Graph-based flow modeling approach adapted to multiscale discrete-fracture-network models

Doolaeghe, Diane; Davy, Philippe; Hyman, Jeffrey D.; Darcel, Caroline

doi:10.1103/physreve.102.053312

Cited by 18 publications

(16 citation statements)

References 40 publications

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“…Then we can define the interfacial length between the sub‐networks as

{\Gamma}=\sum\limits _{ij}{\Vert}{f}_{i}\cap {f}_{j}{\Vert}\qquad \text{such}\,\text{that}\qquad {f}_{i}\in {{\Omega}}^{\prime }\qquad \,\text{and}\,\qquad {f}_{j}\in {{\Omega}}^{\ast },

where ‖ f i ∩ f j ‖ is the length of the intersection between two fractures. We define the secondary network to be comprised of all dead‐end structures, that is, dead‐end fractures and cycles, and the primary sub‐network is its complement (Doolaeghe et al., 2020). This partitioning definition is based solely on the network structure, specifically the topology/connectivity, and does not utilize any hydraulic, geometric, or flow information.…”

Section: Resultsmentioning

confidence: 99%

“…where ‖f i ∩ f j ‖ is the length of the intersection between two fractures. We define the secondary network to be comprised of all dead-end structures, that is, dead-end fractures and cycles, and the primary sub-network is its complement (Doolaeghe et al, 2020). This partitioning definition is based solely on the network structure, specifically the topology/connectivity, and does not utilize any hydraulic, geometric, or flow information.…”

Section: Flow and Reactive Transport Observationsmentioning

confidence: 99%

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A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

Hyman

Navarre‐Sitchler

Andrews

et al. 2022

Geophysical Research Letters

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Hydrology within fractured rocks is complex, with variable Péclet conditions reflecting the relative importance of fluid advection and diffusion on the movement of solutes. In many of these systems, the fluids passing through the fractures will be out of equilibrium with the resident minerals, and, in turn, a variety of reactions, for example, dissolution and precipitation, take place (Deng & Spycher, 2019). These geochemical processes can lead to the evolution of the fracture network by changing fracture permeability (Ellis et al., 2013) and potentially driving or inhibiting fracture propagation (Shovkun & Espinoza, 2019). Because the majority of flow in fractured media passes through a small volume relative to the domain size and the reactions are therein localized, these changes can produce a

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“…Then we can define the interfacial length between the sub‐networks as

{\Gamma}=\sum\limits _{ij}{\Vert}{f}_{i}\cap {f}_{j}{\Vert}\qquad \text{such}\,\text{that}\qquad {f}_{i}\in {{\Omega}}^{\prime }\qquad \,\text{and}\,\qquad {f}_{j}\in {{\Omega}}^{\ast },

Section: Resultsmentioning

confidence: 99%

Section: Flow and Reactive Transport Observationsmentioning

confidence: 99%

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

Hyman

Navarre‐Sitchler

Andrews

et al. 2022

Geophysical Research Letters

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“…This dimension reduction drastically reduces the number of degrees of freedom in the solution matrix increasing the computational efficiency. There has been a recent re‐interest in these CN models, which are now commonly referred to as graph‐based emulators (see Section 5), as they allow for significantly more fractures to be included in networks compared to high‐fidelity DFN models, which in turn facilitates and allows for many more simulations to be performed at low cost to bound uncertainty (Berrone et al., 2020; Doolaeghe et al., 2020; Hyman et al., 2018; Karra et al., 2018; O’Malley et al., 2018; Osthus et al., 2020), a topic which is discussed further in the next section. The CN approach is attractive when there are a large number of fractures or when the fracture intersections or solution enhanced permeability are a dominant factor in determining where flow and transport occur within the network.…”

Section: Models Of T‐h‐m‐c Coupled Processes In Fractured Rockmentioning

confidence: 99%

From Fluid Flow to Coupled Processes in Fractured Rock: Recent Advances and New Frontiers

Viswanathan

Ajo‐Franklin

Birkhölzer

et al. 2022

Reviews of Geophysics

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113

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Quantitative predictions of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far‐reaching economic and environmental impacts. Fractures occupy a very small volume of a subsurface formation but often dominate fluid flow, solute transport and mechanical deformation behavior. They play a central role in CO2 sequestration, nuclear waste disposal, hydrogen storage, geothermal energy production, nuclear nonproliferation, and hydrocarbon extraction. These applications require predictions of fracture‐dependent quantities of interest such as CO2 leakage rate, hydrocarbon production, radionuclide plume migration, and seismicity; to be useful, these predictions must account for uncertainty inherent in subsurface systems. Here, we review recent advances in fractured rock research covering field‐ and laboratory‐scale experimentation, numerical simulations, and uncertainty quantification. We discuss how these have greatly improved the fundamental understanding of fractures and one's ability to predict flow and transport in fractured systems. Dedicated field sites provide quantitative measurements of fracture flow that can be used to identify dominant coupled processes and to validate models. Laboratory‐scale experiments fill critical knowledge gaps by providing direct observations and measurements of fracture geometry and flow under controlled conditions that cannot be obtained in the field. Physics‐based simulation of flow and transport provide a bridge in understanding between controlled simple laboratory experiments and the massively complex field‐scale fracture systems. Finally, we review the use of machine learning‐based emulators to rapidly investigate different fracture property scenarios and accelerate physics‐based models by orders of magnitude to enable uncertainty quantification and near real‐time analysis.

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“…Barthelemy (2018) refers to these types of representations as "primal" and "dual" forms, respectively. Others, such as Doolaeghe et al (2020), call the two representations "intersection graphs" and "fracture graphs".…”

Section: Introductionmentioning

confidence: 99%

Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics

et al. 2021

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Abstract. Rock fractures organize as networks, exhibiting natural variation in their spatial arrangements. Therefore, identifying, quantifying, and comparing variations in spatial arrangements within network geometries are of interest when explicit fracture representations or discrete fracture network models are chosen to capture the influence of fractures on bulk rock behaviour. Treating fracture networks as spatial graphs, we introduce a novel approach to quantify spatial variation. The method combines graph similarity measures with hierarchical clustering and is applied to investigate the spatial variation within large-scale 2-D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. We consider three large, fractured regions, comprising nearly 300 000 fractures spread over 14 200 m2 from the Lilstock pavements. Using a moving-window sampling approach, we first subsample the large networks into subgraphs. Four graph similarity measures – fingerprint distance, D-measure, Network Laplacian spectral descriptor (NetLSD), and portrait divergence – that encapsulate topological relationships and geometry of fracture networks are then used to compute pair-wise subgraph distances serving as input for the statistical hierarchical clustering technique. In the form of hierarchical dendrograms and derived spatial variation maps, the results indicate spatial autocorrelation with localized spatial clusters that gradually vary over distances of tens of metres with visually discernable and quantifiable boundaries. Fractures within the identified clusters exhibit differences in fracture orientations and topology. The comparison of graph similarity-derived clusters with fracture persistence measures indicates an intra-network spatial variation that is not immediately obvious from the ubiquitous fracture intensity and density maps. The proposed method provides a quantitative way to identify spatial variations in fracture networks, guiding stochastic and geostatistical approaches to fracture network modelling.

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Graph-based flow modeling approach adapted to multiscale discrete-fracture-network models

Cited by 18 publications

References 40 publications

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

From Fluid Flow to Coupled Processes in Fractured Rock: Recent Advances and New Frontiers

Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics

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