Modelling of the retention of uncharged molecules with nanofiltration

In this paper, a model is developed for the retention of organic molecules with a given nanofiltration membrane at different pressures as a function of the molecular weight. The Spiegler–Kedem transport equations were used to derive the reflection coefficient, the maximal retention that would theoretically be obtained at infinite transmembrane pressure, from experimental retention values for a large set of molecules with the effective diameter of the molecule as a size parameter. Secondly, the pore size distribution of the membrane is derived from the experimental reflection coefficients. This allows to calculate the reflection coefficient for a molecule with a given effective diameter. Since this parameter is not readily available, a correlation between the effective diameter and the molecular weight has been established and introduced in the model equations. Subsequently, the contribution of diffusion in the transport of molecules through the membrane was evaluated by introducing a membrane diffusion parameter, which was determined experimentally for the membranes NF70, NTR 7450 and UTC-20. Finally, the pore size distribution, the diffusion parameter and the experimental water flux through the membrane were used to calculate the retention as a function of the molecular weight and pressure for the same three membranes. This allows to determine retention curves at different pressures, and to calculate the variation of the MWC with pressure.