THEORETICAL AND NUMERICAL ANALYSES ON THE ONSET AND GROWTH OF CONVECTIVE INSTABILITIES IN A HORIZONTAL ANISOTROPIC POROUS MEDIUM

A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, brine-saturated, horizontal, anisotropic porous layer. Through the upper boundary of the layer, CO2 dissolution is dissolved into the brine and the CO2-saturated brine induces the buoyancy-driven motion. Darcy's law is used to describe this motion, and linear stability theory is employed. The onset of convection is analyzed by employing the exact eigenanalysis, the quasi-steady-state approximation (QSSA), and the initial value problem approach (IVPA). The condition of the onset of buoyancy-driven instability is obtained as a function of the Darcy-Rayleigh number and the anisotropy ratio of permeability which is independent of the solution methods. To find out the anisotropy effect on the motion after the onset of convection, nonlinear numerical simulations also are conducted using the result of the linear analysis as a starting point. Nonlinear numerical simulations show that the fingerlike instability motion is not readily observable at tau(c) and it becomes visible around tau(min). Here tau(c) is the critical time of the onset of convection and tau(min) is the time after the onset of convection at which the total flux reaches the first local minimum.