Modeling the influence of temperature on gel-enhanced concentration polarization in reverse osmosis

Model for concentration polarization enhanced by gel accumulated at membrane surface has been proposed. It provides distribution of concentration in the liquid phase and within the gel layer. Model allows analyzing the influence of thickness of fouling layer on the CP degree, surface concentration, osmotic pressure and membrane permeability. The model is based on the following assumptions: (1) the fluid is incompressible, continuous and isothermal with uniform density field under the steady-state conditions; (2) process is accompanied by accumulation of gel layer at membrane surface along with concentration polarization; (3) diffusion layer and deposited gel contains different components and are characterized by different values of diffusivity coefficients; (4) correlation for effective hindered back diffusion coefficient within deposited layer based on published data is used in the study; (5) transverse transport is based on the following mechanisms: convection due to the pressure difference and back diffusion owing to the concentration gradient. The following conclusions have been drawn: (A) In the presence of gel layer the membrane surface concentration is enhanced due to the hindered back diffusion of salt ions that, in turn, results in growth of osmotic pressure at the membrane surface. The elevated surface concentration also results in elevated salt concentration in permeates and decreases of the net driving force; (B) For membranes with moderated degree of rejection the growth of temperature causes decrease of the CP degree at the surface. The proposed model can be incorporated into the algorithm for calculation of longitudinal distribution of the CP degree, resistance and trans-membrane flux.

Proposed model can be applied for design of processes accompanied by concentration polarization along with gel formation when temperature doesn’t remain constant. It is essential for multi-component systems when the diffusion layer in liquid phase and deposited gel (or cake) are built by different components. The following conclusions have been drawn: (A) In the presence of a gel layer, the membrane surface concentration is enhanced due to hindered back diffusion of ions within the gel that, in turn, results in growth of osmotic pressure at the membrane surface. The enhanced surface concentration will also result in elevated salt concentration in permeate and decrease of the net driving force for water flux; (B) For membranes with moderated degree of rejection the growth of temperature causes decrease of the CP degree at the surface. Proposed model can be incorporated into algorithm for calculation of longitudinal distribution of CP degree, resistance and transmembrane flux. Calculated data and projections are attached. Model allows analyzing the influence of thickness of fouling layer on the CP degree, surface concentration, osmotic pressure and membrane permeability.