Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media

Desbarats, A. J.

doi:10.1007/bf00893749

Cited by 126 publications

(105 citation statements)

References 16 publications

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“…Interestingly, this is the same power as is appropriate for the effective conductivity of an infinite domain, as can be seen from equations (G. 11) and (G. 17). As Desbarats (1992) notes, this observation further supports the empirical result. For an anisotropic media with kh = 10LV and block dimensions of Lh/kh = Lv/~= 3, the optimal averaging exponents were found through numerical experimentation to be ph = 0.59 and p, = -0.33.…”

Section: Review Of Upscaling In the Stochastic Hydrology Literaturesupporting

confidence: 79%

“…O,RegionalGroundwaterFlow Modelfor C, K, L, and P ReactorAreas Desbarats (1992) conjectures that equivalent block conductivities can be formulated as a power-average, a reasonable hypothesis considering the successful use of p-norms in defining effective conductivity. Desbarats (1992) empirically determined the appropriate power through numerical experimentation. For cubic blocks and an isotropic conductivity field, the optimal averaging exponent was determined to be p = 1/3.…”

Section: Review Of Upscaling In the Stochastic Hydrology Literaturementioning

confidence: 99%

“…The discrepancy may be a reflection of equation (G.9) already overpredicting K in infinite anisotropic media for large variances, as previously stated. Desbarats (1992) recommends that numerical calibration experiments be used to define the power exponents for the specific combination of block geometry and correlation scales of interest. However as Desbarats …”

Section: Review Of Upscaling In the Stochastic Hydrology Literaturementioning

confidence: 99%

See 2 more Smart Citations

Regional groundwater flow model for C, K. L. and P reactor areas, Savannah River Site, Aiken, SC

Flach¹

2000

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Section: Review Of Upscaling In the Stochastic Hydrology Literaturesupporting

confidence: 79%

Section: Review Of Upscaling In the Stochastic Hydrology Literaturementioning

confidence: 99%

Section: Review Of Upscaling In the Stochastic Hydrology Literaturementioning

confidence: 99%

See 1 more Smart Citation

Regional groundwater flow model for C, K. L. and P reactor areas, Savannah River Site, Aiken, SC

Flach¹

2000

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“…They have achieved very good results, showing some advantages, limitations, and evolution of the K upscaling techniques in a variety of problems (Cardwell & Parsons, 1945;A. J. Desbarats, 1992;Alexandre J. Desbarats, 1987;Dewandel et al, 2012;Fleckenstein & Fogg, 2008;Gomez-Hernandez & Gorelick, 1989;J.…”

Section: Introductionmentioning

confidence: 99%

“…Power average was also used to determine KV for a range of block shapes for synthetic cases (A. J. Desbarats, 1992).…”

Section: Introductionmentioning

confidence: 99%

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

Godoy¹

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Numerical models are becoming fundamental tools to predict a range of complex problems faced by geotechnical and geo-environmental engineers. However, to render the model reliable for future predictions, the model input parameters must be determined with consideration of the scale effects. If there is a difference of scales between the observation and the model scales there are two possible ways to consider it: or models are constructed with elements of a size similar to that at which the data were measured, or some upscaling rules must be defined. In this context, this thesis focuses on upscaling of water flow and mass transport in a tropical soil by means of numerical, laboratory and field studies. This thesis is organized in four parts.First, the heterogeneity, correlation and cross-correlation between solute transport parameters (dispersivity, α, and partition coefficient, Kd) and soil properties are studied in detail. In this part, it is verified that the hydraulic conductivity (K) and solute transport parameters are highly heterogeneous, while soil properties are not. Spatial correlation of α, K, and statistically significant variables are studied, and it would probably improve the estimation only in a small-scale study, since the spatial correlation are only observed up to 2.5 m. This study is a first attempt to evaluate the spatial variation in the correlation coefficient of transport parameters of a reactive and a nonreactive solute, indicating the more relevant variables and the one that should be included in future studies.In the second part, scale effect on K, dispersivity and partition coefficient of potassium and chloride are studied experimentally by means of laboratory and field experiments. The purpose is to contribute to the discussion about scale effects on K, α and Kd and understanding how these parameters behave with the change in the scale of measurement. Results show that K values increases with scale, regardless of the method of measurement, except for the results obtained from double-ring infiltrometer tests. Dispersivity trends to increase exponentially with the sample height.Partition coefficient tends to increase with sample length, diameter and volume. These differences in the parameters according to the scale of measurement must be considered when these observations are later used as input to numerical models, otherwise the responses can be misrepresented.x Third, stochastic analysis of three-dimensional hydraulic conductivity upscaling is performed using a simple average and the Laplacian-with-skin methods for a variety of block sizes based on real K measurements. In this part it is demonstrated the errors that can be introduced by using a deterministic upscaling using simple averages of the measured K without accounting for the spatial correlation. Results show that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler.The aspects to consider when performing the upscaling are also discussed. Finally, the dependence of the exponent of the p-n...

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

Maillot

Davy

Goc

et al. 2016

Water Resources Research

150

122

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A major use of DFN models for industrial applications is to evaluate permeability and flow structure in hardrock aquifers from geological observations of fracture networks. The relationship between the statistical fracture density distributions and permeability has been extensively studied, but there has been little interest in the spatial structure of DFN models, which is generally assumed to be spatially random (i.e., Poisson). In this paper, we compare the predictions of Poisson DFNs to new DFN models where fractures result from a growth process defined by simplified kinematic rules for nucleation, growth, and fracture arrest. This so‐called “kinematic fracture model” is characterized by a large proportion of T intersections, and a smaller number of intersections per fracture. Several kinematic models were tested and compared with Poisson DFN models with the same density, length, and orientation distributions. Connectivity, permeability, and flow distribution were calculated for 3‐D networks with a self‐similar power law fracture length distribution. For the same statistical properties in orientation and density, the permeability is systematically and significantly smaller by a factor of 1.5–10 for kinematic than for Poisson models. In both cases, the permeability is well described by a linear relationship with the areal density p32, but the threshold of kinematic models is 50% larger than of Poisson models. Flow channeling is also enhanced in kinematic DFN models. This analysis demonstrates the importance of choosing an appropriate DFN organization for predicting flow properties from fracture network parameters.

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Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media

Cited by 126 publications

References 16 publications

Regional groundwater flow model for C, K. L. and P reactor areas, Savannah River Site, Aiken, SC

Regional groundwater flow model for C, K. L. and P reactor areas, Savannah River Site, Aiken, SC

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

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

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