SCAIM Seminar: Lisa Gordeliy
- Date: 10/04/2011
- Time: 12:30
University of British Columbia
Title: Modelling Hydraulic Fractures using a Boundary Element Method(BEM) and the Extended Finite Element Method (XFEM)
Abstract:
This talk presents the development of BEM and XFEM frameworks for
modelling hydraulic fractures, which arise in a wide range of
geoengineering applications. The mathematical formulation of the problem
involves a system of coupled nonlinear partial differential equations
with a moving boundary, arising from the coupling between the fluid flow
in the evolving fracture and the deformation of the parent material.
Each of the discussed approaches has its own advantages: the BEM can
efficiently simulate a propagating crack in linear homogeneous domains,
while the XFEM is able to model complex settings such as multiple
fractures in porous and layered rocks or plastic material deformation.
The first part of the talk presents a BEM algorithm coupled with the
finite-volume fluid flow model. An example of a near-surface radial
crack is investigated, for which the required Green’s functions, that
represent the crack as a distribution of material discontinuities, are
derived. A comparison of the numerical results generated by this
numerical model with data from laboratory experiments identifies
particular physical phenomena that have to be accounted for in the
mathematical formulation for accurately capturing the complex fracture
propagation process.
In the second part of the talk, an XFEM approach to this problem is
discussed. The development includes derivation of shape functions that
enrich the underlying finite element formulation by representing
discontinuities and singularities associated with the hydraulically
driven crack. An example is presented in which a coupled XFEM model
simulates a crack driven by a viscous fluid through a layered material.
