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

Abstract

We numerically examine solutal convection in porous media, driven by the dissolution of carbon dioxide (CO[subscript 2]) into water—an effective mechanism for CO[subscript 2] storage in saline aquifers. Dissolution is associated with slow diffusion of free-phase CO[subscript 2] into the underlying aqueous phase followed by density-driven convective mixing of CO[subscript 2] throughout the water-saturated layer. We study the fluid dynamics of CO[subscript 2] 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 CO[subscript 2], and (ii) a constant, low injection-rate of CO[subscript 2], such that all CO[subscript 2] dissolves instantly and the system remains in single phase. The latter model is found to involve a nonlinear evolution of CO[subscript 2] composition and associated aqueous-phase density, which depend on the formation permeability. We model the full nonlinear phase behavior of water-CO[subscript 2] 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 1500≲Ra≲135000 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. The results provide a new perspective into how boundary conditions may affect the predictive powers of numerical models, e.g., for both the short-term and long-term dynamics of convective mixing rate and dissolution flux in porous media at a wide range of Rayleigh numbers.