Evolution and persistence of cross-directional statistical dependence during finite-Péclet transport through a real porous medium

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Title: Evolution and persistence of cross-directional statistical dependence during finite-Péclet transport through a real porous medium
Author(s): Bijeljic, B
Most, S
Nowak, W
Item Type: Journal Article
Abstract: Transport of passive, dissolved compounds in fully-saturated complex porous media frequently exhibits non-Fickian characteristics. One of the most interesting questions is to ascertain the time scales at which it is possible to describe transport as a statistically independent process. Therefore we study the mechanisms for evolution and then the decrease of non-Fickianity as a function of increasing time. Adopting the Lagrangian perspective, we provide a non-linear copula analysis of advective-diffusive processes by analyzing particle trajectories in a real porous media, as provided by direct numerical simulations on the three-dimensional image of Doddington sandstone. First, we analyze the memory effects between time-consecutive particle position increments and cross-dependence between longitudinal and transver sal particle position increments as a function of given time increments and time lags between consecutive time increments. Second, we investigate the influence of the P´eclet regime on the temporal evolution of dependence. Our main findings are: (a) Cross-dependence between longitudinal and transver sal particle position increments is persistent over the investigated range of time increments, even though this aspect has been neglected up to date. (b) Lower P´eclet numbers lead to a weaker dependence that is, however, more persistent over time than in higher-P´eclet transport regimes. We confirm that non-Fickianity comes from spatial coherence associated with heterogeneities of the velocity field that introduce cross-dependence and memory into the transport process. Overall, we show that memory and cross-dependence are persistent in and among all directions, that the dependence is highly-nonlinear, occurs at different temporal scales, and is dependent on the P´eclet number.
Publication Date: 22-Nov-2017
Date of Acceptance: 23-Oct-2016
URI: http://hdl.handle.net/10044/1/43460
DOI: htttps://dx.doi.org/10.1002/2016WR018969
ISSN: 0043-1397
Publisher: American Geophysical Union (AGU)
Start Page: 8920
End Page: 8937
Journal / Book Title: Water Resources Research
Volume: 52
Issue: 11
Copyright Statement: © 2016. American Geophysical Union. All Rights Reserved.
Keywords: Environmental Engineering
0905 Civil Engineering
0907 Environmental Engineering
1402 Applied Economics
Publication Status: Published
Appears in Collections:Faculty of Engineering
Earth Science and Engineering



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