Numerical Simulation of Fracture Propagation Based on Finite Element Method and Peridynamics
Authors:   , Sun Yanan 
Published: January 2022

Hydraulic fracturing has attracted a tremendous amount of attention due to its abundant applications, such as magma-driven dykes, fracturing of oil and gas reservoirs, heat pro-duction from geothermal reservoirs, ice melt, and fault reactivation in mining. Therefore, the development of fracture propagation models is of great significance to provide more effective technical tools for the dynamic simulation of fracture formation and propagation. Hydraulic fracturing involves a complex process due to the strong coupling between the fluid and solid rock. The finite element method (FEM) is a traditional method for solving the fracture propagation problem. FEM has the advantage of being robust and flexible. However, special treatment is required when dealing with complex fracture problems such as fracture intersection and branching because of discontinuities across fracture surfaces. Instead of seeking to approximate partial differential equations in a conventional framework, the peridynamic approach (PD) uses spatial integral equations that overcome the limitations of defining partial derivatives at discontinuities, which makes it quite suitable for solving complex fracture problems. Therefore, it is of great importance to combine the advantages of both FEM and PD to develop a more robust and flexible fracture propagation model. The main contribution of the thesis is to study fracture propagation problems in fully saturated porous media based on both FEM and PD. Three fracture models based on FEM, PD, hybrid FEM and PD are developed to simulate and explore more “realistic” fracture propagation processes. The main research work of the thesis contains the following four parts.First, comprehensive reviews of the fracture propagation literature, crack branching and PD theory are given. The fracture propagation review includes a review of the fracture propagation process, fracture models and various numerical methods for predicting fracture propagation. The review of crack branching provides a state-of-the-art review of crack branching, including experimental observations, physics, fracture models and associated numerical methods. The latest advances and existing issues of crack branching are discussed. The review of PD theory provides a review of theoretical aspects of PD and related applica-tions of PD in different fields, especially in the field of fracture mechanics. The challenges and new prospects for the development of PD are discussed.Then, a fully implicit, FEM-based fracture model using zero thickness cohesive interface elements is developed. The rock formation is considered as a fully saturated porous medium. The fracture surface is deemed to be permeable, the fracturing fluid is treated as an impressible Newtonian fluid, and the cohesive zone model is employed for the fracture propagation criterion. After verifying the model, the stepwise phenomenon, which has been observed in the field and experiments and reported recently in the numerical modelling literature, is investigated with the model.Then, an explicit PD approach for simulating fracture propagation in saturated porous media is developed. A staggered method is adopted to solve the coupled system. The solid deformation equation is solved for the displacement field, and the fluid flow equation is solved for the pressure field with PD. After verification via benchmark examples, including a 1D consolidation problem and a 2D fluid-filled crack propagation problem, a series of tests are conducted to study the fracture propagation phenomena in porous media, including the crack branching phenomenon and the stepwise phenomenon. Effects of pore pressure in fracture propagation branching are investigated, and the stepwise phenomenon is successfully reproduced. All the examples presented demonstrate the capability of the approach in solving fracture propagation problems in saturated porous media.Finally, a fully coupled hybrid FEM-PD approach for simulating fracture propagation in saturated porous media is presented. Considering the ability of PD in solving discontinuous problems, the area where cracks can potentially occur is discretised by PD and the crack-free area is discretised by FEM. The solid deformation and fracture propagation are captured by PD and FEM, while the fluid flow in both the reservoir and fracture is simulated with FEM. The whole process is solved in a monolithic way with an implicit scheme. The approach demonstrates the capability of modelling complex dynamic crack propagation via benchmark examples. The branching phenomenon is then investigated with the proposed approach. In conclusion, complex crack patterns are prone to form with faster loading rate, more brittle and impermeable media, and with lower energy release rate.