Rayleigh-Taylor convection in confined porous media

Motivated by the dissolution phenomena occurring during carbon sequestration processes, we analyze Rayleigh-Taylor convection in isotropic porous media. In the Rayleigh-Taylor configuration, a layer of dense fluid (CO2+brine) lyes on top of a layer of light fluid (brine). The velocity field is computed with the Darcy law, whereas the concentration field is determined by the advection-diffusion equation. We used a pseudospectral scheme (Fourier discretization in periodic direction and Chebyshev polynomial in wall-normal direction) to run Direct Numerical Simulations (DNS) of the present system. We focused in particular on the behavior of the mixing length $h$ (the tip-to-rear finger distance), a fundamental quantity to characterize all the transfer phenomena (solute, convection and energy) occurring in the analyzed case. In particular, we observed that the time behavior of $h$ is twofold: during the initial transient evolution, $h$ has a self similar universal behavior; later, due to the presence of boundaries, the behavior becomes more complex and hard to predict. Physical implications of the present results on dissolution modeling approaches will be also addressed.