Mathematical Modeling of Nanofiltration-based Deionization from Aqueous Solutions

Nanofiltration-based separation processes have found diverse applications in industrial and environmental problems recently, due to several advantages such as lower energy requirement and elevated flux rates compared with their Reverse Osmosis (RO) counterparts. Several attempts have been made for modelling NF-based separation processes ranging from rigorous space-charge approaches to simpler Irreversible Thermodynamic (IT) models and yet none has satisfied the whole predictive expectations either as a result of unacceptable computational requirements or oversimplifying assumptions. Also, few attempts have been made for the modelling of NF behaviour in strong salt solutions. Thus, a new model incorporating the new phenomena to compensate for the shortcomings can help shed light to find new directions.This study is an effort for modelling the NF-based separation processes by using the Modified extended Nernst-Planck (MENP) equation for solute transport through membrane active layer and advectiondiffusion for concentration and velocity interactions due to feed cross-flow over the membrane surface.MENP takes into account the variations of activity coefficient and its influence on retention due to ionic strength variations. In the case of pure salt solutions (NaCl & Na2SO4), the effect of ionic strength and charge density on the rejection will be investigated. The results show that higher ionic strengths result in lower retentions and charge density has an extended effect in the modified model.