Stability of displacement processes in porous media in radial flow geometries

Abstract

The linear stability of certain displacement processes in porous media for two‐dimensional radial flows induced by a point source is examined. Both two‐phase, immiscible displacement and single‐phase miscible displacement in the presence of equilibrium adsorption are discussed. In agreement with Tan and Homsy [Phys. Fluids 3 0, 1239 (1987)], it is found that disturbances grow or decay algebraically in time. Via appropriate transformations the eigenvalue problems are shown to be identical to those in rectilinear flow geometries with suitably modified base states and parameters. Thus several stability features are inferred directly from the analysis in rectilinear geometries. The results indicate the existence of critical values for the capillary (N_Ca) or Peclet (Pe) number, above which the displacement is unstable for wavenumbers in a band of finite width. For large N_Ca or Pe the most dangerous and the highest cutoff modes scale linearly with N_Ca or Pe. The different scaling found by Tan and Homsy [Phys. Fluids 3 0, 1239 (1987)] follows directly as a singular limit of the miscible displacement problem in the absence of adsorption.