# SCAIM Seminar: Lisa Gordeliy

## Topic

Title: Modelling Hydraulic Fractures using a Boundary Element Method

(BEM) and the Extended Finite Element Method (XFEM)

(BEM) and the Extended Finite Element Method (XFEM)

## Speakers

## Details

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 Greenâ€™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.

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 Greenâ€™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.

## Additional Information

This is a Past Event

Event Type

**Scientific, Seminar**

Date

**October 4, 2011**

Time

**-**

Location

University of British Columbia