Diffusion-limited aggregation on multifractal lattices: A model for fluid-fluid displacement in porous media

Abstract

A simple model for the displacement of a viscous fluid by a nonviscous fluid in a porous medium has been developed. This model is based on the Witten-Sander model for diffusion-limited aggregation and employs a multifractal lattice to represent both short- and long-range heterogeneities in the porous medium. It is shown that such heterogeneities can have important effects on both the local and global structure of the displacement pattern. Long-range heterogeneities enhance the effects of the outer boundary on the overall shape of the cluster and shorter-range heterogeneities reduce the thickness of the ‘‘viscous finger’’ generated by the displacement process. Our results indicate that the effective fractal dimensionality of the displacement patterns is decreased as the magnitude of the heterogeneity is increased.