Numerical investigations of the effect of non-uniform membrane permeability on deposit formation and filtration process

Spatial variations of cake thickness along flat-sheet membranes were previously evidenced from filtration experiments [J. Mendret, C. Guigui, P. Schmitz, C. Cabassud and P. Duru, An optical method for in situ characterization of fouling during filtration, AIChE Journal, 53 (2007) 2265–2274.]. Neither gravity effects nor pressure drop in channel could explain these unexpected variations. Therefore a theoretical model was developed to investigate growth of a cake on a non-uniform permeability membrane. The model considers two dimensional flow of a particle suspension in a rectangular channel with one porous wall under suction. Cake growth is assumed to be proportional to local filtration velocity. Its macroscopic properties are prescribed from empirical power laws obtained from the aforementioned experiments. A finite element method using mesh deformation was adopted to solve the governing equations of the problem, i.e., the coupled Navier-Stokes and Darcy Brinkman equations, to simulate a complete filtration run. Comparisons between simulations and experiments are in good agreement. Then a careful analysis of the numerical results reveals a non-uniform initial filtration velocity along the porous wall which rapidly becomes uniform. On the contrary, a non-uniform cake thickness still remains after a long time of filtration which profile is similar to the initial membrane permeability profile. Moreover increase of the transmembrane pressure significantly reduces the time necessary to recover a uniform behaviour of the filter.