Journal ArticleDOI
Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media
Anthony Peirce,Eduard Siebrits +1 more
TLDR
In this article, uniform asymptotic solutions (UAS) for displacement discontinuities (DDs) that lie within the middle layer of a three layer elastic medium are presented for both 2D and 3D elastic media.Abstract:
We present uniform asymptotic solutions (UAS) for displacement discontinuities (DD) that lie within the middle layer of a three layer elastic medium. The DDs are assumed to be normal to the two parallel interfaces between the leastic media, and solutions will be presented for both 2D and 3D elastic media. Using the Fourier transform (FT) method we construct the leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three layer medium. Although a closed form solution will require an infinite series solution, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We present an explicit UAS for elements in which the DD fields are assumed to be piecewise constant throughout a line segment in 2D and a rectangular element in 3D. We demonstrate the usefulness of this UAS by providing a number of examples in which the UAS is used to solve problems in which cracks just touch or cross an interface. The accuracy and efficiency of the algorithm is demonstrated and compared with other numerical methods such as the finite element method and the boudary integral method.read more
Citations
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Journal ArticleDOI
Computer simulation of hydraulic fractures
TL;DR: In this article, the authors provide a brief historical background of the development of hydraulic fracturing models for use in the petroleum and other industries, and discuss scaling laws and propagation regimes that control the growth of hydraulic fractures from the laboratory to the field scale.
Journal ArticleDOI
An implicit level set method for modeling hydraulically driven fractures
TL;DR: In this paper, an implicit level set algorithm is proposed to locate the free boundary for a propagating hydraulic fracture, which exploits the local tip asymptotic behavior, applicable at the computational length scale, in order to locate a free boundary.
Journal ArticleDOI
Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: A numerical investigation
TL;DR: In this article, a two-dimensional boundary element model is used to investigate the propagation of fluid-driven or hydraulic fractures deflected at bedding interfaces in layered sedimentary rocks and subsequent fluid invasion.
Journal ArticleDOI
A review on hydraulic fracturing of unconventional reservoir
TL;DR: In this article, some issues related to hydraulic fracturing have been reviewed, including the experimental study, field study and numerical simulation, and the existing problems that need to be solved on the subject of hydraulic fracturing has been proposed.
Journal ArticleDOI
Implicit level set schemes for modeling hydraulic fractures using the XFEM
TL;DR: In this paper, the authors describe two XFEM schemes for modeling fluid driven fractures, both of which exploit an implicit level set algorithm (ILSA) for locating the singular free boundary that occurs when the fluid and fracture fronts coalesce.
References
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Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
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Asymptotics and Special Functions
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Propagator matrices in elastic wave and vibration problems
Freeman Gilbert,George E. Backus +1 more
TL;DR: In this paper, the boundary value problem in elastic wave propagation in stratified media is formulated in terms of a finite number of linear, first order, ordinary differential equations with variable coefficients.