Patterns of fluid flow in naturally heterogeneous rocks

Patterns of fluid displacement in porous media have previously been studied extensively on networks with uncorrelated random properties. Percolation network models have received particular attention because of their relevance to simulating capillary dominated flow. Much fluid flow in porous media of economic significance occurs in natural rocks that exhibit long-range correlations in properties. In this paper we present results of invasion percolation in two dimensions with heterogeneity that corresponds to naturally occurring sedimentary rocks. Long-range correlations in properties based on multifractal, fractional Brownian motion and fractional Levy motion models are compared to results on uncorrelated networks. We conclude that results in invasion percolation vary for different long-range correlation in properties and breakthrough of the invasion phase is less sensitive to lattice size on the correlated networks.