Flow Around a Crack in a Porous Matrix and Related Problems

Pouya, Ahmad; Ghabezloo, Siavash

doi:10.1007/s11242-009-9517-8

Cited by 25 publications

(46 citation statements)

References 17 publications

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“…Within the context of fracture upscaling, it has been suggested that this behaviour can be identified with percolation, which is the transition from unconnected to connected fracture networks (Pozdniakov and Tsang, 2004;Barthélémy, 2008;Pouya and Ghabezloo, 2010). Unfortunately, there is no theoretical result justifying this conjecture, and many authors regard the self-consistent percolation estimates as spurious (Guéguen et al, 1997;Torquato, 2002).…”

Section: The Symmetric Self-consistent Methodsmentioning

confidence: 99%

A 3D Computational Study of Effective Medium Methods Applied to Fractured Media

et al. 2013

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This work evaluates and improves upon existing effective medium methods for permeability upscaling in fractured media. Specifically, we are concerned with the asymmetric self-consistent, symmetric self-consistent and differential methods. In effective medium theory, inhomogeneity is modeled as ellipsoidal inclusions embedded in the rock matrix. Fractured media correspond to the limiting case of flat ellipsoids, for which we derive a novel set of simplified formulas. The new formulas have improved numerical stability properties, and require a smaller number of input parameters. To assess their accuracy, we compare the analytical permeability predictions with accurate, three-dimensional finite-element simulations. We also compare the results with a semi-analytical method based on percolation theory and curve fitting, which represents an alternative upscaling approach. A large number of cases is considered, with varying fracture aperture, density, matrix/fracture permeability contrast, orientation, shape and number of fracture sets. The differential method is seen to be the best choice for sealed fractures and thin open fractures. For high-permeable, connected fractures, the semi-analytical method provide the best fit to the numerical data, whereas the differential method breaks down. The two self-consistent methods can be used for both unconnected and connected fractures, although the asymmetric method is somewhat unreliable for sealed fractures. For open fractures, the symmetric method is generally the more accurate for moderate fracture densities, but only the asymmetric method is seen to have correct asymptotic behaviour. The asymmetric method is also surprisingly accurate at predicting percolation thresholds.

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Section: The Symmetric Self-consistent Methodsmentioning

confidence: 99%

A 3D Computational Study of Effective Medium Methods Applied to Fractured Media

et al. 2013

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“…assuming that the flux q in the left-hand side of eqn. (14) is deduced from the results obtained for a single fracture in an infinite body which is given in Pouya and Ghabezloo [14]. However, in the case of high fracture density (or dense fracture networks), the integral of flux on the fracture network, i.e.…”

Section: Numerical Calculationmentioning

confidence: 97%

“…2b), Pouya and Ghabezloo [14] analyzed the masse balance in a small disc centred on the singular point and deduced the following relationship:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The previous problem was derived rigorously by Pouya and Ghabezloo [14] and a general solution of potential was given:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In this approach, the fracture is considered as zero thickness discontinuity line and complex numbers are used. Recently, Pouya and Ghabezloo [14] used a direct approach to obtain a general potential pressure solution function of flux in the fracture network for anisotropic matrix containing intersecting curvilinear fractures. By continuing this work, Pouya and Vu [13] employed the singular integral equation method to establish a fast numerical calculation that can be used to derive the general solution and to show the fluid flow around many intersecting fractures.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling effective permeability of fracture networks in permeable rock formations by singular integral equations method

Pouya

Seyedi

2011

Computational Methods in Multiphase Flow VI

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In this paper, theoretical and numerical formulations of plane steady-state fluid flow in a fractured porous rock are used to investigate its effective permeability. If the far field inflow is uniform, the theoretical solution shows that the pressure field in the matrix is a function of the discharge in the fracture network. A numerical resolution based on singular integral equations is employed to derive the general problem of many intersected fractures in order to obtain the pressure field in anisotropic matrix. This solution allows computing the flux in the fractures which is the key issue for upscalling the equivalent permeability. This paper presents in detail the method for deriving the equivalent permeability from this solution. This method is applied to two real cases: an Excavation Damage Zone (EDZ) around a deep underground gallery and a geological rock formation presenting several families of fractures. The results of the both cases show that the developed method provides an easy and efficient way to determine the equivalent permeability of the fractured porous rock medium. This equivalent permeability can be implemented in analytical and numerical tools for continuous media towards estimating the flow characteristics in the rock formation.

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Modeling of natural fracture initiation and propagation in basin sedimentation context

2017

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During sedimentation, buried rocks are subjected to an increase in vertical stress. This increase leads to a decrease of porosity that is commonly called mechanical compaction. Indeed, the mechanical compaction depending on its rate and on the permeability of the burden rocks can induce significant overpressures. Thus, a competition is initiated between the dissipation of fluid overpressure and sedimentation rate and may result in fracture initiation. The present study deals with the initiation and propagation of natural fracture in sealing formations. A particular emphasis is put on mode I fracture propagation. An analytical solution of the pressure and stresses in a sealing formation is proposed under sedimentation by superposing two problems of poroelasticity. This analytical solution and a damage criterion are used to predict the initiation and propagation of the fracture. The damage parameter affects both the mechanical and hydraulic openings of the fracture, and the flow in the fracture is described by Poseuille's law. The fracture propagation and growth are studied by numerical simulations based on a finite element code dedicated to fractured porous media called Porofis. Interactions between hydraulic and mechanical processes are also studied, and a sensitivity study is carried out in order to find the most important parameters involved in natural fracturing under sedimentation.

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Flow Around a Crack in a Porous Matrix and Related Problems

Cited by 25 publications

References 17 publications

A 3D Computational Study of Effective Medium Methods Applied to Fractured Media

A 3D Computational Study of Effective Medium Methods Applied to Fractured Media

Modelling effective permeability of fracture networks in permeable rock formations by singular integral equations method

Modeling of natural fracture initiation and propagation in basin sedimentation context

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