Modeling of the variations of permeate flux, concentration polarization, and solute rejection in nanofiltration system

A numerical model is presented and experimentally validated for predicting the local concentration polarization and the related separation performance of nanofiltration (NF) system. The model combines computational fluid dynamics for describing the transport phenomena in NF channel, with Spiegler-Kedem-Katchalsky model for considering the permeation properties through NF membrane. Particular attention is given to the modeling of spatially varied solute rejection and solute transport through membrane, representing essential distinctions from the modeling of reverse osmosis (RO) membrane. Also, an experimental-numerical framework is proposed to determine model parameters related to solute transport, including reflection coefficient and solute permeability as functions of feed solute concentration. The usefulness of this model is highlighted by predicting concentration polarization under different conditions related to operations, membrane systems (NF vs. RO), and solute types (NaCl vs. MgSO₄). Also, the contributions by convection and diffusion to solute transport are clarified, benefiting by the modeling of solute transport.