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

Jayabrata Dhar (1) , Patrice Meunier (2) , F. Nadal (3) , Yves Méheust (1)

1 GR - Géosciences Rennes
2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
3 Loughborough University

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 be modeled by buoyancy-coupled Darcy flow and solute transport. The transport equation should 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 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 con- centration of the dissolved CO2; we also determine the onset time of convection, ton. For a given Rayleigh number Ra, the efficiency of convective dissolution over long times is controlled by ton. For porous media with a dispersion anisotropy commonly found in the subsurface, 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, a discrepancy which we explain. More generally, for a given strength of transverse disper- sion, longitudinal dispersion always slows down convective dissolution, while for a given strength of longitudinal dispersion, transverse dispersion always accelerates it. Further- more, systematic comparison between 2D and 3D results shows that they are consistent on all accounts, except for a slight difference in ton and a significant impact of Ra on the dependence of the finger number density on S in 3D.

Domains: Fluid mechanics [physics.class-ph]; Hydrology

Jayabrata Dhar, Patrice Meunier, F. Nadal, Yves Méheust. Convective dissolution of Carbon Dioxide in two- and three-dimensional porous media: the impact of hydrodynamic dispersion. Physics of Fluids, 2022, 34 (6), pp.064114. ⟨10.1063/5.0086370⟩. ⟨insu-03702425⟩