Model of Cake Filtration in Porous Medium

Abstract

Strengthening of loose soil and creation of water-resistant underground walls are associated with filtration of small particles in a porous medium. Liquid solution pumped into a well under pressure spreads through hollow channels and strengthens the soil upon hardening. Many porous filters retain particles near the entrance. The particles deposited on the filter surface form a crust, which does not allow suspended particles to penetrate deep into the porous medium. A model of cake filtration - the formation of a surface crust during filtration of a monodisperse suspension in a homogeneous porous medium is considered. This model is a modification of the standard mathematical description of deep bed filtration with linear accessible fractional flow decreasing to zero. An exact solution is obtained using the method of characteristics. Asymptotics is constructed for a long time. It is shown that the dynamics and profiles of suspended and deposited particles concentrations exponentially decrease.