A numerical study on miscible viscous fingering instability in anisotropic porous media

Abstract

In this paper, the viscous fingering of miscible flow displacements in an anisotropic porous media is investigated for the first time. The effect of anisotropic permeability and dispersion tensor on the generation, form and growth rate of finger-like patterns, is studied using both linear stability analysis and computational fluid dynamics (CFD). The linear stability analysis is performed using the quasi-steady state approximation and six order shooting method to predict the growth rate of the disturbance in the flow. It is found that the flow is more stabilized when the ratio of the longitudinal to transverse anisotropic permeability is increased and longitudinal to transverse anisotropic dispersion is decreased. In CFD simulation, Hartley transformation (as a spectral method) and fourth-order Adams-Bashforth technique is used to solve the governing equations. It is shown that anisotropic permeability and dispersion have significant effects on the development of the fingers and also on the mechanisms of interactions between neighboring fingers. The development of the finger structures is discussed using concentration contours and diagrams of transversely average concentration, mixing length, and sweep efficiency for different anisotropic scenarios.