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Collapse of higher-order solute concentration moments in groundwater transport
KTH, School of Architecture and the Built Environment (ABE), Sustainable development, Environmental science and Engineering, Land and Water Resources Engineering.
KTH, School of Architecture and the Built Environment (ABE), Sustainable development, Environmental science and Engineering, Land and Water Resources Engineering.
2013 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 49, no 8, 4751-4764 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we use numerical simulations based on a Lagrangian framework to study contaminant transport through highly heterogeneous porous media due to advection and local diffusion (under local diffusion, we assume coupled effect of mechanical dispersion and molecular diffusion). The analysis of the concentration field is done for the case of a two-dimensional hydraulic conductivity domain representing the aquifer, with three log-conductivity structures that differ in spatial correlation. In addition to different conductivity structures, we focus our investigation on mild and highly heterogeneous porous media characterized by the values of hydraulic log-conductivity variance (σY2) being equal to 1 and 8. In the concentration moment analysis, we show that a linear relationship exists between higher-order to second-order normalized concentration moments on a log-log scale up to the fourth-order moment. This leads to the important finding that moments of a higher than the second order can be derived based on information about the first two concentration moments only. Such a property has been observed previously for boundary-layer water channels, wind tunnels, and turbulent diffusion in open terrain and laboratory experiments. Normalized moments are shown to collapse for different types of hydraulic conductivity structures, Peclet (Pe) numbers and σY2 values. In the case of local diffusion absence, a linear log-log relationship is derived analytically and is set as a lower limit. The deviation from the lower limit is explained to be predominantly caused by the local diffusion, which needs time to evolve. In the case of local diffusion presence, we define the moment deriving function (MDF) to describe the linear log-log relationship between higher-order concentration moments to the second-order normalized one. Finally, the comparison between numerical results and those obtained from the Columbus Air Force Base Macrodispersion Experiment (MADE 1) is used to demonstrate the robustness of the moment collapse.

Place, publisher, year, edition, pages
2013. Vol. 49, no 8, 4751-4764 p.
Keyword [en]
concentration moment collapse, moment deriving function, heterogeneity, advection, local diffusion, MADE
National Category
Environmental Engineering
Identifiers
URN: urn:nbn:se:kth:diva-133333DOI: 10.1002/wrcr.20371ISI: 000324838300018Scopus ID: 2-s2.0-84880959817OAI: oai:DiVA.org:kth-133333DiVA: diva2:660630
Note

QC 20131030

Available from: 2013-10-30 Created: 2013-10-30 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Significance of transport dynamics on concentration statistics and expected mass fraction based risk assessment in the subsurface
Open this publication in new window or tab >>Significance of transport dynamics on concentration statistics and expected mass fraction based risk assessment in the subsurface
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis relies on a Langrangian framework used for conservative tracer transport simulations through 2-D heterogeneous porous media. Conducted numerical simulations enable large sets of concentration values in both spatial and temporal domains. In addition to the advection, which acts on all scales, an additional mechanism considered is local scale dispersion (LSD), accounting for both mechanical dispersion and molecular diffusion. The ratio between these two mechanisms is quantified by the Peclet (Pe) number. In its base, the thesis gives answers to contaminant concentration features when influenced by: i) different log-conductivity variance; ii) log-conductivity structures defined by the same global variogram but with different log conductivity patterns cor-related; and iii) for a wide range of Peclet values. Results conducted by Monte Carlo (MC) analysis show a complex interplay between the aforementioned pa-rameters, indicating the influence of aquifer properties to temporal LSD evolu-tion. A stochastic characterization of the concentration scalar is done through moment analysis: mean, coefficient of variation (CVC), skewness and kurtosis as well as through the concentration probability density function (PDF). A re-markable collapse of higher order to second-order concentration moments leads to the conclusion that only two concentration moments are required for an accurate description of concentration fluctuations. This explicitly holds for the pure advection case, while in the case of LSD presence the Moment Deriv-ing Function (MDF) is involved to ensure the moment collapse validity. Fur-thermore, the expected mass fraction (EMF) concept is applied in groundwater transport. In its origin, EMF is function of the concentration but with lower number of realizations needed for its determination, compared to the one point PDF. From practical point of view, EMF excludes meandering effect and incorporates information about exposure time for each non-zero concentration value present. Also, it is shown that EMF is able to clearly reflect the effects of aquifer heterogeneity and structure as well as the Pe value. To demonstrate the uniqueness of the moment collapse feature and ability of the Beta distribution to account for the concentration frequencies even in real cases, Macrodisper-sion Experiment (MADE1) data sets are used.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xiii, 53 p.
Series
Trita-LWR. PHD, ISSN 1650-8602 ; 1074
Keyword
Local scale dispersion, Heterogeneity structure, Concentration moments, Moment collapse, Expected mass fraction
National Category
Other Environmental Engineering Environmental Engineering
Identifiers
urn:nbn:se:kth:diva-133455 (URN)978-91-7501-900-0 (ISBN)
Public defence
2013-11-05, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20131104

Available from: 2013-11-04 Created: 2013-11-04 Last updated: 2013-11-12Bibliographically approved

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