Comparison of laboratory-scale solute transport visualization experiments with numerical simulation using cross-bedded sandstone

Klise, Katherine A.; Tidwell, Vincent Carroll; McKenna, Sean Andrew

doi:10.1016/j.advwatres.2008.08.013

Cited by 27 publications

(77 citation statements)

References 31 publications

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“…This was used to analyze the data collected by Klise [15]. The details of the conditioning have only recently appeared [4], but allowed us to rigorously test the sufficiency of the classical, Fickian advection dispersion equation [16].…”

Section: ) Multi-scale Variabilitymentioning

confidence: 99%

“…But is the non-local model demonstrably necessary at all scales? We examined the experiment conducted by [15] in which a 30.5 × 30.5 cm slab of relatively homogeneous, cross-bedded sandstone was exhaustively sampled for K. The slab was sealed, saturated with potassium iodide, and x-rayed ten times while being flushed with fresh water. The 8,649 air-permeameter measurements were down-and up-scaled to make finer and coarser grids on which the velocity field was solved and the ADE applied.…”

Section: ) Multi-scale Variabilitymentioning

confidence: 99%

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Final Report

Benson¹

2012

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Objective: The objective of this project was to characterize the influence that naturally complex geologic media has on anomalous dispersion and to determine if the nature of dispersion can be estimated from the underlying heterogeneous media. Project Description:This project combines outcrop-scale heterogeneity characterization, laboratory experiments, and numerical simulations. The study is designed to test whether established dispersion theory accurately predicts the behavior of solute transport through heterogeneous media and to investigate the relationship between heterogeneity and the parameters that populate these models. The dispersion theory tested by this work is based upon the fractional advection-dispersion equation (fADE) model. Unlike most dispersion studies that develop a solute transport model by fitting the solute transport breakthrough curve, this project will explore the nature of the heterogeneous media to better understand the connection between the model parameters and the aquifer heterogeneity. RESULTS Background:Our work at the Colorado School of Mines was focused on the following questions: 1) What are the effects of multi-scale geologic variability on transport of conservative and reactive solutes? 2) Can those transport effects be accounted for by classical methods, and if not, can the nonlocal fractional-order equations provide better predictions? 3) Can the fractional-order equations be parameterized through a link to some simple observable geologic features? 4) Are the classical equations of transport and reaction sufficient? 5) What is the effect of anomalous transport on chemical reaction in groundwater systems?The work is predicated on the observation that upscaled transport is defined by loss of information, or spatio-temporal averaging. This averaging tends to make the transport laws such as Fick's 2nd-order diffusion equation similar to central limit theory (e.g., Einstein [9]). The fractional-order advection-dispersion equations rely on limit theory for heavytailed random motion that has some diverging moments. The equations predict larger tails of a plume in space and/or time than those predicted by the classical 2nd-order advectiondispersion equation. The heavy tails are often seen in plumes at field sites.

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Section: ) Multi-scale Variabilitymentioning

confidence: 99%

Section: ) Multi-scale Variabilitymentioning

confidence: 99%

Final Report

Benson¹

2012

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“…The X-ray images provide KI concentration data with submillimeter spatial resolution. Klise et al [2008] took the K data and constructed flow and transport models (with grid cells of 0.33 cm on each side) in 2-and 3-D, with and without diffusion and hydrodynamic dispersion. They found that the finely discretized ADE was insufficient to properly simulate transport in the slab, particularly the tails.…”

Section: Introductionmentioning

confidence: 99%

“…[6] A recent experiment by Klise et al [2008] provides an unprecedented data set, in terms of completeness and accuracy, that allows us to test the uniqueness and suitability of the ADE at the finest scale possible. They took a thin slab of Massillon sandstone and exhaustively sampled the permeability using air permeameters.…”

Section: Introductionmentioning

confidence: 99%

“…But is the nonlocal model demonstrably necessary at all scales? We examine the experiment conducted by Klise et al (2008) in which a 30.5 Â 30.5 cm slab of relatively homogeneous, cross-bedded sandstone was exhaustively sampled for K. The slab was sealed, saturated with potassium iodide, and X-rayed 10 times while being flushed with fresh water. The 8,649 air-permeameter measurements were down-and upscaled to make finer and coarser grids on which the velocity field was solved and the ADE applied.…”

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Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab

Major

Benson

Revielle

et al. 2011

Water Resources Research

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[1] It is not a compelling argument, solely on the basis of a better fit to solute breakthrough curve (BTC) data, that a temporally nonlocal model is necessary to simulate transport in an advection-dominated system. One may counter that the classical advection-dispersion equation (ADE) is a valid model at some small scale and that the detailed hydraulic conductivity (K) data must be well-represented : then the nonlocality is only a result of upscaling and loss of information. But is the nonlocal model demonstrably necessary at all scales? We examine the experiment conducted by Klise et al. (2008) in which a 30.5 Â 30.5 cm slab of relatively homogeneous, cross-bedded sandstone was exhaustively sampled for K. The slab was sealed, saturated with potassium iodide, and X-rayed 10 times while being flushed with fresh water. The 8,649 air-permeameter measurements were down-and upscaled to make finer and coarser grids on which the velocity field was solved and the ADE applied. The optimized parameters in the ADE were found to scale predictably, most notably the longitudinal dispersivity ( L ), which grew linearly with upscaling. But at all levels of up-and downscaling, including the original K measurement scale of 0.33 cm, the ADE did not adequately represent the late-time tails. The temporally nonlocal, timefractional ADE (t-FADE) was applied and the optimized parameters ( L and the immobile capacity ) did not depend on scale. The better fit provided by the t-FADE in the late BTC tails did not bring about a sacrificed fit elsewhere in the BTC. Furthermore, the optimized ADE and t-FADE solutions do not converge at the smallest scale, directly implying that the temporal nonlocality is a necessary model component. We conclude that the logical inference ''if the ADE is valid in heterogeneous material, then there is tailing in the BTC'' is not a proof that the reverse is true. We provide a clear counterexample. A corollary is that a mismatch between data and a discretized solution to the ADE does not imply that more data will improve fits or predictive ability.

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On a recent solute transport laboratory experiment involving sandstone and its modeling

Ginn

Nassar

Kamai

et al. 2013

Water Resources Research

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[1] We analyze and simulate laboratory data on flow and solute transport in a submeter scale sample of Massillon sandstone and we re-evaluate studies that have stated that these data indicate a failure of the advection-dispersion, and that nonlocal modeling approaches are necessary. Our examination reveals experimental issues including artificial edge effects in the data, as well as inconsistency in the measured solute injection rates. When the edge effects are removed the data no longer exhibit power-law tailing. Our simulations show that failure of the advection-dispersion equation has not been demonstrated and that nonlocal approaches are not necessary.Citation: Ginn, T. R., M. K. Nassar, T. Kamai, K. Klise, V. Tidwell, and S. McKenna (2013), On a recent solute transport laboratory experiment involving sandstone and its modeling, Water Resour. Res., 49,[7327][7328][7329][7330][7331][7332][7333][7334][7335][7336][7337][7338]

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Comparison of laboratory-scale solute transport visualization experiments with numerical simulation using cross-bedded sandstone

Cited by 27 publications

References 31 publications

Final Report

Final Report

Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab

On a recent solute transport laboratory experiment involving sandstone and its modeling

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