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We study the stability of dissolution-driven convection in the presence of a capillary transition zone and hydrodynamic dispersion in a saturated anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction. While the reaction enhances stability by consuming the solute, porous media anisotropy, hydrodynamic dispersion, and capillary transition zone destabilize the diffusive boundary layer that is unstably formed in a gravitational field. We perform linear stability analysis, based on the quasi-steady-state approximation, to assess critical times, critical wavenumbers, and neutral stability curves as a function of anisotropy ratio, dispersivity ratio, dispersion strength, material parameter, Bond number, Damköhler number, and Rayleigh number. The results show that the diffusive boundary layer becomes unstable in anisotropic porous media where both the capillary transition zone and dispersion are considered, even if the geochemical reaction is significantly large. Using direct numerical simulations, based on the finite difference method, we study the nonlinear dynamics of the system by examining dissolution flux, interaction of convective fingers, and flow topology. The results of nonlinear simulations confirm the predictions from the linear stability analysis and reveal that the fingering pattern is significantly influenced by combined effects of reaction, anisotropy, dispersion, and capillarity. Finally, we draw conclusions on implications of our results on carbon dioxide sequestration in deep saline aquifers.

We study the effect of background flow on the dissolution and transport of carbon dioxide (CO 2 ) during geological storage in saline aquifers, and include the processes of diffusion, advection, and free convection. We develop a semianalytical model that captures the evolution of the dissolution in the absence of free convection. Using the semianalytical solution, we determine scaling relations for the steady rate of dissolution that follow either J st $ ffiffiffiffiffiffiffiffi Pe R p or J st $ Pe depending on the value of Pe/R, where R represents the ratio of the extent of CO 2 plume to the aquifer thickness and Pe is the Peclet number. Using direct numerical simulations, we provide detailed behavior of the convective mixing during the dissolution. We establish the criteria for forced and mixed (combined free and forced) convection in aquifers that is governed by the background flow. Accordingly, we provide the scaling relations J st $ ffiffiffiffiffiffiffiffi Pe R p and J st $ Ra R representing the forced and free convection asymptotes, respectively, where Ra is a Rayleigh number based on aquifer thickness. The results reveal that the background velocity can delay the onset of free convection and can alter the subsequent mixing. This phenomenon is more profound in the systems subject to strong background flows wherein horizontal component of the velocity field generated by background flow hinders the establishments of vertical component of the velocity field. Finally, by applying the proposed relations to several potential storage sites, we demonstrate the screening process in finding aquifers where the background flow exerts an important influence on the dissolution.

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This paper investigates the impact of hydrodynamic dispersion on the stability of free convection in a saturated horizontal porous layer subject to a transient vertical concentration gradient and a steady horizontal background flow. A linear stability analysis (LSA) was conducted using the quasi-steady-state approximation to obtain neutral stability curves, critical times, and the corresponding wavenumbers as a function of dispersivity ratio (α) and longitudinal dispersion strength (β). The LSA results showed that the dispersive boundary layer becomes less unstable as longitudinal and transverse dispersivity increase. In addition, for the isotropic dispersive system with α = 1, the critical time and its corresponding wavenumber follow τc = 167.6/(1 − β) and κc = 0.0696 (1 − β), respectively. The nonlinear dynamics of the system were studied by examining the interaction of convective fingers, dissolution flux, and the time-dependent Sherwood number. Finally, the results were applied to 24 deep saline aquifers in the Alberta Basin.