Estimation of permeability of 3-D discrete fracture networks: An alternative possibility based on trace map analysis

The permeability of 3-D discrete fracture networks (DFNs) is estimated based on the geometrical parameters of 3-D model and permeability of its 2-D trace maps. This is achieved by the analysis of 84 3-D DFN models and 672 2-D DFN models that are cut from 3-D ones. The relationships between permeability of 3-D model and parameters such as fracture density, fracture length exponent of 3-D models and permeability of 2-D cut planes were analyzed. A multi-variable regression function was proposed for predicting 3-D fracture network permeability. The results show that the dimensionless equivalent permeability of 3-D fracture networks increases with the increasing fracture density following linear relationship. For the fracture networks with the fracture length exponent a = 2.0, the fracture network that carries flow is mainly consisted of several long fractures; whereas the fracture network connectivity is dominated by a large amount of relatively small fractures when a = 4.5. The permeability of 2-D DFN models that are cut from an original 3-D one underestimates the permeability of 3-D DFNs by approximately 10.45-80.92%. The regression function estimates the evolution of permeability of 3-D DFNs with a wide range of fracture density from 0.025 to 0.125 m− 3, and the predicted results agree with that calculated using Lang's method. The proposed model provides a simple method to approximate permeability of 3-D fracture networks using parameters that can be easily obtained from analysis on outcrop trace maps of fractured rock masses.