Coupled formulation and algorithms for the simulation of non-planar three-dimensional hydraulic fractures using the generalized finite element method

P. Gupta, C. A. Duarte

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a coupled hydro-mechanical formulation for the simulation of non-planar three-dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non-planar three-dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three-dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies.

Original languageEnglish (US)
Pages (from-to)1402-1437
Number of pages36
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Volume40
Issue number10
DOIs
StatePublished - Jul 1 2016

Keywords

  • GFEM
  • XFEM
  • coupled formulation
  • hydraulic fracturing
  • hydro-mechanical coupling
  • lubrication equation
  • multi-physics
  • solid-fluid coupling

ASJC Scopus subject areas

  • Computational Mechanics
  • Materials Science(all)
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials

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