Mathematical modeling and simulation of the multiple solutes system for nanofiltration process

A one-dimensional model for the multiple solutes filtration system is developed by extending the Spiegler–Kedem model by incorporating the solute–solute interactions. This extended Spiegler–Kedem model is suitable for predicting the performance of multiple solutes system in nanofiltration. The model is characterized by the parameters of Lp, σs, Psi, Pss and ks. The parameters were estimated using the Levenberg–Marquardt method coupled with Gauss–Newton algorithm based on the experimental data obtained from the literature. The simulation results obtained from the proposed model were also compared with the simulation results obtained from the Spiegler–Kedem model and extended Nerst–Plank model, respectively. The simulation results indicate that the flux behavior and the predicted permeate concentrations were in good agreement with that predicted by the two existing models and the experimental data. The extended Spiegler–Kedem model developed is suitable for predicting the performance of multiple solutes for nanofiltration system.