An implicit level set method for modeling hydraulically driven fractures

By Anthony Peirce, Emmanuel Detournay. 2008

332 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fa738e2f3c2e52d7de35c7a0b95f195d3d5fae27

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm (2015, methodology): “We assume [11] that the fracture will grow within a rectangular region that has been tessellated into a fixed uniform rectangular mesh ∪∆Am,n with dimensions ∆χ and ∆ζ in the two coordinate directions (similar to the unscaled fracture shown in Fig.”
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, methodology): “Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model Sanghyun Lee ∗ Mary F. Wheeler † Thomas Wick ‡ This work presents phase field fracture modeling in heterogeneous porous media.”
Implicit level set schemes for modeling hydraulic fractures using the XFEM (2013, methodology): “We ran the ILSA-XFEM schemes for Lx ¼ 12, Ly ¼ 6:04, h ¼ 0:04, and Ds ¼ 0:1.”
Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems (2015, methodology): “However, for planar HF in a 3D elastic medium one may need to change the power law exponent λ, as the propagation regime changes along the fracture boundary [35,25].”
A non-singular integral equation formulation to analyse multiscale behaviour in semi-infinite hydraulic fractures (2015, methodology): “Recognizing the necessity of accurate † Email address for correspondence: peirce@math.ubc.ca ‡ Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204, USA. c© Cambridge University Press 2015 781 R1-1 fracture tip modelling, the hydraulic fracturing methodology kn”
A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag (2011, methodology): “The non-linear system of equations (49) is solved iteratively using either a fixed-point iteration [30] or Newton’s method [43, 44].”
On the moving boundary conditions for a hydraulic fracture (2014, methodology): “First we note that the 1D nature of the solution in the vicinity of the front, i.e., the spatial variation of the fields w and p near CðtÞ, takes place in the direction normal to the front (see Peirce & Detournay (2008) for details).”
Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers (2010, background): “In other words, the average fracture aperture in a vertical cross-section of a PKN or P3D model depends only on the fluid pressure in that crosssection, in contrast to planar fracture models [10,14,17,18] that are characterized by non-local interaction between the pressure and aperture fields.”
Coupling schemes for modeling hydraulic fracture propagation using the XFEM (2013, background): “Though the above scheme suffices for the purposes of this paper, more complex situations will require more generally applicable algorithms such as the implicit level set scheme [24], which exploits the local tip asymptotic behavior to locate the free boundary in space.”