(3) Blunk, R. W., Dept. of Engineering, University of California, Los Angeles, Rept. 64-28 (June 1964). (4) Breton, E. J., Office of Saline Water, U. S. Dept. Interior, R&D Progr. Rept. 16 (April 1957). (5) Erickson, D. L., M.S. thesis, Department of Engineering, University of California, Los Angeles, Calif., 1965. (6) Gainey, R. J., Thorp, C. A., Cadwallader, E. A., Ind. Eng. Chem. 5 5 , 39 (1963). ( 7 ) Hodges, R. M., Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1964. (8) Keilin, B., Office of Saline Water, U. S. Dept. Interior, Rept. 117 (August 1964). (9) Langelier, W. F., Caldwell, D. F., Lawrence, D. F., Inst. Eng. Res. Rept. ERDL, Ft. Belvoir, Va., 1950. (10) Lebeis, E. H., Proceedings of Eighth Annual New Mexico Water Conference, Roswell, N. M., pp. 40-51 (July 1, 1963). (11) Loeb, S., Manjikian, S., Ind. Eng. Chem. Process Design Develop. 4,207 (1965). (12) Loeb, S., Sourirajan, S., Adcan. Chem. Ser., No. 38, 117-32 (1963).
(13) Loeb, S., Sourirajan, S., Dept. of Engineering, University of California, Los Angeles, Rept. 60-60(July 1960). (14) Lonsdale, H. K., Merten, U., Riley, R. L., Vos, K. D., General Atomic Corp., Annual Rept., GA-6370 (June 1965). (15) Lyman, J., Fleming, R. H., J. Marine Res. 3, 134 (1940). (16) McIlhenny, W. F., Office of Saline Water, U. S. Dept. Interior, Rept. 62 (1962). (17) Manjikian, S., Dept. of Engineering, University of Californla, Los Angeles, Rept. 65-13 (March 1965). (18) Reid, C. E., Breton, E. J., J . Appl. Polymer Sci. 1, Issue 2, 133 (1959). (19) Sourirajan, S., IND. ENG. CHEM.FUNDAMENTALS 3, 206 (1964). RECEIVED for review November 9, 1965 ACCEPTED April 25, 1966 LYork supported by Saline Water Research funds provided by the California State Legislature as a special item in the University of California budget.
LIFETIME OF CELLULOSE ACETATE REVERSE OSMOSIS MEMBRANES KENNETH D. VOS, A. P. HATCHER, AND U. MERTEN John Jay Hopkins Laboratory for Pure and Applied Science, General Atomic Division,General Dynamics Corp., San Diego, Calif.
A series of experiments was conducted to investigate the influence of feed water pH on the long-term performance of cellulose acetate reverse osmosis membranes. The decline in salt rejection observed for these membranes after extended exposure to feed solutions is attributed to hydrolysis of the cellulose acetate, and is found to be strongly pH-dependent. The rate of change of the membrane parameters can be correlated with the previous measurements of hydrolysis rates of cellulose acetate, and the dependence of membrane parameters on the acetyl content of the ester.
HE
early work of Reid and Breton showed that cellulose
Tacetate is an effective membrane material for water de-
salination ( 8 ) . With the announcement of Loeb and Sourirajan (5) that, by a suitable casting technique, membranes could be made which would pass considerably greater quantities of water than the membranes used by Reid and Breton and still retain their favorable desalination characteristics, it became clear that reverse osmosis held promise as an economical means of desaiinating brackish and sea waters. I t was observed in the early work that cellulose acetate membranes deteriorated during long-term tests-Le., after a time they lost some of their ability to desalinate (4,9). The present work was initiated in an attempt to gather further data on membrane deterioration. Membranes of the type developed by Loeb and Sourirajan ( 5 ) consist of two parts, a thin rejecting layer and a porous substructure (70). T h e rejecting layer is -0.25 micron thick and is the part of the membrane that excludes the salt. T h e porous region makes u p >99% of the membrane and is a backing for the rejecting layer. The highly selective reverse osmosis membranes used in this study can be usefully characterized in terms of a membrane constant and a salt permeation constant. Lonsdale et al. ( 6 ) have shown that the water flux through the membrane, JI, can be written as J1
A(AP
where AP and AT are the pressure difference and the osmotic pressure difference across the membrane, respectively, and A is the membrane constant. The membrane constant is related to the diffusion coefficient of water in the membrane, D1, and the concentration of water in the membrane, CI, by the equation
where VI is the partial molar volume for water, R is the gas constant, T is the temperature, and Ax is the effective membrane thickness (-0.25 micron). The salt permeation constant is readily arrived at from an equation (6) where the salt flux, Jz,is written as
D Zis the diffusion coefficient for a particular salt in the membrane, K is the distribution coefficient for the salt between the membrane and the brine, and Apz is the difference in the salt concentrations on the two sides of the membrane. We define the salt permeation constant as (4)
- AT) VOL 5
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SEPTEMBER 1966
211
The membrane constant and the salt permeation constant, then, are parameters of the membrane which are ideally independent of the experimental conditions at constant temperature. I n fact, they are not quite independent of pressure or salt concentration, but are sufficiently independent to give a useful indication of the quality of the membrane. Lonsdale et al. (6) have shown that DzK and DlCl both increase as the acetyl content of the membrane decreases. Hydrolysis of the membrane, therefore, increases both the salt permeation constant and the membrane constant. I n this paper we speak of a chloride permeation constant to emphasize that the salt permeation constant was determined in all cases by determining chloride in the feed water and in the permeate. Because sea water salt is largely sodium chloride and the tap water used contains an excess of sodium ions over chloride ions (and other cations to which the membrane is much less permeable), this chloride permeation constant is essentially that which is characteristic of pure sodium chloride solutions. T h e selectivity of reverse osmosis membranes is commonly expressed in terms of the salt rejection, S,under a particular set of experimental conditions, rather than the constants A and B. Salt rejection is defined as (5) where p2( is the salt concentration of the feed brine and p1O is the water concentration of the permeate. The salt rejection can be related to the membrane permeabilities by using Equations l , 3, and 4 through the expression S=
A(AP - AT) A(AP - AT) Bpio
+
Experimental
The membranes used were made from Eastman E-398-3 cellulose acetate (Eastman Chemical Products, Inc., Kingsport, Tenn.) by a procedure similar to that outlined by Loeb and Sourirajan ( 5 ) . The membranes were heat-treated by immersion in water at 80" C. for 30 minutes after fabrication. The reverse osmosis experiments were carried out in a desalination cell in which the circulating brine flowed lengthwise along a rectangular 1 X 3 inch membrane, with the inlet and outlet arranged to make the flow across the membrane reasonably uniform. The membrane chamber was 0.1 inch high. The membrane was supported on a piece of filter paper placed on a porous stainless steel backing plate. (One to four such cells were connected to a single pumping system for each run). In all except the tap water experiment, brine was circulated over the membrane at >lo0 cm. per
Table 1. Expt.
Figure or Table No.
No. of Membranes 1
6 7 8 9 10 11 12 13 14
212
I11 4 5 6 7 8, 9, 10 8, 9, 10 1 1 , 12 11, 12
4 4 4 4 4 1 1 1 2 1 1 2 2
second, so that no significant boundary layer effect was expected (7). The brine was recirculated and fresh brine was added only to replace the water passed through the membrane or removed as samples of the brine. The tap water experiments were made on a once-through basis-Le., no recycling of the brine. The circulation rate on the tap water runs was approximately 0.5 cm. per second. Because of the low pressure, 30 to 60 p.s.i., and the resulting low water flux, no significant boundary layer effect was expected. The effluent water was collected from the porous stainless steel backing plate and analyzed. The Cl- content was determined by the Mohr titration method and the Ca+2 and Mg+* contents were determined using the flame photometer. Some of the membranes were analyzed for acetyl content, using the modified Eberstadt method as outlined by Genung and Mallatt ( Z ) , modified only in a thorough washing and drying of the samples before weighing. Control samples of the starting material gave 39.7 i 0.2 weight % acetyl, in good agreement with the acetyl content of the starting material, 39.8 weight %, specified by the manufacturer. Results
In this paper the results of experiments on 32 membranes are presented. Brief descriptions of the experiments are given in Table I. T h e membrane of experiment 1 deteriorated from 95% to 49y0 rejection in 4 days at 38" C., when operated on p H 8.9 brine (Table 11). Experiment 2 was made with this same brine, but the p H was adjusted with acetic acid from its original value of 8.9 to 5.0 to 6.5 (Table 11). Under these conditions the membranes of experiment 2 showed no measurable deterioration in chloride permeation constant. Experiment 2 clearly showed that the effect of the brine pH was of great importance in the lifetime of the membrane. A series of lifetime measurements was then made using NaCl brine buffered with N a H C 0 3 and Na2C03. Two experiments were made on p H 1 0 brine, at 800 and 1500 p.s.i. I n Figure 1 the change of the membrane constant with time is given for experiments 3 and 4. Also shown is the permeate p H for the 800-p.s.i. experiment. The membrane constant for these experiments showed an increase after an induction period; however, the change in the membrane constant for experiment 4 at 1500 p.s.i. was less rapid than for experiment 3 at 800 p.s.i. Initially, the permeate of experiment 3 was considerably less basic than the feed water. The p H difference between the brine and the effluent is probably due to the different permeation rates of the HCOs- and COa-' ions through the membrane. I n general, the salt permeation constant for divalent ions is lower than that for monovalent ions.
Membrane lifetime Experiments Pressure,
Brine Concentration, Wt. 70
Brine p H
P.S.I.
7.5 NaCl 6-9 NaCl 0.1 NaCl 0.1 NaCl 1 NaCl 1 NaCl 6-12 NaCl and 6.3 sea water 6-12 NaCl 6.3 sea water 6.3 sea water 0.075 tap water 0.075 tap water 0,075tap water 0.075 tap water
8.9 5 .O-6.5 10 10 9 9 5.0-7.0 5.0-6.5 6.5-7.0 6.5-7 .O 8.3 8.3 8.3 6.7
1500 1500 800 1500 1500 1500 1500 1500 1500 1500 30-60 30-60 30-60 30-60
l & E C P R O D U C T RESEARCH A N D DEVELOPMENT
Duration of Experiment, Days 4
50 5 2.3 8.5 1 365 256 305 109 230 135 337 337
T h e acetyl contents of two of the membranes used in experiment 5 were found to be 38.3 and 39.1 weight % a t the conclusion of the experiment; the acetyl content of a membrane stored in the high pressure loop during experiment 5 was 37.3 weight %. Thus, the membranes used in experiment 5 had a higher acetyl content than the membranes stored in the same brine. I n experiment 6 of the two membranes (A and B) that had been stored in the high pressure loop and the membrane (C) that had been stored in the brine under ambient conditions had acetyl contents of 37.3, 37.6, and 38.6 weight 70, respectively, a t the conclusion of that run. This slower hydrolysis in the reverse osmosis experiments is not surprising, since initially only the rejecting surface of each membrane in the cells was exposed to the high p H brine and the remainder
Table II. Data for Experiments 1 and 2 Membrane Constant. lO+&G./Sq.Cm.Sec.-Atm. Inittal Ftnal 0.42 0.30
Ci- RejecMemtion, '%> Expt. brane Initial Ftnal 1,4 A 95 49 days 98 94 2,50 A 98 96 days B C 98 95 98 97 D
Chloride Permeation Constant, 70fe Cm./Sec. Initial Final 9.0 240 3.5 1.3 2.8 1.2
3.1 2.5 2.7 2.6
0.15 0.11 0.13 0.11
0.24 0.24 0.22 0.26
20
IO I
I
I
20
40
I
I
I
I
-
I
w '0 0.8
2,
0.6 0
I
I
I
I
I
60
80
100
I20
ELAPSED TIME (HR)
Figure 1. Membrane constants for experiments 3 and 4 and permeate pH for experiment 3
I n Figure 2 the change with time of the salt flux restated in terms of the salt permeation constant, B , is given. After a short induction period in which the chloride permeation constant showed little change, it started increasing rapidly in both experiments 3 and 4. I n experiment 5 (pII 3 brine), four membranes were run in the reverse osmosis cells, and the change in the membrane parameters with time was followed (Figure 3). The membrane constant gradually decreased during the early part of the run and thereafter remained relatively constant, while the chloride permeation constant increased after an induction period. T h e salt rejection at the end of the experiment was approximately 80%. Additional membranes were stored in the high pressure loop during the experiment, so that they were exposed to the same brine as those in the reverse osmosis cells. A rapid flow of brine was maintained on both sides of the membranes stored in the loop. Membranes were also stored in a separate container of the brine at 23' C. and atmospheric pressure. After the membranes in experiment 5 had shown considerable deterioration (about 8l/2 days), they were removed and two membranes that had been stored in the high pressure loop, one membrane that had been stored in the brine under ambient conditions, and a control membrane that had been stored in distilled water were placed in the reverse osmosis cells for experiment 6. The three membranes previously subjected to the brine had initial rejections close to those found a t the end of experiment 5 (Table 111). Their membrane constant and salt rejection decreased rapidly with time. The control membrane had an initial membrane constant and chloride permeation constant similar to the initial values for the membranes used in experiment 5 .
,
nil 0 ".I
20
I
I
I
I
40
60
80
100
120
ELAPSED TIME ( H R )
Figure 2. Chloride permeation constants for experiments 3 and 4
-1
*..
**' 1.5
0
40
80
120
160
200
2 0
ELAPSED TIME (HR)
Figure 3. Chloride permeation and membrane constants for experiment 5 VOL. 5
NO. 3 S E P T E M B E R 1 9 6 6
213
Table 111.
Results of Reverse Osmosis Experiments on pH 9 Brine at 1500 P.S.I.
(Experiment 6)
Elapsed
Time, Hr. 1
Chloride Membrane PermeaConstant, A , tion ConCl10+6G./ stant, B, Mem- Rejection, Sq. Cm.IOf5 branea yo Sec.-Atm. Cm./Sec. 77 0.57 A 16 B 78 0.53 14 80 0.60 14 C 1.8 97 0.60 D
PREDl CTED 'p
0
5 3
PH
PREDICTED FOR pH 5.0 /
z
0
4
2
P
5 L
A B C D A B
l&EC PRODUCT RESEARCH A N D DEVELOPMENT
AT 27*C
*[
W
a
2
I
SYSTEM DEPRESSURIZED
-
I1 0
MOVED TO SEAWATER SYSTEM
I
I
I
J
100
200
300
400
ELAPSED TIME (DAYS)
Figure 4. Chloride permeation constants for experiment 7 9
214
t
0
8.4 8.4 8.5 7.7 9 . 0 brine
was exposed to the lower p H of the effluent. However, as the membranes deteriorated all of the membrane was exposed to a higher pH. The p H 9 and 10 data clearly show the membranes in the p H 10 experiment to have a more rapid deterioration than those in the p H 9 experiments. Experiments were also made to determine the lifetime under more nearly neutral conditions. Experiments 7 and 8 were started in the same system, using NaCl brine acidified to p H 5.0 to 6.5 with acetic acid. The brine concentration varied between 6 and 12 weight %, and averaged approximately 9 weight %. The results for the membranes of experiments 7 and 8 are shown in Figures 4 and 5, respectively. The system was operated continuously at 1500 p.s.i., except for the 69th day, when it was depressurized and the system was flushed. T h e experiment continued for 256 days, at which time experiment 8 was terminated and the membrane of experiment 7 was transferred to a sea water system described below in connection with experiment 9 ; here it ran an additional 109 days. When the system was depressurized and flushed on the 69th day of the experiment, the membrane of experiment 8 showed a sudden increase in the chloride permeation constant (Figure 5 ) which was not so apparent in the membrane of experiment 7. T h e membrane constants of experiments 7 and 8 did not show an increase of the type shown by the pH 10 runs, although they showed some periodic fluctuations of approximately 10%. The average membrane constant of the membranes in experiments 7 and 8 was 9 X 10-7 and 1 X IO-Ggram/sq. cm.-sec.-atm., respectively, The curves in Figures 4 and 5 are considered below . At the end of the run the membrane of experiment 8 had 38.4 weight % ' acetyl. The membrane of experiment 9 was run in concentrated sea water, 6.3 weight % solids, acidified to p H 6.5 to 7.0 with HzS04. This brine was made by boiling down Pacific Ocean water. T h e experiment ran continuously for 196 days and the system was then depressurized while the membrane of experiment 7 and two new membranes (experiment 10) were inserted into the system. The system then ran an additional 109 days, at which time the experiments were terminated because of pump failure. The change in the chloride permeation constant with time for the membrane of experiment 9 is shown in Figure 6. T h e MgS2 and Ca+2 concentrations were measured
I
6
v)
73 0.38 14 ... 70 0.37 15 ... 69 0.43 18 ... 96 0.49 1.8 ... 22 63 0.31 17 64 0.30 16 67 0.35 16 C D 96 0.42 1.7 a A, stored in high pressure loop; B, stored in high pressure loop; C, stored in p H 9 brine under ambient conditions; D , control. 8
IO
I
I
I
I
I
0%
e
" Y
FOR pH 5.0 AT 2 7 O C
I a W W
n a V
S Y S T E M DEPRESSURIZED e
1.5
I
I
I
I
I
on the 69th day and neither ion was detected; the limit of detectability was 5 p.p.m. (the brine contained 2200 p.p.m. of Mg+2 and 700 p.p.m. of Ca+*). The rejection of these ions was, therefore, >99.8 and >99.3'%, respectively; the rejection of C1- at this time was 96.101,. The membrane constant for this membrane averaged 2.2 X 10-6 gram/sq. cm.-sec.-atm. during the run. The curves in Figure 6 are considered below. T h e change of the chloride permeation constant with time for experiment 10 is given in Figure 7. After an initial decrease during the first 20 days, the membrane constant for these membranes showed little change and averaged 2.8 X 10-6 gram/sq. cm.-sec.-atm. I n addition to these high pressure runs, a series of experiments (1 1 through 14) was made on San Diego tap water at line pressure, 30 to 60 p.s.i. (Figures 8 through 12). San Diego tap water contains -750 p.p.m. total solids and has a p H of approximately 8.3. I n Figure 8 the change in rejection for C1and CatZ ions is shown as a function of time for experiments 11
U
30
I
I
,)
W
PREDICTED
IO
-
FOR pH 6.5 a
a
.
SYSTEM DEPRESSURIZED
W
P a
I
I
I
1
40
o
EXPERIMENT EXPERIMENT 0 CIEXPERIYNT A ca++ EXPERIMENT CI-
A CO+*
,
II II l2\. 12
,
,
,
160
200
30 0
40
00
120
240
ELAPSED TIME (DAYS)
$
1
Figure 8. Chloride and Cafz ion rejections for experiments 1 1 and 12
A
I
t o
I
I
I
I
-
IO 0 -
MEMBRANE I MEMBRANE 2
6 -
% I
I
W
0
i
I '0
, 20
, 40
, 60
, 80
4-
l
2-
100
ELAPSED TIME (DAYS)
Figure
7. Chloride permeation constants for experiment
10 o EXPERIMENT
and 12. T h e Ca+2 ion is rejected much more strongly than the C1- ion. I n Figures 9 and 10 the change of the C1permeation constant and water flux, respectively, is shown for experiments 11 and 12. T h e water flux rather than the membrane constant is shown because the large fluctuations in water pressure with time make it difficult to calculate the membrane constant accurately. Figure 11 shows the change in the chloride permeation constant for experiments 13 and 14. Experiment 13 was made on tap water with a p H of approximately 8.3; experiment 14 was made on tap water with the p H adjusted to approximately 6.7. T h e chloride permeation constants for the membranes of experiment 13 show an increase with time, while in experiment 14 the changes are not nearly so rapid. T h e large amount of scatter in the data of experiment 14A is primarily due to the C1- ion; the samples contained only 2 to 10 p.p.m. C1-. T h e water flux for the membranes of experiments 13 and 14 is shown in Figure 12. While the observed change in water flux for experiment 13 is not large, it is larger than for experiment 14.
I1
EXPERIMENT 12
4
i I
I
0
40
80
120
160
200
240
ELAPSED T I M E (DAYS)
Figure 9. Chloride permeation constants for experiments 1 1 and 12
Discussion
T h e performance of modified cellulose acetate membranes may deteriorate with time for any one of several reasons. Loeb and Manjikian (4)have referred to the possible contribution of deposits found in field tests on the membrane surface, and in these laboratory experiments deposits of rust were encountered in the long-term experiments, >20 days. In addition, deterioration can occur because of compaction of the porous membrane layer. Indeed, this effect is almost certainly VOL. 5
NO. 3 S E P T E M B E R 1 9 6 6
215
I
..’
’
EXPERIMENT 138
- __ L 20
A
A
H
0
FOR pH 6.7 AT 23’C
-1
A A
P ”
-
e 0.8
’ 1; ;
P
0.4
Figure 10. Water fluxes for experiments 1 1 and
12
, A A :
FOR pH 6.7
A
AT23-C
AA
A
ELAPSED TIME (DAYS
A
,
, A *
,
I
0.2
A
O A
responsible for the decrease in membrane constant observed in the early parts of the high pressure runs reported here, and a continuing, gradual membrane compaction throughout the experiments may cause the increase in membrane constant to be less than it would be otherwise. However, neither effect can account for the permeability increases of both salt and water observed as the experiments progress. In their early studies of cellulose acetate membranes prepared by another technique, Reid and Kuppers (9) suggested that membrane deterioration resulted from hydrolysis of the cellulose acetate. One of the first indications that the membrane failure encountered here was due to the same effect was the observation that while the membranes were initially acetone- and pyridine-soluble, after some deterioration they became partially insoluble in acetone and in some cases partially insoluble in pyridine. Cellulose acetate is soluble in acetone down to -37 weight % acetyl and in pyridine down to -32 weight % acetyl. While the observation of insolubility was qualitative, it suggested that the acetyl content of part of the membrane was lower than the acetyl content of the bulk of the membrane, and in particular, that even though the acetyl content of the membranes measured at the end of the experiments might not be greatly different from the original value, the surface exposed to the brine might be severely hydrolyzed. Convincing evidence of a heterogeneous hydrolysis of the surface layer was obtained with the aid of an electron microscope (77). On the basis of this information and because ester hydrolysis reactions are known to be acid- and base-catalyzed (7, 3), the reported experiments were undertaken to measure the lifetime under conditions where the pH of the brine was controlled. The hydrolysis of cellulose acetate results in a lower acetyl content, and therefore a larger membrane constant and a larger chloride permeation constant than the starting material. The osmosis data of Lonsdale et al. ( 6 ) give the dependence of the permeabilities to water and sodium chloride (DLCIand DzK in their terminology) on the acetyl content of cellulose acetate. Their data can be represented in the 33.6 to 39.8 weight % acetyl range by the empirical relationships In DICl = -10.7 In a
+ constant
(9)
and In D2K = -29.6 In a 216
+ constant
(10)
I & E C PRODUCT RESEARCH A N D DEVELOPMENT
,I
A
A
0.I 0
50
100
150
200 250
300 3 5 0 400
ELAPSED TIME (DAYS)
Figure 1 1 . Chloride permeation constants for experiments 13 and 14 I
I
I
I
I
20 - 0 EXPERIMENT I3 A EXPERIMENT 138
I
I
-
ELAPSED T I M E (DAYS)
Figure 12.
Water fluxes for experiments 1 3 and 14
where a is the acetyl content expressed as weight per cent. Since the membrane constant, A , is proportional to DIG‘, (Equation 2) and the salt permeation constant, B, is proportional to D2K (Equation 4 ) ,
+ constant In a + constant
In A = -10.7 In a
(11)
In B = -29.6
(12)
and
No attempt will be made to evaluate the constants numerically, because the significance of the zero time intercept of the In A and In B curves, discussed below, is obscured in any case by the existence of an induction period and because substantial differences in the absolute values of D2K are reported by Lonsdale et al. ( 6 ) ,for two methods of measurement. Fortunately, the slope of Equation 10 is essentially the same whether one uses the “osmosis” or the “immersion” values of (6) for DzK.
T h e hydrolysis of these cellulose acetate membranes may be treated as a pseudo-first-order reaction in the acetyl range 34 to 39.8 weight % (72). T h e first-order rate expression is In a/uo = - h t
(13)
where a. is the initial acetyl concentration, a is the concentration a t some time, t , and kl is the first-order reaction rate constant. T h e rate expression must, of course, be written containing molar concentrations; however, in the limited acetyl range of interest here, weight per cent acetyl is nearly proportional to molar concentration within the cellulose acetate. I n the first-order rate expression, the proportionality constant drops out. T h e hydrolysis of cellulose acetate is catalyzed by H + and OH-ions, and the rate, a t 23' C., has a minimum a t a pH of 4.8. Combining the first-order rate expression with Equations 11 and 12 gives In A = 10.7 klt constant (14) and In B = 29.6
klt
+ + constant
(15)
Equations 14 and 15 predict a linear relationship between In A and t , and between In B and t. Such a relationship is observed in the experiments. In all cases there appears to be an indication period before this relationship is encountered. In the case of the high-pressure experiments, the early-time behavior of the membrane constant is largely determined by the membrane compaction already referred to. In the experiments on basic brines, the induction period may be related, at least in part, to the pH gradient across the membrane (see Figures 1, 2, and 11). Because the hydrolysis rate is a strong function of pH, the pH gradient means that the hydrolysis rate is a function of distance into the membrane, so that the surface is being more rapidly hydrolyzed than the bulk of the membrane. Hence, the hydrolysis rate observed in the reverse osmosis experiments on the basic brines may be expected to be lower than that from the kinetic experiments and to increase as the membrane deteriorates and the pH gradient becomes smaller. When the brine is neutral or slightly acid, as in experiments 7 through 10, there is little p H gradient across the membrane (
