Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media

Sweeney, Matthew; Gable, Carl W.; Karra, Satish; Stauffer, Philip H.; Pawar, Rajesh J.; Hyman, Jeffrey D.

doi:10.1007/s10596-019-09921-9

Cited by 47 publications

(27 citation statements)

References 48 publications

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“…The high fidelity of the simulations allows for the detailed examination of the flow field within each fracture network, thereby providing a basis to develop quantitative measurements of the degree of flow channeling, which is a principal contribution of this work. We use a DFN model rather than a continuum representation because fractures are explicitly represented in a DFN, which allows us to link their attributes directly with flow and transport phenomena (Hadgu et al., 2017; Painter & Cvetkovic, 2005; Sweeney et al., 2020). The networks are semigeneric, meaning that they do not represent a particular field site, but their properties are motivated by field observations.…”

Section: Introductionmentioning

confidence: 99%

Flow Channeling in Fracture Networks: Characterizing the Effect of Density on Preferential Flow Path Formation

Hyman

2020

Water Resources Research

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Flow channelization is a commonly observed phenomenon in fractured subsurface media where the flow of fluids is restricted primarily to highly transmissive fracture networks surrounded by a low-permeability rock matrix. The multiscale structural heterogeneity of these networks results in multiscale flow channelization where preferential flow paths form at length scales ranging from the entire system down to the subfracture size. We present an analysis of how one of the largest scales in fractured media, the network density, influences the degree of flow channeling that occurs using an ensemble of semigeneric three-dimensional discrete fracture network (DFN) simulations. We construct 10 DFNs, whose fracture lengths follow a power law distribution, at four densities for a total of 40 networks. We characterize their structure in terms of the network topology and geometry. Eulerian and Lagrangian observations of the steady-state flow fields obtained within the networks are used to quantify the degree of flow channelization at the network scale. We introduce a measure for the importance-ranking/hierarchy of different flow paths in the network using graph-based analysis of Lagrangian transport by which the degree of flow channeling between networks is compared. These flow observations are then linked to the structural properties of the networks. In general, network-scale flow channeling decreases as the network density increases. However, at low densities, there is more uniform flow within the entire connected network than in high-density networks. We also demonstrate how standard transport observables can be used to infer the degree of flow channelization occurring within a fracture network.

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Section: Introductionmentioning

confidence: 99%

Flow Channeling in Fracture Networks: Characterizing the Effect of Density on Preferential Flow Path Formation

Hyman

2020

Water Resources Research

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“…Berre et al 2018, for a recent overview). The cost associated with DFN models is substantially higher than conventional continuum models, but the trade off is that DFN models can typically represent a wider range of transport phenomena with higher fidelity due to the inclusion of detailed features of the fracture network (Hadgu et al, 2017; Hyman et al, 2019a; Painter et al, 2002; Sweeney et al, 2019). The inclusion of these features introduces additional layers of uncertainty because more parameters have to be calibrated and/or sampled due to uncertainty in fracture location, size, orientation, and hydrological properties.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Predictions of First Passage Times in Three‐Dimensional Discrete Fracture Networks: A Graph‐Based Approach

Berrone

Hyman

Pieraccini

2020

Water Resources Research

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We present a method combining multilevel Monte Carlo (MLMC) and a graph‐based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph‐based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

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“…Recently, Rajeh et al [29] developed a modified semianalytical superposition method considering the hydraulic conductivity of the porous matrix and the fractures, as well as the connectivity of the conductive fracture network. Sweeney et al [30] presented a computational geometry-based upscaling approach to accurately capture the dynamic processes considering the fracture geometric properties and the matrix properties. We should note that flow can also occur between disconnected fractures if the rock mass has some porosity and permeability, which would mean some differences in calculations of equivalent permeability [31,32].…”

Section: Introductionmentioning

confidence: 99%

Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

Chen

2020

Geofluids

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Equivalent fracture models are widely used for simulations of groundwater exploitation, geothermal reservoir production, and solute transport in groundwater systems. Equivalent permeability has a great impact on such processes. In this study, equivalent permeability distributions are investigated based on a state-of-the-art numerical upscaling method (i.e., the multiple boundary method) for fractured porous rocks. An ensemble of discrete fracture models is created based on power law length distributions. The equivalent permeability is upscaled from discrete fracture models based on the multiple boundary method. The results show that the statistical distributions of equivalent permeability tensor components are highly related to fracture geometry and differ from each other. For the histograms of the equivalent permeability, the shapes of k x x and k y y change from a power law-like distribution to a lognormal-like distribution when the fracture length and the number of fractures increase. For the off-diagonal component k x y , it is a normal-like distribution and its range expands when the fracture length and the number of fractures increase. The mean of diagonal equivalent permeability tensor components increases linearly with the fracture density. The analysis helps in generating stochastic equivalent permeability models in fractured porous rocks and reduces uncertainties when applying equivalent fracture models.

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Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media

Cited by 47 publications

References 48 publications

Flow Channeling in Fracture Networks: Characterizing the Effect of Density on Preferential Flow Path Formation

Flow Channeling in Fracture Networks: Characterizing the Effect of Density on Preferential Flow Path Formation

Multilevel Monte Carlo Predictions of First Passage Times in Three‐Dimensional Discrete Fracture Networks: A Graph‐Based Approach

Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

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