13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Implementation of the XFEM for Hydraulic Fracture Problems Zuorong Chen* CSIRO Earth Science & Resource Engineering, Melbourne, Australia * Corresponding author: zuorong.chen@csiro.au Abstract A new finite element has been implemented to incorporate the extended finite element method (XFEM) for the solution of hydraulic fracture problems. The proposed element includes the desired aspects of the XFEM so as to model crack propagation without explicit remeshing. In addition, the fluid pressure degrees of freedom have been defined on the element to describe the fluid flow within the crack and its contribution to the crack deformation. Thus the fluid flow within the crack and crack propagation are fully coupled in a natural way and are solved simultaneously. Verification of the proposed element has been conducted by comparing the finite element results with the analytical solutions available in the literature. Keywords Hydraulic fracture, Extended finite element method, Internal pressure 1. Introduction Hydraulic fracturing is a powerful technology for enhancing conventional petroleum production. It is playing a central role in fast growing development of unconventional gas and geothermal energy. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to understand the complex, multiscale mechanics of hydraulic fracturing, to the efficient application of this technology, and to develop innovative, advanced hydraulic fracturing technologies for unconventional gas production. The accurate numerical simulation of hydraulic fracture growth remains a significant challenge because of the strong nonlinear coupling between the viscous flow of fluid inside the fracture and fracture propagation (a moving boundary), complicated by the need to consider interactions with existing natural fractures and with rock layers with different properties. Great effort has been devoted to the numerical simulation of hydraulic fractures with the first 3-D modeling efforts starting in the late 1970s [1-2]. Significant progress has been made in developing 2-D and 3-D numerical hydraulic fracture models [3-15]. Boundary integral equation methods or displacement discontinuity techniques have generally been employed to investigate the propagation of simple hydraulic fractures such as penny-shaped or plane-strain fractures in a homogeneous, infinite or semi-infinite elastic medium where the appropriate fundamental solutions are available. The finite element method has been used and is particularly useful in modelling the hydraulic fracture propagation in inhomogeneous rocks which may include nonlinear mechanical properties and may be subject to complex boundary conditions. The finite element model is also able to investigate the propagation of hydraulic fractures in infinite or semi-infinite medium by using infinite elements or appropriate analytical solutions to efficiently approximate the far-field boundary [15]. However, the standard finite element model requires remeshing after every crack propagation step and the mesh has to conform exactly to the fracture geometry as the fracture propagates, and thus is computationally expensive. By adding special enriched shape functions in conjunction with additional degrees of freedom to the standard finite element approximation within the framework of partition of unity, the extended finite element method [16-17] (XFEM) overcomes the inherent drawbacks associated with use of the conventional finite element methods and enables the crack to be represented without explicitly meshing crack surfaces, and so the crack geometry is completely independent of the mesh and remeshing is not required, allowing for the convenient simulation of the fracture propagation. The XFEM has been employed to investigate the hydraulic fracture problems [18-19].
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