Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media

Geological carbon dioxide (CO₂) sequestration entails capturing and injecting CO₂ into deep saline aquifers for long-term storage. The injected CO₂ partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO₂-rich brine, a process that greatly accelerates solubility trapping of the CO₂. Here, we investigate the pattern-formation aspects of convective mixing during geological CO₂ sequestration by means of high-resolution three-dimensional simulation. We find that the CO₂ concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing.