An enriched finite element model for wave propagation in fractured media

Komijani, M.; Gracie, Robert

doi:10.1016/j.finel.2016.11.001

Cited by 21 publications

(21 citation statements)

References 16 publications

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“…18,[41][42][43][44][45] The second trend focuses on enhancing the physical aspects of the models by incorporating more physics. Examples are studies that considered nonlinear fluid rheology and proppant transport, 46,47 HF propagation in porous media, 14,48 acoustic emissions, 49 solid nonlinearity due to bulk plasticity and cohesive fractures, 15,50,51 and nonlocal plasticity and damage models. 52,53 For a detailed review of recent advances in the simulation of HFs, the reader is referred to related works.…”

Section: Introductionmentioning

confidence: 99%

On the undrained and drained hydraulic fracture splits

Esfahani

Gracie

2019

Numerical Meth Engineering

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Summary The simulation of hydraulic fracturing (HF) involves the solution of a hydro‐mechanically coupled system. This article presents a new iterative sequential coupling algorithm, the undrained HF split, that improves the simulation of HFs in impermeable media. A poromechanics analogy is used to derive a stable split for the hydro‐mechanically coupled system in which the mechanical subproblem is solved first. The proposed undrained HF split is applied to the simulation of cohesive HFs in an impermeable elastic medium. The cubic law is used as the constitutive model for simulating fluid flow in fractures. A minimum hydraulic aperture is assumed in the cohesive tip zone, where the mechanical aperture smoothly vanishes. While general in its nature, the undrained HF splitting scheme is employed within the context of a two‐dimensional eXtended finite element model for the fractured solid, and a regular finite element model for fluid in the fracture. The undrained HF split is successfully used to simulate self‐similar plane strain HFs as well as the propagation of HFs from a wellbore under anisotropic stress conditions. Fracture trajectories and local alteration of stress field are investigated. The solution of the undrained HF split converges to the same solution as the fully coupled model, whereas the commonly used P→W sequential algorithm, referred to in this article as the drained HF split, generates spurious oscillations and fails to converge in many problems. The undrained HF split is shown to be stable and robust in applications where the drained HF split is unstable.

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Section: Introductionmentioning

confidence: 99%

On the undrained and drained hydraulic fracture splits

Esfahani

Gracie

2019

Numerical Meth Engineering

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“…e standard element domain can be gained by mapping the original element domain. Substituting equations (8) and (9) into equation 7, the principle of Galerkin variation can obtain the finite element equations:…”

Section: Shock and Vibrationmentioning

confidence: 99%

“…Gravenkamp et al [7] resolved the results of high frequencies wave motion by using the following methods: scaled boundary finite element method and the nonuniform rational B-splines. Komijani and Gracie [8] proposed the global enrichment method which adopts the harmonic functions. e merit of global enrichment and the generalized finite element method is that they can analyze wave motion in plane with cracks by using the phantom node method.…”

Section: Introductionmentioning

confidence: 99%

Wave Motion Analysis in Plane via Hermitian Cubic Spline Wavelet Finite Element Method

Xue

Wang

et al. 2020

Shock and Vibration

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A plane Hermitian wavelet finite element method is presented in this paper. Wave motion can be used to analyze plane structures with small defects such as cracks and obtain results. By using the tensor product of modified Hermitian wavelet shape functions, the plane Hermitian wavelet shape functions are constructed. Scale functions of Hermitian wavelet shape functions can replace the polynomial shape functions to construct new wavelet plane elements. As the scale of the shape functions increases, the precision of the new wavelet plane element will be improved. The new Hermitian wavelet finite element method which can be used to simulate wave motion analysis can reveal the law of the wave motion in plane. By using the results of transmitted and reflected wave motion, the cracks can be easily identified in plane. The results show that the new Hermitian plane wavelet finite element method can use the fewer elements to simulate the plane structure effectively and accurately and detect the cracks in plane.

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“…Very recently, a GFEM-enriched PNM model was proposed by Komijani and Gracie [36] to extend the enriched FE model developed in [35] to the case of fractured media. Their enriched FE model, the PNM-GFEM, combines the advantages of the trigonometric enrichments introduced in [35] and the Phantom Node Method.…”

Section: Introductionmentioning

confidence: 99%