Connectivity, formation factor and permeability of 2D fracture network

The purpose of this paper is to investigate the effects of fracture connectivity and length distributions on the electrical formation factor, F, of random fracture network using percolation theory. We assumed that the matrix was homogeneous and low-permeable, but the connectivity and length distributions of fracture system were randomly variable. F of fracture network is analyzed via finite element method. The main result is that: different from the classical percolation “universal” power law for porous-type rocks, F of fracture network obeys a normalized “universal” scaling relation using the length-scale 〈l〉/L (〈l〉 is fracture mean length, and L is the domain size). Our proposed formation factor model, derived from the normalized “universal” scaling relationship, is valid in fracture network with constant fracture length and length distributions, showing that the normalized “universal” scaling law is independent of fracture patterns. The normalized scaling relation is also successfully used to derive the permeability model of 2D random fracture network using the previously published dataset, which obtained better fitting results than before.