Estimation of the representative elementary volume of three-dimensional fracture networks based on permeability and trace map analysis: A case study

Abstract

A three-dimensional (3D) discrete fracture network (DFN) was generated to evaluate the representative elementary volume (REV) of granitic rock masses based on the statistical geometry parameters mapped from outcrop surveys at the Xinchang site, China. Then, extensive numerical simulations were performed to investigate the effect of fracture density on the side length of models of the REV size (LREV). The relationship between LREV of 3D models and the geometric parameters of two-dimensional (2D) cutting planes parallel and perpendicular to the direction of hydraulic gradient variation were analyzed. This relationship was determined by calculating fluid flow through 90 original 3D models, 810 3D submodels, and 270 2D cutting models. Finally, two multivariable regression equations were proposed for predicting the LREV of the 3D fracture network and equivalent permeability of the REV size. The results show that the clustering results obtained from the 3D DFN model are similar to those obtained from field measurements. The values of LREV of the 3D DFN model based on statistical geometry parameters mapped from outcrops are 18.89 m, 19.56 m, and 24.86 m in three flow directions, respectively, which clearly highlights the anisotropic characteristics of fractured rock masses. The LREV decreases with increasing fracture density following an exponential relationship. The multivariable regression function estimates the evolution of the LREV of 3D DFN models with a wide range of fracture densities from 0.53 to 1.33 m/m2. The predicted results are more accurate than those predicted by the fitting function between the fracture density of 2D cutting planes perpendicular to the z-axis and LREV. The proposed model provides a method to approximate the LREV of 3D DFN models and equivalent permeability of the REV size (KREV) using geometric parameters of the 2D cutting planes obtained from trace map analysis of fractured rock masses.