Convective dissolution of Carbon Dioxide in two- and three-dimensional porous media: the impact of hydrodynamic dispersion

Convective dissolution is the process by which CO₂ injected in geological formations dissolves into the aqueous phase and thus remains stored perennially by gravity. It can be modeled by buoyancy-coupled Darcy flow and solute transport. The transport equation should include a diffusive term accounting for hydrodynamic dispersion, wherein the effective diffusion coefficient is proportional to the local interstitial velocity. We investigate the impact of the hydrodynamic dispersion tensor on convective dissolution in two-dimensional (2D) and three-dimensional (3D) homogeneous porous media. Using a novel numerical model we systematically analyze, among other observables, the time evolution of the fingers’ structure, dissolution flux in the quasi-constant flux regime, and mean concentration of the dissolved CO₂; we also determine the onset time of convection, t_on. For a given Rayleigh number Ra, the efficiency of convective dissolution over long times is controlled by t_on. For porous media with a dispersion anisotropy commonly found in the subsurface, t_on increases as a function of the longitudinal dispersion’s strength (S), in agreement with previous experimental findings and in contrast to previous numerical findings, a discrepancy which we explain. More generally, for a given strength of transverse dispersion, longitudinal dispersion always slows down convective dissolution, while for a given strength of longitudinal dispersion, transverse dispersion always accelerates it. Furthermore, systematic comparison between 2D and 3D results shows that they are consistent on all accounts, except for a slight difference in t_on and a significant impact of Ra on the dependence of the finger number density on S in 3D.