PERMEATION EQUATIONS DEVELOPED FOR PREDICTION OF MEMBRANE PERFORMANCE IN PERVAPORATION, VAPOR PERMEATION AND REVERSE-OSMOSIS BASED ON THE SOLUTION-DIFFUSION MODEL

General permeation equations based on the solution-diffusion model were proposed for pervaporation (PV), vapor permeation (VP) and reverse osmosis (RO) on two different assumptions about the pressure gradient inside a membrane: a flat gradient (case 1) and a linear gradient (case 2). With these equations the permeation properties in PV, RO and VP can be estimated once the transport parameter of a membrane is known. The effect of upstream pressure on selectivity and flux in RO and PV was estimated by sample calculations for water- and ethanol-selective membranes in ethanol-water system. Flux and selectivity in RO is smaller and, reaching that in PV at infinite pressure. This ultimate value is different in cases 1 and 2, and in the latter the molar volume ratio of the permeants becomes important. The effect of downstream pressure in PV was also estimated and compared with the case of vacuum-enhanced membrane distillation (MD) with a porous membrane. With increasing pressure the separation factor approaches that of vapor-liquid equilibrium in both PV and MD. With decreasing pressure that in MD is governed by the ratio of diffusion coefficients inside the membrane. Since the Knudsen diffusion coefficient of water is larger than that of ethanol, the separation factor decreases in ethanol-water separation with decreasing downstream pressure. This was verified by experiment, using PTFE membranes.