Effect of swelling on the onset of buoyancy-driven convection during the CO2 dissolution process in a porous medium

By considering the swelling due to the CO2 dissolution, the onset of buoyancy-driven convection in a porous medium is analyzed theoretically. Based on the Darcy equation, the flow and advection-diffusion equations are derived. The base concentration field in an interface movement system due to the volume expansion is slightly different from a fixed interface one. Based on the linear stability theory, new stability equations are obtained in the global (τ,z)-domain and in the semi-infinite (τ,ζ)-domain. Unlike the stability equations in the global (τ,z)-domain, a normal mode analysis is possible in the semi-infinite (τ,ζ)-domain. The normal mode stability equations are solved analytically for the no-swelling system, and numerically for the swelling ones. The critical conditions are obtained as a function of the Darcy-Rayleigh number and the interface movement parameter. The interface movement accelerates the onset of convection with small wavelength instability. The effect of interface movement on the stability is severe, especially in a highly soluble system such as a CO2 improved oil recovery case.