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

TL;DR

This study investigates how long-range spatial correlations in two-dimensional percolation networks affect the distributions of traveling length and time for fluid flow, revealing altered scaling behaviors linked to cluster morphology.

Contribution

It demonstrates that correlations change the scaling exponents of traveling distributions, highlighting the impact of backbone compactness on flow dynamics in correlated porous media.

Findings

Scaling exponents differ from uncorrelated cases

Correlated clusters have more compact backbones

Dynamical exponents are intermediate between uncorrelated and homogeneous cases

Abstract

We study the distributions of traveling length l and minimal traveling time t 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) 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 for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases.