Chapter 4
Steady-State Coupled Transport of HNO Through a Hollow-Fiber Supported Liquid Membrane 3
Richard D. Noble and Pier R. Danesi 1
2,3
National Bureau of Standards, Center for Chemical Engineering, Boulder, C O 80303 Argonne National Laboratory, Chemistry Division, Argonne, IL 60439
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2
Nitric acid removal from an aqueous stream was accomplished by continuously passing the fluid through a hollow fiber supported liquid membrane (SLM). The nitric acid was extracted through the membrane wall by coupled transport. The system was modeled as a series of (SLM)-continuous stirred tank reactor (CSTR) pairs. An approximate technique was used to predict the steady state nitric acid concentration in the system. The comparison with experimental data was very good.
Mass t r a n s f e r i n v o l v i n g c o n v e c t i v e t r a n s p o r t t h r o u g h a c h a n n e l and d i f f u s i v e t r a n s p o r t t h r o u g h t h e c h a n n e l w a l l s has been p r e v i o u s l y s t u d i e d . These s t u d i e s i n v o l v e d a s i n g l e pass o f f l u i d t h r o u g h t h e c h a n n e l . The channel w a l l p e r m e a b i l i t y was assumed c o n s t a n t s i n c e the t r a n s p o r t t h r o u g h t h e c h a n n e l w a l l was p u r e l y d i f f u s i v e and had no r e a c t i v e component. A major impetus f o r t h e s e s t u d i e s was t h e d e s i g n o f b l o o d d i a l y z e r s f o r use a s an a r t i f i c i a l k i d n e y . C o l t o n e t a l . (J_) developed a s o l u t i o n f o r l a m i n a r f l o w i n a f l a t duct w i t h permeable w a l l s . They f o c u s e d t h e i r a t t e n t i o n on t r a n s p o r t i n t h e e n t r a n c e r e g i o n . They a l s o found a s i m p l e , a p p r o x i mate t e c h n i q u e f o r e s t i m a t i n g t h e log-mean Sherwood number and mixi n g cup c o n c e n t r a t i o n . Cooney e t a l . (2,3) a l s o developed s o l u t i o n s f o r mass t r a n s f e r i n d i a l y z e r s w i t h l a m i n a r f l o w and semi-permeable w a l l s . They p r o v i d e d s o l u t i o n s f o r both p l a n a r and c y l i n d r i c a l c o n f i g u r a t i o n s . More r e c e n t l y , Noble W developed an a n a l y t i c a l s o l u t i o n f o r t w o - d i m e n s i o n a l t r a n s p o r t . The s o l u t i o n a l l o w s f o r f a c i l i t a t e d t r a n s p o r t t h r o u g h t h e c h a n n e l w a l l s . The s o l u t i o n does n o t account f o r l a m i n a r f l o w s i n c e i t assumes t h a t p l u g f l o w e x i s t s t h r o u g h t h e channel.
3
Current address: International Atomic Energy Agency, Seibersdorf Laboratories, P.O. Box 200, A-1400 Vienna, Austria This chapter is not subject to U.S. copyright. Published 1987, American Chemical Society
In Liquid Membranes; Noble, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
4.
NOBLE AND DANESI
Steady-State Coupled Transport of
HN0
3
57
Davis (5) p r o v i d e d e x a c t s o l u t i o n s f o r a number o f mass t r a n s f e r problems. The d e t a i l s o f t h e method used i n t h i s paper and some of those noted above can be found i n t h i s r e f e r e n c e . Experimental
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Reagents. The r e a g e n t s scribed (6-8).
used and t h e i r p u r i t y were p r e v i o u s l y de-
Membrane Systems and E x p e r i m e n t s . The t r a n s p o r t o f n i t r i c a c i d t h r o u g h a s u p p o r t e d l i q u i d membrane (SLM) c o n t a i n i n g t r i l a u r y l a m i n e (TLA) as c a r r i e r was s t u d i e d u s i n g a s i n g l e h o l l o w f i b e r module. T h i s c o n f i g u r a t i o n i s s i m i l a r t o one p r e v i o u s l y r e p o r t e d ( 9 ) . The h o l l o w f i b e r s u p p o r t was a p o l y p r o p y l e n e t u b e . The s u p p o r t d e t a i l s have been d e s c r i b e d elsewhere ( 9 ) . The SLM c o n s i s t e d o f a 0.1 M s o l u t i o n o f TLA i n n-dodecane absorbed i n t o t h e pores o f t h e h o l l o w f i b e r support. The t r a n s p o r t p r o p e r t i e s o f t h e system and t h e chemic a l r e a c t i o n s o f t h e n i t r i c a c i d c o - t r a n s p o r t have been d e s c r i b e d a t l e n g t h ( 6 , 7 ) . The f e e d and s t r i p s o l u t i o n s had t h e f o l l o w i n g compos i t i o n s i n i t i a l l y : [HN0 ] = 0.01 M, [NaN0 ] « 1.0 M ( f e e d s o l u t i o n ) and [NaOH] = 1.0 M ( s t r i p s o l u t i o n ) . The h o l l o w f i b e r module was o p e r a t e d i n a r e c y c l i n g mode a t a l i n e a r f l o w v e l o c i t y o f 18 cm/s, c o r r e s p o n d i n g t o a Reynolds number o f 3^6. The volume o f t h e aqueous f e e d s o l u t i o n which c i r c u l a t e d t h r o u g h t h e membrane lumen was 15 cm . The volume o f t h e H c o n c e n t r a t i o n d e t e c t o r c o n t a i n i n g t h e pH e l e c t r o d e was 10.7 cm . The i n t e r n a l volume o f t h e f i b e r lumen and the c o n n e c t i n g l i n e s was 0.46 cm and 3.8 c m , r e s p e c t i v e l y . The I.D. o f t h e h o l l o w f i b e r was 0.172 cm. The volume o f t h e aqueous s t r i p s o l u t i o n which c i r c u l a t e d on t h e s h e l l s i d e o f t h e SLM was 350 cm . 3
3
3
+
3
3
3
3
Methodology and R e s u l t s F i g u r e 1 i s a f l o w diagram o f t h e e x p e r i m e n t a l a p p a r a t u s . The a c i d i c s o l u t i o n i s c o n t i n u o u s l y r e c i r c u l a t e d t h r o u g h t h e system. This c o n t i n u o u s r e c i r c u l a t i o n can be approximated by t h e system shown i n F i g u r e 2. The system i s approximated as a s e r i e s o f s u p p o r t e d l i q u i d membrane (SLM) - c o n t i n u o u s s t i r r e d tank r e a c t o r (CSTR) p a i r s . The t i m e f o r a s i n g l e pass t h r o u g h t h e system ( t ^ ) i s v
t
V"t i s t h e t r a n s i t volume o f t h e system (membrane lumen volume p l u s c o n n e c t i n g t u b i n g ) and Q i s t h e v o l u m e t r i c f l o w r a t e t h r o u g h t h e s y s tem. The v a r i a b l e t ^ d e f i n e s t h e time f o r 1 c y c l e i n F i g u r e 2. The g o v e r n i n g d i f f e r e n t i a l e q u a t i o n which d e s c r i b e s t h e a c i d c o n c e n t r a t i o n i n t h e SLM i s
The boundary c o n d i t i o n s a r e
In Liquid Membranes; Noble, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
58
LIQUID MEMBRANES: THEORY AND APPLICATIONS
(3) C = C
g
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D
z-0
n
- 0
°
x-o k C
X
