Scaling of flow and transport behavior in heterogeneous groundwater systems

Scheibe, Timothy D.; Yabusaki, Steven B.

doi:10.1016/s0309-1708(98)00014-1

Cited by 83 publications

(57 citation statements)

References 34 publications

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“…Effective K are usually estimated for a finite volume in a heterogeneous medium, not for a portion of this volume such as a hydrofacies. The effective K of a volume (V) in a heterogeneous medium is defined as the constant that relates the mean head gradient in this volume to the mean discharge (Scheibe and Yabusaki, 1998). In other words, it is the unique K that replaces a variety of K and allows the same quantity of water to transit through the volume, under identical macroscopic gradient conditions.…”

Section: 2mentioning

confidence: 99%

Remediation Technologies at the INEEL

Link¹,

Mink²

2000

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Section: 2mentioning

confidence: 99%

Remediation Technologies at the INEEL

Link¹,

Mink²

2000

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“…For example, Scheibe and Yabusaki (1998) used an empirical power law-scale averaging technique with calibrating parameter m as,…”

Section: Introductionmentioning

confidence: 99%

“…Hunt and Idriss (2009) used a power law interpolating scheme similar to that of Scheibe and Yabusaki (1998) for estimating the effective permeability of a medium with a bimodal permeability distributions with two distributions and propose,…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts

Masihi

Gago²,

King³

2016

Transp Porous Med

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In this paper we present new methods to estimate the effective permeability (k eff ) of heterogeneous porous media with a wide distribution of permeabilities and various underlying structures, using percolation concepts. We first set a threshold permeability (k th ) on the permeability density function and use standard algorithms from percolation theory to check whether the high permeable grid blocks (i.e., those with permeability higher than k th ) with occupied fraction of "p" first forms a cluster connecting two opposite sides of the system in the direction of the flow (high permeability flow pathway). Then we estimate the effective permeability of the heterogeneous porous media in different ways: a power law (k eff = k th p m ), a weighted power average (with k g the geometric average of the permeability distribution) and a characteristic shape factor multiplied by the permeability threshold value. We found that the characteristic parameters (i.e., the exponent "m") can be inferred either from the statistics and properties of percolation subnetworks at the threshold point (i.e., high and low permeable regions corresponding to those permeabilities above and below the threshold permeability value) or by comparing the system properties with an uncorrelated random field having the same permeability distribution. These physically based approaches do not need fitting to the experimental data of effective permeability measurements to estimate the model parameter (i.e., exponent m) as is usually necessary in empirical methods. We examine the order of accuracy of these methods on different layers of 10th SPE model and found very good estimates as compared to the values determined from the commercial flow simulators.

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“…In earlier studies of transport at the coarse scale, only upscaling of the flow controlling parameters was performed (e.g., Scheibe and Yabusaki, 1998;Cassiraga et al, 2005;Li et al, 2010a). That is, upscaled K c values were derived, and the same advection dispersion equation was used both at the fine and coarse scales.…”

Section: Coarse Scale Equationsmentioning

confidence: 99%

“…Numerical methods, on the contrary, are more general, since they are not restricted by the geometry of the domain, the type of boundary conditions, or the degree of heterogeneity. Scheibe and Yabusaki (1998) examined the impact of hydraulic conductivity upscaling using the power-averaging method with different exponents . They found that although flows and heads can be preserved after upscaling the hydraulic conductivities, the discrepancy on transport predictions is substantial.…”

Section: Introductionmentioning

confidence: 99%

Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers

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The need to reduce the computational cost of stochastic groundwater flow and mass transport predictions calls for efficient upscaling techniques which can transfer the heterogeneity across scales while preserving similar flow and transport behaviors. In addition, due to the scarcity of measurement data, inverse modeling is commonly used to calibrate the parameters by conditioning on direct and indirect data and hence reduce the uncertainty of flow and transport predictions. In this work, an upscaling technique is developed and applied both in a synthetic example and a real case; then upscaling and the Ensemble Kalman Filter (EnKF, a method for inverse modeling) are coupled to handle a high-resolution inverse model; and finally, the EnKF and its variant, the normal-score EnKF, is applied in the context of multiGaussian and nonmultiGaussian media. The work included in this PhD can be grouped in three blocks.First, simple averaging, simple-Laplacian, Laplacian-with-skin, and nonuniform coarsening upscaling techniques are reviewed and assessed in a threedimensional hydraulic conductivity upscaling exercise. The reference is a fine scale conditional realization of the hydraulic conductivities at the MAcroDispersion Experiment site on Columbus Air Force Base in Mississippi (USA). This realization was generated using a hole-effect variogram model and it was shown that flow and transport modeling in this realization (at the fine scale) can reproduce the observed non-Fickian spreading of the tritium plume. The purpose of this work is twofold, first to compare the effectiveness of different upscaling techniques in yielding upscaled models able to reproduce the observed transport behavior, and second to demonstrate and analyze the conditions under which flow upscaling can provide a coarse model in which the standard advection-dispersion equation can be used to model transport in seemingly non-Fickian scenarios. Specifically, the use of the Laplacian-based upscaling technique coupled with a non-uniform coarsening scheme yields the best results both in terms of flow and transport reproduction, for this case study in which the coarse blocks are smaller than the correlation ranges of the fine scale conductivities. However, in some cases, we also observe the impossibility of reproducing transport at the coarse scale solely on the basis of a flow upscaling. For this reason, a methodology for transport upscaling is developed v vi for three-dimensional highly heterogeneous formations. The overall approach requires a prior hydraulic conductivity upscaling using an interblock-centered full-tensor Laplacian-with-skin method followed by transport upscaling. The coarse scale transport equation includes a multi-rate mass transfer term to compensate for the loss of heterogeneity inherent to all upscaling processes. The upscaling procedures for flow and transport are described in detail and then applied to a three-dimensional highly heterogeneous synthetic example. The proposed approach not only reproduces flow and transport at th...

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Scaling of flow and transport behavior in heterogeneous groundwater systems

Cited by 83 publications

References 34 publications

Remediation Technologies at the INEEL

Remediation Technologies at the INEEL

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts

Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers

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