Speaker: Dr. Elizaveta Gordeliy

Abstract

Hydraulic fractures are created in geomaterials for geothermal energy and oil and gas production. The development of a hydraulic fracture simulator is notably challenging and requires a proper verification. Coupling of the rock deformation and the fluid flow within the fracture leads to a system of non-linear equations. The propagation of the fracture front brings an additional complexity and a computational challenge into the model. We present a model for propagation of nonplanar radially-symmetric hydraulic fractures based on the extended finite element method (XFEM). The XFEM represents fractures by augmenting the standard set of finite-element shape functions by enrichment functions corresponding to the singularities in the elastic displacement and stress fields. The underlying finite element mesh does not have to adhere to the geometry of the fractures, and fracture propagation can be modeled without computationally intensive re-meshing. Fluid flow within the fractures is described by the Reynolds lubrication equation and is modeled by a finite volume scheme. The direction of fracture propagation is determined from a maximum tangential stress criterion. The location of the fracture front at each time step is found using the implicit level-set algorithm and fracture tip asymptotics. We validate the numerical results via a detailed comparison with the results from laboratory experiments.

Biography

Elizaveta Gordeliy is a postdoctoral researcher at LMS, École polytechnique.

Document compiled by Filippo Agnelli.