Interaction of Technical and Economic Demands in the Design of

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Interaction of Technical and Economic Demands in the Design of Large Scale Electrodialysis Demineralizers DONALD A. C O W A N Physics Department, University of Dallas, Dallas, Tex., and Texas Electric Service Co., Fort Worth, Tex.

In an electrodialysis demineralizing system, per formance is restricted by changes in the thin un stirred layer next to the membrane. When the layer is so thick that diffusion will not supply the current, polarization, charge concentration, and pH change result. Thickness of the layer and limiting current density are functions of fluid velocity through the cell. Fluid velocity controls current density, which in turn controls the ratio between membrane costs and electrical costs. This ratio sets the lowest cost under given circumstances. The lowest cost of demineralization may be ex pressed as a function of input and output concen tration, membrane cost and resistance, and stream thickness. Large scale experiments in municipalsized demineralizers show that optimum conditions can be very nearly achieved.

I η t h e d e s i g n o f a n e l e c t r o d i a l y s i s p l a n t , e c o n o m i c a n d t e c h n i c a l aspects a r e p o w e r f u l determinants. I n general, economic factors control the q u a n t i t y of membranes required, a n d technical considerations govern their arrangement. T h e f o l l o w i n g cost e q u a t i o n s h o w s t h e e c o n o m i c elements d i v i d e d i n t o t h r e e g r o u p s , each affected d i f f e r e n t l y b y c u r r e n t d e n s i t y .

dN/j

Ν

J

*iV

+EF

I (jr + V)dN JN

+ C

Γ V»

0

+ 0.101 c e n t / k i l o g a l l o n Ε I (jr + V)dN + C JN Ε — cents/kw.-hr. Ν = equivalents/liter r = ohm/sq. cm./cell pair C = cents/kilogallon

Ν where M = cents/sq. f o o t / y e a r ; = ma./sq. cm.

dN/j

224

In SALINE WATER CONVERSION; Advances in Chemistry; American Chemical Society: Washington, DC, 1960.

225

COWAN—LARGE SCALE ELECTRODIALYSIS DEMINERALIZERS

B e c a u s e s a l t is c a r r i e d b y c u r r e n t , less m e m b r a n e a r e a p e r v o l u m e o f w a t e r p r o d u c e d i s r e q u i r e d as c u r r e n t d e n s i t y i n c r e a s e s ; c o n s e q u e n t l y , i n t h e first g r o u p , a l l costs associated w i t h a r e a v a r y i n v e r s e l y w i t h c u r r e n t d e n s i t y . T h e second g r o u p — PR e l e c t r i c c o s t — i n c r e a s e s w i t h c u r r e n t d e n s i t y . T h e e l e c t r o d e a n d c o n c e n t r a t i o n p o t e n t i a l s , V, w h i c h also a p p e a r i n t h i s g r o u p , m a y b e h a n d l e d as a p e r t u r b a t i o n o f r e sistance a n d h e n c e , i n t h e i n t e r e s t o f s i m p l i c i t y , o m i t t e d f r o m f u r t h e r c o n s i d e r a t i o n . A t h i r d g r o u p i s unaffected b y c u r r e n t d e n s i t y .


I f t h e d e r i v a t i v e o f t h e cost e x p r e s s i o n i s set e q u a l t o zero a n d s o l v e d f o r c u r r e n t d e n s i t y , a v a l u e i s o b t a i n e d w h i c h w i l l desalt t h e w a t e r a t s m a l l e s t cost. T h i s s m a l l e s t cost, t h e r e q u i r e d " o p t i m u m " c u r r e n t , a n d t h e r e s u l t i n g m e m b r a n e a r e a are :

Ν C u r r e n t condition

Vr

j = 11.1 y/M/Er

dN + C ma./sq. cm.

M e m b r a n e area 2 X 0.408 Λ/Ε/Μ

rNo I VrdN JN

E l e c t r i c energy

ΓΝ I °-v/r diV k w . - h r . / k i l o g a l l o n JN

sq. f e e t / g a l l o n / d a y

0

1.12 WW/Ë

N o l i m i t a t i o n s are p l a c e d o n t h e a r r a n g e m e n t b y t h i s s m a l l e s t cost r e q u i r e m e n t . M a n y short parallel stacks o r a few long stacks satisfy t h e requirement; only t h e t o t a l a r e a i s specified.

01

.03

.05 Q| .2 INPUT NORMALITY

.3

.5

Figure I. Effect of steam thickness and membrane resistance on cost with optimum current density For cost, multiply by 2.24 cents/kilogallon Λ/MÊ and add C. For membrane area, multiply by 2 X 0.408 VË/M sq. ft./gal./ day. For electric energy, multiply by 1.12 Λ / Μ / Ε kw.-hr./kilogallon (M in cents/sq. ft./yr.; Ε in cents/kw.-hr.)


226

ADVANCES IN CHEMISTRY SERIES

T h e value of the parameters can be determined w i t h only a cursory consideration of d e s i g n . T h e a r e a resistance, r, i s c o m p o s e d o f t h e m e m b r a n e resistance a n d t h e s t r e a m resistance, i t s s q u a r e r o o t a p p e a r i n g i n t h e s m a l l e s t cost e x p r e s s i o n . T h e m e m b r a n e resistance q u o t e d b y m a n u f a c t u r e r s i s a s t a t i c v a l u e , m e a s u r e d w h i l e t h e m e m b r a n e still has its m i n o r i t y carriers a n d consequently is n o t y e t m a r k e d l y p e r m s e l e c t i v e . I n o p e r a t i o n t h e m e m b r a n e has a resistance n e a r l y t w i c e t h e v a l u e s q u o t e d . A v a l u e o f 2 5 o h m s p e r s q . c m . p e r p a i r , m e a s u r e d f o r some t h i n m e m b r a n e s , i s u s e d i n t h e f o l l o w i n g c a l c u l a t i o n s . B e c a u s e t h e resistance o f t h e c o n c e n t r a t e s t r e a m c a n be m a d e a r b i t r a r i l y s m a l l b y a n increase o f c o n c e n t r a t i o n , a v a l u e / o f d i l u t e s t r e a m resistance has b e e n u s e d f o r t h e fluid resistance i n t h e p r e p a r a t i o n of F i g u r e 1. T h e effect o f s t r e a m t h i c k n e s s i s c l e a r l y e v i d e n t i n t h i s figure. O n l y a m i n o r s a v i n g c o u l d b e effected w i t h t h i n n e r s p a c i n g — a b o u t 2-cent difference p e r k i l o g a l l o n f o r b r a c k i s h w a t e r b e t w e e n 100 a n d 5 0 m i l s i n t h i c k n e s s . F u r t h e r m o r e , t h i s s a v i n g i s n o t a v a i l a b l e unless o n e i s o p e r a t i n g n e a r o p t i m u m c u r r e n t . U n t i l 1 2 - i n s t e a d of 3 0 - c e n t w a t e r i s b e i n g c o n s i d e r e d , t h i s 2-cent m a r g i n does n o t w a r r a n t i n t e r e s t . T h e p r o b l e m o f g e t t i n g w a t e r i n a n d o u t o f t h e c e l l , a n d of k e e p i n g i t flowing, i s m u c h m o r e e a s i l y s o l v e d i n w i d e passages t h a n i n t h i n ones. A d m i t t e d l y , i n o r d e r t o a c c o m p l i s h t h e s a m e d i l u t i o n , a c e l l m u s t b e t w i c e as l o n g i f i t i s t w i c e as t h i c k ; b u t t w i c e as m u c h w a t e r i s p r o d u c e d w h e n t h e size i s d o u b l e d . T h e o n l y p e n a l t y i s t h a t s h o w n i n F i g u r e 1. F o r sea w a t e r , t h e p e n a l t y f o r 100 m i l s i n s t e a d o f 5 0 m i l s a m o u n t s t o a b o u t 7 cents; b u t of far more i m p o r t a n c e is the m e m b r a n e resistance, where greater s a v i n g c o u l d b e effected. U n t i l one considers 50-cent w a t e r f r o m t h e sea i n s t e a d o f t h a t c o s t i n g $1.00 o r m o r e , t h e t h i n passages are a n u n n e c e s s a r y c o m p l i c a t i o n .


5

Table I.

Cosh Proportional to Area Amortization, Interest, a n d Insurance

Dollars/Sq. Foot

20-year life Press Side strips Instrumentation Contingencies Engineering

4

0.50 0.40 0.03 0.19 0.21

3-year life Membranes Spacers Inlets a n d outlets Assembly

1.33

0.122

2.03

0.769

1.10 0.50 0.01 0.42

1-year life Electrodes L a b o r , a d m i n i s t r a t i o n , a n d overhead Interest on w o r k i n g c a p i t a l

0.030 0.007 0 001 = 0.929

M M

Table II.

= 92.9 cents/sq. f o o t / y e a r

Costs Proportional to Current Dollars/Kw.-Hr. 0.007 0.0014 0.0002 0.0001 0.0007

D e m i n e r a l i z i n g current A d d 1 0 % , efficiency, a n d 1 0 % , p u m p i n g Instrumentation Rectifiers L a b o r , a d m i n i s t r a t i o n , a n d overhead Ε

=

$0.0094

Ε = 0.94 c e n t / k w . - h r .



227


T h e p a r a m e t e r , M, r e p r e s e n t i n g t h e cost p e r s q u a r e foot o f m e m b r a n e a r e a p e r y e a r ( T a b l e I ) , covers m o s t of t h e cost i t e m s l i s t e d i n t h e s t a n d a r d cost p r o c e d u r e ( # ) . S o m e o f t h e i t e m s a r e p r o j e c t e d f u t u r e costs. F o r e x a m p l e , a m e m b r a n e cost -of 5 0 cents p e r s q u a r e foot i s u s e d . M e m b r a n e costs h a v e b e e n a b o u t $2.00 p e r s q u a r e f o o t , b u t t h e p r e s e n t cost i s l i k e l y t o b e a b o u t h a l f t h i s figure f o r a l a r g e o r d e r , a n d m a n u f a c t u r e r s g i v e a s s u r a n c e t h a t t h e 5 0 - c e n t figure i s i n s i g h t . T h e t o t a l cost p e r s q u a r e f o o t - y e a r i s 9 2 cents, 77 cents o f w h i c h i s f o r 3 - y e a r - l i f e i t e m s — m e m b r a n e s , s p a c e r s , i n l e t s a n d o u t l e t s , a n d a s s e m b l y cost. S h o u l d t h e s t a c k p r o v e t o h a v e a 1 0 - y e a r l i f e , the t o t a l cost w o u l d d r o p t o 4 1 cents p e r s q u a r e f o o t - y e a r , a n d one m i g h t a c c e p t t h i s figure as t h e o p t i m i s t i c l i m i t .

T h e e l e c t r i c cost ( T a b l e I I ) i s t h e cost a t t h e suggested 7 m i l s p e r k i l o w a t t - h o u r of the energy previously calculated, increased b y 1 0 % t o account for p u m p s , lighting, a n d r e c t i f i e r efficiency a n d b y a n o t h e r 1 0 % f o r c u r r e n t efficiency. T h e cost g r o u p u n a f f e c t e d b y c u r r e n t d e n s i t y ( T a b l e I I I ) i n c l u d e s o p e r a t i n g costs a n d certain portions of t h e a m o r t i z a t i o n . Wages have been d i s t r i b u t e d a m o n g t h e t h r e e categories. W i t h these figures, o n e c a n s p e c i f y t h e cost o f 5 0 0 - p . p . m . w a t e r p r o d u c e d b y a p l a n t o f o p t i m u m d e s i g n n o w — t h a t i s , t h e 9 2 cents p e r s q u a r e f o o t p e r y e a r c o s t — a n d t h e cost a t t h e o p t i m i s t i c l i m i t ( F i g u r e 2 ) . T w o a d d i t i o n a l e l e m e n t s of cost a p p l y p r i m a r i l y t o i n l a n d w a t e r s : t h e cost o f c l e a r , r a w w a t e r a n d t h e cost o f s a l t d i s p o s a l . S u r f a c e w a t e r m u s t , i n a l l p r o b a b i l i t y , b e



228

t r e a t e d b e f o r e d e s a l i n i z a t i o n . T h i s cost m a y b e a b o u t 4 cents p e r 1 0 0 0 g a l l o n s . S a l t d i s p o s a l p r o b l e m s h a v e n o t y e t b e e n s o l v e d ; i t seems l i k e l y t h a t t h i s r e q u i r e m e n t w i l l a d d 2 0 t o 5 0 % t o t h e cost o f w a t e r .

Table III.

Costs Proportional to Volume Only


Dollars/Kilogallon/Day Capacity

Dollars/Kilogallon

8.00 6.00 10.00 2.00 7.14 3.14 3.40

B u i l d i n g a n d site R a w water supply, 2 0 % b l o w d o w n P r o d u c t water storage P u m p s a n d pipes Construction Contingencies Engineering

$39.68

Taxes a n d insurance F u e l , chemicals, supplies L a b o r , a d m i n i s t r a t i o n , a n d overhead

0.010 0.003 0.003 0.008 $0,024

C = 2.4 c e n t s / k i l o g a l l o n

S u m m i n g u p t h e e c o n o m i c s , o n e c a n s a y t h a t b r a c k i s h w a t e r of 2100 p . p . m . c a n be m a d e i n t o g o o d w a t e r o f 500 p . p . m . a t a cost o f a b o u t 18 cents p e r 1000 g a l l o n s , i n c l u d i n g salt d i s p o s a l , w i t h a p o s s i b i l i t y o f p r o d u c i n g i t a t a b o u t 14 cents. Similarly, sea w a t e r c a n b e m a d e u s a b l e a t 7 2 cents p e r k i l o g a l l o n , w i t h a n o p t i m i s t i c l i m i t o f 4 8 cents. T h e p r o b l e m t h a t r e m a i n s , t h e n , i s h o w n e a r l y c a n these o p t i m u m c o n d i t i o n s be r e a l i z e d ?

Realization of Optimum Conditions A r r a n g e m e n t o f m e m b r a n e s i n t o l o n g o r s h o r t cells h a s n o b e a r i n g u p o n cost. T h e e c o n o m i c r e q u i r e m e n t o n d e s i g n i s o n l y t h a t i t ensure t h e o p t i m u m c u r r e n t density a t every point i n t h e cell. A technical requirement, however, imposes a f u r t h e r r e s t r i c t i o n u p o n d e s i g n : t h a t the c u r r e n t d e n s i t y b e m a i n t a i n e d i n t h e n e i g h borhood of the "diffusion l i m i t i n g c u r r e n t . " T h e p h e n o m e n o n of l i m i t i n g c u r r e n t i s m a r k e d b y a n o n o h m i c increase o f v o l t a g e as t h e c u r r e n t i s i n c r e a s e d . A r a t h e r s i m p l e s t u d y o f t h e r a t i o o f c u r r e n t t o v o l t a g e w i l l r e v e a l t h i s i n c r e a s e . T h e v o l t a g e i s t h e s u m o f t h e electrode v o l t a g e , V , w h a t e v e r p o l a r i z a t i o n v o l t a g e s a r e p r e s e n t , V , a n d t h e IR d r o p : e

p

V = V + V + IR e

p

T h e d a t a c a n b e s h a r p e n e d b y a change i n t h e v a r i a b l e s : YII

= R + (V + V )/I e

P

N o w t h e p l o t of V/I vs. I- h a s R f o r t h e i n t e r c e p t a n d V f o r t h e slope u n t i l p o l a r i z a t i o n sets i n as a s h a r p change o f slope. A p l o t o f e x p e r i m e n t a l d a t a s h o w s t h i s slope change a t a c r i t i c a l c u r r e n t d e n s i t y ( F i g u r e 3 ) . A t t h i s same c u r r e n t v a l u e , t h e p H begins t o c h a n g e . T h i s d i f f u s i o n l i m i t i n g c u r r e n t p o i n t m o v e s t o h i g h e r c u r r e n t d e n s i t y v a l u e s as s t r e a m v e l o c i t y a n d c o n c e n t r a t i o n i n c r e a s e . I n experimental w o r k a t the Texas E l e c t r i c l a b o r a t o r y this relationship has been e s t a b l i s h e d (1). T h e w o r k r e p o r t e d a p p l i e d t o fluids i n t u r b u l e n t flow a n d hence t o relatively h i g h velocities. Since t h a t time t h e studies have been extended t o lower velocities. T o support t h i n membranes, a pierced, corrugated m a t e r i a l was placed i n t h e s t r e a m s w i t h t h e c o r r u g a t i o n s i n t h e d i r e c t i o n o f flow, i n a m a n n e r t o cause t h e smallest pressure d r o p ; this obstruction i n d u c e d strong m i x i n g a n d s i m u l a t e d t u r b u 1

e


229



lence a t r a t h e r l o w R e y n o l d s n u m b e r s . O n t h e b a s i s o f these s t u d i e s , a n e m p i r i c a l expression has been constructed f o r t h e l i m i t i n g current density over t h e entire range of v e l o c i t i e s : j = 0.04 N/w U

112

(U + 1 . 9 )

1/3

w h e r e U i s t h e flow r a t e o f t h e d i l u t i n g s t r e a m i n g a l l o n s p e r m i n u t e p e r i n c h o f w i d t h , w is stream thickness i n inches, a n d Ν is n o r m a l i t y i n equivalents p e r liter. T h e e x p r e s s i o n i s b a s e d o n studies w i t h s o d i u m s u l f a t e ; o t h e r salts s h o u l d h a v e o n l y s l i g h t l y different l i m i t i n g c u r r e n t densities. A n u m b e r o f effects set i n a t c u r r e n t densities a b o v e t h i s l i m i t i n g v a l u e . T h e v o l t age increases a b o v e o h m i c v a l u e s ; t h e p H changes, d r o p p i n g i n t h e d i l u t e s t r e a m a n d


230



increasing i n t h e concentrate; a n d t h e membranes themselves become polarized, f o r m i n g electrets w h i c h p e r s i s t f o r h o u r s . I t seems l i k e l y t h a t s c a l i n g i s associated w i t h o n e of these effects; hence s c a l i n g p r o b l e m s c a n b e a v o i d e d i f t h e c e l l i s o p e r a t e d b e l o w limiting current. T h e Texas Electric experiments thus f a r indicate that trouble is a s s o c i a t e d w i t h c u r r e n t densities i n excess o f t h e l i m i t , a n d i t h a s b e e n a c c e p t e d as a dictate of n a t u r e t h a t membranes n o t be polarized a n d t h e p H of t h e water n o t be c h a n g e d — t h a t i s , t h a t l i m i t i n g c u r r e n t n o t b e exceeded. O n t h e o t h e r h a n d , t h e r e i s a r e a s o n t o o p e r a t e as n e a r t o t h e l i m i t i n g c u r r e n t as possible. C u r r e n t efficiency of d e m i n e r a l i z a t i o n i s l o w w h e n t h e c e l l i s o p e r a t i n g a t c u r r e n t densities m a r k e d l y b e l o w the l i m i t i n g current. H e r e , then, is t h e technical demand i n electrodialysis plant design: that conditions be fixed so t h a t o p e r a t i o n i s a l w a y s n e a r t h e l i m i t i n g c u r r e n t . T h i s d e m a n d w a s r e vealed i n experimental studies; i t is n o t merely a theoretical nicety, b u t a practical r e q u i r e m e n t . F o r t u n a t e l y , o n e a c h side o f t h e c r i t i c a l c o n d i t i o n s t h e r e i s some l e e w a y w h i c h a l l o w s p r a c t i c a l designs a t s m a l l p e n a l t i e s , b u t i t i s necessary t o c h a n g e t h e flow r a t e f r o m stage t o stage d o w n s t r e a m i n o r d e r t o m a i n t a i n l i m i t i n g c u r r e n t . T h e d e s i g n p r o b l e m resolves i t s e l f , t h u s , t o t h e s a t i s f y i n g o f t w o c o n d i t i o n s , o p t i m u m c u r r e n t a n d l i m i t i n g c u r r e n t . T h e c u r r e n t d e n s i t y c a n b e set a t t h e o p t i m u m v a l u e b y a d j u s t i n g t h e v o l t a g e f r o m stage t o stage. T h i s o p t i m u m current c a n be m a d e t h e l i m i t i n g c u r r e n t b y a n a d j u s t m e n t o f t h e flow r a t e t h r o u g h p a r a l l e l i n g of s t r e a m f r o m stage t o stage. T h u s t h e t w o c o n d i t i o n s c a n b e satisfied. F i g u r e 4 shows

40

5

80

Ί 120

Γ

160

240 200 FEET

.005

Figure 4. Voltage and flow rate per cell which establish optimum current and limiting current simultaneously, as functions of position along path length 0.1-Inch stream thickness and 25 ohm/sq. em. per pair resistance assumed



231


these r e q u i r e d c o n d i t i o n s . B e c a u s e t h e s t r e a m v e l o c i t y i s h i g h a t t h e o u t p u t e n d , i t m a y prove expedient t o accept a s m a l l penalty a n d drop below the o p t i m u m velocity i n t h e l a s t stage o r t w o . T h e r e s u l t i n g d e s i g n w i l l i n e v i t a b l y c a l l f o r a l a r g e p l a n t ; t h e single u n i t s h o u l d a p p r o a c h 2,000,000 g a l l o n s p e r d a y as n o w e n v i s i o n e d , a size q u i t e a c c e p t a b l e f o r c o m m u n i t y s u p p l i e s . A stage l e n g t h o f 4 0 feet a p p e a r s t o b e p r a c t i c a l f o r cells w i t h s t r e a m thicknesses o f 0.1 i n c h . T h e T e x a s E l e c t r i c S e r v i c e C o . i s n o w o p e r a t i n g a 4 0 - f o o t stage a t F o r t h W o r t h a s p a r t o f a d e v e l o p m e n t a l s t u d y . A b r a c k i s h w a t e r p l a n t m i g h t use t h r e e s u c h stages, w h e r e a s a sea w a t e r p l a n t w o u l d r e q u i r e n i n e i n series, w i t h m a n y p a r a l l e l s t a c k s a t t h e i n p u t so t h a t t h e e n t e r i n g w a t e r w o u l d flow s l o w l y .

Conclusions T o produce low-cost water, a plant m u s t meet t w o m a i n conditions: a moderate cost p e r s q u a r e foot o f a c t i v e a r e a a n d a r e l a t i v e f r e e d o m f r o m e x p e n s i v e s u p e r v i s i o n a n d f r e q u e n t o v e r h a u l . T h e s e c o n d i t i o n s c a n b e m e t b y l a r g e cells. I n f a c t , l a r g e scale, c o m m u n i t y - s i z e d e l e c t r o d i a l y s i s p l a n t s c a n a l l o w t h e f r e e d o m of d e s i g n needed t o m a k e d e s a l i n i z a t i o n e c o n o m i c a l l y feasible.

Literature Cited (1) C o w a n , D. Α., B r o w n , J. H., Ind. Eng. Chem. 51, 1445 (1959). (2) Office of Saline W a t e r , W a s h i n g t o n , D. C . ,PB161,375 (1955). RECEIVED for review July 20, 1960. A c c e p t e d A u g u s t 31, 1960.


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