Stability of miscible displacements across stratified porous media

We consider the stability of miscible displacements across stratified porou s media, where the heterogeneity is along the direction of displacement. As ymptotic results for long and short wavelengths are derived. It is found th at heterogeneity has a long-wave effect on the instability, which, in the a bsence of gravity, becomes nontrivial when the viscosity profiles are nonmo notonic. In the latter case, profiles with end-point viscosities, predicted to be stable using the Saffman-Taylor criterion, can become unstable, if t he permeability contrast in the direction of displacement is sufficiently l arge. Conversely, profiles with end-point viscosities predicted to be unsta ble, can become stable, if the permeability decrease in the direction of di splacement is sufficiently large. Analogous results are found in the presen ce of gravity, but without the nonmonotonic restriction on the viscosity pr ofile. The increase or decrease in the propensity for instability as the pe rmeability increases or decreases, respectively, reflects the variation of the two different components of the effective fluid mobility. While permeab ility remains frozen in space, viscosity varies following the concentration field. Thus, the condition for instability does not solely depend on the o verall fluid mobility, as in the case of displacements in homogeneous media , but it is additionally dependent on the permeability variation. (C) 2001 American Institute of Physics.