Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties
Joint Authors
Zhang, Yong
Papelis, Charalambos
Young, Michael H.
Berli, Markus
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-07
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM).
The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown.
To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM) to capture bromide transport through laboratory repacked sand.
Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually.
Late-time tails are observed in the breakthrough curves (BTC) of bromide even in relatively homogeneous glass beads.
The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate.
Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion.
In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM.
Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.
American Psychological Association (APA)
Zhang, Yong& Papelis, Charalambos& Young, Michael H.& Berli, Markus. 2013. Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1011037
Modern Language Association (MLA)
Zhang, Yong…[et al.]. Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties. Mathematical Problems in Engineering No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-1011037
American Medical Association (AMA)
Zhang, Yong& Papelis, Charalambos& Young, Michael H.& Berli, Markus. Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1011037
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1011037