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

Convective dissolution is the process by which CO2 injected in geological formations dis-solves into the aqueous phase and thus remains stored perennially by gravity. It can bemodeled by buoyancy-coupled Darcy flow and solute transport. The transport equationshould include a diffusive term accounting for hydrodynamic dispersion, wherein the ef-fective diffusion coefficient is proportional to the local interstitial velocity. We investi-gate the impact of the hydrodynamic dispersion tensor on convective dissolution in two-dimensional (2D) and three-dimensional (3D) homogeneous porous media. Using a novelnumerical model we systematically analyze, among other observables, the time evolutionof the fingers’ structure, dissolution flux in the quasi-constant flux regime, and mean con-centration of the dissolved CO2; we also determine the onset time of convection, ton. Fora given Rayleigh number Ra, the efficiency of convective dissolution over long times iscontrolled by ton. For porous media with a dispersion anisotropy commonly found in thesubsurface, ton increases as a function of the longitudinal dispersion’s strength (S), in agree-ment with previous experimental findings and in contrast to previous numerical findings, adiscrepancy which we explain. More generally, for a given strength of transverse disper-sion, longitudinal dispersion always slows down convective dissolution, while for a givenstrength of longitudinal dispersion, transverse dispersion always accelerates it. Further-more, systematic comparison between 2D and 3D results shows that they are consistenton all accounts, except for a slight difference in ton and a significant impact of Ra on thedependence of the finger number density on S in 3D.