A high-efficiency 3D boundary element method for estimating the stress/displacement field induced by complex fracture networks

Abstract

The displacement discontinuity method (DDM) is widely used in engineering problems such as hydraulic fracturing stimulation in unconventional reservoir and tunnel excavation simulation. Because the geometry of the artificial/natural fracture is intrinsically three-dimensional and quite complex, the 3D-DDM is more suitable than 2D-DDM to obtain more accurate and reliable calculation results such as the fracture-induced stress/displacement field. However, the analytical solution for 3D-DDM with triangular elements is very complicated and can only be applied to planar fractures and the numerical solution would introduce the singular and hyper-singular integrals in the calculation process. A new method that combines analytical and numerical solutions is proposed in this paper, which is validated by the solution of a penny-shaped fracture and the new Gaussian quadrature formula for standard triangles (GQSTS). Furthermore, we found that the new method is 32% faster than that of the pure numerical solution. The proposed method is then applied to perform sensitivity analyses associated with the fracture opening under a single fracture and multiple hydraulic fractures. Numerical results demonstrate that (1) not the fracture length or height but the aspect ratio is the dominant factor of the rectangular-shaped fracture opening; (2) the fracture inclination angle affects the fracture opening via altering the net pressure; (3) rock elastic properties also have great impact on the fracture opening, which is more sensitive to Young's modulus than Poisson's ratio; (4) both the cluster spacing and the fracture geometry could significantly alter the stress shadowing effect, which can be negligible when the cluster spacing is twice greater than the fracture radius or the short edge; and (5) the fracture opening and the induced stress become more intricate in complex fracture networks, and the potential stress-reorientation regions extend further in the outside directions of the entire network. This study establishes a high-efficiency 3D-DDM with triangular elements for calculating the stress/displacement field induced by complex fractures and may serve as a basis for hydraulic fracturing modeling via incorporating fluid flow and proppant migration.