Free-interface convective mixing in porous media: 2D and 3D numerical simulations

We investigate convective mixing in porous media in the presence of a free interface separating two miscible fluids initially arranged in a stable configuration. This problem is motivated by the dynamics of supercritical ${\text{CO}}_2$ overlying a brine-saturated porous medium, as well as analogous laboratory experiments. Diffusion of the lighter upper layer into the denser lower layer results in a layer with a density greater than that of the denser lower layer, which then induces an unstable stratification that triggers convection. Using high-resolution direct numerical simulations, we analyse the system dynamics in both two- and three-dimensional geometries and for different diffusivities. Our results show that in 2D the process is faster, with dissolution fluxes about $15\%$ higher than in 3D. Convective plumes deform the initially flat interface, creating an iso-concentration surface whose vertical extent increases over time. These findings highlight the need for caution when extrapolating two-dimensional results to three-dimensional applications.