A Fluid-solid Coupling Numerical Model Considering Three-dimensional Fractures

With the accelerated development of industrialization,global energy consumption continues to increase,where shale gas production has increased significantly due to the emergence of horizontal well fracturing technology.Numerical simulation technology is widely used in fracturing technology development research because of its strong operability and good observability.The displacement discontinuity method(DDM)is widely used in hydraulic fracturing stimulation in unconventional reservoirs due to its particular advantages.However,the fully three-dimensional hydraulic fracturing model based on DDM is difficult to establish because of the complexity and large quantity of calculation.A mixed DDM method that combines analytical solution,which is based on triangular elements,and numerical solutions,based on Gaussian quadrature formula for standard triangles(GQSTS),is proposed in this thesis.The author independently wrote the program Mix_DDM based on the C++platform and realized the calculation of the displacement/stress field which induced by fractures with an arbitrary three-dimensional geometry,and totally eliminates some numerical issues related to the singular and hypersingular integrals.The accuracy is higher than that of regular quadrilateral elements.In addition,the computational efficiency of analytical solution and numerical solution is quantitatively estimated and analyzed.Results show that the mixed DDM method is 2.6 times faster than the pure numerical method when calculating the speed of the single second-order partial derivative and 32%faster when assembling Jacobian matrix of the whole fracture model.The proposed method is then applied to build a fluid-solid coupling model and perform sensitivity analyses associated with the fracture opening as well as induced-stress filed calculation under a single fracture,multiple fracture model and complex fracture network.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)the penny-shaped fracture has the shortest average distance between each pair of elements and shows the strongest stress shadowing effect,which is more sensitive to short side for the rectangular-shaped fractures;(5)the fracture spacing 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(6)the induced tensile stress generated by the fracture tip deter the stress-reorientation regions along the tip and the generation of a more complex network.Furthermore,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.The numerical results further demonstrate the universality of this mixed method.The model based on the algorithm can more accurately describe any complex fracture in threedimensional space and can realize the calculation of complex fracture networks,providing theoretical assistance for the further improvement of the fully 3D fracture model.