We present a linear stability analysis of density-driven miscible flow in porous media in the context of carbon dioxide sequestration in saline aquifers. Carbon dioxide dissolution into the underlying brine leads to a local density increase that results in a gravitational instability. The physical phenomenon is analogous to the thermal convective instability in a semi-infinite domain, owing to a step change in temperature at the boundary. The critical time for the onset of convection in such problems has not been determined accurately by previous studies. We present a solution, based on the dominant mode of the self-similar diffusion operator, which can accurately predict the critical time and the associated unstable wavenumber. This approach is used to explain the instability mechanisms of the critical time and the long-wave cutoff in a semi-infinite domain. The dominant mode solution, however, is valid only for a small parameter range. We extend the analysis by employing the quasi-steady-state approximation (QSSA) which provides accurate solutions in the self-similar coordinate system. For large times, both the maximum growth rate and the most dangerous mode decay as $t^{1/4}$. The long-wave and the short-wave cutoff modes scale as $t^{1/5}$ and $t^{4/5}$, respectively. The instability problem is also analysed in the nonlinear regime by high-accuracy direct numerical simulations. The nonlinear simulations at short times show good agreement with the linear stability predictions. At later times, macroscopic fingers display intense nonlinear interactions that significantly influence both the front propagation speed and the overall mixing rate. A dimensional analysis for typical aquifers shows that for a permeability variation of 1—3000 mD, the critical time can vary from 2000 yrs to about 10 days while the critical wavelength can be between 200 m and 0.3 m.

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[1] Geological carbon dioxide (CO 2 ) storage is a means of reducing anthropogenic emissions. Dissolution of CO 2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO 2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO 2 -enriched brine. Laboratory experiments and high-resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO 2 dissolution rates in CO 2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security. [2] The storage of carbon dioxide (CO 2 ) in geological formations has been proposed as a technological means to reduce anthropogenic emissions of this greenhouse gas [Orr, 2009;Benson and Cook, 2006]. The positive buoyancy of supercritical CO 2 relative to the ambient brine filling the pore spaces may lead to leakage along imperfections in the geological seal, which is of considerable concern for the security of long-term storage [Gasda et al., 2004;Pruess, 2005;Neufeld et al., 2009]. One of the primary mechanisms for stable long-term geological storage of CO 2 is the dissolution of injected CO 2 within ambient brine. Under typical conditions injected CO 2 dissolves into the ambient brine thereby increasing the density of the brine [Teng et al., 1997]. This layer of dense, saturated brine forms by the processes of diffusion, dispersion and mechanical mixing during injection and, once it has reached sufficient thickness, becomes rapidly unstable to convective overturning [Ennis-King et al., 2005;Riaz et al., 2006]. The process of convective dissolution of CO 2 has recently been imaged at ambient conditions in a Hele-Shaw cell [Kneafsey and Pruess, 2009], and enhanced mass transfer has been measured at reservoir conditions [Yang and Gu, 2006;Farajzadeh et al., 2007]. Convection is therefore expected in most sequestration sites, and controls the dissolution rate and hence the long-term risk of leakage. Geochemical observations in natural CO 2 reservoirs require large amounts of CO 2 dissolution into the ambient brine and provide field evidence for sustained convective transport of dissolved CO 2 [Gilfillan et al., 2008[Gilfillan et al., , 2009. Convective dissolution of CO 2 is therefore expected in most natural and anthropogenic CO 2 reservoirs, and controls the mobility of carbon in the subsurface. It is therefore an important mechanism in the deep carbon cycle [Sherwood and Ballentine, 2009], and controls the long-term risk of leakage of CO 2 from geological storage.[3] Despi...

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A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy–Brinkman–Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian–Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.