Porous high-pressure membranes have been widely used for both brackish water and seawater desalination. However, fouling (concentration polarization) extensively reduces permeate flux in high-pressure membranes such that reverse osmosis (RO) and/or nanofiltration (NF). In this study, we have attempted to understand the effect of membrane fouling on the permeate water flux by modeling the salt concentration profile within a membrane of interest. A parabolic (or diffusion) partial differential equation was used to describe the change in salt concentration inside the membrane. Subsequently, the PDE equation was solved numerically, under certain assumptions, by using forward finite difference (FFD) explicit method. 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. For waters with an initial salt concentration of 10000 ppm (NaCl) and with an average diffusivity of , results showed that both RO/NF would have flux rates of 74.9, 67.4, 22.5, 0, –37.4, –74.9 LMH for the feed-side surface concentrations 0, 1000, 7000, 10000, 15000 and 20000 ppm, respectively, where negative flux indicates a back-flow scenario.
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