Semi-empirical solutions for fractal-based hydraulic properties of 3D fracture networks

Abstract

Semi-empirical solutions for fractal-based hydraulic properties of unsaturated three-dimensional fracture networks are presented, in which three assumptions are made: (a) the permeability is scale dependent, (b) each fracture cuts through the model and (c) the difference between fractal dimensions for fracture aperture distribution and tortuous length of a fracture is <1·7. The results show that the relationship between the relative permeability of the gas phase and saturation agrees well with those reported in the literature. The fractal dimensions for fracture aperture distributions of the fluid and gas phases are between 2 and 3. The permeability of the saturated fluid phase is influenced by the fractal dimension for the tortuous length of a fracture and maximum fracture aperture. With the increase in saturation, the variation range in fractal dimension for fracture aperture distribution of the fluid phase for different fracture porosities decreases; however, the variation range increases for different ratios of maximum aperture to minimum aperture. The permeability of both phases is more sensitive to the fractal dimension for the tortuous length of a fracture than to the fracture porosity and/or the ratio of maximum aperture to minimum aperture.