Buoyant flow of $\text{CO}_{2}$ through and around a semi-permeable layer of finite extent. (15th November 2016)

• Record Type: Journal Article
• Authors: Ngo, Tri Dat; Mouche, Emmanuel; Audigane, Pascal
• Is Part Of: Journal of fluid mechanics. Volume 809(2016:Dec.)
• Page Start: 553
• Page End: 584
• Publication Date: 2016-11-15
• Subjects: gravity currents, -- multiphase flow, -- porous media; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.684
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : The buoyancy- and capillary-driven counter-current flow of $\text{CO}_{2}$ 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 $\text{CO}_{2}$ 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 $S_{L}$ and $S_{U}$ 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 $\text{CO}_{2}$, and its saturation and shape are derived from the flux and capillary pressure continuity conditions at the interface. This simplified model, which depends on $\text{CO}_{2}$ 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.