Refinement of the model of concentration convection in a porous medium taking into account immobilization of impurity and weak clogging

Abstract

The influence of weak clogging on the process of a heavy impurity transport through a horizontal layer of a porous medium is studied. A constant concentration drop is set at the boundaries of the layer, the flow along the layer is maintained by a constant pressure drop. The present problem is a concentration analog of the well-known Horton-Rogers-Lapwood (HRL) problem. The equations describing the transport of the impurity taking into account the deposition (immobilization) of the impurity particles on the porous skeleton are obtained. The deposition process is described in the framework of the well-known linear sorption model (linear MIM model). Clogging is assumed to be weak in the sense that the influence of deposited particles on porosity is considered to be negligible and is taken into account only with respect to the reduction of the permeability of the medium. It is found that the basic solution to this system admits the regime of stationary filtration along the layer. In this case, the impurity distribution is linear, which coincides with the known HRL solution. The stability of the basic state is analyzed numerically. Neutral curves as well as minimum values of critical parameters (Rayleigh-Darcy number, wave number, and frequency) depending on the system parameters are obtained and analyzed. It is shown that the arising instability, as in the HRL problem, is oscillatory by nature. Taking into account the clogging (along with taking into account the deposition) leads to an increase in the stability of the stationary filtration flow and attenuation of the oscillations. The study determines the limits of applicability of the linear MIM model, widespread in the literature, that does not taking into account the clogging.