Buoyant flow of CO2 through and around a semi-permeable layer of finite extent

The buoyancy- and capillary-driven counter-current flow of CO2 and brine through and around a semi-permeable layer is studied both numerically and theoretically. The continuities of the capillary pressure and the total flux at the interface between the permeable matrix and layer control the CO2 saturation discontinuity at the interface and the balance between the buoyant and capillary diffusion fluxes on each side of the interface. This interface process is first studied in a one-dimensional (1-D) vertical column geometry using the concept of extended capillary pressure and a graphical representation of the continuity conditions in the (S-L, S-U) plane, where SL and SU are the lower and upper saturation traces at the interface, respectively. In two dimensions, we heuristically extend the two-phase gravity current model to the case where the current is bounded by a semi-permeable layer. Consequently, the current is not saturated with CO2, and its saturation and shape are derived from the flux and capillary pressure continuity conditions at the interface. This simplified model, which depends on CO2 saturation only, is compared to fine grid simulations in the capillary-free and gravity-dominant cases. A good agreement is obtained in the second case; the current geometrical characteristics are accurately described. In the capillary-free case, we demonstrate that the local total velocity, which is, on average, zero because the flow is counter-current, must be considered in the total flux at the interface to obtain the same level of agreement.