Dissolution-driven convection of low solubility fluids in porous media

Geological sequestration represents a promising strategy for storing CO₂. In order to further elucidate this process, we simulated the dissolution-driven convection of a CO₂-brine system with a free interface in a porous medium, based on a novel Darcy-Cahn-Hilliard model that accounts for the low solubility of CO₂ with brine. We consider a range of unstable Rayleigh numbers Ra, and we derive a quantitative relationship for the dimensionless solute flux. This flux exhibits distinctly different behaviors during the various stages of the flow. In particular, during the free convection stage, larger Ra-values result in a moderate decrease of the solute flux, while the solute flux is approximately independent of Ra during the constant flux stage. In order to evaluate the solute flux during the shutdown stage, we employ simulations in the two-sided Rayleigh-Bénard cell configuration. With a correction factor a=0.67 to account for the damping effect of the bottom boundary, the model can reproduce the solute flux during the shutdown stage. By accounting for the effects of partial miscibility, the simulation approach developed here holds the potential to yield more accurate estimates of the solute flux in the context of CO₂ sequestration and related applications.