A new fractal approach for describing induced-fracture porosity/permeability/ compressibility in stimulated unconventional reservoirs

The stimulated reservoir volume (SRV) with complex induced-fracture governs dominant flow rates in unconventional reservoirs. The induced-fracture spacing and aperture greatly affect the fracture properties. In this study, a new method to calculate tortuosity index of fractal induced-fracture is proposed, and the fractal dimension of induced-fracture aperture (d(fa)) is presented to describe the distribution of fractal induced-fracture aperture (FFAD). Combined with fractal induced-fracture spacing (FFSD) and FFAD, the fractal fracture porosity/permeability/compressibility models are given. The FFSD and FFAD influenced by fractal dimensions and their influences on fracture properties are analyzed. The results show that the d(fs) has a wider range than that of natural fractures, and it may be larger than 2 in 2D system in some special reservoirs, e.g. re-stimulated reservoirs. As the distance from the reference point increases, the tortuosity index gradually decreases. The larger the fractal dimension (d(fs) or d(fa)) is, the larger the fracture porosity/compressibility will be. In the cases of d(fs) < 2 (or d(fa) < 2), the fracture porosity/compressibility of the uniformly induced-fracture is smaller than the fractal induced-fracture near the reference point, and larger than that far away from the reference point. While in the cases of d(fs) > 2 (or d(fa) > 2), the fracture porosity/compressibility of the uniformly induced-fracture is larger than the fractal induced-fracture near the reference point, and smaller than that far away from the reference point. When d(fa) > 2, the fracture permeability increases first and then decreases as the distance from the reference point increases. In other cases, the fracture permeability decreases as the distance from the reference point increases. The permeability influenced by distribution of induced-fracture aperture is greater than that influenced by induced-fracture spacing.