Topological impact of constrained fracture growth

Hope, Sigmund Mongstad; Davy, Philippe; Maillot, J.; Goc, Romain Le; Hansen, Alex

doi:10.3389/fphy.2015.00075

Cited by 25 publications

(34 citation statements)

References 40 publications

(65 reference statements)

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“…For every fracture that intersects the inflow boundary an edge is added between the vertex in the graph corresponding to that fracture and the vertex representing the inflow boundary; likewise for the outflow boundary. Similar graph theoretical approaches have been used for a variety of studies concerning DFN including topological characterization (Andresen et al, ; Huseby et al, ; Hope et al, ; Hyman & Jiménez‐Martínez, ) and backbone identification (Hyman et al, ; Valera et al, ). The utility of a graph theoretical approach is that topological properties of the networks can be queried and characterized in a formal mathematical framework.…”

Section: Flow and Transport Simulationsmentioning

confidence: 99%

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

et al. 2019

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We investigate large‐scale particle motion and solute breakthrough in sparse three‐dimensional discrete fracture networks characterized by power law distributed fracture lengths. The three networks we consider have the same fracture intensity values but exhibit different percolation densities, geometric properties, and topological structures. We considered two different average transport models to predict solute breakthrough, a streamtube model and a Bernoulli continuous time random walk model, both of which provide insights into the flow fields within the networks. The streamtube model provides acceptable predictions at short distances in two of the networks but fails in all cases to predict breakthrough times at the outlet plane, which indicates that particle motion in such fracture networks cannot be characterized by a constant velocity between the inlet and control plane at which the breakthrough curve is detected. Rather, the structure of the network requires that frequent velocity transitions be made as particles move through the system. Despite the relatively broad distribution of fracture radii and relatively small number of independent velocity transitions, the continuous time random walk approach conditioned on the initial velocity distribution provides reasonable predictions for the breakthrough curves at different distances from the inlet. The application of these averaged transport models provides a richer understanding of the link from the fracture network structure to flow and transport properties.

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Section: Flow and Transport Simulationsmentioning

confidence: 99%

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

et al. 2019

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“…Using this mapping, or one that is similar, topological properties of the fracture network are inherited by the graph as measurable properties such as vertex degree, efficiency, clustering, betweenness, and community structure (Andresen et al, ). Various studies have used this mapping to characterize and study different aspects of fracture network structure in two‐dimensional (Andresen et al, ; Ghaffari et al, ; Santiago et al, ) and three‐dimensional (Aldrich et al, ; Hope et al, ; Hyman et al, ; Valera et al, ) networks (both synthetic and natural). Ghaffari et al () linked the sensitivity of flow properties in two‐dimensional networks, for example, flow field profiles, to the network structures.…”

Section: Topological Inquiriesmentioning

confidence: 99%

“…Andresen et al () used this mapping for quantitative comparisons between real fracture networks and models generating synthetic networks. Hope et al () showed how topological properties of the network, such as clustering (one measure of local connectivity), are related to the growth mechanism by comparing different methods for stochastic network generation. Sævik and Nixon () included topological properties of two‐dimensional fracture networks into analytic expressions for permeability to account for network structure.…”

Section: Topological Inquiriesmentioning

confidence: 99%

“…There are multiple approaches for representing DFNs using graphs. However, many of these approaches seek to characterize the fracture network structure (Andresen et al, 2013;Ghaffari et al, 2011;Hope et al, 2015;Santiago et al, 2014) or simulate flow and transport on the graph itself (Cacas, 1990;Dershowitz & Fidelibus, 1999;Karra et al, 2018;Noetinger & Jarrige, 2012;Nordqvist et al, 1992).…”

Section: Introductionmentioning

confidence: 99%

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Advancing Graph‐Based Algorithms for Predicting Flow and Transport in Fractured Rock

Viswanathan

Hyman

Karra

et al. 2018

Water Resources Research

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Discrete fracture network (DFN) models are a powerful alternative to continuum models for subsurface flow and transport simulations because they explicitly include fracture geometry and network topology, thereby allowing for better characterization of the latter's influence on flow and transport through fractured media. Recent advances in high performance computing have opened the door for flow and transport simulations in large explicit three‐dimensional DFN, but this increase in model fidelity and system size comes at a huge computational cost because of the large number of mesh elements required to represent thousands of fractures (with sizes that can range several orders of magnitude, from millimeter to kilometer). In most subsurface applications, fracture characteristics are only known statistically and numerous realizations are needed to bound uncertainty in flow and transport in the system, thereby exacerbating the computational burden. Graphs provide a simple and elegant way to characterize, query, and interrogate fracture network connectivity. We propose a DFN model reduction framework where various graph representations are used in conjunction with high‐fidelity DFN simulations to increase computational efficiency while retaining accuracy of key quantities of interest. The appropriate choice of a graph representation, namely, which attributes of the DFN are to be represented as nodes and which ones as edges connecting those nodes, depends on the relevant scientific questions. We demonstrate that the proposed DFN model reduction framework provides an efficient means for DFN modeling through both system reduction of the DFN using graph‐based properties and combining DFN and graph‐based flow and transport simulations.

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“…These graph mappings allow for a characterization of the network topology of both two-and threedimensional fracture systems, and moreover enable quantitative comparisons between real fracture networks and models generating synthetic networks. Vevatne, et al [51] and Hope, et al [19] have used this graph construction for analyzing fracture growth and propagation, showing how topological properties of the network such as assortativity relate to the growth mechanism. Hyman, et al [23] used graph representations of three-dimensional fracture networks to isolate subnetworks where the fastest transport occurred by finding the shortest path between inflow and outflow boundaries.…”

Section: Introductionmentioning

confidence: 99%

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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Topological impact of constrained fracture growth

Cited by 25 publications

References 40 publications

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Advancing Graph‐Based Algorithms for Predicting Flow and Transport in Fractured Rock

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

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