Cleaning porous media by an external vertical flow

The paper is devoted to the study of the cleaning process of a clogged porous medium. A flow through a closed domain of porous media is generated by the prescribed pressure drop between the boundaries. The porous media initially contain an immobilized solute which is removed by an external flow. As a result, the porosity and permeability of the media increase. The solute immobilization is modelled within the framework of the mobile/immobile media model taking into account saturation of a solid matrix of the media with the solute. The porosity is assumed as a linear function of the immobile solute concentration, and the dependence of permeability variation due to porosity change is modelled on the base of the Kozeny-Carman expression. The direction of an external flux is assumed to be the same as the gravity force direction. This assumption allows us to obtain a one-dimensional solution for the cleaning process taking into account the buoyancy force. The equation for the flow into the clogged porous media is derived in the general case. The one-dimensional problem of the porous media cleaning by a vertical external flow is formulated and solved. The dependences of the cleaning time on the system parameters are obtained and discussed. The question about the stability of the one-dimensional solution is described, and critical values of the governing parameters are defined in a particular case.