Instabilities of Vertical Time-Dependent Miscible Displacements in Homogeneous Porous Media

Buoyancy-driven instabilities develop at the interface between fluids in miscible flow displacements. Such instabilities significantly affect the efficiency of displacement processes encountered in many applications such as enhanced oil recovery and CO₂ sequestration. Thus, it is imperative to control such instabilities. Most studies on vertical miscible displacements are limited to displacements involving a constant injection rate. However, in some practical processes the injection rate is in fact time-dependent. The objective of this study is to investigate the effects of time-dependent injection rates on the growth of fingering instabilities. The governing equations are solved numerically using the Hartley-Pseudo-spectral method. First, the dynamics of fingering instabilities were examined using nonlinear simulations, under constant injection rates, to determine the criteria for the instability which depends on the mobility ratio, density difference, and the critical injection velocity. Then, utilizing time-dependent injection schemes, it was found that the instability can be attenuated depending on the cycle period and velocity amplitude. Moreover, the flow is always less unstable when the displacement is initiated through an extraction stage rather than an injection one.