Linear Stability of Miscible Displacement Processes in Porous Media in the Absence of Dispersion

Abstract

The linear stability of miscible displacement processes in porous media is examined in the absence of diffusion and dispersion. Bounds for the rate of growth of the disturbance are derived. The asymptotic behavior of the rate of growth as a function of the wavenumber of the disturbance and the mobility profile characteristics is obtained for both small and large wavenumbers. A closed‐form solution is also presented for a particular mobility profile. It is shown that such displacement processes are linearly unstable in the case when the mobility profile contains any segments of decreasing mobility, and marginally stable in the opposite case. The effect of gravity on linear stability, in the case of compressible flows, is also briefly discussed.

Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes

“…To further investigate the influence of differential diffusive effects on the dynamics when δ = 1, we note that the density profile features non-monotonic behavior [19][20][21] for δ > max(1, R 2 ) (not shown here but detailed in Ref. 10) or δ < min(1, R 2 ).…”

An experimental study of the effects of density and viscosity contrasts on macrodispersion in porous media

“…In such cases, a linear stability analysis should lead to similar predictions for an exponential rate of growth (or decay). Hickernell and Yortsos [1986] applied a linear stability analysis to homogeneous porous media in the absence of small-scale dispersion. In a moving frame of reference, the temporal growth of small perturbations is assumed to be of the form exp(st), which in the present context can be replaced by exp(sz/v).…”

“…A related important issue (although not as thoroughly investigated) is the influence of density and/or viscosity contrasts on the macrodispersion of a non-passive tracer. A number of authors [Hickernell and Yortsos, 1986;Homsy, 1987;Bacri et al, 1992;Manickam and Homsy, 1995;Loggia et al, 1995] have used linear stability analyses to obtain criteria on viscosity and/or density contrasts that lead to the development of viscous and/or gravitational fingering instabilities. Except for Liu and Dane [1996] and de Wit and Homsy [1997], most of these studies have focused on homogeneous media.…”

Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses

“…In other situations too, non-monotonic profiles can be observed and modify the stability of interfaces separating fluids [34]. For instance, Yortos et al [35,36] analyzed non-monotonic mobility profiles during two-phase flow in porous media of water and oil. Loggia et al [37] also showed the importance of non-monotonic profiles during miscible displacements involving both viscosity and density changes.…”