Onset of solutal convection in layered sorbing porous media with clogging

Abstract

The effect of pore clogging on the onset of solute-driven convection in a layered sorbing porous medium consisting of two sublayers with distinct permeabilities is investigated. Solute transport in the medium is described by the nonlinear MIM model involving the Langmuir equation. The solute is divided into two phases. The first one is a mobile phase that drifts with flow and the second one is an immobile phase captured by porous matrix and reducing the total pore space. The model takes into account the saturation concentration, which is a maximal possible amount of solute adsorbed by a unit volume of porous medium. The degree of pore clogging is determined through a clogging coefficient proportional to the saturation concentration. Another coefficient is a sorption parameter including the ratio of adsorption and desorption rates. By varying these coefficients, we obtain the threshold solutal Rayleigh–Darcy number for the onset of convection in the following three types of layered sorbing systems: (1) system with the upper thin highly permeable sublayer, (2) system with the lower thin highly permeable sublayer, and (3) system with equal thick sublayers. The results show that convection onset delays due to the enhancement of clogging effect in all of the three systems. It is more difficult to induce convection here because the pore plugging together with an increase in adsorption rate as compared to desorption rate reduces the mean porosity and permeability of porous matrix. Forward and reverse transitions between the critical convective rolls with different wavelengths are found to occur in the systems 1 and 2 containing the upper or lower thin highly permeable sublayers as the sorption parameter increases. A sequence of “local convection – large-scale convection – local convection” transitions is observed in system 1. There is an opposite sequence of “large-scale convection – local convection – large-scale convection” transitions in system 2. The preferred convective roll width at the onset of convection changes by almost fifth times at the described forward and reverse transitions. It roughly corresponds to the ratio of the total thickness of porous system to that of the thin highly permeable sublayer where local convection generates.