Interfacial Instabilities of Shear-Thinning Fluids in Homogeneous Porous Media

Abstract

In this study, radial immiscible flow displacements in homogeneous porous media are modelled numerically in the case where the displacing fluid is Newtonian while the displaced one may be Newtonian or shear-thinning governed by Carreau's rheological model. The governing equations and interfacial jump conditions are solved numerically using the Immersed Interface Method and the Level Set Method to track the two fluids interfaces. The effects of four parameters, namely the mobility ratio and Capillary number for Newtonian flows and the Deborah number De and power-law index n, for shear thinning fluids are examined. Time contours of the interface revealing the finger structures that develop as a result of the viscosity mismatch between the two fluids are obtained to analyse and discuss the effects of the different parameters on the interfacial instability. Even though both characteristics of the shear-thinning fluid; De and n were found to affect the interfacial instability, it is revealed that the latter has a stronger effect, at least for the range of parameters that have been considered in this study.