Density-driven convection enhanced by an inclined boundary: Implications for geological CO${}_2$ storage

We experimentally examine dissolution-generated, density-driven convection with an inclined boundary in both a Hele-Shaw cell and in a porous medium. The convection, manifested by descending, dense fingers, is generated by a diffusive mixing of two liquids at the interface. We investigate the dynamics, widths, and wavelengths of the fingers and characterize the global convective transport for a wide range of permeabilities and tilt angles of the boundaries. Our results have implications for CO${}_2$ storage in a saline aquifer when brine saturated with CO${}_2$ produces a heavier mixture, which may result in an enhanced mass transfer by convection. Our measurements reveal a further enhancement of convection with inclined boundaries, which suggests that sloping formations provide improved sites for CO${}_2$ storage.

Figure 1

(a) Schematic diagram of the experimental setup of a vertically placed Hele-Shaw cell, two parallel plates with a uniform and small separation $b$, at a tilt angle $\alpha$. (b)–(d) Shadowgraph snapshots of the descending plumes due to the dense mixture at the interface [marked by the horizontal red arrow in (a)] between water and propylene glycol (PPG, heavier than water) in a Hele-Shaw cell of a permeability $k=b^2/12=2.2\times {10}^{-4}$ cm${}^2$ and $\alpha ={(10\pm 0.3)}^{\circ }$. The corresponding time sequences are (b) 270, (c) 555, and (d) 1125 sec [19].

Figure 2

Representative spatiotemporal diagrams of the dense fingers (shown by the darker intensity) close to the interface where the dissolution takes place in a vertical cell of $\alpha =0^{\circ }$ in (a) and in an inclined cell of $\alpha ={30}^{\circ }$ in (b). As revealed in (b), the plumes move laterally towards the inclined walls at a later time. The two dashed lines below (b) schematically represent the slopes of the inclined boundaries.

Figure 3

Time evolution of the plume statistics in a Hele-Shaw cell in terms of the ratio of the plume width $\delta$ to the average wavelength $〈\lambda 〉$ for different parameters in ($k,\alpha$): $\alpha =0^{\circ }$ ($○$), $\alpha ={10}^{\circ }$ ($\square$), and $\alpha ={20}^{\circ }$ ($▵$) for the same permeability $k=2.2\times {10}^{-4}$ cm${}^2$, and $\alpha =0^{\circ }$, $k=1.3\times {10}^{-4}$ cm${}^2$ ($⧫$). The inset is a representative snapshot of the descending plumes, showing the measured width ($\delta$) and wavelength ($\lambda$) of the plumes.

Figure 4

The effect of permeability on the dimensionless convective mass transfer in vertical cells ($\alpha =0^{\circ }$). The Darcy-Rayleigh number, Ra, is varied using Hele-Shaw cells with different gaps ($*$) and using porous media of beads ($•$). The solid line shows the best power-law fit of our data with the scaling exponent $0.84$. The upper numerical ($◃$) and experimental ($\diamond$) data are from Fig. 3 of Ref. [12] with different liquids and the lower data ($\square$) are obtained from Ref. [14] for vertical Hele-Shaw cells of different aspect ratios.

Figure 5

Density-driven Hele-Shaw convection with inclined boundaries reveal a larger speed of the interfacial propagation, $V_I$, in comparison to that in a vertical cell, $V_0$, with a fixed permeability $k=2.2\times {10}^{-4}$ cm${}^2$ [28].