Scaling CO2-brine mixing in permeable media via analogue models

Supercritical CO2 injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After injection, CO2 gas phase is buoyancy-driven over the denser aqueous brine, reaching an apparent gravitational stable distribution. However, CO2 dissolution in brine propels convection since the mixture is even denser than the underlying brine. This process still needs to be characterised comprehensively. Here, we investigate the irreversible mixing of dissolved CO2 in brine through laboratory-scale numerical experiments utilising the Hele-Shaw model (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746-767) and a fully miscible two-fluid system. In this scenario, mixing the less dense fluid - mimicking CO2 gas phase - with the heavier fluid - representing aqueous brine - catalyses cabbeling-powered convection. Our numerical simulations recover the laboratory results in porous media by Neufeld et al. (Geophys. Res. Lett., vol. 37, issue 22, 2010, L22404) and may explain the scaling law obtained by Backhaus et al. (Phys. Rev. Lett., vol. 106, issue 10, 2011, 104501) in Hele-Shaw cells. More remarkably, we show that the mass flux between the two analogue fluids, characterised by the Sherwood number Sh, obeys the universal scaling law Sh similar to Ra nu(scalar), with Ra the Rayleigh number and ?(scalar) the mean scalar dissipation rate. This paper sheds light on the fluid dynamics and solubility trapping in geological carbon sequestration.