Effect of pressure and temperature on solvent transport across nanofiltration and reverse osmosis membranes: An activity-derived transport model

The activity coefficients and equations for transport through nanofiltration (NF) and reverse osmosis (RO) membranes were derived to determine the contribution of the heat of vaporization, molar volume, activation energy (diffusion), thermal expansion, and liquid- and vapor-phase compression. These equations have been derived for pure substances; hence, the measured deviations were obtained from the membrane itself. The inclusion of these effects provides a more accurate prediction of membrane transport than that provided by current models. The model presented herein accurately determined fluxes over temperature and pressure ranges for four different membranes, which the Merten model failed to determine. The transport activity model was applied to water, ethanol, methanol, and n-hexane. The molar volume of water for commercial, brackish-water membranes was approximately equal to that of bulk water, while high-flux brackish-water and NF membranes exhibited significantly lower molar volumes, as compared to that of the bulk water. Surprisingly, slight changes in the molar volumes of water, ethanol, and n-hexane in organic NF membranes were observed. Significant changes in the physicochemical properties of water were identified in the Desal 5 membrane. These results indicate that the molar volume and compressibility enabled the pressure dependence of the RO and NF membranes. For all the membrane types, the resistance to flow, heat of vaporization, and diffusion coefficients controlled the magnitude of changes in flux due to pressure and temperature.