Stability of miscible displacements across stratified porous media

Abstract

We consider the stability of miscible displacements across stratified porous media, where the heterogeneity is along the direction of displacement. Asymptotic results for long and short wavelengths are derived. It is found that heterogeneity has a long-wave effect on the instability, which, in the absence of gravity, becomes nontrivial when the viscosity profiles are nonmonotonic. In the latter case, profiles with end-point viscosities, predicted to be stable using the Saffman–Taylor criterion, can become unstable, if the permeability contrast in the direction of displacement is sufficiently large. Conversely, profiles with end-point viscosities predicted to be unstable, can become stable, if the permeability decrease in the direction of displacement is sufficiently large. Analogous results are found in the presence of gravity, but without the nonmonotonic restriction on the viscosity profile. The increase or decrease in the propensity for instability as the permeability increases or decreases, respectively, reflects the variation of the two different components of the effective fluid mobility. While permeability remains frozen in space, viscosity varies following the concentration field. Thus, the condition for instability does not solely depend on the overall fluid mobility, as in the case of displacements in homogeneous media, but it is additionally dependent on the permeability variation.