UBC Theses and Dissertations

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UBC Theses and Dissertations

Fouling in steady and unsteady state electrodialysis Tremblay, André-Yves 1981

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F O U L I N G I N S T E A D Y A N D U N 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 . S c . A . , U n i v e r s i t e d ' O t t a w a , 1 9 7 8 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F T H E F A C U L T Y OF G R A D U A T E S T U D I E S ( C h e m i c a l E n g i n e e r i n g , D e p t . ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g -t o t h e r e q u i r e d s t a n d a r d T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A M a y 1981 b y A n d r e - Y v e s T r e m b l a y M A S T E R O F A P P L I E D S C I E N C E i n A n d r e - Y v e s T r e m b l a y , 1981 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f CH/?t?f£-HL & T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 2 0 7 5 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V 6 T 1W5 D a t e 3 f^JL . / P g / 7 i i ABSTRACT The e f f e c t s of i r o n f o u l i n g on the steady and unsteady s t a t e e l e c t r o d i a l y s i s p rocesses were s t u d i e d . Both processes were compared on a bench s c a l e , under the same o p e r a t i n g c o n d i t i o n s of v o l t a g e (20 and 30 v o l t s ) , f l u i d v e l o c i t y (1.25 cm/sec), and i r o n (II) c o n c e n t r a t i o n i n t h e i r feed streams (0, 1, and 5 ppm). A 2000 mg./l. sodium c h l o r i d e s o l u t i o n c o n t a i n i n g Fe?? as f e r r o u s c h l o r i d e was c i r c u l a t e d through the process f o r 20 hours. The amount of d e p o s i t i o n on a t e s t p a i r of membranes was determined and compared to the change i n s e p a r a t i o n f a c t o r over the run. The power consumption per l i t r e per c e l l ' w a s determined for both processes and found to be a f u n c t i o n of d i a l y s a t e c o n c e n t r a t i o n . Due to l i m i t a t i o n s i n the power supply, the l i m i t i n g c u r r e n t I l i m c o u l d not be used as a f o u l i n g parameter, and the d e p o s i t i o n of i r o n was measured i n s t e a d . The s e p a r a t i o n f a c t o r in both processes decreased with the amount of i r o n accumulated on the membranes, while the p o l a r i z e d c e l l r e s i s t a n c e remained r e l a t i v e l y unchanged. T h i s i s i n agreement with the "sandwich membrane model". i i i T A B L E OF C O N T E N T S P a g e A B S T R A C T i i L I S T O F T A B L E S v i L I S T O F F I G U R E S . . X A C K N O W L E D G E M E N T S • X i i i C h a p t e r I I N T R O D U C T I O N 1 I I L I T E R A T U R E S U R V E Y 3 I I I O B J E C T I V E S A N D T H E O R Y 9 A ) O b j e c t i v e s 9 . B ) T h e o r y 10 1) G e n e r a l C o n s i d e r a t i o n s . . . 10 2 ) P o l a r i z a t i o n a n d W a t e r - s p l i t t i n g 13 3 ) I r o n ( I I ) F o u l i n g . . . 1 7 C ) T h e U n s t e a d y S t a t e P r o c e s s 18 I V A P P A R A T U S A N D E X P E R I M E N T A L 2 0 A ) A p p a r a t u s 2 0 1 ) S t e a d y S t a t e O p e r a t i o n . . . . . . . . . 2 0 a ) E l e c t r o d i a l y s i s S t a c k 2 0 b ) E l e c t r o d e s 24 c ) E l e c t r i c a l S y s t e m 2 7 d ) F l o w S y s t e m 2 7 i v P a g e 2 ) U n s t e a d y S t a t e P r o c e s s 2 8 a ) E l e c t r o d i a l y s i s S t a c k 2 8 b ) E l e c t r o d e s 3 0 c ) E l e c t r i c a l S y s t e m 3 0 d ) F l o w S y s t e m 31 B ) E x p e r i m e n t a l 3 2 1) S t e a d y S t a t e P r o c e s s 3 2 2 ) U n s t e a d y S t a t e P r o c e s s 34 V E X P E R I M E N T A L R E S U L T S A N D D I S C U S S I O N 3 8 A ) D e t e r m i n a t i o n o f a F o u l i n g P a r a m e t e r 3 9 1) L i m i t i n g C u r r e n t . . 3 9 2 ) A . C . R e s i s t a n c e M e a s u r e m e n t s 3 9 3 ) D i r e c t M e a s u r e m e n t o f I r o n D e p o s i t s 41 B ) P e r f o r m a n c e o f t h e S t e a d y a n d U n s t e a d y S t a t e P r o c e s s e s 41 1) V o l t a g e D r o p P e r C e l l P a i r a s a F u n c t i o n o f B u l k S o l u t i o n R e s i s t a n c e 41 2 ) C a l c u l a t i o n o f S e p a r a t i o n F a c t o r s a n d I o n i c S e l e c t i v i t i e s 4 2 3 ) P l o t o f t h e A c t u a l C e l l P a i r R e s i s t a n c e a s a F u n c t i o n o f S t a c k V o l t a g e 4 3 4 ) P r e s s u r e D r o p s 5 0 5 ) P o w e r R e q u i r e m e n t s f o r S e p a r a t i o n 5 0 6 ) D e c r e a s e s i n S e p a r a t i o n d u e t o F o u l i n g 5 6 7 ) M a s s B a l a n c e s o n I r o n a n d S o d i u m 6 0 8 ) V i s u a l E x a m i n a t i o n o f F o u l i n g D e p o s i t s . . . 6 3 C ) S u m m a r y 7 0 V P a g e C O N C L U S I O N S 7 4 o R E C O M E N D A T I O N S 7 5 R E F E R E N C E S 7 7 T A B L E S I I t o I L 7 9 A P P E N D I X A , 1 1 2 A P P E N D I X B 1 1 3 1) C u r r e n t M e a s u r m e n t s 1 1 3 2 ) C u r r e n t D e n s i t y 1 1 3 3 ) S e p a r a t i o n F a c t o r 1 1 4 4 ) P o w e r R e q u i r e m e n t s 1 1 5 5 ) C a l c u l a t i o n o f ( R a + R c + R p ) 1 1 5 6 ) I r o n A c c u m u l a t i o n 1 1 5 A P P E N D I X C . . 1 1 6 vi L I S T OF T A B L E S T a b l e P a g e I C y c l e t i m e u s e d a t d i f f e r e n t f l u i d v e l o c i t i e s 3 5 I I S t e a d y s t a t e , v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s o f b o t h s t a g e s (A a n d ( B ) 7 9 I I I S t e a d y s t a t e , v o l t a g e d r o p p e r c e l l p a i r ( B ) a n d v o l t a g e d r o p i n b u l k s o l u t i o n ( A ) f o r t h e f i r s t s t a g e a t 2 a n d 2 0 h o u r s 8 0 I V S t e a d y s t a t e , v o l t a g e p e r c e l l p a i r ( B ) a n d v o l t a g e d r o p i n b u l k s o l u t i o n ( A ) f o r t h e s e c o n d s t a g e a t 2 a n d 2 0 h o u r s 81 V S t e a d y s t a t e , s t a c k v o l t a g e s - ( A ) a n d c o m b i n e d r e s i s t a n c e s ( R a + R c + R p ) ( B ) f o r f i r s t e f f e c t a t 2 a n d 2 0 h o u r s 8 2 V I S t e a d y s t a t e , s t a c k v o l t a g e s ( A ) a n d c o m b i n e d r e s i s t a n c e s ( R a + R c + R p ) ( B ) f o r s e c o n d e f f e c t a t 2 a n d 2 0 h o u r s 8 3 V I I S t e a d y s t a t e , d i a l y s a t e p r e s s u r e d r o p a t 2 a n d 2 0 h o u r s 8 4 V I I I S t e a d y s t a t e , d i a l y s a t e p r e s s u r e d r o p a t 2 a n d 2 0 h o u r s 8 5 I X P r e s s u r e d r o p a c r o s s t h e d i a l y s a t e c h a n n e l ( A ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . . 8 6 X P r e s s u r e d r o p a c r o s s t h e b r i n e c h a n n e l ( A ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . . 8 6 X I S t e a d y s t a t e , s e p a r a t i o n f a c t o r ( A ) a n d p o w e r r e q u i r e m e n t s / l i t r e o f d i a l y s a t e p r o d u c e d p e r c e l l ( B ) ( J o u l e s / 1 p e r c e l l ) a t 2 a n d 2 0 h o u r s 8 7 X I I S e p a r a t i o n f a c t o r N s ( A ) a n d t h e p o w e r c o n s u m p t i o n ( j o u l e s / l i t r e p e r c e l l ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) 8 8 vi i T a b l e P a g e X I I I S t e a d y a n d u n s t e a d y s t a t e , d i a l y s a t e c o n c e n t r a t i o n s ( m g . / l . ) ( A ) a n d t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d p e r c e l l ( j o u l e s / 1 p e r c e l l ) ( B ) a t 2 a n d 2 0 h o u r s ( 1 , 2 5 c m / s e c o n l y ) 8 9 X I V A m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s , ( s t e a d y s t a t e r u n s ) 9 0 X V A v e r a g e i r o n a c c u m u l a t i o n o n t h e t e s t m e m b r a n e s ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s ( B ) d u r i n g a r u n ( u n s t e a d y s t a t e r u n s ) 91 X V I T h e t o t a l a m o u n t o f i r o n a c c u m u l a t i o n ( b a s e d o n m e m b r a n e s ) ( m g . ) ( A ) a n d t h e t o t a l a m o u n t o f i r o n l o s t i n f e e d s t r e a m ( m g . ) ( B ) ( s t e a d y s t a t e r u n s ) 91 X V I I T o t a l i r o n a c c u m u l a t i o n b a s e d o n t h e m e m b r a n e s ( m g . ) ( A ) a n d t h e a m o u n t o f i r o n l o s t i n t h e f e e d d u r i n g a r u n ( m g . ) ( B ) ( u n s t e a d y s t a t e r u n s ) 92 X V I I I p H o f t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 9 3 X I X p H o f t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t a a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) 94 X X T h e p e r c e n t s e p a r a t i o n b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 94 X X I U n s t e a d y s t a t e , p e r c e n t s e p a r a t i o n b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s 9 5 X X I I I o n i c s e l e c t i v i t y b a s e d o n i r o n i n t h e d i a l y s a t e • ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 9 5 X X I I I I o n i c s e l e c t i v i t y b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) 9 6 vi i i T a b l e P a g e X X I V A v e r a g e c u r r e n t e f f i c i e n c y ( A ) a t 2 a n d 2 0 h o u r s a n d t h e p e r c e n t d r o p i n c u r r e n t e f f i c i e n c y o v e r 18 h o u r s ( s t e a d y s t a t e r u n s ) 97 X X V U n s t e a d y s t a t e , a v e r a g e c u r r e n t e f f i c i e n c y ( A ) a t 2 a n d 2 0 h o u r s a n d t h e p e r c e n t d r o p i n c u r r e n t e f f i c i e n c y o v e r 18 h o u r s ( B ) . 9 8 X X V I T h e p e r c e n t s e p a r a t i o n b a s e d o n s o d i u m f o r t h e d i a l y s a t e ( A ) a n d b r i n e s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 9 9 X X V I I U n s t e a d y s t a t e , p e r c e n t s e p a r a t i o n b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s 1 0 0 X X V I I I I o n i c s e l e c t i v i t y b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) a t 2 a n d 2 0 h o u r s , ( s t e a d y s t a t e r u n s ) 101 X X I X I o n i c s e l e c t i v i t y b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) 102 X X X A b s o l u t e e r r o r s i n t h e a m m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s ( B ) ( s t e a d y s t a t e r u n s ) 1 0 3 X X X I A b s o l u t e e r r o r i n t h e a c c u m u l a t i o n o f i r o n o n t h e t e s t m e m b r a n e s ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r ( B ) ( u n s t e a d y s t a t e r u n s ) . 1 0 4 X X X I I A b s o l u t e e r r o r s i n t h e v a l u e s o f ( R a + R c + R p ) f o r t h e f i r s t s t a g e ( A ) a n d s e c o n d s t a g e ( B ) a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 1 0 5 X X X I I I A b s o l u t e e r r o r i n t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( A ) a n d t h e a m o u n t o f i r o n l o s t i n t h e f e e d s t r e a m ( s t e a d y s t a t e r u n s ) . 1 0 6 X X X I V A b s o l u t e e r r o r i n t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( m g . ) ( A ) a n d t h e a m o u n t o f i r o n l o s t i n t h e f e e d ( m g . ) ( B ) ( u n s t e a d y s t a t e r u n s ) 1 0 6 X X X V A b s o l u t e e r r o r s i n t h e v a l u e s o f i o n i c s e l e c t i v i t i e s b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) . . . . 1 0 7 ix T a b l e P a g e X X X V I A b s o l u t e e r r o r i n t h e i r o n s e l e c t i v i t y b a s e d o n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . . 1 0 7 X X X V I I A b s o l u t e e r r o r i n t h e c u r r e n t e f f i c i e n c i e s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 108 X X X V I I I P e r c e n t e r r o r i n c u r r e n t e f f i c i e n c y a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . . . 1 0 9 X X X I X A b s o l u t e e r r o r s i n t h e v a l u e s o f i o n i c s e l e c t i v i t i e s b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) 110 X L A b s o l u t e e r r o r i n t h e s o d i u m s e l e c t i v i t y b a s e d o n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) c h a n n e l s a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) 111 X L I S T OF F I G U R E S F i g u r e P a g e 1 W a t e r p r o d u c t i o n c o s t v s . s a l i n i t y f o r v a r i o u s d e s a l i n a t i o n p r o c e s s e s ( s c h e m a t i c ) 4 2 T r a n s p o r t n u m b e r s i n a n a n i o n i c m e m b r a n e ( A ) . 1 0 3 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 s t a c k A - a n i o n s e l e c t i v e m e m b r a n e B - c a t i o n s e l e c t i v e m e m b r a n e , 1.1 4 P o l a r i z a t i o n l a y e r s a t t h e s o l u t i o n - m e m b r a n e i n t e r f a c e s 14 5 C o n f i g u r a t i o n o f " s a n d w i c h m e m b r a n e s " 18 6 F l o w d i a g r a m o f t h e s t e a d y s t a t e a p p a r a t u s 21 7 S t e a d y s t a t e s t a c k a s s e m b l y 2 2 8 A - P o l y e t h y l e n e s p a c e r u s e d i n t h e s t e a d y s t a t e p r o c e s s , B - p o l y e t h y l e n e s p a c e r u s e d i n t h e u n s t e a d y s t a t e p r o c e s s 2 3 9 S t e a d y s t a t e c e l l p r e s s 2 5 10 F a c e v i e w o f t h e P l e x i g l a s s e n d b l o c k u s e d i n t h e s t e a d y s t a t e p r o c e s s 2 6 11 F l o w d i a g r a m o f t h e u n s t e a d y s t a t e a p p a r a t u s 2 9 12 F l o w c o n n e c t i o n s a n d v a l v e t i m i n g s e q u e n c e u s e d i n t h e u n s t e a d y s t a t e o p e r a t i o n 36 13 P l o t o f t h e s t e a d y s t a t e s t a c k v o l t a g e v s . t h e c u r r e n t c o n s u m p t i o n f o r b o t h s t a g e s 4 0 • 1 4 P l o t o f t h e f i r s t s t a g e v o l t a g e d r o p p e r c e l l p a i r v s . t h e b u l k s o l u t i o n v o l t a g e d r o p p e r c h a n n e l , f o r a l l 2 h o u r s t e a d y s t a t e r e a d i n g s ( S e k o ' s w o r k i s r e p r e s e n t e d b y t h e s o l i d l i n e ) 4 4 15 P l o t o f t h e s e c o n d s t a g e v o l t a g e d r o p p e r c e l l p a i r v s . t h e b u l k s o l u t i o n v o l t a g e d r o p p e r c h a n n e l , f o r a l l 2 h o u r s t e a d y s t a t e r e a d i n g s ( S e k o ' s w o r k i s r e p r e s e n t e d b y t h e s o l i d l i n e ) . . . . . . . 4 5 xi F i g u r e P a g e 16 P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e f i r s t s t a g e o f t h e s t e a d y s t a t e p r o c e s s , a l l r u n s w i t h o u t f o u l i n g 4 6 17 P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e f i r s t s t a g e o f t h e s t e a d y s t a t e p r o c e s s , a l l r u n s w i t h f o u l i n g 4 7 18 P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e s e c o n d s t a g e o f t h e s t e a d y s t a t e p r o c e s s , r u n s w i t h o u t f o u l i n g 4 8 19 P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e s e c o n d s t a g e o f t h e s t e a d y s t a t e p r o c e s s , a l l r u n s w i t h f o u l i n g 4 9 2 0 P l o t o f t h e d i a l y s a t e a n d b r i n e c h a n n e l p r e s s u r e d r o p s v s . f l u i d v e l o c i t y f o r a l l s t e a d y s t a t e r u n s w i t h o u t f o u l i n g 51 21 P l o t o f t h e d i a l y s a t e a n d b r i n e c h a n n e l p r e s s u r e d r o p s v s . f l u i d v e l o c i t y f o r a l l s t e a d y s t a t e r u n s w i t h f o u l i n g 5 2 2 2 P l o t o f t h e d i a l y s a t e a n d b r i n e c h a n n e l p r e s s u r e d r o p s v s . f l u i d v e l o c i t y f o r a l l u n s t e a d y s t a t e r u n s 5 3 2 3 P l o t o f t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d v s . t h e s e p a r a t i o n f a c t o r N s , f o r a l l s t e a d y s t a t e r u n s 54 24 P l o t o f t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d v s . t h e s e p a r a t i o n f a c t o r N s , f o r a l l u n s t e a d y s t a t e r u n s 5 5 2 5 P l o t o f t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d v s . t h e d i a l y s a t e c o n c e n t r a t i o n , f o r a l l s t e a d y a n d u n s t e a d y s t a t e r u n s 5 7 2 6 P l o t o f t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r o v e r a n 18 h o u r p e r i o d v s . t h e a m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r o v e r t h e 2 0 h o u r r u n , f o r a l l s t e a d y s t a t e r u n s w i t h f o u l i n g 5 8 xi i F i g u r e P a g e 2 7 P l o t o f t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r o v e r a n 18 h o u r p e r i o d v s . t h e a m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r o v e r t h e 2 0 h o u r r u n , f o r a l l u n s t e a d y s t a t e r u n s w i t h f o u l i n g . 5 9 2 8 P l o t o f t h e a m o u n t o f i r o n l o s t i n t h e f e e d v s . t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s d u r i n g t h e 2 0 h o u r r u n , f o r a l l s t e a d y s t a t e r u n s 61 2 9 P l o t o f t h e a m o u n t o f i r o n l o s t i n t h e f e e d v s . t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s d u r i n g t h e 2 0 h o u r r u n , f o r a l l u n s t e a d y s t a t e r u n s 6 2 3 0 I r o n o x i d e f i l m o n a t e s t m e m b r a n e p a i r i n t h e u n s t e a d y s t a t e p r o c e s s a t 2 0 v o l t s , 1 , 2 5 c m / s e c , 0 p p m i r o n i n f e e d ( A ) , a n d a t 3 0 v o l t s , 5 , 0 c m / s e c , 1 p p m i r o n i n f e e d ( B ) . (1 d i v i s i o n = 1mm. ) 6 6 31 I r o n o x i d e f i l m o n a t e s t m e m b r a n e p a i r i n t h e u n s t e a d y s t a t e p r o c e s s a t 2 0 v o l t s , 1 , 2 5 c m / s e c , 5 ppm i r o n i n f e e d ( A ) , a n d a t 3 0 v o l t s , 1 , 2 5 c m / s e c , 5 p p m i r o n i n f e e d ( B ) . (1 d i v i s i o n = 1mm. ) 6 7 3 2 I r o n o x i d e d e p o s i t s o n a c a t i o n a n d a n i o n s e l e c t i v e m e m b r a n e , s t e a d y s t a t e p r o c e s s 6 8 3 3 C o m p a r i s o n b e t w e e n t h e f i l m s f o r m e d i n t h e s t e a d y s t a t e a n d u n s t e a d y s t a t e p r o c e s s e s 6 9 x i i i A C K N O W L E D G E M E N T I w i s h t o t h a n k D r . D . W. T h o m p s o n , f o r h i s g u i d a n c e a n d a s s i s t a n c e t h r o u g h o u t t h e c o u r s e o f t h i s w o r k . I a l s o w i s h t o t h a n k A r l e n e - M a r i o n Y a s f o r h e r h e l p w i t h t h e p r e p a r a t i o n o f t h e m a n u s c r i p t . I am i n d e b t e d t o t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , a n d t h e N a t u r a l S c i e n c e a n d E n g i n e e r i n g R e s e a r c h C o u n c i l o f C a n a d a f o r f i n a n c i a l s u p p o r t . F i n a l l y , I w o u l d l i k e t o a c k n o w l e d g e t h e p a s t h e l p f r o m my p a r e n t s a n d t e a c h e r s . 1 I I N T R O D U C T I O N M e m b r a n e t r a n s p o r t p r o c e s s e s , s u c h a s r e v e r s e o s m o s i s , u l t r a f i l t r a t i o n a n d e l e c t r o d i a l y s i s , h a v e b e e n a d v e r s e l y a f f e c t e d b y t h e a c c u m u l a t i o n o f s c a l e d e p o s i t s , a n d / o r f o u l i n g f i l m s , o n t h e m e m b r a n e s u r f a c e s s i n c e t h e i r f i r s t u s e o n a l a r g e s c a l e b a s i s . I n c o n v e n t i o n a l e l e c t r o d i a l y s i s , s u c h d e p o s i t s h a v e l e d t o c o s t l y m e m b r a n e r e p l a c e m e n t s a n d , i n s o m e c a s e s , t h e c o m p l e t e s h u t d o w n o f p l a n t s . B y 1 9 7 0 , a n o p e r a t i n g f e a t u r e k n o w n a s " P o l a r i t y R e v e r s a l " w a s i n t r o d u c e d a n d a p p l i e d t o l a r g e s c a l e p l a n t s . I t w a s b e l i e v e d t h a t t h e i n t e r m i t t e n t r e v e r s a l o f e l e c t r o d e p o l a r i t y c o u l d b e u s e d t o c o n t r o l s c a l e d e p o s i t s w i t h o u t t h e a d d i t i o n o f a c i d s o r p o l y p h o s p h a t e s t o t h e f e e d s t r e a m . L i t t l e w a s k n o w n , h o w e v e r , a s t o t h e e f f i c i e n c y o f P o l a r i t y R e v e r s a l i n c o n t r o l l i n g f o u l i n g d e p o s i t s s u c h a s i r o n o x i d e f i l m s . I n t h e c o u r s e o f t h i s w o r k , t h e p e r f o r m a n c e o f a n u n s t e a d y s t a t 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 , d e v e l o p e d a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a b y D r D . W . T h o m p s o n , w a s s t u d i e d i n o r d e r t o d e t e r m i n e i f f o u l i n g w o u l d o c c u r i n s u c h a p r o c e s s . T h i s o p e r a t i o n c o m b i n e s t h e p r i n c i p l e s o f p o l a r i t y r e v e r s a l a n d p a r a m e t r i c p u m p i n g i n o r d e r - t o s e p a r a t e a f e e d s t r e a m i n t o b r i n e a n d . d i a l y s a t e s t r e a m s . T h e u n s t e a d y s t a t e 2 process was compared with a conventional steady s t a t e e l e c t r o d i a l y s i s process, both processes having the same i r o n c o n c e n t r a t i o n i n t h e i r feed streams, and both operated under the same voltages and f l u i d v e l o c i t i e s . 3 I I L I T E R A T U R E S U R V E Y L a r g e q u a n t i t i e s o f b r a c k i s h w a t e r s u i t a b l e f o r t h e e l e c t r o d i a l y s i s p r o c e s s a r e a v a i l a b l e i n m a n y a r e a s o f t h e w o r l d h a v i n g s h o r t a g e s o f f r e s h w a t e r ( G i l l i l a n d 1 9 6 5 ) . T h e 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 p r o c e s s h a s b e e n u s e d f o r o v e r t h r e e d e c a d e s f o r t h e p r o d u c t i o n o f p o t a b l e w a t e r . ( K l y a c h c o e t a l 1 9 6 5 , M a t z 1 9 6 5 , M i l l e t 1 9 7 6 , G o v i d a n e t a l 1 9 7 6 , E l H a r e s e t a l 1 9 7 7 , A r n o l d e t a l 1 9 7 8 , I . S e t o e t a l 1 9 7 8 , G o l d s t e i n 1 9 7 9 ) . E a r l y c o s t c o m p a r i s o n s s u g g e s t e d t h a t e l e c t r o d i a l y s i s w a s m o r e e x p e n s i v e t h a n r e v e r s e o s m o s i s o r d i s t i l l a t i o n a t s a l i n i t y l e v e l s o v e r 6 , 0 0 0 m g . / l i t r e s e e F i g . 1 ( L . T . F a n e t a l 1 9 6 8 ) . H o w e v e r , a r e c e n t b a t c h w i s e o p e r a t i o n h a s p r o d u c e d p o t a b l e w a t e r f r o m s e a w a t e r a t a c o s t o f $ 1 . 3 2 / c u . m e t e r ( 1 9 7 7 ) ( S e t o e t a l 1 9 7 7 ) . S e v e r a l o t h e r u s e s o f t h e e l e c t r o d i a l y s i s p r o c e s s h a v e b e e n i m p l e m e n t e d a n d a r e now b e i n g u s e d b y i n d u s t r y . E x a m p l e s o f t h e s e a r e t h e t r e a t m e n t o r t h e r e c y c l i n g o f w a s t e s f r o m m e t a l r e f i n i n g i n d u s t r i e s ( S . I t o i 1 9 7 9 , A s a h i C h e m . I n d . ) , p e t r o c h e m i c a l i n d u s t r i e s ( E P A 1 9 7 9 ) , c o p p e r a n d z i n c p l a t i n g i n d u s t r i e s ( K o r n g o l d e t a l 1 9 7 8 ) a n d d a i r y i n d u s t r i e s ( J . M i l l e t 1 9 7 6 ) . O t h e r u s e s i n c l u d e t h e d e s a l i n a t i o n o f t r e a t e d m u n i c i p a l s e w a g e a n d t h e r e c o v e r y o f n i t r i c a c i d u s e d i n a c r y l i c f i b e r m a n u f a c t u r i n g ( A s a h i C h e m . I n d . ) . 4 1 0 0 9 0 8 to o 0 7 o 8 0 6 O \ 0 3 o o 0 4 0.3 0 2 0 1 1 1 1 1 1 1 1 j 1 1 1 1 i 1 r-electrodiolysis a \m reverse osmosis m l . riiOiiintion superior superior -1 I I u 2 0 0 0 6 0 0 0 1 0 0 0 0 14000 18000 salinity . PPM -1 1 1 L_ 22000 26000 30000 F i g u r e 1 . W a t e r p r o d u c t i o n c o s t v s . S a l i n i t y f o r v a r i o u s d e s a l i n a t i o n p r o c e s s e s ( s c h e m a t i c ) . I n J a p a n , a l l c o n v e n t i o n a l s a l t m a n u f a c t u r i n g p r o c e s s e s w e r e r e p l a c e d p r i o r t o 1 9 7 2 b y a c o m b i n e d e l e c t r o d i a l y s i s -e v a p o r a t i o n p r o c e s s ( A s a h i C h e m . I n d , Y . T s u n o d a 1 9 6 5 ) . A n e a r l y t e x t w r i t t e n b y W i l s o n ( 1 9 6 0 ) r e m a i n s t h e o n l y w o r k t o t a l l y d e d i c a t e d t o e l e c t r o d i a l y s i s . C h a p t e r s i n b o o k s b y S p e i g l e r ( 1 9 6 2 , 1 9 6 6 ) , S p o r n ( 1 9 6 6 ) a n d P o p k i n ( 1 9 6 8 ) d e a l w i t h b a s i c p r i n c i p l e s b u t o f f e r l i t t l e i n f o r m a t i o n o n f o u l i n g . T h e f i r s t l a r g e s c a l e e l e c t r o d i a l y s i s p l a n t s w e r e p u t i n t o o p e r a t i o n o v e r t h r e e d e c a d e s a g o . S c a l e d e p o s i t s , f o u l i n g , a n d p o i s o n i n g o f m e m b r a n e s h a v e p l a g u e d t h e p r o c e s s 5 c a u s i n g i n c r e a s e d s t a c k r e s i s t a n c e s a n d p o w e r c o s t s , l a r g e d o w n t i m e s , c o s t l y m e m b r a n e r e p l a c e m e n t s a n d t o t a l p l a n t s h u t d o w n s ( G . S . S o l t 1 9 6 5 ) . D i f f e r e n t t y p e s o f i n o r g a n i c s c a l e d e p o s i t s h a v e b e e n o b s e r v e d u n d e r n o r m a l p l a n t o p e r a t i o n . C a l c i u m c a r b o n a t e a n d m a g n e s i u m h y d r o x i d e s c a l e s w e r e a t t r i b u t e d t o p H i n c r e a s e s a t t h e m e m b r a n e s u r f a c e s . T h e s e s a l t s p r e c i p i t a t e d i n s i d e t h e d i a l y s a t e a n d b r i n e c o m p a r t m e n t s , a n d , a t t i m e s , w i t h i n t h e m e m b r a n e i t s e l f ( M . S e k o 1 9 6 2 , R . M a t z 1 9 6 5 ) . S u l p h a t e s c a l i n g h a s b e e n o b s e r v e d i n s e v e r a l e l e c t r o d i a l y s i s s t a c k s ( Y . T s u n o d a 1 9 6 5 , H . E . H a r e s e t a l 1 9 7 7 ) . S u l p h a t e s c a l e s a r e h a r d e r t o e l i m i n a t e t h a n c a r b o n a t e s c a l e s b e c a u s e t h e y a r e l e s s s u s c e p t i b l e t o c h a n g e s i n s o l u b i l i t y w i t h p H . B a r i u m a n d s t r o n t i u m s u l p h a t e s c a l e s h a v e b e e n r e p o r t e d t o f o r m o n t h e c a t h o d e s i d e o f c a t i o n p e r m e a b l e m e m b r a n e s . T h e s e s c a l e s w e r e a t t r i b u t e d t o o p e r a t i n g c o n d i t i o n s c l o s e t o t h e s o l u b i l i t y p r o d u c t o f b a r i u m s u l p h a t e ( W i l s o n 1 9 6 0 ) . T h e m o s t c o m m o n t y p e o f f o u l i n g i s d u e t o o r g a n i c c o l l o i d a l a c i d s h a v i n g t h e s t r u c t u r e o f p o l y m e r i c p o l y h y d r i c p h e n o l s . T h e s e a c i d s p r e c i p i t a t e a s t h i n f i l m s o n t h e s u r f a c e o f i o n e x c h a n g e m e m b r a n e s ( B . A . C o o k e 1 9 6 5 ) . K r e s m a n a n d T y e ( 1 9 6 9 ) r e p o r t t h a t c o n c e n t r a t i o n s o f 0 . 0 3 ppm o r g a n i c c o l l o i d s a r e h a r m f u l l t o a n i o n e x c h a n g e m e m b r a n e s . M a n y e l e c t r o d i a l y s i s p l a n t s h a v e h a d t o c o m p l e t e l y r e p l a c e t h e i r m e m b r a n e s w h e n t h i s t y p e o f f o u l i n g o c c u r r e d ( G . S . S o l t e t a l 1 9 6 5 ) . 6 F o u l i n g d u e t o o r g a n i c c o l l o i d s i s a n a u t o c a t a l y t i c r e a c t i o n : a c a t i o n s e l e c t i v e l a y e r o f h u m i c a c i d i s p r e c i p i t a t e d a t t h e s u r f a c e o f a n a n i o n e x c h a n g e m e m b r a n e c a u s i n g t h e f o r m a t i o n o f a c o m p o s i t e " s a n d w i c h m e m b r a n e " ( G r o s m a n a n d S o n i n 1 9 7 3 ) . T h e c a t i o n s e l e c t i v e l a y e r d e c r e a s e s t h e f l o w o f a n i o n s f r o m t h e b u l k s o l u t i o n t o t h e m e m b r a n e i n t e r f a c e . T h e e f f e c t o f t h i s c o n f i g u r a t i o n i s a d e p l e t i o n o f s a l t i o n s a t t h e m e m b r a n e - f i l m i n t e r f a c e , c r e a t i n g m o r e w a t e r s p l i t t i n g , a n d l e a d i n g t o a l a r g e r a c c u m u l a t i o n o f a c i d o n t h e m e m b r a n e s u r f a c e s . F o u l i n g d u e t o c o l l o i d a l i r o n f i l m s i s a s e r i o u s p r o b l e m i n m a n y c o u n t r i e s a n d i s v i e w e d a s t h e m a j o r e l e c t r o d i a l y s i s p r o b l e m i n t h e U . S . S . R . ( V . A . K l y a c h k o e t a l 1 9 6 5 ) . A s w e l l w a t e r c o n t a i n i n g f e r r o u s i o n s i s p a s s e d t h r o u g h a n e l e c t r o d i a l y s i s s t a c k , h y d r o x y l i o n s p r e s e n t a t t h e m e m b r a n e s u r f a c e s d u e t o w a t e r s p l i t t i n g , c o m b i n e w i t h f e r r o u s i o n s t o e v e n t u a l l y y i e l d c o l l o i d a l f i l m s o f f e r r i c o x i d e . T h e f o r m a t i o n o f s u c h d e p o s i t s h a s b e e n o b s e r v e d i n s t a c k s t r e a t i n g w e l l w a t e r c o n t a i n i n g . 0 4 ppm i r o n ( D . H . F u r u k a w a 1 9 6 8 ) . F o u l i n g d u e t o i r o n d e p o s i t s w i l l b e d i s c u s e d i n g r e a t e r d e t a i l l a t e r i n t h i s w o r k . M o s t d e t e r g e n t s , m u l t i v a l e n t i o n s , a n d h u m i c a c i d s p o i s o n m e m b r a n e s b y o c c u p y i n g e x c h a n g e s i t e s o r f o r m i n g m i c e l l e s w i t h i n t h e m e m b r a n e s a s i n t h e c a s e o f d e t e r g e n t s ( P . J . V a n D u i n 1 9 7 0 ) . P o i s o n i n g o f a n i o n s e l e c t i v e m e m b r a n e s b y s o d i u m d o d e c y l s u l p h a t e w a s s t u d i e d b y K o b u s a n d U r t j e s 7 ( 1 9 7 2 ) ; t h e e f f e c t s o f H D P C a n d A r e o s o l O T , b o t h d e t e r g e n t s , w e r e s t u d i e d b y V a n D u r i n 1 9 7 0 . C a t i o n s e l e c t i v e m e m b r a n e s w e r e n o t a f f e c t e d b y d e t e r g e n t s ; h o w e v e r , a n i o n s e l e c t i v e m e m b r a n e s s h o w e d a s u b s t a n t i a l i n c r e a s e i n r e s i s t a n c e a n d a d e c r e a s e i n p e r m s e l e c t i v i t y t o b e u l t i m a t e l y t r a n s f o r m e d i n t o c a t i o n s e l e c t i v e m e m b r a n e s i n t h e p r e s e n c e o f d e t e r g e n t s . T h e p r e s e n c e o f f e r r i c i o n s i n f e e d w a t e r s a t c o n c e n t r a t i o n s o f 0 . 0 2 p p m h a s p o i s o n e d c a t i o n e x c h a n g e m e m b r a n e s , l e a d i n g t o l a r g e i n c r e a s e s i n e l e c t r i c a l r e s i s t a n c e a n d s u b s t a n t i a l d e c r e a s e s i n c o u l o m b e f f i c i e n c y . A n i o n e x c h a n g e m e m b r a n e s r e m a i n r e l a t i v e l y u n a f f e c t e d b y t h e p r e s e n c e o f p o s i t i v e m u l t i v a l e n t i o n s i n f e e d w a t e r s ( J . R . W i l s o n 1 9 6 0 ) . P o i s o n i n g o f m e m b r a n e s b y h u m i c a c i d i s o n e o f t h e m a j o r p r o b l e m s i n t h e e l e c t r o d i a l y s i s p r o c e s s t o d a y a n d i s t h e m o s t d i f f i c u l t t o d e a l w i t h s i n c e t h e p r e t r e a t m e n t o f f e e d s t r e a m s c a n n o t e c o n o m i c a l l y l o w e r c o n c e n t r a t i o n s t o h a r m l e s s l e v e l s . S u c h c o n t a m i n a t i o n h a s c a u s e d i n c r e a s e s i n s t a c k r e s i s t a n c e s o f u p t o 3 0 p e r c e n t o v e r o n e h u n d r e d h o u r s ( K r e s m a n a n d T y e 1 9 6 9 ) , a n d d e c r e a s e s i n c u r r e n t e f f i c i e n c y l e a d i n g t o t h e p a r t i a l o r t o t a l r e p l a c e m e n t o f m e m b r a n e s ( G . S . S o l t e t a l 1 9 6 5 ) . C o o k e ( 1 9 6 5 ) r e p o r t s t h a t a n i o n e x c h a n g e m e m b r a n e s o f t h e " h o m o g e n e o u s t y p e " s h o w l e s s t e n d e n c y t o p o i s o n t h a n o t h e r a n i o n s e l e c t i v e m e m b r a n e s , w h i l e c a t i o n e x c h a n g e m e m b r a n e s r e m a i n u n a f f e c t e d b y t h e p r e s e n c e o f h u m i c a c i d i n f e e d w a t e r s . 8 T h e u n s t e a d y s t a t 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 d e v e l o p e d b y D r . D . W . T h o m p s o n a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , h a s b e e n d e s c r i b e d i n t h e P h . D . T h e s i s o f D . B a s s 1 9 7 2 a n d M . E . A b u - G o u k h 1 9 7 6 . N o p r e v i o u s s t u d i e s o n t h e b e h a v i o u r o f t h e u n s t e a d y s t a t e p r o c e s s u n d e r f o u l i n g c o n d i t i o n s w e r e a v a i l a b l e . 9 I I I O B J E C T I V E S A N D T H E O R Y  A ) O B J E C T I V E S T h e m a i n o b j e c t i v e o f t h i s w o r k w a s t o d e t e r m i n e t h e b e h a v i o u r o f t h e u n 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 p r o c e s s u n d e r f o u l i n g c o n d i t i o n s a n d t o c o m p a r e i t t o a 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 p r o c e s s . B o t h p r o c e s s e s h a d i d e n t i c a l c h a r a c t e r i s t i c s a s l i s t e d b e l o w : ]_) o p e r a t i n g v o l t a g e ( 2 0 a n d 3 0 V o l t s ) 2 ) f l u i d v e l o c i t y ( 1 , 2 5 c m / s e c ) 3>) i r o n c o n c e n t r a t i o n i n f e e d ( 0 , 1 a n d 5 p p m i r o n I I a s f e r r o u s c h l o r i d e ) 4 ) f e e d w a t e r ( i . e . : d i s t i l l e d w a t e r w a s u s e d t o e l i m i n a t e t h e e f f e c t s ' o f o t h e r c o n t a m i n a n t s ) 5 ) s p a c e r t h i c k n e s s a n d m e s h s i z e 6 ) c a t i o n a n d a n i o n s e l e c t i v e m e m b r a n e s 7 ) e l e c t r o d e m a t e r i a l s a n d a s s e m b l i e s T h e u n s t e a d y s t a t e p r o c e s s w a s o p e r a t e d a t 1 , 2 5 a n d 5 , 0 c m / s e c f l u i d v e l o c i t i e s , c o m p a r e d t o 0 , 5 a n d 1 , 2 5 c m / s e c i n t h e s t e a d y s t a t e p r o c e s s w h e r e a h i g h e r v e l o c i t y o f 5 , 0 c m / s e c c a u s e d e x c e s s i v e p r e s s u r e d r o p a n d l e d t o p r e m a t u r e w e a r i n g o f t h e p e r i s t a l t i c p u m p t u b e s w h i c h w o u l d t h e n b u r s t d u r i n g a r u n . T h e f o r m e r p r o c e s s h a d 5 6 c e l l p a i r s w i t h a t o t a l m e m b r a n e a r e a o f 7 . 0 4 1 , 4 c m 2 w h i l e t h e s t e a d y s t a t e p r o c e s s h a d 13 c e l l p a i r s w i t h a t o t a l a r e a o f 1 . 6 3 4 , 7 c m 2 . 1 0 B) THEORY 1) G e n e r a l C o n s i d e r a t i o n s The b a s i c p r i n c i p l e i n v o l v e d i n steady s t a t e e l e c t r o d i a l y s i s i s i l l u s t r a t e d by the f o l l o w i n g example : an a n i o n exchange membrane A, h a v i n g the c a t i o n and a n i o n t r a n s p o r t numbers T'^0 and Tr«r1 , r e s p e c t i v e l y , i s s u b j e c t e d t o a normal c u r r e n t and p l a c e d i n a sodium c h l o r i d e s o l u t i o n ( F i g . 2 ) . A T = 0 , 6 T=1 T =0 ,6 F i g u r e 2. T r a n s p o r t numbers i n an a n i o n i c membrane (A) On the r i g h t s i d e of A, c h l o r i d e i o n s a re c a r r i e d towards the membrane a t a r a t e of T" i / F and a c r o s s the membrane at a r a t e of T" i / F , where i is' the l o c a l c u r r e n t 11 concentra te out c A C [ A dialysate C out CI Na CI Na CI N a CI Na Feed in F i g u r e 3. 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 s t a c k A - a n i o n s e l e c t i v e m e m b r a n e C - c a t i o n s e l e c t i v e m e m b r a n e 1 2 d e n s i t y i n A m p s , p e r s q u a r e c e n t i m e t e r a n d F i s F a r a d a y ' s c o n s t a n t i n u n i t s o f c o u l o m b p e r e q u i v a l e n t . A t t h e s a m e t i m e , s o d i u m i o n s a r e t r a n s f e r r e d f r o m t h e i n t e r f a c e o f A t o w a r d s t h e r i g h t a t a r a t e o f T * i / F b u t a r e n o t r e p l a c e d b y i o n i c t r a n s p o r t a c r o s s t h e m e m b r a n e . I f we i g n o r e t h e e f f e c t s o f d i f f u s i o n , t h e p a s s a g e o f o n e F a r a d a y o f e l e c t r i c i t y f r o m l e f t t o r i g h t r e s u l t s i n t h e r e m o v a l o f T ~ - T " = 0 , 4 m o l e s o f c h l o r i d e i o n s f r o m t h e s o l u t i o n o n t h e r i g h t h a n d s i d e o f A , a n d t h e a p p e a r a n c e o f T + - T + = ' 0 , 4 m o l e s o f s o d i u m i o n s o n t h e l e f t s i d e o f m e m b r a n e A . T h e a b o v e r e a s o n i n g c a n b e e x t e n d e d t o o t h e r i o n s p r e s e n t i n t h e b u l k s o l u t i o n ; t h e r e l a t i o n ( T " + T + = 1 ) a n d ( T / + T + = 1 ) a s s u r e s u s t h a t e l e c t r o n e u t r a l i t y i s p r e s e r v e d . T h e n e t r e s u l t i s a d e c r e a s e i n s a l i n i t y o n t h e r i g h t s i d e o f t h e m e m b r a n e a n d a n i n c r e a s e i n s a l i n i t y o n t h e l e f t s i d e . A n a l o g o u s a r g u m e n t s h o l d f o r t h e c a t i o n s e l e c t i v e m e m b r a n e . I f t h e s e p r i n c i p l e s a r e a p p l i e d t o a s e r i e s o f a l t e r n a t i n g a n i o n a n d c a t i o n s e l e c t i v e m e m b r a n e s a s s e m b l e d i n a s t a c k , u n d e r t h e i n f l u e n c e o f a n o r m a l c u r r e n t , ( F i g . 3 ) , a s a l t s o l u t i o n f l o w i n g p a r a l l e l t o t h e m e m b r a n e s c a n b e s e p a r a t e d i n t o b o t h b r i n e ( c o n c e n t r a t e ) a n d p r o d u c t ( d i a l y s a t e ) s t r e a m s . 13 2 ) P o l a r i z a t i o n a n d W a t e r - s p l i t t i n g I n p r a c t i c e , T ~ > T " f o r a n a n i o n e x c h a n g e m e m b r a n e . T h e r e f o r e , l o o k i n g a t t h e b u l k s o l u t i o n o n t h e r i g h t s i d e o f A ( F i g . 2 ) , t h e f l u x o f c h l o r i d e i o n s f l o w i n g f r o m r i g h t t o l e f t i s i n s u f f i c i e n t t o m e e t t h e r e q u i r e m e n t s o f C I " t r a n s p o r t a c r o s s t h e m e m b r a n e , w h i l e t h e s o d i u m i o n t r a n s p o r t a c r o s s t h e m e m b r a n e i s i n s u f f i c i e n t t o m e e t t h e N a + . t r a n s p o r t i n t h e s o l u t i o n . S i n c e e l e c t r o n e u t r a l i t y i s t o b e p r e s e r v e d , t h e N a + a n d C I " d e f i c i e n c i e s a t t h e r i g h t o f t h e m e m b r a n e i n t e r f a c e a r e e q u a l , a n d t h e n e t N a C l c o n c e n t r a t i o n a t t h e i n t e r f a c e i s r e d u c e d . S i m i l a r l y , t h e c o n c e n t r a t i o n o f N a C l a t t h e l e f t m e m b r a n e i n t e r f a c e i s i n c r e a s e d . T h e i o n s m u s t d i f f u s e t h r o u g h t h e l a y e r o f s o l u t i o n a t t h e m e m b r a n e i n t e r f a c e i n o r d e r t o b e t r a n s p o r t e d a c r o s s t h e m e m b r a n e . T h i s b e h a v i o u r c a n b e r e p r e s e n t e d b y ' t h e f o l l o w i n g m o d e l : u n d e r s t e a d y s t a t e o p e r a t i o n a d i f f u s i o n o r p o l a r i z a t i o n l a y e r o f t h i c k n e s s 6, i s f o r m e d b e t w e e n t h e l i m i t s C1 , C 1 1 o n t h e l e f t h a n d s i d e o f t h e a n i o n m e m b r a n e , a n d a l a y e r o f t h i c k n e s s , b e t w e e n C 2 , C 2 1 o n t h e r i g h t h a n d s i d e ( f i g . 4 ) . P e r f o r m i n g a m a s s b a l a n c e o n a u n i t c r o s s s e c t i o n , we o b t a i n : + ( T + - T + ) i / F = - ( T " - T " ) i / F ( 1 ) 14 A C1 / / C2 F i g u r e 4 . P o l a r i z a t i o n l a y e r s a t t h e s o l u t i o n m e m b r a n e i n t e r f a c e s F r o m F i c k ' s l a w o f d i f f u s i o n , t h e l e f t h a n d s i d e o f e q u a t i o n ( 1 ) i s e q u a l t o ( C 1 1 - C 1 ) D / 6 , , a n d t h e r i g h t h a n d s i d e , ( C 2 - C 2 1 ) D / Si w h e r e D i s t h e d i f f u s i o n c o e f f i c i e n t o f t h e e l e c t r o l y t e . I n g e n e r a l , t h e f o l l o w i n g h o l d s f o r b o t h t y p e s o f m e m b r a n e s : ( T - T ) i / F = ± ( C - C 1 ) D / S ( 2 ) w h e r e £ d e p e n d s o n t h e h y d r o d y n a m i c c o n d i t i o n s p r e v a i l i n g i n t h e c o m p a r t m e n t . A g o o d e s t i m a t e o f S d o e s n o t e x i s t i n e l e c t r o d i a l y s i s c h a n n e l s w h e r e t u r b u l e n c e i s c r e a t e d b y c o r r e g a t e d s p a c e r s a n d v a r i a t i o n i n c h a n n e l t h i c k n e s s o c c u r s d u e t o m e m b r a n e w a r p i n g . H o w e v e r , i t c a n b e e x p e c t e d t h a t t h e m a g n i t u d e & o f w i l l d e c r e a s e d u e t o t h e e f f e c t s o f m i x i n g a s v e l o c i t y i n c r e a s e s i n t h e f l o w c h a n n e l . 1 5 I f C 1 < < C , a n d C 1 a p p r o c h e s z e r o a t a g i v e n v e l o c i t y , t h e c u r r e n t d e n s i t y i w i l l t e n d t o a l i m i t i n g v a l u e : I l i m = C F D / ( T - T ) S l i m ( 3 ) U n d e r t h e s e c o n d i t i o n s , a s i g n i f i c a n t p a r t o f t h e c u r r e n t p a s s i n g t h r o u g h t h e m e m b r a n e s m u s t b e c a r r i e d b y ( H 3 0 * ) a n d ( O H " ) i o n s a r i s i n g f r o m w a t e r s p l i t t i n g . T h e l i m i t i n g c u r r e n t i s u s u a l l y t a k e n a s t h e v a l u e o f i a t t h e p o i n t o f i n f l e c t i o n i n a p l o t o f i v s . v , t h e v o l t a g e p e r c e l l p a i r . O p e r a t i o n c l o s e t o , o r a b o v e i l i m l e a d s t o t h e p r e c i p i t a t i o n o f a n y p H s o l u b l e s u b s t a n c e s o n t o t h e m e m b r a n e s a n d t o e x p e n s i v e p o w e r l o s s e s . I n p r a c t i c e , e l e c t r o d i a l y s i s s t a c k s a r e o p e r a t e d b e l o w i l i m , w i t h t h e o p t i m u m c u r r e n t d e n s i t y a s a f u n c t i o n o f t h e f e e d a n d t h e r a t i o o f e l e c t r i c p o w e r t o m e m b r a n e m a t e r i a l c o s t s . S e e K l y a c h k o e t a l ( 1 9 6 5 ) , f o r f u r t h e r d e t a i l s o n o p t i m u m o p e r a t i n g c o n d i t i o n s . U n d e r n o r m a l o p e r a t i o n , C 1 < < C i n t h e d i l u t i n g c o m p a r t m e n t s , h e n c e , a g r e a t e r p r e c i p i t a t i o n o f s u b s t a n c e s s u c h a s i r o n ( I I ) w o u l d o c c u r o n t h e m e m b r a n e s u r f a c e s f a c i n g t h e d i l u t e s t r e a m . I n o r d e r t o o b s e r v e t h i s , a s e l e c t i v i t y c o e f f i c i e n t i s d e f i n e d a s f o l l o w s : F d = ( D E S d / D E S T O T d ) / ( F E E D / F E E D T O T ) F b = ( D E S b / D E S T O T b ) / ( F E E D / F E E D T O T ) 4 ( a ) 4 ( b ) 16 w h e r e : F b , d = t h e i o n i c s e l e c t i v i t y o f i r o n ( I I ) , i n t h e b r i n e a n d d i a l y s a t e s t r e a m s , r e s p e c t i v e l y . D E S b , d = t h e r a t e a t w h i c h f e r r o u s i o n s a r e t r a n s f e r e d t o o r f r o m s t r e a m s b a n d d . D E S T O T b , d = t h e r a t e a t w h i c h a l l i o n s p r e s e n t i n t h e b u l k s o l u t i o n a r e t r a n s f e r r e d t o o r f r o m s t r e a m s b o r d . F E E D = c o n c e n t r a t i o n o f f e r r o u s i o n i n t h e f e e d s t r e a m . F E E D T O T = t h e r a t e a t w h i c h a l l i o n s e n t e r s t r e a m s b o r d . T h e d i f f e r e n c e i n a c c u m u l a t i o n c a n a l s o b e s e e n b y c o m p a r i n g t h e p e r c e n t d i f f e r e n c e i n i o n s d e s a l t e d p e r s t r e a m . I n t h e c a s e o f i r o n ( I I ) , - i f F d > F b ( t h e p e r c e n t d i f f e r e n c e i n i o n s d e s a l t e d i n t h e d i a l y s a t e s t r e a m i s g r e a t e r t h a n t h a t o f t h e b r i n e ) , l a r g e r a m o u n t s o f f e r r o u s i o n s c a n b e s a i d t o a c c u m u l a t e i n t h e d i a l y s a t e c o m p a r t m e n t s . T h i s c o u l d b e d u e t o t h e e f f e c t s o f p o l a r i z a t i o n a n d w a t e r -s p l i t t i n g . S i m i l a r l y , i f t h e s e l e c t i v i t y o f t h e c a t i o n e x c h a n g e m e m b r a n e s i s a l t e r e d , v e r y l i t t l e , i f a n y , i r o n ( I I ) s e p a r a t i o n i s e x p e c t e d t o o c c u r , a n d F b s h o u l d d e c r e a s e a s t h e s a n d w i c h m e m b r a n e s , d e s c r i b e d i n t h e n e x t s e c t i o n , a r e f o r m e d . 1 7 3 ) I r o n ( I I ) F o u l i n g I r o n ( I I ) e x i s t s i n a q u e o u s s o l u t i o n a s h e x a q u o i r o n ( I I ) i o n , { F e ( H 2 0 ) 6 } 2 + ( C o t t o n F . A . a n d W i l k i n s o n G . ) . I n a b a s i c m e d i u m , t h e f o l l o w i n g r e a c t i o n s o c c u r : F e 2 + + 2 O H " - - > F e ( O H ) 2 ( 5 ) ( u n s t a b l e , w h i t e p p t . ) F e ( O H ) 2 + O H - === 1 / 2 ( F e 2 0 3 - 3 H 2 0 ) + e" E ° = + 0 . 5 6 v o l t s ( 6 ) I f a b a s i c d i f f u s i o n l a y e r i s p r e s e n t a t a n y m e m b r a n e i n t e r f a c e , a p o s i t i v e l y c h a r g e d c o l l o i d a l f i l m o f ( F e 2 0 3 -3 H 2 0 ) l i n k e d t o t h e m e m b r a n e ' s p o l y m e r m a t r i x b y V a n d e r W a a l s f o r c e s ( K r e s m a n a n d T y e 1 9 6 9 ) w i l l f o r m o n t h e s u r f a c e o f t h e m e m b r a n e s . S u c h • d e p o s i t s c r e a t e a s a n d w i c h m e m b r a n e a s s e e n i n F i g . 5 . U n d e r s u c h c o n d i t i o n s , t h e s e l e c t i v i t y o f a n i o n e x c h a n g e m e m b r a n e s r e m a i n s u n a f f e c t e d , w h i l e t h e s e l e c t i v i t y o f c a t i o n e x c h a n g e m e m b r a n e s i s g r e a t l y r e d u c e d . A s t h e c u r r e n t d e n s i t y i n c r e a s e s , a f i n i t e c u r r e n t i s r e a c h e d w h e r e t h e c a t i o n c o n c e n t r a t i o n g o e s t o z e r o a t t h e Z p l a n e s h o w n i n F i g . 5 . A t t h i s p o i n t c u r r e n t s a t u r a t i o n o c c u r s , d u e t o t h e l a c k o f c u r r e n t - c a r r y i n g i o n s i n t h e l a y e r . H e n c e , a v e r y t h i n c h a r g e d f i l m c a n g i v e r i s e t o a r e l a t i v e l y l a r g e r e d u c t i o n i n l i m i t i n g c u r r e n t . S o n i n a n d G r o s m a n ( 1 9 7 3 ) f o u n d t h a t 1 8 + didlysa te channel 1 Z F i g . 5 . C o n f i g u r a t i o n of "sandwich membranes" ( s i g n s r e f e r t o f i x e d charged groups p r e s e n t i n the membranes and f i l m s ) charged f i l m s of f e r r i c o x i d e had low OHMIC r e s i s t a n c e s , and i f the f i x e d charge c o n c e n t r a t i o n i n the f i l m was l a r g e , such f i l m s c o u l d cause a marked decrease i n l i m i t i n g c u r r e n t w i t h o u t c o n t r i b u t i n g measurably t o the OHMIC ( u n p o l a r i z e d ) r e s i s t a n c e of the system as a whole. C THE UNSTEADY STATE PROCESS A l l p r e v i o u s l y mentioned membrane t r a n s p o r t p r o p e r t i e s and f o u l i n g c h a r a c t e r i s t i c s a p p l y t o the unsteady s t a t e p r o c e s s . In t h i s p r o c e s s a membrane assembly, d e s c r i b e d i n Chapter 4, s t o r e s and r e l e a s e s i o n s t o and from a p l u g of s o l u t i o n c i r c u l a t e d back and f o r t h between two b a t t e r i e s of membranes h a v i n g d i f f e r e n t p o l a r i t i e s . The pause t i m e s , f e e d i n p u t s , p r o d u c t removal, e l e c t r o d e p o l a r i t y , and c i r c u l a t i o n 19 t i m e s a r e c o n t r o l l e d b y a c l o c k s e t t o t h e o p e r a t i n g c y c l e s h o w n i n F i g . 12 ( C h a p t e r 4 ) . D u r i n g t h e i n i t i a l p a u s e t i m e ( 4 5 s e c o n d s ) , t h e p o l a r i t y i n t h e t o p c e l l s c a u s e s t h e m e m b r a n e a s s e m b l i e s t o s t o r e i o n s , a n d t h e a s s e m b l i e s i n t h e b o t t o m c e l l s t o r e l e a s e i o n s . F i f t y m i l l i l i t r e s o f f e e d a r e t h e n i n t r o d u c e d i n t o t h e t o p c e l l s a n d a n e q u a l a m o u n t o f d i a l y s a t e r e m o v e d , t h e p r o c e d u r e i s r e p e a t e d i n t h e b o t t o m c e l l s a n d 5 0 m l . o f b r i n e r e c o v e r e d . B o t h s o l u t i o n s a r e c i r c u l a t e d u n t i l t h e t o p a n d b o t t o m s o l u t i o n s e x c h a n g e p o s i t i o n s . T h e e l e c t r o d e p o l a r i t y i n b o t h b a t t e r i e s i s t h e n r e v e r s e d c a u s i n g t h e m e m b r a n e a s s e m b l i e s i n t h e t o p c e l l s t o r e l e a s e i o n s , a n d t h o s e i n t h e b o t t o m c e l l s t o s t o r e i o n s . B o t h s o l u t i o n s a r e r e c i r c u l a t e d a n d t h e c y c l e r e p e a t e d . S u c h a c y c l e p r o d u c e s a c o n c e n t r a t i o n w a v e i n t h e t r a v e l l i n g s o l u t i o n w h i c h c a n b e t a p p e d a t t h e r i g h t m o m e n t t o p r o d u c e t h e d e s i r e d d i a l y s a t e a n d b r i n e p r o d u c t s . P r i o r t o t h i s s t u d y , n e i t h e r t h e l o c a t i o n o f f o u l i n g d e p o s i t s d u e t o i r o n , n o r t h e e f f e c t o f p o l a r i t y r e v e r s a l o n f o u l i n g , h a d b e e n d e m o n s t r a t e d . I t h a d n o t b e e n c o n f i r m e d w h e t h e r o r n o t f o u l i n g i t s e l f a c t u a l l y d i d o c c u r i n t h e u n 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 p r o c e s s . 2 0 I V . A P P A R A T U S A N D E X P E R I M E N T A L (. A ) A P P A R A T U S 1) S T E A D Y S T A T E O P E R A T I O N T h e a p p a r a t u s u s e d i n t h e s t e a d y s t a t e p r o c e s s i s a s i m p l e , o n e a s s h o w n i n F i g . 6 . A f e e d s o l u t i o n c o n t a i n i n g 2 0 0 0 p p m . s o d i u m c h l o r i d e a n d 0 , 1 , o r 5 p p m f e r r o u s i o n , i s p a s s e d t h r o u g h t w o c e l l s , e a c h c o n t a i n i n g 7 m e m b r a n e p a i r s , a n d r e t u r n e d t o a p o l y e t h y l e n e h o l d i n g t a n k . T h e r i n s e s t r e a m , a s o l u t i o n o f 5 0 0 0 p p m . s o d i u m c h l o r i d e i n d i s t i l l e d w a t e r , i s p u m p e d t h r o u g h t h e e l e c t r o d e c o m p a r t m e n t s a n d r e t u r n e d t o a s e p a r a t e p o l y e t h y l e n e t a n k . a ) E l e c t r o d i a l y s i s S t a c k B o t h e l e c t r o d i a l y s i s c e l l s w e r e e q u i p p e d w i t h a s t a c k c o n t a i n i n g 7 c a t i o n i c m e m b r a n e s ( I O N A C MC 3 1 4 2 ) a n d 6 a n i o n i c m e m b r a n e s ( I O N A C MA 3 1 4 8 ) . T h e s t a c k w a s a s s e m b l e d b y a l t e r n a t e l y p l a c i n g a n i o n i c a n d c a t i o n i c m e m b r a n e s b e t w e e n 14 p o l y e t h y l e n e s p a c e r s ( F i g . 7 ) . F o u r 4 mm. I . D . h o l e s , p u n c h e d o u t o f a 7 6 b y 2 2 5 mm. s h e e t o f m e m b r a n e m a t e r i a l , a l i g n e d w i t h p e r f o r a t i o n s i n t h e p o l y e t h y l e n e s e p a r a t o r s , f o r m t h e f o u r m a n i f o l d s . F o u r 13 mm. ( 1 / 2 i n c h ) h o l e s i n a 1 , 6 mm. p o l y e t h y l e n e s p a c e r ( F i g . 8 ) a r e f i l l e d b y t w o t y p e s o f M F i g u r e 6. Flow diagram of the s t e a d y s t a t e a p p a r a t u s M=manometer , P = p e r i s t a l t i c pump , T=feed tank T i = i n t e r m e d i a t e sampling tank r inse so ln . in c o n c e n t r a t e i n dial y s a te i n F i g u r e 7 polyethy lene spacer S t e a d y s t a t e a s s e m b l y . 2 4 i n s e t s , 13 mm. O . D . X 1 , 6 mm. t h i c k . O n e , o f p l a i n p o l y e t h y l e n e , b l o c k s a n y f l o w o f s o l u t i o n , w h i l e a n o t h e r , o f h a r d e r p o l y c a r b o n a t e h a v i n g t h r e e t o f o u r 0 , 4 mm. h o l e s d r i l l e d i n i t s s i d e , p e r m i t s t h e f l o w o f . s o l u t i o n t o a m a n i f o l d . W h e n t h e i n s e t s a r e a l t e r n a t e l y a r r a n g e d i n t h e s t a c k , t h e h a r d - s o f t c o m b i n a t i o n p r o v i d e s e x c e l l e n t s e a l i n g b e t w e e n c o m p a r t m e n t s . T h e e n t i r e c e l l i s h e l d i n a p r e s s , a s s h o w n i n F i g . 9 . b ) E l e c t r o d e s T h e e l e c t r o d e c o m p a r t m e n t s a r e f o r m e d b y m a c h i n i n g a 1 6 5 X 44. X 8 mm. d e p r e s s i o n i n a 2 2 5 X 7 6 X 24 mm. p l e x i g l a s s b l o c k ( F i g . 1 0 ) . T h e e l e c t r o d e , a 1 5 5 X 3 7 X 6 mm. s l a b o f g r a p h i t e , s u p p l i e d b y t h e " R i c h m o n d s t e e l r e c y c l i n g " r e f i n i n g c o m p a n y , i s p l a c e d i n s i d e t h i s d e p r e s s i o n a n d c o v e r e d b y a p o l y e t h y l e n e m e s h , a c a t i o n i c m e m b r a n e ( I O N A C MC 3 1 4 2 ) , a s e c o n d p o l y e t h y l e n e m e s h a n d f i n a l l y a n a n i o n i c m e m b r a n e ( I O N A C MA 3 4 7 5 ) w h i c h s e p a r a t e s t h e e l e c t r o d e c o m p a r t m e n t f r o m t h e s t a c k . T w o f l o w c h a n n e l s c u t i n t h e p l e x i g l a s s b l o c k p e r m i t a n u p w a r d f l o w o f r i n s e s o l u t i o n p a s t t h e e l e c t r o d e , r e m o v i n g a n y g a s s e s f o r m e d d u r i n g a r u n . 25 F i g u r e 9. Steady s t a t e c e l l p r e s s . 26 rinse out rubber plug n i c hi r o m e w i re Pt wire F i g u r e 10. Face view of P l e x i g l a s s e l e c t r o d e housing used i n the steady s t a t e p r o c e s s . 2 7 T h e b a c k o f t h e e l e c t r o d e s a r e i n c o n t a c t w i t h t w o 0 , 0 2 5 mm. p l a t i n u m w i r e s p a s s i n g t h r o u g h a 7 mm. d i a m e t e r r u b b e r p l u g , a n d s i l v e r w e l d e d t o a n i c h r o m e w i r e l i n k e d t o t h e p o w e r s u p p l y b y a 12 g a u g e c o p p e r w i r e . c ) E l e c t r i c a l S y s t e m B o t h c e l l s w e r e h o o k e d u p i n p a r a l l e l a n d p o w e r w a s f e d t o t h e c e l l s b y a 4 0 v o l t , 10 a m p . S o r e n s e n ( D C R 4 0 - 1 OA) p o w e r s u p p l y . A l l v o l t a g e s a r e m e a s u r e d d i r e c t l y u s i n g a K e i t h l e y 1 7 9 T R M S d i g i t a l m u l t i m e t e r . T h e t o t a l c u r r e n t d r a w n b y t h e s y s t e m a n d t h e i n d i v i d u a l c e l l s w a s m o n i t o r e d b y t a p p i n g t h r e e v e r y l o w r e s i s t a n c e s . T o m e a s u r e t h e p o t e n t i a l d r o p a c r o s s t h e s t a c k , t w o 1 0 2 mm. p l a t i n u m w i r e s w e r e i n s e r t e d i n t h e f i r s t a n d l a s t p o l y e t h y l e n e s p a c e r s . A n i c h r o m e w i r e , s i l v e r w e l d e d t o t h e P t . w i r e , l i n k e d i t t o t h e d i g i t a l m u l t i m e t e r . d ) F l o w S y s t e m -A C o l e P a l m e r p e r i s t a l t i c p u m p , h a v i n g a 7 0 1 5 M a s t e r f l e x p u m p h e a d , c i r c u l a t e d t h e f e e d s o l u t i o n t h r o u g h b o t h e l e c t r o d i a l y s i s c e l l s ; 6 , 3 5 mm. ( 1 / 4 i n c h ) p o l y e t h y l e n e t u b i n g w a s u s e d t h r o u g h o u t t h e c i r c u i t . F e e d s o l u t i o n f r o m a h o l d i n g t a n k w a s p u m p e d t o t h e b o t t o m o f c e l l A ( F i g . 6 ) ; l e a v i n g t h e t o p a s t w o s e p a r a t e s t r e a m s , t h e s o l u t i o n s 2 8 e n t e r e d t h e b a s e o f c e l l B i n t h e i r r e s p e c t i v e m a n i f o l d s , a n d l e f t a s t h e f i n a l b r i n e a n d d i a l y s a t e s t r e a m s . T h e s e b o t h f l o w e d i n t o a 0 , 5 l i t r e i n t e r m e d i a t e h o l d i n g t a n k w h e r e t h e y c o u l d b e s a m p l e d a n d t h e i r f l o w r a t e s d e t e r m i n e d v o l u m e t r i c a l l y . T h e r i n s e s o l u t i o n w a s c i r c u l a t e d b y a C o l e - P a l m e r M D X - 3 m a g n e t i c d r i v e c e n t r i f u g a l p u m p . T h e s o l u t i o n l e a v i n g t h e p u m p w a s s p l i t i n t o f o u r e q u a l s t r e a m s w h i c h w e r e t h e n f e d i n t o t h e i n d i v i d u a l e l e c t r o d e c o m p a r t m e n t s a n d r e t u r n e d t o a n 8 1 , 8 l i t r e h o l d i n g t a n k . 2 ) U N S T E A D Y S T A T E P R O C E S S I n t h e u n s t e a d y s t a t e p r o c e s s , t w o b a t t e r i e s o f f o u r c e l l s i n s e r i e s o p e r a t e o u t o f p h a s e b y 1 8 0 d e g r e e s w i t h r e s p e c t t o p o l a r i t y a n d f e e d f l o w ( F i g . 1 1 ) . D u r i n g a p r e d e t e r m i n e d c y c l e , s e t b y a n 1 4 . c h a n n e l t i m e r , o n e s e t o f c e l l s p r o d u c e d b r i n e a n d t h e o t h e r d i a l y s a t e . a ) E l e c t r o d i a l y s i s S t a c k A l l e i g h t c e l l s w e r e e q u i p p e d w i t h s e v e n 1 6 5 X 4 4 mm. m e m b r a n e a s s e m b l i e s , c o n s i s t i n g o f o n e c a t i o n i c m e m b r a n e ( I O N A C MC 3 1 4 2 ) , a W a t m w a n n o . 1 f i l t e r p a p e r a n d a n a n i o n i c m e m b r a n e ( I O N A C 3 1 4 8 ) . T h e s e p a i r s w e r e s a n d w i c h e d w i t h e i g h t dia lysate out V 5 - X — i feed CDC in V3 •CX-V1 8 M feed in - r x— V2 V 4 - X I -c oncen trate out M to F i g u r e 1 1 . F l o w d i a g r a m o f t h e u n s t e a d y s t a t e a p p a r a t u s . M = m a n o m e t e r , P = p e r i s t a l t i c p u m p , V = s o l e n o i d v a l v e 30 p o l y e t h y l e n e s p a c e r s b e t w e e n t w o 2 2 5 X 7 6 X 2 4 mm. p l e x i g l a s s b l o c k s h e l d b y f o u r m e t a l c l a m p s . T h e s p a c e r s s h o w n i n F i g . 8 A ) w e r e m a d e b y i n s e r t i n g a 1 6 5 X 4 4 mm. p o l y e t h y l e n e m e s h i n t o a 2 2 5 X 7 6 X 1 , 6 mm. s h e e t o f p o l y e t h y l e n e a n d p u n c h i n g o u t f o u r h o l e s i n t h e p r o p e r m a n i f o l d l o c a t i o n s . b ) E l e c t r o d e s T h e s a m e e n d p l a t e s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n w e r e u s e d , w i t h t h e e x c e p t i o n t h a t a p l u g w a s n o t p r e s e n t t o c r e a t e s e p a r a t e f l o w c h a n n e l s . T h e g r a p h i t e e l e c t r o d e s e m p l o y e d b y A b u - G o u k h ( 1 9 7 6 ) w e r e u s e d . c ) E l e c t r i c a l S y s t e m A l l c e l l s w e r e h o o k e d u p i n p a r a l l e l , t h e u p p e r a n d l o w e r b a t t e r i e s h a d t h e i r p o l a r i t i e s r e v e r s e d w i t h r e s p e c t t o e a c h o t h e r . P o w e r w a s f e d t o t h e p r o c e s s b y a 4 0 v o l t , 10 a m p . S o r e n s e n p o w e r s u p p l y , v i a a n e t w o r k o f 12 g a u g e 6 0 0 v o l t c o p p e r w i r e s . A l l v o l t a g e s w e r e m e a s u r e d d i r e c t l y u s i n g a d i g i t a l m u l t i m e t e r . T h e c u r r e n t c o n s u m p t i o n w a s m o n i t o r e d f o r b o t h s e t s o f c e l l s a n d t h e t o t a l p r o c e s s b y m e a s u r i n g t h e v o l t a g e d r o p a c r o s s a r e s i s t o r u s i n g a M o s l e y A u t o g r a p h 7 1 0 1 B s i n g l e p e n s t r i p c h a r t r e c o r d e r . 31 d ) F l o w S y s t e m 6 3 A C o l e P a l m e r p e r i s t a l t i c p u m p f i t t e d w i t h a 7 0 1 5 o r a 7 0 1 7 M a s t e r f l e x p u m p h e a d s u p p l i e d f e e d t o t h e p r o c e s s f r o m a n 8 1 . 8 l i t r e h o l d i n g t a n k . T h e d i a l y s a t e a n d b r i n e s t r e a m s p r o d u c e d i n t h e p r o c e s s w e r e r e t u r n e d t o a n i n t e r m e d i a t e t a n k w h e r e t h e y c o u l d b e s a m p l e d a n d t h e i r f l o w r a t e s d e t e r m i n e d v o l u m e t r i c a l l y . O n e q u a r t e r i n c h p o l y e t h y l e n e t u b i n g w a s u s e d t h r o u g h o u t t h e a p p a r a t u s . A l l c e l l s w e r e h o o k e d u p f r o m t o p t o b o t t o m i n t h e d i r e c t i o n o f i n p u t f e e d t o e l i m i n a t e a n y a c c u m u l a t i o n o f g a s s e s p r e s e n t i n t h e s o l u t i o n o r f o r m e d d u r i n g a r u n . A M a s t e r f l e x 7 0 1 7 p e r i s t a l t i c p u m p h e a d , d r i v e n b y a C e n t u r y v a r i a b l e s p e e d m o t o r , c i r c u l a t e d l i q u i d b a c k a n d f o r t h i n t h e s y s t e m . T h e e l e c t r o d e r i n s e s o l u t i o n w a s p u m p e d b y a C o l e P a l m e r p e r i s t a l t i c p u m p w i t h d u a l 7 0 1 8 M a s t e r f l e x p u m p h e a d s , e a c h s u p p l y i n g o n e s e t o f c e l l s . T h e p o s i t i v e a n d n e g a t i v e e l e c t r o d e c o m p a r t m e n t s h a d s e p a r a t e i n t a k e m a n i f o l d s t o e l i m i n a t e a n y e l e c t r i c a l l e a k a g e . S i x t e e n i n d i v i d u a l 6 , 3 5 mm. p o l y e t h y l e n e t u b e s r e t u r n e d t h e r i n s e s o l u t i o n t o a s e p a r a t e 8 1 , 8 1 l i t r e h o l d i n g t a n k . F i v e V a l c o r s o l e n o i d v a l v e s , s h o w n i n F i g . 1 2 , o p e r a t e d b y a c u s t o m b u i l t 8 s e q u e n c e , 14 c h a n n e l t i m e r , r e g u l a t e d t h e f l o w o f l i q u i d t h r o u g h o u t t h e p r o c e s s . 3 2 B E X P E R I M E N T A L 1) S T E A D Y S T A T E P R O C E S S T h e f e e d u s e d i n b o t h p r o c e s s e s w a s m a d e b y a d d i n g 1 6 3 , 6 g r a m s o f N a C l t o 8 1 , 8 l i t r e s o f d i s t i l l e d w a t e r , f o r m i n g a 2 . 0 g r a m / l i t r e s o d i u m c h l o r i d e s o l u t i o n . A m a k e u p s o l u t i o n o f f e r r o u s c h l o r i d e w a s p r e p a r e d b y d i s s o l v i n g a p p r o x i m a t e l y 4 , 3 g r a m s o f f e r r o u s c h l o r i d e i n 2 5 0 m i s . o f w a t e r ; 10 m i s . o f t h i s s o l u t i o n w a s a c i d i f i e d w i t h o n e m l . s u l p h u r i c a c i d a n d 1 m l . p h o s p h o r i c a c i d , a n d t i t r a t e d w i t h a 0 , 0 1 N s t a n d a r d p o t a s s i u m p e r m a n g a n a t e s o l u t i o n . T h e r e q u i r e d a m o u n t o f t h i s s o l u t i o n w a s a d d e d t o t h e 8 1 , 8 l i t r e s t o m a k e a 1 o r a 5 ppm f e r r o u s i o n s o l u t i o n . F l o w r a t e s w e r e s e t m a n u a l l y b e f o r e e a c h r u n b y m e a s u r i n g t h e t i m e r e q u i r e d t o f i l l a 6 0 c c v o l u m e t r i c f l a s k . B a s e d o n t h e a c t u a l c e l l c r o s s - s e c t i o n ( 7 , 9 4 s q u a r e c m . ) , 3 0 , 2 a n d 1 2 , 1 s e c o n d s w e r e n e e d e d t o f i l l t h e f l a s k a t v e l o c i t i e s o f 0 , 5 a n d 1 , 2 5 c m / s e c , r e s p e c t i v e l y . T w o m e r c u r y m a n o m e t e r s , s h o w n i n F i g . 6 , g i v e t h e b r i n e a n d t h e d i a l y s a t e s t r e a m p r e s s u r e d r o p s a c r o s s b o t h c e l l s . T h e f e e d a n d r i n s e s t r e a m s w e r e s a m p l e d a t t h e b e g i n n i n g o f e a c h r u n , a n d a l l f o u r s t r e a m s w e r e s a m p l e d a f t e r 2 a n d 2 0 h o u r s . T o d e t e r m i n e t h e s o d i u m c h l o r i d e c o n c e n t r a t i o n o f a s t r e a m , a 5 0 c c a l i q u o t w a s c o l l e c t e d i n a 1 0 0 c c b e a k e r a n d t e s t e d w i t h O r i o n 9 4 - 1 1 - A s o d i u m a n d 9 0 - 0 2 - 0 0 r e f e r e n c e e l e c t r o d e s . A l l m e t h o d s f o r r e d u c i n g c h a r g e a c c u m u l a t i o n o n 33 t h e s e e l e c t r o d e m e m b r a n e s w e r e u s e d , y e t t h e e l e c t r o d e s s t i l l s h o w e d s o m e d r i f t o v e r t h e 15 m i n u t e s r e q u i r e d t o d o t h e a n a l y s i s . I n o r d e r t o a c c o u n t f o r t h i s , t h e o r d e r i n w h i c h t h e s a m p l e s w e r e t e s t e d w a s n o t e d a n d a l i n e a r i n t e r p o l a t i o n b e t w e e n t h e i n i t i a l a n d f i n a l c a l i b r a t i o n s w a s u s e d t o d e t e r m i n e s o d i u m c o n c e n t r a t i o n s . A p r o g r a m , ( a p p e n d i x C ) , r e a d s t h e c a l i b r a t i o n a n d s a m p l e m e a s u r e m e n t s i n m i l l i v o l t s , c a l c u l a t e s t h e s o d i u m c h l o r i d e c o n c e n t r a t i o n o f a s a m p l e i n p p m , a n d p r o d u c e s s o d i u m a n d i r o n m a s s b a l a n c e s a n d s e p a r a t i o n f a c t o r s f o r a g i v e n t i m e . S e p a r a t e s a m p l e s o f t h e f e e d , b r i n e , a n d d i a l y s a t e s t r e a m s w e r e c o l l e c t e d i n 5 0 c c E r l e n m e y e r f l a s k s a n d t h e i r i r o n c o n c e n t r a t i o n d e t e r m i n e d b y c o l o r i m e t r y u s i n g a t h i o c y a n a t e i n d i c a t o r ; d e t a i l s o f t h i s m e t h o d c a n b e f o u n d i n V o g e l 1 9 6 2 , p p 7 8 6 - 7 . T h e p H o f e a c h s a m p l e w a s m e a s u r e d t o ± 0 . 0 0 1 p H u n i t s u s i n g a n O r i o n 9 1 - 0 2 p r e c i s i o n p H e l e c t r o d e a n d a 7 0 1 - A O r i o n p H m e t e r . C u r r e n t p a s s i n g t h r o u g h e a c h i n d i v i d u a l c e l l w a s m o n i t o r e d b y t a p p i n g a v e r y l o w r e s i s t a n c e ( a p p r o x . 0 . Q 9 O h m s . ) p l a c e d i n s e r i e s w i t h t h e c e l l s . U s i n g a d i g i t a l m u l t i m e t e r , t h i s v o l t a g e d r o p w a s m e a s u r e d a f t e r 2 a n d ' 2 0 h o u r s d u r i n g a r u n . B y m e a s u r i n g t h e v o l t a g e d r o p a c r o s s e a c h s t a c k , t h e i r r e s i s t a n c e s c o u l d b e d e t e r m i n e d a t 2 a n d 20 h o u r s . T o e s t i m a t e t h e . a m o u n t o f i r o n d e p o s i t e d o n t h e m e m b r a n e s d u r i n g a r u n , a p a i r o f t e s t m e m b r a n e s w e r e r e m o v e d 3 4 f r o m t h e c e n t r e o f c e l l B a f t e r e a c h 20 h o u r r u n a n d r e p l a c e d b y a f r e s h p a i r . A 7 8 , 4 X 4 1 , 5 mm. s e c t i o n i s c u t o u t o f e a c h m e m b r a n e a n d p l a c e d i n t o a b e a k e r c o n t a i n i n g 1 0 0 c c o f h o t ( 8 0 ° C . ) h y d r o c h l o r i c a c i d ( 1 0 % b y w t . ) f o r 10 m i n u t e s . T h e b e a k e r w a s t h e n c o o l e d t o r o o m t e m p e r a t u r e . A 5 c c a l i q u o t w a s t a k e n , d i l u t e d t o 2 5 c c , a n d i t s i r o n c o n t e n t d e t e r m i n e d b y c o l o r i m e t r y u s i n g a t h i o c y a n a t e i n d i c a t o r ( V o g e l 1 9 6 2 ) . A f t e r e a c h r u n , b o t h c e l l s w e r e d i s m a n t l e d , t h e i r m e m b r a n e s w a s h e d - i n d i l u t e H C 1 a n d s c r u b b e d w i t h a s o f t n y l o n b r u s h . C a t i o n i c m e m b r a n e s w e r e s o a k e d o v e r n i g h t i n a 0 . 1 M E D T A s o l u t i o n , t o r e m o v e a n y f e r r i c i o n p r e s e n t i n t h e m e m b r a n e s . A n d f i n a l l y , a l l f o u r a n i o n i c m e m b r a n e s s e p a r a t i n g t h e e l e c t r o d e s a n d s t a c k c o m p a r t m e n t s w e r e r e p l a c e d b y f r e s h o n e s . 2 ) U N S T E A D Y S T A T E P R O C E S S I n t h i s s e c t i o n a l l s o l u t i o n s w e r e p r e p a r e d , s a m p l e d a n d a n a l y s e d a s d e s c r i b e d a b o v e . A f t e r e a c h r u n o n e m e m b r a n e a s s e m b l y w a s r e m o v e d f r o m t h e c e n t r e o f c e l l s 3 a n d 7 , ( F i g . 1 1 ) , a n d b o t h r e p l a c e d b y a f r e s h p a i r . A 3 4 , 9 mm. d i a m e t e r c i r c u l a r s e c t i o n w a s c u t o u t o f e a c h u s e d p a i r . T h e f i l t e r p a p e r , a n d t h e a n i o n i c a n d c a t i o n i c m e m b r a n e s w e r e a l l a n a l y s e d s e p a r a t e l y a s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n . T h e c u r r e n t p a s s i n g t h r o u g h b o t h c e l l b a t t e r i e s w a s m e a s u r e d , f o r o n e c o m p l e t e c y c l e , a f t e r 2 a n d 2 0 h o u r s , b y t a p p i n g a r e s i s i s t o r i n s e r i e s w i t h e a c h o f t h e m a n d 3 5 r e c o r d i n g t h e p o t e n t i a l d i f f e r e n c e o n a s i n g l e p e n c h a r t r e c o r d e r . V o l t a g e t o t h e c e l l s w a s s e t a t 2 0 o r 3 0 v o l t s ( + / -0 , 0 2 v o l t s D . C . ) u s i n g a d i g i t a l m u l t i m e t e r . T h e c i r c u l a t i o n p u m p , e l e c t r o d e p o l a r i t y a n d s o l e n o i d v a l v e s w e r e a l l c o n t r o l l e d b y a c l o c k ; t h e c o m p l e t e c y c l e i s s h o w n i n F i g 1 2 , w h e r e 0 i n d i c a t e s a n o p e n v a l v e a n d X a c l o s e d o n e . A s u m m a r y o f t h e c y c l e t i m e s u s e d a t d i f f e r e n t l i q u i d v e l o c i t i e s c a n b e f o u n d i n T a b l e I . T A B L E I C y c l e t i m e u s e d a t d i f f e r e n t f l u i d v e l o c i t i e s ( u n s t e a d y s t a t e p r o c e s s ) V e l y P a u s e B o t . T o p F o r w . P a u s e R e v . ( c m / s e c ) ( s e c ) F e e d f e e d c i r c . ( s e c ) c i r c . ( s e c ) ( s e c ) ( s e c ) - ( s e c ) 1 2 , 4 1 , 2 5 4 5 t o 1 2 , 6 4 5 , 2 4 5 3 8 , 4 1 4 , 6 3 , 8 5 , 0 4 5 t o 3 , 2 1 9 , 2 4 5 1 3 , 6 4 , 2 A t r a c e r w a s u s e d t o f i n d t h e o p t i m u m c i r c u l a t i o n t i m e s ; o n e c c o f s a t u r a t e d N a C l s o l u t i o n w a s i n j e c t e d a t t h e e n t r a n c e o f a b a t t e r y a n d t h e c o n c e n t r a t i o n f r o n t m o n i t o r e d a t t h e e x i t b y t w o s i l v e r w i r e s i m b e d d e d i n a 1 2 . 7 mm. t u b e h o o k e d u p " t o a B e c k m a n S o l u m e t e r a n d t o a c h a r t r e c o r d e r . I n p u t f e e d t i m e s w e r e v a r i e d t o g i v e a d i s p l a c e m e n t o f 5 0 c c p e r b a t t e r y a t l i q u i d v e l o c i t i e s o f a p p r o x . 1 , 2 5 a n d 5 c m / s e c . 36 top cells bottom cells time inter-val item modeX. V1 V2 V3 V4 V5 Pump P Polari-ty t i pause X X X X 0 V + t2 B from bot 0 X X 0 X V + t3 D from top X 0 0 X X V + t4 c i rc. top—bot. X X X X O — + ts pause X X X X O V -te circ. bot.—top X X X X 0 — 0= open valve X = c los ed valve v = pump idle F i g u r e 12. F l o w c o n n e c t i o n s a n d v a l v e t i m i n g s e q u e n c e u s e d i n t h e u n s t e a d y s t a t e o p e r a t i o n . 3 7 F l o w r a t e s d u r i n g r e c i r c u l a t i o n w e r e s e t b y a d i r e c t c a l i b r a t i o n p e r f o r m e d o n t h e c i r c u l a t i n g p u m p . T h e a c t u a l c e l l c r o s s s e c t i o n b e i n g 3 , 1 6 s q u a r e c m . , f l o w r a t e s o f 3 , 9 5 a n d 1 5 , 7 8 c c / s e c w e r e n e e d e d a t v e l o c i t i e s o f 1 , 2 5 a n d 5 c m / s e c , r e s p e c t i v e l y . P r e s s u r e d r o p s w e r e m e a s u r e d f o r a l l f e e d a n d c i r c u l a t i o n s t e p s a t t h e b e g i n n i n g o f e a c h r u n , a n d a f t e r 2 a n d 2 0 h o u r s . A f t e r a r u n , 5 l i t r e s o f d i l u t e H C l w e r e c i r c u l a t e d t h r o u g h t h e c e l l s , w h i c h w e r e t h e n w a s h e d w i t h d i s t i l l e d w a t e r u n t i l t h e p H o f b o t h e n t r a n c e a n d e x i t s t r e a m s w e r e e q u a l . 3 8 V E X P E R I M E N T A L R E S U L T S A N D D I S C U S S I O N D u r i n g t h e c o u r s e o f t h i s w o r k 121 r u n s w e r e p e r f o r m e d . I n i t i a l r u n s w e r e n e e d e d t o d e t e r m i n e t h e o p e r a t i n g p a r a m e t e r s o f t h e u n s t e a d y s t a t e p r o c e s s a n d t o d e v e l o p a s u i t a b l e m e t h o d f o r m e a s u r i n g f o u l i n g . A t o t a l o f 4 0 r u n s w e r e p e r f o r m e d u s i n g t h i s p r o c e s s , o f w h i c h 15 w e r e s u f f i c i e n t l y a c c u r a t e f o r f u r t h e r a n a l y s i s . O u t o f 81 r u n s p e r f o r m e d u s i n g t h e s t e a d y s t a t e p r o c e s s , 2 6 w e r e s u i t a b l e f o r f u r t h e r a n a l y s i s . R e a s o n s f o r t h e r e j e c t i o n o f r u n s w e r e a s f o l l o w s : 1) U n s t e a d y s t a t e p r o c e s s i ) i m p r o p e r c y c l e t i m i n g i i ) p u m p f a i l u r e i i i ) c e l l l e a k a g e d u e t o f a u l t y a s s e m b l y 2 ) S t e a d y s t a t e p r o c e s s i ) l e a k a g e b e t w e e n c o m p a r t m e n t s , w h i c h l e d t o t h e n e e d f o r a new s p a c e r d e s i g n i i ) e r r o r s i n a s s e m b l i n g t h e m e m b r a n e s t a c k i i i ) f a u l t y s t r e a m c o n n e c t i o n s b e t w e e n s t a g e s A l l c o n t r o l l e d r u n s w e r e s e l e c t e d p r i o r t o a n y c o m p a r a t i v e a n a l y s i s b e t w e e n t h e m , e l i m i n a t i n g t h e p o s s i b i l i t y o f s e l e c t i n g s p e c i f i c r u n s t o s u i t t h e a r g u m e n t s a d v a n c e d i n t h i s w o r k . 3 9 A ) D E T E R M I N A T I O N O F A F O U L I N G P A R A M E T E R 1) L i m i t i n g C u r r e n t T h e v a l u e o f i l i m ( s e e C h a p t e r 3 ) c a n b e f o u n d b y p l o t t i n g t h e c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s o f a c e l l . A s C 1 — > 0 , a p o i n t o f i n f l e c t i o n o c c u r s i n t h e I v s V p l o t o n c e a l i m i t i n g c u r r e n t i s r e a c h e d . T h e c u r r e n t d r a w n b y t h e s t e a d y s t a t e c e l l s v s t h e a p p l i e d v o l t a g e h a s b e e n p l o t t e d f o r b o t h c e l l s ( F i g . 1 3 ) . T h e a v a i l a b l e 4 0 v o l t D . C . P o w e r s u p p l y c o u l d n o t p r o v i d e s u f f i c i e n t c u r r e n t t o r e a c h t h i s l i m i t a n d t h i s m e t h o d h a d t o b e d i s c o u n t e d a s a f o u l i n g m e a s u r e m e n t . 2 ) A . C . R e s i s t a n c e M e a s u r e m e n t s T h e d i r e c t m e a s u r e m e n t o f m e m b r a n e r e s i s t a n c e u s i n g a d i g i t a l m u l t i m e t e r a n d a s i g n a l g e n e r a t o r s e t a t 4 0 0 H z . , w a s a t t e m p t e d f o r b o t h p r o c e s s e s . I n t h e s t e a d y s t a t e r u n s , t h e A . C . r e s i s t a n c e o f t h e c e l l s w a s m e a s u r e d b e f o r e a n d a f t e r a 2 0 h o u r r u n . ' I n o r d e r t o e l i m i n a t e a n y p o l a r i z a t i o n r e s i s t a n c e s , a l s o d u e t o t h e n a t u r e o f t h e c i r c u i t , t h e A . C . m e a s u r e m e n t s h a d t o b e p e r f o r m e d w i t h o u t t h e p r e s e n c e o f a n y D . C . p o t e n t i a l . T h i s r e s t r i c t i o n d i d n o t a f f e c t r u n s w i t h o u t i r o n . A n a v e r a g e o f t h r e e r u n s p e r f o r m e d a t d i f f e r e n t v e l o c i t i e s g a v e t h e f o l l o w i n g ( c l e a n ) c e l l r e s i s t a n c e s : 4 0 t o t a l c e l l l I I l 1 1 1 0 200 400 600 c u r r e n t ( m A . ) F i g u r e 13. P l o t of the s teady s t a t e s t a c k v o l t a g e v s . the c u r r e n t consumpt ion f o r both s t a g e s , see T a b l e I I . 41 i ) F i r s t s t a g e ( A ) - 3 1 . 0 2 ± 5% O h m s . I i ) S e c o n d s t a g e ( B ) - 3 2 . 2 9 ± 5% O h m s . I n t e r r u p t i o n o f t h e d i r e c t c u r r e n t c a u s e d s u b s t a n t i a l l o s s e s o f i r o n o x i d e f r o m t h e d i a l y s a t e c h a n n e l s d u e t o t h e s h a r p d e c r e a s e i n p H a s f r e s h f e e d w a s p u m p e d t h r o u g h t h e s t a c k . S i n c e t h e l o s s o f i r o n i m p l i e d a p h y s i c a l C h a n g e i n t h e i r o n o x i d e f i l m , t h e m e a s u r e m e n t o f c e l l r e s i s t a n c e b y t h i s m e t h o d w a s f o u n d u n s u i t a b l e . 3 ) D i r e c t M e a s u r e m e n t o f I r o n D e p o s i t s T h e b e s t f o u l i n g p a r a m e t e r w a s t h o u g h t t o b e t h e d i r e c t m e a s u r e m e n t o f i r o n o x i d e d e p o s i t s o n a m e m b r a n e p a i r . I n t h e s t e a d y s t a t e p r o c e s s , a t e s t p a i r l o c a t e d a t t h e c e n t r e o f t h e s e c o n d s t a g e s t a c k w a s r e m o v e d i m m e d i a t e l y a f t e r e a c h 2 0 h o u r r u n a n d r e p l a c e d b y a s e t o f f r e s h m e m b r a n e s . B o t h m e m b r a n e s w e r e c u t i n h a l f a n d a n a l y z e d s e p a r a t e l y f o r i r o n d e p o s i t s a s d e s c r i b e d i n C h a p t e r I V . B ) P e r f o r m a n c e o f t h e S t e a d y a n d U n s t e a d y S t a t e P r o c e s s e s  1) V o l t a g e D r o p p e r C e l l P a i r a s a F u n c t i o n o f B u l k S o l u t i o n  R e s i s t a n c e I t h a s b e e n r e p o r t e d t h a t t h e b u l k s o l u t i o n r e s i s t a n c e i n t h e d i a l y s a t e c h a n n e l h a s a n e t e f f e c t o n t h e o b s e r v e d v o l t a g e d r o p p e r c e l l p a i r ( S e k o 1 9 6 2 ) . S i n c e t h e s p e c i f i c 4 2 c o n d u c t i v i t y o f t h e d i a l y s a t e a n d b r i n e s t r e a m s w e r e w i t h i n t h e s a m e o r d e r o f m a g n i t u d e i n o u r e x p e r i m e n t , t h e v o l t a g e d r o p p e r c e l l p a i r v e r s u s i d ( 1 / K d + 1 / K b ) w a s p l o t t e d f o r b o t h s t a g e s , s e e F i g s . 14 a n d 1 5 . w h e r e ; V / p a i r = o b s e r v e d s t a c k v o l t a g e p e r n u m b e r o f c e l l p a i r s ( 6 . 5 p a i r s ) i n u n i t s o f V o l t s / p a i r , • i = c u r r e n t d e n s i t y ( A m p s / c m 2 ) , K d , b = s p e c i f i c c o n d u c t i v i t y o f t h e b u l k s o l u t i o n i n t h e d i a l y s a t e a n d b r i n e c h a n n e l s r e s p e c t i v e l y ( O h m s . ' 1 c m . - 1 ) , d = d i s t a n c e b e t w e e n m e m b r a n e s ( 0 . 1 5 9 c m . ) . I n t h e w o r k d o n e b y S e k o , a 0 , 0 7 5 c m . s p a c e r w a s u s e d ; t a k i n g t h i s i n t o a c c o u n t , t h e v a l u e o f ( i X 0 , 0 7 5 / R d ) w a s p l o t t e d a n d i s a l s o s h o w n i n F i g s . 14 a n d 1 5 . I n t h e u n s t e a d y s t a t e p r o c e s s , t w o m e m b r a n e a s s e m b l i e s e a c h l o c a t e d a t t h e c e n t e r o f c e l l s 3 a n d 7 ( F i g . 1 1 ) w e r e r e m o v e d a n d a n a l y z e d s e p a r a t e l y , a s p r e v i o u s l y d e s c r i b e d ( C h a p t e r I V ) a f t e r e a c h 2 0 h o u r r u n . 2 ) C a l c u l a t i o n o f S e p a r a t i o n F a c t o r s a n d I o n i c S e l e c t i v i t i e s I n b o t h p r o c e s s e s , t h e s e p a r a t i o n f a c t o r f o r s o d i u m c h l o r i d e i s d e s c r i b e d a s f o l l o w s : N s = C b / C d ( 7 ) 4 3 w h e r e ; N s = s e p a r a t i o n f a c t o r f o r N a C l C b = N a C l c o n c e n t r a t i o n i n b r i n e s t r e a m ( e q u v . / l . ) C d = N a C l c o n c e n t r a t i o n i n d i a l y s a t e s t r e a m ( e q u v . / l . ) 3 ) P l o t o f t h e A c t u a l C e l l P a i r R e s i s t a n c e a s a F u n c t i o n o f  S t a c k V o l t a g e K n o w i n g t h e r e s i s t a n c e s o f t h e d i a l y s a t e a n d b r i n e s o l u t i o n s , t h e c o m b i n e d m e m b r a n e p l u s p o l a r i z a t i o n r e s i s t a n c e c a n b e f o u n d , s i n c e : R s t a c k = R c + R a + R d + R b + R p ( 8 ) w h e r e : R s t a c k = t o t a l s t a c k r e s i s t a n c e ( O h m s ) R c , a = r e s i s t a n c e o f t h e c a t i o n a n d a n i o n s e l e c t i v e m e m b r a n e s p r o p e r ( O h m s ) R d , b = r e s i s t a n c e o f t h e )H1 d i a l y s a t e a n d b r i n e c h a n n e l s p r o p e r ( O h m s ) R p = r e s i s t a n c e d u e t o p o l a r i z a t i o n ( O h m s ) T h e s u m o f ( R a + R c • + R p ) w a s c a l c u l a t e d a s d e s c r i b e d i n A p p e n d i x A a n d p l o t t e d a g a i n s t V , t h e s t a c k v o l t a g e a c r o s s t h e f i r s t s t a g e , c e l l A ( F i g s . 16 a n d 1 7 ) , a n d t h e s e c o n d s t a g e , c e l l B ( F i g s . 18 a n d 1 9 ) , f o r r u n s w i t h a n d w i t h o u t i r o n . r i i 1 i i 0 0,2 0,4 0,6 0,8 1,0 vol tage d r o p in b u l k so ln . ( v o l t s ) F i g u r e 1 4 . P l o t o f t h e f i r s t s t a g e v o l t a g e d r o p p e r c e l l p a i r v s . t h e b u l k s o l u t i o n v o l t a g e d r o p p e r c h a n n e l , f o r a l l 2 h o u r s t e a d y s t a t e r e a d i n g s , s e e T a b l e I I I ( S e k o ' s w o r k i s r e p r e s e n t e d b y t h e s o l i d l i n e ) U1 0,2 0,4 0,6 0,8 1,0 1,2 V o l t a g e d r o p i n b u l k s o l u t i o n ( v o l t s ) F i g u r e 1 5 . P l o t o f t h e s e c o n d s t a g e v o l t a g e d r o p p e r c e l l p a i r v s . t h e b u l k s o l u t i o n v o l t a g e d r o p p e r c h a n n e l , f o r a l l 2 h o u r s t e a d y s t a t e r e a d i n g s , s e e T a b l e I V ( S e k o ' s w o r k i s r e p r e s e n t e d b y t h e s o l i d l i n e ) . 46 80-1 Stack v o l t a g e ( v o l t s D.C.) F i g u r e 1 6 . P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e f i r s t s t a g e o f t h e s t e a d y s t a t e p r o c e s s , a l l r u n s w i t h o u t f o u l i n g , s e e T a b l e V . 47 F i g u r e 1 7 . P l o t o f ( R a + R c + R p ) v s . t h e s t a c k v o l t a g e , f o r t h e f i r s t s t a g e o f t h e s t e a d y s t a t e p r o c e s s , a l l r u n s w i t h f o u l i n g , s e e T a b l e V . 48 • 0 ,5 c m / s e c + 1,25 cm / s e c I l 10 2 0 3 0 S t a c k v o l t a g e ( v o l t s D . C . ) F i g u r e 18. P l o t of (Ra+Rc+Rp) vs. the stack v o l t a g e , f o r the second stage of the steady s t a t e p r o c e s s , runs without f o u l i n g , see Table V I . 49 • / • / / • • / IS / • / • / ^ / + + + • 0 ,5 cm/sec + 1 , 2 5 cm/sec ' = r 1 r 0 10 2 0 30 S t a c k v o l t a g e ( v o l t s D . C . ) F i g u r e 19. P l o t of (Ra+Rc+Rp) vs. the stack v o l t a g e , f o r the second stage of the steady s t a t e p r o c e s s , a l l runs with f o u l i n g , see Table VI. 5 0 4 ) P r e s s u r e D r o p s T h e l o g o f t h e t o t a l p r e s s u r e d r o p w a s p l o t t e d a g a i n s t t h e l o g o f f l u i d v e l o c i t y f o r b o t h p r o c e s s e s ( F i g s 2 0 t o 2 2 ) . T h e p l o t o b t a i n e d f r o m t h e 2 h o u r r e a d i n g s o f t h e s t e a d y s t a t e r u n s g a v e a s l o p e o f 1 , 5 2 6 , w h i l e t h e c o m b i n e d 2 a n d 2 0 h o u r r u n s f o r t h e u n s t e a d y s t a t e p r o c e s s g a v e a s l o p e o f 1 , 5 7 8 . T h e s e v a l u e s a r e c o n s i s t a n t w i t h t h a t o b t a i n e d b y S e k o ( 1 9 6 2 ) f o r t u r b u l e n t f l o w r e g i m e s i n 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 . ( n o t e : T h e p l o t i n S e k o , ( 1 9 6 2 ) , h a s a s l o p e o f 1 , 4 0 , b u t a s l o p e o f 1 , 5 1 i s r e p o r t e d ) . W h e n t h e 2 0 h o u r p r e s s u r e d r o p s o b t a i n e d f r o m f o u l e d r u n s a r e p l o t t e d a g a i n s t f l u i d v e l o c i t y , a s l i g h t i n c r e a s e i n t h e o v e r a l l p r e s s u r e d r o p i s n o t i c e a b l e Q u e t o i r o n o x i d e a c c u m u l a t i o n i n t h e c h a n n e l s . T h i s i n c r e a s e w a s c o n s i d e r a b l y g r e a t e r i n t h e d i a l y s a t e c h a n n e l o f t h e s t e a d y s t a t e p r o c e s s , a s s e e n i n T a b l e s 2 a n d 3 , w h i l e n o s i g n i f i c a n t d i f f e r e n c e c o u l d b e n o t i c e d f o r t h e u n s t e a d y s t a t e r u n s ' . 5 ) P o w e r R e q u i r e m e n t s f o r S e p a r a t i o n T h e s e p a r a t i o n f a c t o r , N s , w a s p l o t t e d a g a i n s t t h e p o w e r r e q u i r e d ( j o u l e s / l i t r e p e r c e l l ) t o p e r f o r m t h e s e p a r a t i o n f o r b o t h p r o c e s s e s ( F i g s 2 3 , 2 4 ) . N o d i r e c t r e l a t i o n b e t w e e n t h e p o w e r r e q u i r e d a n d t h e s e p a r a t i o n f a c t o r c o u l d b e o b t a i n e d f r o m t h e c o m b i n e d 2 a n d 2 0 h o u r r u n s . 51 Figure 20. P l o t of the d i a l y s a t e and b r i n e channel pressure drops vs. f l u i d v e l o c i t y f o r a l l steady s t a t e runs without f o u l i n g , see Tables VII and V I I I . 52 F l u i d v e l o c i t y (cm/sec) F i g u r e 2 1 . P l o t o f t h e d i a l y s a t e a n d b r i n e c h a n n e l p r e s s u r e d r o p s v s . f l u i d v e l o c i t y f o r a l l s t e a d y s t a t e r u n s w i t h f o u l i n g , s e e T a b l e s V I I a n d V I I I . 53 F i g u r e 2 2 . P l o t o f t h e d i a l y s a t e a n d b r i n e c h a n n e l p r e s s u r e d r o p s v s . f l u i d - v e l o c i t y f o r a l l u n s t e a d y s t a t e r u n s , s e e T a b l e s I X a n d X . 5 4 4 5 S e p a r a t i o n f a c t o r N s ( - ) F i g u r e 2 3 . P l o t o f t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d v s . t h e s e p a r a t i o n f a c t o r N s , f o r a l l s t e a d y s t a t e r u n s , s e e T a b l e X I . 30000. o X rH o U 0) a, <D u -P o CM 1 (TJ m QJ rH o 5000. in •P c (IJ g 0) iH •H QJ 2000-1 10 4 en 10 20 50 1 00 2 00 S e p a r a t i o n f a c t o r Ns (-) F i g u r e 2 4 . P l o t o f t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d v s . t h e s e p a r a t i o n f a c t o r N s , f o r a l l u n s t e a d y s t a t e r u n s , s e e T a b l e X I I . 5 6 H o w e v e r a p l o t o f d i a l y s a t e c o n c e n t r a t i o n v e r s u s p o w e r r e q u i r e d ( J o u l e s / l i t r e p e r - c e l l ) , f o r a l l 1 , 2 5 c m . / s e c . r u n s a t 2 h o u r s , s h o w e d t h a t t h e p o w e r c o n s u m p t i o n i n b o t h p r o c e s s e s i s c l e a r l y d e p e n d e n t o n d i a l y s a t e c o n c e n t r a t i o n ( F i g . 2 5 ) . A s m o o t h c u r v e d r a w n b e t w e e n t h e s t e a d y a n d u n s t e a d y s t a t e d a t a , i s a s y m p t o t i c a t C d = 2 , 0 0 0 p p m a s t h e p o w e r - - > 0 , a n d t e n d s t o w a r d s i n f i n i t y a s t h e d i a l y s a t e c o n c e n t r a t i o n t e n d s t o z e r o s i n c e t h e s p e c i f i c c o n d u c t i v i t y K ( O h m s - 1 c m . - 1 ) o f a s o l u t i o n a t l o w d i l u t i o n i s g i v e n b y : 1 / K = k 1 1 / C (9) k 1 = c o n s t a n t C = s o l u t i o n c o n c e n t r a t i o n ( e q u i v . / l i t r e ) 6 ) D e c r e a s e s i n S e p a r a t i o n d u e t o F o u l i n g T h e p e r c e n t d r o p i n t h e s e p a r a t i o n f a c t o r , N s , o v e r a n 18 h o u r p e r i o d w a s p l o t t e d a g a i n s t t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s o v e r t h e d u r a t i o n o f a r u n f o r t h e s t e a d y s t a t e ( F i g . 2 6 ) a n d u n s t e a d y s t a t e p r o c e s s e s ( F i g . 2 7 ) . F i g u r e 2 6 ( s t e a d y s t a t e p r o c e s s ) , h a s t w o s e p a r a t e l i n e s a t 1 a n d 5 p p m i r o n d u e t o t h e w a r p i n g o f m e m b r a n e s . T h i s c a u s e d " c h a n n e l i n g i n t h e c o m p a r t m e n t s a n d c r e a t e d z o n e s o f l o w e r v e l o c i t y w h i c h a r e p r o n e t o f o u l b e f o r e o t h e r z o n e s . T h e u n e v e n d i s t r i b u t i o n o f d e p o s i t s d o e s n o t r e d u c e t h e Power r e q u i r e m e n t s ( j o u l e s / l i t r e per c e l l ) F i g u r e 25. P l o t o f the d i a l y s a t e c o n c e n t r a t i o n v s . the power r e q u i r e m e n t s per l i t r e o f d i a l y s a t e , f o r a l l unsteady s t a t e runs a t 1,25 cm./sec. f l u i d v e l o c i t y , see T a b l e X I I I . 5 8 I T x • 1 ppm iron x 5 ppm iron 1.0 2.0 3,0 Amount o f i r o n accumulated on the t e s t p a i r (mg.) F i g u r e 2 6 . P l o t o f t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r o v e r a n 1 8 h o u r p e r i o d v s . t h e a m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r o v e r t h e 2 0 h o u r r u n , f o r a l l s t e a d y s t a t e r u n s w i t h f o u l i n g , s e e T a b l e X I V . 59 A m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r s ( a v e r a g e f r o m c e l l s 3 a n d 7) ( m g . ) Figure 2 7 . P l o t of the per cent drop i n separation f a c t o r over an 18 hour p e r i o d vs. the amount of i r o n accumulated on the t e s t p a i r over the 2 0 hour run , f o r a l l unsteady s t a t e runs with f o u l i n g , see Table XV. 60 c u r r e n t e f f i c i e n c y t o a g r e a t e x t e n t b u t d o e s s h o w h i g h v a l u e s o f i r o n a c c u m u l a t i o n . M o s t u n s t e a d y s t a t e r u n s c o u l d b e g r o u p e d u n d e r o n e l i n e , a s s e e n i n F i g . 2 7 . H o w e v e r , r u n n u m b e r 34 s h o w e d a d e c r e a s e i n s e p a r a t i o n o v e r t h e 18 h o u r p e r i o d , a n d r u n n u m b e r 44 s h o w e d a s m a l l e r d e c r e a s e i n N s t h a n w o u l d b e e x p e c t e d b a s e d o n t h e t o t a l i r o n a c c u m u l a t e d f r o m b o t h m e t h o d s o f c a l c u l a t i o n d e s c r i b e d i n t h e n e x t s e c t i o n . S i n c e t h e p e r c e n t d r o p i n N s i s c a l c u l a t e d f r o m f o u r s e p a r a t e s o d i u m d e t e r m i n a t i o n s a n d t h e s t a c k w a s n o t c o m p l e t e l y c l e a n a f t e r t h e a c i d r i n s e , t h e d i s c r e p a n c i e s i n r u n s 34 a n d 4 4 c a n b e a t t r i b u t e d t o e x p e r i m e n t a l e r r o r s . 7 ) M a s s B a l a n c e s o n I r o n a n d S o d i u m P l o t s o f t h e a m o u n t o f i r o n l o s t i n t h e f e e d s t r e a m o v e r a 2 0 h o u r p e r i o d v e r s u s t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s w e r e o b t a i n e d f o r b o t h p r o c e s s e s ( F i g s 2 8 , 2 9 ) . T h e s t e a d y s t a t e r e s u l t s c o u l d b e g r o u p e d u n d e r o n e l i n e h a v i n g t h e a s l o p e o f 4 . 4 9 ( - ) a n d i n t e r c e p t o f 3 1 . 8 ( m g . ) , a s s e e n i n F i g u r e 2 8 . H o w e v e r t h e u n s t e a d y s t a t e d a t a w a s f a i r l y s c a t t e r e d . T h e e x p l a n a t i o n f o r t h e h i g h d e g r e e o f s c a t t e r i n g e x i s t s i n t h e d i f f e r e n t p r e p a r a t i o n m e t h o d s u s e d b e f o r e e a c h r u n . I n t h e s t e a d y s t a t e p r o c e s s , b o t h s t a c k s w e r e d i s a s s e m b l e d a n d a l l m e m b r a n e s ( e x c e p t t h e t e s t p a i r ) r e p l a c e d by- a s e t w h i c h 61 I r o n a c c u m u l a t i o n b a s e d o n m e m b r a n e s ( m g . ) F i g u r e 2 8 . P l o t o f t h e a m o u n t o f i r o n l o s t i n t h e f e e d v s . t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s d u r i n g t h e 2 0 h o u r r u n , f o r a l l s t e a d y s t a t e r u n s , s e e T a b l e X V I . A m o u n t o f i r o n l o s t i n t h e f e e d ( m g . ) Cb < hrj C cn H -i-f • i Q H - C 3 rt i-S rt to 3" rt VD CD O • rt to cu O M H 0 tr 0) rt 3 0 0 C Hi rt rt O C i-i 3 CD CU o c 3 rt l-i Hi H-O i-i n o 3 CD h-1 DJ M O O O Ml c c cn c It H O CD CD 3 PJ rt •< P J O cn to O rt rt 3 CU H-rt rt 3 (0 3" CD i-i C 3 cn rt 3 n> fD 3 i-h tr 0 i-i fD fu Cb 3 CD cn H I-! O 3 CU O O d I—• OJ rt H -O 3 tr fu cn CD Di o 3 rt 3* CD 3 CD 3 tr r i CU 3 CD cn 3 03 3 9 6 3 h a d b e e n t r e a t e d , a s f o l l o w s : t h e a n i o n i c m e m b r a n e s w e r e s c r u b b e d w i t h d i l u t e H C 1 w h i l e t h e c a t i o n s e l e c t i v e m e m b r a n e s w e r e s o a k e d o v e r n i g h t i n a 0 , 1 M E D T A s o l u t i o n . T h e o n l y p r e p a r a t i o n d o n e o n t h e u n s t e a d y s t a t e p r o c e s s w a s a n a c i d w a s h w i t h 2 l i t r e s o f 6 N H C 1 , s i n c e t h e m a n i p u l a t i o n o f 56 m e m b r a n e a s s e m b l i e s w o u l d h a v e b e e n i m p r a c t i c a l . T h i s i s w h y m o s t r u n s a p p e a r t o h a v e m o r e i r o n a c c u m u l a t i o n o n t h e m e m b r a n e s t h a n l o s t i n t h e f e e d s t r e a m o v e r t h e 2 0 h o u r r u n . 8 ) V i s u a l E x a m i n a t i o n o f F o u l i n g D e p o s i t s R e d d i s h - b r o w n d e p o s i t s w e r e i n d e n t i f i e d o n t h e t e s t m e m b r a n e s i n a l l s t e a d y a n d u n s t e a d y s t a t e r u n s h a v i n g i r o n i n t h e i r f e e d s t r e a m . I t c o u l d r e a d i l y b e s e e n t h a t a l l r u n s a t 5 ppm l e v e l s h a d c o n s i d e r a b l y m o r e i r o n a c c u m u l a t i o n o n t h e m t h a n t h o s e a t 1 ppm l e v e l s . T h i s h a s b e e n i l l u s t r a t e d f o r f o u r u n s t e a d y s t a t e r u n s w h o s e t e s t m e m b r a n e s h a v e b e e n p h o t o g r a p h e d ( F i g u r e s 3 0 , 3 1 ) . A l l f i g u r e s w e r e d i v i d e d i n t o 9 s e p a r a t e s e c t i o n s a s f o l l o w s : U p p e r l e f t , f i l t e r p a p e r f a c i n g t h e c a t i o n s e l e c t i v e m e m b r a n e U p p e r c e n t e r , a c l e a n f i l t e r p a p e r , U p p e r r i g h t , f i l t e r p a p e r f a c i n g t h e a n i o n s e l e c t i v e m e m b r a n e C e n t e r l e f t , i n s i d e f a c e o f t h e c a t i o n s e l e c t i v e m e m b r a n e , C e n t e r , a c l e a n c a t i o n s e l e c t i v e m e m b r a n e , C e n t e r r i g h t , o u t s i d e f a c e o f t h e c a t i o n s e l e c t i v e m e m b r a n e , 64 L o w e r l e f t , o u t s i d e f a c e o f a a n i o n s e l e c t i v e m e m b r a n e , L o w e r c e n t e r , a c l e a n a n i o n s e l e c t i v e m e m b r a n e , L o w e r r i g h t , i n s i d e f a c e o f t h e a n i o n s e l e c t i v e m e m b r a n e . F r o m F i g u r e s 3 1 A a n d 3 1 B , we c a n e a s i l y s e e t h a t v o l t a g e w a s a v e r y i m p o r t a n t p a r a m e t e r i n t h e a c c u m u l a t i o n o f i r o n o n t h e t e s t p a i r , a n d t h a t s o m e i r o n d i d d e p o s i t o n t h e f i l t e r p a p e r i n s i d e t h e m e m b r a n e a s s e m b l y . T h e p r e s e n c e o f i r o n o n t h e f i l t e r p a p e r w a s a l s o v e r i f i e d b y c o l o m e t r i c a n a l y s i s . N o i r o n c o u l d b e s e e n o n t h e t e s t m e m b r a n e s a t 0 p p m i r o n f e e d c o n c e n t r a t i o n s . A l t h o u g h i t i s n o t c l e a r l y e v i d e n t f r o m F i g u r e s 3 0 t o 3 1 , t h e i r o n c o n c e n t r a t i o n i n t h e f e e d h a d a m a r k e d e f f e c t o n t h e a c c u m u l a t i o n o f i r o n o n t h e t e s t m e m b r a n e s . I n t h e s t e a d y s t a t e r u n s , t h e v a r i a t i o n i n f l u i d v e l o c i t y w a s f a i r l y s m a l l ( 0 , 5 a n d 1 , 2 5 c m / s e c ) , a n d h a d v e r y l i t t l e e f f e c t . o n t h e a m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t m e m b r a n e s c o m p a r e d t o t h e u n s t e a d y s t a t e r u n s w h e r e t h e v e l o c i t i e s o f 1 , 2 5 a n d 5 , 0 c m / s e c h a d a g r e a t e r e f f e c t . I n t h e s t e a d y s t a t e p r o c e s s , t h e d i s t r i b u t i o n o f i r o n w a s u n e v e n ( F i g s . 3 2 A , 3 2 B a n d 3 3 A ) a s l a r g e r a m o u n t s o f i r o n a r e s e e n t o h a v e a c c u m u l a t e d w h e r e t h e f l u i d v e l o c i t y w a s l o w e s t ( F i g 3 2 A ) , i e . a t o p p o s i t e e n t r y p o r t s , a n d t h e f i l m s e e m s t o h a v e f l a k e d o f f a t c e r t a i n p o i n t s ( F i g . 3 2 A ) . 65 T h e d i f f e r e n c e b e t w e e n b o t h p r o c e s s e s c a n b e s e e n i n F i g . 3 3 A . I n t h i s p h o t o g r a p h , t w o t e s t m e m b r a n e s f r o m s e p a r a t e u n s t e a d y s t a t e r u n s ( l e f t ) w e r e c o m p a r e d w i t h t h o s e o f a s t e a d y s t a t e p r o c e s s ( r i g h t ) , t h e u n e v e n f i l m i n t h e s t e a d y s t a t e p r o c e s s w a s e a s i l y n o t i c e a b l e . T h e p r e s e n c e o f c u r r e n t s h a d o w s o r i g i n a t i n g f r o m t h e s p a c e r c a n b e s e e n i n F i g . 3 3 B . S u c h s h a d o w s w e r e t a k e n i n t o a c c o u n t i n d e t e r m i n i n g t h e a c t u a l c e l l a r e a ( a n i o n i c m e m b r a n e f r o m a n u n s t e a d y - s t a t e r u n a t 3 0 V . 1 , 2 5 c m / s e c 5 ppm F e 2 * ) . 6 6 2 0 1 2 5 0 (A) I I I I I I I I I F i g u r e 30. I r o n o x i d e f i l m on a t e s t membrane p a i r i n the unsteady s t a t e p r o c e s s a t 20 v o l t s , 1,25 cm/sec, 0 ppm i r o n i n f e e d ( A ) , and at 30 v o l t s , 5,0 cm/sec, 1 ppm i r o n i n feed ( B ) . (1 d i v i s i o n = 1mm.) F i g u r e 31. I r o n o x i d e f i l m on a t e s t membrane p a i r i n the unsteady s t a t e p r o c e s s at 20 v o l t s , 1,25 cm/sec, 5 ppm i r o n i n f e e d ( A ) , and at 30 v o l t s , 1,25 cm/sec, 5 ppm i r o n i n fee d ( B ) . (1 d i v i s i o n = 1mm.) A B Figure 32. Iron oxide d e p o s i t s on a c a t i o n s e l e c t i v e membrane (A) (20 v o l t s , 0 , 5 cm/sec,5 ppm i r o n i n feed), and an an-ion s e l e c t i v e membrane (B) (30 v o l t s , 0 , 5 cm/sec,1 ppm i r o n i n feed) (steady s t a t e p r o c e s s ) . 6 9 (B) F i g u r e 33. I r o n a c c u m u l a t i o n i n the stea d y s t a t e p r o c e s s , two membranes on the l e f t s i d e of ( A ) , and the unsteady s t a t e p r o c e s s two membranes on the r i g h t s i d e of ( A ) . C l o s e u p of a f o u l e d a n i o n i c membrane(B) ( 1 d i v i s i o n = 1mm) 7 0 C S U M M A R Y A s e x p e c t e d , t h e s e p a r a t i o n f a c t o r , N s , i n c r e a s e d w i t h i n c r e a s i n g v o l t a g e , a n d d e c r e a s e d w i t h i n c r e a s i n g v e l o c i t y . T h e e f f e c t s o f p o l a r i z a t i o n w e r e a l s o o b s e r v e d i n t h e s t e a d y s t a t e r u n s ( F i g s . 1 4 , 1 5 ) . F o r a g i v e n s o l u t i o n v o l t a g e d r o p , t h e v o l t a g e d r o p p e r c e l l p a i r w a s g r e a t e r a t l o w e r v e l o c i t i e s ; t h i s e f f e c t w a s a t t r i b u t e d t o p o l a r i z a t i o n w h i c h w a s p r o m i n e n t a t l o w e r f l u i d v e l o c i t i e s . P o l a r i z a t i o n w a s a l s o g r e a t e r a t l o w e r d i a l y s a t e c o n c e n t r a t i o n s . T h i s c a n b e s e e n b y c o m p a r i n g t h e v a l u e s o f ( R a + R c + R p ) a t a g i v e n v e l o c i t y f o r t h e f i r s t s t a g e w i t h t h o s e o f t h e s e c o n d s t a g e . T h e d i f f e r e n c e i n p H b e t w e e n t h e d i a l y s a t e a n d b r i n e s t r e a m s i n d i c a t e s t h e p r e s e n c e o f w a t e r s p l i t t i n g d u e t o p o l a r i z a t i o n ( T a b l e s X V I I I , X I X ) . F o r s o m e i n i t i a l s t e a d y s t a t e r u n s w i t h o u t t h e p r e s e n c e o f i r o n , t h e p H o f t h e b u l k s o l u t i o n s h o w e d a s u b s t a n t i a l i n c r e a s e w i t h t i m e , w h i l e t h e p H o f t h e d i a l y s a t e s t r e a m w a s l o w e r t h a n t h a t o f t h e c o n c e n t r a t e d s t r e a m . T h i s b e h a v i o u r w a s a t t r i b u t e d t o i m p r o p e r m a n i f o l d d e s i g n _ w h i c h d i d n o t p r o v i d e a n e q u a l f l o w r a t e t o t h e c e l l c o m p a r t m e n t s a d j a c e n t t o t h e e l e c t r o d e s . I n v e r t i n g t h e e l e c t r o d e p o l a r i t y s o l v e d t h i s p r o b l e m ( n . b . t h i s w a s t h e c a s e f o r a l l r u n s h a v i n g a n u m b e r g r e a t e r t h a n 7 5 ) . T h e s e r e s u l t s s t e m f r o m t h e f a c t t h a t i n a c l e a n s y s t e m t h e v a l u e o f R p i s t h e o n l y f a c t o r t h a t c a n c h a n g e t h e 71 r e s i s t a n c e o f t h e c e l l p a i r a s a w h o l e . T h e e f f e c t s o f v o l t a g e o n p o l a r i z a t i o n c a n a l s o b e s e e n i n F i g u r e s 16 t o 1 9 , w h e r e a n i n c r e a s e i n v o l t a g e c a u s e d a s u b s t a n t i a l i n c r e a s e i n t h e p a r a m e t e r ( R a + R c + R p ) a t a g i v e n v e l o c i t y . H e n c e , i n c r e a s e s i n v o l t a g e , a n d d e c r e a s e s i n v e l o c i t y a n d d i a l y s a t e c o n c e n t r a t i o n c a u s e i n c r e a s e d p o l a r i z a t i o n a n d w a t e r -s p l i t t i n g . F o r m o s t r u n s , t h e p H o f t h e d i a l y s a t e s t r e a m w a s f o u n d t o b e h i g h e r t h a n t h a t o f t h e c o n c e n t r a t e s t r e a m . T h i s i s i n a g r e e m e n t w i t h t h e m o d e l d i s c u s s e d i n C h a p t e r I V ; a t t h e m e m b r a n e i n t e r f a c e s o p p o s i t e t h e d i a l y s a t e s t r e a m , t h e b o u n d a r y l a y e r s , £> , b e c o m e d i l u t e d i n c o n c e n t r a t i o n . D u e t o t h e l a c k o f N a + a n d C I " i o n s i n t h i s l a y e r , h y d r o x y l a n d h y d r o n i u m i o n s m u s t c a r r y s o m e p a r t o f t h e c h a r g e , h e n c e w a t e r - s p l i t t i n g o c c u r s , c a u s i n g p H i n t h e t w o s t r e a m s t o d i f f e r . I n m o s t s t e a d y s t a t e r u n s , t h e p r e s s u r e d r o p w a s f o u n d t o i n c r e a s e w i t h t i m e w h e n f o u l i n g o c c u r r e d , t h e i n c r e a s e i n p r e s s u r e d r o p i n t h e d i a l y s a t e s t r e a m b e i n g l a r g e r t h a n t h a t o f t h e c o n c e n t r a t e s t r e a m d u e t o t h e p H d i f f e r e n c e b e t w e e n t h e s t r e a m s ( T a b l e s V I I I , I X a n d X ) . T h e s e d i f f e r e n t p r e s s u r e d r o p s w e r e n o t o b s e r v e d i n t h e u n s t e a d y s t a t e p r o c e s s w h e r e a p l u g o f l i q u i d w a s c o n s t a n t l y r e c i r c u l a t e d b e t w e e n t h e t o p a n d b o t t o m s t a c k s . T h e s o l u t i o n i n t h e b o u n d a r y l a y e r s w a s n o t r e c i r c u l a t e d , c a u s i n g s u b s t a n t i a l l o s s e s o f i r o n i n t h e 7 2 c o n c e n t r a t e s t r e a m . T h e p o w e r r e q u i r e m e n t s f o r s e p a r a t i o n a t a g i v e n v e l o c i t y a n d d i a l y s a t e c o n c e n t r a t i o n w e r e f o u n d t o b e a p p r o x i m a t e l y t h e s a m e i n b o t h p r o c e s s e s ( F i g . 2 5 ) . T h e e r r o r s i n v o l v e d i n c a l c u l a t i n g t h e e f f e c t s o f f o u l i n g o n t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s i n t h e s t e a d y s t a t e p r o c e s s w e r e f o u n d t o b e t o o l a r g e t o m a k e a n y q u a n t i t a t i v e c o n c l u s i o n s . H o w e v e r , t h e r u n s c o n t a i n i n g 1 p p m F e 2 + i n t h e i r f e e d s t r e a m w e r e f o u n d t o r e a c h a l i m i t i n g a c c u m u l a t i o n o f i r o n w h i c h w a s p r o b a b l y d u e t o t h e s e v e r e r e d u c t i o n i n t h e i r o n c o n t e n t o f t h e s o l u t i o n c o n t a i n e d i n t h e f e e d t a n k o v e r a 2 0 h o u r p e r i o d . T h e f a c t t h a t r u n s a t 5 p p m F e 2 + s h o w e d l e s s e f f e c t o n t h e d r o p i n s e p a r a t i o n f a c t o r i s d u e t o t h e u n e v e n d e p o s i t i o n o f i r o n o n t h e m e m b r a n e s d u r i n g t h e s e r u n s . T h i s g a v e h i g h e r a c c u m u l a t i o n s o f i r o n f o r t h e s a m e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r ( s e e F i g u r e s 2 6 , 3 2 A a n d B , a n d 3 3 A ) . T h e i r o n s e p a r a t e d p e r s t r e a m , a n d t h e s e l e c t i v i t y c o e f f i c i e n t b o t h i n d i c a t e t h a t i r o n w a s p r e f e r e n t i a l l y a c c u m u l a t i n g i n t h e d i a l y s a t e s t r e a m ( T a b l e s X X t o X X I I I ) . T h e u n s t e a d y s t a t e r e s u l t s a r e s o m e w h a t h a r d e r t o i n t e r p r e t , t h e n e g a t i v e v a l u e s o f t h e b r i n e s t r e a m s e l e c t i v i t y a n d t h e p e r c e n t i r o n s e p a r a t e d i n d i c a t e t h a t i r o n i s a c c u m u l a t i n g a t a h i g h e r r a t e i n t h i s p r o c e s s a s o p p o s e d t o t h e s t e a d y s t a t e p r o c e s s . H o w e v e r , i n a b s o l u t e v a l u e , t h e d i a l y s a t e s t r e a m 73 s t i l l i n d i c a t e d a g r e a t e r a c c u m u l a t i o n o f i r o n ( T a b l e s X X I , a n d X X I I I ) . I n t h e s t e a d y s t a t e p r o c e s s , a n e g a t i v e p e r c e n t a c c u m u l a t i o n o f i r o n i n t h e c o n c e n t r a t e s t r e a m i n d i c a t e d a c e r t a i n r e d u c t i o n i n t h e s e l e c t i v i t y o f t h e c a t i o n i c m e m b r a n e ; s i n c e i r o n w a s a c c u m u l a t i n g i n t h e s t r e a m , s u c h b e h a v i o u r w a s p r o n o u n c e d a t l o w v e l o c i t i e s a n d h i g h v o l t a g e s . I n t h e s t e a d y s t a t e p r o c e s s , c u r r e n t e f f i c i e n c i e s w e r e s o m e w h a t b e l o w 1,0 i n d i c a t i n g t h a t a l t h o u g h p r e s e n t t h e e f f e c t s o f w a t e r s p l i t t i n g w e r e q u i t e s m a l l . A n o v e r a l l d e c r e a s e i n c u r r e n t e f f i c i e n c y w a s n o t i c e d i n f o u l i n g r u n s ( T a b l e s X X I V , X X V ) . I n t h e u n s t e a d y s t a t e p r o c e s s , t h e c u r r e n t e f f i c i e n c i e s w e r e q u i t e l o w ; t h i s w a s a t t r i b u t e d t o t h e l o w t h r o u g h - p u t o f t h e s y s t e m , t h e p r e s e n c e o f a p a u s e t i m e w h e r e n o f l u i d w a s f l o w i n g t h r o u g h t h e c e l l s a n d l o w d i a l y s a t e c o n c e n t r a t i o n s w h i c h i n c r e a s e c e l l r e s i s t a n c e c r e a t i n g m o r e p o l a r i z a t i o n a n d w a t e r - s p l i t t i n g . T h e i n c e a s e i n c e l l r e s i s t a n c e d u e t o t h e p r e s e n c e - o f a p a u s e t i m e c o u l d a c t u a l l y b e s e e n b y o b s e r v i n g t h e d r o p i n c u r r e n t p a s s i n g t h r o u g h a b a t t e r y o f c e l l s d u r i n g t h e 45 s e c o n d p a u s e t i m e . 74 C O N C L U S I O N S A l t h o u g h t h e e r r o r i n c a l c u l a t i n g t h e p e r c e n t d r o p i n e f f i c i e n c y o f t h e s t e a d y s t a t e r u n s w i t h f o u l i n g w a s q u i t e h i g h , i t c a n b e c o n c l u d e d t h a t t h e s t e a d y s t a t e r u n s g e n e r a l l y e x h i b i t e d s o m e d r o p i n s e p a r a t i o n e f f i c i e n c y o v e r a 20 h o u r r u n , a n d t h a t t h e r e s i s t a n c e o f t h e s y s t e m a s a w h o l e d i d n o t e x p e r i e n c e a n y s u b s t a n t i a l c h a n g e . T h e p o w e r c o n s u m p t i o n i n t h e u n s t e a d y s t a t e p r o c e s s d i d n o t c h a n g e c o n s i s t e n t l y i n a l l f o u l i n g r u n s , b u t t h e s e p a r a t i o n f a c t o r d i d s h o w a c o n s i d e r a b l e d r o p o v e r t h e 20 h o u r p e r i o d . T h e p r e s e n c e o f i r o n o x i d e f i l m s o n t h e m e m b r a n e s u r f a c e s w a s c o n f i r m e d b y v i s u a l e x a m i n a t i o n . ' S i n c e t h e s e p a r a t i o n f a c t o r a n d c u r r e n t e f f i c i e n c i e s d e c r e a s e d d u r i n g t h e r u n s w i t h f o u l i n g w h i l e t h e r e s i s t a n c e o f t h e c e l l r e m a i n e d r e l a t i v e l y c o n s t a n t , a n d s i n c e i r o n w a s a c c u m u l a t i n g i n t h e c o n c e n t r a t e s t r e a m a t t h e e n d o f t h e r u n s w h e n t h e f i l m s h a d b e e n f o r m e d , i t c a n b e s t a t e d t h a t t h e " s a n d w i c h m e m b r a n e " m o d e l h a s b e e n v e r i f i e d e x p e r i m e n t a l l y a n d , t h a t s u c h c o m b i n a t i o n s o f m e m b r a n e s w e r e p r e s e n t i n b o t h p r o c e s s e s . T h e a c i d w a s h u s e d i n t h e u n s t e a d y s t a t e p r o c e s s w a s i n e f f e c t i v e i n r e m o v i n g t h e i r o n o x i d e f i l m . S c r u b b i n g t h e m e m b r a n e s w i t h a n y l o n b r u s h a n d s o a k i n g t h e m o v e r n i g h t i n a n E D T A s o l u t i o n w a s f o u n d t o b e t h e m o s t e f f e c t i v e m e t h o d t o r e m o v e t h e d e p o s i t s . 75 F i n a l l y , d u e t o t h e r e l a t i v e i r r e v e r s i b i l i t y i n t h e f o r m a t i o n o f i r o n o x i d e f r o m a f e r r o u s h y d r o x i d e p r e c i p i t a t e , we c a n c o n c l u d e t h a t p o l a r i t y r e v e r s a l i n t h e u n s t e a d y s t a t e p r o c e s s w a s i n e f f e c t i v e i n c o n t r o l l i n g i r o n o x i d e f o u l i n g . R E C O M M E N D A T I O N S 1) D e v e l o p a m e t h o d o f f e r i n g g r e a t e r p r e c i s i o n i n d e t e r m i n i n g s o d i u m c o n c e n t r a t i o n s t o a t l e a s t ± 0 , 1 % . 2) U s e f e w e r m e m b r a n e s p e r s t a c k s o t h a t t h e r e p l a c e m e n t o f a l l m e m b r a n e s b e f o r e e a c h r u n i s p o s s i b l e . 3 ) U s e a s m a l l e r s u r f a c e a r e a o r a t h i n n e r s p a c e r t o p r e v e n t m e m b r a n e w a r p i n g , a n d t o r e d u c e t h e c o s t o f m e m b r a n e r e p l a c e m e n t . 4 ) D e v e l o p a m o r e v e r s a t i l e m e t h o d o f m e a s u r i n g f l o w r a t e s , b y u s i n g , f o r e x a m p l e , r o t a m e t e r s . 5) I n c r e a s e t h e f e e d t a n k s i z e o r b l e n d a m a k e - u p s o l u t i o n o f s o d i u m c h l o r i d e w i t h d i s t i l l e d w a t e r t o f o r m t h e f e e d s t r e a m . T h i s w o u l d e l i m i n a t e t h e d e p l e t i o n o f i r o n i n t h e f e e d t a n k ( t h e u s e o f a C o l e P a l m e r P e r i s t a l t i c p u m p f o r b l e n d i n g i s n o t r e c o m m e n d e d s i n c e a l l m a k e s o f t u b i n g w e r e f o u n d t o g i v e s l i g h t v a r i a t i o n s i n f l o w r a t e s o v e r a 20 h o u r p e r i o d ) . 6) T a k e s a m p l e s a t t h e b e g i n n i n g o f a r u n ; i t i s p o s s i b l e t h a t s o m e f o u l i n g o c c u r r e d b e f o r e t h e f i r s t s a m p l i n g t i m e o f 2 h o u r s . 7 6 7 ) U s e a l a r g e r D . C . p o w e r s u p p l y i n o r d e r t o u s e t h e l i m i t i n g c u r r e n t a s a f o u l i n g p a r a m e t e r . 8 ) U s e a c c u r a t e f l o w - t h r o u g h c o n d u c t i v i t y m e t e r s i n s t e a d o f a n i o n s e l e c t i v e e l e c t r o d e t o d e t e r m i n e s o d i u m c o n c e n t r a t i o n s . T h e u s e o f s u c h a m e t e r w o u l d r e d u c e t h e e r r o r i n b o t h t h e s e p a r a t i o n f a c t o r a n d t h e p e r c e n t d r o p i n s e p a r a t i o n d u r i n g a r u n . 9 ) T h e f e e d s y s t e m s h o u l d b e f r e e o f i r o n o r a n y o t h e r s o u r c e o f c o n t a m i n a t i o n , s t a i n l e s s s t e e l b o l t s i n a f e e d t a n k h a v e c a u s e d i r o n o x i d e f i l m s i n s o m e b e n c h s c a l e a p p a r a t u s . 7 7 R E F E R E N C E S A b u - G o u k h M o h a m e d E . 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 v e s t i g a t i o n o f O p e n S y s t e m s , P h . D . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , N o v e m b e r 1 9 7 6 . A s a h i C h e m i c a l I n d u s t r y C o . L t d . I o n E x c h a n g e M e m b r a n e a n d  i t s A p p l i c a t i o n 1 9 7 5 . B a s s D . 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 v e s t i g a t i o n o f  C l o s e d S y s t e m s , P h . D . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 9 7 2 . C o o k e B . A . S o m e P h e n o m e n a A s s o c i a t e d w i t h C o n c e n t r a t i o n P o l a r i z a t i o n i n E l e c t r o d i a l y s i s F i r s t I n t e r n a t i o n a l S y m p . O n W a t e r D e s a l i n a t i o n , W a s h i n g t o n D . C . V 2 O c t o b e r 1 9 6 5 . C o t t o n F . A . A n d W i l k i n s o n G . A d v a n c e d I n o r g a n i c C h e m i s t r y , I n t e r s c i e n c e P u b l i s h e r s , New Y o r k , 1 9 6 7 . E l H a r e s H . A n d A s w e d M . P r a c t i c a l B e h a v i o u r o f E l e c t r o d i a l y s i s a n d R e v e r s e O s m o s i s P l a n t s i n L i b y a , D e s a l i n a t i o n , 22 , p p 2 9 1 - 2 9 8 , 1 9 7 7 . E . P . A . T o t a l R e c y c l e S y s t e m s f o r P e t r o c h e m i c a l W a s t e B r i n e s  C o n t a i n i g R e f r a c t o r y C o n t a m i n a n t s , E P A 6 0 0 2 7 9 - 0 2 1 , J a n u a r y , 1 9 7 9 ( P B 2 9 3 1 5 8 ) . F u r u k a w a D . H . I n v e s t i g a t i o n o f M e m b r a n e S t a c k R e s i s t a n c e  I n c r e a s e W i t h a N a t u r a l B r a c k i s h W a t e r , U n i t e d S t a t e s D e p a r t e m e n t o f t h e I n t e r i o r , R . A n d D . P r o g r e s s R e p o r t N o . 2 8 5 , J a n u a r y 1 9 6 8 . U r u k a w a D . H . S p e c i f i c P r o b l e m s i n E l e c t r o d i a l y s i s D e s a l t i n g  o f B r a c k i s h W a t e r , U n i t e d S t a t e s D e p a r t e m e n t o f t h e I n t e r i o r , D e n v e r , C o l o r a d o 1 9 6 7 . G i l l i l a n d E d w i n R . T h e C u r r e n t E c o n o m i c s o f E l e c t r o d i a l y s i s , F i r s t I n t e r n a t i o n a l S y m p o s i u m o n W a t e r D e s a l i n a t i o n , W a s h i n g t o n D . C . O c t o b e r 1 9 6 5 . G o l d s t e i n A r t h u r L . E l e c t r o d i a l y s i s o n t h a A m e r i c a n C o n t i n e n t , D e s a l i n a t i o n , 3 0 , p p 4 9 ~ 5 8 , 1 9 7 9 . G o v i d a n K . P . A n d N a r a y a n a n P . K . D e m i n e r a l i z a t i o n b y E l e c t r o d i a l y s i s , D e s a l i n a t i o n , j_9 , p p 2 2 9 - 2 3 9 , 1 9 7 6 . G r o s s m a n G e r s h o n a n d S o n i n A i n A . M e m b r a n e F o u l i n g i n E l e c t r o d i a l y s i s ; A M o d e l a n d E x p e r i m e n t s , D e s a l i n a t i o n , p p 1 0 7 - 1 2 5 , 1 9 7 3 . 78 G r o s s m a n G e r s h o n a n d S o n i n A i n A . E x p e r i m e n t a l S t u d y o f t h e  E f f e c t s o f H y d r o d y n a m i c s a n d M e m b r a n e F o u l i n g i n  E l e c t r o d i a l y s i s , D e s a l i n a t i o n , p p 157-180, 1971. G u n n i n g H . E . A n d G o r d o n A . R . T h e C o n d u c t a n c e a n d I o n i c M o b i l i t i e s f o r A q u e o u s S o l u t i o n s o f P o t a s s i u m a n d S o d i u m  C h l o r i d e a t T e m p e r a t u r e s f r o m 15° t o 45°C , J o u r n a l o f C h e m i c a l P h y s i c s , V o l . 10, F e b r u a r y 1942. I t o i S h i g e r u E l e c t r o d i a l y s i s o f E f f l u e n t s f r o m T r e a t m e n t o f  M e t a l i c S u r f a c e s D e s a l i n a t i o n , 28 , p p 193-205, 1979. K o b u s E . J . M . a n d H e e r t j e s P . M . T h e P o i s o n i n g o f A n i o n - S e l e c t i v e M e m b r a n e s b y S o d i u m D o d e c y l s u l p h a t e , D e s a l i n a t i o n , p p 383-401, D e c e m b e r , 1971. K o r n g o l d E . E l e c t r o d i a l y s i s P r o c e s s U s i n g I o n E x c h a n g e R e s i n s  B e t w e e n M e m b r a n e s D e s a l i n a t i o n , J_6 , p p 225-233, 1975. K o r n g o l d E . , K o c k K . u n d S r a t h m a n n H . E l e c t r o d i a l y s i s i n  A d v a n c e d W a s t e W a t e r T r e a t m e n t , D e s a l i n a t i o n , 2_4 , p p 129-139, 1978. K r e s m a n T . R . E . a n d T y e F . L . P H C h a n g e s a t A n i o n S e l e c t i v e  M e m b r a n e s u n d e r R e a l i s t i c F l o w C o n d i t i o n s , J . E l e c t r o c h e m . S o c . ; E l e c t r o c h e m i c a l S c i e n c e , p p 25 -31 , J a n u a r y 1969. M a t z R . E l e c t r o d i a l y s i s - P i l o t P l a n t a n d G e n e r a l D e v e l o p m e n t , F i r s t I n t e r n a t i o n a l S y m p . On W a t e r D e s a l i n a t i o n , W a s h i n g t o n D . C , U . S . D e p a r t e m e n t o f t h e I n t e r i o r , V o l . 3 , 1 965. M i c h a e l s A l a n S . U l t r a f i l t r a t i o n : a n a d o l e s c e n t t e c h n o l o g y C h e m t e c h , J a n u a r y 1981. M i l l e t J . E l e c t r o d i a l y s e i n t r o d u c t i o n , S o c i e t e d e s E l e c t r i c i e n s , d e s E l e c t r o n i c i e n s e t d e s R a d i o e l e c t r i c i e n s ( R G E ) , T o m e 86, N ° 5, M a i 1977. S e k o M a o m i L a r g e S c a l e B r a c k i s h W a t e r C o n v e r s i o n -E l e c t r o d i a l y s i s D e m o n s t r a t i o n P l a n t a t W e b s t e r , S o u t h  D a k o t a , U . S . A . D e c h e m a M o n o g r a p h i e n , B a n d 47, N R . 805-834, V o l . 2, 1962. S o l t G . S . I n f l u e n c e o f M e m b r a n e P h e n o m e n a o n E l e c t r o d i a l y s i s  O p e r a t i o n F i r s t I n t e r n a t i o n a l S y m p . On W a t e r D e s a l i n a t i o n , D e p a r t e m e n t o f t h e I n t e r i o r , W a s h i n g t o n D . C , V o l . 2, O c t o b e r 1965. V a n D u i n P . J . P o i s o n i n g o f E l e c t r o d i a l y s i s M e m b r a n e s , 4@Th I n t e r n a t i o n a l S y m p o s i u m o n F r e s h W a t e r F r o m t h e S e a , V o l . 3, p p 253-259, 1973. 79 T a b l e I I ( F i g . 1 3 ) S t e a d y s t a t e , v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s o f b o t h s t a g e s ( A ) a n d ( B ) T O T A L C E L L F i r s t e f f e c t S e c o n d e f f e c t ( C e l l A ) ( C e l l B ) C u r r e n t V o l t a g e C u r r e n t V o l t a g e ( m A . D . C . ) ( V o l t s ) ( m A . D . C . ) ( V o l t s ) 5 6 , 1 4 , 9 9 5 5 , 4 4 , 9 9 1 4 9 9 , 9 7 1 4 9 9 , 9 7 3 1 5 - 1 9 , 9 4 2 6 8 1 9 , 9 4 4 2 2 2 9 , 9 3 3 7 8 2 9 , 9 3 521 3 9 , 8 9 4 6 2 3 9 , 8 9 5 5 7 4 3 , 7 9 4 9 0 4 3 , 7 9 S T A C K O N L Y F i r s t e f f e c t S e c o n d e f f e c t ( C e l l A ) ( C e l l B ) C u r r e n t V o l t a g e C u r r e n t V o l t a g e ( m A . D . C . ) ( V o l t s ) ( m A . D . C . ) ( V o l t s ) 5 6 , 1 1 , 8 6 5 5 , 4 2 , 1 1 1 4 9 5 , 3 0 1 4 9 5 , 7 0 3 1 5 1 2 , 7 1 2 6 8 1 2 , 3 4 4 2 2 1 9 , 7 3 3 7 7 1 8 , 6 6 521 2 7 , 4 7 4 6 2 2 6 , 8 6 5 5 7 3 0 , 1 8 4 9 0 2 9 , 3 8 8 0 T a b l e I I I ( F I G . 1 4 ) S t e a d y s t a t e , v o l t a g e d r o p p e r c e l l p a i r ( B ) a n d v o l t a g e d r o p i n b u l k s o l u t i o n ( A ) f o r t h e f i r s t s t a g e a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M 2 h o u r s 2 0 h o u r s NUM c m / s e c I R O N B 6 7 2 0 0 , 5 0 0 , 0 0 , 5 4 3 2 , 2 0 0 , 5 3 4 2 , 1 5 9 1 2 0 0 , 5 0 0 , 0 N . A . 2 , 2 6 N . A . - 0 , 0 0 7 1 2 0 0 , 5 0 0 , 0 0 , 5 3 2 2 , 2 2 0 , 5 4 6 2 , 1 8 7 9 2 0 0 , 5 0 0 , 9 2 0 , 5 0 3 2 , 2 3 0 , 5 1 5 2 , 2 2 8 1 2 0 0 , 5 0 1 , 1 1 0 , 6 3 1 2 , 2 2 0 , 6 0 8 2 r 1 8 8 8 2 0 0 , 5 0 5 , 2 4 0 , 5 4 2 2 , 4 5 0 , 5 1 1 2 , 2 2 9 0 2 0 0 , 5 0 5 , 5 0 0 , 5 0 5 2 , 2 9 0 , 5 2 8 2 , 2 9 6 5 2 0 1 , 2 5 0 , 0 0 , 5 5 4 2 , 1 2 0 , 5 4 2 2 r 1 1 7 5 2 0 1 , 2 5 0 , 0 0 , 5 9 2 2 r 1 5 0 , 6 4 5 2 , 1 1 7 3 2 0 1 , 2 5 0 , 0 0 , 7 7 7 2 1 3 0 , 7 4 4 2 r 0 9 7 7 2 0 1 , 2 5 1 , 0 9 0 , 7 3 1 2 1 0 0 , 7 0 4 2 r 1 1 8 2 2 0 1 , 2 5 1 , 0 1 0 , 6 1 9 2 1 4 0 , 6 2 4 2 , 1 0 8 5 2 0 1 , 2 5 5 , 6 6 0 , 6 2 1 2 1 0 0 , 6 3 5 2 , 0 7 6 6 3 0 0 , 5 0 0 , 0 0 , 6 8 2 3 5 6 0 , 6 6 8 3 5 7 7 0 3 0 0 , 5 0 0 , 0 0 , 6 9 0 3 5 3 0 , 7 2 0 3 , 5 4 9 2 3 0 0 , 5 0 0 , 0 N . A . 3 5 9 N . A . -o 0 0 8 0 3 0 0 , 5 0 1 , 0 4 0 , 7 7 0 3 4 7 0 , 7 6 9 3 5 1 8 9 3 0 0 , 5 0 5 , 3 1 0 , 7 9 6 3 , 6 8 0 , 7 8 6 3 6 5 9 4 3 0 0 , 5 0 5 , 3 1 0 , 6 6 4 3 , 5 7 0 , 6 6 8 3 5 9 6 8 3 0 1 , 2 5 0 , 0 0 , 8 2 7 3 , 2 7 0 , 8 1 4 3 , 3 2 7 4 3 0 1 , 2 5 0 , 0 1 , 0 9 6 3 , 1 9 1 , 0 4 5 3 , 0 8 7 6 3 0 1 , 2 5 0 , 0 0 , 8 1 8 3 , 2 6 0 , 8 6 5 3 , 0 8 8 3 3 0 1 , 2 5 1 , 0 2 1 , 0 7 6 3 , 2 3 0 , 9 8 9 3 , 1 5 8 4 3 0 1 , 2 5 1 , 0 7 0 , 9 9 1 3 , 4 4 0 , 9 1 0 3 , 4 5 8 6 3 0 1 , 2 5 5 , 0 0 0 , 8 3 6 3 , 3 8 0 , 8 3 6 3 , 4 1 8 7 3 0 1 , 2 5 5 , 6 4 0 , 9 0 5 3 , 2 2 0 , 8 6 2 3 , 3 4 81 T a b l e I V ( F i g . 1 5 ) S t e a d y s t a t e , v o l t a g e p e r c e l l p a i r ( B ) a n d v o l t a g e d r o p i n b u l k s o l u t i o n ( A ) f o r t h e s e c o n d s t a g e a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M 2 h o u r s NUM c m / s e c I R O N A B 6 7 2 0 0 , 5 0 0 , 0 0 , 5 3 8 2 , 2 2 91 2 0 0 , 5 0 0 , 0 N . A . 2 , 4 7 71 2 0 0 , 5 0 0 , 0 0 , 4 7 3 2 , 3 6 7 9 2 0 0 , 5 0 0 , 9 2 0 , 5 0 5 2 , 3 5 81 2 0 0 , 5 0 1 , 1 1 0 , 6 1 7 2 , 3 9 8 8 2 0 0 , 5 0 5 , 2 4 0 , 6 2 6 2 , 2 2 9 0 2 0 0 , 5 0 5 , 5 0 0 , 4 7 6 2 , 4 4 6 5 2 0 1 , 2 5 0 , 0 0 , 5 3 0 2 , 1 9 7 5 2 0 1 , 2 5 0 , 0 0 , 6 0 2 2 , 2 6 7 3 2 0 1 , 2 5 0 , 0 0 , 7 6 5 2 , 2 8 7 7 2 0 1 , 2 5 1 , 0 9 0 , 7 1 9 2 , 3 1 8 2 2 0 1 , 2 5 1 , 0 1 0 , 5 6 3 2 , 3 1 8 5 2 0 1 , 2 5 5 , 6 6 0 , 5 3 8 2 , 3 7 6 6 3 0 0 , 5 0 0 , 0 0 , 7 0 2 3 , 6 6 7 0 3 0 0 , 5 0 0 , 0 0 , 6 2 5 3 , 8 2 9 2 3 0 0 , 5 0 0 , 0 N . A . 3 , 9 2 8 0 3 0 0 , 5 0 1 , 0 4 0 , 8 0 5 3 , 8 4 8 9 3 0 0 , 5 0 5 , 3 1 0 , 8 7 6 3 , 8 5 9 4 3 0 0 , 5 0 5 , 3 1 0 , 6 1 5 3 , 9 3 6 8 3 0 1 , 2 5 0 , 0 0 , 7 7 3 3 , 5 5 74 3 0 1 , 2 5 0 , 0 1 , 1 0 4 3 , 5 7 7 6 3 0 1 , 2 5 0 , 0 0 , 7 9 5 3 , 6 5 8 3 3 0 1 , 2 5 1 , 0 2 1 , 0 6 9 3 , 4 0 8 4 3 0 1 , 2 5 1 , 0 7 0 , 8 5 7 3 , 5 9 8 6 3 0 1 , 2 5 5 , 0 0 0 , 8 5 8 3 , 5 4 8 7 3 0 1 , 2 5 5 , 6 4 0 , 8 1 9 3 , 8 4 2 0 h o u r s A B 0 , 5 2 7 N . A . 0 , 4 7 5 0 , 5 6 1 0 , 6 1 5 0 , 6 5 4 0 , 5 0 5 0 , 5 3 1 0 , 6 5 3 0 , 7 3 1 0 , 6 8 0 0 , 5 5 0 0 , 5 4 3 0 , 6 7 9 0 , 5 9 3 N . A . 0 , 7 7 6 0 , 8 4 4 0 , 7 2 7 0 , 7 3 4 1 , 0 5 8 0 , 7 9 0 1 , 0 8 0 0 , 7 8 4 0 , 8 9 9 0 , 7 3 2 2 , 2 2 • 0 , 0 0 2 , 3 6 2 , 3 5 2 , 3 3 2 , 3 8 2 , 3 9 2 , 1 7 2 , 2 4 2, 2 , 2 , 2 , 3 , 21 2 0 30 3 3 68 3 , 8 5 - 0 , 0 0 3 , 8 3 3 , 8 7 3 3 3 3 81 57 52 50 3 , 4 2 3 , 6 7 3 , 6 5 3 , 8 4 8 2 T a b l e V ( F i g s . 1 6 , 1 7 ) S t e a d y s t a t e , s t a c k v o l t a g e s ( A ) a n d c o m b i n e d r e s i s t a n c e s ( R a + R c + R p ) ( B ) f o r f i r s t e f f e c t a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M NUM c m / s e c I R O N 6 7 2 0 0 , 5 0 0 , 0 1 4 9 1 2 0 0 , 5 0 0 , 0 1 4 7 1 2 0 0 , 5 0 0 , 0 1 4 7 9 2 0 0 , 5 0 0 , 9 2 1 4 8 1 2 0 0 , 5 0 1 , 1 1 1 4 8 8 2 0 0 , 5 0 5 , 2 4 1 5 9 0 2 0 0 , 5 0 5 , 5 0 1 4 6 5 2 0 1 , 2 5 0 , 0 1 3 7 5 2 0 1 , 2 5 0 , 0 1 4 7 3 2 0 1 , 2 5 0 , 0 1 3 7 7 2 0 1 , 2 5 1 , 0 9 1 3 8 2 2 0 1 , 2 5 1 , 0 1 1 3 8 5 2 0 1 , 2 5 5 , 6 6 1 3 6 6 3 0 0 , 5 0 0 , 0 2 3 7 0 3 0 0 , 5 0 0 , 0 2 2 9 2 3 0 0 , 5 0 0 , 0 2 3 8 0 3 0 0 , 5 0 1 , 0 4 2 2 8 9 3 0 0 , 5 0 5 , 3 1 2 3 9 4 3 0 0 , 5 0 5 , 3 1 2 3 6 8 3 0 1 , 2 5 0 , 0 2 1 7 4 3 0 1 , 2 5 0 , 0 2 0 7 6 3 0 1 , 2 5 0 , 0 2 1 8 3 3 0 1 , 2 5 1 , 0 2 2 1 8 4 3 0 1 , 2 5 1 , 0 7 2 2 8 6 3 0 1 , 2 5 5 , 0 0 2 1 8 7 3 0 1 , 2 5 5 , 6 4 2 0 2 h o u r s 2 0 h o u r s A B A B 3 0 3 9 , 6 9 1 4 , 0 0 3 9 , 5 1 6 7 N . A. N . A . N . A . 4 0 4 0 , 4 3 1 4 , 1 9 3 8 , 5 6 5 2 4 1 , 1 8 1 4 , 4 5 4 0 , 5 8 4 3 3 4 , 8 6 1 4 , 1 8 3 5 , 0 5 9 1 4 9 , 0 7 1 4 , 4 0 4 5 , 4 8 8 8 4 2 , 4 8 1 4 , 8 9 4 1 , 9 2 8 0 3 7 , 9 4 1 3 , 7 0 3 7 , 9 3 0 0 3 3 , 2 5 1 3 , 7 0 2 9 , 5 8 8 6 2 8 , 1 5 1 3 , 5 6 2 8 , 0 3 6 6 3 0 , 0 6 1 3 , 7 2 3 0 , 4 1 9 3 3 0 , 5 9 1 3 , 6 8 3 0 , 5 7 6 6 3 2 , 1 1 1 3 , 4 5 3 1 , 2 0 1 4 5 4 , 0 2 2 3 , 2 1 5 5 , 0 3 9 5 4 6 , 8 4 2 3 , 0 4 4 6 , 9 3 3 3 N . A . N . J N . A . 5 3 4 9 , 6 4 2 2 , 8 4 4 9 , 5 0 9 1 5 9 , 1 6 2 3 , 7 5 5 3 , 5 4 2 0 5 2 , 9 4 2 3 , 3 5 5 4 , 1 5 2 8 3 7 , 5 9 2 1 , 6 1 3 9 , 3 8 7 2 2 9 , 1 8 2 0 , 0 1 2 8 , 7 1 2 2 3 7 , 2 9 2 0 , 0 3 3 2 , 3 9 0 0 2 9 , 7 1 2 0 r 4 7 3 0 , 0 2 3 4 3 4 , 5 1 2 2 , 4 5 3 8 , 0 2 9 9 3 8 , 0 5 2 2 r 1 7 4 0 , 7 4 9 4 3 9 , 0 3 2 1 , 7 2 4 0 , 3 6 8 3 T a b l e V I ( F i g s . 1 8 , 1 9 ) S t e a d y s t a t e , s t a c k v o l t a g e s ( A ) a n d c o m b i n e d r e s i s t a n c e s ( R a + R c + R p ) ( B ) f o r s e c o n d e f f e c t a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M 2 h o u r s 2 0 h o u r s NUM c m / s e c I R O N A B A B 6 7 2 0 0 , 5 0 0 , 0 1 4 , 4 0 4 2 , 8 0 1 4 , 4 2 4 4 , 7 9 91 2 0 0 , 5 0 0 , 0 1 6 , 0 5 N . A . N . A . N . A . 71 2 0 0 , 5 0 0 , 0 1 5 , 31 5 6 , 30 1 5 , 3 1 5 6 , 19 7 9 2 0 0 , 5 0 0 , 9 2 1 5 , 3 0 5 2 , 6 3 1 5 , 2 8 4 7 , 7 7 81 2 0 0 , 5 0 1 , 1 1 1 5 , 5 3 4 8 , 9 7 1 5 , 1 4 4 6 , 3 3 8 8 2 0 0 , 5 0 5 , 2 4 1 4 , 4 5 4 3 , 0 5 1 5 , 4 9 4 2 , 7 8 9 0 2 0 0 , 5 0 5 , 5 0 1 5 , 8 3 5 6 , 8 0 1 5 , 5 5 5 3 , 8 6 6 5 2 0 1 , 2 5 0 , 0 1 4 , 2 3 4 2 , 67 1 4 , 1 1 4 0 , 6 9 7 5 2 0 1 , 2 5 0 , 0 1 4 , 6 9 3 5 , 5 7 1 4 , 5 9 3 2 , 6 7 7 3 2 0 1 , 2 5 0 , 0 1 4 , 8 0 3 3 , 2 2 1 4 , 3 7 3 2 , 3 6 7 7 2 0 1 , 2 5 1 , 0 9 1 5 , 0 4 3 6 , 5 5 1 4 , 2 7 3 4 , 9 2 8 2 2 0 1 , 2 5 1 , 0 1 1 5 , 0 0 3 9 , 3 1 1 4 , 9 8 4 1 , 8 1 8 5 2 0 1 , 2 5 5 , 6 6 1 5 , 41 4 6 , 4 8 1 5 , 1 6 4 6 , 18 66 3 0 0 , 5 0 0 , 0 2 3 , 8 0 5 9 , 0 5 2 3 , 9 3 61 , 3 6 7 0 3 0 0 , 5 0 0 , 0 2 4 , 8 0 7 0 , 8 8 2 5 , 0 5 7 7 , 5 9 9 2 3 0 0 , 5 0 0 , 0 2 5 , 4 6 N . A . N . A . N . A . 8 0 3 0 0 , 5 0 1 , 0 4 2 4 , 9 4 7 3 , 12 2 4 , 9 0 71 , 0 4 8 9 3 0 0 , 5 0 5 , 3 1 2 5 , 0 0 7 7 , 5 8 2 5 , 1 3 7 0 , 6 7 94 3 0 0 , 5 0 5 , 3 1 2 5 , 5 2 8 0 , 6 9 2 4 , 7 5 6 6 , 12 6 8 3 0 1 , 2 5 0 , 0 2 3 , 0 9 4 5 , 8 0 2 3 , 2 0 4 9 , 1 9 7 4 3 0 1 , 2 5 0 , 0 2 3 , 2 2 3 7 , 5 6 2 2 , 8 8 3 7 , 16 7 6 3 0 1 , 2 5 0 , 0 2 3 , 7 0 4 7 , 16 2 2 , 7 2 4 5 , 4 0 8 3 3 0 1 , 2 5 1 , 0 2 2 2 , 10 3 5 , 74 2 2 , 2 1 3 2 , 6 3 8 4 3 0 1 , 2 5 1 , 0 7 - 2 3 , 3 5 4 7 , 4 6 2 3 , 8 3 5 2 , 2 1 8 6 3 0 1 , 2 5 5 , 0 0 2 3 , 0 0 41 , 3 7 2 3 , 7 2 4 2 , 2 4 8 7 3 0 1 , 2 5 5 , 6 4 2 4 , 9 5 5 8 , 8 5 2 4 , 9 4 61 , 0 6 8 4 T a b l e V I I ( F i g s . 2 0 , 2 1 ) S t e a d y s t a t e , d i a l y s a t e c h a n n e l p r e s s u r e d r o p a t 2 a n d 2 0 h o u r s R U N V O L T V E L Y P P M P r e s s P r e s s NUM c m / s e c I R O N D r o p D r o p c m H g c m H g 2 h o u r s 2 0 h o u r s 6 7 2 0 0 , 5 0 0 , 0 1 , 6 5 1 , 6 5 9 1 2 0 0 , 5 0 0 , 0 1 , 5 0 - 0 , 0 0 7 1 2 0 0 , 5 0 0 , 0 1 , 6 0 1 , 6 0 7 9 2 0 0 , 5 0 0 , 9 2 1 , 7 0 1 , 8 0 8 1 2 0 0 , 5 0 1 , 1 1 2 , 0 5 2 , 4 5 8 8 2 0 0 , 5 0 5 , 2 4 2 , 2 0 2 r 9 0 9 0 2 0 0 , 5 0 5 , 5 0 1 , 3 5 1 , 9 5 6 5 2 0 1 , 2 5 0 , 0 7 r 1 5 7 , 1 5 7 5 2 0 1 , 2 5 0 , 0 7 r 1 0 7 , 3 0 7 3 2 0 1 , 2 5 0 , 0 6 r 3 5 6 4 0 7 7 2 0 1 , 2 5 1 , 0 9 8 , 7 0 9 , 4 0 8 2 2 0 1 , 2 5 1 , 0 1 9 5 0 1 1 4 0 8 5 2 0 1 , 2 5 5 , 6 6 9 8 0 1 3 5 0 6 6 3 0 0 , 5 0 0 , 0 2 0 6 2 1 6 7 0 3 0 0 , 5 0 0 , 0 1 3 0 1 7 0 9 2 3 0 0 , 5 0 0 , 0 1 5 0 - 0 0 0 8 0 3 0 0 , 5 0 1 , 0 4 2 2 0 2 6 0 8 9 3 0 0 , 5 0 5 , 3 1 1 7 0 2 5 0 9 4 3 0 0 , 5 0 5 , 3 1 1 7 0 2 4 0 6 8 3 0 1 , 2 5 0 , 0 7 , 7 0 7 , 8 0 7 4 3 0 1 , 2 5 0 , 0 6 , 7 0 6 , 9 0 7 6 3 0 1 , 2 5 0 , 0 7 , 0 0 7 , 5 0 8 3 3 0 1 , 2 5 1 , 0 2 1 0 , 0 5 1 3 , 4 0 8 4 3 0 1 , 2 5 1 , 0 7 1 1 , 1 0 1 3 , 3 0 8 6 3 0 1 , 2 5 5 , 0 0 1 2 , 9 0 1 5 , 2 0 8 7 3 0 1 , 2 5 ' 5 , 6 4 7 , 1 0 8 , 2 0 85 T a b l e V I I I ( F i g s . 2 0 , 2 1 ) S t e a d y s t a t e , b r i n e c h a n n e l p r e s s u r e d r o p a t 2 a n d 20 h o u r s R U N V O L T V E L Y P P M P r e s s P r e s s NUM c m / s e c I R O N D r o p D r o p cm H g c m H g 2 h o u r s 20 h o u r s 67 20 0 r 5 0 0 0 1 , 6 5 1 , 7 5 91 20 0 , 50 0 0 2 70 - 0 , 0 0 71 20 0 ,50 0 0 1 70 1 , 8 0 79 20 0 50 0 92 2 05 2 , 3 5 81 20 0 50 1 1 1 1 80 2 , 00 88 20 0 50 5 24 1 60 1 , 60 90 20 0 r 5 0 5 50 1 40 1 , 50 65 20 1 25 0 0 7 72 7 72 75 20 1 25 0 0 8 70 9 00 73 20 1 25 0 0 8 70 8 , 70 77 20 1 25 1 09 10 70 1 3 45 82 20 1 25 1 01 9 40 10 70 85 20 1 25 5 66 1 4 00 1 5 20 66 30 0 50 0 0 2 01 2 08 70 30 0 50 0 0 3 15 3 60 92 30 0 50 0 0 3 00 - 0 00 80 30 0 50 1 , 04 1 75 1 , 8 5 89 30 0 50 5 , 31 1 65 1 70 94 30 0 50 5 , 31 3 15 3 20 68 30 1 25 o , 0 8 00 8 30 74 30 1 25 o , 0 9 05 9 20 76 30 1 25 o , 0 8 80 9 90 83 30 1 25 1 , 02 9 85 10 50 84 30 1 25 1 , 07 16 , 90 17 70 86 30 1 25 5 , 00 10 , 00 1 0 50 87 30 1 25 5 , 64 8 ; 50 9 25 8 6 T A B L E I X ( F I G . 2 2 ) P r e s s u r e d r o p a c r o s s t h e d i a l y s a t e c h a n n e l ( A ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) NUM c m / s e c I R O N 2 2 0 h o u r s h o u r s 41 2 0 1 , 2 5 0 , 0 3 , 5 6 3 , 5 6 3 0 20 1 , 2 5 0 , 8 5 0 , 0 0 , 0 3 8 2 0 1 , 2 5 0 , 9 7 3 , 6 8 3 , 8 1 3 9 2 0 1 , 2 5 0 , 6 8 3 , 5 1 3 , 7 1 32 2 0 1 , 2 5 4 , 7 8 3 , 3 0 3 , 8 1 34 2 0 5 , 0 0 0 , 9 9 2 4 , 5 1 2 6 , 4 2 3 5 2 0 5 , 0 0 4 , 6 8 2 6 , 2 9 2 7 , 4 3 4 3 ' 2 0 5 , 0 0 4 , 6 6 3 0 , 9 9 3 8 , 0 0 4 0 30 1 , 2 5 0 , 0 3 , 5 6 3 , 7 6 31 30 1 , 2 5 1 , 0 3 3 , 5 1 0 , 0 4 2 3 0 1 , 2 5 0 , 9 2 3 , 9 4 3 , 6 8 3 3 3 0 1 , 2 5 4 , 7 3 3 , 5 6 3 , 7 1 3 6 3 0 5 , 0 0 0 , 8 7 31 , 0 9 3 4 , 0 4 37 30 5 , 0 0 4 , 6 1 2 6 , 6 7 2 7 , 6 9 44 3 0 5 , 0 0 4 , 6 8 2 6 , 9 2 2 8 , 7 0 T A B L E X ( F I G . 2 2 ) P r e s s u r e d r o p a c r o s s t h e b r i n e c h a n n e l ( A ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) NUM c m / s e c I R O N 2 2 0 h o u r s h o u r s 41 20 1 , 2 5 0 , 0 3 , 3 5 3 , 1 5 3 0 2 0 1 , 2 5 0 , 8 5 0 , 0 0 , 0 3 8 2 0 1 , 2 5 0 , 9 7 4 , 1 1 4 , 3 2 3 9 2 0 1 , 2 5 0 , 6 8 4 , 2 7 4 , 5 2 3 2 2 0 1 , 2 5 4 , 7 8 3 , 0 0 3 , 1 7 34 20 5 , 0 0 0 , 9 9 3 4 , 9 2 3 7 , 8 5 3 5 20 5 , 0 0 4 , 6 8 3 7 , 3 4 3 9 , 12 4 3 2 0 5 , 0 0 4 , 6 6 2 9 , 4 6 3 5 , 0 5 4 0 3 0 1 , 2 5 0 , 0 3 , 5 6 3 , 6 6 31 30 1 , 2 5 1 , 0 3 3 , 1 7 0 , 0 4 2 30 1 , 2 5 0 , 9 2 3 , 6 1 3 , 5 6 3 3 30 1 , 2 5 4 , 7 3 3 , 4 3 3 , 1 0 36 30 5 , 0 0 0 , 8 7 4 4 , 7 0 4 8 , 5 1 3 7 3 0 5 , 0 0 4 , 6 1 3 7 , 0 8 3 7 , 0 8 44 30 5 , 0 0 4 , 6 8 2 4 , 8 9 2 6 , 4 2 8 7 T a b l e X I ( F i g . 2 3 ) S t e a d y s t a t e , s e p a r a t i o n f a c t o r ( A ) a n d p o w e r r e q u i r e m e n t s / l i t r e o f d i a l y s a t e p r o d u c e d p e r c e l l ( B ) ( J o u l e s / 1 p e r c e l l ) a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M 2 h o u r s 2 0 h o u r s NUM c m / s e c I R O N A B A B 6 7 2 0 0 , 5 0 0 , 0 1 r 8 9 3 1 3 5 7 , 1 , 8 7 2 1 3 2 1 , 91 20 0 , 5 0 0 , 0 3 , 1 4 4 1 2 3 5 , N . A . N . A . 71 2 0 0 , 5 0 0 , 0 2 , 4 1 0 1 2 5 8 , 2 , 4 4 2 1 2 7 4 , 7 9 2 0 0 , 5 0 0 , 9 2 3 , 2 5 5 1 2 9 2 , 3 , 4 4 4 1 3 3 5 , 81 2 0 0 , 5 0 1 , 1 1 3 , 5 5 1 1 3 7 9 , 3 , 4 4 8 1 3 8 0 , 8 8 2 0 0 , 5 0 5 , 2 4 3 , 2 1 4 1 2 7 6 , 3 , 0 5 5 1 3 1 0 , 9 0 20 0 , 5 0 5 , 5 0 2 , 7 7 7 1 2 7 9 , 2 , 7 4 7 1 2 9 0 , 6 5 2 0 1 , 2 5 0 , 0 1 2 4 6 5 4 0 , 1 , 2 9 3 5 4 9 , 7 5 2 0 1 , 2 5 0 , 0 1 , 5 2 7 6 3 0 , 1 , 5 8 7 6 6 5 , 7 3 2 0 1 , 2 5 0 , 0 1 7 8 9 6 3 9 , 1 , 6 9 0 6 3 7 , 7 7 2 0 1 , 2 5 1 , 0 9 1 6 5 2 6 0 6 , 1 , 6 7 1 6 0 9 , 8 2 2 0 1 , 2 5 1 , 0 1 1 5 9 0 6 3 4 , 1 , 5 7 3 6 1 0 , 8 5 2 0 1 , 2 5 5 , 6 6 1 4 8 0 5 7 6 , 1 , 4 4 5 571 , 6 6 3 0 0 , 5 0 0 , 0 2 251 2 5 8 4 , 2 , 2 4 7 2 5 3 9 , 7 0 3 0 0 , 5 0 0 , 0 3 4 2 5 2 6 4 5 , 3 , 1 4 4 2 5 5 3 , 9 2 3 0 0 , 5 0 0 , 0 4 7 0 0 2 3 9 8 , N . A . N . A . 8 0 3 0 0 , 5 0 1 , 0 4 4 6 0 0 2 4 0 2 , 4 , 0 0 9 2 4 6 9 , 8 9 30 0 , 5 0 5 , 3 1 4 7 3 2 2 1 8 4 , 4 , 4 1 9 2 4 1 8 , 9 4 30 0 , 5 0 5 , 3 1 3 4 9 3 2 3 9 7 , 3 , 6 2 3 2 5 1 7 , 6 8 3 0 1 , 2 5 0 , 0 1 3 3 7 1 2 6 6 , 1 , 2 9 4 1221 , 74 3 0 1 , 2 5 0 , 0 2 3 6 6 1 401 , 2 , 2 3 5 1 3 9 5 , 7 6 3 0 1 , 2 5 0 , 0 1 8 7 0 1 2 6 9 , 1 , 8 8 1 1 2 8 6 , 8 3 30 1 , 2 5 1 , 0 2 2 , 3 3 6 1 4 0 3 , 2 , 2 5 2 1 4 5 7 , 8 4 30 1 , 2 5 1 , 0 7 2 , 0 4 0 1 2 9 2 , 1 , 8 3 6 1 2 2 9 , 8 6 30 1 , 2 5 5 , 0 0 1 , 9 4 9 1 3 2 5 , 1 , 7 9 7 1 291 , 8 7 30 1 , 2 5 5 , 6 4 1 , 9 0 9 1 1 1 5 , 1 , 7 8 2 1 1 2 9 , 88 T a b l e X I I ( F I G . 2 4 ) S e p a r a t i o n f a c t o r N s ( A ) a n d t h e p o w e r c o n s u m p t i o n ( j o u l e s / l i t r e p e r c e l l ) a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) . RUN V O L T V E L Y PPM 2 1 rIOURS NUM C M / S E C IRON ( A ) ( B ) 41 20 1 , 2 5 0 , 0 41 , 6 7 6 8 5 4 9 , 30 20 1 , 2 5 0 , 8 5 4 8 , 2 5 o , 38 20 1 , 2 5 0 , 9 7 1 6 , 5 6 6 4 2 1 7 , 39 20 1 , 2 5 0 , 6 8 4 5 , 4 2 6 4 3 7 1 , 32 20 1 , 2 5 4 , 7 8 4 0 , 9 0 o , 34 20 5 , 0 0 0 , 9 9 9 , 8 2 4 4 0 5 2 , 35 20 5 , 0 0 4 , 6 8 1 1 , 3 5 4 8 1 6 3 , 43 20 5 , 0 0 4 , 6 6 1 0 , 3 2 5 1 6 4 2 , 40 30 1 , 2 5 0 , 0 1 0 4 , 8 5 1 0 7 2 8 3 , 31 30 1 , 2 5 1 , 0 3 7 2 , 18 1 1 8 1 0 1 , 42 30 1 , 2 5 0 , 9 2 3 2 , 8 3 1 1 9 3 5 6 , 33 30 1 , 2 5 4 , 7 3 2 7 , 9 9 1 1 9 3 8 2 , 36 30 5 , 0 0 0 , 8 7 2 9 , 6 1 9 4 3 6 5 , 37 30 5 , 0 0 4 , 6 1 2 0 , 9 9 9 5 4 7 8 , 44 30 5 , 0 0 4 , 6 8 1 3 , 6 0 1 0 2 5 7 3 , 2 0 HOURS ( A ) ( B ) 2 6 3 3 1 3 2 4 21 1 0 , 3 , 5 , 9 2 , 6 7 , 2 9 , 1 6 , 1 9 , 4 , 1 2 , 0 4 9 3 5 6 3 2 6 7 6 5 7 4 7 9 7 0 3 9 4 7 7 2 9 0 9 9 81 7 0 2 2 3 , 0 , 6 6 4 0 0 , 6 7 6 6 2 , 0 , 4 5 8 6 9 , 4 6 9 4 0 , 4 7 8 7 2 , 1 1 8 9 8 9 , 1 1 6 6 0 9 , 1 2 8 2 5 6 , 1 1 8 6 9 1 , 9 1 0 4 9 , 9 6 7 9 8 , 1 0 7 1 8 5 , 8 9 T a b l e X I I I ( F i g . 2 5 ) S t e a d y a n d u n s t e a d y s t a t e , d i a l y s a t e c o n c e n t r a t i o n s ( m g . / l . ) ( A ) a n d t h e p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d p e r c e l l ( j o u l e s / 1 p e r c e l l ) ( B ) a t 2 a n d 2 0 h o u r s ( 1 , 2 5 c m / s e c o n l y ) . R U N V O L T V E L Y P P M 2 h o u r s 2 0 h o u r s NUM c m / s e c I R O N A B A B 6 5 2 0 1 , 2 5 0 , 0 1 9 1 3 , 5 4 0 , 1 8 2 8 , 5 4 9 7 5 2 0 1 , 2 5 0 , 0 1 7 0 0 , 6 3 0 , 1 5 3 1 , 6 6 5 7 3 2 0 1 , 2 5 0 , 0 1 1 7 7 , 6 3 9 , 1 2 4 6 , 6 3 7 7 7 2 0 1 , 2 5 1 , 0 9 1 3 0 4 , 6 0 6 , 1 2 9 8 , 6 0 9 8 2 2 0 1 , 2 5 1 , 0 1 1 5 6 9 , 6 3 4 , 1 5 4 9 , 6 1 0 8 5 2 0 1 , 2 5 5 , 6 6 1 6 3 8 , 5 7 6 , 1 5 6 6 , 571 6 8 3 0 1 , 2 5 0 , 0 1 8 6 3 , 1 2 6 6 , 1 8 0 9 , 1221 7 4 3 0 1 , 2 5 0 , 0 9 8 3 , 1 401 , 1 0 3 9 , 1 3 9 5 7 6 3 0 1 , 2 5 0 , 0 1 521 , 1 2 6 9 , 1 4 1 0 , 1 2 8 6 8 3 3 0 1 , 2 5 1 , 0 2 1 0 4 2 , 1 4 0 3 , 1 1 0 2 , 1 4 5 7 8 4 3 0 1 , 2 5 1 , 0 7 1 1 8 0 , 1 2 9 2 , 1 2 7 4 , 1 2 2 9 8 6 3 0 1 , 2 5 5 , 0 0 1 3 8 7 , 1 3 2 5 , 1 3 8 7 , 1291 8 7 3 0 1 , 2 5 5 , 6 4 1 1 6 9 , 1 1 1 5 , 1271 , 1 1 2 9 41 2 0 1 , 2 5 0 , 0 1 0 3 , 6 8 5 4 9 , 1 6 0 , 702 .23 3 0 2 0 1 , 2 5 0 , 8 5 3 6 6 , o , 3 0 3 , 0 3 8 2 0 1 , 2 5 0 , 9 7 2 9 3 , 6 4 2 1 7 , 3 3 2 , 6 6 4 0 0 3 9 2 0 1 , 2 5 0 , 6 8 91 , 6 4 3 7 1 , 1 6 9 , 6 7 6 6 2 3 2 2 0 1 , 2 5 4 , 7 8 9 9 , o , 1 5 8 , 0 4 0 3 0 1 , 2 5 0 , 0 3 9 , 1 0 7 2 8 3 , 4 7 , 1 1 8 9 8 9 31 3 0 1 , 2 5 1 , 0 3 5 8 , 1 1 8 1 0 1 , 5 8 , 1 1 6 6 0 9 4 2 3 0 1 , 2 5 0 , 9 2 1 3 7 , 1 1 9 3 5 6 , 1 4 7 , 1 2 8 2 5 6 3 3 3 0 1 , 2 5 4 , 7 3 1 7 3 , 1 1 9 3 8 2 , 2 6 3 , 1 1 8 6 9 1 9 0 T a b l e X I V ( F i g . 2 6 ) A m o u n t o f i r o n a c c u m u l a t e d o n t h e t e s t p a i r ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s . ( s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M • ( A ) ( B ) NUM c m / s e c I R O N M g . 6 7 2 0 0 , 5 0 0 , 0 N . A . 1 , 1 2 91 2 0 0 , 5 0 0 , 0 N . A . N . A . 71 2 0 0 , 5 0 0 , 0 N . A . -1 , 3 4 7 9 2 0 0 , 5 0 0 , 9 2 0 , 2 4 - 5 , 8 1 81 2 0 0 , 5 0 1 , 1 1 0 , 3 6 2 , 9 0 8 8 2 0 0 , 5 0 5 , 2 4 1 , 8 6 4 , 9 6 9 0 2 0 0 , 5 0 5 , 5 0 1 , 2 5 1 , 0 5 6 5 2 0 1 , 2 5 0 , 0 N . A . - 3 , 7 0 7 5 2 0 1 , 2 5 0 , 0 N . A . - 3 , 9 2 7 3 2 0 1 , 2 5 0 , 0 N . A . 5 , 5 3 7 7 2 0 1 , 2 5 1 , 0 9 0 , 9 2 - 1 , 1 5 8 2 2 0 1 , 2 5 1 , 0 1 0 , 4 3 1 , 0 5 8 5 2 0 1 , 2 5 5 , 6 6 1 , 2 5 2 , 4 0 6 6 3 0 0 , 5 0 0 , 0 N . A . 0 , 1 9 7 0 3 0 0 , 5 0 0 , 0 N . A . 8 , 2 2 9 2 3 0 0 , 5 0 0 , 0 N . A . N . A . 8 0 30 0 , 5 0 1 , 0 4 0 , 5 1 1 2 , 8 5 8 9 3 0 0 , 5 0 5 , 3 1 2 , 2 4 6 , 6 2 9 4 3 0 0 , 5 0 5 , 3 1 1 , 1 6 - 3 , 7 3 6 8 3 0 1 , 2 5 0 , 0 N . A . 3 , 2 2 74 3 0 1 , 2 5 0 , 0 N . A . 5 , 5 4 7 6 30 1 , 2 5 0 , 0 N . A . - 0 , 5 9 8 3 3 0 1 , 2 5 1 , 0 2 0 , 4 9 3 , 6 2 8 4 3 0 1 , 2 5 1 , 0 7 0 , 5 4 9 , 9 7 8 6 30 1 , 2 5 5 , 0 0 2 , 5 8 7 , 7 7 8 7 3 0 1 , 2 5 5 , 6 4 2 , 9 1 6 , 6 6 91 T a b l e X V ( F i g . 2 7 ) A v e r a g e i r o n a c c u m u l a t i o n o n t h e t e s t m e m b r a n e s ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r N s ( B ) d u r i n g a r u n ( u n s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) ( B ) NUM c m / s e c I R O N 41 2 0 1 , 2 5 0 , 0 0 , 3 4 3 7 , 5 0 3 0 2 0 1 , 2 5 0 , 8 5 0 , 4 5 2 9 , 6 8 3 8 2 0 1 , 2 5 0 , 9 7 1 , 4 7 1 8 , 1 4 3 9 2 0 1 , 2 5 0 , 6 8 1 , 3 2 4 6 , 4 6 3 2 2 0 1 , 2 5 4 , 7 8 2 , 0 0 4 7 , 0 3 3 4 2 0 5 , 0 0 0 , 9 9 1 , 0 2 - 8 , 4 5 3 5 2 0 5 , 0 0 4 , 6 8 2 , 4 2 6 7 , 0 2 4 3 2 0 5 , 0 0 4 , 6 6 2 , 5 9 4 3 , 9 0 4 0 3 0 1 , 2 5 0 , 0 0 , 7 8 1 1 , 5 9 31 3 0 1 , 2 5 1 , 0 3 0 , 22 6 , 6 3 4 2 3 0 1 , 2 5 0 , 9 2 • 0 , 3 1 1 0 , 2 4 3 3 3 0 1 , 2 5 4 , 7 3 4 , 0 7 4 0 , 2 5 3 6 3 0 5 , 0 0 0 , 8 7 1 , 5 1 3 2 , 7 9 3 7 3 0 5 , 0 0 4 , 6 1 3 , 2 0 7 6 , 2 3 44 3 0 5 , 0 0 4 , 6 8 3 , 0 5 5 , 8 6 T a b l e X V I ( F i g . 2 8 ) T h e t o t a l a m o u n t o f i r o n a c c u m u l a t i o n ( b a s e d o n m e m b r a n e s ) , ( m g . ) ( A ) a n d t h e t o t a l a m o u n t o f i r o n l o s t i n f e e d s t r e a m ( m g . ) ( B ) ( s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) ( B ) c m / s e m I R O N M g . M g . 7 9 2 0 0 , 5 0 0 , 9 2 3 , 1 7 4 6 , 8 81 2 0 0 , 5 0 1 , 1 1 4 , 7 3 41 , 4 8 8 2 0 0 , 5 0 5 , 2 4 2 4 , 12 1 2 7 , 5 9 0 2 0 0 , 5 0 5 , 5 0 1 6 , 2 0 1 7 9 , 6 7 7 2 0 1 , 2 5 1 , 0 9 1 1 , 9 0 7 5 , 2 8 2 2 0 1 , 2 5 1 ,01 5 , 5 8 31 , 6 8 5 2 0 1 , 2 5 5 , 6 6 1 6 , 2 2 9 9 , 5 8 0 3 0 0 , 5 0 1 , 0 4 6 , 6 5 4 2 , 2 8 9 3 0 0 , 5 0 5 , 3 1 2 9 , 0 9 1 7 8 , 9 9 4 3 0 0 , 5 0 5 , 3 1 1 5 , 04 1 5 3 , 1 8 3 3 0 1 , 2 5 1 , 0 2 6 , 3 5 51 , 4 8 4 3 0 1 , 2 5 1 , 0 7 6 , 9 8 5 5 , 0 8 6 3 0 •1 , 2 5 5 , 0 0 3 3 , 51 1 4 8 , 8 8 7 3 0 1 , 2 5 5 , 6 4 3 7 , 8 2 1 8 9 , 6 9 2 T a b l e X V I I ( F i g . 2 9 ) T o t a l i r o n a c c u m u l a t i o n b a s e d o n t h e m e m b r a n e s ( m g . ) ( A ) a n d t h e a m o u n t o f i r o n l o s t i n t h e f e e d d u r i n g a r u n ( m g . ) ( B ) ( u n s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) ( B ) NUM C M / S E C I R O N 41 2 0 1 , 2 5 0 , 0 1 9 , 3 0 , 0 3 0 2 0 1 , 2 5 - 0 , 8 5 2 5 , 3 1 6 , 4 3 8 2 0 1 , 2 5 0 , 9 7 8 2 , 1 1 2 , 3 3 9 2 0 1 , 2 5 0 , 6 8 7 3 , 7 3 , 2 3 2 2 0 1 , 2 5 4 , 7 8 1 1 2 , 2 1 1 3 , 2 3 4 2 0 5 , 0 0 0 , 9 9 5 7 , 3 2 7 , 4 3 5 2 0 5 , 0 0 4 , 6 8 1 3 5 , 3 1 4 1 , 4 4 3 2 0 5 , 0 0 4 , 6 6 1 4 4 , 9 1 4 6 , 3 4 0 3 0 1 , 2 5 0 , 0 4 3 , 9 0 , 0 31 3 0 1 , 2 5 1 , 0 3 1 2 , 2 1 3 , 9 4 2 3 0 1 , 2 5 0 , 9 2 1 7 , 3 2 9 , 5 3 3 3 0 1 , 2 5 4 , 7 3 2 2 8 , 2 1 0 1 , 7 3 6 3 0 5 , 0 0 0 , 8 7 8 4 , 6 7 , 8 3 7 3 0 5 , 0 0 4 , 6 1 1 7 9 , 4 1 5 6 , 0 4 4 3 0 5 , 0 0 4 , 6 8 1 7 0 , 8 1 4 2 , 5 9 3 T a b l e X V I I I p H o f t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) . r u n v o l t v e l y ppm ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s 6 7 2 0 0 5 0 0 . 0 5 231 6 4 4 2 6 , 4 4 2 9 , 4 7 5 91 20 0 5 0 0 0 4 471 4 7 0 9 4 , 7 0 9 N . A . 71 2 0 0 r 5 0 0 0 6 1 9 5 9 0 6 9 9 , 0 6 9 1 0 , 4 1 5 7 9 2 0 0 , 5 0 0 9 2 6 1 3 8 8 9 6 3 8 , 9 6 3 3 , 4 4 7 81 2 0 0 , 5 0 1 1 1 6 1 9 4 9 1 6 5 9 , 1 6 5 3 , 2 1 7 8 8 2 0 0 r 5 0 5 , 24 6 0 9 3 6 1 6 9 6 , 1 6 9 2 , 9 1 6 9 0 2 0 0 r 5 0 5 5 0 5 0 4 3 6 2 0 7 6 , 2 0 7 2 , 9 9 9 6 5 2 0 1 r 2 5 0 0 6 3 4 2 9 5 7 9 9 , 5 7 9 1 0 , 6 6 8 7 5 2 0 . 1 , 2 5 0 0 6 01 1 6 5 4 3 6 , 5 4 3 6 , 8 5 6 7 3 2 0 1 2 5 0 0 6 0 8 6 8 761 8 , 7 6 1 9 , 5 7 4 7 7 2 0 1 , 2 5 1 0 9 4 581 9 1 0 6 9 , 1 0 6 8 , 7 3 6 8 2 2 0 1 , 2 5 1 , 01 5 1 2 7 4 2 5 6 4 , 2 5 6 2 , 9 9 2 8 5 2 0 1 , 2 5 5 , 6 6 4 2 0 4 4 2 8 5 4 , 2 8 5 2 , 9 9 6 6 6 3 0 0 , 5 0 0 0 4 1 6 8 7 5 7 8 7 , 5 7 8 1 0 , 6 6 9 7 0 3 0 0 5 0 0 0 3 5 2 4 4 081 4 , 081 7 , 5 2 8 9 2 30 0 , 5 0 0 0 3 4 7 6 9 6 8 8 9 , 6 8 8 N . A . 8 0 3 0 0 , 5 0 1 , 04 9 8 7 3 10 3 2 4 1 0 , 3 2 4 2 , 8 2 0 8 9 3 0 0 , 5 0 5 31 10 071 9 961 9 , 961 2 , 7 9 7 9 4 3 0 0 , 5 0 5 , 31 9 9 3 3 10 0 0 7 1 0 , 0 0 7 2 , 8 1 9 6 8 3 0 1 , 2 5 0 0 4 6 4 0 9 0 6 9 9 , 0 6 9 9 , 7 0 9 7 4 30 1 , 2 5 0 0 4 431 4 2 8 4 4 , 2 8 4 6 , 4 4 7 7 6 3 0 1 , 2 5 0 0 9 521 5 131 5 , 131 1 0 , 4 8 4 8 3 3 0 1 , 2 5 1 0 2 4 5 2 2 5 0 4 2 5 0 4 2 2 , 8 8 4 8 4 3 0 1 , 2 5 1 0 7 3 8 2 4 9 3 6 0 9 , 3 6 0 2 , 9 0 2 8 6 30 1 , 2 5 5 0 0 4 7 3 9 4 7 0 0 4 , 7 0 0 2 , 7 6 5 8 7 30 1 , 2 5 5 , 64 4 5 8 3 6 1 18 6 , 1 1 8 2 , 7 2 2 9 4 T a b l e X I X p H o f t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t a a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y ppm ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 41 2 0 1 , 2 5 0 , 0 4 , 0 7 4 , 0 2 2 , 9 9 2 , 9 8 3 0 2 0 1 , 2 5 0 , 8 5 3 , 9 2 3 , 9 8 2 , 4 8 2 , 7 4 3 8 2 0 1 , 2 5 0 , 9 7 4 , 5 3 6 , 12 2 , 8 8 3 , 0 6 3 9 2 0 1 , 2 5 0 , 6 8 5 , 8 2 6 , 5 8 2 , 7 7 2 , 9 5 3 2 2 0 1 , 2 5 4 , 7 8 3 , 9 6 4 , 6 8 2 , 6 2 2 , 9 5 34 2 0 5 , 0 0 0 , 9 9 3 , 6 8 3 , 9 3 3 , 3 0 3 , 4 3 3 5 2 0 5 , 0 0 4 , 6 8 3 , 7 4 6 , 2 9 2 , 9 0 3 , 0 7 4 3 2 0 5 , 0 0 4 , 6 6 4 , 4 0 9 , 1 8 3 , 1 0 3 , 1 4 4 0 3 0 1 , 2 5 0 , 0 4 , 1 1 3 , 7 8 2 , 8 0 2 , 3 7 31 3 0 1 , 2 5 1 , 0 3 3 , 6 7 3 , 9 6 2 , 3 0 2 , 5 0 4 2 3 0 1 , 2 5 0 , 9 2 3 , 7 9 4 , 1 0 2 , 8 4 2 , 9 4 3 3 3 0 1 , 2 5 4 , 7 3 4 , 0 2 5 , 1 1 2 , 6 2 2 , 7 6 3 6 3 0 5 , 0 0 0 , 8 7 3 , 8 8 4 , 3 6 2 , 7 6 2 , 9 2 3 7 3 0 5 , 0 0 4 , 6 1 4 , 5 2 9 , 3 8 2 , 8 5 2 , 9 0 44 3 0 5 , 0 0 4 , 6 8 6 , 0 5 9 , 9 0 2 , 8 4 2 , 7 7 T a b l e X X T h e p e r c e n t s e p a r a t i o n b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) R U N V O L T V E L Y P P M ( A ) ( B ) c m / s e c I R O N 2 h o u r s 2 0 h o u r s 7 9 2 0 0 , 5 0 0 , 9 2 5 2 , 0 9 4 , 4 2 , 2 " 4 , 8 81 2 0 0 , 5 0 1 , 1 1 5 3 , 2 5 9 , 4 4 , 2 - 1 3 , 0 8 8 2 0 0 , 5 0 5 , 2 4 3 2 , 6 2 7 , 7 8 , 2 6 , 3 90 2 0 0 , 5 0 5 , 5 0 3 9 , 2 3 8 , 3 1 1 , 8 2 , 2 77 2 0 1 , 2 5 1 , 0 9 2 2 , 8 0 , 0 2 3 , 2 2 1 , 5 8 2 2 0 1 , 2 5 1 , 0 1 1 2 , 7 1 4 , 9 9 , 7 5 , 3 8 5 2 0 1 , 2 5 5 , 6 6 1 6 , 8 3 , 5 7 , 7 5 , 0 8 0 3 0 . 0 , 5 0 1 , 0 4 6 0 , 1 6 7 , 7 4 , 3 - 1 4 , 5 8 9 3 0 0 , 5 0 5 , 3 1 3 2 , 9 2 8 , 1 1 , 3 - 5 , 4 94 3 0 0 , 5 0 5 , 3 1 4 7 , 4 4 4 , 9 2 , 6 - 1 8 , 9 8 3 3 0 1 , 2 5 1 , 0 2 3 5 , 6 2 3 , 7 1 5 , 7 - 1 1 , 1 8 4 3 0 1 , 2 5 1 , 0 7 3 0 , 2 3 3 , 1 1 0 , 7 - 2 0 , 9 8 6 3 0 1 , 2 5 5 , 0 0 1 7 , 1 8 , 1 1 8 , 4 0 , 5 8 7 3 0 1 , 2 5 5 , 6 4 0 , 9 1 1 , 9 6 , 8 - 3 , 7 95 T a b l e X X I U n s t e a d y s t a t e , p e r c e n t s e p a r a t i o n b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M NUM c m / s e c I R O N ( A ) ( B ) 2 2 0 2 2 0 h o u r s h o u r s h o u r s h o u r s 41 2 0 1 , 2 5 0 , 0 N . A . N . A . N . A . N . A . 30 2 0 1 , 2 5 0 , 8 5 9 9 , 9 9 0 , 9 - 3 7 , 2 - 2 4 , 7 38 2 0 1 , 2 5 0 , 9 7 9 7 , 4 9 3 , 9 6 7 , 6 - 2 2 , 1 3 9 2 0 1 , 2 5 0 , 6 8 5 8 , 0 5 6 , 8 - 3 9 , 9 - 3 3 , 1 32 2 0 1 , 2 5 4 , 7 8 9 7 , 2 9 6 , 0 - 7 4 , 9 - 5 9 , 0 34 2 0 5 , 0 0 0 , 9 9 9 6 , 5 9 7 , 0 - 6 0 , 7 - 3 6 , 8 3 5 2 0 5 , 0 0 4 , 6 8 9 4 , 3 8 5 , 8 - 6 6 , 5 - 3 0 , 6 4 3 2 0 5 , 0 0 4 , 6 6 9 2 , 5 8 3 , 4 - 3 9 , 5 - 4 4 , 3 4 0 3 0 1 , 2 5 0 , 0 N . A . N . A . N . A . N . A . 31 3 0 1 , 2 5 1 , 0 3 9 9 , 1 9 9 , 9 - 2 0 , 6 - 5 1 , 8 4 2 3 0 1 , 2 5 0 , 9 2 9 9 , 9 9 9 , 8 - 4 7 , 7 - 7 5 , 1 3 3 3 0 1 , 2 5 4 , 7 3 9 8 , 6 91 , 8 - 1 8 , 2 - 6 5 , 0 36 3 0 5 , 0 0 0 , 8 7 8 5 , 3 9 0 , 6 9 5 , 5 - 2 , 5 37 3 0 5 , 0 0 4 , 6 1 9 9 , 7 9 8 , 3 - 6 6 , 3 - 5 1 , 7 44 3 0 5 , 0 0 4 , 6 8 8 5 , 3 8 5 , 3 - 3 1 , 9 - 5 0 , 0 T a b l e X X I I I o n i c s e l e c t i v i t y b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s , ( s t e a d y s t a t e r u n s ) . r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 • 2 0 h r s 7 9 2 0 0 , 5 0 0 , 9 2 1 , 0 2 5 1 , 8 0 0 0 , 0 3 6 - 0 , 0 7 4 81 2 0 0 , 5 0 1 , 1 1 0 , 9 9 0 1 , 1 0 9 0 , 0 6 6 - 0 , 2 1 6 8 8 2 0 0 , 5 0 5 , 2 4 0 , 6 4 5 0 , 571 0 , 1 4 1 0 , 1 1 1 90 2 0 0 , 5 0 5 , 5 0 0 , 8 5 4 0 , 8 3 7 0 , 2 3 6 0 , 0 4 4 77 2 0 1 , 2 5 1 , 0 9 0 , 9 4 8 0 , 0 0 , 9 1 1 0 , 8 1 7 8 2 2 0 1 , 2 5 1 , 0 1 0 , 5 7 1 0 , 6 8 6 0 , 4 0 9 0 , 2 2 7 8 5 2 0 1 , 2 5 5 , 6 6 0 , 8 5 2 0 , 1 8 3 0 , 4 1 1 0 , 2 9 8 8 0 3 0 0 , 5 0 1 , 0 4 0 , 9 4 5 1 , 1 3 8 0 , 0 6 3 - 0 , 2 3 2 8 9 3 0 0 , 5 0 5 , 3 1 0 , 5 0 3 0 , 4 5 8 0 , 0 2 1 - 0 , 0 7 7 94 3 0 0 , 5 0 5 , 3 1 0 , 8 5 9 0 , 7 9 4 0 , 0 4 7 - 0 , 3 3 0 8 3 3 0 1 , 2 5 1 , 0 2 0 , 8 9 0 0 , 6 1 9 0 , 3 9 1 - 0 , 2 8 5 8 4 3 0 1 , 2 5 1 , 0 7 0 , 8 9 9 1 , 1 4 9 0 , 3 0 3 - 0 , 6 8 1 8 6 3 0 1 , 2 5 5 , 0 0 0 , 5 4 8 0 , 2 9 6 0 , 5 4 6 0 , 0 1 8 8 7 3 0 1 , 2 5 5 , 6 4 0 , 031 0 , 4 6 3 0 , 2 0 7 - 0 , 1 1 4 9 6 T a b l e X X I I I I o n i c s e l e c t i v i t y b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 20 h o u r s ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 41 2 0 1 , 2 5 0 , 0 0 0 0 0 , 0 0 , 0 3 0 2 0 1 , 2 5 ' 0 , 8 5 1 0 9 8 0 , 9 7 7 - 0 , 1 1 1 - 0 , 1 8 1 38 2 0 1 , 2 5 0 , 9 7 1 1 15 1 , 1 0 0 0 , 6 1 5 - 0 , 2 2 6 3 9 2 0 1 , 2 5 0 , 6 8 0 6 0 8 0 , 6 1 8 - 0 , 3 8 0 - 0 , 3 4 2 3 2 2 0 1 , 2 5 4 , 7 8 1 0 3 0 1 , 0 7 6 - 0 , 5 8 4 - 0 , 4 4 0 3 4 2 0 5 , 0 0 0 , 9 9 1 1 8 4 1 , 1 6 9 - 0 , 7 4 8 - 0 , 4 5 4 3 5 2 0 5 , 0 0 4 , 6 8 1 1 4 8 1 , 5 6 0 - 0 , 6 4 7 - 0 , 4 4 7 4 3 2 0 5 , 0 0 4 , 6 6 1 1 34 1 198 - 0 , 4 3 9 - 0 , 5 8 5 4 0 3 0 1 , 2 5 0 , 0 0 0 , 0 0 , 0 0 , 0 31 3 0 1 , 2 5 1 , 0 3 1 0 2 2 1 0 3 2 - 0 , 1 6 9 - 0 , 4 4 1 4 2 3 0 1 , 2 5 0 , 9 2 1 0 6 8 1 , 0 7 3 - 0 , 4 2 5 - 0 , 7 2 0 3 3 3 0 1 , 2 5 4 , 7 3 1 0 6 9 1 , 0 3 8 - 0 , 1 5 3 - 0 , 6 9 4 36 3 0 5 , 0 0 0 , 8 7 0 9 1 6 1 0 0 5 0 , 9 0 2 - 0 , 0 2 6 37 3 0 5 , 0 0 4 , 6 1 1 1 0 3 1 4 8 9 - 0 , 6 5 7 - 0 , 7 4 5 4 4 3 0 5 , 0 0 4 , 6 8 0 9 9 0 0 9 9 3 - 0 , 3 6 6 - 0 , 6 2 3 9 7 T a b l e X X I V A v e r a g e c u r r e n t e f f i c i e n c y ( A ) a t 2 a n d 2 0 h o u r s a n d t h e p e r c e n t d r o p i n c u r r e n t e f f i c i e n c y o v e r 1 8 h o u r s ( s t e a d y s t a t e r u n s ) . R U N V O L T V E L Y P P M ( A ) ( B ) NUM c m / s e c I R O N 2 2 0 h o u r s h o u r s 6 7 2 0 0 , 5 0 0 r 0 0 , 6 1 2 0 , 6 0 8 0 , 6 5 9 1 2 0 0 , 5 0 0 , 0 0 9 7 0 N . A . 1 0 0 , 0 0 7 1 2 0 0 , 5 0 0 r 0 0 9 3 5 0 , 9 1 2 2 , 5 1 7 9 2 0 0 5 0 0 9 2 1 2 4 5 1 , 1 7 3 5 , 7 7 8 1 2 0 0 , 5 0 1 , 1 1 0 9 7 0 0 , 9 7 7 -o , 6 6 8 8 2 0 0 , 5 0 5 , 2 4 0 9 5 7 0 9 2 3 3 , 5 0 9 0 2 0 0 , 5 0 5 , 5 0 1 0 3 3 0 9 6 0 7 , 0 7 6 5 2 0 1 2 5 0 0 0 5 8 5 0 , 6 5 2 - 1 1 , 3 4 7 5 2 0 1 2 5 0 0 0 9 0 0 0 9 0 3 - 0 , 3 6 7 3 2 0 1 2 5 0 0 0 9 7 3 0 9 0 4 7 , 1 0 7 7 2 0 1 2 5 1 0 9 0 9 3 9 0 9 5 6 - 1 , 8 0 8 2 2 0 1 2 5 1 0 1 0 9 7 7 0 9 7 5 0 , 2 4 8 5 2 0 1 2 5 5 6 6 0 9 1 6 0 8 1 8 1 0 7 5 6 6 3 0 0 5 0 0 0 0 6 1 6 0 6 1 6 0 , 0 5 7 0 3 0 0 5 0 0 0 0 8 9 5 0 8 7 2 2 , 5 5 9 2 3 0 0 5 0 0 0 0 9 6 0 N A . 1 0 0 , 0 0 8 0 3 0 0 5 0 1 0 4 0 9 7 1 0 8 9 3 8 , 0 4 8 9 3 0 0 5 0 5 3 1 0 8 8 8 0 8 8 1 0 8 5 9 4 3 0 0 5 0 5 3 1 o, 9 5 1 0 8 7 6 7 8 7 6 8 3 0 1 2 5 0 0 0 4 9 9 0 4 3 8 1 2 2 2 7 4 3 0 1 2 5 0 0 o, 9 1 1 0 9 2 5 - 1 5 5 7 6 3 0 1 , 2 5 0 0 1 , 0 4 5 0 9 7 4 6 7 8 8 3 3 0 1 2 5 1 , 0 2 o, 9 6 4 0 9 5 5 0 8 8 8 4 3 0 1 , 2 5 1 , 0 7 o, 9 5 5 0 8 7 2 8 6 7 8 6 3 0 1, 2 5 5 , 0 0 1, 0 0 3 0 8 6 0 1 4 2 1 8 7 3 0 1 , 2 5 5 , 6 4 o, 9 5 8 0 8 8 6 7 5 7 98 T a b l e X X V U n s t e a d y s t a t e , a v e r a g e c u r r e n t e f f i c i e n c y ( A ) a t 2 a n d 2 0 h o u r s a n d t h e p e r c e n t d r o p i n c u r r e n t e f f i c i e n c y o v e r 18 h o u r s ( B ) . r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h o u r s h o u r s 41 2 0 1 , 2 5 3 0 2 0 1 , 2 5 3 8 2 0 1 , 2 5 3 9 2 0 1 , 2 5 3 2 2 0 1 , 2 5 34 2 0 5 , 0 0 3 5 2 0 5 , 0 0 4 3 2 0 5 , 0 0 4 0 3 0 1 , 2 5 31 3 0 1 , 2 5 4 2 3 0 1 , 2 5 3 3 3 0 1 , 2 5 3 6 3 0 5 , 0 0 37 3 0 5 , 0 0 44 3 0 5 , 0 0 0 , 0 0 , 0 1 8 0 , 8 5 N . A . 0 , 9 7 0 , 0 2 1 0 , 6 8 0 , 0 1 8 4 , 7 8 N . A . 0 , 9 9 0 , 0 2 3 4 , 6 8 0 , 0 2 5 4 , 6 6 0 , 0 2 4 0 , 0 0 , 0 1 6 1 , 0 3 0 , 0 1 5 0 , 9 2 0 , 0 1 6 4 , 7 3 0 , 0 1 7 0 , 8 7 0 , 0 1 9 4 , 6 1 0 , 0 1 9 4 , 6 8 0 , 0 1 7 0 , 0 1 7 7 , 4 8 N . A . 0 , 0 0 , 0 1 9 9 , 5 8 0 , 0 1 7 5 , 6 9 N . A . 0 , 0 0 , 0 2 4 - 5 , 3 2 0 , 0 1 9 2 6 , 0 1 0 , 0 2 2 6 , 8 1 0 , 0 1 6 1 , 9 1 0 , 0 1 5 4 , 2 9 0 , 0 1 6 1 , 9 1 0 , 0 1 6 9 , 8 0 0 , 0 1 9 0 , 6 6 0 , 0 1 4 2 5 , 4 5 0 , 0 1 7 0 , 7 4 9 9 T a b l e X X V I T h e p e r c e n t s e p a r a t i o n b a s e d o n s o d i u m f o r t h e d i a l y s a t e ( A ) a n d b r i n e s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) . cUN V O L T V E L Y P P M ( A ) ( B ) c m / s e c I R O N 2 h o u r s 2 0 h o u r s 67 2 0 0 , 5 0 0 , 0 3 0 , 3 3 2 , 8 31 , 9 2 5 , 9 91 2 0 0 , 5 0 0 , 0 5 0 , 1 N . A . 56 , 9 N . A . 71 2 0 0 , 5 0 0 , 0 4 0 , 6 4 0 , 2 4 3 , 0 4 5 , 9 7 9 2 0 0 , 5 0 0 , 9 2 5 0 , 7 5 2 , 4 6 0 , 4 6 3 , 9 81 2 0 0 , 5 0 1 , 1 1 5 3 , 8 5 3 , 6 64 , 1 6 0 , 1 8 8 2 0 0 , 5 0 5 , 2 4 5 0 , 6 4 8 , 6 58 , 7 5 6 , 9 9 0 2 0 0 , 5 0 5 , 5 0 4 5 , 9 4 5 , 8 5 0 , 3 4 8 , 9 6 5 2 0 1 , 2 5 0 , 0 1 3 , 8 1 2 , 4 7 , 5 1 3 , 3 7 5 2 0 1 , 2 5 0 , 0 ' 21 , 0 2 2 , 7 2 0 , 6 2 2 , 6 7 3 2 0 1 , 2 5 0 , 0 2 8 ,2 2 4 , 7 28 , 5 2 7 , 3 7 7 2 0 1 , 2 5 1 , 0 9 24 , 1 2 4 , 4 2 5 , 4 2 6 , 4 8 2 2 0 1 , 2 5 1 , 0 1 2 2 , 2 2 1 , 7 2 3 , 6 2 3 , 2 8 5 2 0 1 , 2 5 5 , 6 6 19 , 7 1 9 , 2 18 , 8 1 6 , 8 6 6 3 0 0 , 5 0 0 , 0 37 , 6 3 8 , 0 4 0 , 4 3 9 , 3 7 0 3 0 0 , 5 0 0 , 0 5 3 , 1 4 9 , 0 6 0 , 6 6 0 , 2 92 3 0 0 , 5 0 0 , 0 6 3 , 3 N . A . 7 2 , 4 N . A . 8 0 3 0 0 , 5 0 1 , 0 4 6 3 , 6 5 9 , 4 6 7 , 4 6 2 , 6 8 9 3 0 0 , 5 0 5 , 3 1 6 5 , 6 61 , 6 6 2 , 7 6 9 , 9 94 3 0 0 , 5 0 5 , 3 1 5 5 , 2 5 6 , 5 56 , 5 5 7 , 5 68 3 0 1 , 2 5 0 , 0 1 3 , 7 1 1 , 5 15 , 4 1 4 , 5 74 3 0 1 , 2 5 0 , 0 3 9 , 6 3 6 , 9 4 2 , 9 4 1 , 1 7 6 3 0 1 , 2 5 0 , 0 3 0 , 6 3 0 , 3 2 9 , 9 3 1 , 1 8 3 3 0 1 , 2 5 1 , 0 2 4 0 , 0 3 8 , 3 40 , 3 3 9 , 0 8 4 3 0 1 , 2 5 1 , 0 7 3 3 , 6 2 8 , 8 3 5 , 5 3 0 , 7 8 6 3 0 1 , 2 5 5 , 0 0 31 , 3 2 7 , 4 3 3 , 8 3 0 , 4 8 7 3 0 1 , 2 5 5 , 6 4 30 , 4 2 5 , 8 3 2 , 8 3 2 , 2 1 0 0 T a b l e X X V I I U n s t e a d y b a s e d o n s o d i u m i n t h e s t r e a m s a t s t a t e , p e r c e n t s e p a r a t i o n d i a l y s a t e ( A ) a n d b r i n e ( B ) 2 a n d 2 0 h o u r s . R U N V O L T V E L Y P P M ( A ) ( B ) NUM c m / s e c I R O N 2 2 0 2 2 0 h o u r s h o u r s h o u r s h o u r s 41 2 0 1 , 2 5 0 , 0 9 5 , 1 9 2 , 4 1 0 6 , 0 9 8 , 2 3 0 2 0 1 , 2 5 0 , 8 5 91 , 0 9 3 , 0 3 3 6 , 3 1 3 6 , 7 3 8 2 0 1 , 2 5 0 , 9 7 8 7 , 3 8 5 , 4 1 1 0 , 0 9 7 , 8 3 9 2 0 1 , 2 5 0 , 6 8 9 5 , 5 91 , 9 1 0 5 , 0 9 6 , 9 3 2 2 0 1 , 2 5 4 , 7 8 9 4 , 4 8 9 , 2 1 2 9 , 3 1 3 4 , 9 3 4 2 0 5 , 0 0 0 , 9 9 8 1 , 5 8 3 , 0 8 1 , 3 8 1 , 2 3 5 2 0 5 , 0 0 4 , 6 8 8 2 , 1 5 4 , 9 1 0 3 , 5 6 8 , 7 4 3 2 0 5 , 0 0 4 , 6 6 81 , 6 6 9 , 6 9 0 , 5 7 6 , 1 4 0 3 0 1 , 2 5 0 , 0 9 8 , 0 9 7 , 7 1 0 7 , 2 1 1 4 , 1 31 30 1 , 2 5 1 , 0 3 9 6 , 9 9 6 , 8 121 , 8 1 1 7 , 7 4 2 3 0 1 , 2 5 0 , 9 2 9 3 , 5 9 3 , 1 1 1 2 , 3 1 0 4 , 5 3 3 3 0 1 , 2 5 4 , 7 3 9 2 , 1 8 8 , 4 1 1 9 , 9 9 4 , 3 3 6 3 0 5 , 0 0 0 , 8 7 9 3 , 0 9 0 , 1 1 0 5 , 8 9 6 , 5 3 7 3 0 5 , 0 0 4 , 6 1 9 0 , 4 6 6 , 0 1 0 1 , 6 6 9 , 8 4 4 3 0 5 , 0 0 4 , 6 8 8 6 , 2 8 5 , 9 8 7 , 8 8 0 , 7 101 T a b l e X X V I I I I o n i c s e l e c t i v i t y b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) a t 2 a n d 2 0 h o u r s . ( s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 67 •20 0 , 5 0 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 91 2 0 0 , 5 0 0 , 0 1 , 0 0 0 N . A . 1 , 0 0 0 N . A . 71 2 0 0 , 5 0 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 9 2 0 0 , 5 0 0 , 9 2 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 0 81 2 0 0 , 5 0 1 , 1 1 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 8 8 2 0 0 , 5 0 5 , 2 4 1 , 0 0 2 1 , 0 0 2 1 , 0 0 5 1 , 0 0 4 9 0 2 0 0 , 5 0 5 , 5 0 1 , 0 0 1 1 , 0 0 1 1 , 0 0 4 1 , 0 0 3 6 5 2 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 5 2 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 3 2 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 7 2 0 1 , 2 5 •1 , 0 9 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 8 2 2 0 1 , 2 5 1 , 0 1 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 0 8 5 2 0 1 , 2 5 5 , 6 6 1 , 0 0 1 1 , 0 0 4 1 , 0 0 3 1 , 0 0 3 6 6 3 0 0 , 5 0 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 0 3 0 0 , 5 0 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 9 2 3 0 0 , 5 0 0 , 0 1 , 0 0 0 N . A . 1 , 0 0 0 N . A . 8 0 3 0 0 , 5 0 1 , 0 4 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 8 9 3 0 0 , 5 0 5 , 3 1 1 , 0 0 3 1 , 0 0 2 1 , 0 0 6 1 , 0 0 4 94 3 0 0 , 5 0 5 , 3 1 1 , 0 0 1 1 , 0 0 1 1 , 0 0 5 1 , 0 0 5 6 8 3 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 4 3 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 7 6 3 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 8 3 3 0 1 , 2 5 1 , 0 2 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 8 4 3 0 1 , 2 5 1 , 0 7 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 ' 1 , 0 0 1 8 6 3 0 1 , 2 5 5 , 0 0 1 , 0 0 2 1 , 0 0 2 1 , 0 0 2 1 , 0 0 3 8 7 3 0 1 , 2 5 5 , 64 1 , 0 0 6 1 , 0 0 2 1 , 0 0 5 1 , 0 0 4 T a b l e X X I X I o n i c s e l e c t i v i t y b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 20 h o u r s ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 41 2 0 1 , 2 5 0 , 0 1 r 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 3 0 2 0 1 , 2 5 0 , 8 5 1 r 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 3 8 2 0 1 , 2 5 0 , 9 7 1 r 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 3 9 2 0 1 , 2 5 0 , 6 8 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 3 2 2 0 1 , 2 5 4 , 7 8 1 , 0 0 0 1 , 0 0 0 1 , 0 0 9 1 , 0 0 7 3 4 2 0 5 , 0 0 0 , 9 9 1 , 0 0 0 1 , 0 0 0 1 , 0 0 2 1 , 0 0 1 3 5 2 0 5 , 0 0 4 , 6 8 0 , 9 9 9 0 , 9 9 9 1 , 0 0 7 1 , 0 0 4 4 3 2 0 5 , 0 0 4 , 6 6 0 , 9 9 9 1 , 0 0 0 1 , 0 0 6 1 , 0 0 4 4 0 3 0 1 , 2 5 0 , 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 31 3 0 1 , 2 5 1 , 0 3 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 4 2 3 0 1 , 2 5 0 , 9 2 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 1 , 0 0 1 3 3 3 0 1 , 2 5 4 , 7 3 1 , 0 0 0 1 , 0 0 0 1 , 0 0 5 1 , 0 0 5 3 6 3 0 5 , 0 0 0 , 8 7 1 , 0 0 0 1 , 0 0 0 1 , 0 0 0 1 , 0 0 1 3 7 3 0 5 , 0 0 4 , 6 1 1 , 0 0 0 0 , 9 9 9 1 , 0 0 7 1 , 0 0 4 4 4 3 0 5 , 0 0 4 , 6 8 1 0 0 0 1 , 0 0 0 1 , 0 0 6 1 , 0 0 5 103 T a b l e X X X A b s o l u t e e r r o r s i n t h e a m m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( A ) a n d t h e p e r c e n t d r o p s e p a r a t i o n f a c t o r N s ( B ) ( s t e a d y s t a t e r u n s ) . r u n v o l t v e l y ppm ( A ) ( B ) num c m / s e c i r o n 67 20 0 ,50 0 0 - 0 ,000 3 ,978 91 20 0 50 0 ,0 - 0 ,000 2 ,000 71 20 0 ,50 0 0 - 0 000 4 ,027 79 20 0 50 0 92 0 003 4 ,116 81 20 0 50 1 1 1 0 005 3 942 88 20 0 50 5 24 0 023 3 ,901 90 20 0 50 5 50 0 015 3 979 65 20 1 25 0 0 - 0 000 4 ,074 75 20 1 25 0 0 - 0 000 4 078 73 20 1 25 0 0 - 0 000 3 ,889 77 20 1 25 1 09 0 01 1 4 023 82 20 1 25 1 01 0 005 3 979 85 20 1 25 5 66 0 015 3 952 66 30 0 50 0 0 - 0 000 3 996 70 30 0 50 0 0 - 0 000 3 836 92 30 0 50 0 0 - 0 000 2 000 80 30 0 50 1 04 0 006 3 743 89 30 0 50 5 31 0 028 3 868 94 30 0 50 5 31 0 0*1 4 4 075 68 30 1 25 0 0 - 0 000 3 936 74 30 1 25 0 0 - o 000 3 889 76 30 1 25 0 0 - 0 000 4 012 83 30 1 25 1 02 0 006 3 928 84 30 1 25 1 07 0 007 3 801 86 30 1 25 5 00 0 032 3 845 87 30 1, 25 5, 64 0 036 3 867 1 04 T a b l e X X X I A b s o l u t e e r r o r i n t h e a c c u m u l a t i o n o f i r o n o n t h e t e s t m e m b r a n e s ( m g . ) ( A ) a n d t h e p e r c e n t d r o p i n s e p a r a t i o n f a c t o r ( B ) ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 41 2 0 1 , 2 5 0 , 0 0 , 0 0 4 3 , 2 5 0 3 0 2 0 1 , 2 5 0 , 8 5 0 , 0 0 6 3 , 4 0 6 3 8 2 0 1 , 2 5 0 , 9 7 0 , 0 1 8 3 , 6 3 7 3 9 2 0 1 , 2 5 0 , 6 8 0 , 0 1 6 3 , 0 7 1 3 2 2 0 1 , 2 5 4 , 7 8 0 , 0 2 5 3 , 0 5 9 3 4 2 0 5 , 0 0 0 , 9 9 0 , 0 1 3 4 , 1 6 9 3 5 2 0 5 , 0 0 4 , 6 8 0 , 0 3 0 2 , 6 6 0 4 3 2 0 5 , 0 0 4 , 6 6 0 , 0 3 2 3 , 1 2 2 4 0 30 1 , 2 5 0 , 0 0 , 0 1 0 3 , 7 6 8 31 3 0 1 , 2 5 1 , 0 3 0 , 0 0 3 3 , 8 6 7 4 2 3 0 1 , 2 5 0 , 9 2 0 , 0 0 4 3 , 7 9 5 3 3 3 0 1 , 2 5 4 , 7 3 0 , 0 5 1 3 , 1 9 5 3 6 3 0 5 , 0 0 0 , 8 7 0 , 0 1 9 3 , 3 4 4 3 7 3 0 5 , 0 0 4 , 6 1 0 , 0 4 0 2 , 4 7 5 4 4 3 0 5 , 0 0 4 , 6 8 0 , 0 3 8 3 , 8 8 3 1 0 5 T a b l e X X X I I A b s o l u t e e r r o r s i n t h e v a l u e s o f ( R a + R c + R p ) f o r t h e f i r s t s t a g e ( A ) a n d s e c o n d s t a g e ( B ) a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) . r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 6 7 2 0 0 , 5 0 0 , 0 0 , 8 1 0 , 8 1 0 , 8 6 0 , 8 8 91 2 0 0 , 5 0 0 , 0 N . A . N . A . N . A . N . A . 71 2 0 0 , 5 0 0 , 0 0 , 8 0 0 , 8 0 0 , 9 1 0 , 9 1 7 9 2 0 0 , 5 0 0 , 9 2 0 , 7 6 0 , 7 7 0 , 9 2 0 , 9 4 81 2 0 0 , 5 0 1 , 1 1 0 , 8 5 0 , 8 3 1 , 0 6 1 , 0 3 8 8 2 0 0 , 5 0 5 , 2 4 0 , 8 8 0 , 8 6 1 , 0 4 1 , 0 0 9 0 2 0 0 , 5 0 5 , 5 0 0,-7 6 0 , 7 9 0 , 8 9 0 , 9 2 6 5 2 0 1 , 2 5 0 , 0 0 , 8 3 0 , 8 2 0 , 8 5 0 , 8 2 7 5 2 0 1 , 2 5 0 , 0 0 , 7 8 0 , 7 9 0 , 8 0 0 , 8 2 7 3 2 0 1 , 2 5 0 , 0 0 , 9 6 0 , 9 3 1 , 0 1 0 , 9 6 7 7 2 0 1 , 2 5 1 , 0 9 0 , 9 6 0 , 9 2 1 , 0 0 0 , 9 5 8 2 2 0 1 , 2 5 1 , 0 1 0 , 7 6 0 , 7 9 0 , 7 9 0 , 8 2 8 5 2 0 1 , 2 5 5 , 6 6 0 , 8 2 0 , 8 4 0 , 8 6 0 , 8 8 6 6 3 0 0 , 5 0 0 , 0 0 , 8 3 0 , 8 2 0 , 9 1 0 , 9 0 7 0 3 0 0 , 5 0 0 , 0 0 , 7 3 0 , 7 7 0 , 9 2 0 , 9 4 9 2 3 0 0 , 5 0 0 , 0 N . A . N . A . N . A . N . A . 8 0 3 0 0 , 5 0 1 , 0 4 0 , 9 0 0 , 8 8 1 , 2 4 1 , 1 6 8 9 3 0 0 , 5 0 5 , 3 1 1 , 0 4 0 , 9 3 1 , 4 5 1 , 2 5 94 3 0 0 , 5 0 5 , 3 1 0 , 7 9 0 , 8 0 1 , 0 0 1 , 0 1 6 8 3 0 1 , 2 5 0 , 0 0 , 7 9 0 , 8 0 0 , 8 1 0 , 8 2 7 4 3 0 1 , 2 5 0 , 0 0 , 9 2 0 , 8 9 1 , 0 2 0 , 9 7 7 6 30 1 , 2 5 0 , 0 0 , 7 8 0 , 7 8 0 , 8 4 0 , 8 4 8 3 3 0 1 , 2 5 1 , 0 2 0 , 8 9 0 , 8 3 0 , 9 9 0 , 9 1 8 4 3 0 1 , 2 5 1 , 0 7 0 , 8 6 0 , 8 4 0 , 9 3 0 , 9 0 8 6 3 0 . 1 , 2 5 5 , 0 0 0 , 7 8 0 , 8 3 0 , 8 3 0 , 8 6 8 7 3 0 1 , 2 5 5 , 6 4 0 , 9 4 0 , 8 7 1 , 0 2 0 , 9 3 1 0 6 T a b l e X X X I I I A b s o l u t e e r r o r i n t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( A ) a n d t h e a m o u n t o f i r o n l o s t t h e f e e d s t r e a m ( s t e a d y ' s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 7 9 2 0 0 , 5 0 0 , 9 2 0 , 0 3 9 1 , 0 3 4 81 2 0 0 , 5 0 1 , 1 1 0 , 0 5 9 1 , 4 0 4 8 8 2 0 0 , 5 0 5 , 2 4 0 , 2 9 9 7 , 2 9 1 9 0 2 0 0 , 5 0 5 , 5 0 0 , 2 0 1 7 , 1 9 5 7 7 2 0 1 , 2 5 1 , 0 9 0 , 1 4 8 1 , 0 2 9 8 2 2 0 1 , 2 5 1 , 0 1 0 , 0 6 9 1 , 3 4 1 8 5 2 0 1 , 2 5 5 , 6 6 0 , 2 0 1 8 , 2 5 9 8 0 3 0 0 , 5 0 1 , 0 4 0 , 0 8 2 1 , 2 8 3 8 9 3 0 0 , 5 0 5 , 3 1 0 , 3 6 1 6 , 8 9 5 9 4 3 0 0 , 5 0 5 , 3 1 0 , 1 8 6 7 , 1 5 2 8 3 3 0 1 , 2 5 1 , 0 2 0 , 0 7 9 1 , 1 5 1 8 4 3 0 1 , 2 5 1 , 0 7 0 , 0 8 7 1 , 1 9 7 8 6 3 0 1 , 2 5 5 , 0 0 0 , 4 1 6 6 , 6 8 9 8 7 3 0 1 , 2 5 5 , 6 4 0 , 4 6 9 7 , 3 2 4 T a b l e X X X I V A b s o l u t e e r r o r i n t h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s ( m g . ) ( A ) a n d t h e a m o u n t o f i r o n l o s t i n t h e f e e d ( m g . ) ( B ) ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 41 2 0 - 1 , 2 5 0 , 0 0 , 2 N . A . 3 0 2 0 1 , 2 5 0 , 8 5 0 , 3 1 , 2 3 8 2 0 1 , 2 5 0 , 9 7 1 , 0 1 , 5 3 9 2 0 1 , 2 5 0 , 6 8 0 , 9 1 , 1 3 2 2 0 1 , 2 5 4 , 7 8 1 , 4 6 , 7 34 2 0 5 , 0 0 0 , 9 9 0 , 7 1 , 3 3 5 2 0 5 , 0 0 4 , 6 8 1 , 7 6 , 2 4 3 2 0 5 , 0 0 4 , 6 6 1 , 8 6 , 2 4 0 3 0 1 , 2 5 0 , 0 0 , 5 N . A . 31 3 0 1 , 2 5 1 , 0 3 0 , 2 1 , 6 4 2 3 0 1 , 2 5 0 , 9 2 0 , 2 1 , 2 3 3 3 0 1 , 2 5 4 , 7 3 2 , 8 6 , 7 36 3 0 5 , 0 0 0 , 8 7 1 , 0 1 , 4 3 7 3 0 5 , 0 0 4 , 6 1 2 , 2 6 , 0 44 3 0 5 , 0 0 4 , 6 8 2 , 1 6 , 2 1 07 T a b l e X X X V A b s o l u t e e r r o r s i n t h e v a l u e s o f i o n i c s e l e c t i v i t i e s b a s e d o n i r o n i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 20 h o u r s ( s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 20 h r s . 2 20 h r s . 79 20 0,50 0,92 0,080 0, 1 07 0,036 0,026 81 20 0,50 1,11 0,074 0,079 0,036 0,017 88 20 0,50 5,24 0,065 0,065 0,045 0,044 90 20 0,50 5,50 0,081 0,080 0,059 0,045 77 20 1 ,25 1 ,09 0, 162 0,0 0, 187 0, 170 82 20 1 ,25 1,01 0,141 0, 1 55 0, 1 36 0,115 85 20 1 ,25 5,66 0, 188 0, 124 0, 1 67 0, 167 80 30 0,50 1 ,04 0,061 0,072 0,034 0,015 89 30 0,50 5,31 0,046 0,047 0,034 0,023 94 30 0,50 5,31 0,067 0,064 0,039 0,010 83 30 1 ,25 1 ,02 0,095 0,085 0,085 0,025 84 30 1 ,25 1 ,07 0,113 0, 149 0,085 -0 ,006 86 30 1 ,25 5,00 0,099 0,095 0,113 0,068 87 30 1 ,25 5,64 0,068 0,114 0,082 0,051 T a b l e X X X V I A b s o l u t e e r r o r i n t h e i r o n s e l e c t i v i t y b a s e d o n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 20 h o u r s ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y ppm num c m / s e c i r o n ( A ) ( B ) 20 h r s . 2 20 h r s . N . A . N . A . N . A . 0,043 0,001 0,005 0,049 0,054 0,007 0,035 -0 ,003 -0 ,000 0,047 -0 ,017 -0 ,009 0,052 -0 ,024 - 0 , 0 0 5 0,093 -0 ,019 -0 ,002 0,063 -0 ,005 -0 ,012 N . A . N . A . N . A . 0,042 0,007 -0 ,008 0,045 -0 ,007 -0 ,023 0,046 0,008 -0,021 0,044 0,072 0,019 0,075 -0 ,019 -0 ,022 0,046 -0 ,000 -0 ,016 41 20 1 ,25 0,0 N . A . 30 20 1 ,25 0,85 0,046 38 20 1 ,25 0,97 0,048 39 20 1 ,25 0,68 0,034 32 20 1 ,25 4,78 0,043 34 20 5,00 0,99 0,054 35 20 5,00 4,68 0,052 43 20 5,00 4,66 0,052 40 30 1 ,25 . 0,0 N . A . 31 30 1 ,25 1 ,03 0,042 42 30 1 ,25 0,92 0,044 33 30 1 ,25 4,73 0,045 36 30 5,00 0,87 0,041 37 30 5,00 4,61 0,047 44 30 5,00 4,68 0,046 108 T a b l e X X X V I I A b s o l u t e e r r o r i n t h e c u r r e n t e f f i c i e n c i e s a t 2 a n d 20 h o u r s ( s t e a d y s t a t e r u n s ) . r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 67 20 0 r 5 0 0 0 0 023 0 , 0 2 4 91 20 0 ,50 0 0 0 025 N . A . 71 20 0 ,50 0 ,0 0 028 0 , 0 2 7 79 20 0 ,50 0 92 0 031 0 , 0 2 8 81 20 0 50 1 , 1 1 0 023 0 , 0 2 4 88 20 0 50 5 24 0 024 0 , 0 2 4 90 20 0 50 5 50 0 028 0 , 0 2 6 65 20 1 25 0 0 0 057 0 , 0 5 5 75 20 1 25 0 0 0 049 0 , 0 4 5 73 20 1 25 0 0 0 040 0 , 0 4 1 77 20 1 25 1 09 0 044 0 , 0 4 4 82 20 1 25 1 01 0 049 0 , 0 5 0 85 20 1 25 5 66 0 053 0 , 0 5 0 66 30 0 50 0 0 0 020 0 , 0 2 0 70 30 0 50 0 0 0 022 0 , 0 2 2 92 30 0 50 0 0 0 021 N . A . 80 30 0 50 1 04 0 021 0 , 0 2 0 89 30 0 50 5 31 o , 019 0 , 0 1 9 94 30 0 50 5 31 o , 023 0 , 0 2 1 68 30 1 25 0 0 o , 038 0 , 0 3 7 74 30 1 25 0 0 o , 028 0 , 0 3 0 76 30 1 25 0 0 o , 041 0 , 0 3 8 83 30 1 25 1 02 o , 030 0 , 0 3 1 84 30 1 25 1 07 o , 034 0 , 0 3 5 86 30 1 25 5 00 o , 037 0 , 0 3 5 87 30 1, 25 5 , 64 o , 036 0 , 0 3 7 1 0 9 T a b l e X X X V I I I P e r c e n t e r r o r i n c u r r e n t e f f i c i e n c y a t 2 a n d 20 h o u r s ( u n s t e a d y s t a t e r u n s ) . r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 41 2 0 1 , 2 5 0 , 0 2 , 5 9 9 2 , 6 3 0 3 0 2 0 1 , 2 5 0 , 8 5 N . A . N . A . 3 8 2 0 1 , 2 5 0 , 9 7 2 , 6 7 9 2 , 7 0 9 3 9 2 0 1 , 2 5 0 , 6 8 2 , 5 9 5 2 , 6 3 6 3 2 2 0 1 , 2 5 4 , 7 8 N . A . N . A . 34 2 0 5 , 0 0 0 , 9 9 2 , 7 7 7 2 , 7 5 7 3 5 2 0 5 , 0 0 4 , 6 8 2 , 7 4 3 3 , 2 7 9 4 3 2 0 5 , 0 0 4 , 6 6 2 , 7 6 5 2 , 9 6 7 4 0 3 0 1 , 2 5 0 , 0 2 , 5 6 9 2 , 5 7 2 31 3 0 1 , 2 5 1 , 0 3 2 , 5 7 8 2 , 5 8 0 4 2 3 0 1 , 2 5 0 , 9 2 2 , 6 1 3 2 , 6 2 0 3 3 3 0 1 , 2 5 4 , 7 3 2 , 6 2 4 2 , 6 7 7 3 6 3 0 5 , 0 0 0 , 8 7 2 , 6 2 0 2 , 6 5 6 3 7 3 0 5 , 0 0 4 , 6 1 2 , 6 5 0 3 , 0 5 1 4 4 3 0 5 , 0 0 4 , 6 8 2 , 7 0 9 2 , 7 1 9 1 1 0 T a b l e X X X I X A b s o l u t e e r r o r s i n t h e v a l u e s o f i o n i c s e l e c t i v i t i e s b a s e d o n s o d i u m i n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) s t r e a m s a t 2 a n d 2 0 h o u r s ( s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 6 7 2 0 0 r 5 0 0 r 0 0 1 3 2 0 , 1 2 2 0 1 6 5 - 0 , 1 9 5 91 2 0 0 , 5 0 0 r 0 0 0 8 0 N . A . 0 1 1 0 N . A . 7 1 2 0 0 , 5 0 0 r 0 0 0 9 8 0 , 0 9 9 0 1 3 3 0 , 1 2 7 7 9 2 0 0 , 5 0 0 , 9 2 0 0 7 9 0 , 0 7 6 0 1 0 6 0 , 1 0 3 8 1 2 0 0 , 5 0 1 r 1 1 0 0 7 4 0 , 0 7 5 0 1 0 3 0 , 1 0 7 8 8 2 0 0 5 0 5 r 2 4 0 0 7 9 0 , 0 8 2 0 1 0 9 0 , 1 1 1 9 0 2 0 0 , 5 0 5 , 5 0 0 0 8 7 0 , 0 8 7 0 1 2 0 0 , 1 2 2 6 5 2 0 1 2 5 0 , 0 0 2 9 1 0 , 3 2 3 0 5 7 5 0 , 3 4 2 7 5 2 0 1 2 5 0 r O 0 1 9 1 0 , 1 7 6 0 2 3 4 0 , 2 1 7 7 3 2 0 1 , 2 5 0 0 o ( 1 4 2 0 , 1 6 2 0 1 8 0 0 , 1 8 7 7 7 2 0 1 2 5 1 0 9 o, 1 6 6 0 , 1 6 4 0 1 9 7 0 , 1 9 2 8 2 2 0 1 2 5 1 0 1 o , 1 8 0 0 , 1 8 5 0 2 0 9 0 , 2 1 3 8 5 2 0 1 2 5 5 6 6 o , 2 0 3 0 , 2 1 0 0 2 5 3 0 , 2 7 9 6 6 3 0 0 5 0 0 0 o , 1 0 6 0 , 1 0 5 o , 1 3 9 0 , 1 4 2 7 0 3 0 0 5 0 0 0 o , 0 7 5 0 , 0 8 2 0 1 0 6 0 , 1 0 6 9 2 3 0 0 5 0 0 0 o , 0 6 3 N . A . 0 0 9 5 N . A . 8 0 3 0 0 5 0 1 0 4 o , 0 6 3 0 , 0 6 7 0 0 9 9 0 , 1 0 4 8 9 3 0 0 5 0 5 3 1 o , 0 6 1 0 , 0 6 5 0 1 0 5 0 , 0 9 8 9 4 3 0 0 5 0 5 3 1 o , 0 7 3 0 , 0 7 1 o , 1 1 1 0 , 1 1 0 6 8 3 0 1 2 5 0 0 o , 2 9 2 0 , 3 4 7 o , 2 9 9 0 , 3 1 6 7 4 3 0 1 2 5 0 0 o , 1 0 1 0 , 1 0 8 o , 1 3 3 0 , 1 3 7 7 6 3 0 1 2 5 0 0 o , 1 3 1 0 , 1 3 2 o , 1 7 4 0 , 1 6 9 8 3 3 0 1 2 5 1 0 2 o , 1 0 0 0 , 1 0 5 o , 1 3 9 0 , 1 4 3 8 4 3 0 1 , 2 5 1 0 7 o , 1 1 9 0 , 1 3 9 o , 1 5 3 0 , 1 7 1 8 6 3 0 1 , 2 5 5 , 0 0 o , 1 2 8 0 , 1 4 6 o , 1 5 9 0 , 1 7 2 8 7 3 0 1 , 2 5 5 , 6 4 o , 1 3 3 0 , 1 5 5 o , 1 6 3 0 , 1 6 5 111 T a b l e X L A b s o l u t e e r r o r i n t h e s o d i u m s e l e c t i v i t y b a s e d o n t h e d i a l y s a t e ( A ) a n d b r i n e ( B ) c h a n n e l s a t 2 a n d 2 0 h o u r s ( u n s t e a d y s t a t e r u n s ) r u n v o l t v e l y p p m ( A ) ( B ) num c m / s e c i r o n 2 2 0 h r s . 2 2 0 h r s . 41 2 0 1 , 2 5 0 , 0 0 , 0 4 2 0 , 0 4 3 0 , 0 7 8 0 , 0 8 1 3 0 2 0 1 , 2 5 0 , 8 5 0 , 0 4 4 0 , 0 4 3 0 , 0 5 2 0 , 0 6 9 3 8 2 0 1 , 2 5 0 , 9 7 0 , 0 4 6 0 , 0 4 7 0 , 0 7 6 0 , 0 8 1 3 9 2 0 1 , 2 5 0 , 6 8 0 , 0 4 2 0 , 0 4 4 0 , 0 7 8 0 , 0 8 1 3 2 2 0 1 , 2 5 4 , 7 8 0 , 0 4 2 1 0 , 0 4 5 0 , 0 7 2 0 , 0 7 0 3 4 2 0 5 , 0 0 0 , 9 9 0 , 0 4 9 0 , 0 4 8 0 , 0 8 9 0 , 0 8 9 3 5 2 0 5 , 0 0 4 , 6 8 0 , 0 4 9 0 , 0 7 3 0 , 0 7 9 0 , 0 9 9 4 3 2 0 5 , 0 0 4 , 6 6 0 , 0 4 9 0 , 0 5 7 0 , 0 8 5 0 , 0 9 3 4 0 3 0 1 , 2 5 0 , 0 0 , 0 4 1 0 , 0 4 1 0 , 0 7 7 0 , 0 7 5 31 3 0 1 , 2 5 1 , 0 3 0 , 0 4 1 0 , 0 4 1 0 , 0 7 3 0 , 0 7 4 4 2 3 0 1 , 2 5 0 , 9 2 0 , 0 4 3 0 , 0 4 3 0 , 0 7 6 0 , 0 7 8 3 3 3 0 1 , 2 5 4 , 7 3 0 , 0 4 3 0 , 0 4 5 0 , 0 7 4 0 , 0 8 3 3 6 3 0 5 , 0 0 0 , 8 7 0 , 0 4 3 0 , 0 4 4 0 , 0 7 8 0 , 0 8 2 3 7 3 0 5 , 0 0 4 , 6 1 0 , 0 4 4 0 , 0 6 1 0 , 0 8 0 0 , 0 9 8 4 4 3 0 • 5 , 0 0 4 , 6 8 0 , 0 4 6 0 , 0 4 7 0 , 0 8 6 0 , 0 9 0 1 1 2 A P P E N D I X A C a l c u l a t i o n o f R a + R c + R p A f r a c t i o n a l d e m i n e r a l i s a t i o n f o r m u l a w a s u s e d t o c a l c u l a t e t h e s e c o n d s t a g e ( c e l l B ) e n t r a n c e c o n c e n t r a t i o n f o r b o t h t h e d i l u t e a n d b r i n e s t r e a m s . ( 1 - F t ) = ( 1 - F s ) ' ) w h e r e ; F t = t o t a l f r a c t i o n a l d e m i n e r a l i s a t i o n , F s = f r a c t i o n a l d e m i n e r a l i s a t i o n p e r s t a g e , n = n u m b e r o f s t a g e s , T h e l o g - m e a n s o d i u m c h l o r i d e c o n c e n t r a t i o n b e t w e e n t h e i n l e t a n d o u t l e t w a s c a l c u l a t e d f o r b o t h s t r e a m s a n d i n s e r t e d i n t o t h e e x t e n d e d O n s a g e r - S h e d l o v s k y e q u a t i o n ( G u n n i n g a n d G o r d o n 1 9 4 2 ) t o c a l c u l a t e t h e e q u i v a l e n t c o n d u c t i v i t y o f b o t h s t r e a m s , s i n c e : R d , b = ( 1 / K d , b ) • d / A w h e r e ; A = u s e f u l o r e f f e c t i v e a r e a f o r i o n i c t r a n s f e r b a s e d o n o n e c e l l . i e . t o t a l a r e a i s 6 2 , 8 7 c m 2 , m e s h a r e a 2 4 , 6 9 c m 2 a n d A = 3 8 . 1 8 c m 2 . a n d : K d , b = j\a,b C d , b / 1 0 0 0 / \ = e q u i v a l e n t c o n d u c t i v i t y ( i n O h m s " 1 c m 2 e q u i v - 1 ) c a l c u l a t e d b y t h e e x t e n d e d O n s a g e r - S h e d l o v s k y e q u a t i o n . C d , b = l o g - m e a n d i a l y s a t e , b r i n e c o n c e n t r a t i o n i n e q u i v . p e r l i t r e . 1 13 A P P E N D I X B T h e e r r o r s i n v o l v e d i n t h e d i r e c t m e a s u r e m e n t o f t h e d a t a w e r e a s f o l l o w s : V o l t a g e m e a s u r e m e n t s ± 0 . 0 5 % S o d i u m c o n c e n t r a t i o n s ± 1 . 0 % I r o n c o n c e n t r a t i o n s ± 1 . 0 % F l o w r a t e s : S t e a d y s t a t e ± 0 . 5 % : U n s t e a d y s t a t e ± 1 . 0 % T e m p e r a t u r e m e a s u r e m e n t s ± 0 . 2 % p H m e a s u r e m e n t s ± 0 . 1 % P r e s s u r e d r o p ± 0 . 0 5 c m . 1) C u r r e n t M e a s u r e m e n t s A l l t h r e e r e s i s t a n c e s u s e d i n t h e d e t e r m i n a t i o n o f c u r r e n t w e r e m e a s u r e d t o w i t h i n ± 0 , 0 5 mOhms ( ± 0 , 0 5 3 % ) u s i n g a K e i t h l y M u l t i m e t e r . I n t h e s t e a d y s t a t e p r o c e s s t h e e r r o r i n c u r r e n t m e a s u r e m e n t w a s ± 0 , 1 % ( 0 , 0 5 + 0 , 0 5 3 ) . H o w e v e r , i n t h e u n s t e a d y s t a t e , t h e c o m b i n e d e r r o r s i n d i g i t i z i n g t h e t i m e -c u r r e n t p l o t s p r o d u c e d b y t h e M o s e l y A u t o g r a p h s t r i p c h a r t r e c o r d e r r e a d o n a T e x t r o n i c s d i g i t i z e r , h a v i n g a r e s o l u t i o n o f ± 0 . 0 0 2 5 c m . (1 t h o u . ) r e s o l u t i o n a d d e d u p t o ± 0 . 5 % . 2 ) C u r r e n t D e n s i t y T h e a c t u a l a r e a f o r c u r r e n t t r a n s f e r c o u l d n o t b e o b t a i n e d d u e t o t h e a c c u m u l a t i o n o f f o u l i n g d e p o s i t s i n t h e c h a n n e l s . I t w a s n o t i c e d i n b o t h p r o c e s s e s f o r r u n s w i t h f o u l i n g t h a t t h e m e s h ' h a d a s h a d o w e f f e c t o n t h e c u r r e n t f l o w 114 ( s e e F i g 3 3 B ) ) . A t y p i c a l s p a c e r h a d 7 2 , 0 , 0 6 3 5 c m . O . D . , 5 , 4 0 c m . l o n g p o l y e t h y l e n e s t r a n d s i n c o n t a c t w i t h t h e m e m b r a n e ' s s u r f a c e ; t h e s h a d o w a r e a w a s f o u n d t o b e 2 4 , 6 9 c m 2 , a n d s i n c e t h e t o t a l a r e a w a s 6 2 , 8 7 c m 2 , t h e a c t u a l t r a n s f e r a r e a u s e d w a s 3 8 , 1 8 c m 2 . T h e r e l a t i v e e r r o r s , i n e a c h m e a s u r e m e n t w e r e c o m b i n e d t o g i v e a t o t a l e r r o r o f ± 2 . 0 2 c m 2 . I n d e t e r m i n i n g t h e v a l u e o f i X d X ( 1 / K d + 1 / K b ) , i w a s c a l c u l a t e d t o h a v e a n e r r o r o f ± 5 , 4 % ( 0 , 1 + 5 , 3 ) a n d d , a n e r r o r o f ± 1 , 2 5 % ( 0 , 0 0 2 / 0 , 1 5 9 ) . T h e v a l u e s o f t h e e q u i v a l e n t - c o n d u c t i v i t y o b t a i n e d f r o m t h e e x t e n d e d O n s a g e r - S h e d l o v s k y e q u a t i o n h a d a , ± 0 , 0 2 % d e v i a t i o n f r o m e x p e r i m e n t a l m e a s u r e m e n t s ( G u n n i n g a n d G o r d o n 1 9 4 2 ) , a n d t h e e r r o r i n c a l c u l a t i n g t h e i X d X ( 1 / K d + 1 / K b ) w a s ± 7 , 7 % ( 5 , 4 + 1 , 2 5 + 1 , 0 2 ) . E r r o r s i n t h e c u r r e n t e f f i c i e n c y w e r e c a l c u l a t e d b y c o m b i n i n g t h e ± 1 , 0 % e r r o r i n i o n s d e s a l t e d , ± 0 , 5 % e r r o r i n f l o w r a t e s , a n d ± 0 , 1 % e r r o r i n c u r r e n t m e a s u r e m e n t s , r e s u l t i n g i n a t o t a l e r r o r o f ± 1 , 6 % . 3 ) S e p a r a t i o n F a c t o r T h e e r r o r i n v o l v e d i n c a l c u l a t i n g t h e s e p a r a t i o n f a c t o r N s w a s ± 2 , 0 % ( 1 , 0 + 1 . 0 ) . E r r o r s i n t h e p e r c e n t d r o p i n . s e p a r a t i o n f a c t o r w e r e p r o g r a m m e d a n d c a n b e f o u n d i n T a b l e s X X X a n d X X X I . T h e p e r c e n t s e p a r a t i o n b a s e d o n s o d i u m h a d a n e r r o r o f a p p r o x . ± 2 , 0 % 1 1 5 4 ) P o w e r r e q u i r e m e n t s I n t h e s t e a d y s t a t e p r o c e s s t h e e r r o r i n d e t e r m i n i n g p o w e r r e q u i r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d w a s ± 0 , 1 5 % ( 0 , 0 5 + 0 , 1 ) , a n d t h e f l o w r a t e m e a s u r e m e n t e r r o r w a s ± 0 , 5 % , t h e t o t a l b e i n g ± 0 , 6 5 % . I n t h e u n s t e a d y s t a t e t h e e r r o r i n t h e t i m e a v e r a g e c u r r e n t w a s a p p r o x . ± 1 , 0 % . S i n c e P = I V t h e e r r o r i n t h i s p o w e r d e t e r m i n a t i o n w a s ( 1 , 0 + 0 , 0 5 ) ± 1 , 0 5 % . T h i s e r r o r c o m b i n e d w i t h a ± 0 , 5 % e r r o r b u i l t i n t o t h e r e c o r d e r g i v i n g a t o t a l e r r o r o f ± 2 , 0 5 % . 5 ) C a l c u l a t i o n o f ( R a + R c + R p ) T h e t o t a l s t a c k r e s i s t a n c e h a d a n e r r o r o f ± 0 , 1 5 % ( 0 , 0 5 + 0 , 1 ) , w h i l e t h e b u l k s o l u t i o n r e s i s t a n c e s e a c h h a d a n e r r o r o f a p p r o x . ± 6 , 3 4 % . A n d t h e t o t a l e r r o r i n t h i s t e r m w a s c a l c u l a t e d a c c o r d i n g l y s e e c o m p u t e r p r o g r a m a n d T a b l e X X X I I . 6 ) I r o n A c c u m u l a t i o n F o r r e a d i n g s b a s e d o n t h e m e m b r a n e s t h e e r r o r s i n v o l v e d w e r e ± 1 , 0 % f o r t h e i r o n d e t e r m i n a t i o n s , a n d ± 0 . 2 4 % i n m e a s u r i n g t h e s a m p l e s e c t i o n o f t h e t e s t m e m b r a n e . H e n c e a ± 1 , 2 4 % e r r o r c a n b e e x p e c t e d i n t h e s e v a l u e s . T h e e r r o r i n t h e p e r c e n t s e p a r a t i o n b a s e d o n i r o n w a s t a k e n a s . ± 2 , 0 % a n d t h a t o f t h e i r o n l o s t i n t h e f e e d a s a m a x i m u m o f ± 2 , 0 % ( T a b l e s X X X I I I , X X X I V ) . 1 16 A P P E N D I X C I n p u t v a l u e s f o r b o t h F O R T R A N p r o g r a m s (#1 a n d 2 ) h a n d l i n g t h e d a t a f r o m t h e s t e a d y s t a t e a n d u n s t e a d y s t a t e p r o c e s s e s . M = t h e n u m b e r o f s a m p l e t i m e s N = t h e n u m b e r o f s o d i u m d e t e r m i n a t i o n s p e r r u n , R U N N U M = T h e a c t u a l r u n n u m b e r f o u n d i n t h e l a b o r a t o r y b o o k s P P M F = P a r t s p e r m i l l i o n s o d i u m c h l o r i d e i n f e e d s t r e a m N V O L T S = v o l t a g e a c c r o s s t h e c e l l , V E L Y = b u l k s t r e a m v e l o c i t y V , S I G M A , L A M B O , B C O N D a n d DCOND = a r e p a r a m e t e r s i n t h e e x t e n d e d O n s a g e r - S h e d l o v s k y e q u a t i o n P P M C A = C a l i b r a t i o n f o r t h e d e t e r m i n a t i o n o f i r o n i n t h e m e m b r a n e s ( m g . ) T R C A L = T h e t r a n s m i t t a n c e a t a g i v e n i r o n c o n c e n t r a t i o n ( P P M C A L ) C A L = S o d i u m c a l i b r a t i o n s a t 1 0 0 , 1 0 0 0 a n d 5 0 0 0 p p m N a C l . N O R D = T h e s o d i u m s a m p l i n g o r d e r T I M E = T h e t i m e a t w h i c h t h e s a m p l e w a s t a k e n A M V = T h e m i l l i v o l t r e a d i n g o f t h e s o d i u m e l e c t r o d e ( m v . ) P R E S S D F = T h e p r e s s u r e d i f f e r e n c e a c r o s s t h e b r i n e a n d d i a l y s a t e s t r e a m s ( i n c h H g . ) C U R = T h e c u r r e n t c o n s u m p t i o n o f b o t h s t a g e s a n d t h e t o t a l ( m A . ) V S T A C K = T h e s t a c k v o l t a g e a s m e a s u r e d b y t h e P t . P r o b e s ( v o l t s ) T 6 0 C C = T h e t o t a l a m o u n t o f t i m e r e q u i r e d t o f i l l a 6 0 c c . V o l u m e r i c f l a s k ( s e c ) p H = T h e v a l u e o f p H 1 17 F E T R = T h e m e a s u r e d i r o n t r a n s m i t t a n c e o f a s a m p l e S O L C A L a n d S O L T R = T h e c o n c e n t r a t i o n a n d t r a n s m i t t a n c e f o r t h e d e t e r m i n a t i o n s o f i r o n c o n t a i n e d i n a s t r e a m ( P P M . A n d % t r a n s m i t t a n c e r e s p e c t i v e l y ) T E M P E R = T h e s o l u t i o n t e m p e r a t u r e s T R B C A T = T h e p e r c e n t t r a n s m i t t a c e o f t h e d i s s o l v e d i r o n f r o m t h e c a t i o n i c m e m b r a n e T R B A N I = T h e p e r c e n t t r a n s m i t t a n c e o f t h e d i s s o l v e d i r o n f r o m t h e c a t i o n i c m e m b r a n e . B o t h c o m p u t e r p r o g r a m s h a d t h e f o l l o w i n g o u t p u t v a l u e s ; R U N N U M = T h e a c t u a l r u n n u m b e r N V O L T S = V o l t a g e a c c r o s s t h e c e l l i n v o l t s D . C . V E L Y = f l u i d v e l o c i t y i n c m / s e c P P M = I r o n c o n c e n t r a t i o n i n f e e d p p m . V S O L P = V o l t a g e d r o p i n t h e b u l k s o l u t i o n ( v o l t s ) V s p = V o l t a g e d r o p p e r c e l l p a i r ( v o l t s ) R A C P = T h e t o t a l r e s i s t a n c e s ( R a + R c + R p ) ( O h m s ) . V S T A C K = T h e s t a c k v o l t a g e ( v o l t s D . C . ) P R E S D F = P r e s s u r e d r o p a c r o s s t h e b r i n e o r d i a l y s a t e s t r e a m ( c m . H g . ) S E P F = T h e s e p a r a t i o n f a c t o r ( - ) P L I T R E = T h e p o w e r r e q u r e m e n t s p e r l i t r e o f d i a l y s a t e p r o d u c e d ( j o u l e s / l i t r e p e r c e l l ) T O T A L = t h e a m o u n t o f i r o n a c c u m u l a t e d ( m g . ) D E L N S = P e r c e n t d r o p i n s e p a r a t i o n f a c t o r (%) T M F E = T h e t o t a l a m o u n t o f i r o n a c c u m u l a t e d o n t h e m e m b r a n e s o v e r t h e d u r a t i o n o f t h e r u n ( m g . ) A M L O S T = T h e a m o n t o f i r o n l o s t i n t h e f e e d s t r e a m o v e r t h e d u r a t i o n o f a r u n ( m g . ) 118 F E = T h e p e r c e n t i r o n s e p a r a t e d p e r s t r e a m (%) N A = T h e p e r c e n t s o d i u m s e p a r a t e d p e r s t r e a m (%) C E = T h e c u r r e n t e f f i c i e n c y C E = T h e c u r r e n t e f f i c i e n c y a t 2 a n d 20 h o u r s E R R A C P = T h e a b s o l u t e e r r o r i n t h e v a l u e o f ( R a + R c + R p ) ( O h m s ) E R R T F E = T h e a b s o l u t e e r r o r i n t h e v a l u e o f T O T A L ( m g . ) E R R D L N = T h e a b s o l u t e e r r o r i n t h e v a l u e o f S E P F ( - ) E R R T M F = T h e a b s o l u t e e r r o r i n t h e v a l u e o f T M F E ( m g . ) E R R A M L = T h e a b s o l u t e e r r o r i n t h e v a l u e o f A M L O S T ( m g . ) E R R C E = T h e a b s o l u t e e r r o r i n t h e v a l u e o f C E t h e c u r r e n t e f f i c i e n c y S E L N A = T h e s o d i u m s e l e c t i v i t y ( - ) S E L N A = T h e s o d i u m s e l e c t i v i t y p e r s t r e a m ( - ) S E L F E = T h e i r o n s e l e c t i v i t y p e r s t r e a m ( - ) E S E N A = T h e a b s o l u t e e r r o r i n t h e v a l u e o f S E L N A ( - ) E S E F E = T h e a b s o l u t e e r r o r i n t h e v a l u e o f S E L F E ( - ) P H = T h e p H o f t h e d i a l y s a t e a n d b r i n e s t r e a m s a t 2 a n d 20 h o u r s . P r o g r a m n u m b e r 3 r e a d t h e d i g i t i z e d v a l u e s o f t h e p o t e n t i a l d r o p a c c r o s s a r e s i t o r a s a f u n c t i o n o f t i m e a n d g a v e t h e p o w e r c o n s u m p t i o n p e r c y c l e f o r t h e t o p b a t t e r y , t h e b o t t o m b a t t e r y , a n d a l l t h e ' c e l l s c o m b i n e d . T h e s e r e s u l t s w e r e t h e n i n s e r t e d i n t o t h e d a t a f i l e o f p r o g r a m #2. T h e i n p u t a n d o u t p u t v a l u e s a r e a s f o l l o w s ; R U N N U M = T h e a c t u a l r u n n u m b e r V O L T S = V o l t a g e a c c r o s s t h e e l e c t r o d e s i n v o l t s D . C . P P M = T h e s o d i u m c o n c e n t r a t i o n i n t h e f e e d ( p p m . ) V E L Y = L i n e a r f l u i d v e l o c i t y i n t h e c e l l c o m p a r t m e n t ( c m / s e c . ) 1 1 9 I T E M = T h e s e c t i o n o f t h e a p p a r a t u s d r a w i n g t h e c u r r e n t , i e . t h e t o p o r b o t t o m c e l l s , a n d t h e t o t a l a p p a r a t u s . N = T h e i t e m n u m b e r f o r ; N=1 - T o p c e l l s , N=2 - B o t t o m c e l l s , a n d N=3 - T o t a l a p p a r a t u s . WHEN = T i m e a t w h i c h t h e d a t a w a s t a k e n a t 2 a n d 2 0 h o u r s . T I M E 1 , 2 = T i m e e l a p s e d d u r i n g a c y c l e ( s e c o n d s ) . C M V 1 , 2 = P o t e n t i a l d r o p a c c r o s s a r e s i s t o r i n s e r i e s w i t h t h e c e l l s ( m v . D . C . ) . P T O T = T h e t o t a l p o w e r c o n s u m p t i o n f o r a g i v e n i t e m ( W a t t s ) . P ( J ) = T h e p o w e r c o n s u m p t i o n d u r i n g a s e g m e n t o f t h e c y c l e a t ; J=1 I n i t i a l p a u s e t i m e J = 2 F e e d t i m e s a n d r e c y c l e J = 3 S e c o n d p a u s e t i m e J = 4 S e c o n d r e c y c l e . A T O T T I = T o t a l c y c l e t i m e i n ' s e c o n d s . F E E D C R = C u r r e n t c o n s u m p t i o n a t f e e d t i m e ( D . C . A m p . ) C PROGRAM 1 C PROGRAM TO TREAT DATA FROM THE STEADY STATE PROCESS C DIMENSION V(3 ) , P P M C A L ( 3 ) , C A L ( 3 , 3 ) , N O R D ( 4 , 3 ) , T I M E ( 3 ) , A M V ( 4 , 3 ) , P R E S D F ( 2 6 , 2 , 3 ) , C U R ( 3 , 3 ) , V S T A C K ( 2 6 , 2 , 3 ) , T 6 0 C C ( 2 , 3 ) , S O L C A L ( 3 ) , S 0 L T R ( 3 ) DIMENSION D I A L ( 2 6 , 3 j , T E M P E R ( 3 ) , P H ( 2 6 , 2 , 3 ) , V E L O C ( 2 6 ) , F L O W ( 2 , 3 ) , X ( 3 ) , E R R A C P ( 2 6 , 2 , 3 ) , E R R A M L ( 2 6 ) . E R R C E ( 2 6 , 3 ) DIMENSION S IGMA(3 ) ,BC0ND(3 ) ,DCOND(3 ) ,TRCAL(3 ) ,NVOLTS(26 ) ,FETR(3 , 3 ) , P P M F E ( 3 , 3 ) , P P M ( 2 6 ) , S E P F ( 2 6 , 3 ) , A C C N A ( 2 6 , 3 ) , C E ( 2 6 , 3 ) , P E R C E ( 2 6 ) , F E ( 2 6 , 2 , 3 ) DIMENSION V E L Y ( 2 6 ) , A L M D ( 2 , 3 ) , A L M B ( 2 , 3 ) , S P D I A L ( 3 , 3 ) , S P B R I N ( 3 , 3 ) , C U R D E N ( 3 ) , R A C P ( 2 6 , 2 , 3 ) , V S L O P ( 2 6 , 2 , 3 ) . T O T A L ( 2 6 ) , AML0ST(26) DIMENSION E L E C T R ( 2 6 , 3 ) , V S P ( 3 ) , P L I T R E ( 2 6 , 3 ) , V S O L P ( 2 6 , 2 , 3 ) , S E L N A ( 2 6 , 2 , 3 ) , S E L F E ( 2 6 , 2 , 3 ) , E S E F E ( 2 6 , 2 , 3 ) , E S E N A ( 2 6 , 2 . 3 ) INTEGER RUNNUM(26),PPMF REAL I N T E R , N A C L ( 3 , 3 ) , L A M B O ( 3 ) , N A ( 2 6 , 2 , 3) NUM=0 AAA=0.0 C 9 FORMAT ( 6 F 8 . 4 ) 10 FORMAT ( F 8 . 4 . 6 F 5 . 1 ) 1 1 FORMAT ( 3 F 5 . 1) 12 FORMAT ( 2 1 5 , 1 3 , 1 4 , 1 2 , F 6 . 4 ) 14 FORMAT (412) 16 FORMAT ( F 8 . 4 , 4 F 5 . 1 ,3F6 . 1 , 2 F 6 . 2 , 2 F 5 . 1 ) 18 FORMAT ( 2 F 6 . 2 . 4 F 6 . 3 . 3 F 5 . 1 ) 19 FORMAT ( 3 F 6 . 2 ) 20 FORMAT ( 2 F 5 . 1 ) C DO 25 1=1,3 R E A D ( 5 , 9 ) V( I ) ,S IGMA( I ) ,LAMB0( I ) ,BCOND( I ) ,DCOND( I ) 25 CONTINUE ro READ(5 ,9 ) ( P P M C A L ( K ) , K = 1 , 3 ) , ( T R C A L ( K ) , K = 1 , 3 ) ° 30 NUM=NUM+1 IF (NUM.EQ.27 ) GOT0800 READ(5 ,12 ) M.N.RUNNUM(NUM),PPMF,NVOLTS(NUM),VELY(NUM) C 35 SUMX=0.0 SUMY=0.0 SUMXY=0.0 SUMX2=0.0 I F ( L S F . E O - 1 ) G O T 0 7 0 0 C DO 40 d= 1 , 2 READ(5 ,11 ) ( C A L ( K , J ) , K = 1 , 3 ) 40 CONTINUE C DO 45 J=1,M READ(-5,14) (NORD(K.d),K=1 ,4) 45 CONTINUE C READ(5 , 10) T I M E ( 1 ) , ( AMV(K, 1 ) ,K=1 ,4 ) , (PRESDF(NUM,K , 1 ) ,K=1,2) DO 70 d = 2,M READ(5 ,16 ) T I M E ( J ) , ( A M V ( K , J ) , K = 1 , 4 ) , ( C U R ( K , J ) , K = 1 , 3 ) , ( V S T A C K ( N U M , K , d ) , K = 1 , 2 ) , ( P R E S D F ( N U M , K , d ) , K = 1 , 2 ) 70 CONTINUE DO 74 d=1 ,M READ(5 , 18) ( T 6 0 C C ( K , d ) .K=1 ,2) , ( P H ( N U M . K . d ) , K = 1 , 4 ) , ( F ETR (K ,d) ,K=1 ,3) 74 CONTINUE IF(RUNNUM(NUM) .LT.77.OR.RUNNUM(NUM).EO . 9 1 . OR . RUNNUM(NUM).EQ.92)G0T078 READ(5 ,9 ) ( S O L C A L ( K ) , K = 1 , 3 ) , ( S O L T R ( K ) , K = 1 ,3) 78 READ(5 .19 ) (TEMPER(d) ,d=1 ,3 ) IF (RUNNUM(NUM)-77) 82 ,81 ,81 81 READ(5 ,20 ) TRBCAT,TRBANI C 82 DO 86 K= 1 ,2 DO 85 d=1,3 P R E S D F ( N U M , K , J ) = P R E S D F ( N U M , K , J ) * 0 . 1 85 CONTINUE 86 CONTINUE C C NA CONCENTRATION WITH DRIFT ELECTRODE CORRECTIONS C DO 148 L=1 ,3 DO 146 d=1 ,M DO 130 K = 1 ,3 X(K) = ( ( C A L ( K , 2 ) - C A L ( K , 1 ) ) * ( N O R D ( L , J ) * 1 .0 ) / (N*1 .0 ) )+CAL(K, 1) 130 CONTINUE IF ( A M V ( L , d ) - X ( 2 ) ) 1 3 1 , 1 3 2 , 1 3 2 131 B B B = ( ( 3 . * X ( 1 ) ) - ( 2 . * X ( 2 ) ) ) / ( X ( 1 ) - X ( 2 ) ) S L 0 P E = ( 3 . 0 - B B B ) / X ( 2 ) AAA=(SLOPE*AMV(L,d) )+BBB GO TO 144 132 B B B = ( ( 3 . 6 9 8 9 7 * X ( 2 ) ) - ( 3 . * X ( 3 ) ) ) / ( X ( 2 ) - X ( 3 ) ) S L 0 P E = ( 3 , 0 - B B B ) / X ( 2 ) AAA=(SLOPE*AMV(L,d) )+BBB 144 N A C L ( L , J ) = ( 1 0 * * A A A ) / 5 8 4 4 0 . 0 146 CONTINUE 148 CONTINUE C DO 170 d= 1 , 3 DO 160 K=1,2 F L O W ( K , d ) = 0 . 0 6 / T 6 0 C C ( K , d ) 160 CONTINUE 170 CONTINUE C I F ( RUNNUM(NUM).LT.77.OR.RUNNUM(NUM).EO.91.OR.RUNNUM(NUM).EO.92)GOTO 195 DO 180 K= 1 , 3 SUMX=SOLCAL(K)+SUMX SUMY = ALOG10(SOLTR(K)) + 5UMY SUMXY=(AL0G10(S0LTR(K))*SOLCAL(K))+SUMXY SUMX2=(S0LCAL(K)**2. )+SUMX2 180 CONTINUE C SLOPE=( (SUMY*SUMX) - (3 . *SUMXY) ) / ( (SUMX**2 . ) - ( 3 . *SUMX2) ) INTER=(SUMY-(SLOPE*SUMX)) /3 . DO 190 1=1,3 DO 185 d=1,3 I F ( F E T R ( I ,d ) .EQ.00 .0 )GOTO 185 P P M F E ( I , d ) = ( A L 0 G 1 0 ( F E T R ( I , d ) ) - I N T E R ) / S L O P E I F ( P P M F E ( I , d ) . G T . 0 . 0 ) G O T O 1 8 5 PPMFE( I ,d )=0 .001 185 CONTINUE 190 CONTINUE GOTO 198 195 DO 197 1=1,3 ro DO 196 J=1 ,3 P P M F E ( I , J ) = 0 . O 196 CONTINUE 197 CONTINUE 198 PPM(NUM)=PPMFE(2,1) CALCULATION OF NA MATERIAL BALANCE AND SEPARATION FACTOR DO 200 d = 2,M Z = N A C L ( 2 , d ) * ( F L O W ( 1 , J ) + FLOW( 2 , J ) ) *60 . O U=((NACL( 1 , d ) * F L O W ( 1 , d ) ) + (NACL(3 ,d) *FLOW( 2 , d ) ) ) * 6 0 . 0 S E P F ( N U M , d ) = N A C L ( 3 , d ) / N A C L ( 1 , d ) ACCNA(NUM,d)=(Z-U) CURRENT EFFICIENCY BASED ON NACL AND IRON TOTNA = ( N A C L ( 3 , d ) - N A C L ( 1 , d ) ) / 2 . CE(NUM,d )=T0TNA*FL0W(2 ,d ) *96487 . * 1 0 0 0 . / ( 6 . 5 * C U R ( 3 , d ) ) E R R C E ( N U M , d ) = C E ( N U M , d ) * ( ( ( ( N A C L ( 3 , d ) + N A C L ( 1 , d ) ) * 0 . 0 1 ) / ( N A C L ( 3 , d ) - N A C L ( 1 , d ) ) ) + 0 . 0 0 6 ) 200 CONTINUE PERCE(NUM)=(CE(NUM,2 ) -CE(NUM,3 ) ) *100 . /CE(NUM,2 ) 400 CONTINUE AFE=(PPMFE(2 , 1 ) - P P M F E ( 2 , 3 ) ) * 8 1 .81 T0TFE = PPMFE(2 , 1 ) *8 1 .81 CALCULATION OF SODIUM AND IRON SELECTIV IT IES DO 610 d=2,M I F ( P P M F E ( 2 , d ) . E Q . O . O ) GOTO 501 FE(NUM, 1,d) = ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) * 1 0 0 . / P P M F E ( 2 , d ) F E ( N U M , 2 , d ) = ( P P M F E ( 3 , d ) - P P M F E ( 2 , d ) ) * 100.O/PPMFE ( 2 , d ) 501 NA(NUM, 1,d) = ( N A C L ( 2 , d ) - N A C L ( 1 , d ) ) * 100 .0 /NACL(2 , d) NA(NUM,2 ,d ) = ( N A C L ( 3 , d ) - N A C L ( 2 , d ) ) * 100.O/NACL ( 2 , d) CALCULATION OF SODIUM AND IRON SELECT IV IT IES D E S F E = ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) * 2 . / 5 5 8 4 7 . 0 I F ( P P M F E ( 2 , d ) . E O . O . O . O R . P P M F E ( 2 , d ) . E Q . P P M F E ( 1 , d ) ) GOTO 510 E F E = ( P P M F E ( 2 , d ) + P P M F E ( 1 , d ) ) * 0 . 0 1 / ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) GOTO 515 510 EFE=0 .0 515 DESNA = N A C L ( 2 , d ) - N A C L ( 1 ,d ) E N A = ( N A C L ( 2 , d ) + N A C L ( 1 , d ) ) * 0 . 0 1 / ( N A C L ( 2 , d ) - N A C L ( 1 ,d) ) DESTOT=DESNA+DESFE ETOT=( (EFE*DESFE)+(ENA*DESNA) ) /DESTOT F E E D F E = P P M F E ( 2 , d ) * 2 . / 5 5 8 4 7 . 0 T0TC0N=NACL(2,d)+FEEDFE SELNA(NUM, 1 , d) = ( D E S N A / D E S T 0 T ) / ( N A C L ( 2 , d ) / T O T C O N ) ESENA(NUM,1 ,d)=(ENA+ET0T+0.01+0.01) *SELNA(NUM,1 ,d) I F ( P P M F E ( 2 , d ) . E Q . O . O ) GOTO 520 SELFE(NUM, 1,d) = ( D E S F E / D E S T O T ) / ( F E EDFE/TOTCON) ESEFE(NUM, 1,d ) = (EFE+ETOT+0.01+0.01)*SELFE(NUM,1 , d) GOTO 525 520 S E L F E ( N U M , 1 , d ) = 0 . 0 SELECTIV ITY BASED ON CONC STREAM 525 DESFE=(PPMFE(3,d ) -PPMFE(2,d ) ) * 2 . / 55847 .0 I F ( P P M F E ( 2,d) . E Q . O . O ) GOTO 530 EFE = ( P P M F E ( 3 .d ) + P P M F E ( 2 , J ) ) * 0 . 0 1 / ( P P M F E ( 3 ,d ) - P P M F E ( 2 . d)) GOTO 535 530 E F E = 0 . 0 535 DESNA=NACL(3,d)-NACL(2,d) ENA=(NACL(3,d )+NACL(2 ,d) ) *0 .01 / (NACL(3 ,J ) -NACL(2,d)) DESTOT=DESNA+DESFE ETOT=( (EFE*DESFE)+'(ENA*DESNA) ) /DESTOT S E L N A ( N U M , 2 , J ) = ( D E S N A / D E S T O T ) / ( N A C L ( 2 , J ) / T O T C O N ) E S E N A ( N U M , 2 , J ) = (ENA+ETOT+0.01+0.01)*SELNA(NUM,2, <J) I F ( P P M F E ( 2 , J ) . E Q . O . O ) GOTO 607 S E L F E ( N U M , 2 , d )= (DESFE/DESTOT) / (FEEDFE/TOTCON) ESEFE(NUM,2,d )= (EFE+ET0T+O.01+0.01)*SELFE(NUM,2,d) GOTO 610 607 SELFE(NUM,2,d )=0 .0 610 CONTINUE CALCULATION OF LOG MEAN CONCENTRATIONS IN BOTH STAGES DO 61 1 d = 2 ,3 AAAA=1. -SQRT( 1 . - ( ( N A C L ( 2 , J ) - N A C L ( 1 ,d ) ) / N A C L ( 2 ,d))) I F ( A A A A . E Q . 1 . ) G O T O 611 F = N A C L ( 1 ,d)/(1 . -AAAA) ALMD ( 2 , d ) = ( F - NACL ( 1 , ij ) ) / A LOG ( F/NACL ( 1 , d) ) ALMD(1 ,d )= (NACL(2.d ) -F ) /AL0G(NACL(2,d ) / F ) AAAA= 1 . -SQRT( 1 . - ( ( N A C L ( 3 ,d ) - N A C L ( 2 ,d ) ) / N A C L ( 2 , d))) F = NACL(3,d)/(1 . -AAAA) ALMB(1,d )= (NACL(2,d ) -F ) /ALDG(NACL(2,d ) /F ) ALMB(2,d) = ( F - N A C L ( 3,d) ) / A L O G ( F / N A C L ( 3 , d)) 611 CONTINUE CALCULATION OF DIALYSATE CONDUCTIVITY IN MOHS BY THE EXTENTED ONSAGER-SHEDLOVSKY EQUATION DO 619 d=2,3 I F ( T E M P E R(d ) - 2 5 . 0 ) 614 ,614 ,615 614 L=1 T= 15 .0 GOTO 616 615 L=2 T = 25 .0 616 D I F T E M = ( T E M P E R(d ) - T ) / 1 0 . 0 V INT=(D IFTEM*(V(L+1) -V (L ) ) )+V( L) S IGINT=(DIFTEM*(SIGMA(L+1) -SIGMA(L) ) )+SIGMA(L) LAMINT=(DIFTEM*(LAMBO(L+1)-LAMBO(L)))+LAMBO(L) BC0INT=(DIFTEM*(BC0ND(L+1)-BCOND(L)) )+BCOND(L) DCOINT=(DIFTEM*(DC0ND(L+1)-DCOND(L)))+DCOND(L) DO 617 K=1,2 A=LAMINT+(BCOINT*ALMD(K,d))+(DCOINT*ALMD(K,d)*ALOG10(ALMD(K,d))) E Q C O N D = ( A * ( 1 . - ( V I N T * S Q R T ( A L M D ( K ,d ) ) )) ) - ( 2 . * S I G I N T * S Q R T ( A L M D ( K ,d))) SPDIAL(K,d )=EQCOND*ALMD(K,d)/1000.0 A=LAMINT+(BCOINT*ALMD(K,d))+(DCOINT*ALMD(K,d)*ALOG10(ALMD(K,d))) EQCOND=(A* (1 . - (V INT*SQRT(ALMD(K,d)) ) ) ) - ( 2 . *S IG INT*SQRT(ALMD ( K , d))) SPBRIN(K.d)=EQCOND*ALMB(K,d)/1000.0 617 CONTINUE 619 CONTINUE PLOT OF VOLTS PER CELL PAIR VERSUS CURRENT DENSITY/CONDUCTIVITY DO 630 K=1,2 DO 620 J=2 ,3 CURDEN(d)=CUR(3,J ) * . 0 0 1 / ( ( 3 . 8 1 * 3 3 . 0 ) - 3 7 . 88 ) IF(RUNNUM(NUM).E0.91.OR.RUNNUM(NUM).EO.92)GOT0620 R B = . 9 5 2 5 / ( S P B R I N ( K , d ) * 3 8 . 1 8 ) RD= . 9 5 2 5 / ( S P D I A L ( K , d ) * 3 8 . 18) C U R D = C U R ( K , d ) * 0 . 0 0 1 / 3 8 . 1 8 RTOT=VSTACK(NUM, K , d ) * 1000. /CUR( K , J ) RACP(NUM,K,d)=RTOT-RB-RD ERRACP(NUM,K,d)=(RTOT*0.0015)+((RB+RD) *0 .063 ) V S O L P ( N U M , K , d ) = C U R D * 0 . 1 5 9 * ( ( 1 . / S P D I A L ( K . d ) ) + ( 1 . / S P 8 R I N ( K , d ) ) ) 620 CONTINUE 630 CONTINUE IRON DEPOSIT ON TEST MEMBRANE IN CELL B LEAST SQUARES FIT ON CALIBRATION I F ( P P M F E ( 2 . 1 ) . N E . 0 . 0 ) G 0 T 0 650 TOTMGB=0.0 GOTO 730 650 LSF=1 G0T035 700 DO 710 K=1,3 SUMX=PPMCAL(K)+SUMX SUMY=AL0G1O(TRCAL(K))+SUMY SUMXY=(PPMCAL(K)*AL0G1O(TRCAL(K)))+SUMXY SUMX2=(PPMCAL(K)**2.)+SUMX2 710 CONTINUE SLOPE = ( (SUMY*SUMX)- (3 . * S U M X Y ) ) / ( ( S U M X * * 2 . ) - ( 3 . *SUMX2) ) FEINT=(SUMY-(SLOPE*SUMX)) /3 . PPMCAT=(ALOG10(TRBCAT)-FEINT) /SLOPE PPMANI=(ALOG10(TRBANI) -FEINT) /SLOPE IF(PPMCAT)71 1 ,71 1 ,712 711 PPMCAT=0.0 712 IF (PPMANI )714 ,714 ,715 714 PPMANI=0.0 715 TOTAL(NUM) = (PPMCAT+PPMANI)*2 .150*0 .1 AML0ST(NUM)= (PPMFE(2 ,1 ) -PPMFE(2 ,3 ) ) *81 .81 ERRAML(NUM)=AMLOST(NUM)* ( (PPMFE(2 ,1 )+PPMFE(2 ,3 ) ) *0 .01 ) / (PPMFE(2 ,1 ) -PPMFE(2 ,3 ) ) LSF=0 POWER CALCULATIONS 730 DO 750 d=2,M TOTPOW=(CUR(1,d)+CUR(2,d) ) *NVOLTS(NUM)/ ( (FLOW(1,d)+ F L O W ( 2 , d ) ) * 1000.0) S T K P O W = ( ( C U R ( 1 , d ) * V S T A C K ( N U M , 1 , d ) ) + ( C U R ( 2 , d ) * V S T A C K ( N U M . 2 , d ) ) ) / ( ( F L O W ( 1 , d ) + F L O W ( 2 , d ) ) E LECTR(NUM,d) = (TOTPOW-STKPOW)* 100.0/TOTPOW PLITRE(NUM,d)=TOTPOW/2.0 750 CONTINUE DO 762 d=1 ,3 DIAL(NUM,0) = N A C L ( 1 , J ) * 5 5 4 4 0 . 0 762 CONTINUE C GOT030 C C PRINTING OF RESULTS C 800 DO 810 NUM=1,26 DO 805 <J = 2 , 3 V S P ( J ) = V S T A C K ( N U M , 1 , d ) / 6 . 5 805 CONTINUE PRINT 1001,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),VSOLP(NUM, 1 , 2 ) , V S P ( 2 ) , V S O L P ( N U M , 1 , 3 ) , V S P ( 3 ) 810 CONTINUE PRINT 1500 DO 815 NUM=1,26 DO 812 d=2,3 V S P ( J ) = V S T A C K ( N U M , 2 . U ) / 6 . 5 812 CONTINUE PRINT 1002,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),VSOLP(NUM , 2 , 2) , VSP ( 2 ) , V S O L P ( N U M , 2 , 3 ) , V S P ( 3 ) 815 CONTINUE PRINT 1500 DO 820 NUM=1,26 PRINT 1003,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM) , VSTACK(NUM, 1 ,2 ) ,RACP(NUM, 1 , 2 ) , V S T A C K ( N U M , 1 , 3 ) , R A C P ( N U M , 1,3) 820 CONTINUE PRINT 1500 DO 825 NUM=1,26 PRINT 1004,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),VSTACK(NUM, 2 , 2) , R A C P ( N U M , 2 , 2 ) , V S T A C K ( N U M , 2 , 3 ) , R A C P ( N U M , 2 , 3 ) 825 CONTINUE PRINT 1500 DO 830 NUM=1,26 PRINT 1005,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),PRESDF (NUM, 1,2) .PRESDF (NUM, 1,3) 830 CONTINUE PRINT1500 DO 835 NUM= 1 ,26 PRINT 1006,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM).PRESDF(NUM,2,2) ,PRESDF(NUM,2,3) 835 CONTINUE PRINT 1500 DO 840 NUM=1,26 PRINT 1007,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),SEPF(NUM,2),PL ITRE(NUM,2 ) ,SEPF(NUM,3 ) ,PL ITRE(NUM,3 ) 840 CONTINUE PRINT 1500 DO 843 NUM=1,26 PRINT 1015,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),DIAL(NUM,2) , P L I T R E ( N U M , 2 ) , D I A L ( N U M , 3 ) , P L I T R E ( N U M , 3 ) 843 CONTINUE PRINT 1500 DO 845 NUM=1,26 DELNS=(SEPF(NUM,2 ) -SEPF(NUM,3 ) ) * 100 .0 /SEPF(NUM,2) PRINT1009,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),TOTAL(NUM),DELNS 845 CONTINUE PRINT 1500 DO 850 NUM=1,26 TMFE = TOTAL(NUM)* 13. PRINT 1010,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),TMFE,AMLOST(NUM) 850 CONTINUE PRINT 1500 DO 855 NUM=1,26 PRINT 1011,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM).PPM(NUM),FE(NUM,1,2) , FE(NUM, 1 , 3 ) , F E ( N U M , 2 , 2 ) , F E ( N U M , 2 , 3 ) 855 CONTINUE PRINT 1500 DO 860 NUM=1,26 PRINT 1012,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),NA(NUM, 1 ,2) ,NA(NUM, 1 , 3 ) , N A ( N U M , 2 , 2 ) , N A ( N U M , 2 , 3 ) 860 CONTINUE PRINT1500 DO 865 NUM=1,26 PRINT 1013,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),CE(NUM,2) ,CE(NUM,3) ,PERCE(NUM) 865 CONTINUE PRINT 1500 DO 870 NUM=1,26 PRINT 1004,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM).PPM(NUM),ERRACP(NUM,1,2) ,ERRACP(NUM,1,3) ,ERRACP(NUM,2,2) ,ERRACP(NUM , 2 ,3 ) 870 CONTINUE PRINT 1500 DO 875 NUM=1,26 DESNS=(SEPF(NUM,2 ) -SEPF(NUM,3 ) ) *100 .O /SEPF(NUM,2 ) ERRDLN=DELNS* ( ( (SEPF(NUM,2 )+SEPF(NUM,3 ) ) *0 .02 / (SEPF(NUM;2 ) -SEPF(NUM,3 ) ) )+0 .02 ) E R R D L N = ( 1 , + ( S E P F ( N U M , 3 ) / S E P F ( N U M . 2 ) ) ) * 0 . 0 2 * 1 0 0 . 0 ERRTFE=T0TAL(NUM)*0.0124 PRINT 1014,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM) , ERRTFE , ERRDLN 875 CONTINUE PRINT 1500 DO 880 NUM=1,26 ERRTMF=T0TAL(NUM)*13*O.O124 PRINT 1014.RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),ERRTMF , ERRAML(NUM) 880 CONTINUE PRINT 1500 D0r885 NUM=1,26 PRINT 1014,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),ERRCE (NUM, 2 ) ,ERRCE (NUM,3) 885 CONTINUE PRINT 1500 DO' 890 NUM= 1 , 26 PRINT 1014,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),SE LNA (NUM , 1 , 2 ) , S E LNA(NUM, 1 , 3 ) , SELNA ( N U M , 2 , 2 ) , S E LNA(NUM,2,3) 890 CONTINUE PRINT 1500 DO 895 NUM=1,26 PRINT 1014,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),SELFE (NUM, 1 , 2 ) , S E L F E ( N U M , 1 , 3 ) , SELFE (NUM, 2 , 2 ) , S E L F E ( N U M , 2 , 3 ) 895 CONTINUE PRINT 1500 DO 900 NUM =1,26 PRINT 1014 ,RUNNUM(NUM) .NVOLTS(NUM) ,VELY(NUM) ,PPM(NUM) ,ESENA(NUM,1 ,2 ) ,ESENA(NUM,1 ,3 ) .ESENA(NUM,2 ,2 ) ,ESENA(NUM,2 ,3 ) 900 CONTINUE PRINT 1500 DO 901 NUM=1,26 PRINT 1014,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM) , ESEFE(NUM , 1 , 2 ) , E S E F E ( N U M , 1 , 3 ) , E S E F E ( N U M , 2 , 2 ) , E S E F E ( N U M , 2 , 3 ) 901 CONTINUE PRINT 1500 DO 902 NUM =1,26 PRINT 1014.RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM).PH(NUM,1 .2 ) ,PH(NUM,1 ,3 ) ,PH(NUM,3 ,2 ) ,PH(NUM,3 ,3 ) 902 CONTINUE 1000 FORMAT(' ' , 2 X , 2 1 5 , 2 F 7 . 2 , 3 X , 4 F 1 2 . 4 ) 1001 FORMAT(' ' , 2 X , 2 I 5 , 2 F 7 . 2 , 2 ( F 8 . 3 , F 8 . 2 ) ) 1002 FORMAT( ' ' ', 2X ,215,2F7 .2,2(F8 .3,F8. 2)) 1003 FORMAT(' ' ,2X, ,215,2F7 .2,2(F8 .2,F8. 2)) 1004 FORMAT( ' ' ,2X. ,215,2F7 .2,2(F8 .2.F8. 2)) 1005 FORMAT(' ' , 2X , ,215,2F7 2,2(F8 .2)) 1006 FORMAT( ' ' , 2X , ,215,2F7 2,2(F8 .2)) 1007 FORMAT(' ' ,2X, ,215,2F7. 2,2(F8 .3,F8. 0)) 1008 FORMAT( ' ',2X,2I5,2F7. 2,2(F8 .3,F8. 0)) 1009 FORMAT( ' ' . 2X , ,215,2F7. 2,2(F8 2)) 1010 FORMAT( ' ' , 2X , ,215,2F7. 2.F8.2, , F8. 1) 101 1 FORMAT(' ' ,2X, 215,2F7. 2,4(F8, . D ) 1012 FORMAT(' ',2X,2I5,2F7. 2,4(F8. O ) 1013 FORMAT( ' ' , 2X , 215,2F7. 2,2(F8. 3) , F8 .2) 1014 FORMAT( ' • ' ,2X,2I5,2F7. 2,4(F8. .3)) 1015 FORMAT(' ' ' ,2X, 215,2F7. 2,4(F8. 0)) 1500 FORMAT( ' 1 ' STOP END ' ) PROGRAM 2 PROGRAM TO TREAT DATA FROM THE UNSTEADY STATE PROCESS DIMENSION S 0 L C A L ( 3 ) , S 0 L T R ( 3 ) , P P M T R ( 3 , 3 ) , T E S T M 3 ( 3 ) , T E S T M 7 ( 3 ) , T I M E ( 3 ) , C A L ( 3 , 2 ) , A M V ( 4 , 3 ) , N 0 R D ( 4 , 3 ) , F L 0 W ( 2 , 3 ) , P H ( 1 5 , 4 , 3 ) , P P M F E ( 3 , 3 ) , S E P F ( 1 5 , 3 ) , F E E C U R ( 2 , 3 ) DIMENSION E R R C E ( 1 5 , 3 ) , E R R A M L ( 1 5 ) , S E L N A ( 1 5 , 2 , 3 ) , S E L F E ( 1 5 , 2 , 3 ) , E S E N A ( 1 5 , 2 , 3 ) , E S E F E ( 1 5 , 2 , 3 ) , C C ( 2 , 3 ) , P 0 W ( 3 ) , P P M C A L ( 3 ) , T R C A L ( 3 ) , P T R 3 ( 3 ) , P T R 7 ( 3 ) , A C C N A ( 3 ) , P L I T R E ( 1 5 , 3 ) , P R E S D F ( 1 5 , 2 , 3 ) DIMENSION D I A L ( 1 5 , 3 ) , V E L Y ( 1 5 ) , N V O L T S ( 1 5 ) , P P M ( 1 5 ) , C E ( 1 5 , 3 ) , P E R C E ( 1 5 ) , P A P ( 1 5 ) , T O T A L ( 1 5 ) , F E ( 1 5 , 2 , 3 ) , A M L O S T ( 1 5 ) , X ( 5 ) ,FEEDTI (2 ) INTEGER RUNNUM(15),PPMF REAL N A C L ( 3 , 3 ) , N A ( 1 5 , 2 , 3) 10 FORMAT (F8 . 4 . 4 F 5 . 1 ,4F5 . 2 , 3 F 5 . 1) 1 1 FORMAT ( 3 F 5 . 1) , 12 FORMAT ( 2 1 5 , 1 3 , 1 4 , 1 2 , F 6 . 4 ) 14 FORMAT (412) 16 FORMAT (F8 . 4 , 4 F 5 . 1 , 3 F 6 . 1 , 2 F 6 . 2 , 2 F 5 . 1) 18 FORMAT(2F5. 1 , 2 F 5 . 2 ) 19 F0RMAT(2F6 .3 ) 20 FORMAT(13G10.5) 21 FORMAT(F7.2 ) 22 F0RMAT(6F10 .6 ) R E A D ( 5 , 2 0 ) VCOND.SIG,ALAMB,BCOND.DCOND NUM=0 30 NUM=NUM+1 IF (NUM.EQ.16 ) GOTO 800 R E A D ( 5 , 1 2 ) M,N,RUNNUM(NUM),PPMF,NVOLTS(NUM),VELY(NUM) 35 SUMX=0.0 SUMY=0.0 SUMXY=0.0 SUMX2=0.0 I F ( L S F . E Q . OG0T0505 DO 40 d=1,2 READ(5 ,11 ) ( C A L ( K , d ) , K = 1 , 3 ) 40 CONTINUE DO 45 <J=1 ,M READ(5 ,14 ) (NORD(K.d ) ,K=1 ,4 ) 45 CONTINUE DO 70 d=1 ,M READ(5 , 10) TIME(1 ) , ( A M V ( K , d ) , K = 1 , 4 ) , ( P H ( N U M , K , d ) , K = 1 , 4 ) , ( P P M T R ( K . d ) ,K=1 ,3) 70 CONTINUE I F(RUNNUM(NUM).EQ.40.0R.RUNNUM(NUM).EQ.41)G0T075 READ(5 ,22 ) ( S O L C A L ( K ) , K = 1 , 3 ) , ( S O L T R ( K ) , K = 1 ,3) 75 DO 80 d=2,M READ(5 , 18) ( C C ( K . d ) ,K=1 , 2 ) , ( P R E S D F ( N U M , K , J ) , K = 1 ,2) 80 CONTINUE READ(5 ,19 ) ( F E E D T I ( K ) , K = 1 , 2 ) R E A D ( 5 , 2 1 ) P0W(2) READ(5 ,21 ) P0W(3) R E A D ( 5 , 2 2 ) ( F E E C U R ( I , 2 ) , I = 1 , 3 ) , ( F E E C U R ( I , 3 ) , I = 1 , 3) R E A D ( 5 , 2 1 ) CYTIME READ(5 ,20 ) ( P P M C A L ( K ) , K = 1 , 3 ) . ( T R C A L ( K ) , K = 1 . 3 ) , D I L U T . ( P T R 3 ( K ) , K = 1 , 3 ) , ( P T R 7 ( K ) , K = 1 , 3 ) DO 86 K=1,2 DO 85 d = 2,M PRESDF(NUM,K,d )=PRESDF(NUM,K,d ) *2 .54 85 CONTINUE 86 CONTINUE DO 95 K=1,2 DO 90 'd=1 ,M F L O W ( K , d ) = C C ( K , d ) / ( C Y T I M E * 1 0 0 0 . 0 ) 90 CONTINUE 95 CONTINUE C C NA CONCENTRATION WITH DRIFT ELECTRODE CORRECTION C DO 148 L=1,3 DO 146 d=1,M DO 130 K=1,3 X ( K ) = ( ( C A L ( K , 2 ) - C A L ( K , 1 ) ) * ( N O R D ( L , d ) * 1 . 0 ) / ( N * 1 . 0 ) ) + C A L ( K . 1 130 CONTINUE IF ( A M V ( L , d ) - X ( 2 ) ) 1 3 1 , 1 3 2 , 1 3 2 131 B B B = ( ( 3 . * X ( 1 ) ) - ( 2 . * X ( 2 ) ) ) / ( X ( 1 ) - X ( 2 ) ) S L 0 P E = ( 3 . 0 - B B B ) / X ( 2 ) AAA=(SLOPE*AMV(L,d) )+BBB GO TO 144 132 B B B = ( ( 3 . 6 9 8 9 7 * X ( 2 ) ) - ( 3 . * X ( 3 ) ) ) / ( X ( 2 ) - X ( 3 ) ) S L 0 P E = ( 3 . 0 - B B B ) / X ( 2 ) AAA=(SLOPE*AMV(L,d) )+BBB 144 N A C L ( L , d ) = ( 1 0 * * A A A ) / 5 8 4 4 0 . 0 146 CONTINUE 148 CONTINUE C IF(RUNNUM(NUM).EQ.40.OR.RUNNUM(NUM).EQ.41)G0T0165 DO 150 K =1,3 SUMX=SOLCAL(K)+SUMX SUMY=AL0G10(S0LTR(K))+SUMY SUMXY=(AL0G1O(S0LTR(K))*SOLCAL(K))+SUMXY SUMX2=(S0LCAL(K)**2. )+SUMX2 150 CONTINUE SLOPE = ( ( S U M X * S U M Y ) - ( 3 . * S U M X Y ) ) / ( ( S U M X * * 2 . ) - (3 . *SUMX2)) FE INT=(SUMY- (SLOPE*SUMX) ) /3 . C DO 160 1=1,3 DO 155 d=1 ,3 IF ( P P M T R ( I , d ) . E Q . 0 . 0 ) G O T O 155 P P M F E ( I , d ) = ( A L O G 1 0 ( P P M T R ( I , d ) ) - F E I N T ) / S L O P E I F ( P P M F E ( I , d ) . G T . 0 . 0 ) G O T O 155 PPMF E ( I , d ) = 0 . 0 0 1 155 CONTINUE 160 CONTINUE GOTO 190 165 DO 175 1=1,3 DO 170 d=1,3 P P M F E ( I , d ) = 0 . 0 170 CONTINUE 175 CONTINUE 190 PPM(NUM)=PPMFE(2,1) vo CALCULATION OF NA MATERIAL BALANCE AND SEPARATION FACTOR DO 200 0=2,M Z = N A C L ( 2 , d ) * ( C C ( 1 , d ) + C C ( 2 , J ) ) / 1 0 0 0 . 0 U=( ( N A C L ( 1 , d ) * C C ( 1 , d ) ) + ( N A C L ( 3 , d ) * C C ( 2 , d ) ) ) / 1 0 0 0 . 0 S E P F ( N U M , d ) = N A C L ( 3 , d ) / N A C L ( 1 , d ) ACCNA(d)= (Z -U) T 0 T D E S = ( N A C L ( 2 , d ) - N A C L ( 1 , d ) ) + ( 2 . 0 * ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) / 5 5 8 4 7 . 0 ) AVGCUR=POW(d)/ (NV0LTS(NUM)*1.0) IF ( C Y T I M E . E Q . O . O . O R . A V G C U R . E Q . O . 0 ) G O T O 2 0 0 T 0 T D E S = ( N A C L ( 3 , d ) - N A C L ( 1 , d ) ) / 2 . 0 CE ( N U M , d ) = T O T D E S * C C ( 2 , d ) * 0 . 0 0 1 * 9 6 4 8 7 . 0 / ( C Y T I M E * A V G C U R * 7 . 0 ) E R R C E ( N U M , d ) = 1 0 0 . 0 * ( ( ( ( N A C L ( 3 , d ) + N A C L ( 1 , d ) ) * 0 . 0 1 ) / ( N A C L ( 3 , d ) - N A C L ( 1 . d ) ) ) + 0 . 0 1 5 5 ) 200 CONTINUE PERCE(NUM) = ( C E ( N U M , 2 ) - C E ( N U M , 3 ) ) * 100.O/CE(NUM,2) CALCULATION OF IRON DEPOSIT ON TEST MEMBRANES IN CELLS 3 (DILUTE STREAM) AND 7 (CONCENTRATE STREAM) LEAST SQUARES FIT ON CALIBRATION LSF=1 G0T035 505 DO 510 K=1,3 SUMX=PPMCAL(K)+SUMX SUMY=AL0G10(TRCAL(K))+SUMY SUMXY=(AL0G1O(TRCAL(K))*PPMCAL(K)J+SUMXY SUMX2=(PPMCAL(K)**2.)+SUMX2 510 CONTINUE LSF=0 SL = ( ( S U M X * S U M Y ) - ( 3 . * S U M X Y ) ) / ( ( S U M X * * 2 . ) - (3 . *SUMX2)) FE INTR=(SUMY- (SL*SUMX) ) /3 . T0TAL3=0. T0TAL7=0. ' DO 520 K=1,3 PPM3=(AL0G1O(PTR3(K) ) -FE INTR) /SL PPM7=(AL0G10(PTR7(K) ) -FE INTR) /SL IF(PPM3)51 1 ,511 ,512 511 PPM3=0.0 512 IF (PPM7)514 ,514 ,515 514 PPM7=0.0 515 TESTM3(K)= (PPM3*0 ILUT*5 .987 /1OOO.0 ) TESTM7(K)= (PPM7*D ILUT*5 .987 /1000 .0 ) T0TAL3=T0TAL3+TESTM3(K) T0TAL7=T0TAL7+TESTM7(K) 520 CONTINUE LSF=0 PAP(NUM)=(PAPER3+PAPER7)/3 T0TAL(NUM) = (T0TAL3+T0TAL7) /2 . AML0ST(NUM)= (PPMFE(2 ,1 ) -PPMFE(2 ,3 ) ) *81 .81 I F ( P P M F E ( 2 , 1 ) . E Q . O . O ) GOTO 530 ERRAML(NUM)=AML0ST(NUM)*(((PPMFE(2, 1 ) + P P M F E ( 2 , 3 ) ) * 0 . 0 1 ) / ( P P M F E ( 2 , 1 ) - P P M F E ( 2 , 3 ) ) ) CALCULATION OF SODIUM AND IRON SELECTIV IT IES ' 530 DO 610 J=2,M I F(PPMF E ( 2 , J ) . E Q . O . O ) G0T0550 FE(NUM, 1 , d ) = ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) * 1 0 0 . / P P M F E ( 2 , d ) F E ( N U M , 2 , d ) = ( P P M F E ( 3 , d ) - P P M F E ( 2 , d ) ) * 1 0 0 . 0 / P P M F E ( 2 , d ) 550 NA(NUM, 1,d) = ( N A C L ( 2 , d ) - N A C L ( 1 , d ) ) * 100.O/NACL ( 2 , d) NA(NUM,2 ,d) = ( N A C L ( 3 , d ) - N A C L ( 2 , d ) ) * 100.O/NACL ( 2 , d) CALCULATION OF SODIUM AND IRON SELECTIV IT IES DESFE = ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) * 2 . / 5 5 8 4 7 .0 I F ( P P M F E ( 2 , d ) . E Q . O . O . O R . P P M F E ( 2 , d ) . E Q . P P M F E ( 1 , d ) ) GOTO 560 E F E = ( P P M F E ( 2 , d ) + P P M F E ( 1 . d ) ) * 0 . 0 1 / ( P P M F E ( 2 , d ) - P P M F E ( 1 , d ) ) GOTO 565 560 EFE=0 .0 565 DESNA=NACL(2 ,d ) -NACL(1 ,d ) ENA = ( N A C L ( 2 , d ) + N A C L ( 1 , d ) ) * 0 . 0 1 / ( N A C L ( 2 , d ) - N A C L ( 1 , d ) ) DESTOT=DESNA+DESFE ETOT=( (EFE*DESFE)+(ENA*DESNA) ) /DESTOT F E E D F E = P P M F E ( 2 , d ) * 2 . / 5 5 8 4 7 . 0 T0TC0N=NACL(2,d)+FEEDFE SE LNA(NUM, 1.d ) = (DESNA/DESTOT) / (NACL(2 ,d ) /TOTCON) ESENA(NUM,1 ,d ) = (ENA+ETOT+0.01+0.01)*SELNA(NUM , 1 ,d ) I F ( P P M F E ( 2 , d ) . E Q . O . O ) GOTO 570 SE LF E(NUM, 1,d) = ( D E S F E / D E S T O T ) / ( F E E D F E / T O T C O N ) ESEFE(NUM,1 ,d )= (EFE+ETOT+0 .01+0 .01 ) *SELFE(NUM,1 ,d ) GOTO 575 570 S E L F E ( N U M , 1 , d ) = 0 . 0 SELECTIV ITY BASED ON CONC STREAM 575 D E S F E = ( P P M F E ( 3 , d ) - P P M F E ( 2 , d ) ) * 2 . / 5 5 8 4 7 . 0 I F ( P P M F E ( 2 , d ) . E Q . O . O . O R . P P M F E ( 3 , d ) . E Q . P P M F E ( 2 , d ) ) GOTO 580 E F E = ( P P M F E ( 3 , d ) + P P M F E ( 2 , d ) ) * 0 . 0 1 / ( P P M F E ( 3 , d ) - P P M F E ( 2 , d ) ) GOTO 585 580 EFE=0 .0 585 DESNA=NACL(3 ,d ) -NACL(2 ,d ) E N A = ( N A C L ( 3 , d ) + N A C L ( 2 , d ) ) * 0 . 0 1 / ( N A C L ( 3 , d ) - N A C L ( 2 , d ) ) DESTOT=DESNA+DESFE ETOT=( (EFE*DESFE)+(ENA*DESNA) ) /DESTOT SELNA(NUM,2 ,d )= (DESNA/DESTOT) / (NACL(2 ,d ) /TOTCON) E SENA(NUM,2 ,d) = (ENA + ETOT+0.01+0.01)*SE LNA(NUM,2,d) I F ( P P M F E ( 2 , d ) . E Q . O . O ) GOTO 607 S E L F E ( N U M , 2 , d ) = ( D E S F E / D E S T O T ) / ( F E E D F E / T O T C O N ) ESEFE(NUM,2 ,d )= (EFE+ETOT+0 .01+0 .01 ) *SELFE(NUM,2 ,d ) GOTO 610 607 S E L F E ( N U M , 2 , d ) = 0 . 0 610 CONTINUE ACTUAL POWER EFFICIENCY DO 620 d=2,M P L I T R E ( N U M , d ) = P 0 W ( d ) * C Y T I M E * 1 0 0 0 . 0 / ( C C ( 1 , d ) * 8 . 0 ) 620 CONTINUE DO 625 d=1,M D IAL(NUM,d )=NACL(1 ,d ) *58440 .0 625 CONTINUE DMBNA=DMBNA*58440.0 GOTO 30 PRINTING OF RESULTS 800 DO 830 NUM=1,15 PRINT1001,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),PRESDF(NUM,1,2) ,PRESDF(NUM,1,3) 830 CONTINUE PRINT 1500 DO 835 NUM=1 , 15 PRINT1002,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),PRESDF(NUM,2,2) ,PRESDF(NUM,2,3) 835 CONTINUE PRINT 1500 DO 840 NUM=1 , 15 PRINT1003,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),SEPF(NUM,2) ,PL ITRE(NUM,2 ) ,SEPF(NUM,3 ) ,PL ITRE(NUM, 3 ) 840 CONTINUE PRINT 1500 DO 843 NUM=1 , 15 PRINT 1004,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),DIAL(NUM , 2) , PL ITRE(NUM,2 ) ,D IAL(NUM,3 ) ,PL ITRE(NUM,3 ) 843 CONTINUE PRINT 1500 DO 845 NUM=1, 15 DELNS=(SEPF(NUM,2 ) -SEPF(NUM,3 ) ) * 100.O/SEPF(NUM,2) PRINT 1005,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),TOTAL (NUM) , DELNS 845 CONTINUE PRINT 1500 DO 850 NUM=1,15 TMFE = TOTAL(NUM)*56 . PRINT1006,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),TMFE,AMLOST (NUM) 850 CONTINUE / PRINT 1500 DO 855 NUM =1,15 PRINT 1007,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),FE(NUM, 1 , 2 ) , F E ( N U M , 1 , 3 ) , F E ( N U M , 2 , 2 ) , F E ( N U M , 2 , 3 ) 855 CONTINUE PRINT 1500 DO 860 NUM=1,15 PRINT 1008,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),NA(NUM, 1 ,2) ,NA(NUM, 1 , 3 ) , N A ( N U M , 2 , 2 ) , N A ( N U M , 2 , 3 ) 860 CONTINUE PRINT 1500 DO 865 NUM=1,15 PRINT 1009,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),CE(NUM,2) ,CE(NUM,3) ,PERCE(NUM) 865 CONTINUE PRINT 1500 DO 870 NUM=1,15 ERRDLN=( 1 . + ( S E P F ( N U M , 3 ) / S E P F ( N U M , 2 ) ) ) * 0 . 0 2 * 100. 0 ERRTFE=T0TAL(NUM)*O.O124 PRINT1009,RUNNUM(NUM).NVOLTS(NUM),VELY(NUM),PPM(NUM),ERRTFE,ERRDLN 870 CONTINUE PRINT 1500 DO 875 NUM=1,15 ERRTMF=T0TAL(NUM)*56*0.0124 PRI NT 1008,RUNNUM(NUM),NVOLTS(NUM),VELY(NUM),PPM(NUM),ERRTMF,ERRAML(NUM) 875 CONTINUE PRINT 1500 DO 880 NUM=1.15 PRINT 1010,RUNNUM(NUM) 880 CONTINUE PRINT 1500 DO 885 NUM=1, 15 PRINT 1010,RUNNUM(NUM) 885 CONTINUE PRINT 1500 DO 890 NUM=1,15 PRINT 1010,RUNNUM(NUM) 890 CONTINUE PRINT 1500 DO 895 NUM=1, 15 PRINT 1010,RUNNUM(NUM) 895 CONTINUE PRINT 1500 DO 900 NUM=1 , 15 PRINT 1010,RUNNUM(NUM), 900 CONTINUE PRINT 1500 DO 905 NUM=1,15 PRINT1011,RUNNUM(NUM) , 905 CONTINUE NVOLTS(NUM),VELY(NUM),PPM(NUM),ERRCE(NUM,2) ,ERRCE(NUM,3) NVOLTS(NUM),VELY(NUM),PPM(NUM),SELNA(NUM,1,2) ,SELNA(NUM, 1 , 3 ) , S E L N A ( N U M , 2 , 2 ) , S E L N A ( N U M , 2 , 3 ) N V O L T S ( N U M ) . V E L Y ( N U M ) , P P M ( N U M ) . S E L F E ( N U M , 1 , 2 ) , S E L F E ( N U M , 1 , 3 ) , S E L F E ( N U M , 2 , 2 ) , S E L F E ( N U M , 2 , 3 ) NVOLTS(NUM) ,VELY(NUM) ,PPM(NUM) ,ESENA(NUM,1 ,2 ) ,ESENA(NUM,1 ,3 ) ,ESENA(NUM,2 ,2 ) ,ESENA(NUM,2 ,3 ) NVOLTS(NUM),VELY(NUM),PPM(NUM),ESEFE(NUM, 1 , 2 ) , E S E F E ( N U M , 1 , 3 ) , E S E F E ( N U M , 2 , 2 ) , E S E F E ( N U M , 2 , 3 ) NVOLTS(NUM) ,VELY(NUM) ,PPM(NUM) ,PH(NUM,1 .2 ) ,PH(NUM,1 .3 ) ,PH(NUM,3 ,2 ) ,PH(NUM,3 ,3 ) 1000 1001 1002 1003 1004 1005 100G 1007 1008 1009 1010 101 1 1500 FORMAT( FORMAT( FORMAT( FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' FORMAT(' STOP END ' , 2 X , 2 I 5 ' . 2 X . 2 I 5 , 2 X , 2 1 5 , ' , 2 X , 2 I 5 . ' . 2 X . 2 I 5 , , 2 X , 2 I 5 , . 2 X . 2 I 5 , . 2 X . 2 I 5 , , 2 X , 2 I 5 , , 2 X , 2 I 5 , . 2 X . 2 I 5 , . 2 X . 2 I 5 , 1') 2 F 7 . 2 , 3 X , 4 F 1 2 . 4 ) 2 F 7 . 2 , 2 ( F 8 . 2 ) ) 2 F 7 . 2 , 2 ( F 8 . 2 ) ) 2 F 7 . 2 . 2 ( F 8 . 2 , F 8 . 0 ) ) 2 F 7 . 2 , 2 ( F 8 - . 0 , F 8 . 0 ) ) 2 F 7 . 2 , 2 ( F 8 . 2 ) ) 2 F 7 . 2 , 2 ( F 8 . 1 ) ) 2F7 .2 ,4 (F8 . 1 ) ) 2 F 7 . 2 , 4 ( F 8 . 1 ) ) 2 F 7 . 2 , 2 ( F 8 . 3 ) , F 8 . 2 ) 2 F 7 . 2 , 4 ( F 8 . 3 ) ) 2 F 7 . 2 , 4 ( F 8 . 2 ) ) C PROGRAM 3 C PROGRAM TO COMPUTE THE POWER R E Q U I R E M E N T S PER C Y C L E I N THE U N S T E A D Y S T A T E P R O C E S S ( R U N S 30 TO 44) C BY I N T E G R A T I N G THE C U R R E N T C O N S U M P T I O N OVER A C Y C L E ( T H E S E R E S U L T S WERE ADDED TO THE DATA F I L E OF'PROGRAM 2) C DIMENSION CY(6).SA(4),P(4).T(4) INTEGER RUNNUM,VOLTS,PPM 6 FORMAT(4G7.2) 8 F0RMAT(2I1, 2A4 ) 10 F0RMAT(2G9.3) C 40 READ(5,6) RUNNUM,VOLTS,PPM , VELY IF(RUNNUM.EQ.99) STOP C PRINT600,RUNNUM,VOLT S,VELY,PPM PRINT605 50 READ(5,8) N,M,ITEM,WHEN IF(N.EQ.9) G0TO3OO I F(N.EQ. 1 ) RES = 92.85 IF(N.EQ.2) RES=95.88 IF(N.EQ.3) RES=95.84 DO 60 J=1,4 SA(J)=0.0 60 CONTINUE C READ(5, 10) TIME 1,CMV1 TSTART=TIME1 70 READ(5,10) TIME2,CMV2 IF ((TIME2-TSTART) .GT.45.0) GOT080 SA(1)=((TIME2-TIME1)*(CMV1+CMV2)/2.)+SA(1) £ TIME 1=TIME2 -p=> CMV1=CMV2 GOT070 C 80 SA(1) = ((45.0-TIME1)*(CMV1+CMV2)/2 . )+SA(1) C SA(2)=((TIME2-45.)*(CMV1+CMV2)/2.)+SA(2) FEEDMV=CMV2 90 TIME 1=TIME2 CMV1=CMV2 READ(5,10) TIME2,CMV2 IF(CMV2.LT.0.0) G0T01OO SA(2)=((TIME2-TIME1)*(CMV1+CMV2)/2.)+SA(2) G0T09O C 100 TS=TIME2 110 TIME1=TIME2 CMV1=CMV2 READ(5,10) TIME2,CMV2 IF((TIME2-TS).GT.45.) GOT0150 SA(3)=SA(3)-((TIME2-TIME1)*(CMV1+CMV2)/2.) G0T01 10 150 SA(3)=SA(3)-((45.+TS-TIME1)*(CMV1+CMV2)/2 . ) C SA(4)=SA(4)-((TIME2-45.-TS)*(CMV1+CMV2)/2.) 170 TIME 1=TIME2 CMV1=CMV2 READ(5 ,10 ) TIME2.CMV2 I F ( T I M E 2 . G T . 7 0 0 . ) GOT0200 SA(4 )=SA(4 ) - ( (T IME2-T IME1) * (CMV1+CMV2) /2 . ) GOTO 170 200 T(1)=45 .0 • T ( 2 ) = T S - 4 5 - T S T A R T T ( 3 ) = 4 5 . 0 T ( 4 ) = T I M E 1 - T S - 4 5 . 0 TOTTI=TIME1-TSTART+TOTTI C DO 250 K= 1 , 4 P(K) = ( S A ( K ) / R E S . ) * V O L T S / T ( K ) FEEDCR=FEEDMV/RES 250 CONTINUE PTOT = P( 1 ) + P (2 ) + P(3) + P(4) P R I N T 6 1 0 , ( P ( d ) , d = 1 , 4 ) , P T O T , I T E M , W H E N PRINT650,FEEDCR G0T05O 300 A T 0 T T I = T 0 T T I / 6 . 0 PRINTG20,ATOTTI T0TTI=O.O GOTO 40 C GOO FORMAT( ' ' , / / , 30X , ' RUN N U M B E R ' , 1 3 , / , 10X , 'STACK VOLTAGE' , 1 8 , 2 X , ' VOLTS ' ,3X , ' V E L O C I T Y ' ,F 16 .2 , ' C M / S E C , 3 X , ' I RON CONC. IN FEE 605 FORMAT( 'O ' , 14X, 'PAUSE + ' , 2 X , ' C I R C + ' , 2X , 'PAUSE - ' , 1 X , ' C I R C - ' , 3 X , ' T O T A L ' , 3 X , ' S T R E A M ' , 3 X , ' W H E N STAR = 2 HRS' , / , 15X, ' W A T T S ' , 4 ( 610 FORMAT( ' ' ; 1 1 X , 5 F 8 . 2 , 3 X , A 4 , 10X,A4) 620 FORMAT( 'O ' , 27X , 'TOTAL CYCLE T I M E ' , F 1 0 . 1 , 2 X , ' S E C O N D S ' ) 650 FORMAT( ' ' , 2 7 X , 'CURRENT AT FEED INPUT' ,F 15 . 4) END CO cn 

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