Viscous Fingering in Heterogeneous Porous Media

Abstract

SUMMARY Formulation of a particle-tracking model for calculation of unstable flow in heterogeneous porous media is described. Model calculations are compared with unstable laboratory-scale displacement experiments, and excellent agreement is demonstrated. Simulations of unstable displacements in heterogeneous porous media are also described. They indicate that if variations in permeability are uncorrelated, or if the variance of the permeability field is small, then finger patterns are similar to those observed for homogeneous porous media. When the permeability is sufficiently variable and the correlation length is a significant fraction of the flow length, however, the permeability distribution dominates the formation of ringers, and the fingers follow the same path regardless of the mobility ratio. A heterogeneity index, defined as the product of variance and dimensionless correlation length, is used to characterize the transition from flow dominated by viscous fingering to flow dominated by the spatial distribution of permeability.