Gravitational instability and its scaling relation of a partially miscible two‐component system in a porous medium

In the context of the co-injection of CO₂ and impurities, such as H₂S, SOx and N₂, in the carbon capture and geological sequestration, the effect of the double diffusion on the onset and the growth of buoyancy-driven convection are studied theoretically and numerically. Based on the density profile, asymptotic stability limits are suggested as a function of the diffusivity ratio, δ_B, and the buoyancy ratio, −r_βr_C. In order to obtain more accurate features of the stability characteristics, the linear stability analysis and the nonlinear numerical simulations are also conducted. It is interesting that the present asymptotic, linear and nonlinear analyses are in good agreement. Based on the present stability analyses, we tried to find out the scaling relations which can be used as control parameters in related systems. In the double diffusive (DD) convection and the extended double diffusive (EDD) convection regimes, a new scaling relation is suggested by the temporal change of the density gradient rather than the density difference or the density gradient.