Successfully creating multiple hydraulic fractures in horizontal wells is critical for unconventional gas production economically. When multiple hydraulic fractures propagate simultaneously, each open fracture exerts additional stresses on the adjacent fractures, which is often named as stress-shadow effect. Stress-shadow effect has significant influence on the local stress field in the surrounding rock, which will influence the geometry of hydraulic fractures. With the framework of partition of unity for discontinuity modelling, this paper developed a high-order Generalized Finite Element Method (high-order GFEM) to investigate the propagation of three dimensional (3D) non-planar fractures including hydraulic fractures without re-meshing. In this paper, this high-order GFEM is developed to investigate the behavior of hydraulic fractures. The present method can be regarded as a development of the FE-Shepard-based GEEM and mesh-free method for discontinuity modelling. Compared to the FE-Shepardbased GFEM, the salient feature of this method is to construct high-order global approximation without generation of extra unknowns. In the first numerical test, this high-order GFEM is validated by an existing experiment. In the second numerical tests, this high-order GFEM is used to investigate the influence of stress-shadow effects and confirming stress.


Shale gas/oil production has played a critical role in meeting US energy demands. Handling the development of hydraulic fractures is critical for enhancing gas/oil production and reducing the risk of reservoir treatment. It is already known that in-situ stress has significant impact on the geometry of fracture development. Therefore, realistic three dimensional (3D) non-planar fracturing simulation is critical to the design and optimization of reservoir treatment. With the development of computer science, numerical methods have become one of the most effective approaches to understand the evolution of fractures, because it offers a physically consistent and numerically accurate way to model the underground large-scale geometric discontinuities.

Finite Element Method (FEM) (Zienkiewicz and Taylor, 2000; Tang et al., 2013, Paluszny et al., 2013) is the most widely used numerical approach in engineering and have been utilized for 3D fracture propagation last several decades. However, finite element meshes and fracture surfaces are required to be coincident which will significantly increase the difficulty of simulation. If fracture propagation is taken into account, the mesh sizes are required to be updated in each step and the difficulty associated to mesh generation is furtherly increased. In addition, the meshes are required to be more refined in the vicinity of fracture tips than in the remainder of the model, in order to obtain sufficiently accurate solution for the fracture analysis (Moes et al., 2014).

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