Problem of Deep Bed Filtration in a Porous Medium with the Initial Deposit

Abstract

The macroscopic model of long-term deep-bed filtration flow of a monodisperse suspension through a porous medium with size-exclusion particle-capture mechanism and without retained-particle mobilization is considered. It is assumed that the pore accessibility and the fractional particle flux depend on the deposit concentration and at the initial time the porous medium contains a nonuniformly distributed deposit. The aim of the study is to find the analytical solution in the neighborhood of a mobile curvilinear boundary, namely, of the suspended-particle concentration front. The property of having fixed sign is proved for the solution. The exact solution of the filtration problem on the curvilinear front is found in explicit form. The sufficient condition of existence of the solution on the concentration front is obtained. An asymptotic solution is constructed in the neighborhood of the front. The time interval of applicability of asymptotics is determined from the numerical solution.