Filtration of a highly concentrated suspension in a porous medium

Abstract

Abstract The problems of filtration in porous media are in demand when strengthening foundations and building waterproof walls in rocks. Deep bed filtration of a highly concentrated monodisperse suspension in a homogeneous porous medium with size-exclusion particle retention mechanism is considered. When filtering a suspension in a porous medium, some solid particles get stuck on the porous frame and form a deposit. The concentration of suspended particles injected at the porous medium inlet decreases when moving from inlet to outlet. The mathematical model for a highly concentrated suspension in a porous medium assumes a nonlinear dependence of the deposit growth rate on the concentration of suspended particles. The exact solution to the filtration problem in implicit integral form and the Riemann invariant relating the concentrations of suspended and retained particles are obtained. The problem is solved for a linear filtration function and a general nonlinear concentration function. An asymptotic solution is constructed near the concentrations front of suspended and retained particles. It is shown that the asymptotics is close to the exact solution, the error decreases with increasing order of asymptotic expansions. The asymptotic solution explicitly defines the dependence of the solution on model parameters and can be used to solve the inverse filtration problem.