Continuum Modeling of Coupled Thermo-Hydro-Mechanical Processes in Fractured Rock

Ababou, Rachid; Millard, Alain; Treille, E.; Durin, M.; Plas, F.

doi:10.1007/978-94-010-9204-3_79

Cited by 10 publications

(7 citation statements)

References 3 publications

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“…This basic approach was later reproduced or extended by several authors (Oda 1986;others). Thus, a general expression of the conductivity tensor K ij for a two-dimensional medium traversed by infinite size fractures was developed, and the final result K ij was shown to depend only on the specific area and volume fraction of each individual fracture (Ababou et al 1994). Defining an ensemble of M subsets of planar fractures, each with hydraulic apertures, sizes, and geometric parameters (orientation angles of the normal to the fracture plane), they obtained the equivalent conductivity tensor of an arbitrary set of infinite-length fractures where each subset (labeled "m") is composed of N m parallel fractures.…”

Section: General Description Of the Methodsmentioning

confidence: 99%

“…The power average is of the form: K ii,EFF E(K Pi ) 1/Pi . Thus, Ababou (1990), Ababou et al (1994) proposed a power average expression for the principal components of the effective conductivity tensor K ij,EFF in an N-dimensional medium, where the N exponents (powers Pi) were expressed in terms of N correlation scales (λi). Other authors investigated various semi-empirical formulae for power average upscaling (Journel et al 1986;Deutsch 1989;Le Loc'h 1988;Dimitrakopoulos and Desbarats 1997;Desbarats 1992).…”

Section: Introductionmentioning

confidence: 99%

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Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

et al. 2019

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A fast upscaling procedure for determining the equivalent hydraulic conductivity of a three-dimensional fractured rock is presented in this paper. A modified semi-analytical superposition method is developed to take into account, at the same time, the hydraulic conductivity of the porous matrix (K M ) and the fractures (K F ). The connectivity of the conductive fracture network is also taken into account. The upscaling approach has been validated by comparison with the hydraulic conductivity of synthetic samples calculated with full numerical procedures (flow simulations and averaging). The extended superposition approach is in good agreement with numerical results for infinite size fractures. For finite size fractures, an improved model that takes into account the connectivity of the fracture network through multiplicative connectiv-ity indexes determined empirically is proposed. This improved model is also in good agreement with the numerical results obtained for different configurations of fracture networks.

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Section: General Description Of the Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

et al. 2019

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“…Superposition methods have been used in the literature for obtaining macro-scale coefficients such as permeability, mechanical stiffnesses, and hydro-mechanical coefficients in fractured media under various restrictive hypotheses. Previous works [6][7][8][9] used a flux and strain superposition approach to develop upscaled hydraulic and HM properties of fractured rock assuming that the deformable matrix is impervious to flow and does not contribute to hydro-mechanical pressure/ stress coupling. Saevik et al 10 studies hydraulic upscaling for fractured media also with impervious matrix, where they consider either superposition methods (also called "effective medium approximation"), or various extensions of the Self Consistent approach.…”

Section: Structure Of Fractured Claystone Around the Gmr Gallerymentioning

confidence: 99%

Upscaling 3D coupled hydro mechanical properties of fractured porous rocks

Cañamón

Ababou

Poutrel

et al. 2019

International Journal of Rock Mechanics and Mining Sciences

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Coupled hydro-mechanics Stiffness Biot coefficient and modulus Upscaled equivalent continuum A methodology for upscaling 3D coupled Hydro-Mechanical (HM) properties of fractured porous rocks is developed theoretically, tested on synthetic fractured rock samples, and applied to a real site. The upscaled HM equations take into account the HM coupling in the dual matrix/fracture medium, comprising the cracks system as well as the intact porous matrix, yielding the equivalent stiffness tensor and two different sets of equivalent tensorial Biot coefficients B ij (I) and B ij (II) and moduli M (I) and M (II) for the upscaled system (I and II become identical only under certain hypotheses). We provide detailed theoretical expressions in the general tensorial case,and in the particular case of statistically homogeneous and isotropic cracks. The real site application is performed in a damaged and fractured claystone around the GMR gallery (Meuse/Haute-Marne Underground Research Laboratory). The geometric structure of the fracture set around the "Excavation Damage Zone" of the GMR gallery is described by a hybrid model comprising: (i) a set of 10 000 fissures with radially inhomogeneous statistics (size, thickness and density increasing towards the wall) and; (ii) a deterministic set of large curved fractures, periodically spaced along the axis of the gallery according to a 3D chevron pattern. Both "3D" and "2D transverse" distributions of the upscaled coefficients are calculated, and displayed using spheres or ellipsoids. Global tensorial coefficients are also obtained by upscaling the entire annular fractured zone. Equivalent isotropic coefficients are extracted from these tensors: Young modulus E, bulk modulus K, Lamé shear modulus μ, Poisson ratio ν, and HM coupling coefficients: the Biot coefficient B and the Biot modulus M. In all cases considered, we discuss the impact of the degree of fissuring and fracturing on the upscaled stiffness and hydromechanical coefficients.

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“…In particular, fracture network tools relate field observations (at core scale, seismic exploration scale, etc.) to basic parameters like fracture apertures, lengths, orientations, density, and connectivity (or coordination number), and these parameters have been used subsequently to derive 'effective properties', such as fracture permeability, associated to a continuum description of the fracture network [1][2][3]. The description of matrix flow and its connection to fracture network flow has also led to an important literature [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Matrix-fracture exchange in a fractured porous medium: stochastic upscaling

Kfoury

Ababou

Nœtinger

et al. 2004

Comptes Rendus. Mécanique

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We present in this Note a stochastic approach to the matrix-fracture exchange in a heterogeneous fractured porous medium. We introduce an intermediate scale, called the unit-scale, between the local-scale (fracture-scale) and the large-scale characteristic of the reservoir mesh (reservoir block). This paper focuses on the problem of upscaling fluid exchange phenomena from the unit scale to the reservoir mesh or block scale. Simplifying the Darcian flow terms enables us to obtain a probabilistic solution of the dual continuum problem, in continuous time, in the case of a purely random exchange coefficient. This is then used to develop several upscaling approaches to the fluid exchange problem, and to analyze the so-called 'effective' exchange coefficient. The results are a first contribution to the more general problem of upscaling multidimensional flow-exchange processes in space and time, in randomly heterogeneous dual continua. To cite this article: M.

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Continuum Modeling of Coupled Thermo-Hydro-Mechanical Processes in Fractured Rock

Cited by 10 publications

References 3 publications

Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

Upscaling 3D coupled hydro mechanical properties of fractured porous rocks

Matrix-fracture exchange in a fractured porous medium: stochastic upscaling

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