Effective permeability of fractured porous media with fracture density near the percolation threshold

Abstract

This study investigates the effective permeability of fractured porous media with fracture density near the percolation threshold. A new equivalent matrix-fracture network (EMFN) model was introduced, the code was used to efficiently deal with the huge number of modeling works for steady state flow in fractured porous media. The numerical model was verified by comparing with two previous seepage methods. We conducted a series of Monte Carlo simulations to explore the relationship between permeability discontinuity and three factors, namely fracture density, contrast between fracture and matrix permeability, and the scale of research domain. It was found that the effective permeability presents a bimodal distribution with specified fracture density in the transition regime. Each bimodal function can be subdivided into two well-fitting log-normal functions according to the percolation state to obtain analyzable average permeabilities. The results revealed significant differences between percolating and non-percolating configurations in the response to the change of each of the three factors mentioned above. More importantly, the finite-size effect plays an important role when fracture density is lower than or close to the percolation threshold; but this effect disappears gradually as the increase of fracture density. A stereoscopic approach is introduced to rationalize the scale effect.