Abstract: With the further study of the extended finite element theory, the extended finite element method (XFEM) has been widely used to simulate hydraulic fracturing. In comparison with the conventional FEM, the XFEM method has substantial advantages, such as high precision and low computational complexity. However, there are still many difficult challenges including how to simulate the perforation and the interaction between fluid and rock and to analyze propagation law of hydraulic fracturing. In this paper, to study the propagation law of hydraulic fracturing, the stress equilibrium equation of rock porous medium, fluid continuity equation and boundary conditions are established. Through finite element discretization method, the coupling equation matrix is treated. The initial fracture (or propagation) is defined through enrichment functions, and the maximum principal stress and damage variable D are selected respectively as the criterion of fracture initiation and propagation. Hydraulic fracturing propagation process is simulated by using the level set method. Numerical results show that the increase of perforation azimuth, fracture fluid displacement and the reduction of the horizontal stress difference cause the increase of the fracture initiation pressure, and the viscosity has no obvious effect on the fracture initiation pressure. It helps to widen the fracture width by increasing the perforation azimuth, the fracturing fluid displacement, the fracturing fluid viscosity and decreasing the horizontal stress difference. Increasing the horizontal stress difference, fracturing fluid displacement and decreasing the perforation azimuth and the viscosity of fracturing fluid can help to increase the fracture length and vice versa. Different well types and parameters of reservoir and fracturing operation are analyzed by hydraulic fracture XFEM based on ABAQUS platform. The fracture shape is lifelike and the image of degree of concave-convex on the fracture surface is clear. In consequence the result is accurate. As a simple and effective research method for studying the criterion of hydraulic fracturing propagation, this study provides the reference for hydraulic fracturing design and operation in oil field.

Key words: fracture propagation, extended finite element method, hydraulic fracturing, ABAQUS, numerical simulation