Modeling the transport of the finite volume of impurity in a vertical porous column

Abstract

We consider a problem of vertical percolation (bottom-up) of a mixture portion through a porous medium array under constant pressure drop. Contaminant transport is modeled within the MIM (mobile/immobile media) approach. Sorption processes are described by a nonlinear MIM model accounting for the limit of contaminant deposition on pore walls. Filtration is modeled using the Darcy–Boussinesq approximation, which enables the inclusion of gravity effects and consequently the development of concentration convection. The permeability-porosity dependence is given by the Kozeny-Carman relation. The basic non-convective state was obtained analytically. The convection onset problem was solved numerically using the finite difference method. The field of concentration and stream function perturbations were obtained, as well as the average instantaneous concentration profile along the flow direction at different time moments. It is demonstrated how the growth of the Darcy–Rayleigh number affects the solution injection and breakthrough times, as well as the breakthrough curve.