Rayleigh–Taylor instability in porous media under sinusoidal time-dependent flow displacements

Linear stability analysis and nonlinear simulations have been carried out to analyze the Rayleigh–Taylor instability in homogeneous porous media under time-dependent flow displacements. The flow processes consist of a sinusoidal time-dependent velocity characterized by its period (T) and amplitude (Γ) and ensure that the same amount of fluid is injected over a full flow period. A new, more efficient approach to determine instability characteristics has been developed for the stability analysis of these time-dependent injection flows and showed a growth rate that varies in time like the displacement velocity. The effects of the period T and amplitude Γ as well as the fluids’ viscosity (R) and density differences (ΔG) have been analyzed. Consistent with constant injection displacements, a larger ΔG leads to stronger instabilities. Furthermore, it is found that a larger R tends to attenuate the instability during extraction and soaking periods and to enhance it during injection. This study also revealed that for a given total injection time, the time-dependent flow can be less or more unstable than its constant injection counterpart. In particular, for Γ < −1, larger periods lead to stronger instabilities with longer more developed fingers. For Γ > 1, on the other hand, it is found that larger periods tend to attenuate the instability resulting in a smaller number of fingers and a more diffused front. Flows with unit amplitude (Γ = 1) exhibit the same qualitative trends as but are overall more unstable than their counterparts with Γ > 1.