Permeability prediction of 3D complex fracture networks in deep underground based on fractal analysis of trace maps

Estimating the permeability of a three-dimensional (3D) discrete fracture network (DFN) based on its geometric properties can provide a useful alternative to the resource-intensive direct hydraulic computation of the 3D DFN. The analysis of the relationships between the dimensionless equivalent permeability of the 3D model (K' 3D) and its geometric properties was conducted to elucidate the linkage between permeability and geometric characteristics. The geometric characteristics encompass fracture density (ρ), the power-law exponent (a) governing the fracture length distribution in the 3D model, and the fractal dimensions of the 2D cutting planes (D_f). A regression function with variables (ρ, a, and D_f) was proposed to predict K' 3D. The results show that the calculated K' 3D is in good agreement with the values predicted by the regression function reported in the literature. The K' 3D increases following a linear relationship with the increment of ρ and decreases linearly with the increasing a. For the fracture network with a = 2.0, flow paths are composed of a few long fractures, whereas with a = 4.5, the flow path is composed of numerous minor fractures. The D_f follows an exponential relationship where it increases with increasing ρ and a linear one where it decreases with increment of a. The regression function with D_f can estimate the permeability of the 3D DFN model despite whether there are continuous flow paths in cutting planes. Compared to the findings predicted by the dimensionless equivalent permeability of the 2D cutting planes (K' 2D), the anticipated outcomes from the regression function demonstrate a closer alignment with the simulated results.