  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.
