Scaling CO₂–brine mixing in permeable media via analogue models

Abstract

Supercritical ${\rm CO}_2$ injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After injection, ${\rm CO}_{2}$ gas phase is buoyancy-driven over the denser aqueous brine, reaching an apparent gravitational stable distribution. However, ${\rm CO}_2$ dissolution in brine propels convection since the mixture is even denser than the underlying brine. This process still needs to be characterised comprehensively. Here, we investigate the irreversible mixing of dissolved ${\rm CO}_2$ in brine through laboratory-scale numerical experiments utilising the Hele-Shaw model (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746–767) and a fully miscible two-fluid system. In this scenario, mixing the less dense fluid – mimicking ${\rm CO}_{2}$ gas phase – with the heavier fluid – representing aqueous brine – catalyses cabbeling-powered convection. Our numerical simulations recover the laboratory results in porous media by Neufeld et al. (Geophys. Res. Lett., vol. 37, issue 22, 2010, L22404) and may explain the scaling law obtained by Backhaus et al. (Phys. Rev. Lett., vol. 106, issue 10, 2011, 104501) in Hele-Shaw cells. More remarkably, we show that the mass flux between the two analogue fluids, characterised by the Sherwood number $ {{Sh}}$ , obeys the universal scaling law $ {{Sh}}\sim {{Ra}}\, \vartheta _{scalar}$ , with $ {{Ra}}$ the Rayleigh number and $\vartheta _{scalar}$ the mean scalar dissipation rate. This paper sheds light on the fluid dynamics and solubility trapping in geological carbon sequestration.

Effect of Formation Heterogeneity on CO2 Dissolution in Subsurface Porous Media

“…A similar proportional relationship between finger growth velocity (calculated using the migration distance of the rising fingertip) and characteristic Darcy velocity was also observed in the work of Teng et al 69 The evolution equation of characteristic Darcy velocity can be represented as in eq 14. 23,26 = U gk C…”

“…The Hele–Shaw cell, a simple apparatus built with a small aperture between two transparent flat plates, has been extensively used to visualize the Darcy flow, including density-driven CO 2 transport. Furthermore, by varying several parameters in the cell, such as aperture, porosity, and vertical or horizontal permeability, it is possible to mimic the transport mechanism similar to that of CO 2 storage in different geological structures. − These experimental studies have adopted different visualization techniques to investigate the finger morphology during density-driven CO 2 transport, such as the pH indicator-based method, Schlieren method, particle image velocimetry, laser-induced fluorescence, and interferometry method. ,,− Furthermore, several studies have investigated scaling relationships to characterize the convective dissolution rate of CO 2 in brine formations. − Mojtaba et al developed a relationship between Sherwood and Rayleigh numbers and CO 2 convective flux at different Rayleigh numbers under 3.45 MPa and 182 < Ra < 20,860. Mahmoodpour et al showed scaling relationships between compensated flux and transition times between successive regimes in the system for experimental fluid with different salt types (NaCl and CaCl 2 ).…”