Scaling the irreversible mixing of carbon dioxide in brine-rich permeable media

The supercritical CO₂ injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After its injection, CO₂ is placed over the denser brine in an apparent gravitational stable distribution. However, mixing CO₂ and brine leads to a cabbeling-like process, i.e. the resulting mixture is even denser than the pure brine. Here, we investigate the fluid dynamics of CO₂ sequestration in underground brines at a laboratory scale utilising the Hele-Shaw model (Letelier et al., 2019). At this scale, the CO₂-brine mixture density meets the miscible model ρ(S_ω) = ρ_b+aS_ω+cS_ω², with S_ω the CO₂ mass fraction. We performed direct numerical simulations to quantify the irreversible mixing of CO₂ in brines, recovering the experimental results by Neufeld et al. (2010) and Guo et al. (2021) in porous media. More remarkably, for the Hele-Shaw model we found that the mean scalar dissipation rate, Θ_scalar, depends on the Rayleigh number, Ra, a novel result not predicted by previous works. The results show that the dissolved CO₂ mass flux, characterised by the Sherwood number Sh, satisfies the scaling law Sh ~ Ra Θ_scalar within the time window between the onset of convection and the arrival of the first megaplume at the Hele-Shaw cell bottom.