Dissolution-driven porous-medium convection in the presence of chemical reaction

Abstract

AbstractMotivated by processes occurring during ${\mathrm{CO}}_2$ sequestration in an underground saline aquifer, we examine two-dimensional convection in a finite-depth porous medium induced by a solute introduced at the upper boundary. Once dissolved, the solute concentration is assumed to decay via a first-order chemical reaction, restricting the depth over which solute can penetrate the domain. Using spectral and asymptotic methods, we explore the resulting convective mixing using linear stability analysis, computation of nonlinear steady solution branches and time-dependent simulations, as a function of Rayleigh number, Damköhler number and domain size. Long-wave eigenmodes show how deep recirculation can be driven by a shallow solute field while explicit approximations are derived for the growth of short-wave eigenmodes. Steady solution branches undergo numerous secondary bifurcations, forming an intricate network of mixed states. Although many of these states are unstable, some play an important role in organising the phase space of time-dependent states, providing approximate bounds for time-averaged mixing rates.