Effects of a capillary transition zone on the stability of a diffusive boundary layer

In geological storage of carbon dioxide (CO2), the buoyant CO2 plume eventually accumulates under the caprock. Due to interfacial tension between the CO2 phase and the water phase, a capillary transition zone develops in the plume. This zone contains supercritical CO2 as well as water with dissolved CO2. Under the plume, a diffusive boundary layer forms. We study how cross-flow between the capillary transition zone and the diffusive boundary layer affects gravitational stability of the diffusive boundary layer. Linear stability analysis shows that this cross-flow has no significant effect on the selection of the critical mode. However, interaction with the capillary transition zone enhances the instability of the boundary layer, such that the onset of instabilities occurs earlier, when the diffusive boundary layer is thinner. The onset time may be reduced by a factor of five, which corresponds to the thickness of the diffusive boundary layer at onset being reduced by a factor of two. This reduced thickness of the boundary layer at onset can be interpreted in terms of a reduced portion of the critical mode that must ’fit’ inside the boundary layer when the other portion of the mode is confined within the capillary transition zone. Direct numerical simulations for the non-linear regime show that the mass transfer rate can be enhanced up to four times when the cross-flow is accounted for. This increase is related to advective inflow of CO2-saturated water across the interface. Therefore, the contribution from dissolution to the safety of geological storage of CO2 begins earlier and can be considerably larger than showed by estimates that neglect the capillary transition zone.