Onset of buoyancy-driven convection in a variable viscosity liquid saturated in a porous medium

In connection with carbon dioxide (CO2) improved oil recovery (IOR), the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer is analyzed. Through the upper boundary, CO2 is gradually dissolved into heavy oil to significantly reduce its viscosity but increase its density. By considering the variation of viscosity, Darcy's law is used to explain characteristics of fluid motion. Under the linear stability theory, the exchange of the stabilities is proved analytically. The critical conditions for the onset of buoyancy-driven convection are obtained as a function of the viscosity variation parameter of the Frank-Kamenetskii approximation. Based on the result of the linear stability analysis, the growth of disturbance is pursued by the direct nonlinear numerical simulation. The present linear and nonlinear analyses show that the viscosity variation parameter plays a critical role in the onset and the growth of the instability motion.