Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models

Maillot, J.; Davy, Philippe; Goc, Romain Le; Darcel, Caroline; Dreuzy, J.-R. de

doi:10.1002/2016wr018973

Cited by 144 publications

(125 citation statements)

References 86 publications

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“… We did not discuss the application of percolation theory, CPA, and the EMA to characterization of fractures and fracture networks, and modeling of their flow and transport properties, as the problems need a review of their own. We do, however, point out that much progress has been made (see, for example, Darcel et al, ; de Dreuzy et al, ; Davy et al, , ; Ebigbo et al, ; Maillot et al, ; Pyrak‐Nolte & Nolte, ). Much of the progress has been reviewed by Meakin and Tartakovsky (), Adler and Thovert (), Sahimi (), Rutqvist and Tsang (), and Adler et al ().Meakin and Tartakovsky address complications to modeling flow and transport in porous media due to complex geometries, density contrasts of the fluids, and dynamic changes in contact angles.…”

Section: Possible Future Directions For Application Of Percolation Thmentioning

confidence: 82%

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Hunt

Sahimi

2017

Reviews of Geophysics

125

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We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

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Section: Possible Future Directions For Application Of Percolation Thmentioning

confidence: 82%

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Hunt

Sahimi

2017

Reviews of Geophysics

125

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“…In ,

S_{f}

is the nonisolated fracture surface area, and

V

is the total size of the domain. While

P_{32 *}

provides a compact value that can be compared across networks, it is also useful when compared to the amount of the domain that is actively flowing within a single network, which can be measured using the flow channeling density indicator

d_{Q}

(Maillot et al, ):

d_{Q} = \frac{1}{V} \cdot \frac{{(\underset{f}{false\sum} S_{f} \cdot Q_{f})}^{2}}{false(\sum_{f} S_{f} \cdot Q_{f}^{2} false)} .

…”

Section: Velocity Field and Particle Trajectory Observationsmentioning

confidence: 99%

Characterizing the Influence of Fracture Density on Network Scale Transport

et al. 2020

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The topology of natural fracture networks is inherently linked to the structure of the fluid velocity field and transport therein. Here we study the impact of network density on flow and transport behaviors. We stochastically generate fracture networks of varying density and simulate flow and transport with a discrete fracture network model, which fully resolves network topology at the fracture scale. We study conservative solute trajectories with Lagrangian particle tracking and find that as fracture density decreases, solute channelization to large local fractures increases, thereby reducing plume spreading. Furthermore, in sparse networks mean particle travel distance increases and local network features, such as velocity zones where flow is counter to the primary pressure gradient, become increasingly important for transport. As the network density increases, network statistics homogenize and such local features have a reduced impact. We quantify local topological influence on transport behavior with an effective tortuosity parameter, which measures the ratio of total advective distance to linear distance at the fracture scale; large tortuosity values are correlated to slow-velocity regions. These large tortuosity, slow-velocity regions delay downstream transport and enhance tailing on particle breakthrough curves. Finally, we predict transport with an upscaled, Bernoulli spatial Markov random walk model and parameterize local topological influences with a novel tortuosity parameter. Bernoulli model predictions improve when sampling from a tortuosity distribution, as opposed to a fixed value as has previously been done, suggesting that local network topological features must be carefully considered in upscaled modeling efforts of fracture network systems. and topology, and the corresponding flow field. The flow field within an individual fracture is typically highly correlated, commonly causing solute velocity to display persistent, low variability behavior over the in-fracture scale; consequently, the greatest Lagrangian accelerations occur at fracture intersections . As the fracture density increases, solute encounters more intersections on average, and the velocity correlation scale decreases. Furthermore, strong preferential flow paths form within interconnected networks of large fractures and channel a significant portion of mass, enabling solute to persist at high velocities for distances greater than the single fracture scale Sherman et al., 2019). This channelization becomes enhanced in sparse networks, where particles encounter fewer intersections, enabling them to persist on single fractures for longer distances. Resolving all these intranetwork features in 3-D DFN models is still computationally costly, and so upscaled modeling approaches, which account for network variability through effective parameter schemes, while maintaining a parsimonious framework, present an attractive alternative. However, how to properly parameterize network properties, such as velocity correlation and geometry, and inco...

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“…The effects of these multiple scales on the fluid velocity field within the fracture network are borne witness in the breakthrough curves (BTCs) of dissolved chemicals transported by the flow. For example, fluid flow channeling, where a majority of flow occurs in a subregion of the domain, is well documented in both field experiments (Abelin et al, , ; Rasmuson & Neretnieks, ) and in numerical simulations (de Dreuzy et al, ; Frampton & Cvetkovic, ; Hyman et al, ; Maillot et al, ). Transport in fractured media commonly exhibits non‐Gaussian (anomalous) behavior.…”

Section: Introductionmentioning

confidence: 97%

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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Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models

Cited by 144 publications

References 86 publications

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Characterizing the Influence of Fracture Density on Network Scale Transport

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

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