A simple analytical model for estimating the dissolution-driven instability in a fluid saturated porous medium

This presentation provides a more detailed description of the alternative view at tackling the stability problem that was put forth by  Vo and Hadji (Phys. Fluids., 2018) and Wanstall and Hadji (J. Eng. Math., 2017). This new approach, which is based on a step-function base profile, is contrasted with the usual transient base state. While both provide only estimates for the instability threshold values, the step-function base profile approach has one great advantage in the sense that the problem at hand can be viewed as a stationary Rayleigh-Benard problem, the stability of which can be analyzed by a variety of existing analytical methods using only paper and pencil. We show results of both linear and weakly nonlinear studies which include the effect of permeability variation with depth, diffusivity anisotropy and a first order chemical reaction between the carbon-rich brine and host mineralogy. We derive interfacial flux conditions and use them to describe the time evolution of the sharp interface between the carbon-rich layer and the underlying ambient brine.