Calculation of Retention Profiles in Porous Medium

Abstract

To construct the foundations, tunnels and underground structures in loose rocks, the soil has to be strengthened and protected from formation and flood waters. Liquid grout pumped into the loose soil under pressure, filters in the pores and strengthens the porous rock. A porous rock with a hardened hardener forms a new building material. The use of reinforcements with dissimilar particles makes it possible to obtain a variety of building materials with desired properties. The paper purpose is modeling of filtration of a bidisperse suspension or colloid in a porous media with linear filtration and concentration functions and a size-exclusion particle capture mechanism. The problem is solved numerically by the finite difference method. The retention profiles of large and small particles and the total retention are constructed for different times. The main result of the work is the uneven distribution of the sediment depending on the particle size. The profiles of large particles always decrease monotonically, the profiles of small particles decrease monotonically at a short time and monotonically increase at a long time. The profiles of the total retention retain or change their monotonicity depending on the parameters of the problem. At some time, a maximum point appears on the plots of non-monotonic profiles, moving from the entrance to the exit of the porous media with increasing time. The limit velocity of maximum points movement of non-monotonic profiles depends on the model coefficients. This makes it possible to describe the properties of materials obtained by filtration of bidisperse suspensions in a porous medium theoretically.