Observations of 3-D transverse dispersion and dilution in natural consolidated rock by X-ray tomography

Boon, Maartje; Bijeljic, Branko; Niu, Ben; Krevor, Samuel

doi:10.1016/j.advwatres.2016.07.020

Cited by 19 publications

(26 citation statements)

References 46 publications

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“…The power‐law regime is defined by

\frac{D_{t}}{D_{m}} = β {Pe}^{δ} 5 < Pe < 300,

in which β and δ are fitting parameters obtained from experimental or model results. Sublinear behavior where

δ < 1

in the power‐law regime is observed both experimentally [ Carvalho de and Delgado , ; Klenk and Grathwohl , ; Olsson and Grathwohl , ; Boon et al ., ] and in pore‐scale modeling [ Sahimi et al ., ; Bijeljic and Blunt , ]. The obtained power‐law coefficients are significantly lower for bead and sand packs, 0.5–0.72 [ Carvalho de and Delgado , ; Klenk and Grathwohl , ; Olsson and Grathwohl , ] than for consolidated rock, 0.84–0.95 [ Sahimi et al ., ; Bijeljic and Blunt , ; Boon et al ., ].…”

Section: Measures Of Spreading and Mixingmentioning

confidence: 95%

“…Sublinear behavior where

δ < 1

Section: Measures Of Spreading and Mixingmentioning

confidence: 99%

“…The obtained power‐law coefficients are significantly lower for bead and sand packs, 0.5–0.72 [ Carvalho de and Delgado , ; Klenk and Grathwohl , ; Olsson and Grathwohl , ] than for consolidated rock, 0.84–0.95 [ Sahimi et al ., ; Bijeljic and Blunt , ; Boon et al ., ]. This sublinear behavior is explained by incomplete mixing at the pore throats [ Klenk and Grathwohl , ] or the more pronounced effect of the decrease of D t with distance due to flow focusing [ Boon et al ., ].…”

Section: Measures Of Spreading and Mixingmentioning

confidence: 99%

“…This work builds on the technique developed by Boon et al . [], using X‐ray tomography to obtain three‐dimensional observations of the steady state distribution of nonreactive NaI solute in a brine flowing through consolidated rock cores. In Boon et al .…”

Section: Introductionmentioning

confidence: 98%

“…In Boon et al . [], the technique is demonstrated on a homogeneous rock and the analysis is focused on different approaches to quantifying transverse dispersion, one measure of spreading. Here the observations and analysis are extended to heterogeneous rocks and descriptions of commensurately complex transport processes.…”

Section: Introductionmentioning

confidence: 99%

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Observations of the impact of rock heterogeneity on solute spreading and mixing

Boon

Bijeljic

Krevor

2017

Water Resources Research

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Rock heterogeneity plays an important role in solute spreading and mixing in hydrogeologic systems. Few observations, however, have been made that can spatially resolve these processes in 3-D, in consolidated rocks. We make observations of the spatially resolved steady state concentration of a sodium iodide solute while flowing brine through cylindrical rock cores using X-ray CT imaging. Three rocks with an increasing level of heterogeneity are chosen: a Berea sandstone, a Ketton carbonate, and an Indiana carbonate. The impact of heterogeneity on solute transport is analyzed by: (1) quantifying spreading and mixing using metrics such as the transverse dispersion coefficient, the dilution index, the reactor ratio, and the scalar dissipation rate and (2) visualizing and analyzing flow structures such as meandering, flow-focusing, and flow-splitting using isoconcentration contour maps. The transverse dispersion coefficient, D t , and the variation in D t throughout the rock core, increases with Pecl et number (Pe) and rock heterogeneity. The reactor ratio indicates that mixing is Fickian for the Berea sandstone and Ketton carbonate, but diverges for the Indiana carbonate. The temporal evolution of the scalar dissipation rate, a measure of the mixing rate, remains close to that of Fickian mixing for the Berea and Ketton rocks but not for the Indiana. Heterogeneous rock features are observed to cause meandering, focusing, or splitting of the plume depending on Pe.

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“…The power‐law regime is defined by

\frac{D_{t}}{D_{m}} = β {Pe}^{δ} 5 < Pe < 300,

in which β and δ are fitting parameters obtained from experimental or model results. Sublinear behavior where

δ < 1

Section: Measures Of Spreading and Mixingmentioning

confidence: 95%

“…Sublinear behavior where

δ < 1

Section: Measures Of Spreading and Mixingmentioning

confidence: 99%

Section: Measures Of Spreading and Mixingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observations of the impact of rock heterogeneity on solute spreading and mixing

Boon

Bijeljic

Krevor

2017

Water Resources Research

Self Cite

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Entropy‐based critical reaction time for mixing‐controlled reactive transport

Chiogna

Rolle

2017

Water Resources Research

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Entropy‐based metrics, such as the dilution index, have been proposed to quantify dilution and reactive mixing in solute transport problems. In this work, we derive the transient advection dispersion equation for the entropy density of a reactive plume. We restrict our analysis to the case where the concentration distribution of the transported species is Gaussian and we observe that, even in case of an instantaneous complete bimolecular reaction, dilution caused by dispersive processes dominates the entropy balance at early times and results in the net increase of the entropy density of a reactive species. Successively, the entropy of the reactant decreases until it vanishes. We show the existence of a unique critical value of dilution, which corresponds to the complete consumption of one of the reactants. This critical dilution index is independent of advective and dispersive processes, and depends only on the dimensionality of the problem, on the stoichiometry of the reaction and on the initial concentrations of the reactants. Furthermore, we provide simple analytical expressions to compute the critical reaction time, i.e., the time at which the critical dilution index is reached, for selected flow configurations. Our results show that, differently from the critical dilution index, the critical reaction time depends on solute transport processes such as advection and hydrodynamic dispersion.

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Calibration of astigmatic particle tracking velocimetry based on generalized Gaussian feature extraction

Franchini

Charogiannis

Markides

et al. 2019

Advances in Water Resources

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Flow and transport in porous media are driven by pore scale processes. Particle tracking in transparent porous media allows for the observation of these processes at the time scale of ms. We demonstrate an application of defocusing particle tracking using brightfield illumination and a CMOS camera sensor. The resulting images have relatively high noise levels. To address this challenge, we propose a new calibration for locating particles in the out-of-plane direction. The methodology relies on extracting features of particle images by fitting generalized Gaussian distributions to particle images. The resulting fitting parameters are then linked to the out-of-plane coordinates of particles using flexible machine learning tools. A workflow is presented which shows how to generate a training dataset of fitting parameters paired to known out-of-plane locations. Several regression models are tested on the resulting training dataset, of which a boosted regression tree ensemble produced the lowest cross-validation error. The efficiacy of the proposed methodology is then examined in a laminar channel flow in a large measurement volume of 2048, 1152 and 3000 μm in length, width and depth respectively. The size of the test domain reflects the representative elementary volume of many fluid flow phenomena in porous media. Such large measurement depths require the collection of images at different focal levels. We acquired images at 21 focal levels 150 μm apart from each other. The error in predicting the out-of-plane location in a single slice of 240 μm thickness was found to be 7 μm, while in-plane locations were determined with sub-pixel resolution (below 0.8 μm). The mean relative error in the velocity measurement was obtained by comparing the experimental results to an analytic model of the flow. The estimated displacement errors in the axial direction of the flow were 0.21 pixel and 0.22 pixel at flows rates of 1.0 mL/h and 2.5 mL/h, respectively. These results demonstrate that it is possible to conduct three-dimensional particle tracking in a representative elementary volume based on a simple apparatus comprising a microscope with standard brightfield illumination and a camera with CMOS sensor.

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Observations of 3-D transverse dispersion and dilution in natural consolidated rock by X-ray tomography

Cited by 19 publications

References 46 publications

Observations of the impact of rock heterogeneity on solute spreading and mixing

Observations of the impact of rock heterogeneity on solute spreading and mixing

Entropy‐based critical reaction time for mixing‐controlled reactive transport

Calibration of astigmatic particle tracking velocimetry based on generalized Gaussian feature extraction

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