Effective Permeability in Fractured Reservoirs: Discrete Fracture Matrix Simulations and Percolation‐Based Effective‐Medium Approximation

Abstract

Fractured reservoirs are complex and multi‐scale systems composed of matrix and fractures. Accordingly, modeling flow in such geological media has been a great challenge. In this study, we investigated the effect of scale as well as matrix and fracture network characteristics on the effective permeability (keff) in matrix‐fracture systems under fully saturated conditions. We generated fracture networks, embedded within a matrix of permeability of 10−18 m2, with fracture lengths followed a truncated power‐law distribution with exponent α = 1.5, 2.0, and 2.5. We set fracture permeability equal to 10−16, 10−14, and 10−12 m2 and numerically simulated fluid flow to determine the keff at six fracture densities for 36 fractured reservoirs. Results showed that the effect of α and scale on the keff became more significant as the contrast between matrix and fracture permeabilities increased. We also fit the percolation‐based effective‐medium approximation (P‐EMA) to the simulations and optimized its two parameters critical fracture density and scaling exponent. Results exhibited that both P‐EMA model parameters were scale‐dependent. Through linear regression analysis, we found that the critical fracture density and scaling exponent were highly correlated to other matrix‐fracture system properties and proposed two regression‐based models evaluated using a new six sets of simulations. Comparing the estimated keff values with the simulated ones demonstrated the reliability and predictability of the P‐EMA. The matrix‐fracture systems studied here were finite in size. We also showed that one may extend results to infinitely large reservoirs using the P‐EMA framework.