Dynamics and mass transport of solutal convection in a closed porous media system

Most of the recent studies of CO$_2$ sequestration are performed in open systems where the constant partial pressure of CO$_2$ in the vapor phase results in a time-invariant saturated concentration of CO$_2$ in the brine ($C_s$). However, in some closed natural CO$_2$ reservoirs, e.g., Bravo Dome in New Mexico, the continuous dissolution of CO$_2$ leads to a pressure drop in the gas that is accompanied by a reduction of $C_s$ and thereby affects the dynamics and mass transport of convection in the brine. In this talk, I discuss the characteristics of convective CO$_2$ dissolution in a closed system. The gas is assumed to be ideal and its solubility given by Henry's law. An analytical solution shows that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly. Scaling analysis reveals that the volume ratio of brine and gas $\eta$ determines the behavior of the system. DNS show that no constant flux regime exists for $\eta > 0$; nevertheless, the quantity $F/C_s^2$ remains constant, where $F$ is the dissolution flux. The onset time is only affected by $\eta$ when the Rayleigh number $Ra$ is small. In this case, the drop in $C_s$ during the initial diffusive regime significantly reduces the effective $Ra$ and therefore delays the onset.