Traveling length and minimal traveling time for flow through percolation networks with long-range spatial...

We study the distributions of traveling length l and minimal traveling time t(min) through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites ("wells") separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t(min)) follow the same scaling ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents d(l) and d(t) for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases, where l(*) approximately r(d(l)) and t(*)(min) approximately r(d(t)), and l(*) and t(*)(min) are the most probable values of l and t(min), respectively.