A three-dimensional Generalized Finite Element Method for simultaneous propagation of multiple hydraulic fractures from a wellbore

Nathan Shauer, C. Armando Duarte

Research output: Contribution to journalArticlepeer-review


In this article, a 3-D methodology for the simulation of hydraulic fracture propagation using the Generalized Finite Element Method (GFEM) is extended for the simultaneous propagation and interaction of multiple hydraulic fractures. A 3-D isotropic elastic material for the rock and Reynolds lubrication theory for the fluid flow in the fractures are assumed. The elastic solid governing equation is discretized in space with a quadratic GFEM and the equation for the flow in the fractures is discretized in space with a quadratic FEM. With the GFEM, the solid mesh does not need to fit the fracture and accuracy is improved around the fracture front with the use of singular enrichment functions. Discretization error is further controlled by employing mesh adaptivity around the fracture front. The injected fluid partitioning among fractures is computed by modeling the wellbore, where the flow is assumed to be governed by the Hagen–Poiseuille relation. The pressure losses between wellbore and hydraulic fractures are modeled with the sharp-edged orifice equation and with the use of 1-D connecting elements. A linear FEM is adopted for the spatial discretization of the equation governing the flow in the wellbore and the connection between wellbore and hydraulic fracture. A propagation criterion based on a regularization of Irwin's criterion is adopted and a methodology to automatically estimate the time step that leads to the propagation of fractures based on linear interpolation/extrapolation is presented. Three verification problems are solved and compared with results from the literature. A problem with initial fractures not aligned with the in situ stresses is analyzed. Complex final fracture geometries are observed due to this misalignment.

Original languageEnglish (US)
Article number108360
JournalEngineering Fracture Mechanics
StatePublished - Apr 15 2022
Externally publishedYes


  • Finite Element Method (FEM)
  • Generalized Finite Element Method (GFEM)
  • Hydraulic fracturing
  • Multi-stage hydraulic fracturing
  • Multiple hydraulic fractures

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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