Mathematical modeling of onset of convection in a porous layer with viscosity variation

Abstract

Instability theory is applied to diffusion-convection phenomenon in porous media, where the area in direction of transfer is large and viscosity of the oil varies due to gas dissolution. An important application of this theory arises where diffusion-convection is employed as an EOR technique in oil reservoirs. As a bed of gas is formed below a column of oil, gas starts to diffuse into the oil. Therefore, the oil becomes lighter and an inverse gradient of density is developed as more gas diffuses in. Although this inverse density gradient is potentially unstable, convection will not initiate until the gradient extends to a certain value. The condition at which convection begins is known as "the onset of convection" and is well specified by the dimensionless Rayleigh number. In this study, an instability analysis is made for convection-diffusion in large porous media. Unlike other studies where viscosity is assumed constant, in this work viscosity is postulated to be a function of gas concentration. It is shown that the mathematical model developed reduces to previous models if the viscosity variations are ignored.