Rayleigh-Taylor Instability in Homogenous/Heterogenous Porous Media Under Time-Dependent Displacements

Abstract

The density mismatch between fluids in porous media during displacement processes leads to the formation of flow instabilities manifested as finger-like intrusions. These buoyancy-driven instabilities are thoroughly studied in this dissertation to address different aspects of the flow instability in miscible displacements. The research is conducted in two phases. In the first phase, the problem is studied under time-dependent flow displacements in homogeneous porous media. One must note that a new, more efficient approach to determine instability characteristics has been developed for the stability analysis of these time-dependent flow displacements. The effects of the cycle period and the velocity amplitude on the flow instability have been examined. The results showed that the smaller the period, the larger the growth rate but the stronger the subsequent decay over time. Finally, the first phase revealed that it is possible to control the buoyancy-driven instability through a proper choice of the period and the amplitude. In particular, the choice of the period determines the nature of the finger patterns as well as other important flow characteristics. The buoyancy-driven instabilities are analyzed in the second phase of this study for horizontally-layered heterogeneous porous media. The role of the frequency of layers and variance of the permeability distribution are examined under different scenarios of density mismatches. Qualitative analysis of the concentration fields revealed that heterogeneity induces undulated more diffuse finger structures compared to the homogeneous case. Moreover, it is found that the onset time of the instability increases with increasing number of layers and decreases with increasing variance of the permeability distribution. Finally, the study shows that for the case of shifted permeability distribution, an unstable flow in a homogeneous medium can be fully stabilized when a small number of layers is used in the heterogeneous case.