Synthetic Membranes: Volume I - ACS Publications - American

2 Reverse Osmosis: A New Field of Applied Chemistry and Chemical Engineering S. SOURIRAJAN

Downloaded by PRINCETON UNIV on August 25, 2013 | http://pubs.acs.org Publication Date: May 21, 1981 | doi: 10.1021/bk-1981-0153.ch002

Division of Chemistry, National Research Council of Canada, Ottawa, Canada, K1A 0R9

F i r s t I wish to thank the American Chemical Society and the officers of the Cellulose Division for organizing this symposium. I deeply appreciate this honor, and I would l i k e to share this honor equally with every one of my past and present associates who have together contributed the most i n all work on reverse osmosis with which I am associated. In this lecture, I wish to c a l l attention to some of the fundamental aspects of reverse osmosis, and point out that what we are commemorating today (1) is truly the emergence of a new f i e l d of applied chemistry and chemical engineering, immensely relevant to the welfare of mankind. Reverse Osmosis and Reverse Osmosis Membranes "Reverse osmosis" i s the popular name of a general process f o r the s e p a r a t i o n of substances i n s o l u t i o n . The process c o n s i s t s i n l e t t i n g the s o l u t i o n flow under pressure through an appropriate porous membrane ( c a l l e d the "reverse osmosis membrane") and withdrawing the membrane permeated product g e n e r a l l y a t atmospheric pressure and surrounding temperature. The product i s enriched i n one or more c o n s t i t u e n t s of the mixture, l e a v i n g a s o l u t i o n of higher or lower c o n c e n t r a t i o n on the high pressure s i d e o f the membrane. No heating of the membrane i s necessary, and no phase change i n product recovery i s i n v o l v e d i n t h i s s e p a r a t i o n process. Reverse osmosis i s a p p l i c a b l e f o r the s e p a r a t i o n , concentration, and/or f r a c t i o n a t i o n o f i n o r g a n i c or organic substances i n aqueous o r nonaqueous s o l u t i o n s i n the l i q u i d or the gaseous phase, and hence i t opens a new and v e r s a t i l e f i e l d of separation technology i n chemical process engineering. Many reverse osmosis processes are a l s o p o p u l a r l y c a l l e d " u l t r a f i l t r a t i o n " , and many reverse osmosis membranes a r e a l s o p r a c t i c a l l y u s e f u l as u l t r a f i l t e r s .

0097-6156/81/0153-0011$13.00/0 © 1981 American Chemical Society

In Synthetic Membranes:; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12

SYNTHETIC

MEMBRANES:

DESALINATION


Object of This Lecture The emergence of reverse osmosis i s a major scLent'lf'Le event i n the f i e l d of a p p l i e d chemistry and chemical engineering; a l l a p p l i c a t i o n s and technology of reverse osmosis a r i s e from the science of reverse osmosis; a fundamental approach to the science of reverse osmosis, and the development of t h i s science i n a l l i t s aspects based on such approach are a b s o l u t e l y necessary f o r the e f f e c t i v e u t i l i z a t i o n of reverse osmosis f o r any a p p l i c a t i o n whatsoever. To present t h i s point of view i s the object of t h i s lecture. Reverse osmosis i s commonly recognized as a t e c h n o l o g i c a l accomplishment, and indeed, i t i s ; however, i t i s seldom recognized as an accomplishment i n a p p l i e d s c i e n c e . Such l a c k of r e c o g n i t i o n and i t s consequences r e t a r d the s c i e n t i f i c and i n d u s t r i a l progress of reverse osmosis; t h e r e f o r e , t h i s s i t u a t i o n must change. Fundamental Question on Reverse Osmosis From the p o i n t of view of the science of reverse osmosis, the fundamental question i s "what governs reverse osmosis separations?". This i s an i n t e n s e l y p r a c t i c a l question; because, to the extent t h i s question i s answered c o r r e c t l y , p r e c i s e l y , and completely, to that extent - and, to that extent only - the a p p l i c a t i o n s and technology of reverse osmosis can be made e f f e c t i v e . Further, t h i s o v e r r i d i n g question becomes s p e c i a l l y s i g n i f i c a n t when one considers the obvious p o t e n t i a l a p p l i c a t i o n s of reverse osmosis, and t h e i r immense s o c i a l relevance i n the context of today. Reverse osmosis touches many v i t a l areas of everyday l i f e such as water, a i r , food, medicine and energy. The most w e l l known a p p l i c a t i o n of reverse osmosis i s of course i n the broad area of water treatment i n c l u d i n g water d e s a l i n a t i o n , water p u r i f i c a t i o n , water p o l l u t i o n c o n t r o l , water reuse, and waste recovery. This a p p l i c a t i o n i s c u r r e n t l y under growing i n d u s t r i a l u t i l i z a t i o n i n many parts of the world. That reverse osmosis i s e q u a l l y a p p l i c a b l e f o r gas separations i s much l e s s well-known, but no l e s s s i g n i f i c a n t . A p p l i c a t i o n s such as oxygen enrichment i n a i r , helium recovery from n a t u r a l gas, a i r p o l l u t i o n c o n t r o l , s e p a r a t i o n and p u r i f i c a t i o n of i n d u s t r i a l gases, and treatment of gases a r i s i n g i n c o a l , petroleum and biomass conversion processes, though i n d u s t r i a l l y very important, are f a r l e s s developed today. From an economic stand p o i n t , p o t e n t i a l l y the most p r o f i t a b l e use of reverse osmosis i s i n i t s a p p l i c a t i o n s i n the area of food processing i n v o l v i n g separation, c o n c e n t r a t i o n and/or f r a c t i o n a t i o n of p r o t e i n s , food sugars and f l a v o r components, and treatment of milk, whey, f r u i t j u i c e s , i n s t a n t foods and beverages. S i m i l a r operations i n the pharmaceutical i n d u s t r y , and the a p p l i c a t i o n s of reverse osmosis membranes i n



2.

SOURIRAJAN

Reverse

Osmosis

13

medical and biomedical areas such as kidney machines, medical implantations and c o n t r o l l e d drug r e l e a s e devices i l l u s t r a t e the relevance of reverse osmosis and reverse osmosis membranes i n the area of medicine. The relevance of reverse osmosis to the f i e l d of energy i s o f f a r reaching s i g n i f i c a n c e . The use o f reverse osmosis membranes f o r d i r e c t production o f energy i s s t i l l a v i r g i n f i e l d , but the p o t e n t i a l i s easy to recognize. When a r i v e r o f r e l a t i v e l y pure water j o i n s a sea of s a l t water, we have i n e f f e c t a n a t u r a l l y o c c u r r i n g chemical w a t e r f a l l i n terms of chemical p o t e n t i a l gradient; using a reverse osmosis membrane a t the r i v e r water-sea water j u n c t i o n , the d i f f e r e n c e i n chemical p o t e n t i a l of water can be converted d i r e c t l y i n t o mechanical o r e l e c t r i c a l energy. I n d i r e c t l y , the relevance of reverse osmosis to the area of energy production and conservation i s even f a r g r e a t e r , by v i r t u e of the a p p l i c a b i l i t y of reverse osmosis f o r the s e p a r a t i o n , c o n c e n t r a t i o n , and f r a c t i o n a t i o n of c o n s t i t u e n t s i n nonaqueous s o l u t i o n s , and a l s o i n aqueous s o l u t i o n s c o n t a i n i n g high concentrations of organic s o l u t e s ; consequently, a l a r g e p a r t of d i s t i l l a t i o n operations i n petroleum r e f i n i n g , s y n t h e t i c f u e l , and fermentation i n d u s t r i e s can be replaced by reverse osmosis o p e r a t i o n s . Key

to I n d u s t r i a l Progress

of Reverse Osmosis

The terms "osmosis" and "semipermeable", which a r e p o p u l a r l y a s s o c i a t e d with reverse osmosis processes and reverse osmosis membranes r e s p e c t i v e l y , have a b s o l u t e l y no science-content i n them, and they c o n t r i b u t e d nothing to the emergence of reverse osmosis. E x p l a i n i n g reverse osmosis as the reverse of osmosis i s j u s t i n c o r r e c t . Under isothermal operating c o n d i t i o n s , the tendency f o r m a t e r i a l t r a n s p o r t i s always i n the d i r e c t i o n of lower chemical p o t e n t i a l i n both osmosis and reverse osmosis; hence reverse osmosis i s not the reverse of osmosis. Further, simply c a l l i n g a reverse osmosis membrane as a "semipermeable" membrane does not, and cannot, explain why the membrane i s semipermeable i n the f i r s t p l a c e . Therefore, i n s p i t e of enormous amount o f published l i t e r a t u r e on the s u b j e c t , a comprehensive answer to the fundamental question r a i s e d e a r l i e r has not y e t emerged. When t h i s i s r e a l i z e d , i t should be c l e a r that the key to i n d u s t r i a l progress o f reverse osmosis l i e s i n understanding f u l l y the fundamental b a s i s of reverse osmosis separations and a s s i d u o u s l y developing the o v e r a l l s c i e n c e of reverse osmosis (based on such understanding) s u i t a b l e f o r i t s e f f e c t i v e p r a c t i c a l u t i l i z a t i o n i n a l l i t s a p p l i c a t i o n s ; that of course i s not enough; i t i s indeed a b s o l u t e l y important that the necessary technology o f reverse osmosis i s developed f u l l y and brought i n t o the market p l a c e to serve the s o c i e t y . For such i n d u s t r i a l progress, the primary problem of reverse osmosis today i s not technology; i t i s understanding which i s the b a s i s of technology.


14

SYNTHETIC


Emergence of Reverse Osmosis Processes Membranes

MEMBRANES:

DESALINATION

and Reverse Osmosis

The o r i g i n of the development of the f i r s t p r a c t i c a l c e l l u l o s e acetate reverse osmosis membrane f o r sea water d e s a l i n a t i o n , announced i n 1960 (_1) , was the conception o f reverse osmosis i t s e l f i n 1956 based on an appreciation of the already well-known chemistry a t i n t e r f a c e s , of which the Gibbs adsorption equation (2) i s j u s t one expression. This equation i n d i c a t e s that surface f o r c e s can give r i s e to steep concentration gradients a t i n t e r f a c e s . Such concentration gradient a t an i n t e r f a c e i n e f f e c t c o n s t i t u t e s p o s i t i v e or negative adsorption, or preferential sorption, of one of the c o n s t i t u e n t s of the s o l u t i o n a t the i n t e r f a c e . The d e t a i l s of such p r e f e r e n t i a l s o r p t i o n must n e c e s s a r i l y depend on the nature of the i n t e r f a c e i n v o l v e d . This means that, f o r a given membrane-solution system, the d e t a i l s of p r e f e r e n t i a l s o r p t i o n at the membrane-solution i n t e r f a c e depend on the chemical nature of the surface of the membrane m a t e r i a l i n contact with the s o l u t i o n . Since surface f o r c e s are n a t u r a l and ever-present, p r e f e r e n t i a l s o r p t i o n a t a membrane-solution i n t e r f a c e i s a l s o n a t u r a l and i n e v i t a b l e , and the concentration p r o f i l e of the s o l u t i o n i n the i n t e r f a c i a l region i s d i f f e r e n t from that of the bulk s o l u t i o n that i s s u f f i c i e n t l y away from the membrane s u r f a c e . By l e t t i n g the p r e f e r e n t i a l l y sorbed i n t e r f a c i a l f l u i d under the i n f l u e n c e of surface f o r c e s , flow out under pressure through s u i t a b l y created pores ( i . e . , i n t e r s t i c e s or v o i d spaces) i n the membrane m a t e r i a l , a new physicochemical separation proces-s unfolds i t s e l f . That was how reverse osmosis was conceived i n 1956. In r e t r o s p e c t , l o o k i n g back i n t o the l i t e r a t u r e (3,.4,5), even that conception was not fundamentally new. What was indeed new, i s the f a c t that the above conception arose, independently, d i r e c t from a true a p p r e c i a t i o n of chemistry a t i n t e r f a c e s , and such a p p r e c i a t i o n n a t u r a l l y generated a program of dedicated work to t r a n s l a t e that conception i n t o p r a c t i c e to achieve a d e s i r e d o b j e c t i v e r e s u l t i n g i n the development i n 1960 of the now well-known asymmetric porous c e l l u l o s e acetate reverse osmosis membranes (6a,6b) f o r water d e s a l i n a t i o n a p p l i c a t i o n s . This approach to reverse osmosis i s designated i n the l i t e r a t u r e as the " p r e f e r e n t i a l s o r p t i o n - c a p i l l a r y flow mechanism" f o r reverse osmosis, s c h e m a t i c a l l y i l l u s t r a t e d i n Figure 1. The various s c i e n t i f i c consequences of t h i s mechanism are discussed i n the l i t e r a t u r e (6a,7,8). I t needs only to be pointed out here that the above mechanism was not proposed as an explanation of reverse osmosis a f t e r i t s accomplishment; on the other hand, reverse osmosis processes and reverse osmosis membranes emerged from that mechanism, and the above 1960-development i t s e l f was j u s t the f i r s t , and indeed a very b e f i t t i n g , p r a c t i c a l expression of the approach represented by that mechanism.


SOURIRAJAN

Reverse

Osmosis

HIGH

PRESSURE


1

H 0 Na+Cr H 0 HgO" Na CI" H 0 2

+

t 2°

Na CI"

H

+

2

H0

2

2

H0 H0

Na+CT Na

+

Na+Cf

2

Cr

NaCI" +

2

BULK SOLUTION PHASE

H0 2

Na CI"

H0 2

No CI~~

H0

No Cf

H0

Na Cl"

2

+

T

~Na cT"~ H7O~ +

+

H 0 Na^cr H 0

+

2

2

Na CI" +

Na CI" +

2

FILM SURFACE OF APPROPRIATE CHEMICAL NATURE

H0 H,0 H 0 H 0 H0 H2O H 0 HgO H 0 H 0 9

9

2

2

H,0 JH 0 H 0 H 0 H 0 'H 0 H 0 H 0 H 0 2

2

2

2

2

2

2

2

ATMOSPHERIC

Figure 1.

CRITICAL PORE

2

2

DIAMETER

2

H0

H0

9

9

H0 H0 H 0 H 0 H0 H0 H 0 H 0 2

2

2

2

2

2

2

2

PRESSURE

Schematic of preferential sorption-capillary flow mechanism for reverseosmosis separations of sodium chloride from aqueous solutions


16

SYNTHETIC

MEMBRANES:

DESALINATION


The Approach and The Science According to the above mechanism, reverse osmosis separation i s governed by two d i s t i n c t f a c t o r s , namely ( i ) an e q u i l i b r i u m e f f e c t which i s concerned with the d e t a i l s of p r e f e r e n t i a l s o r p t i o n i n the v i c i n i t y of the membrane s u r f a c e , and ( i i ) a k i n e t i c e f f e c t which i s concerned with the m o b i l i t i e s of s o l u t e and solvent through membrane pores. While the former ( e q u i l i b r i u m e f f e c t ) i s governed by r e p u l s i v e and a t t r a c t i v e p o t e n t i a l gradients i n the v i c i n i t y of the membrane s u r f a c e , the l a t t e r ( m o b i l i t y e f f e c t ) i s governed both by the p o t e n t i a l gradients ( e q u i l i b r i u m e f f e c t ) and the s t e r i c e f f e c t s a s s o c i a t e d with the s t r u c t u r e and s i z e of molecules r e l a t i v e to those of pores on the membrane s u r f a c e . Consequently, an appropriate chemical nature of the membrane surface i n contact with the s o l u t i o n and the existence of pores of appropriate s i z e and number on the area of the membrane a t the i n t e r f a c e together c o n s i t u t u t e the i n d i s p e n s a b l e twin-requirement f o r the p r a c t i c a l success of t h i s s e p a r a t i o n process. For reverse osmosis separation to take p l a c e , a t l e a s t one of the c o n s t i t u e n t s of the feed s o l u t i o n must be p r e f e r e n t i a l l y sorbed at the membrane-solution i n t e r f a c e ; t h i s means that a concentration gradient, a r i s i n g from the i n f l u e n c e of surface f o r c e s , must e x i s t i n the v i c i n i t y of the membrane surface i n contact with the feed s o l u t i o n . Further, to be p r a c t i c a l l y u s e f u l , the reverse osmosis membrane must have a microporous and heterogeneous surface l a y e r a t a l l l e v e l s of s o l u t e s e p a r a t i o n , i t s e n t i r e porous s t r u c t u r e must be asymmetric, and there should be no chemical r e a c t i o n between the c o n s t i t u e n t s of the feed s o l u t i o n and the m a t e r i a l of the membrane s u r f a c e . There i s no one p a r t i c u l a r l e v e l of s o l u t e separation or solvent f l u x uniquely s p e c i f i c to any given material of the membrane s u r f a c e . With an appropriate chemical nature f o r the m a t e r i a l of the membrane s u r f a c e , a wide range of s o l u t e separations i n reverse osmosis i s p o s s i b l e by simply changing the average pore s i z e on the membrane surface and the operating c o n d i t i o n s of the experiment. Aside from the process requirements i n d i c a t e d above, reverse osmosis i s fundamentally not limited to any p a r t i c u l a r solvent, s o l u t e , membrane m a t e r i a l , l e v e l of s o l u t e s e p a r a t i o n , l e v e l of s o l v e n t f l u x , or operating c o n d i t i o n s of the experiment. Consequently, the o v e r a l l science of reverse osmosis a r i s i n g from the above approach unfolds i t s e l f through proper i n t e g r a t i o n of the physicochemical parameters governing p r e f e r e n t i a l s o r p t i o n of solvent or s o l u t e a t membrane-solution i n t e r f a c e s , m a t e r i a l s science of reverse osmosis membranes, and the engineering science of reverse osmosis transport and process design. While there i s s t i l l a long way to go towards the f u l l development of the science of reverse osmosis i n a l l i t s aspects, considerable progress has already been made (8,9); that t h i s progress o f f e r s a f i r m b a s i s f o r a f u l l e r understanding of reverse osmosis i s the theme of the r e s t of t h i s paper.


2.

SOURIRAJAN

Reverse

Osmosis

17

For purposes of i l l u s t r a t i o n , the f o l l o w i n g d i s c u s s i o n , unless otherwise s p e c i f i e d , i s l i m i t e d to s i n g l e - s o l u t e aqueous feed s o l u t i o n s , c e l l u l o s e acetate membranes, and reverse osmosis systems f o r which osmotic pressure e f f e c t s are e s s e n t i a l l y negligible.


Surface Forces and Reverse Osmosis Following the foregoing approach, i f s u r f a c e f o r c e s govern d e t a i l s of p r e f e r e n t i a l s o r p t i o n a t membrane-solution i n t e r f a c e s and transport of s o l u t e and s o l v e n t through membrane pores i n reverse osmosis, then, under otherwise i d e n t i c a l experimental c o n d i t i o n s , membrane performance ( f r a c t i o n s o l u t e s e p a r a t i o n , f , and membrane permeated product r a t e f o r a given area of membrane s u r f a c e (PR)) must change, i f there i s any change i n one or more of the f o l l o w i n g v a r i a b l e s , namely, chemical nature of s o l u t e , that of s o l v e n t , that of the surface of the membrane m a t e r i a l , and the porous s t r u c t u r e of the membrane s u r f a c e . That such change i n membrane performance always takes p l a c e i s common experience i n a l l experimental work on reverse osmosis. Further, the e f f e c t s of s u r f a c e forces on the c o n c e n t r a t i o n gradient a t the membrane-solution i n t e r f a c e , and the t r a n s p o r t of s o l u t e and s o l v e n t through membrane pores during reverse osmosis must a l s o account f o r the d i f f e r e n t types of changes i n membrane performance experimentally observed as a r e s u l t of changes i n operating pressure or average pore s i z e on the membrane s u r f a c e , even when the chemical nature of s o l v e n t and that of the s u r f a c e of the membrane m a t e r i a l remain the same. For example, with c e l l u l o s e acetate membranes and aqueous feed s o l u t i o n systems, a t l e a s t four d i f f e r e n t types of changes i n membrane performance data have been observed experimentally (10,11,12) depending on the chemical nature of the s o l u t e and the operating pressure i n v o l v e d , as i l l u s t r a t e d i n Figures 2(a) to 2 ( d ) . Figure 2(a) shows experimental reverse osmosis data obtained with 0.5 molal NaCl-R^O feed s o l u t i o n s (10); i n t h i s system, the osmotic pressure e f f e c t s are s i g n i f i c a n t because of the f a i r l y high concentration of the feed s o l u t i o n . The r e s u l t s show that both s o l u t e s e p a r a t i o n and product r a t e i n c r e a s e with i n c r e a s e i n operating pressure, w h i l e , a t any given pressure, s o l u t e s e p a r a t i o n i n c r e a s e s and product r a t e decreases with decrease i n average pore s i z e on the membrane s u r f a c e . The reverse osmosis data given i n Figures 2(b), 2 ( c ) , and 2(d) are f o r very d i l u t e aqueous feed s o l u t i o n s f o r which osmotic pressures are practically negligible. F i g u r e 2(b) shows that f o r the pchlorophenol-water system (11), s o l u t e s e p a r a t i o n can be p o s i t i v e or negative depending on experimental c o n d i t i o n s ; s o l u t e s e p a r a t i o n can pass through a minimum with decrease i n average pore s i z e on membrane s u r f a c e ; f u r t h e r , a t a s u f f i c i e n t l y low operating pressure, s o l u t e s e p a r a t i o n i s p o s i t i v e , and i t


18

SYNTHETIC

MEMBRANES:

DESALINATION

SYSTEM: CELLULOSE ACETATE( E-398)NaCI - W A T E R , F E E D FLOW R A T E : 2 5 0 x I 0 " m / m i n c


6

I 0

1 2

I 4

I 6

» 8

i

o

10

OPERATING PRESSURE xlO" ,kPag 3

3

1 1

1

0

1

1

1

2

' 3

' 4

5

FEED MOLALITY

Figure 2a. Experimental data on the effect of operating pressure, average pore size on membrane surface, and feed concentration on solute separation and product rate for the reverse osmosis system cellulose acetate membrane-sodium chloridewater (\0)


Reverse

Osmosis


SOURIRAJAN

Figure 2b. Experimental data on the effect of operating pressure and average pore size on membrane surface on solute separation and (PR)/(PWP) ratio for the reverse osmosis system cellulose acetate membrane-p-chlorophenol-water


SYNTHETIC

MEMBRANES:

DESALINATION


20

Figure 2c. Experimental data on the effect of operating pressure and average pore size on membrane surface on solute separation and (PR)/(PWP) ratio for the reverse osmosis system cellulose acetate membrane-benzene-water (12)


Reverse

Osmosis


SOURIRAJAN

Figure 2d. Experimental data on the effect of operating pressure and average pore size on membrane surface on solute separation and (PR)/(PWP) ratio for the reverse osmosis system cellulose acetate membrane-cumene-water (\2)



22

SYNTHETIC

MEMBRANES:

DESALINATION

increases with decrease i n average pore s i z e on the membrane surface; a t a s u f f i c i e n t l y high operating pressure, s o l u t e s e p a r a t i o n i s negative, and i t decreases with decrease i n average pore s i z e on the membrane s u r f a c e ; and a t a l l operating pressures, the (PR)/(PWP) (product rate/pure water permeation r a t e ) r a t i o i s l e s s than u n i t y , and i t decreases with decrease i n average pore s i z e on the membrane s u r f a c e . Figures 2(c) and 2(d) show experimental reverse osmosis data f o r the systems benzene-water and cumene-water r e s p e c t i v e l y (12). For both these systems, s o l u t e s e p a r a t i o n i s p o s i t i v e , and (PR)/(PWP) r a t i o i s l e s s than u n i t y under the i n d i c a t e d experimental c o n d i t i o n s . Further, f o r the system benzene-water, s o l u t e s e p a r a t i o n tends to decrease with increase i n operating pressure, and i t tends to increase with decrease i n average pore s i z e on the membrane surface; f o r the system cumene-water, s o l u t e s e p a r a t i o n again tends to decrease with increase i n operating pressure, but i t passes through maxima and minima with decrease i n average pore s i z e on the membrane s u r f a c e . The above r e s u l t s are s i g n i f i c a n t . They show that reverse osmosis i s not l i m i t e d to 100%, near 100%, or any p a r t i c u l a r l e v e l of s o l u t e s e p a r a t i o n . Depending upon membrane-solutionoperating systems and other experimental c o n d i t i o n s , reverse osmosis can give r i s e to wide v a r i a t i o n s , and a l s o d i f f e r e n t types of v a r i a t i o n s , i n s o l u t e s e p a r a t i o n s . Reverse osmosis can give r i s e to high separations or low separations, p o s i t i v e separations, negative separations and a l l separations in-between, i n c r e a s e i n separation or decrease i n s e p a r a t i o n with i n c r e a s e i n operating pressure, i n c r e a s e i n separation or decrease i n separation with decrease i n average pore s i z e on the membrane s u r f a c e , and s o l u t e separations which pass through maxima and minima with decrease i n average pore s i z e on the membrane s u r f a c e . Reverse osmosis includes a l l such v a r i a t i o n s i n s o l u t e separations; i n p a r t i c u l a r , reverse osmosis i s not limited to one or any set of such v a r i a t i o n s . Consequently, any v a l i d mechanism of reverse osmosis must show that a l l such v a r i a t i o n s i n s o l u t e separations are indeed n a t u r a l . The p r e f e r e n t i a l s o r p t i o n - c a p i l l a r y flow mechanism of reverse osmosis does that. In the N a C l - t ^ O - c e l l u l o s e acetate membrane system, water i s p r e f e r e n t i a l l y sorbed at the membranes o l u t i o n i n t e r f a c e due to e l e c t r o s t a t i c r e p u l s i o n of ions i n the v i c i n i t y of m a t e r i a l s of low d i e l e c t r i c constant (13) and also due to the p o l a r character of the c e l l u l o s e acetate membrane m a t e r i a l . In the p-chlorophenol-water-cellulose acetate membrane system, s o l u t e i s p r e f e r e n t i a l l y sorbed at the i n t e r f a c e due to higher a c i d i t y (proton donating a b i l i t y ) of p-chlorophenol compared to that of water and the net proton acceptor (basic) character of the p o l a r p a r t of c e l l u l o s e acetate membrane m a t e r i a l . In the benzene-water-cellulose acetate membrane, and cumene-water-cellulose acetate membrane systems, again s o l u t e i s p r e f e r e n t i a l l y sorbed at the i n t e r f a c e due to nonpolar



2.

SOURIRAJAN

Reverse

23

Osmosis

(hydrophobic) character of s o l u t e s and that of the membrane m a t e r i a l ; f u r t h e r , cumene i s r e l a t i v e l y more nonpolar than benzene. How these physicochemical c h a r a c t e r i s t i c s n a t u r a l l y give r i s e to the types of v a r i a t i o n s i n reverse osmosis separations shown i n Figures 2(a) to 2(d) i s discussed i n d e t a i l i n the l i t e r a t u r e (11-18). On the b a s i s of the p r e f e r e n t i a l s o r p t i o n - c a p i l l a r y flow mechanism, the types of v a r i a t i o n s i n reverse osmosis separations shown i n Figures 2(a) to 2(d) should a l s o be predictable from an a n a l y s i s of mass transport through c a p i l l a r y pores under the i n f l u e n c e of surface forces expressed e x p l i c i t l y ; that t h i s i s indeed so has been demonstrated r e c e n t l y (19). In t h i s a n a l y s i s (19), the r e l a t i v e solute-membrane m a t e r i a l i n t e r a c t i o n s a t the membrane-solution i n t e r f a c e a r e expressed i n terms of e l e c t r o s t a t i c or Lennard-Jones-type surface p o t e n t i a l f u n c t i o n s ($) and the transport of s o l u t e and s o l v e n t through the membrane under the i n f l u e n c e of such f o r c e s i s expressed through appropriate mass t r a n s p o r t equations a p p l i c a b l e f o r an i n d i v i d u a l c i r c u l a r c y l i n d r i c a l pore. The p o t e n t i a l f u n c t i o n representing e l e c t r o s t a t i c r e p u l s i o n of ions a t the i n t e r f a c e due to r e l a t i v e l y l o n g range coulombic f o r c e s i s expressed as A (1)

d

and the Lennard-Jones-type p o t e n t i a l f u n c t i o n f o r nonionic s o l u t e s (representing the sum of the r e l a t i v e l y short-range van der Waals a t t r a c t i v e f o r c e and the s t i l l shorter-range r e p u l s i v e f o r c e due to overlap of e l e c t r o n clouds a t the i n t e r f a c e r e s p e c t i v e l y ) i s expressed as

+

10 or

d» when d = D

(2)

$ = when d > D

and, the p o t e n t i a l f u n c t i o n ¥ r e p r e s e n t i n g f r i c t i o n f o r c e a g a i n s t the movement of s o l u t e (under the i n f l u e n c e of the above s u r f a c e f o r c e s ) through the membrane pore i s expressed as

*

=

d

(3)

where A, B, C, and E a r e the r e s p e c t i v e f o r c e constants c h a r a c t e r i s t i c of the i n t e r f a c e , d i s the distance between the membrane surface or pore w a l l and the s o l u t e molecule, and D i s



24

SYNTHETIC

MEMBRANES:

DESALINATION

the value of d a t which $ becomes very l a r g e . A s s i g n i n g appropriate values f o r the above q u a n t i t i t i e s , one can o b t a i n the above p o t e n t i a l f u n c t i o n s f o r the membrane m a t e r i a l - s o l u t i o n systems discussed above, as shown i n Figures 3(a) and 3(d). Using these p o t e n t i a l f u n c t i o n s , one can then c a l c u l a t e (19) s o l u t e s e p a r a t i o n , product r a t e , and (PR)/(PWP) r a t i o obtainable f o r the reverse osmosis systems corresponding to data given i n Figures 2(a) to 2(d). The r e s u l t s of such c a l c u l a t i o n s are given i n Figures 4(a) to 4(d) where the i n d i c a t e d values of pore radius R represent only r e l a t i v e v a l u e s . Figure 4(a) shows that f o r 0.2 molal NaCl-H20 feed s o l u t i o n s , both s o l u t e s e p a r a t i o n and product r a t e i n c r e a s e with i n c r e a s e i n operating pressure, and at any given operating pressure, s o l u t e separation increases and product r a t e decreases with decrease i n R. Figure 4(b) shows that f o r d i l u t e p - c h l o r o phenol-water feed s o l u t i o n s , s o l u t e separation can be p o s i t i v e , or negative, or zero depending on experimental c o n d i t i o n s , s o l u t e separation decreases with increase i n operating pressure and passes through a minimum with decrease i n R, and (PR)/(PWP) r a t i o i s l e s s than u n i t y . Figures 4(c) and 4(d) show that f o r d i l u t e benzene-water and cumene-water feed s o l u t i o n s , s o l u t e s e p a r a t i o n i s p o s i t i v e , and (PR)/(PWP) r a t i o i s l e s s than u n i t y ; f u r t h e r , f o r the benzene-water system, s o l u t e separation tends to decrease with increase i n operating pressure, and i t tends to i n c r e a s e with decrease i n R; f o r the cumene-water system, s o l u t e s e p a r a t i o n again tends to decrease with i n c r e a s e i n operating pressure, and i t passes through maxima and minima with p r o g r e s s i v e decrease i n R. Thus the r e s u l t s presented i n Figures 4(a) to 4(d) show that an a n a l y s i s of reverse osmosis transport through c a p i l l a r y pores under the i n f l u e n c e of surface f o r c e s c o r r e c t l y p r e d i c t s a l l the d i f f e r e n t types of v a r i a t i o n s i n reverse osmosis separations obtained experimentally as shown i n Figures 2(a) and 2(d). Such p r e d i c t a b i l i t y o f f e r s d e c i s i v e c o n f i r m a t i o n that an a p p r e c i a t i o n of s u r f a c e f o r c e s a t membrane-solution i n t e r f a c e and the e f f e c t s of such surface f o r c e s on s o l u t e and solvent t r a n s p o r t through c a p i l l a r y pores i n the membrane, o f f e r s a v a l i d means of understanding reverse osmosis s e p a r a t i o n s . P r e f e r e n t i a l Sorption at Membrane-Solution I n t e r f a c e s and Separation i n Reverse Osmosis

Solute

The solute-solvent-polymer (membrane m a t e r i a l ) i n t e r a c t i o n s , s i m i l a r to those governing the e f f e c t of s t r u c t u r e on r e a c t i v i t y of molecules (20,21,22,23,24) a r i s e i n general from p o l a r - , s t e r i c - , nonpolar-, and/or i o n i c - c h a r a c t e r of each one of the three components i n the reverse osmosis system. The o v e r a l l r e s u l t of such i n t e r a c t i o n s determines whether s o l v e n t , or s o l u t e , or n e i t h e r i s p r e f e r e n t i a l l y sorbed at the membranesolution interface. While d e t a i l s of p r e f e r e n t i a l s o r p t i o n represent mainly the


SOURIRAJAN


10

Reverse

N a C I - WATER

Osmosis

BENZENE-WATER

p-CLOROPHENOLWATER

_L

o

o

(a)

L

c)

/ ( b )

30 3 B = l3.5xlO *V D= I.5xl0"'°m E=l0.5xl0~ m

B^.SxIO-SOm D=0.6xl0- m E = 0.05xl0" m

_ ;

3

, 0

, 0

, 0

d= D I S T A N C E B E T W E E N P O R E W A L L A N D SOLUTE

5

o d,A

10

_ J

5

•

o

10

l

d,A CELLULOSE

] ;=29l6xlO m D= 7 x l 0 m E=49xl0-'°m _ 3 0

MOLECULE

D = VALUE O F d WHEN S

•

5

o

10

I

d, A ACETATE

_ l 0

BECOMES VERY L A R G E

(E-398)

5

10

o

15

d , A MATERIAL

Figure 3. Potential functions for surface (®) and friction (V) forces as a function of the distance d from cellulose acetate membrane material for different solution systems (\9)


3

26

SYNTHETIC

MEMBRANES:

DESALINATION


200

O

70

I

1 2000

1 4000

I

6000

I

8000

I

10000

I

OPERATING PRESSURE, kPag Figure 4a. Effect of operating pressure and average pore size on membrane surface on solute separation and product rate for the reverse osmosis system cellulose acetate membrane-sodium chloride-water calculated on the basis of data on potential functions given in Figure 3


SOURIRAJAN

Reverse

Osmosis

MEMBRANE MATERIAL:CELLULOSE

ACETATE

(E-398)

690-l0 342kPag ~+

0.8


Q.

t

0.4

p - C H L O R O P H E N O L - WATER

OPERATING

PRESSURE

(psig)

kPag 690

O QC

-io

-15

FEED

C O N C E N T R A T I O N : I.Og-mol/m k =200 x I0" m/s 6

-20 -

_L 10

PORE

20

RADIUS,

30

R, A

Figure 4b. Effect of operating pressure and average pore size on membrane surface on solute separation and (PR)/(PWP) ratio for the reverse osmosis system cellulose acetate membrane-p-chlorophenol-water calculated on the basis of data on potential functions given in Figure 3


28

SYNTHETIC

MEMBRANE

MATERIAL: CELLULOSE

MEMBRANES:

ACETATE

DESALINATION

(E-398)

.00


_

!724-l0 342kPag

0.99|-

%

0.98

~

0.97

BENZENE - WATER

QC 0 . 9 6 -

Q.

0.95

J

L

70 OPERATING

PRESSURE

(psig) 60 (250) H-

d ( a r o m a t i c polyamides) > d ( c e l l u l o s e ) ; and by progressive h y d r o l y s i s of a c e l l u l o s e p


39

Osmosis

n

n

S

s p

sp

-

S

s p

a v

a v

av

a v


40

SYNTHETIC

CA:CELLULOSE ACETATE C P : CELLULOSE PROPIONATE PA : AROMATIC POLYAMIDE 0

2

PAH CA

^

^

^

K

1

C P J Z V ^

DCTD

PAH 0

-2.0

(a) i

i


8 &

o ,J h

Figure 9.

i

10

12 \

/

2

i

-

i

14

DESALINATION

CTA : CELLULOSE TRIACETATE CTD: CELLULOSE TRIDECANOATE PAH : AROMATIC POLYAMIDE-HYDRAZIDE

-

-1.0

MEMBRANES:

~£

^ ^ C T D

A

cT

(b) 1 16

16

0

T A

i * d ,

-3/2

cm

d

1 18 J

.

1 20

J/2 - 3/2 cm

Correlations of (a) a and h and (b) a„ and B for different polymeric membrane materials (53) p

d

CVJ

CTA: CELLULOSE PA:

TRIACETATE

A R O M A T I C OOPOLYAMI D E

PAH: AROMATIC COPOLYAMIDEHYDRAZIDE

CE:

_J

I

I

20

30

40

Ssp, Figure JO.

CELLULOSE

J

, / 2

cm-

I 50

3 / 2

Correlations of solubility parameter with (a) S /Sdh ratio and (b) ^-parameter for different polymeric membrane materials (56) h

P


2.

SOURIRAJAN

Reverse

Osmosis

41

acetate polymer, i t s 6 value can be increased and i t s Bparameter can be decreased approaching the corresponding values of pure c e l l u l o s e , which i n d i c a t e s the p o s s i b i l i t y of o b t a i n i n g a c e l l u l o s i c polymer whose 6 and B values are i d e n t i c a l to those o f an aromatic polyamide polymer, by c o n t r o l l e d h y d r o l y s i s of a c e l l u l o s e e s t e r polymer. These conclusions have important consequences i n reverse osmosis (some of which have already been v e r i f i e d (54,56), and they c o n t r i b u t e to a f u l l e r understanding of i n t e r f a c i a l p r o p e r t i e s of membrane m a t e r i a l s and s o l u t e separations i n reverse osmosis. s p


s p

M a t e r i a l s Science o f Reverse Osmosis Membranes - F a c t o r s Governing Porous S t r u c t u r e of Membranes Having chosen an a p p r o p r i a t e membrane m a t e r i a l , one s t i l l has to create a u s e f u l membrane out of that m a t e r i a l s u i t a b l e f o r the s p e c i f i c a p p l i c a t i o n on hand. A d i r e c t i o n f o r accomplishing the l a t t e r o b j e c t i v e i s shown by the p r e f e r e n t i a l s o r p t i o n c a p i l l a r y flow mechanism f o r reverse osmosis. According to t h i s mechanism, as already pointed out, the e n t i r e membrane must be porous; only the l a y e r of the membrane s u r f a c e which comes i n t o contact with the feed s o l u t i o n needs to have pores of a p p r o p r i a t e s i z e and number s u i t e d f o r the s p e c i f i c a p p l i c a t i o n ; the m a t e r i a l of the membrane underneath the surface l a y e r can be and, f o r p r a c t i c a l advantage, must be g r o s s l y porous with b i g i n t e r connected pores. This means that the surface l a y e r of a u s e f u l membrane must be as t h i n as p o s s i b l e , and the e n t i r e porous s t r u c t u r e of the membrane must be asymmetric. This d i r e c t i o n has been the b a s i s of numerous s u c c e s s f u l s t u d i e s on the development of f l a t and tubular c e l l u l o s e acetate membranes f o r p r a c t i c a l reverse osmosis a p p l i c a t i o n s (6b,10,57,63-85). These s t u d i e s i n v o l v e an a p p r e c i a t i o n of s u r f a c e chemistry, c o l l o i d chemistry, and p h y s i c a l chemistry of polymer s o l u t i o n s as they r e l a t e to f i l m c a s t i n g s o l u t i o n s , f i l m c a s t i n g c o n d i t i o n s , f i l m c a s t i n g techniques, and the mechanism of pore formation and development of asymmetric porous s t r u c t u r e i n r e s u l t i n g membranes. In view of the d i f f e r e n t requirements of reverse osmosis membranes f o r d i f f e r e n t a p p l i c a t i o n s and the l a r g e number of v a r i a b l e s i n v o l v e d i n the f i l m making process, such s t u d i e s may be expected to continue f o r e v e r , b u i l d i n g s t e a d i l y the foundations of a new and ever-expanding area of a p p l i e d chemistry and reverse osmosis membrane technology. Even though t h i s area of m a t e r i a l s science of reverse osmosis membranes i s s t i l l i n i t s e a r l y stages of development, the work r e f e r r e d above has a l r e a d y provided c e r t a i n broad g u i d e l i n e s i n terms of cause and e f f e c t r e l a t i o n s h i p s governing the porous s t r u c t u r e of such membranes. The f i l m c a s t i n g s o l u t i o n i s u s u a l l y a mixture of the polymer (e.g., c e l l u l o s e a c e t a t e ) , a s o l v e n t (e.g., acetone), and an e s s e n t i a l l y nonsolvent s w e l l i n g agent (e.g., aqueous s o l u t i o n of magnesium p e r c h l o r a t e , or formamide). The f i l m making



42

SYNTHETIC

MEMBRANES:

DESALINATION

procedure involves g e n e r a l l y the f o l l o w i n g steps: ( i ) casting the polymer s o l u t i o n as a t h i n f i l m on a surface; ( i i ) evaporation (or removal by other means) of solvent from the surface; ( i i i ) immersion of the f i l m i n an appropriate g e l a t i o n medium such as c o l d water or an aqueous ethanol s o l u t i o n ; and f i n a l l y ( i v ) thermal s h r i n k i n g , p r e s s u r i z a t i o n and/or other membrane p r e t r e a t ment techniques. Each one of the above steps a f f e c t s the ultimate porous s t r u c t u r e of the e n t i r e membrane, and hence i t s subsequent performance i n reverse osmosis. Further the solute separation versus shrinkage temperature c o r r e l a t i o n , c a l l e d the shrinkage temperature p r o f i l e , expresses pore s i z e d i s t r i b u t i o n on the membrane surface, and hence i t i s an important guide f o r q u a l i t y c o n t r o l i n membrane research and development. The s t a t e or the s t r u c t u r e of the c a s t i n g s o l u t i o n and the rate of solvent evaporation (or solvent removal) from the surface during f i l m formation together c o n s t i t u t e an important i n t e r connected v a r i a b l e governing the ultimate porous s t r u c t u r e and hence the performance of the r e s u l t i n g membrane i n reverse osmosis. The s t r u c t u r e of the c a s t i n g s o l u t i o n ( i . e . , the s t a t e of supermolecular polymer aggregation i n the c a s t i n g s o l u t i o n ) i s a f u n c t i o n of i t s composition and temperature; no p r e c i s e q u a n t i t a t i v e parameter has y e t been developed to s p e c i f y that s t r u c t u r e . Solvent evaporation rate during f i l m formation i s a f u n c t i o n of s o l u t i o n temperature, temperature of the c a s t i n g atmosphere and the ambient nature of the c a s t i n g atmosphere. With reference to a given c a s t i n g s o l u t i o n , i t s temperature and that of the c a s t i n g atmosphere (together with the ambient nature of the c a s t i n g atmosphere) are two separate v a r i a b l e s i n the s p e c i f i c a t i o n of f i l m c a s t i n g c o n d i t i o n s ; by appropriate choice of these two v a r i a b l e s alone, the p r o d u c t i v i t y of r e s u l t i n g membranes can be changed and improved as i l l u s t r a t e d i n Figure 11(a). The s i z e of the supermolecular polymer aggregate i n the c a s t i n g s o l u t i o n can be decreased by i n c r e a s i n g solvent/polymer r a t i o , decreasing nonsolvent/solvent r a t i o , and/or i n c r e a s i n g the temperature of the c a s t i n g s o l u t i o n (Figures 11(a) and 11(b)). Smaller s i z e of polymer aggregates tends to create a l a r g e r number of smaller s i z e nonsolvent d r o p l e t s i n the i n t e r d i s p e r s e d phase during f i l m formation, r e s u l t i n g u l t i m a t e l y i n l a r g e r number of smaller s i z e pores on the membrane s u r f a c e . Since higher droplet density favors droplet-coalescence, there i s an optimum s i z e of polymer aggregate i n the c a s t i n g s o l u t i o n f o r maximum p r o d u c t i v i t y of r e s u l t i n g membranes. High solvent evaporation r a t e favors both d r o p l e t formation and d r o p l e t coalescence. The solvent evaporation r a t e should be high enough to generate the l a r g e s t number of i n t e r d i s p e r s e d d r o p l e t s , and low enough to prevent excessive d r o p l e t coalescence during f i l m formation. For each c a s t i n g s o l u t i o n s t r u c t u r e , there e x i s t s an optimum solvent evaporation rate f o r maximum membrane p r o d u c t i v i t y . A given s o l u t i o n structure-evaporation rate


SOURIRAJAN

Reverse


CELLULOSE

ACETATE

,

SOLUTE SEPARATION —

MEMBRANES 0 %

80%

UJ90
' V AA3 3 / X

=

(11)

A 3

X

A2~ A3\ - — A1" A3/

(13)

X

A l l symbols are defined a t the end of the paper. Equation 10 defines the pure water p e r m e a b i l i t y constant A f o r the membrane which i s a measure of i t s o v e r a l l p o r o s i t y ; eq 12 d e f i n e s the s o l u t e transport parameter Dpj^/K6 f o r the membrane, which i s a l s o a measure o f the average pore s i z e on the membrane surface on a r e l a t i v e s c a l e . The important feature of the above s e t of equations i s that n e i t h e r any one equation i n the s e t of equations 10 to 13, nor any part of t h i s s e t of equations i s adequate r e p r e s e n t a t i o n of reverse osmosis t r a n s p o r t ; the l a t t e r i s governed simultaneously by the entire set of eq 10 to 13. Further, under steady s t a t e operating c o n d i t i o n s , a s i n g l e s e t of experimental data on (PWP), (PR), and f enables one to c a l c u l a t e the q u a n t i t i e s A, X 2> A M / ^ * ^ P ( p o s i t i o n or time) i n the reverse osmosis system using eq 10 to 13. For the purpose of t h i s review, i t i s assumed that f o r a given membrane a t any s p e c i f i e d operating temperature and pressure, the value of Dp^/K6 f o r a given s o l u t e i s independent of X 2> t h i s assumption i s not, and need not be, v a l i d i n a l l cases, but i t i s v a l i d with respect to c e l l u l o s e acetate membranes and many organic and i n o r g a n i c s o l u t e s , i n c l u d i n g sodium c h l o r i d e , i n aqueous s o l u t i o n s . In any case, the above assumption does not r e s t r i c t the p r a c t i c a l scope of t h i s a n a l y s i s (113). D

K (

a n c

a

t

a

n

y

o i n t

A

A

Membrane S p e c i f i c a t i o n s . At a s p e c i f i e d operating temperature and pressure, a c e l l u l o s e acetate membrane i s completely s p e c i f i e d i n terms of i t s pure water p e r m e a b i l i t y constant A and s o l u t e transport parameter D^/K6 f o r a convenient reference s o l u t e such as sodium c h l o r i d e . A single s e t of experimental data on (PWP), (PR), and f a t known operating c o n d i t i o n s i s enough to o b t a i n data on the s p e c i f y i n g parameters A and (DAM^^NaC! Y gi temperature and pressure. a

t

an

v

e

n

P r e d i c t a b i l i t y of Membrane Performance. and 13,

Combining eq 11, 12


46

SYNTHETIC

( c2XA2' " 3 A3

A[P-7r(X )+7T(X )] A2

( c

X

c

X

K 6

/ V A3 X

)

2 A2" 3 A3

A

9

A3

\

MEMBRANES:

/ X

C

X

DESALINATION

(14)

)

X

/ A2" A3\

n

(15)

(D /K6)

*A3

AM

For a membrane s p e c i f i e d i n terms of A and D /K6, eq 14 and 15, together with eq 11, enable one to p r e d i c t membrane performance (X 3 and Ng, and hence f and (PR)) f o r any feed concentration X i and any chosen feed flow c o n d i t i o n as s p e c i f i e d i n terms of k. Several t h e o r e t i c a l and experimental methods of s p e c i f y i n g k f o r d i f f e r e n t s o l u t e s under d i f f e r e n t c o n d i t i o n s are a v a i l a b l e i n the l i t e r a t u r e (6c,6d,18b,90,100). The q u a n t i t i e s f and (PR) are r e l a t e d to X and Ng through the f o l l o w i n g equations: AM


A

A

A 3

m

l

—

m

/

3

f =

X

A \ A-XAA

V -^/ N

B

x M

"-A3

3

1

V A1 X

X

/

(16)

A1

x s x 3600

B

(17)

(PR) 1

/l+

(f

0

0

0

\

m (l-f)M j A

1

Using eq 11, 14, 15, 16 and 17, one can f o r example c a l c u l a t e the e f f e c t of feed concentration and feed flow r a t e on f and (PR) f o r NaCl-H20 feed s o l u t i o n s obtainable with a c e l l u l o s e acetate membrane s p e c i f i e d i n terms of A and (DAM/ ^NaCl • K(

R e l a t i o n s h i p s Between ( D

A M

/K6)

and

N a C 1

(D^/Kfi) f o r Other

S o l u t e s . For completely i o n i z e d i n o r g a n i c and simple ( i . e . , where s t e r i c and nonpolar e f f e c t s are n e g l i g i b l e ) organic solutes,

D

< AM

/K6

a

>solute

e x

P

n

jc

(- |f)

+ c

a

t

±

o

n

n

a

(18)

W^j

("

where n and n represent the number of moles of c a t i o n and anion r e s p e c t i v e l y i n one mole of i o n i z e d s o l u t e . Applying eq 18 to ( D ^ / K S ) ^ ! , Q

m

a

(DAM/K*)

NaC1

= m

C*

N a C 1

+

J (-

+

(-

^

[

(19)

where In C * i s a constant representing the porous s t r u c t u r e of the membrane surface expressed i n terms of (DAM^^^NaCl • N a C 1


2.

SOURIRAJAN

Reverse

47

Osmosis

+

Using the data on (-AAG/RT) f o r N a and C I " ions f o r the membrane m a t e r i a l i n v o l v e d (Table I ) , the value of In C NaCl ^ p a r t i c u l a r membrane used can be c a l c u l a t e d from the s p e c i f i e d value of (DAM/ °^NaCl* Using the value of In C * ^ so obtained, the corresponding value of D^/K6 f o r any completely i o n i z e d i n o r g a n i c or simple organic s o l u t e can be obtained from the relation: o r

t

n

e

K

N a C


In

& /m

Bolute = In C *

M

(- m\

+ jn 5^ / c a t i o n

N a C 1

c

w)

(20)

>

x

£ /anioi Thus, f o r any s p e c i f i e d value of (DAM/ ^NaCl> * corresponding values of (D^/Kfi) f o r a l a r g e number of completely i o n i z e d s o l u t e s can be obtained from eq 20 using data on (-AAG/RT) f o r d i f f e r e n t ions a v a i l a b l e i n the l i t e r a t u r e ( 8 , 9 ) . With r e s p e c t to e l e c t r o l y t i c i n o r g a n i c s o l u t e s , a few s p e c i a l cases a r i s e . For a s o l u t i o n system i n v o l v i n g ions and i o n - p a i r s , eq 20 can be w r i t t e n as K(

In ( D A M / K 6 )

s o l u t e

= In C *

+ Oj,

N a C 1

j

n

c

t

(-

i e

fr)

cation

• ( - t r ) . (• «-v (-&\ \

~

/anion)

\

~

Ap

where a represents the degree of d i s s o c i a t i o n , and the s u b s c r i p t i p r e f e r s to the i o n - p a i r formed; f o r the p a r t i c u l a r case where the i o n - p a i r i t s e l f i s an i o n , eq 20 assumes the more general form D

In ( % / . I ) ,

l

t

o

t

e

- In C * ^

(

\

\

~

~

\ ~

/ip

+ (l-a )(n D

/cation

a

n i

\

)

/anion)

~

/cati

/_ A A G \

\

~

(22)

/anion

where n^p and n^p represent number of moles of c a t i o n and anion r e s p e c t i v e l y i n v o l v e d i n one mole of i o n - p a i r . For the case of a feed s o l u t i o n which i s s u b j e c t to p a r t i a l h y d r o l y s i s , C

eq 20 becomes

a

American Chemical Society Library 1155 16th St. N. W. In Synthetic Membranes:; 1. D. C. Turbak, 20036A.;

ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

SYNTHETIC

48 In ( 0 ^ 6 ) ^ ^ ^

= In C *

MEMBRANES:

DESALINATION

N a C 1

* «-«»> k (- m (

\

~

. * ^ (- §r). |

/cation

\

~

/anion)

-»K(-r) /(-fL„ i h

-

H+

where represents the degree of h y d r o l y s i s and the s u b s c r i p t hy r e f e r s to the hydrolyzed species r e s u l t i n g from the h y d r o l y s i s r e a c t i o n and the s u b s c r i p t s 0H~ and H represent the hydroxyl and hydrogen ions r e s p e c t i v e l y . In eq 21, 22, and 23, the a p p l i c a b l e values of and are those corresponding to the boundary concentration X^2» For a completely nonionized polar organic s o l u t e ,


+

l n

D

K6

< AM/ > s o l u t e =

l

n

C

*NaCl

+

l

n

A

*

+

f

w)

+ 6*EE + a)*Zs*

(24)

S

R e f e r r i n g to the q u a n t i t i e s on the r i g h t side of eq 24, the quantity In C * ^ i s obtained from eq 19; the q u a n t i t y In A i s a s c a l e f a c t o r s e t t i n g a s c a l e f o r In ( D / K 6 ) i t e In C * j r C l when the p o l a r (-AAG/RT), s t e r i c (6*EE ) and nonpolar (CL)*ZS ) parameters a p p l i c a b l e f o r the system are each s e t equal to zero. The methods of computing the l a t t e r three parameters f o r d i f f e r e n t s o l u t e s , membrane m a t e r i a l s and membranes are i l l u s t r a t e d i n d e t a i l i n the l i t e r a t u r e (8,9,56). The quantity In A i s a f u n c t i o n of the chemical nature of the membrane m a t e r i a l (such as that represented by the 3-parameter) and the porous s t r u c t u r e of the membrane surface (such as that represented by the quantity In (C*NaCl/ )• The s t e r i c c o e f f i c i e n t 6* i s a l s o a f u n c t i o n of the chemical nature of the membrane m a t e r i a l and the porous s t r u c t u r e of the membrane surface; i n a d d i t i o n , i t i s a l s o a f u n c t i o n of the chemical nature of the s o l u t e . Figure 12 gives a s e t of c o r r e l a t i o n s of In A* and 6* (obtained experimentally) (56) expressing t h e i r above p r o p e r t i e s ; the data given i n Figure 12 can be used i n conjunction with eq 24 f o r obtaining the values of In (D^/K6) for different solutes. The object o f the foregoing d i s c u s s i o n i s two-fold: eq 19 to 24, together with Figure 12, show how one can o b t a i n the values of T)fift/K& of s o l u t e s f o r a very l a r g e number of membrane-solution systems from D^/K6 data f o r a s i n g l e reference s o l u t e such as sodium c h l o r i d e ; they a l s o show how the physicochemical parameters c h a r a c t e r i z i n g s o l u t e s , membrane-materials and membrane-porosities are i n t e g r a t e d i n t o the transport equations i n the o v e r a l l development of the science of reverse osmosis. N a C

i

A M

a

s o

n

t

e

r

u

g

A


m

s

o

f


2.

SOURIRAJAN

Reverse Osmosis

49

P r e d i c t a b i l i t y of Membrane Performance f o r Aqueous Feed S o l u t i o n Systems I n v o l v i n g Mixed S o l u t e s . This subject i s obviously of great p r a c t i c a l i n t e r e s t . Even though a f u l l development of the subject i s yet to come, considerable progress has been made at l e a s t with respect to c e r t a i n kinds of mixed s o l u t e systems (6e,44,101,102,103,104). The l a t t e r i n c l u d e ( i ) mixtures of any number of e l e c t r o l y t i c s o l u t e s i n v o l v i n g a common i o n , ( i i ) mixtures of any number of nonionized organic s o l u t e s with no s o l u t e - s o l u t e i n t e r a c t i o n s , and ( i i i ) mixtures of two e l e c t r o l y t i c s o l u t e s i n v o l v i n g four different ions ( e i t h e r a l l of them u n i v a l e n t , or one of them d i v a l e n t and the r e s t univalent). The p r e d i c t i o n techniques i n v o l v e d f o r the mixeds o l u t e systems ( i ) and ( i i ) use the b a s i c transport equations given above, t r e a t i n g each s o l u t e independently, so that the net r e s u l t i s simply the a d d i t i v e e f f e c t of each i n d i v i d u a l component i n the mixed-solute system. In the p r e d i c t i o n technique f o r the mixed s o l u t e system ( i i i ) , the b a s i c t r a n s p o r t equations are w r i t t e n f o r each i o n along with the necessary a d d i t i o n a l equations f o r o v e r a l l e l e c t r o n e u t r a l i t y f o r the system; these equations, together with eq 20 w r i t t e n f o r each p o s s i b l e e l e c t r o l y t i c s o l u t e combining the c a t i o n s and the anions present i n the system y i e l d a set of equations which can be solved to give the necessary data on i o n separations and product r a t e s from data on membrane s p e c i f i c a t i o n s only. Even though these techniques r e q u i r e considerable e f f o r t i n s o l v i n g the computational complexities i n v o l v e d , they are simple i n p r i n c i p l e , fundamental i n approach, and o f f e r a f i r m b a s i s f o r the a n a l y t i c a l treatment of more complex systems. A n a l y s i s of Reverse Osmosis Modules. The b a s i c t r a n s p o r t eq 10 to 13 apply to any p o i n t ( p o s i t i o n or time) i n a reverse osmosis module, where the f r a c t i o n recovery ( A ) of product water i s assumed i n f i n i t e l y small f o r purposes of a n a l y s i s . A p r a c t i c a l reverse osmosis module i n v o l v e s a f i n i t e and o f t e n a high value of A , which means s o l u t e concentrations and membrane f l u x e s change continuously from the entrance to the e x i t of the module (or time t=0 to t=t of module o p e r a t i o n ) . Thus the product water l e a v i n g the module as a whole has an average concentration corresponding to a s p e c i f i e d A v a l u e . The performance of the module as a whole can then be p r e d i c t e d by a p p l y i n g the b a s i c transport equations to the e n t i r e reverse osmosis system and a n a l y z i n g the v a r i o u s r e l a t i o n s h i p s a p p l i c a b l e to the e n t i r e system which can be represented as shown i n Figure 13. The technique f o r such a n a l y s i s has been developed i n d e t a i l with p a r t i c u l a r reference to water treatment a p p l i c a t i o n s of reverse osmosis (6d,8,9,105-113). The e s s e n t i a l features of t h i s a n a l y s i s are as f o l l o w s . System S p e c i f i c a t i o n . Any reverse osmosis system may be s p e c i f i e d i n terms of three nondimensional parameters Y> 6> d a n



50

SYNTHETIC

MEMBRANES:

DESALINATION

Figure 12. Variations of 8 * for alcohols, aldehydes, ketones, and ethers and In A* for nonionized polar organic solutes with ^-parameter for the polymeric membrane material as a function of surface porosity (correlations with C* in centimeters/second and A in gram-moles H 0 centimeters /second atm) (56) 2

2

Figure 13. Schematic of a reverse osmosis system for process design


2.

SOURIRAJAN

Reverse Osmosis

51

A defined as follows: TT(X°

_

)

A l _ osmotic pressure of i n i t i a l feed s o l u t i o n P operating pressure (D -/K6) AM _

^ 5 )

A1

Q -


^ _

k (D^/K6)

(76)

s o l u t e transport parameter pure water permeation v e l o c i t y mass t r a n s f e r c o e f f i c i e n t on the high pressure side of membrane s o l u t e transport parameter

=

where v* = — w c

(27)

(28)

and the quantity ^ ( X ^ ) r e f e r s to the osmotic pressure of the feed s o l u t i o n a t membrane entrance i n a flow process or s t a r t of operation i n a batch process. The q u a n t i t i e s y, 6 and A6(=k/v*) may be described as the osmotic pressure c h a r a c t e r i s t i c , membrane c h a r a c t e r i s t i c , and the mass t r a n s f e r c o e f f i c i e n t c h a r a c t e r i s t i c r e s p e c t i v e l y of the system under c o n s i d e r a t i o n . The s i g n i f i c a n c e of system s p e c i f i c a t i o n i s that a s i n g l e s e t of numerical parameters can represent an i n f i n i t e number of membrane-solutionoperating systems; conversely, any two membrane-solution-operating systems can be simply and p r e c i s e l y d i f f e r e n t i a t e d i n terms of unique combinations of numerical parameters. System A n a l y s i s and P r e d i c t a b i l i t y of System Performance. For the purpose of t h i s a n a l y s i s , the f o l l o w i n g assumptions and d e f i n i t i o n a r e made. Assumptions: l 2 3 » ( A^ A> A 3 > D /K6 i s independent of X f ° the A value considered; and l o n g i t u d i n a l d i f f u s i o n i s n e g l i g i b l e ; these assumptions are p r a c t i c a l l y v a l i d f o r many reverse osmosis systems i n water treatment a p p l i c a t i o n s . Definitions: c

=

c

=

c

=

c

71

X

a

X

X

Synthetic Membranes: Volume I - ACS Publications - American

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