Ind. Eng. Chem. Res. 1990, 29, 278-282
278
An Evaluation of Reverse Osmosis Solute Rejection Model Performance at Elevated Pressure and High Feed Concentration Vito L. Punzi,* Gregory P. Muldowney,+a n d Thomas J. Hull: Department of Chemical Engineering, Villanova University, Villanova, Pennsylvania 19085
Experimental separation data collected for the system water-sodium chloride-cellulose acetate are used to evaluate four solute rejection models a t conditions typically encountered in saline water desalination applications. At the elevated pressures and high feed concentrations used in this study, no apparent superiority among models is established. However, the general results of this study are similar to those obtained earlier a t low pressures and feed concentrations. Most significantly, the results indicate that the solute rejection models developed at low pressures and feed concentrations are also valid a t elevated pressures and high feed concentrations and that separation is accurately correlated over a wide range of pressure, feed rate, and feed concentration by either the corrected diffusive flow model or the corrected viscous flow model. Distribution coefficient ratios are predicted at elevated pressures and high feed concentrations by using three different approaches which produce nearly identical results. Earlier investigations (Muldowney and Punzi, 1988; Punzi et al., 1989,1990)have addressed the following three issues related to the solute rejection mechanism in reverse osmosis (RO):(1)the mass-transport mechanism; (2) the mechanistic (physical) parameters that best characterize a real membrane with respect to an ideal (perfect) separator; and (3) whether ideal and real models can be applied in parallel to quantify nonidealities present in real membranes. The earlier investigations were limited to those pressure and feed concentrations typically encountered in brackish water desalination applications. A major question that remains is whether the four models developed and the results obtained in the earlier studies are valid at the elevated pressures and high feed concentrations typically encountered in saline water desalination. This paper addresses this question and presents the results of a pilot study which extends the results of earlier studies to a wider range of operating pressures and feed Concentrations. This paper also presents values of the mechanistic parameters obtained in this pilot study and compares them to those values obtained in an earlier two-part study (Muldowney and Punzi, 1988) which used cellulose acetate membranes of comparable selectivity. All of the analyses described in this paper are based on a single experimental RO data base collected using the system water-sodium chloride-cellulose acetate membranes.
Theory and Analysis For highly selective membranes, the most sensitive measure of performance is the solute separation factor, a , defined as CY
=
c21/c21f
(1)
Two models evolve from the diffusive transport mechanism; the variables in the ideal diffusive flow model and the corrected diffusive flow model are grouped as follows: ideal
* Author to whom correspondence should be addressed. ‘Present address: Mobil R&D Corp., Paulsboro, N J 08066. *Present address: U.S. Naval Shipyard, Portsmouth, VA 23707.
corrected
Two models evolve from the convective transport mechanism; the variables in the ideal viscous flow model and the corrected viscous flow model are grouped as ideal
( Y:;,)
(4)
(
(5)
where X,* = 1 - exp corrected
where X, = -exp --
--
Detailed derivations of eqs 2-5 are presented elsewhere (Muldowney and Punzi, 1988). As in earlier investigations involving eqs 1-5, RO process data ( a , Ap, VI’, T ) are measured experimentally, solvent-solute data (Dim, T , Dzl) are obtained from the literature (Sourirajan, 1970), and membrane structure data ( A , A, T , c) are obtained from discussions of membrane morphology. Membrane performance is measured in terms of CY (or a*);known properties of the RO process, the solventsolute pair, and the membrane are then grouped in X (or X *). Each model linearly relates CY to X through mechanistic parameters which summarize the solvent-solute-membrane interaction. For the viscous flow models, a linear form results either from the equations as written or upon substituting the approximation exp(-x) = 1 - x (values of X * in this study are typically on the order of in this analysis, eqs 4 and 5 are used directly. A standard linear regression analysis is used to objectively compare the two corrected models (eqs 3 and 5). From the analysis, it is possible to conclude which mode of transport better describes solute rejection. (A standard linear regression analysis can also be used to compare the two ideal models. However, the results obtained from such
0S88-~8~5/90/2629-0278$02.50/0 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 279 an analysis are not as significant as those obtained from a comparison of the two corrected models.) Equations 3 and 5 can also be used to determine system-specific mechanistic parameters. Three parameters follow from the data fit and are used to physically describe membrane behavior: (P,/P2)for diffusion, ( c / K i ) for convection, and (K,“/K,’) for both modes. All three ratios are expected to be insensitive to pressure and flow rate over the range of conditions tested. In addition, the ideal forms of these three variables can be determined from eqs 2 and 4 and are used to quantify membrane nonideality. In eqs 2-5, a and a* denote the ratio of solute concentrations at the high- and low-pressure membrane surfaces. These may differ from measured feed and permeate (bulk) concentrations due to concentration polarization. The surface and bulk solute concentrations are related through a mass-transfer coefficient (k) and the permeate flux (V”/A) by a single equation. Conversion to bulk concentrations using this relationship preserves the linearity of the rejection equations (eqs 2-5) but introduces into the mechanistic parameters the multiplier exp(-V”/Ak) (Muldowney and Punzi, 1988). However, this adjustment has little numerical impact because typical values of (V”/Ak) are of the order of and vary by at most a factor of 4 within any fitted data set so that the multiplier exp(-V”/Ak) is typically 0.98. Hence, rejection models are fit as eqs 2-5 using bulk concentrations and noting that the adjustment for concentration polarization is absorbed into the mechanistic parameters with negligible distortion of their physical significance. Membrane Morphology The skin layer thickness (A), porosity (e), and mean tortuosity (7)in cellulose acetate membranes are discussed throughout the literature (Meares, 1966; Jonsson and Boesen, 1975; Soltanieh and Gill, 1981; Kesting, 1985; Osmonics, Inc., 1988). Assimilating the range of typical values of each of these three parameters gives AT/^) values of 9.6-51.7 pm (Muldowney and Punzi, 1988). Since the fit of the viscous flow equations is apparently unaffected by (Xr/e) due in part to the approximately linear behavior of the exponential term noted earlier, the discussion presented below focuses on the results obtained using ( A T / € ) of 51.7 pm. In addition, the results of the analysis obtained using a value of ( A T / € ) of 89.3 pm are presented. This value is chosen because it produces an identical value of the grouping (A7/Ae) (found in eqs 4 and 5) as that implicitly chosen in the earlier study performed at low pressures and feed concentrations. Experimental Section Separation data are obtained by using a commercial RO unit (Osmonics PES 1960) representative of saline water desalination systems. The unit features a spiral-wound cellulose acetate membrane which has an area (A) of 1.77 m2 (19 ft2) and provides 0.007 kg/(m2.s) (15 gpd/ft2) maximum product water flux. A total of 66 conditions (combinations of feed flow rate, feed-side gauge pressure, and temperature) are studied. Seven nominal feed chloride concentrations (750, 2250, 4500, 6000, 9000, 15000, and 21 500 mg/L) are used, at temperatures ranging between 13 and 28 OC. Flow rates to the membrane are 94.6-328 cm3/s (1.5-5.2 gpm) and pressures are 3450-4550 kPa (500-660 psig). This pilot study encompassed a broader range of operating pressures, feed concentrations, and temperatures than the earlier low pressure and concentration study. Experimental data collection and analysis procedures are otherwise identical with those used earlier.
General Results and Discussion The values of a obtained in this plot study range between 3.4 and 9.2 (71-89% rejection). Approximately 50% of the a values are between 4 and 6.3; approximately 85% of the a values are between 3.7 and 8.3. Flow rates (V”) range between 3 and 11.9 cm3/s. As expected, both a and V” generally increase with increasing applied pressure and decrease with increasing feed concentration. Since the values of both a and V” are similar to those obtained from two of the membranes used in the earlier study, meaningful comparisons of the results of the investigations are possible. Comparison of Solute Rejection Models via Regression Analysis The results of the regression analysis indicate that the ideal models produce a significant reduction in the unaccounted variation in a*. Typically, the residual squares (a typical measure of the quality of the fit) are 1or 2 orders of magnitude smaller than the total squares. In nearly every case, the fraction of squares removed by either model ranges between 98% and 99%, indicating that the ideal models provide a reasonable description of solute rejection. The results of the regression analysis also indicate that using the corrected rejection equations produces further improvement over the ideal models, although the improvement is not as consistent as in the other studies that have used this approach. The results of the regression analysis can also be used to identify the solute rejection mechanism. In this pilot study, similar results are obtained by using either the corrected diffusive flow model or the corrected viscous flow model. This indicates that a two-parameter linear functionality of a either to the pressure difference (Ap - AT) or to the exponential of permeate flow (V”) can be used to represent the basic mechanism of solute rejection in cellulose acetate membranes operating at elevated pressures and high feed concentrations. Although the data set developed for this study is small and additional investigation is warranted, this basic conclusion is identical with that of the earlier studies involving cellulose acetate, homogeneous asymmetric polyamide, and thin film composite polyamide. Again it appears that this observation does little to resolve the persistent disagreement over the solute rejection mechanism in reverse osmosis. It is nervertheless significant that the same conclusion is reached for three different membrane materials at low operating pressures and feed concentrations and for one of these materials over the entire range of pressure and feed concentrations likely to be encountered in any desalination applications. These results also suggest that a composite model that incorporates the independent variables of both corrected equations might provide a better description of solute rejection than either corrected model alone. The investigation of such a relationship is being studied further. Interpretation of Mechanistic Parameters The fitted mechanistic parameters presented and discussed below are determined from the four solute rejection models and can be used to quantify membrane nonideality. In addition, distribution coefficient ratios (Ki‘IK,’ ) are calculated from each corrected equation and compared. Finally, estimates of the physical quantities K i and K / obtained from the corrected parameters are presented. In general, since the cellulose acetate membrane used in this study and those identified as membranes 1and 2 in the earlier study are of comparable selectivity, a certain degree of similarity and agreement of results is expected. Thus, a comparison of the results of the two studies also
280 Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 Table I. Best-Fit Mechanistic Parameters for the Ideal and Corrected Viscous Flow Models fitted parameters based on ( h i l t ) = 51.7 pm ( X r / c ) = 89.3 pm nominal feed correctedb ideal” correctedb concn, mg/L ideal” 4.6 22 5.7 750 34 2 250 (
