A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks

Santiago, Elizabeth; Hernández, Juan González; Romero-Salcedo, Manuel

doi:10.1016/j.eswa.2013.08.011

Cited by 20 publications

(25 citation statements)

References 24 publications

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“…Then, a potential criticism to these works is the fact that rock networks are three-dimensional (Andersson and Dverstorp (1987); Long and Billaux (1987); Koike et al (2012)) and that inferring these 3D networks from 2D information is hard. However, as has been previously documented, the analysis of 2D rock fractures identifies important parameters that allow the characterization of real rock samples (Jafari and Babadagli (2012); Sarkar et al (2002); Santiago et al (2013Santiago et al ( , 2014Santiago et al ( , 2016). In addition, note that the generalized proximity graphs that are introduced in this work can be easily extended to the 3D case.…”

Section: Introductionmentioning

confidence: 99%

“…4. In total 29 rock samples are considered here, kindly provided by Santiago et al (2013Santiago et al ( , 2016Santiago et al ( , 2014. The number of nodes n and edges m in the 29 networks studied here are provided in Table ( 2.0 Table 2 Rock fracture networks studied in this work, their number of nodes n, and number of edges m.…”

Section: Rock Fracture Networkmentioning

confidence: 99%

“…In many of the analyses described in the literature the use of synthetic fracture networks facilitates the analysis due to the sometimes scarce availability of real-world data (Barton (1995); Nolte et al (1989); Damjanac and Cundall (2013); ;Neuman (1988); Seifollahi et al (2014); Garipov et al (2016)). In contrast, Santiago et al have published a series of papers (Santiago et al (2013(Santiago et al ( , 2014(Santiago et al ( , 2016) in which they used real fracture networks derived from original hand-sampled images of rocks extracted from a Gulf of Mexico oil reservoir. These works have used a graph-theoretic analysis of these real-world networks in order to extract information about the topological (static) characteristics of this group of rocks.…”

Section: Introductionmentioning

confidence: 99%

“…The diffusion through the real RFNs is compared to diffusion on the synthetic model, showing that this random model reproduces not only the most important structural properties of the real networks but also their diffusive properties. As in the series of papers by Santiago et al (2013Santiago et al ( , 2014Santiago et al ( , 2016, two-dimensional cuts of rocks that show a fracture network embedded into the rock sides are considered. Then, a potential criticism to these works is the fact that rock networks are three-dimensional (Andersson and Dverstorp (1987); Long and Billaux (1987); Koike et al (2012)) and that inferring these 3D networks from 2D information is hard.…”

Section: Introductionmentioning

confidence: 99%

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Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis

Estrada

Sheerin

2017

Applied Mathematics and Computation

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We propose a new model to account for the main structural characteristics of rock fracture networks (RFNs). The model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces. We study a series of 29 real-world RFNs and find the best fit with the random rectangular neighborhood graphs (RRNGs) proposed here. We show that this model captures most of the structural characteristics of the RFNs and allows a distinction between small and more spherical rocks and large and more elongated ones. We use a diffusion equation on the graphs in order to model diffusive processes taking place through the channels of the RFNs. We find a small set of structural parameters that highly correlates with the average diffusion time in the RFNs. We found analytically some bounds for the diameter and the algebraic connectivity of these graphs that allow to bound the diffusion time in these networks. We also show that the RRNGs can be used as a suitable model to replace the RFNs in the study of diffusion-like processes. Indeed, the diffusion time in RFNs can be predicted by using structural and dynamical parameters of the RRNGs. Finally, we also explore some potential extensions of our model to include variable fracture apertures, the possibility of long-range hops of the diffusive particles as a way to account for heterogeneities in the medium and possible superdiffusive processes, and the extension of the model to 3-dimensional space.

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Section: Introductionmentioning

confidence: 99%

Section: Rock Fracture Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis

Estrada

Sheerin

2017

Applied Mathematics and Computation

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“…The number of branches for a particular brine channel has potentially significant implications for fluid flow and permeability, such as influencing the rate at which chemical species may pass through the sea ice (Santiago et al, 2014;Yang et al, 1995;Newman, 2011). By increasing the number of branches, split points increase the number of potential paths through 5 the sample.…”

Section: Throat Sizes Of Channels and Branchesmentioning

confidence: 99%

A Network Model for Characterizing Brine Channels in Sea Ice

Lieb-Lappen¹,

Kumar²,

Pauls³

et al. 2017

Preprint

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Abstract. The brine network in sea ice is a complex labyrinth whose precise microstructure is critical in governing the movement of brine and gas between the ocean and the sea ice surface. Recent advances in three-dimensional imaging using x-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in-situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can 5 characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.

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Machine learning for graph-based representations of three-dimensional discrete fracture networks

Valera

Guo²,

Kelly

et al. 2018

Comput Geosci

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Structural and topological information play a key role in modeling flow and transport through fractured rock in the sub-surface. Discrete fracture Restricting the flowing fracture network to this backbone provides a significant reduction in the network's effective size. However, the particle tracking simulations needed to determine the reduction are computationally intensive. Such methods may be impractical for large systems or for robust uncertainty quantification of fracture networks, where thousands of forward simulations are needed to bound system behavior.In this paper, we develop an alternative network reduction approach to characterizing transport in DFNs, by combining graph theoretical and machine learning methods. We consider a graph representation where nodes signify fractures and edges denote their intersections. Using random forest and support vector machines, we rapidly identify a subnetwork that captures the flow patterns of the full DFN, based primarily on node centrality features in the graph. Our supervised learning techniques train on particle-tracking backbone paths found by dfnWorks, but run in negligible time compared to those simulations. We find that our predictions can reduce the network to approximately 20% of its original size, while still generating breakthrough curves consistent with those of the original network.

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A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks

Cited by 20 publications

References 24 publications

Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis

Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis

A Network Model for Characterizing Brine Channels in Sea Ice

Machine learning for graph-based representations of three-dimensional discrete fracture networks

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