Ind. Eng. Chem. Process Des. Dev. 1904, 23, 674-684
674
and that after the transition to film boiling such fluxes do not occur again until the temperature.difference reaches 10 000 OF. Thus the assumed value, Q = lo6 Btu/(h ft2) is a maximum plausible estimate. We may further compute that if there had been no volume expansion, the internal energy of the fluid in the heated section would be rising by (37) which for this example is
In the time to reach maximum pressure the internal energy increase is 138 Btu/(lb, s) X 0.05 s = 6.9 Btu/lb,. For the fluid like LPG this would raise the temperature by about 12 "C. Thus, even using this highest plausible heat flux, we see that in the length of time it takes the liquid to vent, through a 100-ft pipe, the temperature would only be expected to rise about 1 2 O . This entire calculation assumes that the pressure is relieved by driving the adjacent fluid away from the heated section. It takes no account of the stretching of the walls of the heated section and the adjacent section due to the increased pressure in the fluid. That would tend to lower the maximum pressure, so that this calculation tends to overpredict the maximum pressure. Neither does it consider the possibility of vapor formation, because the formation of vapor in this circumstance would be accompanied by a lowering in the pressure. Spontaneous nucleation, as occurs in smelt-tank explosions and LNG noncombustion explosions (Reid, 1979), can only occur with substantial superheat, which is not expected in the situation of inertially confined high-rate heating.
Conclusion
It appears that this proposed mechanism for generating the necessary pressures to rupture a pipe is implausible. Other mechanisms must be sought. Nomenclature
a = group of variables defined by eq 14, psi/s b = group of variables defined by eq 15, l / s 2 c = group of variables defined by eq 31, l / s c = heat capacity at constant pressure, Btu/(lb, OF)
8 = pipe diameter, ft
F = force, lbf L = length of unheated pipe section, ft m = mass of fluid on length x o at time t o = 0, lb,; also used in eq 3 only as mass of fluid in section L at time t = 0 P = pressure, psia Po = pressure in system at t = 0, psia Q = heat, Btu Q = heat flux, Btu/(h ft2) t = time, s T = temperature, O R or K u = internal energy per lb,, Btu/lb, u = velocity, ft/s V = volume, ft3 u = specific volume, ft3/lb, W = work, ft lbf or equivalent x = distance, f t xo = length of heated section, ft po = original density of fluid in heated section, lb,/ft3 L i t e r a t u r e Cited Hougen, 0. A,; Watson, K. M.;Ragatz, R. A. "Chemical Process Principles", Vol. 11, 2nd ed.; Wiley: New York, 1959; p 545. Kreith, F. "Principles of Heat Transfer", 3rd ed.; IEP. New York, 1973. Pitt, C. Report on Trlp Made to the Southwest Research Institute to Observe the Preliminary Analysis Made on a Failed Anaconda Connector and Examination of the Failed Parts, private communication. Reid, R. C. Science 1979, 203 (No.4386), 1263-5. Starling, K. E. "Fluid Thermodynamic Properties for Light Petroleum Systems"; Gulf Publishing Co.: Houston, 1973.
Received for review August 30, 1982 Revised manuscript received November 8, 1983 Accepted December 27, 1983
Predictability of Performance of Reverse Osmosis Membranes from Data on Surface Force Parameters Takeshl Matsuura, T. A. Tweddle, and S. SourIraJan" Division of Chemistty, National Research Council of Canada. Ottawa, Canada K I A OR9
Reverse osmosis data of many inorganic and organic solutes from aqueous and nonaqueous solutions by cellulose acetate and aromatic polyamidohydrazide membranes were collected, and force constants associated with steric hindrance, electrostatic repulsion and van der Waals attraction were generated from appropriate reverse osmosis and liquid chromatography data. These force constants enable the prediction of reverse osmosis and ultrafiltration data for many different membrane-solvent-solute systems.
Introduction
The separations of inorganic and organic solutes from aqueous and nonaqueous solutions by reverse osmosis and ultrafiltration processes are of practical and fundamental interest. Most of the water pollution control and wastewater treatment applications require the removal of many inorganic and organic solutes from dilute aqueous solu0196-4305/84/ 11 23-0674$01.50/0
tions, while the removal of trace amounts of solutes from alcoholic solvents abates the metallic corrosion when alcohols are used as combustion engine fuels (A.P.I. Report, 1976; Foulkes, 1977). From a fundamental point of view, on the other hand, the effect of the interaction forces working in a membrane material-solvent-solute system and that of average pore size and pore size distribution on
Published 1984 by the American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
reverse osmosis and ultrafiltration performance are of special importance, since appropriate transport equations which involve these factors enable us to interpret and predict the membrane performance data. Aside from the works of this laboratory (Matsuura et al., 1981a,b, 1983; Matsuura and Sourirajan, 1981) those of Martynov et al. (1981) and Zeman and Wales (1981) take into consideration the above factors in connection with transport through porous membranes. In our previous papers (Matsuura et al., 1981a,b, 1983) the method of obtaining force constants A, B, and D, which are associated with the electrostatic force, the van der Waals force, and the steric hindrance, respectively, from the combined data of reverse osmosis and liquid chromatography experiments was described. These interaction force constants enable us to calculate the reverse osmosis and ultrafiltration performance data including the solute separation and the (PR)/(PWP) ratio for a given average pore size and pore size distribution in conjunction with transport equations which are developed on the basis of the surface force-pore flow model (Matsuura and Sourirajan, 1981; Matsuura et al., 1981a). This paper is an extension of the above works, where force constants A, B, and D are generated for many inorganic and organic solutes with respect to cellulose acetate (Eastman E-398, abbreviated below as CA-398) and aromatic polyamidohydrazide (PPPH 8273) (Matsuura et al., 1977) materials, when either water or methanol is used as solvent. These force constants, collected and presented in this paper, enable the prediction of reverse osmosis and ultrafiltration data for the membrane material-solventsolute systems involved. In addition to generation and listing of interaction force parameters, several combinations of parameters associated with steric hindrance and van der Waals attractive forces are used for simulated calculation in order to study the effecta of such interaction forces, the average pore size and the pore size distribution, and the operating pressure on the reverse osmosis and ultrafiltration data. The calculation is conducted with respect to dilute solution systems for purposes of illustration. Such a study is also relevant for the removal of trace organic contaminants for aqueous or nonaqueous solutions. The range of the force contant D, which can be approximated as the radius of solute m, molecule, covered in this calculation is from 2 X corresponding to the Stokes law radius of ethyl alcohol (2.05 X 10-lo m), to 30 X 10-lo m, corresponding to the Stokes law radius of pepsin (28 X m). While the former molecule is usually treated by reverse osmosis membranes of very small pore sizes, the latter molecule is treated by ultrafiltration membranes. Thus, the applicability of the approach to both reverse osmosis and ultrafiltration is illustrated in this paper. Theoretical Section Interfacial Interaction Force Potential Function and Its Relation to Liquid Chromatography Data. The interaction force working between the membrane polymer material and the solute can be expressed by the following potential functions. In the case of an electrolyte solute the potential 4 is expressed by 4 = very large (when d 5 D) (la) 4 = (A/d)RT (when d > D) (1b) While eq l a represents the steric hindrance working on the electrolyte solute, eq l b describes the electrostatic repulsive force working on an ionic solute from the interface between two phases of different dielectric constants (Onsager and
675
Samaras, 1934). The quantity A is the force constant associated with the electrostatic repulsion. In the case of a nonionized organic solute the potential function is expressed by
4 = very large
(when d ID)
4 = -(B/d3)RT
(when d
> D)
(24 (2b)
Equation 2a represents the steric hindrance working on the solute molecule and eq 2b describes the van der Waals force working from the polymer surface (regarded as a flat surface) onto the solute molecule (regarded as a point) (Israelachivili and Tabor, 1973). The quantity B is the force constant associated with the van der Waals force. These potential functions can be related to the surface excess of the solute, r, by (Chuduk et al., 1981)
r -- &:m,(e-4’RT _ cA
- 1) d(d)
(3)
Note that the integration starts from Dsolvent instead of zero, since in the range of distance zero to DmlWt from the polymemlution interface, no continuous phase of solvent exists. The quantity r/cA which appears on the left side of eq 3 is further related to the liquid chromatographic (LC) data on retention volumes by (Chuduk et al., 1978)
r
CA
= ~[vR’lsolute -
[VR’l~olvent~/A
(4)
when the solute concentration used in the chromatography experiment is sufficiently dilute. The quantity [ VR’]&ent is represented by the retention volume of deuterated solvent; i.e., D20 or CH30D, while the surface area of polymer powder in the chromatography column, A, can be obtained experimentally either by gas chromatography (Matsuura et al., 1983) or by adsorption experiment (Matsuura and Sourirajan, 1978). The surface area A used in this work was 224.8 m2 (0.92 g), 92.0 m2 (0.6 g), and 792.6 m2 (1.0 g) for CA-39&water, CA-398-methanol and PPPH 8273-water systems, respectively. Membrane Transport Equations on the Basis of Surface Force-Pore Flow Model. The most essential data obtained from reverse osmosis and ultrafilatration experimentsare solute separation, f , pure water permeation rate, (PWP), and the permeation rate (PR) of product solution. The experimental solute separation is based on the solute concentrations in the feed solution, CAI, and in the product solution, cA3, as expressed by f=-
cAl
- cA3 cAl
(5)
However, this quantity is not adequate to express the actual solute separation taking place by the membrane pore, since the concentration at the membrane-solution boundary phase is different from the bulk of the feed solution, as a result of solute and solvent mass transfer at the boundary phase. Based on the solute concentration in the boundary phase which is designated as cA2,another solute separation, f‘, can be defined as f‘=
cA2 - cA3 CA2
(6)
I t is known that these two separations, f and f’, are related to each other by (Matsuura and Sourirajan, 1981)
f‘
f
= f’
+ (1- f ’ ) exp(u,/k)
(7)
676
Ind. Eng; Chem. Process Des. Dew, Vol. 23, No. 4, 1984
the solute separation f’can be expressed as
and the dimensionless radial velocity profile in the pore, a ( p ) , is obtained by solving the differential equation Figure 1. Schematic illustration of the membrane pore.
where us designates the linear permeation velocity of the solution through membrane and can be calculated by
(PR)
v, = -
(8) 36008 The mass transfer coefficient of the solute, k, is approximated by
(9) (Matsuura et al., 1974). The mass transfer coefficient of NaCl for the particular reverse osmosis equipment and the solution velocity used for the experiment can be obtained by applying Kimura-Sourirajan’s analysis to experimental reverse osmosis data with sodium chloride solution (Sourirajan, 1970). Before presenting the transport equations, the concept of two radii, Ra and Rb, has to be clarified. As the cross section of the cylindrical membrane pore is illustrated in Figure 1,the entire area of the pore is not utilized for the transport. There is an area into which the center of solvent molecule cannot enter due to its collision onto the pore wall. This area is illustrated in Figure 1as the area surrounded by coaxial circles of radii Ra and Rb, where = Ra + Dsolvent (10) It is assumed that a laminar solvent flow develops in the area surrounded by the small circle. On the other hand, the interaction force between membrane pore wall and the solute molecule is exerted from the circumference of the larger circle of radius Rb Using the above concept, the surface force-pore flow model leads to the following equations for reverse osmosis transport (Matsuura and Sourirajan, 1981; Matsuura et al., 1981a). Defining the following dimensionless quantities dimensionless radial distance
d2&) dp2
P
= r/Ra
(11)
CAb) = cA3(r.)/cA2
(12)
dimensionless solution velocity in the pore = UB(r)h.AB/RT
(13)
dimensionless solution viscosity
81 = q / x A B R z c A 2
(14)
dimensionless operating pressure 82
= P/RTCA2
dr)/RT
d~
81
81
- 1)-
with boundary conditions d 4-P ) - 0 dP
a(p) = 0
(whenp = 0)
(20)
(when p = 1)
(21)
The dimensionless potential function used in eq 17-19 is given by: for an electrolyte solute b(p) = very
large
{ f:
when - - p IE) (22a) Ra
for a nonionized organic solute @(p)
= very large
(234
Equations 22a, 22b, 23a, and 23b are the dimensionless forms of eq la, lb, 2a, and 2b, respectively. The friction parameter (b), which appears in eq 17-19, is defined as the ratio of the frictional force working on the solute molecule moving in the membrane pore to that in the bulk solution and can be given by the empirical expression (Matsuura et al., 1981a) b= (when X 5 0.22) 1/(1- 2.104X + 2.09X3 - 0.95X5) (24a) b = 44.57 - 416.2X + 934.9X2 + (when 1 > X 302.4X3
> 0.22) (24b)
where X = D/Rb
(15)
dimensionless potential function NP) =
P
where
Rb
dimensionless solute concentration at the pore outlet
d4P) 8 2 + -1 + - + -1 (1- e-*‘”)(C,(p)
(16)
Equation 24a is based on the Faxen equation (Faxen, 1959),while eq 24b was developed in an attempt to connect the above equation to the data by Satterfield et al. (1973) on the restricted diffusion of solutes in the micropores.
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 677
Furthermore, the ratio (PR)/(PWP) is given by
Determination of Data on Average Pore Size (Rb) on the Membrane Surface. For the purpose of this determination, an appropriate organic solute was chosen as a reference solute, and its Stokes law radius was equated to D for use in eq 2. Then using the data on r/c, from the liquid chromatography (LC) experiment, the quantity B for the reference solute was calculated from eq 3. Values of B and D so obtained for the reference solute were then used in the reverse osmosis transport eq 17 (along with the related expressions given by eq 7-16 and 18-25) to obtain data on R b following the sequence of calculation outlined by Matsuura et al. (1981a). A reasonably high solute separation in reverse osmosis and a value of r/cAnot too much higher or lower than zero were the criteria for the choice of the reference solute. On this basis, glycerol and N,N-dimethylbenzylamine were chosen as the reference solutes for water and methyl alcohol solvent systems, respectively. Determination of Data on A, B, and D. The force constants A, B, and D should be expected to be dependent only on the chemical nature of the surface of the membrane material, solute, and solvent and independent of the porous structure of the membrane. Consequently, the above parameters for different combinations of membrane material-solvent-solute could be determined from the appropriate LC data and reverse osmosis or ultrafiltration data for any membrane sample of the particular membrane matekial under consideration, if the pore radius of the membrane sample is determined by the foregoing procedure, following the computational technique described by Matsuura et al. (1981a). Prddictability of Solute Separation and Product Rate Data in Reverse Osmosis. Using the B and D values for the nondissociated organic solutes and the A and D values for the electrolyte solutes, one can predict reverse osmosis separation and product rate data for any combinatiofl of solute-solvent-membrane material systems for which the force constants are presented for any average pore size of the membranes using eq 7-26, following the calculation procedure reported in Matsuura et al. (1981a). Inclusion of Pore Size Distribution in the Transport Equations. For the purpose of integrating the pore size distribution into the transport equations, normal distribution of pores on the membrane surface is assumed. Let R b represent the mean pore radius and u represent standard deviation. The pore size distribution function Y(R) can be written as
With such distribution of pores, solute separation, f', can be calculated by (Matsuura and Sourirajan, 1981)
Furthermore, the (PR)/(PWP) ratio is given by
Accordingly, eq 28 and 29 are used instead of eq 17 and 26 in the prediction of solute separation and (PR)/(PWP) ratio, when the pore size distribution is taken into consideration. In the actual calculation thejower and the higher integration limits for Y(R) were R b f 2a which covers 97% of the entire pore distribution.
Results of Calculation and Discussion The interfacial interaction constants A, B, and D were calculated for different inorganic and organic solutes (including macromolecdes) in aqueous solution with respect to cellulose acetate (Eastman E-398, abbreviated below as CA-398) and aromatic polyamidohydrazide PPPH 8273 (abbreviated below as PPPH 8273) materials and the results are listed in Tables I and 11. In the case of CA-398 material, calculations were also made for methanol solvent system and the results are listed in Table 111. The results show that with respect to nonionized organic solutes, the values of B and D are independent of average pore size on the membrane surface ( R b or R b ) for both the CA-398 and the PPPH 8273 membranes, and also for both water and methanol solvent systems (Tables I and 111). With respect to ionized inorganic solutes, the constancy of A and D values for each solute appears to depend on the nature of the membrane material, solvent, and the magnitude of the value of R b or &,; for example, the available results show that for the CA-398 membranes involving aqueous solutions, the values of A increased and the corresponding values of D decreased with increase in pore size on the membrane surface in the Rb range 8 X to 11.2 X lo-" m (Table 11); for the CA-398 membranes involving methanol solutions, the values of A and D did not change significantly for R b values in the range 11x W0to 13 x W0 m (Table 111); and, for the PPPH 8273 membranes involving aqueous solutions, the values of A and D did not change significantly for the R b values in the range 3.7 X 10-loto 8.8 X m. Since one would naturally expect that the interfacial parameters A, B, and D to be independent of pore size on the membrane surface, the latter observations on the variations of A and D with R b call for an explanation. When the surface of a reverse osmosis membrane is in equilibrium with an electrolytic solution, in general, each ion is repelled from the membrane surface to different extents, thus setting up an electrical double layer at the membrane-solution interface; in this double layer, the ionic concentrations and the electrical potentials are highly nonuniform. In other words, eq l a and l b must strictly be applied for each individual ion, and the numerical values of A and D must strictly be generated for each individual ion; the values of A and D so generated may naturally be expected to be functions of the chemical nature of the ion, solvent and membrane material, and independent of the porous structure of the membrane surface. The values of A and D were calculated in this work for each ionic solute (and not for the individual ions involved in the solute); hence the values of A obtained in this work can only represent some kind of a mean of the corresponding values of A for the ions involved in the solute, and any change in the value of A also brings about a change in the value of D by virtue of their interrelationship in the method of calculation. Since the profile of the variation of A and d (distance from the pore wall)
678
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
Table I. Interfacial Force Constants and Other Physicochemical Quantities Pertinent to Solutes in Aaueous Solutions Stokes law" CA-398 polymerC PPPH 8273 polymer D , X los, radius X lolo, r/cA X lolo, D x 1O1O, A X lolo, r/cA x 1O1O, D x 1O1O, A x solute mz/s m m m m m m m Inorganic Solutes LiF 1.213 2.01 -3.64 2.905" 0.465' LiCl 1.367 1.79 -3.30 2.694 0.418 LiBr 1.378 1.77 -4.75 2.573 0.868 NaF 1.401 1.74 -2.86 2.929 0.230 NaCl 1.611 1.52 -3.23 2.812 0.367 NaBr 1.626 1.50 -1.07 2.807 0.238 NaI 1.616 1.51 -1.79 2.800 0.039 KF 1.683 1.45 -4.70 2.790 0.806 KCl 1.995 1.22 -2.16 2.894 0.037 1.21 -1.79 2,900 0.068 KBr 2.018 RbCl 2.052 1.19 4.36 3.164 -1.773 CSCl 2.045 1.19 3.75 3.108 -1.598 CsBr 2.070 1.18 3.94 3.047 -1.621 Stokes lawb CA-398 polymer PPPH 8273 polymer D, x IOs, radius x lolo, r / c A X lolo, D X lolo, B X loM, r/cA X lolo, D X 1O1O, B X lom, solute m2/s m m m m3 m m m3 Organic Solutes methanol 1.69 1.45 0.732 1.85 8.31 1.89 1.41 5.71 ethanol 1.19 2.05 21.54 5.88 4.50 2.03 1.94 21.99 1.15 1-propanol 2.12 37.77 13.16 2.15 12.17 2.13 36.40 2-propanol 1.08 2.26 9.62 38.40 5.36 2.45 3.06 89.74 1.05 1-butanol 2.33 47.27 35.20 2.10 58.34 2.57 95.50 1.05 2.33 2-butanol 62.15 20.46 2.45 26.72 3.14 134.6 0.80 2-methyl-1-propanol 3.05 35.43 95.57 30.45 2.75 3.78 243.6 2-methyl-2-propanol 0.73 3.35 134.3 8.52 3.67 5.87 3.79 132.2 0.93 1-pentanol 2.63 221.88 3.75 361.3 1.24 1.97 1- hexanol 56.76 209.29 1.97 1.91 acetone 1.28 26.90 12.43 1.91 18.56 2.22 47.16 methyl ethyl ketone 1.08 1.92 35.87 31.42 1.92 39.35 2.39 71.38 methyl isopropyl ketone 0.943 2.59 83.67 65.77 2.45 87.38 4.02 360.9 methyl isobutyl ketone 0.853 2.86 97.88 139.56 2.45 cyclohexanone 0.883 2.77 120.8 91.11 2.72 diisopropyl ketone 0.786 3.11 131.7 260.87 2.62 1.19 methyl acetate 2.05 36.30 1.73 27.88 35.56 2.58 85.88 ethyl acetate 1.02 2.39 36.41 59.93 1.83 56.25 2.90 132.7 propyl acetate 0.91 2.68 144.57 3.46 265.3 ethyl propionate 0.91 2.68 126.64 1.88 45.63 ethyl butyl ether 0.834 2.93 50.66 2.53 86.45 ethyl tert-butyl ether 0.834 2.93 901.2 184.68 5.30 0.767 isopropyl tert-butyl ether 3.18 918.2 101.84 5.60 propionamide 2.24 1.09 3.90 1.98 19.13 acetonitrile 1.47 28.49 1.66 29.72 1.78 propionitrile 1.32 1.85 34.20 61.14 1.78 nitromethane 1.65 1.48 67.23 1.80 36.00 1-nitropropane 1.22 2.00 65.76 257.93 2.05 1.16 phenol 2.10 45.39 705.00 1.71 resorcinol 2.74 0.89 45.16 521.27 1.73 aniline 2.42 1.01 48.98 431.87 1.80 2.99 dimethyl aniline 0.816 125.8 446.22 2.50 2.11 1,2-ethanediol 1.16 -2.93 2.20 -16.82 glycerol 1.06 2.30 -52.30 -4.63 2.30 2,3-butanediol 0.994 2.46 -1.46 2.75 -11.97 xylitol 0.815 -135.0 3.00 -6.57 3.30 1,2,6-hexanetriol -16.95 0.796 3.07 -3.16 2.82 du 1cito1 0.737 3.31 -5.50 2.16 -104.4 D-sorbitol 0.739 -7.55 4.64 -180.2 3.30 D-glucose 0.67 3.66 -7.79 3.36 -203.1 -4.47 -67.94 2.29 D-fructose 0.758 -7.55 4.51 3.22 -181.6 sucrose 0.52 -9.50 5.11 -343.2 4.67 maltose 0.49 -346.0 4.98 -9.50 4.98 polyethylene polyethylene polyethylene polyethylene polyethylene polyethylene polyethylene bacitracin a-casein pepsin albumin y-globulin
glycol-600 glycol-1000 glycol-1500 glycol-2OOO glycol-3000 glycol-4OOO glycol-6000
0.389 0.309 0.245 0.214 0.174 0.159 0.976 0.110 0.067 0.087 0.057 0.048
6.27 7.89 9.95 11.43 14.06 15.34 25.00 22.10 36.71 28.06 38.70 56.28
Macromolecular Solute -4.47 6.27 -4.75 7.89 -5,51 -6.03 -6.72 -8.48
11.43 14.06 15.34 25.00 22.10 36.71 28.06 38.70 50.00
69.6 254.6 1119 2408 3053 16283 419X103 1196X103 874X103 1307Xlo3 1382Xlo3
-4.94
6.27
-3.09 -1.86 -0.62 -1.24 -1.24
9.95 11.43 14.06 15.34 25.00
599.8 2194 3313 6012 7536 29575
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 679
Table I (Continued) "The A and D values given for the polymer material PPPH 8273 are applicable to Rb values in the range 3.7 Obtained from solute DAB. See Table I1 for these values.
to 8.8
X
m.
X
Table 11. Interfacial Force Constants and Other Physicochemical Quantities Pertinent to Inorganic Solutes in Aqueous Solutions (Polymer Material, Cellulose Acetate CA-398) D or A D~ x 109, Stokes law r/cA x lolo, x lolo, Rb x lolo, ma solute m2/s radius X lolo, m m m 8.07 8.73 9.47 10.33 11.21 4.15 3.61 3.47 LiF 1.213 2.01 -6.62 D 4.67 4.09 1.09 1.23 1.26 A 0.949 1.11 3.41 3.19 3.11 LiCl 1.367 1.79 -6.34 D 3.65 3.62 1.12 1.13 1.18 1.23 1.25 A 3.23 3.05 3.00 LiBr 1.378 1.77 -6.62 D 3.52 3.46 A 1.25 1.26 1.31 1.35 1.36 3.74 3.56 3.41 NaF 1.401 1.74 -6.62 D 3.91 3.86 A 1.15 1.17 1.20 1.24 1.27 3.74 3.74 3.54 3.27 3.21 NaCl 1.611 1.52 -6.34 D A 1.10 1.16 1.15 1.21 1.22 3.80 3.70 3.47 3.33 3.12 NaBr 1.626 1.50 -5.76 D A 0.895 0.920 0.976 1.011 1.058 3.30 3.13 3.01 NaI 1.616 1.51 -4.89 D 3.53 3.46 A 0.686 0.703 0.746 0.787 0.814 KCl 1.995 1.22 -6.34 D 3.88 3.93 3.58 3.33 3.30 A 1.07 1.05 1.14 1.20 1.20 KBr 2.018 1.21 -5.76 D 3.82 3.83 3.52 3.26 3.26 A 0.888 0.888 0.963 1.03 1.03 RbCl 2.052 1.19 -5.47 D 3.97 4.02 3.77 3.49 3.50 A 0.757 0.742 0.810 0.881 0.879 3.99 3.96 3.85 3.60 CSCl 2.045 1.19 -5.76 D A 0.844 0.852 0.882 0.945 CsBr 2.070 1.18 -6.34 D 3.91 3.94 3.63 3.39 3.43 A 1.058 1.05 1.13 0.774 1.17 'These data may be expressed by the following empirical equations: D = -0.171Rb + (A)R,,,B.WX~O-~'' - 0.33 X lo-''.
can be Significantly different for different ions, membrane materials and solvent systems, the mean value of A for the ionic solute must naturally change with change in d and hence the average pore size on the membrane surface (fib or &,); that is what is observed experimentally as shown in Table 11. On the other hand, when the value of A for the solute is not significantly different from the corresponding values of A for the ions involved, no significant variations in A and D with Rb may be observed; this is obviously the case with respect to the data on A and D presented for the inorganic solutes in Tables I and 111, which data,however, must be considered valid strictly for the indicated ranges in the values of average pore size on the membrane surface (fib or This problem of observed variations of A and D with &,or R b is an important one with respect to all ionized solutes whether they are inorganic or organic; this problem will be even more important if the membrane material involved is also a charged one, in which case ionk concentration in the feed solution will have an added effect on A and D. Therefore, a detailed analysis of this problem is called for. In the meanwhile, the data presented in Tables I, 11, and I11 have practical value, and they are strictly valid for dilute solutions and for the indicated range of pore sizes on the membrane surface in the interfacial systems involved. A few solutes, namely NaC1, i-PrOH, and phenol, were chosen arbitrarily to test the validity of the A, B, and D values generated in this work. Figure 2 shows the effect of pore radius on solute separations and (PR)/ (PWP) ratio calculated from the transport equations for the specified operating conditions using the values of A, B, and D generated in this work for the above solutes; a set of corresponding experimental reverse osmosis data obtained with CA-398 and PPPH 8273 membranes is also included
ab).
+
(D)~b.s.07Xlo-101.380
CELLUUISE ACETATE CA-398
-
CALCD RJNTS EXPTL
0
2.0
(10
10.0
11.0
A = 0.041Rb +
X
AROMATIC FOLYAMIDOHYDRAZIDE PPPH 8273 ,
4.0
3.0
PORE RADIUS ( R b )
I
5.0
6.0
7.0
8.0
9.0
IO".m
Figure 2. Separations and (PR)/(PWP) ratios of some solutes at different average pore sizes: operating pressure, 1724 kPag (= 250 psig); feed concentrations for NaCl5 mol/m3; for isopropyl alcohol and phenol, 1mol/m3; feed flow rate, equivalent to kNaCl= 10-40 X 10" m/s.
in Figure 2 for comparison. The good agreement between the calculated and the experimental data testifies to the essential validity of the numerical values of the parameters involved. It may be noted that the range of the average pore size for membranes of CA-398 material is considerably larger than that for PPPH 8273 material, which accounts for relatively high separations of nonionized organic solutes (such as 2-propanol and phenol) by membranes made of the latter polymer materials. The significantly lower D and A values for PPPH 8273 material than those for CA398 material, however, maintain the separation of sodium chloride by membranes of both materials at about the same level. Some Results on Parametric Studies. On the basis of the validity of the parameters listed in Tables I, 11, and 111, the separation and the (PR)/(PWP) ratio were cal-
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Table 111. Interfacial Force Constants and Other Physicochemical Quantities Pertinent to Methanol Solutions (Polymer Material. Cellulose Acetate CA-398)
D, x
109, m2/s
solute LiCl LiBr LiNOS NaCl NaBr NaI KF KCl
1.207 1.256 1.105 1.317 1.337 1.403 1.188 1.424 1.441 1.520 1.433 1.498 1.516 1.087 1.105 1.105 1.109
KBr KI RbCl CSCl CsBr MgC12 CaCl, SrCl, BaCl,
Stokes l a e r/ radius X lolo, CA x lolo, m m Inorganic Solutesb 3.26 -14.65 3.14 -13.45 3.57 -12.85 2.99 -13.45 2.95 -13.51 2.81 -4.06 3.32 1.20 2.77 -2.91 2.73 -2.31 2.59 2.97 2.75 1.75 1.82 2.63 2.60 4.12 3.60 -14.65 3.57 -13.45 3.57 -13.45 3.55 -12.29
D, x 109,
X
solute
mz/s
acetonitrile propionitrile valeronitrile benzonitrile nitromethane 1-nitropropane 2-nitropropane propionamide n-butyramide i-butyramide aniline triethylamine N,N-dimethylbenzylamine N,N-dimethylaniline benzene toluene ethylbenzene o-xylene p-xylene cumene n-propylbenzene mesitylene n-butylbenzene sec-butylbenzene isobutylbenzene tert-butylbenzene
2.734 2.159 1.965 1.681 2.583 1.876 1.876 2.079 1.82 1.76 1.95 1.55 1.39 1.479 2.20 1.768 1.590 1.604 1.577 1.46 1.435 1.45 1.377 1.36 1.31 1.28
Stokes la+ radius x 1Olo, m Organic Solutes 1.44 1.82 2.00 2.34 1.53 2.10 2.10 1.89 2.16 2.23 2.02 2.54 2.83 2.66 1.78 2.23 2.48 2.46 2.50 2.67 2.75 2.72 2.86 2.90 3.01 3.08
D
3.55 3.54 3.55 3.18 3.12 3.29 3.46 3.18 3.15 3.23 3.27 3.24 3.25 6.34 5.79 6.84 6.34
r/
CA
A
lO’O, m
X
x 10”, m 36.81 30.65 23.86 23.23 55.62 32.07 25.28 2.37 -0.32 -1.74 35.39 -5.21 4.11 21.96 11.06 7.11 3.00 8.53 5.06 0.32 0.32 1.74 -1.74 -3.63 -3.63 -3.00
D
lolo, m
X
3.826 3.413 3.209 3.465 3.495 0.602 -0.810 0.313 0.172 -1.188 -0.878 -0.881 -1.420 3.243 2.944 2.660 2.385 lO’O, m
X
2.54 2.31 2.54 2.55
B x 1030, m3 79.76 50.04 70.43 70.01
-
-
2.55 2.66 2.69 2.51 2.69 2.83 2.44 2.41 2.38 2.45 2.54 2.51 2.58 2.47 2.64 2.44 2.48 2.50 2.66
-
26.57 0 -8.03 76.41 -105.4 43.95 61.21 46.59 37.29 26.84 47.72 36.67 13.31 11.09 25.07 -10.37 -50.40 -50.37 -32.30
“Obtained on the basis of DAB of solute. *From Farnand et al. (1982); the values of A and D are applicable to R b values in the range 11 to 13 X m.
culated with respect to several potential functions corresponding to imaginary membrane material-solvent-solute systems for different average pore sizes and pore size distributions under different operating pressures. Two assumptions were made in the calculation; i.e., mass transfer coefficient k in the boundary phase is equal to infinity and therefore CAI = cA2,and the feed solution is so dilute that the osmotic pressure effect is negligible. Figure 3 shows the potential functions used for the model calculation conducted in the following with respect to the nonionized organic solutes using dilute feed solution systems. As the parameter D, 2 X m (case I and V), 4X m (case I1 and VI), 20 X m (case111and VII) m (case IV and VIII) were considered. and 30 X Though the parameter D is the force constant associated with the steric hindrance, it can be equated, as a first approximation, to the molecular size such as that represented by the Stokes law radius. Therefore, the parameter
D is called the “effective molecular size” for convenience throughout this paper. The first two D values chosen are close to Stokes radii of ethyl alcohol (2.05 X m) and D-glucose (3.66 X m) which solutes are usually separated by reverse osmosis membranes, while D values of last two solutes are close to the Stokes radii of bacitracin (22 X m) which are usually m) and pepsin (28 X classified as solutes separated by ultrafiltration membranes. Furthermore, the potential functions of solutes I-IV, shown in Figure 3a, are characterized by the deep potential wells indicating strong attractive forces working on solute molecules from the membrane pore wall, while those of solutes V-VI11 shown in Figure 3b are characterized by positive potential values over the entire range of distance, d , indicating the rejective force working on such solute molecules. The results of calculation of solute separation and (PR)/(PWP) ratio are illustrated in Figure 4 with respect
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 681
IP Y -I5
b REJECTIVE FORCE WORKING ON SOLUTE
I
Figure 3. Interfacial potential functions used for the model calculation.
loor-
ao-
2
60-
m
mo
4
ID' 2110'
20
H
Y
-Mo
2
P
w
201
140-
P3
30
2
-20
1
Figure 4. Effect of the average pore size on the solute separation and (PR)/(PWP) ratio under different interaction forces: operating pressure, 1724 kPag (= 250 psig); feed solute concentration, dilute: mass transfer coefficient k = a.
to the eight model potential functions given in Figures 3a and 3b. When the molecule is small and the membrane material-solute attraction is strong (case I) the separation is positive in a relatively narrow range of small pore radii, then turns into negative, passes through a minimum, and gradually approaches to zero. The general trend of solute separation of case I was experienced with p-chlorophenol solute separation by CA-398 membranes (Dickson et al., 1979; Matauura and Sourirajan, 1972). When the molecular size is increased (case 11)both the magnitude and the range of the positive separation increase; however, the separation ultimately turns into negative. When the solute is strongly rejected (cases V and VI) the magnitude of the solute separation increases enormously and the positive
separation prevails the entire range of the pore radius. The general trend of case V and case VI has been experienced in the separation of the organic solutes with polyfunctional groups such as sugars and polyhydric alcohols by CA-398 membranes (Matsuura and Sourirajan, 1973). It is interesting to note that the membrane cannot distinguish the smaller and larger solute molecules when the average m (cases V and VI). pore size is more than 22 X Comparing cases I1 and VI, both solutes are highly separated when the pore size is small. However, the separation of the case I1 solute declines sharply with the increase in the average pore size due to the strong attractive force working from the membrane material and finally turns into negative separation, while the separation of the case VI solute is relatively high in a wide range of the average pore size. This is in accordance with the experimental result that the separation of a very bulky hydrophobic solute such as methyl isobutyl ketone decreases more rapidly with the increase in the average pore size of the PPPH 8273 membrane than the separation of a polyhydric alcohol such as D-sorbitol which is highly rejected by this membrane material (Matsuura et al., 1977), though both solutes are highly separated in the range of the small average pore size. As for the (PR)/(PWP) ratio, that of case I potential function is significantly lower than unity, while the organic solutes corresponding to the rest of potential functions, 11, V, and VI, exhibit the ratio of nearly equal to unity. The lower (PR)/(PWP) ratio even for the dilute solution where the effect of osmotic pressure is negligible was experimentally obtained with respect to CA-398-water-pchlorophenol system. It should be noted that the (PR)/ (PWP) ratio is nearly equal to unity even when the solute molecule is strongly attracted toward the membrane material if the molecular size is sufficiently large as indicated by the data for the case 11. It is also interesting to note that the general tendency of the correlation between solute separation versus average pore radius reflects the shape of the potential functions. In case the molecular size is in the range of macromolecules, the solute separation is significantly lower than 100% when strong attractive forces are working (cases I11 and IV),while the separation is approximately 100% when rejective forces are working (cases VI1 and VIII). A remarkable decrease in the (PR)/(PWP) ratio is expected when a strong attractive force is working and the magnitude of the decrease in the above ratio increases as the average pore radius increases. This effect may, at least partially, account for the large decrease in the product permeation rate when macromolecular solutes such as proteins are treated by ultrafiltration membranes. Such an effect is usually attributed to the gel formation on the membrane surface or to the blocking of the membrane pore. Figure 5 illustrates the results of calculations examining the effect of the operating pressure on solute separations and (PR)/(PWP) ratios with respect to organic solutes corresponding to the potential functions of cases I, 11, V, and VI. Two average pore radii (Rb) of the membrane, i.e., 3.87 X 10-lom and 8.87 X 10-lo m were used for the calculation. These radii correspond to R, values of 3.0 X lO-'O m and 8.0 X 10-lo m, respectively, when the solvent is water. Except in case I, all solutes corresponding to the rest of potential functions exhibit significantly high solute separations (>83%) and the (PR)/(PWP) ratio is nearly equal to unity. The solute separation increases with increase in the operating pressure and reaches an asymptotic value, though the tendency is not quite visible when the separation is extremely high (>99%). This trend (increase
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
n 601
100
Y-XK, m-500
4 2 4
P, kPog
Figure 6. Effect of the operating pressure on the solute separation and (PR)/(PWP) ratio for macromolecules: feed concentration, dilute; mass transfer coefficient k = m. -40
8 87 x @m 3.87 xldlom
CASEWI,~OS~XO'~~
-----.=---:----
Figure 5. Effect of the operating pressure on the solute separation and (PR)/ (PWP) ratio for small molecules: feed concentration, dilute; mass transfer coefficient k = a.
CASEY , 5 87
XIO% bA~
90
in solute separation with increase in operating pressure) is consistent with the experimental solute separation, by CA-398 membranes, of the sugar solutes which are highly rejected (Matsuura and Sourirajan, 1971) or of the solutes of high bulkiness such as tert-butyl alcohol (Matsuura et al., 1974). With respect to case I which involves a small molecular radius and a high affinity to the membrane material, the separation is significantly lower than the rest of the potential functions and the (PR)/(PWP) ratios are significantly less than unity. In the pore whose average pore radius is 3.87 X m, the solute separation is about 40% and increases only slightly with increase in operating pressure. When the average pore radius of the membrane is 8.87 X m, solute separation is positive in the low pressure range, decreases with increase in the operating pressure, and turns into negative when the operating pressure is sufficiently high. The latter trend is again consistent with the experimental data of CA-398-waterp-chlorophenol system. The (PR)/(PWP) ratio for the m is membrane of the average pore radius of 3.87 X smaller than that for the membrane of the pore radius of m and the ratio remains almost constant 8.87 X throughout the entire range of the operating pressure, which is also consistent with the result reported for CA398-water-p-chlorophenol (Dickson et al., 1979; Matsuura and Sourirajan, 1972). The effect of operating pressure on the separation of macromolecular solutes (cases 111, IV, VII, and VIII) and on the (PR)/(PWP) ratios was studied with the average m (R, = 40.0 X for water pore radius of 40.87 X solvent) and the results are shown in Figure 6. When macromolecules are strongly attracted to the membrane material (case 111and case IV) the solute separations are significantly lower than 100% and decrease as the operating pressure increases, while macromolecular solutes without such affmity force (cases VI1 and VIII) are almost completely separated. It is worth noting that the molecule of radius 30 X lO-'O m is almost completely separated by the membrane with the average pore radius of 40.87 X m. Thus, the separation mechanism involved is not a sieving mechanism. A decrease in the separation of a macromolecular solute with increase in operating pressure has also been reported in the literature (Blatt et al., 1970). The (PR)/(PWP) ratio is significantly lower than unity when the macromolecular solute is strongly attracted to the membrane material (case 111and case IV), while the
CASE Ip,Rb = 40 87 x l d ' h
CASE I , Rb = 5 8 7 ~ I o ' ~ m b ' . .
0
01
02
03
04
u/Fib
Figure 7. Effect of the pore size distribution on the solute separation and (PR)/(PWP) ratio: feed concentration, dilute; mass transfer coefficient k = a.
ratio is approximately unity when the solutes are not attracted. The pressure effect on the (PR)/(PWP) ratio is practically nonexistent, in accordance with the similar result obtained for solute molecules corresponding to case I and case I1 potential functions. Figures 7a and 7b show the effect of pore size distribution on solute separation. The pore size distribution is characterized by the ratio of the standard deviation c of the Gaussian normal distribution to Rb,where the increase in a / R b indicates a broader (less uniform) pore size distribution. In Figure 7a computational results for two solutes with strong attractive forces to the membrane material (cases I and IV) are shown with respect to the avm for erage pore radii of 5.87 X lO-'O m (R, = 5.0 X water solvent) and 40.87 X 10-lo m (R, = 40.0 X 10-lo m for water solvent) under the operating pressure of 1724 and 10342 Wag. In Figure 7b similar results are shown for two solutes which are rejected from the membrane material (cases V and VIII). To facilitate the computation an assumption was introduced that (PR)/(PWP) ratio is unity. Except for this assumption which corresponds to the elimination of last two terms of eq 18, the entire computation procedure is rigorous. Though the assumption may not be valid, particularly for the case IV potential function, the solution obtained in terms of solute separation is precise. This was confirmed by the rigorous solution of the entire transport equations for the case a = 0. The general tendency in both Figure 7a and Figure 7b is that solute separation decreases with increase in a J R b . This is due to the higher contributions to the solute and
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
a
683
E
R, = 7.87 x 16''m P = I724 k R g ( 2 5 0 ~ isg ) Bx 10ym3
pow, I
i
,
w
,D x "01
,m
0
W
20
40
60
80
100
SEPARATION OF SOLUTE WITH = -500 x
E
Figure 8. Effective solute size versus solute separation for different pore size distributions: feed concentration, dilute; mass transfer coefficient k = a.
solvent fluxes from the pores of larger radii when a number distribution is used for the Gaussian normal distribution. It is worth noting that the solute of case I potential shows a higher separation at a higher operating pressure (10342 Wag)than that at a lower operating pressure (1724 kPag) when the average pore size is 5.87 X 10-lo m and the standard deviation is 0.0. However, the separation at the lower operating pressure becomes higher when the "/Rb ratio is increased to 0.4. In order to understand the change in the effect of the operating pressure, let us recall the pressure effect illustrated in Figure 5. It was shown that, with respect to the same potential curve (case I), the separation increased with increase in operating pressure when the pore radius, Rb, was 3.87 X m, while the trend was reversed when Rb was 8.87 X lo-'' m. Coming back to Figure 7a, as the result of inclusion of smaller and larger pore radii than the average pore radius of 5.87 X 10-lom by increasing the standard deviation, the separation goes down with the increase in the operating pressure, since the effect of the larger pore size is more strongly exhibited. Thus, the change in the pore size distribution may reverse the effect of the operating pressure. In Figure 8 the effect of size of solute on solute separation is illustrated at two pore size distributions of = 0.0 and U / R b = 0.4. Figure 8a shows the results of calculations for the average pore radius of 7.87 X 10-lom (R, = 7.0 X m for water solvent), representing a typical reverse osmosis membrane. Calculations were made at B values of -500 X and 100 X m3, which represent the cases of strong rejective and attractive forces working on the solute molecule, respectively. The results show that the broader pore size distribution brings down the solute separation in the entire range of D value (which can be approximately equated to the molecular radius of the solute) regardless of the sign and magnitude of B value. The conclusion obtained from Figure 8a is twofold; one, that there is a possibility of the effect of pore size distribution on solute separation by a membrane of such a small average pore radius as 7.87 X m which corresponds to the pore size on a reverse osmosis membrane, and the other, that the separation always decreases with increase in standard deviation of the pore size distribution in terms of the number of pores. The latter conclusion is in contrast to the concept that the broader distribution leads to higher solute separation in the range of the smaller solute size and to lower solute separation in the range of the larger solute size, and consequently to a less steep correlation in solute separation versus solute size (Michaels, 1968). None of such features appears in Figure 8a. Similarly, the results of calculations are presented in Figure 8b with respect to
Figure 9. Effect of the pore size distribution on the correlation of the separations of solutes with different B values: operating pressure, 1724 Wag (= 250 psig); feed solute concentration, dilute; mass transfer coefficient k = a,
the average pore radius of 40.87 X m (R, = 40.0 X 10-lo m for water solvent), which corresponds to a pore radius of a typical ultrafiltration membrane. The calculations were conducted for both cases of no interaction (B = 0) and a high attractive interaction (B = 4000 X m3) changing the D value of the potential function, with respect to two pore size distributions of U/Rb = 0 and a/Rb = 0.4. The general conclusion obtained is quite similar to that obtained from Figure 8a, except in the presence of a high attractive interaction the slope of the separation vs. D correlation is much steeper and the separation turns into negative when there is a broad pore size distribution. Again, it is shown that the steepness of the curve does not necessarily mean a more uniform pore size distribution. Figure 9 illustrates the correlation of calculated separations for two solutes (B = -500 X m3,D = 4 X 10-lo m; B = 100 X m3, D = 4 X 10-lo m) by membranes of different average pore sizes. Accordingly, on one line data of several membranes of different average pore radii are involved. Again, the calculations were made for a / R b = 0 and 0.4. This figure shows that the above calculations generate two discrete lines for different values though the effect of a / R b is not remarkable. This result is similar to the one which was obtained for the comparison of p chlorophenol and sodium chloride separation data in our previous work (Matsuura and Sourirajan, 1981). In terms of the calculated results shown in Figure 7-9, it is worth noting that the pore size distribution can, at least, be conceived in both cases of reverse osmosis and ultrafiltration membranes and the effect of the change in the pore-size distribution can be predicted according to the surface force-pore flow model. The major consequence of such a calculation is the possibility of different pressure effects on the separation of the same solute by membranes of the same polymer material, and also the possibility of different correlations between the separations of two different solutes, though the effect of the pore size distribution on the latter correlation is not remarkable. Conclusion Theoretical calculations on the basis of surface forcepore flow model using force constants representing typical solute organic molecules and macromolecules predict the effect of the average pore radius and pore size distributions, and of the operating pressure on reverse osmosis and ultrafiltration data of dilute solution systems such as the solute separation and (PR)/(PWP) ratio. Some of the predictions are supported by experimental results already available in the literature, and the other predictions illustrate what may be expected for systems not yet experimentally investigated. The approach presented in this
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
paper is particularly relevant for the choice of the membrane material and the membrane pore structure, and for the process design of the membrane separation process for use in waste water treatment. Nomenclature A = the surface area of polymer powder in the chromatography column, m2 A = constant characterizing electrostatic repulsion force, m B = constant characterizing the van der Waals attraction force, m3 b = frictional function defined by eq 24a and 22b C A = dimensionless solute concentration cA = molar concentration of solute, mol/m3 D = constant characterizing the steric repulsion at the interface, m Dsolvent = molecular radius of solvent (= 0.87 X m for m for methanol) water, 1.69 X D, = diffusivity of solute in solvent at 25 O C and infinite dilution, m2/s d = distance between polymer material surface and the center of solute molecule, m f = fraction solute separation based on the feed concentration f’ = fraction solute separation based on the solute concentration in the boundary phase k = mass transfer coefficient for solute on the high-pressure side of the membrane, m/s P = operating pressure, kPag (PR) = product rate through given area of membrane surface, kgf h (PWP) = pure water permeation rate for given area of membrane surface, kg/h Ra = R b - Dsolvent, m R b = pore radius, m Rb = average pore radius, m R = gas constant r = radial distance in cylindrical coordinate, m S = effective area of membrane surface, m2 T = absolute temperature, K UB = velocity of solvent in the pore, m/s [ V,’] = retention volume of the solute, m3 u, = permeation velocity of product solution, m/s Y(R) = normal pore size distribution function, l / m Greek Letters a ( p ) = dimensionless solution velocity profile in the pore PI = dimensionless solution viscosity P2 = dimensionless operating pressure r = surface excess of the solute, mol/m2 6 = length of cylindrical pore, m 7 = solution viscosity, Pa.s X = dimensionless quantity defined by eq 25 p = dimensionless radial distance = standard deviation of pore size distribution, m = dimensionless potential function 4 = potential function of interaction force exerted on the solute from the pore wall, J/mol XAB = D m / R T Registry No. LiF, 7789-24-4;LEI, 7447-41-8;LBr, 7550-35-8; NaF, 7681-49-4; NaC1,7647-14-5;NaBr, 7647-15-6;NaI, 7681-82-5; KF, 7789-23-3;KC1,7447-40-7;KBr, 7758-02-3; RbC1,7791-11-9; CsC1,7647-17-8;CsBr, 7787-69-1;LiN03,7790-69-4;KI, 7681-11-0; MgC12, 7786-30-3; PPPH 8273, 74665-71-7; cellulose acetate, 9004-35-7; methanol, 67-56-1;ethanol,64-17-5; 1-propanol,71-23-8; 2-propanol, 67-63-0; 1-butanol, 71-36-3; 2-butanol, 78-92-2; 2methyl-1-propanol, 78-83-1; 2-methyl-2-propano1,75-65-0; 1(r
pentanol, 71-41-0;1-hexanol,111-27-3;acetone, 67-64-1;methyl ethyl ketone, 78-93-3;methyl isopropyl ketone, 563-80-4; methyl isobutyl ketone, 108-10-1;cyclohexanone,108-94-1;diisopropyl ketone, 565-80-0; methyl acetate, 79-20-9; ethyl acetate, 141-78-6; propyl acetate, 109-60-4;ethyl propionate, 105-37-3;ethyl butyl ether, 628-81-9;ethyl tert-butyl ether, 637-92-3; isopropyl tertbutyl ether, 17348-59-3;propionamide, 79-05-0;acetonitrile, 7505-8; propionitrile, 107-12-0; nitromethane, 75-52-5; l-nitropropane, 108-03-2;phenol, 108-95-2;resorcinol, 108-46-3;aniline, 62-53-3; dimethyl aniline, 121-69-7; 1,2-ethanediol, 107-21-1; glycerol, 56-81-5; 2,3-butanediol, 513-85-9; xylitol, 87-99-0; 1,2,6-hexanetriol,106-69-4;dulcitol, 608-66-2;D-sorbitol,50-70-4; D-glucose, 50-99-7;D-fructose,57-48-7;sucrose,57-50-1;maltose, 69-79-4; polyethylene glycol (SRU),25322-68-3; bacitracin, 1405-87-4;pepsin, 9001-75-6;valeronitrile, 110-59-8;benzonitrile, 100-47-0; 2-nitropropane, 79-46-9; propionamide, 79-05-0; nbutyramide, 541-35-5;isobutyramide, 563-83-7;triethylamine, 121-44-8;NJV-dimethylbenzylamine,103-83-3;benzene, 71-43-2; toluene, 108-88-3;ethylbenzene, 100-41-4;o-xylene,95-47-6;p xylene, 106-42-3;cumene, 98-82-8; n-propylbenzene, 103-65-1; mesitylene, 108-67-8;n-butylbenzene, 104-51-8;sec-butylbenzene, 135-98-8;isobutylbenzene,538-93-2;tert-butylbenzene, 98-06-6.
Literature Cited A.P.I. Report No. 4261 “Alcohols: A Technical Assessment of Thelr Appiicatlon as Fuels”, 1976. Blatt, W. F.; Dravki, A.; Michaels, A. S.;Nelsen, L. “Solute Polarizatlon and Cake Formation in Membrane Ultrafiltration: Causes, Consequences, and Control Techniques”, Flinn, J. E., Ed.; Plenum Press: New York, 1970; p 73. Chuduk, N. A.; Eltekov, Yu. A,; Kisekv. A. V. J. Colk~ldInterface Sci. 1881, 84, 149. Dickson, J. M.; Matsuura, T.; Sourirajan, S. Ind. Eng. Chem. Process D e s . Dev. 1878, 18, 841. Farnand, B. A.; Talbot, F. D. F.; Matsuura, T.; Sourlrajan, S. 4th Bioenergy R8D Seminar; National Research Council of Canada: Winnipeg, March 29, 1982. Faxen:-% Kolbld Z. 1858, 167, 146. Foulkes, F. R. “Literature Survey for the Corrosion and Degradation of Vehicle Components kr Methanol”, Ministry of Transport and Communications, Ontarlo, March 1977. IsraelacMviil, J. N.; Tabor, D. “Progress in Surface and Membrane Science”, Danielli, J. F.; Rosenberg. M. D.; Cadenhead, D.A,, Ed.; Academic: New YWk. 1973; VOl. 7, pp 1-55. Martynov, G. A.; Starov, V. M.; Churaev, N. V. KolloMn. Zh. 1881, 42, 489. Matsuura, T.; Bednas, M. E.; Sourlrajan, S. J. Appl. Polym. Sci. 1874, 18, 587
Matsuura, T.; Blals, P.; Pageau, L.; Sowirajan, S. Ind. Eng. Chem. Process Des. Dev. 1877, 16, 510. Matsuura, T.; SwriraJan, S. Ind. Eng. Chem. Process Des. D e v . 1871, 10, 102. Matsuura. T.; Sourkajan, S. J. Appl. Polym. Sci. 1872, 16, 2531. Matsuura, T.; Sourirajan, S. J. Appl. Polym. Scl. 1873, 17, 1043. Matsuura, T.; Sourirajan, S. J. Colloid Interface Sci. 1878, 86, 589. Matsuura, T.; Sourirajan, S.Ind. Eng. Chem. Process Des. D e v . 1881, 20, 273. Matsuura, T.; Taketani, Y.; Sowirajan, S. “Synthetic Membranes”, Voi. 11, Turbak. A. F., Ed.; ACS Symposium Series 154. 1981a; pp 315-338. Matsuura, T.; Taketani, Y.; Sourirajan. S. Desalination 188lb, 38,319. Matsuura, T.; Taketani, Y.; Sourirajan, S. J. Colloid Interface Sci. 1983, 95(1), 10. Michaels, A. S. “Rcgress in Separation and Purification”, Voi. I,Perry, E. S., Ed.; Wiiey: New York, 1988; pp 297-334. Onsager, L.; Samaras, N. N. T. J. Chem. W y s . 1834, 2 , 528. Satterfkki, C. N.; Conon, C. K.; Pircher, W. H. AIChE J. 1973, 19, 628. Sourirajan, S. “Reverse Osmosis”; Academic: New York, 1970; Chapter 3. Zeman, L.; Wales, M. “Synthetic Membranes”, Vol. 11, Turbak, A. F., Ed., ACS Symposium Series 154, 1981; pp 41 1-434.
Receiued for reuiew September 13, 1982 Accepted November 28, 1983 Presented at the Symposium on Membrane Processes for Industrial Wastewater Treatment in the Summer National AIChE Meeting, Aug 29-Sept 1,1982, Cleveland, OH. Issued as N.R.C. No. 23545.
