Retention profiles of multiparticle filtration in porous media

A one-dimensional deep bed filtration model of a polydisperse suspension or colloid in a porous medium is considered. The model includes a quasilinear system of 2n equations for concentrations of suspended and retained particles of n types. The problem is reduced to a closed 3 x 3 system for total concentrations of suspended and retained particles and of occupied rock surface area, which allows an exact solution. The exact solution to the n-particle problem is derived, the existence and uniqueness of the solution are proven, and the solution in the form of a traveling wave is obtained. The retention profiles (dependence of the deposit concentration on the coordinate at a fixed time) of different size particles and the total profile are studied. It is shown that the profile of large particles decreases monotonically, while the profile of small particles is nonmonotonic. Conditions for the monotonicity/nonmonotonicity of the intermediate particle profiles and the total profile are obtained. The maximum point of the small particles profile tends to infinity with unlimited growth of time, and the maximum points of nonmonotonic profiles of intermediate particles are limited. The asymptotical expansion of the maximum points of nonmonotonic profiles is constructed.