Estimation of REV size of 2-D DFN models in nonlinear flow: Considering the fracture length-aperture correlation

Abstract

Determining the representative elementary volume (REV) of fractured rock masses is the foundation for studying the properties of such rock masses using the equivalent continuum model. This paper focuses on estimating the REV sizes of a fractured rock mass, considering the linked trace length and fracture aperture in both linear and nonlinear flow regimes. To achieve this, Monte Carlo simulations were employed to create discrete fracture network (DFN) models based on the geometric characteristics of fractures. The linear element method, modified by the Forchheimer law, was used to calculate the equivalent permeability coefficient tensor K and the equivalent non-Darcy coefficient tensor β. These calculations were performed to determine the REV size of DFNs under nonlinear flow conditions. The findings of this study demonstrate a general consistency in the computed K values for the two flow regimes. It was observed that the REV size, determined by β value, exceeded that obtained using K for the identical fracture network. Furthermore, when considering the same flow regime, the REV size was found to be smallest when the fracture aperture remained constant, followed by cases where it was independent of the trace length and finally when it was correlated with the trace length.