Upscaled modeling of convective CO2 dissolution in water using an effective diffusivity approach

Subsurface storage of carbon dioxide can be complicated by the convective mixing of CO2 with water. The convection cells can be just a few meters wide, whereas the storage reservoir can span over several kilometers. This difference in space scales is difficult to resolve in the numerical modeling of subsurface flows, which requires the development of effective approaches similar to those employed in the effective turbulence modeling. In the manuscript, we present an approach for the numerical modeling of the convective mixing using coarse simulation grids. We consider a sector of a water-saturated porous medium right beneath a CO2 plume. The approach utilizes an artificial amplification of the molecular diffusivity of CO2 in water. We develop the relations describing the amplification changes with time by adjusting the approach to the results of two-dimensional (2D) modeling of the mixing at different Rayleigh–Darcy numbers. Herewith, the diffusive mixing stage and the early and late convective stages are specifically addressed. We thereby construct an effective model that regards the mixing as a submesh process. The approach is validated by comparing the results of the effective model for a thin porous column with those of 2D modeling. We thus evaluate the range of the Rayleigh–Darcy number at which the approach is most accurate. The presented results may be of interest for researchers working in the field of subsurface CO2 storage.