Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

We numerically examine solutal convection in porous media, driven by the dissolution of carbon dioxide (CO2) into water—an effective mechanism for CO2 storage in saline aquifers. Dissolution is associated with slow diffusion of free-phase CO2 into the underlying aqueous phase followed by density-driven convective mixing of CO2 throughout the water-saturated layer. We study the fluid dynamics of CO2 convection in the single aqueous-phase region. A comparison is made between two different boundary conditions in the top of the formation: (i) a constant, maximum aqueous-phase concentration of CO2, and (ii) a constant, low injection-rate of CO2, such that all CO2 dissolves instantly and the system remains in single phase. The latter model is found to involve a nonlinear evolution of CO2 composition and associated aqueous-phase density, which depend on the formation permeability. We model the full nonlinear phase behavior of water-CO2 mixtures in a confined domain, consider dissolution and fluid compressibility, and relax the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characteristics of spreading, mixing, and a dissolution flux in two- and three-dimensional media for both boundary conditions. We also revisit the scaling behavior of Sherwood number (Sh) with Rayleigh number (Ra), which has been under debate for porous-media convection. Our measurements from the solutal convection in the range 1, 500<Ra<135, 000 show that the classical linear scaling Sh ~ Ra is attained asymptotically for the constant-concentration case. Similarly linear scaling is recovered for the constant-flux model problem.