Definition of percolation thresholds on self-affine surfaces

Marrink, Siewert J.; Paterson, Lincoln; Knackstedt, Mark

doi:10.1016/s0378-4371(99)00608-1

Cited by 10 publications

(5 citation statements)

References 24 publications

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“…Indeed if the invariance with L seems rather robust, we notice some variations with the multifractal spectrum. Such a complementary study relates to the models studied by [ Meakin , 1991; Sahimi and Mukhupadhyay , 1996; Marrink et al , 2000], who analyzed the percolation transition on regular lattices with long‐range correlations. It will be the subject of a separate work.…”

Section: Connectivity Properties Of 2‐d Fractal Network Made Up Of Smentioning

confidence: 99%

Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

Darcel

Bour

Davy

et al. 2003

Water Resources Research

176

156

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[1] We present a theoretical and numerical study of the connectivity of fracture networks with fractal correlations. In addition to length distribution, this spatial property observed on most fracture networks conveys long-range correlation that may be crucial on network connectivity. We especially focus on the model that comes out relevant to natural fracture network: a fractal density distribution for the fracture centers (dimension D) and a power law distribution for the fracture lengths (exponent a, n(l) $ l Àa ). Three different regimes of connectivity are identified depending on D and on a. For a < D + 1 the length distribution prevails against fractal correlation on network connectivity. In this case, global connectivity is mostly ruled by the largest fractures whose length is of the order of the system size, and thus the connectivity increases with scale. For a > D + 1 the connectivity is ruled by fractures much smaller than the system size with a strong control of spatial correlation; the connectivity now decreases with system scale. Finally, for the self-similar case (a = D + 1), which corresponds to the transition between the two previous regimes, connectivity properties are scale invariant: percolation threshold corresponds to a critical fractal density and the average number of intersections per fracture at threshold is a scale invariant as well.

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Section: Connectivity Properties Of 2‐d Fractal Network Made Up Of Smentioning

confidence: 99%

Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

Darcel

Bour

Davy

et al. 2003

Water Resources Research

176

156

View full text Add to dashboard Cite

show abstract

“…To produce the percolation clusters of the self-affine model we have used the percolation thresholds provided in Ref. [16]. In Fig.…”

Section: Resultsmentioning

confidence: 99%

“…It has been observed that percolation transitions on long-range self-affine structures behaves differently from ordinary percolation in some important aspects [15]. For example, Marrink et al [16] found that percolation thresholds p c of self-affine lattices are strongly dependent on the spanning rule employed even when the lattice is effectively infinite. Following the work of Reynolds et al [17] on un-correlated square lattices, they considered three different spanning rules for percolation on self-affine models, R 0 , the probability of spanning either horizontally or vertically or both, R 1 , the probability of spanning in a specified direction (e.g.…”

Section: Simulation Methodsmentioning

confidence: 99%

The anisotropy of two dimensional percolation clusters of self-affine models

Ebrahimi

2008

Preprint

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The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both persistent and anti-persistent long-range correlations in 2-D models. It is seen that self affinity makes the shape of percolation clusters slightly more isotropic. Moreover, we find that the sign of correction to scaling term is determined by the nature of correlation. For persistent correlation the correction to scaling term adds a negative contribution to the anisotropy of percolation clusters, while for the anti-persistent case it is positive.

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“…Tyukhova and Willmann showed that based on information on the resistance and geometry of the connected channel network, the static connectivity metrics can predict effective flow and transport of heterogeneous fields through comparison with flow simulations [25]. In previous studies, the percolation thresholds on self-affine surfaces were investigated [26], and the difference between the static and dynamic connectivity metrics for the characterization of heterogeneous porous reservoirs was clarified [27]. In detail, the static connectivity metrics are only related to the connectivity geometrical parameters, such as hydraulic conductivity or geological structures.…”

Section: Introductionmentioning

confidence: 99%

A Connectivity Metrics-Based Approach for the Prediction of Stress-Dependent Fracture Permeability

Deng,

Shang,

2024

Water

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Rapid and accurate assessment of fracture permeability is critical for subsurface resource and energy development as well as rock engineering stability. Fracture permeability deviates from the classical cubic law under the effect of roughness, geological stress, as well as mining-induced stress. Conventional laboratory tests and numerical simulations are commonly costly and time-consuming, whereas the use of a connectivity metric based on percolation theory can quickly predict fracture permeability, but with relatively low accuracy. For this reason, we selected two static connectivity metrics with the highest and lowest prediction accuracy in previous studies, respectively, and proposed to revise and use them for fracture permeability estimation, considering the effect of isolated large-aperture regions within the fractures under increasing normal stress. Several hundred fractures with different fractal dimensions and mismatch lengths were numerically generated and deformed, and their permeability was calculated by the local cubic law (LCL). Based on the dataset, the connectivity metrics were counted using the revised approach, and the results show that, regardless of the connectivity metrics, the new model greatly improves the accuracy of permeability prediction compared to the pre-improved model, by at least 8% for different cutoff aperture thresholds.

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Definition of percolation thresholds on self-affine surfaces

Cited by 10 publications

References 24 publications

Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

The anisotropy of two dimensional percolation clusters of self-affine models

A Connectivity Metrics-Based Approach for the Prediction of Stress-Dependent Fracture Permeability

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