A numerical model to simulate fracture network induced by hydraulic fracturing for 3D shale gas reservoir with geo-stress interference

Abstract

In the two-dimensional (2D) stimulated reservoir volume (SRV) model, the positions of natural fractures are only determined by the approaching angle, and only the influence of horizontal principal stress is considered in its failure criterion. In the three-dimensional (3D) shale reservoir model, the positions of natural fractures must be determined by the dip and approaching angles, while considering the influences of the vertical and horizontal principal stresses on the failure criterion. In addition, the simultaneous opening of several hydraulic cracks will lead to a change in the geo-stress, thus causing a change in the conditions of the natural fracture and shear failure by the induced stress. To analyze the generation of 3D fracture networks, this study establishes a mathematical model based on elastic mechanics, 3D rock failure criterion, full permeability tensor, and material conservation equation. First, the finite element method model of geological stress caused by fracturing is established based on the crack propagation model, and the finite difference method module based on the 3D fluid diffusion control equation and full permeability tensor is used to solve the reservoir pressure distribution. Subsequently, the 3D tensile and shear failure criteria are used to determine whether any grid units are destroyed. Once a grid  has occurred in any form of rock failure criterion, the permeability of the corresponding grid unit will also change owing to the change in the natural fracture opening. Finally, the SRV is represented by the region of increased permeability. This work presents a sensitivity analysis of the multifactor after applying the microseismic data to validate the numerical model, including the influences of the injected fluid volume, natural fracture approaching angle, dip angle, and horizontal principal stress difference on the size of the SRV (such as shape, border width, and length). Our results show that, compared to the condition where no stress is induced, the tensile failure volume decreases and the shear failure volume increases, whereas the total SRV increases owing to the induced stress when the vertical principal stress is maximum among the three principal stress components. The length of the SRV increases with increasing approaching angle, dip angle, and horizontal principal stress difference of the natural fracture, but its width decreases. The width and length increase simultaneously only with increasing volume of injected fluid; the SRV size increases with increasing injection fluid volume and natural fracture dip, but decreases with increasing approaching angle and horizontal principal stress difference.