Dispersion in Sub‐Representative Elementary Volume Fracture Networks: Percolation Theory and Random Walk Approaches

Abstract

A law for dispersion in fracture networks below the representative elementary volume (REV) is established by analyzing random walks in two‐dimensional fracture networks in conjunction with percolation theory. Irregular fracture networks near the percolation threshold were obtained by removing some of the fractures of a regular orthogonal network, consisting of fractures of equal length and different apertures, drawn randomly from a lognormal distribution. The random walk was directed by an exact solution of flow through the network, and Monte Carlo simulations were performed to track particles through the fracture system. The percolation theory analysis indicates a proportionality between the mean square displacement and time raised to the power 1.27, in excellent agreement with the simulations in the fracture networks, which indicate a proportionality with time raised to the power 1.3.