Dispersion driven instability in miscible displacement in porous media

Abstract

The effect of dispersion on the stability of miscible displacement in rectilinear porous media is examined. Following a convection–dispersion (CDE) formalism, the base state of Tan and Homsy [Phys. Fluids 2 9, 3549 (1986)] at conditions of unfavorable mobility contrast is analyzed. Emphasis is placed on the dependence of the dispersion coefficient on flow rate (e.g., mechanical dispersion). It is found that such a dependence induces a destabilizing contribution at short wavelengths. This effect, which is in contrast to the stabilization commonly associated with dispersion, is highly pronounced near the onset of the displacement. It is also near this onset that, for a certain condition, the cutoff wavenumber becomes infinitely large. An analytical expression is derived for this condition and the origin and implications of the instability are discussed. It is also suggested that the present CDE formulation may be inadequate in providing stability criteria for a range of unstable flows.