Analysis of solvent flux through nanofiltration membranes by mechanistic, chemometric and hybrid modelling

Abstract This paper addresses the modelling of the transport of solvents through nanofiltration (NF) membranes. Experimental data generated by the authors and collected from other published studies of 32 different solvent–membrane systems was used for comprehensive model validation. It was found that the most used mechanistic models are not sufficiently general to cover such a wide range of membrane–solvent systems. A set of alternative membrane and solvent descriptors was defined based on published studies, in order to improve the modelling of this system. Since the relationship between the solvent flux and the new selected descriptors is currently not known or poorly known at the mechanistic level, alternative chemometric and hybrid chemometric–mechanistic modelling methodologies were adopted. The main results that can be withdrawn from this study are the following. The analysis of the data by Projection to Latent Structures (PLS) showed that solvent flux through NF membranes could be mainly related to bulk solvent properties such as viscosity and density, and to membrane MWCO. The solvent–membrane systems were classified into clusters of systems with similar properties on the basis of the two most important latent variables. Among the model structures studied, the hybrid solution-diffusion/PLS model was determined to be the best approach for predicting solvent permeability data. For this latter model, the analysis of descriptors contribution showed that the dipole moment, Hildebrand solubility parameter, dielectric constant and ellipsoidal ratio were able to capture up to 40% of variance of the solution-diffusion model residuals. Among these the dipole moment introduced the highest improvement. This model can be further improved by designing new experiments outside the identified membrane–solvent clusters.