0.1828 11.76 12 10.00 2 9 2 1 . 156. 2.28 0.1222 18.62 14 11.67 3039. 107. 2.37 0.0638 ^ 28.23 16 13.33 3128. 7 5 . 2.44 0.0586 41.60 18 15.00 3229. 5 3 . 2.52 0.0411 6 1 . 19 20 16.67 3 2 9 1 . 3 7 . 7.56 0.0292 87.83 25 20.83 3376. 2 2 . 2.63 0.0169 155.90 30 25.00 3427. 17. 2.67 0.0133 200.21 35 2<».17 3466. 15. 2.70 0.0121 222.77 TABLE C.2.23 t NUMERICAL EVALUATION OF EXPERIMENT E011-S1-8/928 CYCLE REAL CONCENTRATION COMCENTRATION SEPARATION NO. TIME BRINE D I A L . NORMALIZED FACTOR NC T CB CT XB XT NS l - l IMINI (PPM) (PPM) (-) (-) (-) 0 0.0 1263. 1254. 1.00 l.COOO 1.00 1 1.32 1666. 8 3 2 . 1.32 0.6636 1.99 2 2.63 1983. 587. 1.57 0.4681 3.36 3 3.95 2 2 2 2 . 387. 1.76 0.3086 5.70 4 5.27 2397. 252. 1.90 0.2006 9.46 5 6.58 2 5 0 1 . 163. 1.98 0.1296 15.28 6 7.90 2584. 107. 2.05 0.0854 23.96 7 9.22 2 6 3 3 . 7 7 . 2.09 0.0617 33.79 10 13.17 2 6 9 4 . 4 3 . 2.13 0.0345 61.91 12 15.80 2 7 0 5 . 3 9 . 2.14 0.0314 68.29 14 18.43 2 7 3 8 . 37. 2.17 0.0298 72.69 16 21.07 2 7 6 0 . 37. 2.19 0.0293 74.56 TAOLe C.2.24 I NUMERICAL EVALUATION OF EXPERIMENT E 0 l l - S l - 8 / « 2 9 394 CYCLE Rf AL CONCIN1RAIION Co'tci - n f A i u i ' i SLI'ARAI ION NO. T 1 MG DRINF- U I A L . NORMAL 1 ZED FACTOR NC T cn CT XII XT NS l - l (MINI (PPMI (PPMI l - l (-1 (-1 0 0.0 1209. 1267. 1.00 l.COOO 1.00 t 1.00 1448. 955. 1.12 0.7536 1.47 2 2.00 15BI. 826. 1.23 0.6517 l.RB 3 3.00 1 709. 716. 1.33 0.5652 2.15 4 4.00 1822. 619. 1.41 0.4888 2.89 6 6.00 2010. 462. 1.56 0.3646 4.28 8 8.00 2157. 347. 1.67 0.2739 6.11 10 10.00 2266. 264. 1.76 0.2088 8.42 15 15.00 2419. 159. 1.88 0.1253 14.98 20 20.00 2474. 129. 1.92 0.1018 10.14 25 25.00 2501. 116. 1.94 0.0916 21.17 TAOLE C.2.23 3 NUMERICAL EVALUATION OF EXPERIMENT E D l l - S l - a / t 3 0 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS l - l (MINI IPPMI IPPMI l - l (-) l - l 0 0.0 1226. 1210. 1 0.68 1379. 916. 2 1.37 1506. 707. 3 2.05 1629. 677. 4 2.73 1757. 583. 6 4.10 1983. 430. 8 5.47 2184. 315. 10 6.83 2369. 228. 14 9.57 2650. 119. 18 12.30 2821. 68. 22 15.03 2927. 45. 26 17.77 2988. 35. 30 20.50 3027. 32. 34 23.23 3055. 29. 1.00 L.COOO 1.00 1.12 0.7569 1.49 1.23 0.6503 1.89 1.33 0.5597 2.37 1.43 0.4819 2.97 1.62 0.3550 4.56 1.78 0.2601 6.85 1.93 0.1887 10.24 2.16 0.0981 22.04 2.30 0.0560 41.13 2.39 0.0375 63.64 2.44 0.0293 83.16 2.47 0.0261 94.56 2.49 0.0240 103.92 TABLE C.2.26 J NUMERICAL EVALUATION OF EXPCRIMCNT 11  E0II-S1-B/831  1 I I I I 395 CYCLE HF AL CUNCf NTRATI ON CCNCtNTRAT II1N STMAUAf ION NO. T i l t UR1ND OIAL. NORMALIZED FACtllf NC T CB CT XII XT N5 -1 (MINI ( PCM I (PPMI l - l l - l l - l 0 0.0 1247. 1238. 1.00 1.C0C0 1.00 I 0.83 15'17. 071. 1.2H 0.70)1 1.H2 2 1.67 1902. 655. 1.53 0.5292 2.88 3 2.50 2184. 484. 1.75 0.31C6 4.48 A 3.33 2435. 350. 1 . -75 0.2823 6.92 5 4. 17 2644. 248. 2.12 0.2000 10.1.0 6 5.00 2827. 173. 2.27 0.1396 16.24 8 6.67 3078. 84. 2.47 0.0675 36.57 10 8.33 3224. 42. 2.59 0.0)41 75.91 12 10.00 3308. 24. 2.65 0.0197 134.77 14 11.67 3370. 16. 2.70 0.0127 212. 70 18 15.00 3466. 10. 2.78 0.0078 355.87 22 18.33 3546. 8. 2.84 0.0062 455.02 26 21.67 3620. 7. 2.90 0.0053 546.48 TABLE C.2.27 r NUMERICAL EVALUATION OF EXPERIMENT EDlI-Sl-8/»32 CONCENTRATION CCNCENTRATION SEPARATION BRINE OIAL. NORMAL IZEO FACTOR CB CT XB XT NS (PPMI IPPM! (-) I-) I-) i; 0 0.0 1205. 1191. 1.00 l.COOO 1.00 1 0.98 1666. 787. 1.38 0.6609 2.09 2 1.97 2064. 529. 1.71 0.4442 3.86 3 2.95 2408. 342. 2.00 0.2871 6.96 4 3.93 2677. 217. 2.22 0. 1820 12.21 5 4.92 2871. 134. 2.38 0.1127 21.15 6 5.90 3027. 83. 2.51 0.0693 36.24 7 6.88 3128. 52. 2.60 0.0433 59.92 e 7.87 3201. 33. 2.66 0.0276 96.19 9 8.85 3263. 22. 2.71 0.0181 149.71 10 9.83 3314. 15. 2.75 0.0125 220.78 12 11.80 3410. 8. 2.83 0.0065 435.42 14 13.77 3478. 5. 2.89 0.0038 761.30 16 15.73 3551. 3. 2.95 0.0027 1088.42 18 17.70 3620. 2. 3.00 0.0021 1459.64 20 19.67 3677. 2. 3.05 0.0015 2012.11 25 24.58 3R19. 1. 3.17 O.C009 3657.97 CYCLE REAL NO. TIME NC T l - l (PIN) TABLE C.2.28 t NUMERICAL EVALUATION OF EXPERIMENT EUII-S1-8/I33 396 C Y C L E R E A L CONClNTHA TI O N C O N C I : N T R A T I O N S E P A R A T I O N N O . 11 M L B R I N E P I A L . N O R M A L 1 ZF 0 F A C I O R N C T C B C T X I X T N S (-) ( H 1 N > ( P P M I ( P P M I ( - 1 ( - 1 ( - 1 0 0 . 0 1 2 3 4 . 1 2 7 6 . 1 . 0 0 l.COOO 1 . 0 0 1 1 . 3 0 1 9 1 8 . 8 0 6 . 1 . 4 9 0 . 6 3 2 0 2 . 3 6 2 2 . 6 0 2 4 1 9 . 4 9 4 . 1 . 8 H 0 . 3 8 7 3 4 . 8 7 3 3 . 9 0 2 8 1 6 . 2 9 4 . 2 . 1 9 0 . 2 3 0 5 9 . 5 1 4 5 . 2 0 3 1 1 1 . 1 7 0 . 2 . 4 2 0 . 1 3 3 5 1 8 . 1 6 5 6 . 5 0 3 3 3 1 . 9 8 . 2 . 5 9 0 . 0 7 6 8 3 3 . 7 6 6 7 . 8 0 3 4 7 2 . 8 5 . 2 . 7 0 0 . 0 6 6 7 4 0 . 5 3 7 9 . 1 0 3 5 8 0 . 3 7 . 2 . 7 9 0 . 0 2 8 8 9 6 . 7 7 8 1 0 . 4 0 3 6 8 2 . 2 4 . 2 . 8 7 0 . 0 1 9 0 1 5 0 . 9 0 9 1 1 . 7 0 3 7 6 2 . 1 7 . 2 . 9 3 0 . 0 1 3 3 2 1 9 . 5 8 1 0 1 3 . 0 0 3 8 3 1 . 1 3 . 2 . 9 8 0 . 0 1 0 0 2 9 8 . 1 2 1 5 1 9 . 5 0 4 1 7 6 . 5 . 3 . 2 5 0 . 0 0 4 0 8 0 4 . 3 6 2 0 2 6 . 0 0 4 4 8 4 . 2 . 3 . 4 9 0 . 0 0 1 5 2 3 0 3 . 1 3 2 5 3 2 . 5 0 4 7 4 8 . 1 . 3 . 7 0 0 . C 0 0 6 6 0 9 6 . 3 2 TABLE C.2.29 i NUMERICAL EVALUATION OF EXPERIMENT E D I I - S 1 - 8 / I 3 4 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DI A L . NORMALIZED FACTOR NC T CB CT XB XT NS t - l (KIN) (PPMI IPPHI l - l i (-1 l - l 0 0 . 0 1 2 1 5 . 1 2 0 0 . I 0 . 8 3 1 3 4 2 . 1 0 1 3 . 2 1 . 6 7 1 4 4 8 . 9 4 2 . 3 2 . 5 0 1 5 4 9 . 8 7 1 . 4 3 . 3 3 1 6 3 9 . 8 0 S . 6 5 . 0 0 1 8 1 1 . 6 8 4 . 8 6 . 6 7 1 9 6 2 . 5 7 7 . 1 0 8 . 3 3 2 0 9 7 . 4 8 5 . 1 5 1 2 . 5 0 2 3 6 9 . 3 0 3 . 2 0 1 6 . 6 7 2 5 6 7 . 1 8 6 . 2 5 2 0 . 8 3 2 6 9 9 . 1 1 9 . 3 0 2 5 . 0 0 2 7 8 8 . 8 1 . 3 5 2 9 . 1 7 2 8 4 4 . 6 5 . 1 . 0 0 l . C O O O 1 . 0 0 1 . 1 0 0 . 8 4 4 1 1 . 3 1 1 . 1 9 0 . 7 8 4 9 1 . 5 2 1 . 2 7 0 . 7 2 5 8 1 . 7 6 1 . 3 5 0 . 6 7 1 0 2 . 0 1 1 . 4 9 0 . 5 6 9 9 2 . 6 1 1 . 6 1 0 . 4 8 0 6 3 . 3 6 1 . 7 3 0 . 4 0 4 3 4 . 2 7 1 . 9 5 0 . 2 5 2 7 7 . 7 2 2 . 1 1 0 . 1 5 4 8 1 3 . 6 4 2 . 2 2 0 . 0 9 8 9 2 2 . 4 6 2 . 2 9 0 . 0 6 7 7 3 3 . B 7 2 . 3 4 0 . 0 5 3 8 4 3 . 5 3 TABLE C.2.30 t NUMERICAL EVALUATION OF EXPERIMENT E O I L - S l - 8 / f 35 397 CYCLE HT AL CIINCI N1HAI HIN CU^Ci NTrfAl ION SKPAHAT ION NO. 11 Ml. UK INI- DIAL. NOW PAL 1 / El) FACinB NC T cn CI XII XT NS C-l ("INI (prM) i P P M i l - l l - l l - l 0 0.0 1220. 12 1«. 1.00 l.COOO I . 00 1 1.00 1575. 429. 1.29 0.7627 1.69 2 2.00 1465. 7 )4. 1.5 3 0.6028 2.53 3 3.00 212'). 562. 1.74 0.4619 ) . 78 4 4.00 2 304 . 421. 1.44 0.345) 5.61 5 5.00 2561 . .310. 2. i c 0.7542 0.76 6 6.00 2727. 227. 2.23 0.1864 11.99 7 7.00 2U60. 165. 2.34 0.1)56 17.20 8 B.OO 2966. 119. 2.43 0.0975 24.94 10 10.00 3111. 65. 2.55 0.0531 48.04 12 12.00 3201. 39. 2.62 0.0321 81. 72 14 14.00 3257. 27. 2.67 0.C225 t18.85 16 16.00 3302. 21. 2.71 0.0169 154.65 18 18.00 3342. 18. 2.74 0.0151 100.77 20 20.00 3370. 17. 2.76 0.0138 200.52 25 25.00 3444. 15. 2.82 0.0122 231.6*2 30 30.00 3506. 14. 2.87 0.0117 246.53 TABLE C.2.31 » NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/*35eL CYCLE REAL CONCENTRATION CCNCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CD CT XB XT NS (-) IMIN) (PPM) (PPMI I-) (-) (-1 0 0.0 1252. 1251. 1 1.00 1448. 1099. 2 2.00 1607. 984. 3 3.00 1757.. 869. 4 4.00 1902. 765. 6 6.00 2157. 578. 8 8.00 2380. 427. 10 10.00 2572. 311. 15 15.00 2888. 137. 20 20.00 3039. 68. 25 25.00 3123. 52. 30 30.00 3167. 37. 35 35.00 3201. 34. 40 40.00 3224. 32. 1.00 l.COOO 1.00 1.16 0.8784 1.32 1.28 0.7866 1.63 1.40 0.6948 2.02 1.52 0.6113 2.49 1.72 0.4619 3.73 1.90 0.3412 5.57 2.05 0.2485 8.27 2.31 0.1093 21.11 2.43 0.0546 44.42 2.49 0.0412 60.48 2.53 0.0297 85.21 2.56 0.0269 95.02 2.57 0.0258 99.90 TABLE C.2.32 t NUMERICAL EVALUATION OF EXPERIMENT EUll-Sl-8/«36 398 CYCLE HE AL CEINCTN 1R A1 1 (IN CCNCl N1HAI ION STPAKATION NU. 1IMC l\«INF. DIAL. NORMAL 1/CO MCIOR NC T ClI CI XP XT NS (-) (MINI (PPMI (PPMI l - l (-1 (-1 0 0.0 1147. 1157. 1.00 l.COOO 1.00 1 2.25 1511. 70 3. 1.3? 0. 61,' lb 2.17 2 4.50 1745. 50). 1.56 0.4)48 3.60 3 6.75 2054. 348. 1.79 0.3010 5.95 4 q . o o 2298. 235. 2.00 0.2029 9. B8 5 11.25 2512. 156. 2.19 0.1149 16.24 6 13.50 2683. 103. 2.34 ,0.0892 26.7) 8 18.00 2916. 52. 2.54 0.0446 57.02 10 22.50 3055. 31. 2.66 0.C270 93.75 15 33.75 3201. 18. 2.79 0.0154 181.44 20 45.00 32BO. 14. 2.86 0.U123 2 ) ) . 22 25 56.25 3365. 13. 2.93 0.0110 265.82 30 67.50 3427. 12. 2.99 0.0105 285.13 TABLE C.2.33 t NUMERICAL EVALUATION OF EXPERIMENT E0I1-S1-8/K3T CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS (-» (MINI (PPMI (PPM) (-) (-) (-1 0 0.0 1252. 1242. 1 1.18 1432. 948. 2 2.37 1575. 819. 3 3.55 1714. 710. 4 4.73 1838. 606. 5 5.92 1962. 516. 6 7.10 2081. 436. 8 9.47 2287. 310. 10 11.83 2463. 213. 15 17.75 2783. 84. 20 23.67 2933. 44. 25 29.58 3000. 32. 30 35.50 3039. 28. 35 41.42 3067. 27. 40 47.33 3083. 26. 1.00 t.COCO I.00 1.14 0.7632 1.50 1.26 0.6594 1.91 1.37 0.5711 2.40 1.47 6.4881 3.01 1.57 0.4154 3.77 1.66 0.3510 4.73 1.83 0.2492 7.33 1.97 0.1713 11.48 2.22 0.0675 32.93 7.34 0.0351 66.73 2.40 0.0254 94.17 2.43 0.0224 108.20 2.45 0.0214 114.50 2.46 0.0208 118.58 T A B L E C.2.34 I N'JMFRICAL EVALUATION OF EXPERIMENT E O I I - S I - B / H S CYCLE RIAL CONCENTRATION CCNCI NIHAI II.1N SCPAKAIION NO. TIME HHINE DIAL. NORMALI ZfcU I AC ItlR NC T cn CT XII XT NS -) (PIN) 1 PPMI IPPMI I-) (-) (-) 0 0.0 1268. 1256. 1.00 l.COOO 1.00 1 2.42 1795. 729. 1.4? 0.5801 2.44 2 4.83 2266. 461. 1.79 0.3665 4.48 3 T.75 2683. 2B0. 2. 12 0.2228 9.50 4 9.67 3005. 161. 2.37 0.12U3 18.47 5 12.08 32 35. 95. 2.55 0.0758 33.67 6 14.50 3398. 59. 2.68 0.0467 5 7. 18 8 19.33 3591. 29. 2.83 0.0227 124.83 10 24.17 3716. 20. 2.93 0.0156 187.83 15 36.25 3946. 13. 3.11 O.U103 303.10 20 48.33 4107. 10. 3.24 0.0083 389.50 25 60.42 4222. 9. 3.33 0.0074 450.52 30 72.50 4309. 8. 3.40 0.0062 551.77 TABLE C.2.35 t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/139 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS t-> (MINI (PPMI (PPMI (-) (-) J - l 0 0.0 1289. 1286. 1.00 1.0000 I.00 1 1.53 1768. 884. 1.37 0.6871 2.00 2 3.07 2135. 658. 1.66 0.5115 3.24 3 4.60 2479. 458. 1.92 0.3561 5.40 4 6.13 2760. 310. 2.14 0.2407 8.90 5 7.67 2994. 201. 2.32 0.1565 14.84 6 9.20 3162. 130. 2.45 0.1013 24.21 8 12.27 3381. 58. 2.62 0.0451 58.12 10 15.33 3500. 30. 2.72 0.0236 115.21 15 23.00 3648. 15. 2.83 0.0115 245.37 20 30.67 3762. 12. 2.92 0.C090 323. 33 25 38.33 3865. 10. 3.0C 0.0060 373. 71 TABLE C.2.36 < NUMERICAL EVALUATION OF EXPERIMENT E0ll-SI-8/«40 400 CYCLE RIAL CONCENTRATION CUNCLNTRATION SEI'ARAT ION NO. T I Hi. URINE OIAL. NORMALIZCD TACIOR NC T cn CT 1  XP XT NS (-1 (MINI (PPMI (PPMI (-» (-1 (-1 0 0.0 1305. 1300. 1.00 l.COOO 1.00 1 0.27 1342. 1258. 1.03 0.9673 1.06 2 0.53 1374. 12)7. 1.05 0.9514 I.11 4 1.07 1448. 1197. 1.11 0.9206 1.21 6 1.60 1501. 1158. 1.15 0.89C9 1.29 e 2.13 1554. 1122. 1.19 0.8631 1 . IB 10 2.67 1607. 1086. 1.23 0.8353 1.47 15 4.00 1725. 1006. 1.32 0.7738 1.71 20 5.33 1848. 934. 1.42 0.7183 1.97 25 6.67 1956. 864. 1.50 0.6647 2.26 30 8.00 2064. 800. 1.53 0.6151 2.57 35 9.33 2178. 742. 1.67 0.57C4 2.93 40 10.67 2271. 686. 1.74 0.5278 3.30 45 12.00 2369. 633. 1.82 0.4871 3.73 50 13.33 2463. 587. 1.89 0.4514 4.18 60 16.00 2639. 501. 2.02 0.3849 5.25 70 18.67 2805. 426. 2.15 0.3274 6.57 80 21.33 2949. 361. 2.26 0.2778 8.14 90 24.00 3100. 306. 2.38 0.2351 10.11 100 26.67 3235. 258. 2.48 0.1984 12.50 110 29.33 3336. 219. 2.56 0.1687 15.16 TABLE C.2.37 s NUMERICAL EVALUATION OF EXPERIMENT E0 U - S l - 8 / * 4 l CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIHE BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS (MINI (PPMJ (PPMI l - l (-) (-1 0 0.0 1184. 1171. 1.00 l.COOO 1.00 1 0.58 1421. 1045. 1.20 0.8921 1.35 2 1.17 1618. 928. 1.37 0.7919 , 1.73 3 1.75 1811. 823. 1.53 0.7026 2.18 4 2.33 1983. 720. 1.68 0.6145 2.73 6 3.50 2364. 555. 2.00 0.4736 4.22 8 4.67 2716. 423. 2.29 0.3612 6.35 10 5.83 3055. 322. 2.58 0.2753 9. 38 14 8.17 3688. 182. 3.12 0.1553 20.07 18 10.50 4234. 108. 3.58 0.0920 38.90 22 12.83 4689. 65. 3.96 0.0557 71.09 26 15.17 5013. 42. 4.24 0.0358 118*34 30 17.50 5317. 29. 4.49 0.0246 182.40 34 19.83 5454. 21. 4.61 0.0180 256.70 38 22.17 5671. 16. 4.79 0.0138 348.02 42 24.50 5822. 13. 4.92 0.0110 446.62 46 26.83 5882. 10. 4.97 0.0089 557.12 50 29.17 6004. 9. 5.07 0.0073 697.85 54 31.50 6126. 7. 5.18 0.0064 810.23 i, I, , .. ., ._ _ TABLE C.2.38 8 NUMERICAL EVALUATION OF EXPERIMENT EUll-Sl-8/142 CYCLE RIAL CONCENTR AT I ON CC'iXENTR AT I ON SEPARATION NO. TIME BKINIi OIAL. NORMALIZED FACTOR NC T CO CT xn XT NS l - l ( M I N I 1 P P M 1 I P P M I I - I l - l l - l 0 0.0 1226. 1204. l . 00 l.COOO 1.00 I 0.52 1310. 1064. 1.07 0.8842 1.21 2 1.03 1374. 1005. 1.12 0.8349 I . 34 3 1.55 1442. 942. l . , l f l 0.7824 1.50 4 2.07 1453. 865. 1.19 0.7353 1.61 6 3.10 1623. 780. 1 • 1.32 0.6484 2.04 8 4.13 1730. 818. 1.41 0.6795 2.08 10 5.17 1838. 738. 1.50 0.6131 2.45 15 7.75 2059. 449. 1.68 0.3730 4.50 20 10.33 2233. 335. 1.82 0.2787 6.54 25 12.92 2364. 257. 1.93 0.2133 9.04 30 15.50 2463. 204. 2.01 0.1693 11.R6 35 18.08 2528. 170. 2.06 0. 1415 14.58 40 20.67 2572. 148. 2.10 0.1233 17.03 45 23.25 2622. 133. 2.14 0.1104 19.38 50 25.83 2644. 125. 2.16 0.1040 20.75 55 28.42 2672. 117. 2.18 0.0975 22.35 60 31.00 2694. 115. 2.20 0.0954 23.04 TABLE C.2.39 I NUMERICAL EVALUATION OF EXPERIMENT EDM.-SI-8/S43 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMAL IZEO FACTOR NC T CB CT XB XT NS I - ) IMIN) IPPM) (PPMI !-) I-) (-) 0 0.0 1231. 1224. 1 0.83 1549. 987. 2 1.67 1805. 805. 3 2.50 2037. 648. 4 3.33 2238. 517. 5 4.17 2413. 406. 6 5.00 2572. 321. 8 6.67 2799. 196. 10 8.33 2955. 124. 14 11.67 3139. 58. 18 15.00 3241. 38. 22 18.33 3314. 30. 26 21.67 3376. 27. 1.00 l.COOO 1.00 1.26 0.8061 1.56 1.47 0.6575 2.23 1.66 0.5290 3.13 1.82 0.4225 4.30 1.9,6 0.3319 5.91 2.09 0.2624 7.96 2.27 0.1602 14.20 2.40 0.1012 23.73 2.55 0.0472 54.02 2.63 0.0307 85.85 2.69 0.0248 108.71 2.74 0.0223 122.76 TABLE C.2.40 r NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/f44 402 C Y C L C R E A L CONCI N I R A 1 1 ON ClTiCI NT R AT I O N S F P A R A T I O N N O . t I M F !1KINF D I A L . N O R M A L 1 Z E D I < F A C T O R N C T cn C T X(j X T N S l - l ( M I N I I P P M ) ( P P M ) (-) (-) (-) 0 0.0 127R. 1276. 1.00 l.COOO 1.00 1 0.67 1506. 1103. l . i n 0.8645 1.36 ^ 1.33 1693. 96 d. l . 32 0.7583 1.75 3 2.00 1881. 842. 1.4 7 0.66C3 2.23 <v 2.67 2040. 730. 1.60 0.5723 2.80 6 4.00 2331. 542. 1.82 0.4247 4.79 a 5.33 2561. 396. 2.00 0.3104 6.45 10 6.67 2738. 293. 2.14 0.2295 9.33 14 9.33 2977. 165. 2.33 0.1294 17.99 18 12.00 3123. 103. 2.44 0.08C9 30.70 22 14.67 3218. 74. 2.52 0.0576 41.68 26 17.33 3302. 61. 2.58 0.0480 53.79 30 20.00 3353. 54. 2.62 0.0425 61.76 34 22.67 3410. 51. 2.67 0.0403 66.11 TAOLE C.2.41 I NUMERICAL EVALUATION OF EXPERIMENT E0II-Sl-8/»45 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS l - l (MINI (PPMI (PPMI (-)i (-) l - l 0 0.0 1242. 1233. 1 0.35 1273. 1158. 2 0.70 1300. 1118. 3 1.05 1331. 1080. 4 1.40 1358. 1045. 6 2.10 1416. 982. 8 ' 2.80 1464. 929. 10 ; 3.50 1517. 878. 15 5.25 1634. 775. 20 7.00 1730. 691. 25 8.75 1816. 627. 30 10.50 1886. 575. 35 12.25 1940. 531. 40 14.00 1978. 501. 50 17.50 2059. 451. 60 21.00 2113. 421. 70 24.50 2146. 404. 80 28.00 2173. 395. 1.00 l.COOO 1.00 1.03 0.9393 1.09 1.05 0.9069 1.15 1.07 0.8755 1.22 1.0910.8473 1.29 1.14 0.7960 1.43 1.18 0.7531 1.57 1.22 0.7123 1.72 1.32 0.6287 2.09 1.39 0.5607 2.49 1.46 0.5084 2.88 1.52 0.4665 3.26 1.56 0.4310 3.63 1.59 0.4059 3.93 1.66 0.3661 4.53 1.70 0.3410 4.99 1.73 0.3274 5.78 1.75 0.32C1 5.47 TABLE C.2.42 I NUMERICAL EVALUATION OF EXPERIMENT EDII-S1-8/H46 "I 403 CYCLE REAL CONCENIRAT l l l ' l CUMCENTRAT ION SEPARATION NO. TIMC BRINI: DIAL. NORMAL I ZED FACIOR NC T CU CT XP XT NS (MINI (PPM) (PPHI (-) I-I (-1 0 0.0 1226. 1224. 1 0.35 1342. 1152. 2 0.70 1465. 1084. 3 1.05 1618. 1011. A 1.40 1730. 943. 6 2.10 1945. 815. e 2.80 2119. 707. 10 3.50 2276. 606. 15 5.25 2419. 426. 20 7.00 2694. 308. 25 8.75 2855. 232. 30 10.50 2949. 187. 35 12.25 3039. 155. 40 14.00 3089. 137. 45 15.75 3151. 125. 50 17.50 3196. 116. 1.00 1.0000 1.00 1.09 0.9410 1.16 1.21 0.6851 1.37 1.32 0.8261 1.60 1.41 0.7703 1.83 1.59 0.6660 2.38 1.73 0.5774 2.99 1.86 0.4953 3.75 1.97 0.3477 5.67 2.20 0.2518 8.73 2.33 0.1897 12.28 2.41 0.1528 15.75 2.48 0.1264 19.61 2.52 0.1117 22.56 2.57 0.1022 25.15 2.61 0.0948 27.49 TABLE C.2.43 * NUMERICAL EVALUATION OF EXPERIMENT ED1I-S1-8/947 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTOR NC T CB CT XB XT NS I-) I MINI IPPMI (PPM) («| (-) 1-) 0 0.0 1270. 5 0.92 1297. 10 1.83 1333. 15 2.75 1369. 20 3.67 1402. 30 5.50 1461. 40 7.33 1508. 50 9.17 1544. 60 11.00 1575. 70 12.83 1603. 60 14.67 1620. 90 16.50 1632. 100 18.33 1646. 1246. 1.00 1184. 1.02 1126. 1.05 1081. 1.08 1055. l . l O 984. 1.15 938. 1.19 903. 1.22 877. 1.24 855. 1.26 841. 1.28 829. 1.28 819. 1.30 l.COOO 1.00 0.9503 1.08 0.9037 1.16 0.8675 1.24 0.8468 1.30 0.7899 1.46 0.7526 1.58 0.7246 1.68 0.7039 1.76 0.6863 1.B4 0.6749 1.B9 0.6656 1.93 0.6573 1.97 TABLE C.2.44 7 NUMERICAL EVALUATION OF EXPERIMENT ED1I-S1-8/D48 4 0 4 CYCLE RC AL CONCtNTRAI I ON CrflCfNTKAr ION StPARAT ION NO. I |Mh I'.R 1 NC DIAL. NORMAL 1/.CO FACTOR NC T CD cr xn X T NS I-) (MINI 1 PPM) (PPM) (-) (-) l - l 0 0.0 1289. 1264. 1 ! 1.00 l.COCO 1.00 1 1.33 191 1. 897. 1.40 0.7092 1.98 2 2.67 2200. 640. 1.71 0.5C61 3.37 3 4.00 2528. 4 4 1 . 1.96 0.3490 5.62 4 5.33 27 8 8 . 3 0 1 . 2.16 0.2378 9. 10 5 6.67 2994. 2 0 3 . 2.32 0. 16C2 14.50 6 8.00 3145. 133. 2.44 0.1051 23.22 7 9.33 3263. 9 4 . 2.53 0.0740 34.22 8 10.67 3348. 6 5 . 2.60 0.0510 50.90 9 12.00 34 2 7 . 4 7 . 2.66 0.0372 71.38 10 13.33 3495. 3 5 . 2.71 0.0281 96.62 12 16.00 3603. 2 3 . 2.79 0.0184 152.17 14 18.67 3682. 18. 2.86 0.0143 199.97 16 21.33 3762. 1 5 . 2.92 0.0122 238.36 20 26.67 3 9 1 1 . 1 3 . 3.03 0.0105 288.70 25 33.33 4 0 7 8 . 12. 3.16 0.C092 344.49 30 40.00 4 2 5 1 . 1 1 . 3.30 0.0095 389.44 35 46.67 4 3 6 8 . 10. 3.39 0.0081 420.34 40 53.33 4 4 6 1 . 1 0 . 3.46 O.0077 452.20 TARLB C.2.45 » NUMERICAL EVALUATION OF EXPERIMENT E D l l - S l - 8 / f j.9 CYCLE REAL CONCENTRATION CONCENTRATION — — — ^ . •• • • SEPARATION NO. TIME BRINE DI A L . NORMAL 17.E0 FACTOR NC T CB CT XB XT NS l - l (MINI (PPMI (PPMI I-1 (-) (-) 0 0.0 1315. 1280. 1.00 1.0000 1.00 1 1.52 1784. 9 2 2 . 1.36 0.7208 1.B8 2 3.03 2 1 4 0 . 6 2 6 . 1.63 0.4889 3.33 . 3 4.55 2490. 4 5 8 . 1.89 0.3579 5.29 4 6.07 2 8 0 5 . 2 9 4 . 2.13 0.2298 9.28 5 7.58 3 0 5 5 . 184. 2.32 0.1442 16.11 6 9.10 3 2 4 1 . 119. 2.46 0.0927 26.56 8 12.13 3472. 5 4 . 2.64 0.0423 62.34 10 15.17 3597. 3 2 . 2.73 0.0252 108.50 15 22.75 3796. 2 1 . 2t.;89 0.0161 178.95 20 30.33 3934. • 16. 2.99 0.0126 237.35 25 37.92 4 0 2 0 . 14. 3.06 0.0109 200.74 30 4 5 . 50 4 0 5 5 . 12. 3.08 0.0094 328.82 TABLE C.2.46 : NUMERICAL EVALUATION OF EXPERIMENT EDLI-S1-8/I50 405 CVCIE RCAL CONCENTRATION CLNCTNIKUION SEPARATION NO. TIME OR INC OIAL. NORPALIZEO FACTOR NC T CB CT XD . XT NS l - l (MINI (PPMI IPPM) (-) (-) (-1 0 0.0 1294. 1271. 1 0.67 1337. 1264. 1 0.67 102907. 1251. 3 2.00 1501. 1206. 5 3.33 1650. 1148. 9 6.00 1956. 1018. 14 9.33 2298. 864. 19 12.67 2572. 733. 24 16.00 2799. 613. 29 19.33 2968. 522. 39 26.00 3269. 377. 49 32.67 3466. 275. 59 39.33 3620. 201. 69 46.00 3762. 155. 79 52.67 3877. 116. 69 59.33 3974. 97. 99 66.00 4055. 77. 109 72.67 4124. 65. 1.00 l.COOO 1.00 1.03 0.9949 1.04 79.51 0.4848 80.74 1.16 0.9492 1.22 1.27| [0.9036 1.41 1.51 0.8010 1.89 1.78 0.6802 2.61 1.99 0.5766 3-45 2.16 0.4822 4.48 2.31 0.4112 5.62 2.53 !o.2964 8.52 2.68 0.2162 12.39 7.80 0.1584 17.66 2.91 0.1218 23.86 3.00 0.0914 32.78 3.07 0.0761 40.33 3.13 0.0609 51.43 3.19 0.0508 62.77 TABLE C.2.47 : NUMERICAL EVALUATION OF EXPERIMENT EDII-SI-8/S51 CYCLE REAL CONCENTRATION CONCENTRATION SEPARATION NO. TIME BRINE DIAL. NORMALIZED FACTO*. NC T CB . CT XB XT' NS l - l (MINI (PPM) (PPMI (-) • (-) (-1 0 0.0 1321. 1206. 1 0.67 1395. 1138. 2 1.33 1501. 1058. 3 2.00 1597. 983. 4 2.67 1671. 909. 5 3.33 1779. 839. 10 6.67 2146. 555. 15 10.00 2457. 362. 20 13.33 2S84. 236. 25 16.67 2705. 144. 30 20.00 2794. 115. 40 26.67 2899. 68. 50 33.33 2977. 53. 60 40.00 3039. 48. 1.00 l.COOO 1.00 1.06 0.9433 1.12 1.14 0.8770 1.30 1.21 0.8150 1.48 1.27 0.7540 1.68 1.35 0.6952 1.94 1.62 0.4599 3.53 1.86 0.3005 6.19 1.96 0.1957 10.00 2.05 0.1198 17.10 2.12 0.0952 22.22 2.20 0.0567 38.73 2.25 0.0439 51.41 2.30 0.0390 58.14 TABLE C.2.46 : NUMERICAL EVALUATION OF EXPERIMENT EDM-SlrB/f52 I CYCLE REAL C0NCENTRA1ION CONCENTRATION SEPARATION fJO. T1MF BRINE DIAL. NORMAL 12 ED FACTOR NC T CB CT XB XT NS (-) IMIN) (PPM) (PPM) l - l (-) (-» 0 0.0 1278. 1262. 1 0.67 1581. 980. 2 1.33 1741. 800. 3 2.00 1822. 645. 4 2.67 1902. 516. 5 3.33 1983. 439. 6 4.00 2064. 387. 8 5.33 2227. 310. 10 6.67 2364. 271. 12 8.00 2446. 232. 14 9.33 2484. 210. 16 10.67 2578. 193. 21 14.00 2749. 168. 26 17.33 2944. 142. 31 20.67 3083. 132. 36 24.00 3196. 116. 41 27.33 3297. 110. 46 30.67 3365. 103. SI 34.00 3421. 97. 56 37.33 3449. 90. 1.00 l.COOO I.00 1.24 0.7771 1.59 1.36 0.6339 2.15 1.42 0.5112 2.79 1.49 0.4090 3.64 1.55,6.3476 4.46 1.61 0.3067 5.26 1.74 0.2454 7.10 1.B5 0.2147 8.61 1.91 0.1840 10.40 1.94 0.1667 11.66 2.02 0.1534 13.15 2.15 0.1329 16.18 2.30 0.1125 20.47 2.41 0.1043 23.13 2.50 0.0920 27.16 2.58 0.0869 29.67 2.63 0.0818 32.17 2.68 6.0767 34.90 2.70 0.0716 37.70 TABLE C.2.49 t NUMERICAL EVALUATION OF EXPERIMENT EDII-Sl-8/»53 Table C-2-50 Average Current and Voltage Distributions 1n Second ED Experiments 1 2 5 H 5 6 7 8 9 10 11 12 13 IU 15 16 17 18 19 20 21 " 22 RUtl NO. CURRENT CYCLE AVERAGE CURRENT [ampere] CYCLE AVERAGE PROBE VOLTAGE [volt] VOLTAGE Lamp erej NO. TO STAGE NO NO. IN STAGE NO. APPLIED C-] INITIAL FINAL [-] 1 2 3 4 5 6 7 8 C-] 1 2 3 4 5 6 7 8 [volt] 12 5.4 2.6 70-85 .02 .03 .04 .1 .26 .55 .83 .85 70-85 8.5 8.5 8.2 7.3 6.5 6.0 3.9 4.2 10 10 5.1 4.1 20-40 .3 .31 .35 .40 .52 .69 .71 .76 20-40 5.8 6.2 5.9 5.5 5.3 4.9 3.6 4.0 10 8 5.6 3.8 25-35 .15 .22 .34 .46 .65 .82 .78 .89 10 11 5.5 4.6 10-20 .36 .45 .51 .59 .64 .70 .70 .69 10-20 5.5 5.2 5.0 4.5 4.5 4.5 3.8 4.0 10 15 5.6 5.5 10-20 .30 .45 .55 .68 .73 .86 .72 .73 5-12 4.7 4.6 4.4 4.4 3.6 4.1 10 14 5.5 5.7 25-35 .5- .58 .63 .70 .74 .84 .73 .71 23-35 4.6 4.5 4.4 4.4 4.2 4.3 3.5 3.8 10 7 5.6 5.6 20-30 .6 .62 .64 .70 .71 .79 .75 .74 10 47 0.70 0.36 45-46 _ _ _ _ .1 .25 _ 47-49 9.0 8.5 10 45 1.32 0.68 8-12 - - - - .06 .10 .25 .36 16-20 _ _ 8.5 8.7 7~9 7.2 10 44 1.88 1.04 13-19 - - .04 .06 .11 .2 .31 .38 22-27 _ 9.0 9.0 9.0 9.0 7.1 7.0 10 35a 2.60 1.40 16-24 .020 .025 .05 .08 .16 .275 .36 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 10 19 1.45 0.88 37-38 - _ _ _ _ .29 .61 34-35 — _ 7.6 6.2 10 20 1.75 1.00 36-37 . - - - .39 . 71 _ _ - 42-43 _ 7.6 6.1 10 18 3.00 " 1.72 22-25 - - - .20" .33 .56 .75 27-31 _ 8.1 7.6 5.8 5.2 10 17 4.70 2.60 19-25 - - .15 .20 .34 .52 .67 .80 31-33 _ 8.3 7.5 4.9 4.8 10 6 5.60 3.20 30-40 .05 .08 .16 .30 .'45 .62 .72 .95 27 2.2 1.1 18-24 .01 .02 .04 .07 .12 .22 .28 .31 6-14 8.7 8.8 8.9 8.7 8.3 8.2 7.6 7.6 10 22 4.0 1.5 18-25 .02 .03 .05 .08 .17 .25 .38 .5 5-12 8.2 8.2 8.3 8.3 8.0 7.6 7.0 6.3 10 9 5.5 2.0 15-25 .05 .08 .10 .19 .31 .45 .55 .74 10 35a 2.6 1.4 16-24 .02 .025 .05 .08 .16 .275 .36 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 10 23 4.2 2.1 19-27 .02 .04 .09 .15 .26 .39 .48 .59 7-15 7.3 7.6 7.7 7.5 7.0 6.8 5.6 5.6 10 6 5.6 3.2 30-40 .05 .08 .16 .30 .45 .62 .72 .95 10 33 3.5 2.0 16-24 .01 .025 .05 .1 .25 .44 .58 .70 6-14 13.8 13.8 13.6 13.6 13.2 12.8 10.8 10.8 15 24 5.8 3.0 16-24 .02 .04 .07 .13 .22 .58 .80 .94 25-34 13.2 13.3 13.0 12.4 12.5 11.6 9.7 9.4 15 21 8.8 3.4 16-24 .03 .05 .09 .16 .26 .71 .96 1.2 25-34 13.5 13.3 12.9 12.4 11.5 11.1 8.8 8.8 15 41 3.6 3.4 50-58 .26 .30 .34 .38 .42 .50 .56 .55 73-85 7.5 7.5 7.6 7.3 7.1 7.1 6.0 6.1 10 25 3.0 2.4 18-26 .13 .15 .20 .25 .35 .45 .50 .53 25-35 8.25 8.25 8.1 7.5 7.2 6.4 5.4 5.75 10 30 3.0 2.6 17-25 .10 .13 .20 .26 .37 .45 .52 .51 6-14 7.0 7.0 6.8 6.8 6.8 6.5 5.5 5.7 10 o CONTINUED Table C-2-50 (Continued) i 2 3 4 5 -.6-7 8 9 10 11 12 13 IU 15 16 17 18 19 ,20 21 22 RUN NO. CURRENT CYCLE AVERAGE CURRENT [ampere]. CYCLE AVERAGE PROBE VOLTAG E [volt] VOLTAGE [ampere] NO. TO STAGE NO NO. IN STAGE NO. APPLIED C-3 INITIAL FINAL [-3 1 2 3 4 5 6 7 8 [-3 1 2 3 4 5 6 7 8 [volt] 42 2.56 .93 18-26 .04 .05 .05 .08 .12 .15 .28 .42 38-46 9.3 9.3 9.2 9.3 9.2 9.0 8.6 7.2 10 35a 2.6 1.4 16-24 .02 .025 .05 .08 .16 . 27E .36 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 10 29 2.65 1.8 12-15 .07 .16 .32 .39 7-11 8.5 7.8 7.3 6.3 10 35 1.3 1.05 19-27 .05 .06 .08 .10 .13 .18 .21 .23 28-36 4.3 4.3 4.2 4.0 3.8 3.6 3.0 2.9 5 28 2.7 1.8 24-32 .024 .038 .06 .12 .24 .36 .50 .51 13-22 8.4 8.5 8.3 8.0 7.75 7.45 6.25 6.25 10 " 32 4.2 2.75 17-25 .016 .03 .06 .13 .28 .46 .70 .82 7-15 13.4 13.4 13.2 13.0 12.5 12.0 10.0 10.0 15 36 1.4 .8 15-23 .03 .05 .06 .08 .10 .13 .18 .21 23-31 4.5 4.4 4.3 4.2 4.0 3.8 3.3 3.0 5 35a 2.6 1.4 16-24 .02 .025 .05 .08 .16 .27' .36 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 10 : 33 3.5 2.0: . 16-24 .01- .025 .0.5 .1 .25 .44 .58 -.70 6-14 13.8 13.8: 13-.6 13.6 13.2 12.8 , 10.8 10.8 15 13 2.2 2.0 40-50 .19 .21 .22 .24 .28 .34 .29 .28 40-50 2.4 2.5 2.2 2.0 2.1 2.0 1.6 1.5 5 8 5.6 3.8 25-35 .15 .22 .34 .46 .65 .82 .78 .89 10 16 9.5 6.9 20-30 .11 .19 .31 .50' .78 1.15 1.3 1.4 11-19 9.2 9.3 9.2 8.8 8.5 8.2 6.0 6.5 15 37 2.0 1.55 17-25 .01 .02 .03 .06 .18 .31 .42 .49 6-14 8.2 8.3 8.1 7.9 7.4 6.9 5.4 5.7 10 38 2.65 2.2 17-25 .04 .06 .11 .18 .29 .43 .52 .51 29-37 8.8 8.5 8.3 7.8 7.3 6.9 5.2 5.5 10 25 3.0 2.4 18-26 .13 .15 .20 .25 .35 .45 .50 .53 25-35 8.25 8.25 8.1 7.5 7.2 6.4 5.4 5.75 10 39 2.08 1.44 17-25 .01 • .02 .03 .06 .15 .20 .39 .46 5-13 8.6 8.7 8.5 8.3 7.6 7.0 5.8 5.7 10 40 2.32 1.6 15-23 .01 .02 .03 .06 .16 .31 .40 .47 4-12 8.0 8.3 8.2 8.2 7.9 7.8 6.8 6.5 10 35a 2.6 1.4 16-24 .02 .025 .05 .08 .16 .275 .36 .41 5-12 8.2 8.3 8.4 8.0 7.9 7.5 6.9 7.0 10 APPENDIX C.3 COMPUTER PROGRAM FOR SPACER MODEL i i The input data are: ( in text ) M = number of mixing c e l l s m N = number of s l i c e s in sorpt ion membrane n PE = Four ier number Fo R = width ra t i o P CHALE = channel length i/b COMLE = Ce l l length ! d ' /b EPSILO = layer thickness 6/b W = ve loc i t y v/b / v/l i PODRO = potent ia l drop Ai|> XSI = membrane res is tance 5 DTAU = s ta r t i ng in tegra t ion step length At ERROR = maximum to lerab le in tegra t ion er ro r TAU1 = duration of f i r s t ha l f cyc le TAU2 = duration of second ha l f cycle OMEG = acce lera t ion fac tor for Gauss-Seidel i t e ra t i on 408 . 408 r\ ERRIT = maximum tolerable i t e r a t i o n error DTAUP = printing step length ICYC = number of cycles ! i INIT = control d i g i t to read in i n i t i a l data or to auto matically i n i t i a l i z e . \ 409 1 7 C C SPACER MODEL < I'ACKViAKfl OIFFFRLNCE SCHEME 3 c CAUSS - SEIOFL 1 IE RAH ION 4 c AUTOMATIC A|)IUSI»ENT OF TIME STEP SUE J 5 c 1 VERSION FOR PLOT 1 INC 1 6 7 c OIMFNSION CI 1C0,20),CH(1C0,2()),CI'( 100,20I,CPHI 100,20) 8 CI MENS ION Z(6),ZM6) ,IH 12),ZZHt 121 <J COMMON It.N.PrORCSl , CPS ILC,R.XSI 10 REAC 15,1) M,N,PE,»,CHALE,COMLF,FPSILO,W,HOOROtXSI,OTAU,ERROR 11 1 FORMAT (213, ICE6.4I 12 RE AO 15,21 IAL1,TAU2,0ALA,ERRIT,0TAUP,ICYC,1NlT 13 2 FORMAT (5E6.4,2Ii) 14 C 15 C SETTING OF INITIAL VALUES 16 C 17 NCCNT=0 18 NINT=0 19 N2=Nf2 20 N3=N*3 21 M1=M*1 22 M2=M»2 23 DTAU=l.O/DTAU 1 24 Z(1I=2./PE/EPSILC*0TAU 25 Z(2)=2.*EPSUC*M*N«C0MLE/R/CHALE*2lll 26 Z(3)=4.*N*N/R/R/PE*DTAU 27 Z(4)=W/CCMLE»0TAU 28 Z(5)=0TAU/EPSILC/(O.5-EPSILO)/PE 29 Z(6)=(1.-EPSIL0I/EPSILC«ZI5I 30 00 200 1=1,6 31 2C0 ZH(I)=Z(11*0.5 32 CALL PAMPA(Z,ZH,ZZ,ZZHI 33 STROH=0.0 34 DH=0.5*DTAU 35 IF (1NLT.EC.CI GO TO 35 , 36 READ (3,37) C t l . l l . S I 37 37 FORMAT (5EIS.7I 38 DC 36 J=2,Ml 39 36 REAC (3,371 (C(J,KI,K-1,N3I 40 GO TO 38 41 35 00 3 J=»2.K1 42 00 4 K=1,N3 43 4 C(J,K)=1.0 44 3 CCNTINUE 45 SI=STR0M(N,PCCRC,EPSILC,R,XSI,C,2I 46 C I U D ' U C 47 38 C P ( i . i i = c ( i , n 48 C H i i , n = c i i . i ) 49 CPH(1,1)=CI1,1I 50 00 34 J»2,M1 SI OC 39 K=1,N3 52 CPtJ,K)»C(J.Kl  1 53 39 CH<J,K)*C(J.KI 54 34 CCNTINUE 55 TAU=0.0 56 CEFF«C(M1,1) . ' 57 CURR»SI 58 . TAUP'OTAUP 59 L - l 60 I C - l 61 Tl-TAUl 62 / XXY*>0.09S*ERR0R 63 C 64 C PRINTOUT OF PARAMETER VALUES 65 C 66 WRITE (6,51 CHALE,R,W,PE,M,COMLE, EPSILO,P0DR0,XSI,N,ERROR,DTAU, 67 1 ERR IT 68 5 FORMAT ( 1HI/////20X,• FIRST SPACER MODEL•//////1 OX,•PARAMETER-VALU 69 1ES'///V» CHANNEL-LENGTH » •,F0.1//' WIDTH-RATIO 70 2 » ',F8.1//» RELATED FLOW VFLCCITY * ' . F a . l / / ' PECLET NUMB 71 3ER » S F a . l / / 1  NUMBER OF COMPARTMENTS « «,|B / / t COMPAR 72 4TMENT-LENGTH = ',f6.l//' ASSUMED LAYER THICKNESS = «,FI1.4// 73 5/« APPLIED VOLTAGE » ',F1C3///' MEMBRANE RESISTANCE 74 6 - ».Fl0.3////» NUMBER,OF SLICES « ',!«////• ALLOWEO INTE 75 7GRATICN ERROR - '.FI0.5///' INTEGRATION STEP LENGTH » SF10.5/ 76 8 //• ITERATION FRRCR • SF10.5//) 77 WRITEI6.I0) 78 1C FORMAT 1 WMII 79 1» NC. OF CONCENTRATION SEPARATION CURRENT DENSITY 80 2 MASSV, 81 3« CYCLES TOP BOTTOM FACTOR DEPLETING ENRICH 82 4ING BALANCCV , 81 5' N CT CB NS 10 IE 84 6 1 * 1 • / 1 85 WP III(4,471 CURR | 86 4 7 FPMMAT ' II 10.6) 'i 410 f 1 C eH c MUST HALF CYCl l 84 c CCRR=(1.«J.*Z(»)l/ll.»9.»Z<3> 1 90 91 6 NCCNI-NCCNT*1 92 TA«TAU»OTAt 93 CC=0.00001 •TA-TAUP 9-, OC 8 J » 2 , M 95 CALL GASFICCPtZZ.SRRtT.J) 96 CALL GASC(CH,CM,7Zt J .0KRIT,J) 97 DC 11 K=1,N3 50 11 CPHlJ.KI=CH(J.KI 99 8 CCMINUC  1 ICO 9 • CC«0.0 1CI DC 12 J>2,P1 1C2 CALL GASE(CH,CPH,ZZH,ERRI T.Jl 103 0 = 0.0 104 00 13 K=1,N3 , IC5 ET=CH(J,K)-CIJ.KI 1C6 IF (ABStETI.GT.ERROR) CO TC 50 107 CIJ.KI*Il.C*CCRR*ET)«CHIJ.K) 108 IF (ARSIETI.GT.ABSIC)) D=ET 1C9 13 CONTINUE , 110 IF (CC.GE.O.C) STHCH*STRCH»SI 111 25 IF (ABS(C).GT.ABSICD)) C0-C 112 12 CONTINUE 113 TAU=TAU->CTAU 114 IF (NCCN7.EC.1) GO TO 40 115 NINT=NINT+1 116 IF ICC.LT.C.CI CC TO 40 117 STRCH = STROH/iv 118 WRITE (4,48) C(2.1),CI>n.l).STROH. 119 48 FORMAT (3F10.6,F15.71 . 120 IF (TAU.GE.(Tl-O.COOOl)l GC TO 100 121 TAUP=TAUP+CTAUP  1 122 L=L+l 123 IF (L-2) 15,15,16 124 15 CEFF=CEFF»4.C*C(Plttl 125 CURR=CURR*4.C*STR0H )• 126 STR0H=0.0 127 GO TO 40 128 16 CEFF=CEFF*2.C*C(l'l.ll 129 CURR=CURR*2.C»STR0H 130 STROH'0.0 131 L=l  1 132 4C DC 17 J=2,fl 133 DC 18 K»1,N3 i 134 CHIJ,K)=C(J,K) 135 ie CP!J,K)-CIJ,K) 136 17 CONTINUE 1 137 IF (NCONT.EQ.l) GO TO '6 138 IF <ABS(COl.LE.XXY) GO TO 30 139 NCONT'O ; 140 CO TO 6 1 141 30 IF (NINT/2-ININTMI/2I31.32.31 142 32 NCONT»0 143 GO TO 33 144 31 NC0NT»1 145 33 NINT=NINT/2 .1 146 DH»DTAU 147 DTAU=2.»CTAU 1 1 148 DO 210 1*1,6 149 f Z H i u - z m i 150 210 Z(l)=2.*Z(I) 151 CALL PAMPAIZ.ZH.ZZ.2ZH) 152 CCRR-=U.-»3.*Z(3I l / U . * 9 . * 2 I 3 l l 153 GC TO 6 154 5C DC 20 J=2,Pl 155 DO 21 K=1,N3 156 C(J,K)=CPH(J.K) 157 21 CHI J,K)=CP(J.KI 158 2C CONTINUE 159 OTAU=0.5«OTAU 160 0H=CH*0.5  1 161 DO 201 1=1.6 162 ZII)=ZH(I) 1 163 2C1 7 H 1 l*0.5*/HI 1) 164 CALL PAMPAIZ,ZM,/Z,ZZH) 165 CC"-C.OCOCI»IAU*GIAU-TALP 166, NCCNI-l 167 NINI«2»NINT !• 168 DC 72 J--7.P1 169 CALL CAST(CH.CP.Z/H.IRHIT,Jl 170 UC 23 K ' l . M 171 21 CI'IM J,KI«CM J.KI 172 27 CCMINUl 113 CCRN'I!.«].*/I 3 1 l / l 1 . f l . * ! 1 3 1 1 174 GC 10 9 ' Ill, C SECOND HALF CVCIE 411 17/ C 178 ICO PCnRO=-POI)«0 171 CIM2, I )=ClALP/l.C/lAUl-MCEFF*-CtMl, III 180 SI=C(P2, I )/C( 1,1» l e i CUMR = DMUP/1.0/t/>Ul*ICtBH»STRtH 182 SCL'0.0 18 J SCT'0.0 i e * s c i » o . o , 18,S SC2--0.0 186 SC3=0.0 187 UC 202 J=7,MI 168 SCT*>SCT<C(J,1 I , 189 SCl=SCL*ClJ,2) 190 S C I » S C 1 * C ( J . 3 ) » C ( J . N 3 I 191 OC 203 K=4.N2,2 192 SC2-=SC2»CI J,K) 193 2C3 SC3=-SC3»C< J.K-l) [ 194 2C2 SC3-=SC3-C< J , 3 I 195 SCL-=0.5*(SCl--SCT ) i 196 SCT=SCT*(1.0-2.OEPSUC) 197 SCL=SCL*2.C*EPSIL0 190 SC1=(SC1»4.C«SC2»2.0*SC3)«R/FLCATCN)/3.0 199 SC=(SCT + S C L « S C 1 l / F L O A T ( H ) * C ( M 2 , l ) * ( 1.0-2.0*EPSILO)*TAUI 2C0 SC=1SC-BALAM1C0.0/BALA 2CI IF ( I C / 2 - I I C « 1 > / 2 ) 120,122,120 2C2 120 WRITE (6,121) IC,C(M2.1),CURR,SC 203 121 FORMAT (15,13X, F11.5,15X, F11.4,13X,F1 1.51 204 CC TO 124 2C5 122 WRITE (6,123)IC,C(M2tI),SF,CURR,SC 2C6 123 FORMAT (15,F13.5,1IX,F15.4,1IX.F13 . 4.Fl1.51 207 124 J*K2 208 00 102 JR=2.H 209 J=J-l 210 DC 103 K=1,N3 211 CP(JR,K)=C(J.K) 212 103 CHIJR,K)=C(J,K) 213 1C2 CONTINUE i 214 DC 104 J=2,M1 215 00 105 KM.N3 216 1C5 C(J,K)=CPfJ.K) 217 IC4 CCNTINUE i 218 C(I,1I=C(M2,II 219 CP(1,1)=C(M2,1) 220 CH(1,1)=C(1,1) 221 C P H ( l , l ) = C ( l , l ) 222 STRCH=0.0  1 223 00 110 J ' 2 , M 1 224 110 STROH=STRCH+STROP(N,POORO,EPSILO,R,XS1,C.JI 225 STHCH=STRCH/P 226 IF IIC.GE.ICVC) CO TO 1000 227 CURR=STR0H  1 228 WRITE (4,471 CURR  1 229 STRCH=0.0 230 CEFF-=C(Ml,l> 231 Tl*Tl+TAU2 232 TAU2-TAU1  1 233 TAUl'Tt-TAUP 234 TAUP=TAUP*OTAUP 235 1*1  r 236 IC=IC*1 237 NINT=0 238 ( NCCNT-0 239 GO TO 6 240 f 1C00 WRITE (4.37) Cd.D.STROH 241 DO 300 J« 2 , K 1 242 3C0 WRITE (4,37) (C(J,K),K=1.N3) 243 STOP 244 ENO 245 C 246 SUPROUTINE PAPPA(2,ZH,22,ZZH) 247 DIMENSION Z(6),ZH16),ZZ(12>,ZZHI121 248 ZZ(1I=ZI4)*(1.0-Z(5)*Z(6)) 249 Z Z H ( l ) = Z H ( 4 ) » ( l . C - Z H ( 5 ) + Z H ( 6 ) l 250 //(?)=!.0»/(6) 251 ZZH(2) = 1 . 0 « Z H 6 ) 252 Z Z ( 3 ) = l . / l / Z ( l ) » Z Z ( 2 ) » Z ( 5 l ) 253 ZZH3)=I./IZZHI1).ZZHI2)*ZM(5)1 254 Z Z ( 4 ) = Z ( 4 ) » Z ( 6 I 255 2 7 M 4 ) « Z H I 4 ) 0 / M | 6 1 256 Z Z ( 5 l » Z ( 4 ) * ( Z ( 6 ) - l . C - Z I 5 ) ) 257 / /H(5)«-/l-(4l«(7Ht&l-l l .C-ZHI5l» 258 Z 7 ( 6 > » l . C » Z ( 4 ) . / ( 5 ) 259 ZZh(6)*l.Ct/M4)./H(5) 260 17(71-7.*/(3l 261 l ( K ( H = / l ! l 762 ; / I B | - | . / l l . t / / I T M 763 7 / M f i l ' l . / I l . « / l IM 264 ZZ(9)'Z(5) 265 / / H ( 9 ) » Z I ( S » 412 266 7 / U O W i n 267 / / l - l 10WHI3) 268 / / l l l l ' / l l l 269 / / h i 11 l = /HII) 2/0 //(12l=/(?» 271 ZZM12I«/H(2I 272 RETURN 273 ENC ! 274 C 275 C SUBROUTINE FCR C1MENSICNLESS CURRENT CENSIIY 276 C 277 FUNCTION STRCMIN,PCDRC IEPSILO,H,XSI,C,Jl 278 DIMENSION CI 100.20) 279 N3 = NO 280 A=2.0*ALCGICtJ.31/CIJ,2)l 281: IF (C I J,? I-EC.CI J , I ) 1 GO TO 2 2e2 B»(1.0-2.0*EPSILC)/C(J,1) »2. 0*EPSt LOMfcOG (CI J.1I/CCJ.2I l / I C C J , 11- 283 1  I C I J . 2 ) ) 28V GC TO 3 285 2 B'l.O/C(J,l) 286 3 X=1.0/C(J,3) 287 OC I K=5.N3,2 288 1 X=X*4.0/C(J,K-ll*2.0/C(J,K1 289 X=(X-1.0/CIJ,N31)*R/t3;0*FLOATIN)I 290 STROM=(PCCRO-AI/IB*X*XS1) 291 RETURN 292 ENO 293 C 294 C SUBROUTINE FOR BACKWARD DIFFERENCE SCHEME 295 C i 296 SUBROUTINE GASEIC,CP,Z,ERR IT,J I 297 DIMENSION CI ICO,20).CP 1100,201,Z(121 25B COMMON IT,N,PODRC,SI.EPSILC,R,XSI 299 N2=N+2 3C0 N3=N*3 3C1 IT«0 302, 1 0=0.0 ! 303 1T-IT+I 304 S1-STR0M(N,PC0RC,EPSILC,R,XSI,C,Jl 3C5 RHG«SI*ZI11) 3C6, ETA=SI*Z(12I i 307 C 308 X=Zt3)*(Ztl>»'C(J-l,l)*Z(2)*CP(J,U*Z(9)*(CPIJ.2>-RHOII 3C9 IF (ABSIX-CIJ,l)I.GT.DI D=ABSIX-CtJt111 310 C(J,1)°X 311 C 312 XcZ(3)*(Z(5)*C(J-l.l)->Z(4)*CP(J,lt»Z(6l*ICPUt2)-RH0l> 313 IF IABSIX-C(J,2) I.GT.DI C C ABSIX—CC J,2)I 314 C(J,2)*X 315 C 316 X=Z(8)*(CP(J.3)+Z(7)*CCJ,4)+ETA| 317 IF 1ABStX-CIJ,3)I.GT.CI 0»ABSIX-CCJ,311 318 CU,31=X 319 C 320 00 2 K=4,N2 321 X=Z(8)*(CP(J,KI»Z(10)*tC(J.K+1)*CCJ.K-l))1 322 IF (ABSIX-CIJ,K)I.GT.DI 0=ABS(X-CCJ,K11 323 C(J,K)=X 324 2 CONTINUE 325 C 326 X*Z(8)*tCP(J,N3)»Z(7l*C(J,N2l) 327 ' IF (ABS(X-C(J,N3>I.GT.C) 0«ABS(X-CIJ.N3M 328 CIJ.N31-X 329 C 330 IF ID.IT.ERR IT I RETURN 331 IF (IT.LT.40I GO TO 1 332 WRITE (6,3) J 333 3 FCRMAT (//'NC CCNVERGENCE AFTFR 40 ITERATIONS*// 334 1 • OCCUREC IN COMPARTMENT NC.« '.131 335 RETURN  1 336 ENC ENO OF FILE i. I - • • . . . .

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 30 6
China 25 30
United Kingdom 5 0
Republic of Korea 2 0
City Views Downloads
Beijing 22 0
Unknown 11 1
Ashburn 11 5
Norfolk 7 0
Winter Park 3 0
Hangzhou 3 0
Saddle Brook 2 0
Wilmington 2 0
Dallas 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items