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

Abstract

Geological carbon dioxide (CO[subscript 2]) sequestration entails capturing and injecting CO[subscript 2][subscript 2]into deep saline aquifers for long-term storage. The injected CO[subscript 2] 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 CO[subscript 2]-rich brine, a process that greatly accelerates solubility trapping of the CO[subscript 2]. Here, we investigate the pattern-formation aspects of convective mixing during geological CO[subscript 2] sequestration by means of high-resolution three-dimensional simulation. We find that the CO[subscript 2] 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.