Numerical Modeling of Hydraulic Fracturing using the XFEM
Safdar Abbas (Schlumberger), Elizaveta Gordeliy (University of British Columbia), Brice Lecampion (Schlumberger), Anthony Peirce (University of British Columbia)
Engineering Mechanics and Materials in the Oilfield
Wed 9:00 - 10:30
CIT 227
Numerical modeling of hydraulic fracture propagation consists of solving the coupled elasto-hydrodynamics equations and incorporating various fracture propagation regimes. The eXtended Finite Element Method (XFEM) has been very successful in numerical modeling of dry fracture propagation. In the current approach we leverage the XFEM for hydraulic fracture propagation in an elastic medium. The fluid flow in the fracture (lubrication theory) and the elastic response (XFEM solution) are solved in a strongly coupled manner. The singular asympotic solutions in the fracture tip region are incorporated by using a mixed formulation. The fracture front is represented as a free boundary in space. For a specified time, the free boundary is located using an implicit level set algorithm (ILSA) by using the applicable tip asymptotic solution. This algorithm, along with a new set of crack tip enrichment functions, ensures that the fracture front is positioned consistent with the applicable crack-tip asymptotics. The numerical method has been applied to various published benchmark problems of hydraulic fracture propagation in plane-strain and axisymmetric geometries. The results agree extremely well with the benchmark solutions.