Topological analysis of 3D fracture networks: Graph representation and percolation threshold

Cañamón, Israel; Rajeh, Tawfik; Ababou, Rachid; Marcoux, Manuel

doi:10.1016/j.compgeo.2021.104556

Cited by 15 publications

(5 citation statements)

References 19 publications

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“…211-217)., which is also presented in Zijl and Nawalany [69] (Section 3.5 "Directly calculated velocity components", pp. [55][56][57][58][59][60][61][62][63].…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…The case of 3D planar fractures is more complex. The percolating subset and other properties of a 3D network of planar disc fractures were analyzed recently by Cañamón et al [63]. In these works, the rock matrix was assumed impervious, and the emphasis was on the topological graph properties of the fracture networks.…”

Section: Introductionmentioning

confidence: 99%

“…The case of networks of planar fractures in 3D space is another matter, which involves a richer class of "links" and "intersections" compared to 2D networks. We refer the reader to Noetinger and Jarrige [109] for semi-analytical/numerical approaches to 3D fracture network flow, to Rajeh et al [64] for a semi-empirical approach to the equivalent permeability tensor of 3D fractured porous media with permeable porous matrix, and to Cañamón et al [63], and references therein, for a generalized graph-based approach to percolation phenomena in 3D networks of planar fractures.…”

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confidence: 99%

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Equivalent Permeability Tensor of Heterogeneous Media: Upscaling Methods and Criteria (Review and Analyses)

Renard

Ababou

2022

Geosciences

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When conducting numerical upscaling, either for a fractured or a porous medium, it is important to account for anisotropy because in general, the resulting upscaled conductivity is anisotropic. Measurements made at different scales also demonstrate the existence of anisotropy of hydraulic conductivity. At the “microscopic” scale, the anisotropy results from the preferential flatness of grains, presence of shale, or variation of grain size in successive laminations. At a larger scale, the anisotropy results from preferential orientation of highly conductive geological features (channels, fracture families) or alternations of high and low conductive features (stratification, bedding, crossbedding). Previous surveys of homogenization techniques demonstrate that a wide variety of approaches exists to define and calculate the equivalent conductivity tensor. Consequently, the resulting equivalent conductivities obtained by these different methods are not necessarily equal, and they do not have the same mathematical properties (some are symmetric, others are not, for example). We present an overview of different techniques allowing a quantitative evaluation of the anisotropic equivalent conductivity for heterogeneous porous media, via numerical simulations and, in some cases, analytical approaches. New approaches to equivalent permeability are proposed for heterogeneous media, as well as discontinuous (composite) media, and also some extensions to 2D fractured networks. One of the main focuses of the paper is to explore the relations between these various definitions and the resulting properties of the anisotropic equivalent conductivity, such as tensorial or non-tensorial behavior of the anisotropic conductivity; symmetry and positiveness of the conductivity tensor (or not); dual conductivity/resistivity tensors; continuity and robustness of equivalent conductivity with respect to domain geometry and boundary conditions. In this paper, we emphasize some of the implications of the different approaches for the resulting equivalent permeabilities.

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“…211-217)., which is also presented in Zijl and Nawalany [69] (Section 3.5 "Directly calculated velocity components", pp. [55][56][57][58][59][60][61][62][63].…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Equivalent Permeability Tensor of Heterogeneous Media: Upscaling Methods and Criteria (Review and Analyses)

Renard

Ababou

2022

Geosciences

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“…However, the disc model is equal‐dimensional in all directions and cannot represent the anisotropic behavior of joints. Therefore, scholars have proposed the elliptical model based on the disc model that can reflect the anisotropic characteristics of joints 14–17 . Compared with the disc model, the elliptical model uses two parameters to reflect the trace length of joints in different directions and can achieve higher accuracy 6 .…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, scholars have proposed the elliptical model based on the disc model that can reflect the anisotropic characteristics of joints. [14][15][16][17] Compared with the disc model, the elliptical model uses two parameters to reflect the trace length of joints in different directions and can achieve higher accuracy. 6 However, the actual joint shape in nature is diverse, and the modeling results will be significantly different from the different joint models.…”

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A precise modeling method of three‐dimensional discrete fracture network based on rectangular joint model

Kang,

Fu,

Sheng

et al. 2024

Num Anal Meth Geomechanics

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As the weak structure and main seepage channel of rock mass, the discrete fracture network (DFN) has a significant influence on the physical and mechanical properties of rock mass. In this paper, based on the rectangular joint model, two algorithms are proposed to realize the precise modeling of the DFN in any polyhedron. First, the equivalence of DFN modeling with the rectangular joint model and the elliptical joint model is theoretically deduced. On this basis, the chain splicing algorithm suitable for the rectangular joint model is proposed, which can generate the DFN model according to the actual distribution of joint spacing, trace, and bridge length. Aiming at the concave boundary in the model domain, the segmentation‐stitching operation is put forward, and the continuity of the joint when passing through the interface is ensured. Finally, the effectiveness of the above algorithm is verified by several simple cases, and the relationship between the size of the geometrical representative elementary volume (REV) and discontinuity parameters is discussed. The results show that when the mean values of the joint distribution parameters are the same, even if the distribution rules are different, the number of joints generated in the same spatial region is approximately equal. The size of the geometrical REV is independent of the spacing and bridge length and is approximately three to five times the mean of the trace. The relevant algorithms and conclusions in this paper can be used as the basis for subsequent rock mass stability analysis and seepage calculation.

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Stochastic Geomodeling of Karst Morphology by Dynamic Graph Dissolution

Kanfar,

Mukerji

2023

Math Geosci

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Topological analysis of 3D fracture networks: Graph representation and percolation threshold

Cited by 15 publications

References 19 publications

Equivalent Permeability Tensor of Heterogeneous Media: Upscaling Methods and Criteria (Review and Analyses)

Equivalent Permeability Tensor of Heterogeneous Media: Upscaling Methods and Criteria (Review and Analyses)

A precise modeling method of three‐dimensional discrete fracture network based on rectangular joint model

Stochastic Geomodeling of Karst Morphology by Dynamic Graph Dissolution

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