Competition of gravity and viscous forces in miscible vertical displacement in a three-dimensional porous medium

Abstract

When viscosity and density contrast exist in the vertical miscible displacement in porous media between two fluids, the interplay between the viscous force and gravity determines the interface stability. Two stability criteria are derived to determine the interface stability. Hill's and Dumore's stability criteria are used to determine the interface stability of the sharp and diffused interface, respectively. In this study, we visualized the crossover between unstable displacement and stable displacement for a vertical displacement in porous media using microfocused x-ray computed tomography. The experiments were divided into four possible configurations: (1) unconditionally stable (gravitationally stable-viscously stable), (2) unconditionally unstable (gravitationally unstable-viscously unstable), (3) conditionally stable (gravitationally stable-viscously unstable), and (4) conditionally stable (gravitationally unstable, viscously stable). The structure of the displacement interface was visualized for the critical velocity ratio (V/Vc) in the range of 0.5–11.9. In the conditionally stable configurations 3 and 4, a crossover between stable and unstable displacements was observed. We found that Dumore's stability criterion is more appropriate for predicting interface stability than Hill's stability criterion. Viscous fingering occurs in configuration 3 when V/Vc is higher than Dumore's critical velocity, whereas gravity fingering occurs in configuration 4 when V/Vc is lower than Dumore's critical velocity. Similar events in two-dimensional experiments, such as tip-splitting, shielding, and coalescence, were also observed three-dimensionally. The significant changes in the mixing length and sweep efficiency signify the crossover between the stable and unstable displacements.