An extended finite element method for hydraulic fracture problems

In this paper, the extended finite element method (X‐FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are...

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Vydáno v:Communications in numerical methods in engineering Ročník 25; číslo 2; s. 121 - 133
Hlavní autor: Lecampion, Brice
Médium: Journal Article
Jazyk:angličtina
Vydáno: Chichester, UK John Wiley & Sons, Ltd 01.02.2009
Wiley
Témata:
Computational techniques
Crystalline rocks
Earth sciences
Earth, ocean, space
Exact sciences and technology
extended finite element
fluid-driven cracks
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Geophysics: general, magnetic, electric and thermic methods and properties
hydraulic fracturing
Igneous and metamorphic rocks petrology, volcanic processes, magmas
Internal geophysics
Mathematical methods in physics
Physics
Solid mechanics
Structural and continuum mechanics
tip asymptotics
Internal crack
Singularity
extended finite element
fluid-driven cracks
finite element analysis
asymptotic approximation
Modeling
tip asymptotics
Crack propagation
rupture
Fracture toughness
hydraulic fracturing
viscosity
Plane strain
Rotation group
Unity partition
eXtended Finite Element Method
Internal pressure
ISSN:1069-8299, 1099-0887
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Shrnutí:In this paper, the extended finite element method (X‐FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness‐dominated regime of propagation and the so‐called ⅔ asymptote in fracture width for the viscosity‐dominated regime. Different variants of the X‐FEM are tested for the case of a plane‐strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point‐wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd.
Bibliografie:ArticleID:CNM1111
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ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.1111