Connectivity and Permeability for Rock Fracture Network in Both Radial and Unidirectional Flow Configurations

Wang, Zhechao (Northeastern University) | Li, Wei (Northeastern University) | Qiao, Liping (Northeastern University)

OnePetro 

Abstract There are critical geometric parameters related to the geotechnical properties in fractured rock mass, such as connectivity threshold and the size of Representative Element Volume (REV). Based on the percolation theory, the connectivity of fracture network was investigated, and the percolation thresholds in radial and unidirectional flow configurations were obtained. Using discrete fracture network method, the REV sizes and equivalent permeability coefficients of rock fracture networks with different percolation parameters, which are related to the combined effect of fracture spacing and trace length, were obtained, and it also found that the REV size is decreased with the percolation parameter, while the equivalent permeability coefficient is increased with the percolation parameter. Finally, the connectivity and probability of existence of REV under different geological conditions were obtained, which had a good guidance for choosing an appropriate method to analyze the problems associated with fluid flow in fractured rock mass in practice. 1 Introduction Fractures are extensively developed in the fractured rock masses, which introduce discontinuity, inhomogeneity and anisotropy into the fractured rock masses. The fluid flow properties in rock mass vary with not only the fracture density and trace length, but also the volume of fractured rock mass. On one hand, a rock fracture network can be connected or disconnected depending on the fracture density and trace length. The connectivity threshold is usually employed to characterize the transition from connectedness to disconnectedness. On the other hand, the concept of equivalent permeability coefficient valid only when the volume of fractured rock mass contains enough fractures to stabilize the overall permeable property. The critical size of the fractured rock mass is termed as the size of Representative Element Volume (REV), which characterize fractured rock masses from discontinuity to equivalent continuity, as shown in Figure 1. The connectivity threshold, which is also termed as percolation threshold, is determined based on percolation theory. Percolation theory applies to a system where the flow is concentrated into a sparse population of elements, such as fractures or faults, in an impervious matrix. The theory links the global physical properties (connectivity, permeability, etc.) to an average measure of its geometrical properties (Bour et al. 1997). Robinson et al. (1982 & 1984) carried out the numerical simulation with different trace lengths and angles, and the average number of intersections per line at percolation and critical percolation densities were obtained. Berkowitz et al. (1993, 1995 & 2000) analyzed connectivity aspects of fracture networks in terms of percolation theory, and it was shown that percolation theory can predict connectivity reasonably. Bour et al. (1997 & 1998) presented theoretical and numerical studies of the connectivity of fracture network following power law length distribution. It was shown that the connectivity of the fault network was related to the geometric parameter, i.e., fracture length and areal density, and the percolation threshold was approximately 5.6 when the fracture network followed power law length distribution.

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