Abstract: Fluid flow tests are conducted on an artificial model constituted by two crossed fractures with an intersecting angle of 90°. The nonlinear fluid flow patterns within the fracture intersection are observed by using the visualization technique with a charge-coupled device (CCD) camera. Two discrete fracture network (DFN) models are established with and without considering the fracture surface roughness, respectively. The nonlinear flow behaviors of fluid in these two DFN models are characterized by directly solving the Navier-Stokes equations under two kinds of boundary conditions. Experimental results show that the obvious nonlinear flow behaviors in the segment connected to outlet_3 are observed, and measurements also exhibit a nonlinear correlation between the flow rate Q and pressure P. Numerical results demonstrate that, when the hydraulic gradient J is to some extent high (i.e., J > 0.1), the flow rate Q through the DFN is nonlinearly related to the pressure P between two opposite boundaries. However, when J is relatively low (i.e., J < 10-4), Q is linearly proportional to P. Based on these two DFN models in the current study, the critical condition of applying the local cubic law to calculate fluid flow in every fracture in the DFNs is J ≤10-4. The fracture surface roughness can significantly influence the permeability of the DFNs, however, it has negligible influences on the relative flow rate errors.

Key words: discrete fracture network, nonlinear seepage, Navier-Stokes equations, local cubic law