Modelling the separation by nanofiltration of a multi-ionic solution relevant to an industrial process

The current work focuses on the application of nanofiltration (NF) to the isolation of a pharmaceutical product, clavulanate (CA−), from clarified fermentation broths, which show a complex composition with five main identified ions (K+, Cl−, NH4+, SO42− and CA−). Our aim is to predict the rejection rates of these five ions, with the NF membrane Desal-DK, which may influence the separation of CA− and play a role in the whole downstream process. Concentration polarization of this multi-ionic solution was addressed both through the application of the extended Nernst–Planck equations in the film layer, assuming limiting values for the boundary layer thickness, and by applying a new methodology which dispenses this arbitrary assumption. The latter approach was chosen to calculate the intrinsic rejection rates. The transport through the membrane pores was modelled using the Steric, Electric, Dielectric and Exclusion (SEDE) model in order to predict the intrinsic rejections of the five ions in solution. The membrane volume charge density was assessed from tangential streaming potential measurements for the system membrane/five ions solution. With a single fitted parameter, ɛp (the dielectric constant of the solution inside pores) and considering that the ion selectivity is governed by steric, Donnan and Born dielectric exclusion mechanisms, the predicted intrinsic rejections rates of the five ions are in good agreement with the experimental values.