Numerical Simulations of Concentration Polarization and Mineral Scaling in Reverse Osmosis Systems

Fluid flow and mass transport in reverse osmosis (RO) systems are difficult to simulate numerically due to the coupling between the transmembrane filtrate flow, pressure, and osmotic pressure. This coupling is particularly challenging for real-world systems in which the local filtrate flow varies both spatially and temporally, and is further complicated for systems in which filtrate flow is also affected by mineral scaling and membrane fouling. Consequently, previous simulations of RO tend to focus on two dimensional steady cases. We present a numerical method specifically tailored to simulating RO. Using the method, we simulate the transient formation of concentration polarization layers as a function of feed Reynolds number, solute concentration, and transmembrane pressure. From the computed flow fields, we investigate the importance of advection and diffusion of solutes both normal and tangential to the membrane surface. Contrary to the thin-film approximation, we find that normal diffusion can be balanced by both normal and tangential advection within the concentration polarization layer. Finally, we use our method to simulate the transient decline in filtrate flux due to the precipitation of sparingly soluble salts on the membrane surface.