Prediction of concentration polarization and flux behavior in reverse osmosis by numerical analysis

A Galerkin finite elements program was developed to compute the concentration profiles throughout a reverse osmosis membrane module to predict the performance of the module. Parametric studies were performed to establish program consistency. Diffusivity was taken as a function of concentration, and the error of assuming an isotropic diffusivity is discussed. Multicomponent solutions were studied assuming no interactions between solutes. The finite element method allowed rapid evaluation of various membrane module configurations, such as tapered cell geometry and channels containing spacers. A spiral wound module was approximated using a straight channel with spacers, and the results obtained were closer than previously published approximate solutions when compared with experimental data. Computer analysis was also extended from a Newtonian fluid to a Bingham fluid.