Two-scale Modelling of the Concentration Polarization in a Reverse Osmosis Membrane

In the design and control of reverse osmosis desalination plants, the clean water flux, which passes through the membranes, is the most important variable. Flux depends on several parameters, such as the membrane permeability or the temperature, but mainly on the salt concentration on the membrane surface. The salt concentration is easily measured in the bulk of the feed, but not on the membrane surface, where it should be estimated. The concentration polarization creates an unwanted increase of the salt concentration between the bulk side and the membrane surface. The polarization effect is due to the convective transport of salt molecules by the water flow to the boundary layer of the membrane, and their subsequent blockage by the membrane itself. A correct estimation of the concentration polarization is fundamental to predict the clean water flux, and finally, to be able to carry out a good design and control of the desalination plant. Several models have been proposed in the literature to calculate the concentration polarization (or the salt concentration on the membrane surface). This paper presents a new model, which aims to solve some of the disadvantages of the previous models.