Stability of miscible displacements in porous media: Radial source flow

A linear stability analysis of miscible displacement for a radial source flow in porous media is presented. Since there is no characteristic time or length scale for the system, it is shown that solutions to the stability equations depend only upon a similarity variable, with disturbances growing algebraically in time. Two parameters, the mobility ratio and a Peclet number based upon the source strength, determine the stability. Results for the growth constant as a function of mobility ratio and Peclet number are given. It is shown that there is a critical Peclet number Pec above which displacement becomes unstable. For Pe>Pec, there is always a cutoff scale attributable to dispersion, and a most dangerous mode, with the two corresponding wavenumbers increasing with Pe. The growth constant increases with Pe as well. The effect of mobility ratio is also studied. The result indicates that, as expected, increasing mobility ratio destabilizes the displacement. Asymptotic results for the growth rate, cutoff, a...