Stability of two-phase vertical flow in homogeneous porous media

Abstract

Immiscible two-phase flow in porous media, which results from the downward injection of a heavier fluid or upward injection of a lighter fluid, is characterized by two shocks, one at each end of a rarefaction wave. The specific details of the saturation profile, such as the shock speeds and the shock saturations, are determined by the fractional flow function for given values of the mobility ratio and the gravity number. We employ a normal mode, matched asymptotic expansion analysis to obtain analytical expressions governing the stability behavior of such flows. Instability occurs at both ends of the one-dimensional base saturation profile with unique characteristics such that the maximum growth rate decreases both when the mobility ratio is increased at the front end and decreased at the back end. This unusual behavior is explained in terms of vorticity eigenfunctions related to nonmonotonic mobility profiles. Analysis of stability behavior as a function of fractional flow profile shows that although the fundamental mechanisms are qualitatively similar, they are associated with different parameter values in view of particular mobility profiles. Growth rates and wavenumbers predicted by the linear stability analysis are observed at the onset of the nonlinear displacement process, which is followed by the fully developed nonlinear flow with large-scale unstable structures.