The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles

Cushman, John H.

doi:10.1007/978-94-015-8849-2

Cited by 209 publications

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“…In this study we will focus on the influence of the spatial variability of a on the transport process, and a stochastic perturbation method will be applied to conduct the study. In the last 2 decades, stochastic theory has been extensively applied to study flow and solute transport in heterogeneous porous media [Dagan, 1989;Gelhar, 1993;Cushman, 1997]. The theory is mainly used to study chemical dispersion processes caused by the spatial velocity variation, which is, in turn, caused by the heterogeneity of hydraulic conductivity [e.g., Dagan, 1982Dagan, , 1984 ].…”

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confidence: 99%

Nonlocal nonreactive transport in heterogeneous porous media with interregional mass diffusion

Huang¹,

Hu²

2000

Water Resources Research

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Abstract. We present a Eulerian stochastic analysis for nonreactive transport in a heterogeneous, structured medium. A first-order mass diffusion model (or mobile and immobile model) is applied to describe interregional mass diffusion between advection and nonadvection (mobile and immobile) regions. Spatial variabilities in the media motivate us to treat the interregional mass diffusion coefficient a and hydraulic conductivity K as spatial random variables. The two random variables are assumed to correlate with each other. The analytical solution for mean concentration is given explicitly in Fourier and Laplace transforms and is numerically inverted to real space via fast Fourier transform. Various factors that affect mass diffusion and transport processes are investigated by plotting spatial moments up to third and mean concentration contours. It is shown from the calculation results that interregional mass diffusion will significantly increase plume dispersion in both longitudinal and transverse directions and make the plume negatively skewed and give the breakthrough curve a long tail. In comparison with the case with a deterministic a, randomness of the parameter will increase the plume dispersion and make the plume more skewed, especially for the case where a is negatively correlated with K.

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confidence: 99%

Nonlocal nonreactive transport in heterogeneous porous media with interregional mass diffusion

Huang¹,

Hu²

2000

Water Resources Research

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“…Such a model may be most appropriate in regions with homogeneous structure. With added complexity Cushman [1990Cushman [ , 1997 considers a discrete hierarchy where multiple RES occur at various scales ( Figure 1b). Cushman's model may be appropriate in regions with largescale structural transition (e.g., when crossing dissimilar fracture populations).…”

Section: Representative Elementary Scalementioning

confidence: 99%

“…Cushman's model may be appropriate in regions with largescale structural transition (e.g., when crossing dissimilar fracture populations). Cushman [1990Cushman [ , 1997 and Wheatcraft and Cushman [1991] also consider the case of a continuous hierarchy where RES cannot be identified. Their model predicts smoothly varying, monotonic parameter behavior.…”

Section: Representative Elementary Scalementioning

confidence: 99%

Evaluating uncertainty in predicting spatially variable representative elementary scales in fractured aquifers, with application to Turkey Creek Basin, Colorado

Wellman

Poeter

2006

Water Resources Research

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[1] Computational limitations and sparse field data often mandate use of continuum representation for modeling hydrologic processes in large-scale fractured aquifers. Selecting appropriate element size is of primary importance because continuum approximation is not valid for all scales. The traditional approach is to select elements by identifying a single representative elementary scale (RES) for the region of interest. Recent advances indicate RES may be spatially variable, prompting unanswered questions regarding the ability of sparse data to spatially resolve continuum equivalents in fractured aquifers. We address this uncertainty of estimating RES using two techniques. In one technique we employ data-conditioned realizations generated by sequential Gaussian simulation. For the other we develop a new approach using conditioned random walks and nonparametric bootstrapping (CRWN). We evaluate the effectiveness of each method under three fracture densities, three data sets, and two groups of RES analysis parameters. In sum, 18 separate RES analyses are evaluated, which indicate RES magnitudes may be reasonably bounded using uncertainty analysis, even for limited data sets and complex fracture structure. In addition, we conduct a field study to estimate RES magnitudes and resulting uncertainty for Turkey Creek Basin, a crystalline fractured rock aquifer located 30 km southwest of Denver, Colorado. Analyses indicate RES does not correlate to rock type or local relief in several instances but is generally lower within incised creek valleys and higher along mountain fronts. Results of this study suggest that (1) CRWN is an effective and computationally efficient method to estimate uncertainty, (2) RES predictions are well constrained using uncertainty analysis, and (3) for aquifers such as Turkey Creek Basin, spatial variability of RES is significant and complex.Citation: Wellman, T. P., and E. P. Poeter (2006), Evaluating uncertainty in predicting spatially variable representative elementary scales in fractured aquifers, with application to Turkey Creek Basin, Colorado, Water Resour. Res., 42, W08410,

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“…(Mathematical representations of deterministic parameters, e.g., hydraulic conductivity, as random fields explain a seeming contradiction of using stochastic tools to deal with epistemic uncertainty.) Despite significant theoretical advancements, including an explanation of anomalous behavior of contaminant transport in heterogeneous subsurface environments [e.g., Cushman, 1997], stochastic hydrogeology remains a largely academic pursuit.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic risk analysis in subsurface hydrology

Tartakovsky

2007

Geophysical Research Letters

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[1] We present a general framework for probabilistic risk assessment (PRA) of subsurface contamination. PRA provides a natural venue for the rigorous quantification of structural (model) and parametric uncertainties inherent in predictions of subsurface flow and transport. A typical PRA starts by identifying relevant components of a subsurface system (e.g., a buried solid-waste tank, an aquitard, a remediation effort) and proceeds by using uncertainty quantification techniques to estimate the probabilities of their failure. These probabilities are then combined by means of fault-tree analyses to yield probabilistic estimates of the risk of system failure (e.g., aquifer contamination). Since PRA relies on subjective probabilities, it is ideally suited for assimilation of expert judgment and causal relationships.

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The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles

Cited by 209 publications

References 0 publications

Nonlocal nonreactive transport in heterogeneous porous media with interregional mass diffusion

Nonlocal nonreactive transport in heterogeneous porous media with interregional mass diffusion

Evaluating uncertainty in predicting spatially variable representative elementary scales in fractured aquifers, with application to Turkey Creek Basin, Colorado

Probabilistic risk analysis in subsurface hydrology

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