CORRELATIONS OF THE REVERSE OSMOSIS SEPARATION DATA FOR THE SYSTEM GLYCEROL-WATER USING POROUS CELLULOSE ACETATE MEMBRANES
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S. S O U R I R A J A N A N D S H O J I K I M U R A Division of Applied Chemistry, National Research Council, Ottawa, Canada The experimental separation data for the system glycerol-water using porous cellulose acetate membranes illustrate the extended validity of the empirical and theoretical correlations tested earlier with systems involving inorganic salts in aqueous solution. The results lead to a useful method of membrane specification in terms of a system of four parameters, a, p, and A and DA,/K6 a t a specified operating pressure; a and p express the pressure effect on the pure water permeability constant A, and the solute transport parameter D A M / K G , respectively. A new method of specifying membrane selectivity also seems possible. Some general equations of process design applicable for the batchwise reverse osmosis concentration process are derived, and illustrated with a typical set of calculations using the experimental data for the system glycerol-water.
of the characteristics of the recently developed porous cellulose acetate membranes (Loeb and Sourirajan, 1963, 1964; Sourirajan and Govindan, 1965) for the separation of glycerol in aqueous solution are summarized here. This work is of interest from several points of view. The experimental data illustrate the possible general applicability of the empirical and theoretical correlations demonstrated earlier (Govindan and Sourirajan, 1966 ; Kimura and Sourirajan, 1967a, 1967b) for the reverse osmosis separation process. Such correlations predict membrane performance from a minimum number of experimental data. Further, they lead to a useful method of membrane specification, and indicate the possibility of developing a new scale of membrane selectivity. The data also illustrate the calculations of some design parameters for the application of the process as a general batchwise concentration technique. OME
Experimental Details
Reagent grade glycerol, and porous cellulose acetate membranes (designated here as CA-NRC-18 type films) made in the laboratory, were used. These films were cast a t -10’ C. in accordance with the general method described earlier (Loeb and Sourirajan, 1963, 1964; Sourirajan and Govindan, 196.) using the following composition (weight per cent) for the film casting solution: acetone 68.0, cellulose acetate (acetyl content = 39.8%) 17.0, water 13.5, and magnesium perchlorate 1.5. The film details, the apparatus, and the experimental procedure have been reported (Sourirajan, 1964; Sourirajan and Govindan, 1965). Membranes shrunk a t different temperatures were used to give different levels of solute separation at a given set of operating conditions. The aqueous glycerol solution (feed) was pumped under pressure past the surface of the membrane held in a stainless steel pressure chamber provided with two separate outlet openings, one for the flow of the membrane permeated solution, and the other for that of the concentrated effluent. A porous stainless steel plate, specified to have pores of average size equal to 5 microns, was mounted between the pump and the cell to act as a filter for dust particles which might otherwise clog the pores of the membrane surface. Unless otherwise stated, the experiments were of the short-run type, each lasting for about 2 hours, and were carried out a t the laboratory temperature. The reported product rates are those corrected to 25’ C. using the relative viscosity and density data for pure 504
I&EC PROCESS DESIGN AND DEVELOPMENT
water. I n most of the experiments, the feed rates were maintained at 380 cc. per minute. I n each experiment, the solute separation, f, defined as
f=
molality of feed ( m l ) - molality of product (md molality of feed ( m l )
the product rate, [PR], and the pure water permeability, [PWP], in grams per hour per 7.6 sq. cm. of effective film area, were determined a t the preset operating conditions. I n all cases, the terms “product’’ and “product rate” refer to the membrane-permeated solutions. The concentrations of the solute in the feed and product solutions were determined by refractive index measurements using a precision Bausch and Lomb refractometer. The accuracy of the separation data is within 1%, and that of the [PR] and [PWP] data is within 3% in all cases. Results and Discussion
Osmotic Pressures, Molar Densities, and Kinematic Viscosities of Aqueous Glycerol Solutions. Table I gives the osmotic pressures, a , molar densities, c, and kinematic viscosities, Y , of aqueous glycerol solutions a t 25’ C. in the concentration range 0.1 to 6.OM. The osmotic pressures were calculated from the relation (Robinson and Stokes, 1959) RT M, a = --m$ 1000
v,
The osmotic coefficient data, $, and the density and viscosity data were taken from the literature (Perry, 1950; Scatchard et al., 1938; Sheely, 1932). Maximum Possible Solute Separations in the Reverse Osmosis Process. T h e effective driving pressure (AP) for fluid flow through the capillary pores on the membrane surface may be given by the relation
AP = P
- An
(2)
where P i s the operating gage pressure, and AT =
RF
-
~p
(3)
is the osmotic pressure of the concentrated boundary solution on the high pressure side of the membrane, and n p is that
np
Downloaded by UNIV OF MANITOBA on September 9, 2015 | http://pubs.acs.org Publication Date: October 1, 1967 | doi: 10.1021/i260024a019
Table 1. Osmotic Pressures, Molar Densities, and Kinematic Viscosities of Aqueous Glycerol Solutions at 25' C. Concmtration of Glycerol Molar Kinematic Viscosity, Mole Osmotic Density, fraction Weight Pressure, MolelCc. Sq . C m ./See. P.S.I. x 102 x 702 Molality X ?03 7c 0 0 0 0 5.535 0.8963 5.505 0.9106 0.1 1.798 0.91 36 0.9287 0.2 3.590 1.81 5.478 72 0.9467 5.375 2.69 108 0.3 5.450 5.422 0.4 0.9647 144 7.154 3.55 0.5 8.927 4.40 0.9876 181 5.395 5.368 0 6 1 ,0054 217 10 693 5 24 0 7 1 ,0282 253 12 453 6 06 5.341 1 ,0480 290 0 8 14 207 6 86 5.315 5.288 15 955 7 65 1 ,0688 326 0 9 1,0865 1.0 17.696 8.43 5.262 363 1.1268 5.212 1.2 21.160 9.95 436 1.1668 5.163 1.4 24.600 11.42 510 1.2116 5.115 1.6 28.016 12.84 584 1.2559 5.069 1.8 31.408 14.22 658 5.023 2.0 34.777 15.55 1 ,3004 732 4.914 1.4202 2.5 43.096 '18.72 91 9 4.811 21.65 1107 1.5485 3.0 51.273 4.714 1295 24.38 1 ,6874 3.5 59.312 1 ,8207 4,622 1485 4.0 67.216 26.92 1675 1 ,9646 4,535 4.5 74 988 29 30 1866 2.1167 4.453 5 0 82 631 31.53 4.375 2059 2.2771 5.5 90 149 33 62 2,4459 4.300 6 0 97.545 35.59 2252
of the product solutiori As the feed rate on the membrane surface approaches infinity, rF approaches the osmotic pressure of the feed solution. When P is equal to o r less than rF, Equation 2 gives also the maximum solute separ,ition possible in this process whatever be the membrane used, under which condition Air
:=
P and L P = 0
(4)
Using Equation 4, and letting rF = osmotic pressure of the feed solution, Figure 1 gives the plots of the maximum solute
separation possible (fmSx) for the system glycerol-water a t different operating pressures and feed concentrations. Figure 1 illustrates the thermodynamic significance of osmotic pressure as applied to this separation process. 'CVhen P is equal to or less than r p , the values off,,, given in Figure 1 correspond to the condition that the product rate is zero; when P is greater than rF there is no thermodynamic limitation 01-1the extent of solute separation and product rate obtainable ii I this process. \Yhile Equation 2 is true whatever be the value of the osmotic pressure of the feed solution, it says nothing about the separation characteristics of any membrane. I n other words, the actual performance of any particular membrane with respect to a given solution system depends, not on the osmotic pressure of the feed solution, but on the physical and chemical nature of the membrane. Range of Experimental Data. For a given membrane material- solution system, the reverse osmosis separation process is best understood only in terms of the entire 0 to 100% range of solute separation; further, it is the intermediate range of separation which offers the real testing ground for any hypothesis concerning the transport of material through porous membranes having separation properties. Consequently in this work, the characteristics of 12 different membranes, chosen to give a wide range of solute separations (f = 0 037 to 0.995),\yere studied involving an operating prmsure range of 125 to 1.500 p.s.i.g., feed concentration range of 0.25 to 4.0M, and f e d flow rate range of 25 to 725 cc. per minute. Application of Some Empirical Correlations of Data for the System Glycerol-Water. Following the work of Govindan and Sourirajan (1366), the applicability of the following relations was tested for correlating the experimental separation and product rate data for different films: EFFECTO F PRESWRE alp =
ZP-+7
0' .9' O K
EFFECTO F FEEDCONCEKTRATIOS Oa7;
0.6
I
(7) !\:hen [PR] represents [ P W P ] ,AP = P, and the form of Equations 6 and 7 still holds. Combining the [ P W P ] data, Equation 7 becomes
0.5 -
fmax.
0*3[11//,//
SYSTEM:GLYCEROL-WATER
0.2
0
500
1000
1500
OPERATING PRESSURE p a s .i.g.
Figure 1. Maximum possible solute separations for the system glycerol-water in the reverse osmosis process a t different operating pressures and feed concentrations
In Equations 6, 7, and 8, AP is based on the osmotic pressure of the feed solution; hence the left side of Equation 8 may be considerrd a measure of the concentration polarization on the high pressure side of the membrane. The results of the correlations are shown in Figures 2$3, and 4. 1he straight-line plots of l / f us. 1 / P (Figure 2), e-'IPmax us. { ( [ P R ] , ' S P )p / p 1 (Figure 3), and the left side of Equation 8 us. feed molality on a log-log scale (Figure 4),confirm the validity of I'qiiations 5, 6: and 7 for the system glycerol-water for the range of pressure and feed concentration tested. The fact VOL. 6
NO. 4
OCTOBER 1 9 6 7
505
12
-
II
-
IO
-
FEED MOLALITY
:
0.5
M
FILM
FEED
II FILM TYPE : CA-NRC-18 SYSTEM : GLYCEROL-WATER FEED RATE : 380 cc/minute
NO. 31
MOLALITY: 2.0
M
OPERATING PRESSURE: P p.s.i.g.
9-
87
-f I
8FILM NO. 35
-
7-
6-
-1 6 -
5-
5-
30
f
29
Downloaded by UNIV OF MANITOBA on September 9, 2015 | http://pubs.acs.org Publication Date: October 1, 1967 | doi: 10.1021/i260024a019
43-
Q)
2I -
0
I I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
0
1
2
3
5 IO
6
7
8
3
Effect of operating pressure on solute separation for the system glycerol-water
that the films tested involved a wide range of solute separations (f = 0.086 to 0.995) indicates that Equations 5, 6, and 7, though empirical in nature, have a firm experimental basis. Using the experimental data a t two different pressures and two different concentrations, Equations 5 and 6 can predict the effect of pressure on solute separation and product rate, and Equation 7 can predict the effect of feed concentration on product rate (provided the corresponding separation data are available), under otherwise identical operating conditions. However, the above equations do not predict solute separation as a function of feed concentration, nor membrane performance as a function of feed flow rate. In spite of these limitations, the simplicity and validity of the above equations make them useful in membrane research and process development. Flow of Fluids through Porous Membranes Having Separation Characteristics. A more useful set of correlations is given by the analysis of Kimura and Sourirajan (1967a). This analysis is based on a generalized capillary diffusion model for the transport of solute through the membrane, applicable for the entire possible range of solute separations in the reverse osmosis process. I t is considered that when the size of the pores on the membrane surface is only a few times bigger than the size of the permeating molecules, and the interfacial forces are important enough to cause solute separation, the transport of solvent water through the porous membrane is proportional to the effective pressure, and that of the solute is due to pore diffusion and hence proportional to its concentration difference across the membrane. Accordingly, in the transport equation for solvent water, the effective 506
4 1 --x P
Lx IO P Figure 2.
3
I&EC PROCESS D E S I G N A N D DEVELOPMENT
pressure is based on the osmotic pressure of the concentrated boundary solution, and the proportionality constant is obtained from the pure water permeability data which involve no concentration polarization. The above analysis gives rise to the concept of two interconnected parameters, A (the pure water permeability constant), and DA,+I/K6 (the solute transport parameter) which characterize a particular membrane-solution system with reference to this separation process. Both A and DAAlf/K6 are dependent on the porous structure of the membrane surface, and hence they are different for different membranes; both are functions of operating pressure, and in addition, DA,w/K6 is dependent on the chemical nature of the solute. Since the solute in the concentrated boundary solution also diffuses back to the feed solution, a mass transfer coefficient, k , characteristic of the flow conditions on the high pressure side of the membrane, can be calculated. The analysis gives rise to the following basic equations relating A , DA.MIK6, and k (Kimura and Sourirajan, 1967a) :
A=
ljrB
=
[PLVP] M , X 7.6 X 3600 X P A[P
- T(xA2)
+
r(xA8)]
(9)
(10 )
26 24
FILM NO. 31
FILM NO. 31
SYSTEM: G L Y C E R O L - W A T E R F E E 0 RATE
X
N
0 x
*’
-
/-
e-
/-
9
9
FEED
12
MOLALITY: 2.0
M
12c
IO
0
10
8 Downloaded by UNIV OF MANITOBA on September 9, 2015 | http://pubs.acs.org Publication Date: October 1, 1967 | doi: 10.1021/i260024a019
380 c c / m i n u l e
*‘
‘6
x i 1 4 &
:
18
P/d’
16
7
20
/*
18
2
22
/“
20
FEED MOLALITY: 0.5 M
24
FEED:PURIZ WATER
22
N
/26
8 dO-O
6
6
4
2
-
1
0.5
0.4
0.6
I
I
I
0.7
0.8
0.9
1 2 1.0
I
I
I
I
I
0.4
0.5
0.6
0.7
0.8
e- ”l 5 O0 Figure 3.
e
I
qq \
0.4
0.5
e
0.6
0.7
-P/1500
Effect of operating pressure on pure water permeability and product rate for the system glycerol-water
0.5 0.4 -
I .o A A0
I
I
FILM T Y P E : C A - N R C - I 0
PURE WATER PERMEABILITY DATA
0.9 0.8
0.7
0.6
On3
0.15
2
- P / I500
0.6
-
I 0.9
0.5 I
31
0,0054 I
I
20
40
1
I
60
80
100
-
