9 Model and Preliminary Experiments on Membrane Fouling in Reverse Osmosis 1
2
R. F. PROBSTEIN, K. K. CHAN , R. COHEN, and I. RUBENSTEIN
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Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
One of the principal limitations to the optimum performance of reverse osmosis systems is membrane fouling, which leads to a decrease in membrane flux with time. Materials that form fouling films on the flow side of membrane surfaces include colloidal impurities, macromolecules, biological contaminants, and inorganic precipitates. Moreover, the foulant film may be electrically neutral or carry a fixed charge. The rate of formation, the extent, and the nature of the fouling film will depend on the properties and characteristics of the foulant, the membrane surface, the working fluid, and the operating conditions. An understanding of how fouling films grow as a function of these parameters might make i t possible to minimize or delay the fouling by suitable variations of the process design or operating conditions. The general problem of fouling is a complex one and the aim of this paper is limited to presenting a summary of some preliminary results on the kinetics of the colloidal fouling of asymmetric reverse osmosis membranes. A simple model is suggested for the rate of growth of a colloidal fouling film in steady, obstruction free, laminar and turbulent reverse osmosis systems. Preliminary experimental results are presented on the fouling of cellulose acetate membranes by colloidal iron hydroxide suspended in a flowing saline solution. F o u l i n g Model The f o u l i n g process may be c h a r a c t e r i z e d as a rate dependent k i n e t i c process d e s c r i b a b l e by the m a t e r i a l balance r e l a t i o n c f
f = m "dT d
- m r
1
Current address: General Electric Co., Wilmington, M A 01887. - Current address: Weizmann Institute of Science, Rehovot, Israel.
0097-6156/81/0153-0131$05.00/0 © 1981 American Chemical Society
In Synthetic Membranes:; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
(1)
SYNTHETIC MEMBRANES: DESALINATION
132
Here, C f i s the mean concentration o f f o u l a n t i n the f i l m whose thickness at any time t i s 6f, and md and m are, r e s p e c t i v e l y , the mass o f f o u l a n t deposited and removed per u n i t area per u n i t time. Assuming the d e p o s i t i o n r a t e to be independent of the f o u l a n t f i l m thickness and the removal r a t e to be l i n e a r l y dependent on the f i l m t h i c k n e s s , we may w r i t e a f i r s t - o r d e r r a t e equation f o r the f i l m growth. From Eq. (1) t h i s equation i s given by r
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d
6
f
=
6
f "
6
f
(2)
T
dt
* where 6f i s the asymptotic e q u i l i b r i u m f i l m thickness at l a r g e time a n d T i s a c h a r a c t e r i s t i c f i l m buildup time. The f i l m thickness as a f u n c t i o n of time i s given from the i n t e g r a t i o n o f Eq. (2) by «
f
= «J
(1 - e "
t A
)
(3)
Based on c o n s i d e r a t i o n s to be discussed i n a more d e t a i l e d v e r s i o n of t h i s work we assume that the d e p o s i t i o n r a t e i s d i f f u s i o n c o n t r o l l e d , and the c h a r a c t e r i s t i c buildup time i s c o n t r o l l e d by the chemical and p h y s i c a l p r o p e r t i e s of the f o u l a n t and a s s o c i a t e d foulant-membrane surface f o r c e s . The consequence of the f i r s t assumption i s that
v
a
=
6*
Ac
—f ^ —c- ^— T
V 6 o c
rD —
(4)
Equation (4) s t a t e s that the l i n e a r d e p o s i t i o n r a t e v^ i s a d i f f u s i o n c o n t r o l l e d boundary l a y e r e f f e c t . The q u a n t i t y Ac i s the d i f f e r e n c e i n f o u l a n t concentration between the f i l m and that i n the bulk flow and c i s an appropriate average concentration across the d i f f u s i o n l a y e r . The l a s t term approximately c h a r a c t e r i z e s the "concentration p o l a r i z a t i o n " e f f e c t f o r a developing concentration boundary l a y e r i n e i t h e r a laminar or t u r b u l e n t pipe or channel flow. Here, V i s the permeate f l u x through the unfouled membrane, 6 the f o u l a n t concentration boundary l a y e r thickness and D the d i f f u s i o n c o e f f i c i e n t . In reverse osmosis systems the permeate f l u x i s e x p r e s s i b l e by the semi-empirical r e l a t i o n Q
C
Ap R
ATT
=
^e R
(5)
where Ap i s the a p p l i e d pressure d i f f e r e n c e across the membrane, ATT the osmotic pressure d i f f e r e n c e , R the t o t a l h y d r a u l i c
In Synthetic Membranes:; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
9.
PROBSTEIN ET AL.
Membrane
Fouling
in RO
133
r e s i s t a n c e and A p the e f f e c t i v e d r i v i n g p r e s s u r e . The t o t a l r e s i s t a n c e may be taken to be the l i n e a r sum o f the membrane and foulant f i l m resistance: e
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R = R + R m f
(6)
The apparent r e s i s t a n c e due t o the r e d u c t i o n i n d r i v i n g f o r c e from 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 s g e n e r a l l y small i n most reverse osmosis systems and i s neglected. The r e s i s t a n c e can a l s o be w r i t t e n i n terms o f a c h a r a c t e r i s t i c thickness and permeability R. = 6./K. l i i
(7)
where i = m o r f . The p e r m e a b i l i t y i s p r o p o r t i o n a l to the l i q u i d d i f f u s i o n c o e f f i c i e n t and i t s temperature dependence i s given by K
±
^ D(T)/T ^ 1/n
(8)
where n i s the l i q u i d v i s c o s i t y . We can t h e r e f o r e w r i t e f o r the f l u x through the unfouled membrane V
o
= Ap /R e m
^ Ap /n e
(9)
with the membrane thickness 6 assumed t o be constant and independent o f temperature and the a p p l i e d pressure. For developing c o n c e n t r a t i o n d i f f u s i o n l a y e r s i n channel o r pipe flow the c o n c e n t r a t i o n boundary l a y e r thickness i s e x p r e s s i b l e by the p r o p o r t i o n a l i t y m
6 .D c
1 / 3
U-
1 / 3
(10)
and i n t u r b u l e n t flow by
6 . V C
l
/
\
5
/
1
2
V -
3
/
4
(
U
)
Both D and r\ have an exponential dependence on temperature but over the narrow range o f temperatures o f i n t e r e s t we approximate the temperature behavior by the power-law r e l a t i o n s 8
D ^ T ' n
*
T~
1
7 , 1
(12a) (12b)
In Synthetic Membranes:; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
134
SYNTHETIC
MEMBRANES:
DESALINATION
I n s e r t i n g Eqs. (9)-(12) i n t o Eq. (4) we f i n d that the d e p o s i t i o n rate may be w r i t t e n i n laminar flow as v and
i n turbulent
-0.33+1.7 i Ap U T
flow as 75
V j
d
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.... (13)
A
d
* Ap U ° ' T e
1
-
3
(14)
The second assumption o f the model that the c h a r a c t e r i s t i c buildup time i s c h e m i c a l - p h y s i c a l c o n t r o l l e d , implies that t h i s time i s dependent on the chemical, p h y s i c a l and e l e c t r i c a l p r o p e r t i e s o f the foulant and the membrane but not on the flow. We may lump a l l o f the temperature e f f e c t s i n t o a van't Hoff-type r e l a t i o n by w r i t i n g the c h a r a c t e r i s t i c time i n the form
T = T
o
-AG/&T e
(15)
where AG i s an " e f f e c t i v e " a s s o c i a t i o n energy, which c o r r e l a t e s the p r o b a b i l i t y o f foulant a s s o c i a t i o n i n the f i l m o r with the membrane. For purposes o f comparison with the preceding r e l a t i o n s we may approximate Eq. (15) over the temperature range of i n t e r e s t by the power-law p r o p o r t i o n a l i t y x ^ T
m
(m > 0)
(16)
Experiments and Data Reduction Experiments were c a r r i e d out i n a continuous flow t u b u l a r reverse osmosis module with i n t e n t i o n a l f o u l i n g o f the membrane by mixing i n with the s a l i n e feed s o l u t i o n a high c o n c e n t r a t i o n of c o l l o i d a l i r o n hydroxide, a known f o u l i n g m a t e r i a l . The use of i r o n hydroxide i n membrane f o u l i n g experiments has been p r e v i o u s l y employed by Jackson and Landolt (_1) , however, t h e i r t e s t s were not o f long enough d u r a t i o n t o enable a determination of the f o u l i n g k i n e t i c s . The b a s i s f o r the experiments as c a r r i e d out was that the f l u x d e c l i n e with time, which i s an e a s i l y measured q u a n t i t y , could be c o r r e l a t e d with the foulant f i l m growth by the model o f Eq. (2), o r some other appropriate semi-empirical model. In t h i s way the f o u l i n g f i l m thickness could be deduced i n d i r e c t l y . To show t h i s we w r i t e from Eqs. (5)-(7)
In Synthetic Membranes:; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
9.
PROBSTEIN
ET AL.
Membrane
Fouling
in
135
RO
where Vf i s the permeate f l u x when the membrane i s f o u l e d . So long as the r e d u c t i o n i n f l u x due to f o u l i n g i s not l a r g e then 6 f / K f
