An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model
01 Oct 2013-Finite Elements in Analysis and Design (Elsevier Science Publishers B. V.)-Vol. 73, pp 77-95
TL;DR: In this article, a fully coupled numerical model is developed for the modeling of the hydraulic fracture propagation in porous media using the extended finite element method in conjunction with the cohesive crack model, where the fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well known cubic law.
About: This article is published in Finite Elements in Analysis and Design.The article was published on 2013-10-01. It has received 289 citations till now. The article focuses on the topics: Fracture mechanics & Poromechanics.
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11 Jun 2010
Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.
1,557 citations
TL;DR: A review of the basic approaches for hydraulic fracture simulation can be found in this article, where the authors discuss both continuum and meso-scales numerical methods as well as engineering models which typically make use of additional assumptions to reduce computational cost.
280 citations
TL;DR: In this paper, a coupled hydro-mechanical (HM) model is incorporated into the enriched NMM to simulate fluid driven fracturing in rocks, and several benchmark problems are investigated to verify the coupled HM model.
168 citations
TL;DR: In this article, a fully coupled finite element/finite volume approach is proposed to simulate field-scale hydraulically driven fractures in 3D, using massively parallel computing platforms.
Abstract: Summary
This paper describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions. © 2016 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.
162 citations
Cites background from "An extended finite element method f..."
...Khoei AR, Hirmand M, Vahab M, Bazargan M....
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...Mohammadnejad and Khoei [7] described an XFEM approach for a cohesive crack model in a deformable porous medium....
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...Khoei et al. [8] presented an XFEM approach for modeling hydraulically driven cohesive fracture propagation in the presence of frictional natural faults....
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...Mohammadnejad T, Khoei AR....
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References
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Abstract: The settlement of soils under load is caused by a phenomenon called consolidation, whose mechanism is known to be in many cases identical with the process of squeezing water out of an elasticporous medium. The mathematical physical consequences of this viewpoint are established in the present paper. The number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three‐dimensional problems. Simple applications are treated as examples. The operational calculus is shown to be a powerful method of solution of consolidation problems.
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TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
Abstract: Y ielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
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TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Abstract: SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright ? 1999 John Wiley & Sons, Ltd.
5,815 citations
01 Jan 2008
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.
5,564 citations
TL;DR: In this article, fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened, which may be regarded as a way of expressing the energy adsorption in the energy balance approach.
5,505 citations