Using XFEM To Estimate the Permeability of Shales During Hydraulic Fracturing Operation

Abstract

Hydraulic fracturing (HF) is used to increase the production of hydrocarbons from shale reservoirs by increasing shale permeability. In this work, we analyze the efficiency of hydraulic fracturing operations under various far-field stresses and injection rates, and we determine the effect of the degree of anisotropy on fracture propagation. Hydraulic fracturing of unconventional reservoirs is simulated using the coupled pressure/deformation extended finite element method (XFEM) in ABAQUS. We model the reservoir as a vertical transversely isotropic (VTI) medium with a degree of anisotropy that varies between 1 and 6, while the injection rate varies between 1E-5 to 1E-2 m3/s. Multistage HF models are considered to compare the fractured area when applying close and wide cluster spacing. The numerical model is validated using the KGD model and three experimental studies available in the literature. We calculate the permeability of the fractured medium using the analytical model of Gueguen and Dienes, enhanced to account for the proppants' presence within the fractures using the Kozeny-Carmen equation. Our results show that the length and width of fractures, and the direction of the crack growth are strongly affected by the borehole stresses, the injection rate, and the degree of anisotropy. The cracks expand towards the maximum principal stress in the isotropic formation and kink towards the weakest plane in the VTI formation as the mechanical contrast exceeds 4 and when the injection rate is between 1E-4 and 1E-3 m3/s. A decrease in the fracture aperture is observed for these cases. Moreover, crack propagation paths and geometries are affected by the far-field stresses when the distance between cracks is less than 12 m. However, cracks grow independently when the distance between the cracks exceeds 12 m (the beginning of a planar growth is observed), and a planar propagation is observed for a distance above 20 m. In multistage HF, the length, width, and extent of the fractured area are larger for close cluster spacing (<12m) than for high cluster spacing (>12m). This work allows the identification of the best fracturing scenario to optimally enhance the permeability of unconventional reservoirs under different hydro-mechanical conditions.