A 2-D streamline upwind Petrov/Galerkin finite element model for concentration polarization in spiral wound reverse osmosis modules

To accurately simulate concentration polarization in spiral wound reverse osmosis modules and quantitatively study the effects of the spacer on this phenomenon, a 2-D streamline upwind Petrov/Galerkin (SUPG) finite element model was developed by numerically solving the coupled convection-diffusion equation and Navier-Stokes equations in the feed channel. The model was verified with published experimental data of permeate flux in an empty channel. The numerical simulation results agreed well with the experimental data. The model was then used to simulate the velocity profile and concentration polarization in a segment (5 cm long) of a reverse osmosis feed channel with single filament attached to a membrane or submerged in the feed channel. It was found that velocity and concentration profiles in the regions near the filament were dramatically affected by the filament. In the regions immediately in front of and behind the filament which was attached to a membrane surface, salt concentration increased compared with those in an empty channel under the same operating conditions. This simulation study also showed that the wall concentration would be underestimated if flow direction transition (from crossflow direction to the direction approaching membrane surfaces) regions near the membrane surface were not adequately represented in the simulations. This could be one of the criteria for accurate simulation of concentration polarization. Numerical simulations suggest that the model could be a reliable tool for quantitative study of concentration polarization in spiral wound modules and for spacer design and optimization.