Analytical model for deep bed filtration with multiple mechanisms of particle capture

Abstract

A model for deep bed filtration of a monodisperse suspension in a porous medium with multiple geometric particle capture mechanisms is considered. It is assumed that identical suspended particles can block pores of different sizes. The pores smaller than the particle size are clogged by single particles; if the pore size exceeds the diameter of the particles, it can be blocked by bridging — several particles forming various stable structures.An exact solution is obtained for constant filtration coefficients. Exact solutions for non-constant filtration functions are obtained on the concentrations front of the suspended and retained particles and at the porous medium inlet. Asymptotic solutions are constructed near these lines. For small and close to constant filtration functions, global asymptotic solutions are obtained.A basic model with two mechanisms of particle capture is studied in detail. Asymptotic solutions are compared to the results of numerical simulation. The applicability of various types of asymptotics is analyzed.