Activity-derived model for water and salt transport in reverse osmosis membranes: A combination of film theory and electrolyte theory

Abstract

A framework of reformulation of the classic solution-diffusion model is presented by combining the film theory and electrolyte theory to include the concentration polarization and thermodynamic non-idealities in mass transport of NaCl/NH4Cl solutions during reverse osmosis in a large range of feed concentrations. In this activity-derived model, concentration polarization was evaluated using the film theory to estimate the salt concentrations at the membrane surface. Non-ideal thermodynamic effects from the electrolyte theory were considered to correct the activity coefficients due to the strong concentration dependence. The concentration polarization modulus and salt activities were found to substantially affect the effective local salt transport coefficients (Ba). At low salt concentrations, the combined result of the two effects was negligible (i.e., Ba ≈ B). However, at high feed concentrations (>0.09 mol L−1 for both NaCl and NH4Cl), the influence of the two effects was significant: the ratio Ba/B ranged from 1.12 to 1.50. The concentration polarization effects on the osmotic coefficient and the effective local water transport coefficient (Afm) were very small. This activity-derived model indicates that the concentration dependence of the salt and water transport in RO is a complex function of the combined effects from concentration polarization and thermodynamic non-idealities.