Volume averaged reduced order Donnan Steric Pore Model for nanofiltration membranes

A reduced order model (ROM) is derived for the Donnan Steric Pore Model (DSPM) [Bowen and Welfoot, Chem. Engng. Sci. 57 (2002) 1121], using volume averaging principles. DSPM has coupled ordinary differential equations and requires an iterative solution procedure. The proposed ROM reduces the original differential equations to set of algebraic equations. It has a direct solution, leading to elegant parameter extraction and spreadsheet implementation. When applied to desalination data at nominal salt concentrations, charge density and salt rejections predicted by ROM compare well with detailed DSPM results. The water flux across desalination membranes reduces as feed salinity increases. This experimental data can be used to back-calculate the concentration polarization mass transfer coefficient using the method developed by Sutzkover et al. Desalination 131 (2000) 117. Once concentration polarization effects are accounted for using their method, the proposed ROM describes the water flux and salt rejection data accurately for a wide range of feed concentrations without any additional parameters.