The XFEM for Hydraulic Fracturing in Three Dimensions
Monday, May 11, 2015 - 3:10pm - 3:35pm
The extended finite element method (XFEM) is the method of choice for the simulation of crack propagation. The XFEM enriches the approximation space such that discontinuities and singularities within elements, such as those introduced by cracks, may be captured with optimal accuracy. There is no need to adapt the mesh during the simulation. Herein, the XFEM is used for the simulation of hydraulic fracturing in three spatial dimensions. The crack surface may evolve arbitrarily. The Reynolds equation, modeling the fracking fluid, is solved on the curved surface based on an explicit crack mesh. This crack mesh, composed by flat triangles, is also used to update the crack surface during propagation. For the XFEM-part of the simulation, where displacements, stresses and strains in the rock are computed, this explicit crack description is converted into an implicit description based on level sets. Numerical results show the success of this complex coupled problem.