Hydraulic fracturing is a technique for extracting unconventional resources by injecting high pressure fluid to crack the reservoir layer. This is a multi-scale and multi-physics problem that involves the behavior of rock matrix and injected fluid flow, as well as their interaction and resulting fracture propagation. The heterogeneities in the reservoir rocks make the fracture propagation a complex phenomenon and hydraulic fracturing an even more challenging problem.
In this study, a C++ based three dimensional Lattice Element Method (LEM) simulator is developed, which is capable of simulating both mechanical and fluid induced fracturing behavior in heterogeneous media. In this model, the mechanical response of solid is represented with a 3D lattice structure. The Timoshenko beam with embedded discontinuity is used as a solid lattice model, and exponential softening law is incorporated. The fracture surface is represented by the discontinuity generated in the lattice once it yields. While the fluid lattice network is a pipe flow system generated at fracture surfaces. This fluid lattice model follows Darcy's law and the principle of mass conservation, and interacts with solid lattice network through hydrostatic pressure. The 3D multi-physics problem is simplified into a network composed of 1D beam and pipe lattice, which can be simulated with a relatively low computational cost. The validations and comparisons between numerical and experimental results indicate that LEM is a promising tool for investigating the process of fracture development. Its simplicity makes it capable of simulating branching and complex interactions between multiple fractures, which is extremely difficult in continuum-based methods. A nonlinear softening law is implemented in the solid lattice model, which allows the simulation of the failure of materials with different degrees of ductility. In addition, the potential application of LEM to early crack detection is explored.
The model is used to investigate the influence of rock heterogeneities on the hydraulic fracturing process, especially the fracture pattern. The results show that, all the factors, including in situ stress field, scale of weakness and statistical distribution of properties, affect the results to a different degree. The nodal arrangement is one of the main factors that affect potential fracture path. The interactions between hydraulic fractures and pre-existing natural joints are also investigated. The hydraulic fracture penetrates into a joint when the normal stress on the joint surface is too small to stop the joint from opening under fluid pressure. Whereas a fracture crossing is more likely to occur when there is little or no slippage between two sides of the joints. This implies a possible mechanism of fracture crossing in which the fracture reinitiates on the other side of the joint due to tensile stress generated by the friction applied on the joint surface.
