Spreading and mixing during solutal convection in uniform porous media with application to geologic CO2 storage

Convective dissolution in saline aquifers is expected to positively impact subsurface storage of carbon dioxide (CO2) by accelerating its dissolution rate into reservoir brines. By largely focusing on the dissolution flux, previous studies lack a systematic evaluation of the mixing process following CO2 emplacement, including a quantitative analysis at conditions representative of subsurface traps (Rayleigh number, Ra≤1 000). Here, we investigate solutal convection numerically in a two-dimensional uniform porous medium in the regime Ra=100−10 000. The macroscopic evolution of the convective process is characterized by means of fundamental macroscopic measures of mixing that use the local spatial structure of the solute concentration field. It is shown that the intensity of segregation closely mimics the evolution of the in situ convective pattern arising from the stretching and merging of downwelling plumes. The spreading length and the dilution index both confirm that the mixing process accelerates over time (t) with a power law scaling (∝tα) that transitions from diffusive (α=0.5) to superdiffusive mixing (α≥1) irrespective of Ra. This transition time scales τon∝Ra−2 and is used as a measure of the onset time of convection. The dilution index indicates that the time needed to reach close-to-complete mixing reduces linearly with Ra. On the contrary, the non-dimensional mass flux, expressed in terms of the Sherwood number, Sh, reveals a natural logarithmic scaling for Ra≤2 500