Modelling the performance of membrane nanofiltration—critical assessment and model development

Abstract A critical assessment of previous theoretical descriptions of membrane nanofiltration shows that the good agreement with experimental data is due to the use of the ratio of effective membrane thickness to membrane porosity as an arbitrary fitting parameter. A more rigorous analysis shows that rejection is independent of membrane thickness. A model allowing calculation of uncharged solute rejection on the basis of a single membrane parameter (pore radius) is developed. The theoretical description is based on a hydrodynamic model of hindered solute transport in pores. The dependence of solute chemical potential on pressure is included, although its effect is shown to be small. A variation of solvent viscosity with pore radius is also included. For pores of a single size, such variation has no effect on rejection, though it will become important for overall membrane rejection if a pore size distribution is included. The good agreement between this model and experimental data confirms that uncharged solute rejection in nanofiltration membranes may be well-described by such a continuum model. A two-parameter model (pore radius and membrane charge) for electrolyte rejection has been developed that includes dielectric exclusion in the form of an energy barrier to ion partitioning into the pores. Reassessment of the pore dielectric constant using NaCl rejection at the isoelectric point of a Desal-DK membrane resulted in significantly better agreement with experimental rejection data than use of the high frequency solvent dielectric constant for an oriented layer of water molecules at the pore walls. The predicted values of effective membrane charge density were not only significantly reduced in magnitude, and hence more realistic, than those from previous models, but their variation with concentration for divalent salts was in better agreement with physical models of ion adsorption. The theoretical descriptions of the present paper are developed more rigorously than those previously published. Their overall agreement with experimental data is good and the resulting membrane parameters are likely to be more closely related to physical membrane properties than those obtained from previous models. The descriptions are useful for membrane process assessment and prediction. They also provide a sound basis for further developments.