Instability and mixing flux in frontal displacement of viscous fluids from porous media

Abstract

The goal of the present study is to investigate the instability of viscous fluid displacement by a less viscous one in a two-dimensional channel, and to the determine the characteristics of displacement quality and entrapment zones. Experiments on miscible displacement of fluids in Hele-Shaw cells were conducted under microgravity conditions. Extensive direct numerical simulations allowed to investigate the sensitivity of the displacement process to the variation of values of the main governing parameters. Validation of the code was performed by comparing the results of model problems simulations with experiments and with the existing solutions published in literature. Numerical simulations allowed to explain new experimental results on the pear shape of fingers and periodical separation of their tip elements from the main body of displacing fluid. These separated blobs of less viscous fluid move much faster than the mean flow of the displaced viscous fluid. The results of numerical simulations processed on the basis of dimensions analysis allow to introduce parameters characterizing the quality of displacement and the mixing flux induced by instability. Functional forms describing additional mixing induced by displacement instability were developed. The influence of inhomogeneity of porous matrix on displacement instability is being investigated. The modified Hele-Shaw cell containing regular and randomized obstacles is used to study the effect of inhomogeneity on displacement instability. The result of numerical simulations as well as physical experiment shows that the presence of inhomogeneity of a definite length scale could stabilize unstable displacement and could destabilize a stable one.