Journal ArticleDOI
An enriched–FEM technique for numerical simulation of interacting discontinuities in naturally fractured porous media
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In this article, an extended finite element method is presented for simulation of interaction between hydraulic fracturing and natural fractures in saturated porous media, where the Darcy law is employed in conjunction with an aperture dependent permeability for the fracture channel to describe the interfacial inflow.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2018-04-01. It has received 81 citations till now. The article focuses on the topics: Extended finite element method & Finite element method.read more
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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship
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.
Journal ArticleDOI
Hydro-mechanical simulation of the saturated and semi-saturated porous soil–rock mixtures using the numerical manifold method
Wenan Wu,Yongtao Yang,Hong Zheng +2 more
TL;DR: In this article, a numerical manifold model is presented for hydro-mechanical simulation of the saturated and semi-saturated soil-rock mixtures (SRMs) by imposing a stick-slip contact constraint using an augmented Lagrange multiplier approach.
Journal ArticleDOI
X-FEM Modeling of Multizone Hydraulic Fracturing Treatments Within Saturated Porous Media
M. Vahab,Nasser Khalili +1 more
TL;DR: In this paper, a fully coupled hydro-mechanical model is presented for the study of multizone hydraulic fracturing, where the momentum balance equation of the bulk together with the mass balance and momentum balance equations of the fluid phase are employed in order to derive the hydromagnetic coupled system of governing equations of porous media known as the $$({\mathbf{u}} - p)$$ fixme formulation.
Journal ArticleDOI
A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams
TL;DR: In this paper, a nonlocal finite element model is proposed to analyze the thermo-elastic behavior of imperfect functionally graded porous nanobeams (P-FG) on the basis of nonlocal elasticity theory and employing a double-parameter elastic foundation.
Journal ArticleDOI
An X-FEM investigation of hydro-fracture evolution in naturally-layered domains
TL;DR: In this article, a computational model is developed for the simulation of hydro-fracture growth in naturally layered impervious media using the extended finite element method (X-FEM).
References
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Journal ArticleDOI
A finite element method for crack growth without remeshing
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.
Journal ArticleDOI
Elastic crack growth in finite elements with minimal remeshing
Ted Belytschko,T. Black +1 more
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
Journal ArticleDOI
Validity of Cubic Law for fluid flow in a deformable rock fracture
TL;DR: 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.
VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship
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.
Journal ArticleDOI
A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures
J. Geertsma,F. De Klerk +1 more
TL;DR: In this article, the authors present a mathematical formulation of the fracture-extension process, equations for fracture width and shape, effect of formation permeability on fracture dimensions, and fracture design charts.
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