The averaged potential gradient approach to model the rejection of electrolyte solutions using nanofiltration: Model development and assessment for highly concentrated feed solutions

• We show the evolution of the transmembrane potential with the concentration.
• Using pore averaged potential gradient, the SEDE model is simplified.
• Good agreement is obtained between the simplified and the original model.
• Computation time is greatly reduced.
• Good agreement with experimental data for moderate to high concentrations.

Some of the recent publications in nanofiltration modelling converge on the importance of dielectric effects and numerous models have been developed in order to take them into account. However several works reported lately in the literature suggest a screening of image charges effect at high electrolyte concentration and the predominance of the Born effect, due to the change of dielectric constant inside the confined nanopore regarding that of the feed solution. In pursuit of an exhaustive and simple model for nanofiltration, a new approach is developed that account for both dielectric phenomena. Based on the Steric, Electric and Dielectric Exclusion (SEDE), the introduction of an average potential gradient approximation is shown to greatly improve the computational performance of the model without being detrimental to its predictive accuracy. The results obtained with this simplified model (SEDE-APG) are compared to the original SEDE model and an excellent agreement is obtained even in the case of electrolyte mixtures. Ultimately this model is confronted to experimental data of separation obtained for moderately to highly concentrated feed flows and exhibits promising results.