2-D network model simulations of miscible two-phase flow displacements in porous media: Effects of heterogeneity and viscosity

There are long-standing uncertainties regarding the relative significance of the role of porous medium heterogeneities vs. the role of fluid properties in determining the efficiencies of various strategies for fluid injection into porous media. In this paper, we study both the role of heterogeneities and of viscosity ratio in determining the characteristics of miscible, two-phase flow in two-dimensional (2-D) porous media. Not surprisingly, we find that both are significant in determining the flow characteristics. For a variety of statistical distributions of pore-throat radii, we find that the coefficient of variation (the ratio of the standard deviation of the radii to their mean) is a reliable predictor of the injected fluid saturation as well as the width of the interfacial region. Consistent with earlier results, we find that viscosity ratio causes a crossover from fractal viscous fingering to standard compact flow at a characteristic crossover time which varies inversely with viscosity ratio. The studies in this paper show that the power law relating characteristic time to viscosity ratio does not depend upon the distribution of pore-throat radii or upon the connectivity (coordination number) of the medium each of which affects the porosity; this suggests that the power law may be entirely independent of the structure of the porous medium. This power law relationship leads to a robust dependence of the flow properties upon a particular ratio of the saturation to a given power of the viscosity ratio. This dependence is reminiscent of the empirical “quarter power mixing rule” in three dimensions. As such, this work provides a physical understanding of the origin and limitations of this empirical mixing rule.