Numerical Modelling of the Effect of Fouling on the Permeate Flux in Membranes

Porous membranes have been widely used for brackish water desalination. However, fouling (concentration polarization) extensively reduces permeate flux in reverse osmosis (RO) and nanofiltration (NF) membranes. In this study, we attempted to model salt concentration profile and find the effect of fouling on the permeate water flux. Parabolic (or diffusion) partial differential equation and forward finite difference method (explicit) were used in the numerical analysis. Selected membranes were RO and NF with the following assumptions: NaCl rejections of RO and NF are 95% and 50%, respectively, initial salt (NaCl) concentration is 10000 ppm, water has an average membrane diffusivity of 1.3×10^(-6) cm^2/s and membrane feed-side surface (fouling) concentrations are 0 ~ 20000 ppm. It was found that salt accumulation occurs at the membrane feed-side surface and there was a noticeable decrease in water flux as fouling increased. Flux results were 74.9, 67.4, 22.5, 0, –37.4, –74.9 LMH for the feed-side surface concentrations 0, 1000, 10000, 15000 and 20000 ppm, respectively, where negative flux indicates a back-flow scenario.