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