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Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium

Received: 1 April 2023     Accepted: 28 April 2023     Published: 18 May 2023
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Abstract

Contaminated groundwater has been a serious problem across the world for many years as it has a bad impact on the quality of groundwater as well as on the environment. This study considers the solute transport problem in a heterogeneous porous medium with scale and time-dependent dispersion. The heterogeneity of porous media at the microscopic level facilitates dispersion, which affects groundwater flow patterns and solute distribution. For this work, the porous formation is assumed to be of semi-infinite length and of adsorbing nature. The key parameters such as dispersion coefficient and groundwater velocity are considered to be spatially and temporally dependent functions in degenerated forms. In addition, the first-order decay and zero-order production terms are also considered as time-dependent functions. Initially, it is assumed that the aquifer is uniformly polluted. Two different types of input sources namely uniform and varying nature are considered along the flow at one end in two separate cases, while concentration gradient, at non-source end boundary, is supposed to be zero. An analytical solution of the current boundary value problem is obtained using the Laplace Integral Transform Technique (LITT). The results obtained from the proposed problem are demonstrated graphically for a particular time functions in dispersion and groundwater velocity.

Published in Journal of Water Resources and Ocean Science (Volume 12, Issue 1)
DOI 10.11648/j.wros.20231201.11
Page(s) 1-11
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Advection, Dispersion, Scale and Time Dependent, Groundwater Velocity, Porous Media

References
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[16] Li-Tang Hu, Zhong-Jing Wang, Wei Tian & Jian-Shi Zhao. (2009). Coupled surface water–groundwater model and its application in the Arid Shiyang River basin, China. Hydrological Processes An International Journal. 23 (14), 2033-2044.
[17] Chen Jui-Sheng, Chen-Wuing Liu, Ching-Ping Liang & Keng-Hsin Lai. (2012). Generalized analytical solutions to sequentially coupled multi-species advective–dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition. Journal of hydrology. 456, 101-109.
[18] Guerrero, JS Perez, Luiz Claudio Gomes Pimentel & Todd H. Skaggs. (2013). Analytical solution for the advection-dispersion transport equation is layered media. International Journal Heat Mass Transfer. 56274-282.
[19] Mritunjay Kumar Singh & Pintu Das. (2015). Scale dependent solute dispersion with linear isotherm in heterogeneous medium. Journal of Hydrology. 520, 289-299.
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Cite This Article
  • APA Style

    Raja Ram Yadav, Sujata Kushwaha, Joy Roy, Lav Kush Kumar. (2023). Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium. Journal of Water Resources and Ocean Science, 12(1), 1-11. https://doi.org/10.11648/j.wros.20231201.11

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    ACS Style

    Raja Ram Yadav; Sujata Kushwaha; Joy Roy; Lav Kush Kumar. Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium. J. Water Resour. Ocean Sci. 2023, 12(1), 1-11. doi: 10.11648/j.wros.20231201.11

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    AMA Style

    Raja Ram Yadav, Sujata Kushwaha, Joy Roy, Lav Kush Kumar. Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium. J Water Resour Ocean Sci. 2023;12(1):1-11. doi: 10.11648/j.wros.20231201.11

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  • @article{10.11648/j.wros.20231201.11,
      author = {Raja Ram Yadav and Sujata Kushwaha and Joy Roy and Lav Kush Kumar},
      title = {Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium},
      journal = {Journal of Water Resources and Ocean Science},
      volume = {12},
      number = {1},
      pages = {1-11},
      doi = {10.11648/j.wros.20231201.11},
      url = {https://doi.org/10.11648/j.wros.20231201.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wros.20231201.11},
      abstract = {Contaminated groundwater has been a serious problem across the world for many years as it has a bad impact on the quality of groundwater as well as on the environment. This study considers the solute transport problem in a heterogeneous porous medium with scale and time-dependent dispersion. The heterogeneity of porous media at the microscopic level facilitates dispersion, which affects groundwater flow patterns and solute distribution. For this work, the porous formation is assumed to be of semi-infinite length and of adsorbing nature. The key parameters such as dispersion coefficient and groundwater velocity are considered to be spatially and temporally dependent functions in degenerated forms. In addition, the first-order decay and zero-order production terms are also considered as time-dependent functions. Initially, it is assumed that the aquifer is uniformly polluted. Two different types of input sources namely uniform and varying nature are considered along the flow at one end in two separate cases, while concentration gradient, at non-source end boundary, is supposed to be zero. An analytical solution of the current boundary value problem is obtained using the Laplace Integral Transform Technique (LITT). The results obtained from the proposed problem are demonstrated graphically for a particular time functions in dispersion and groundwater velocity.},
     year = {2023}
    }
    

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    T1  - Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium
    AU  - Raja Ram Yadav
    AU  - Sujata Kushwaha
    AU  - Joy Roy
    AU  - Lav Kush Kumar
    Y1  - 2023/05/18
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    N1  - https://doi.org/10.11648/j.wros.20231201.11
    DO  - 10.11648/j.wros.20231201.11
    T2  - Journal of Water Resources and Ocean Science
    JF  - Journal of Water Resources and Ocean Science
    JO  - Journal of Water Resources and Ocean Science
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    EP  - 11
    PB  - Science Publishing Group
    SN  - 2328-7993
    UR  - https://doi.org/10.11648/j.wros.20231201.11
    AB  - Contaminated groundwater has been a serious problem across the world for many years as it has a bad impact on the quality of groundwater as well as on the environment. This study considers the solute transport problem in a heterogeneous porous medium with scale and time-dependent dispersion. The heterogeneity of porous media at the microscopic level facilitates dispersion, which affects groundwater flow patterns and solute distribution. For this work, the porous formation is assumed to be of semi-infinite length and of adsorbing nature. The key parameters such as dispersion coefficient and groundwater velocity are considered to be spatially and temporally dependent functions in degenerated forms. In addition, the first-order decay and zero-order production terms are also considered as time-dependent functions. Initially, it is assumed that the aquifer is uniformly polluted. Two different types of input sources namely uniform and varying nature are considered along the flow at one end in two separate cases, while concentration gradient, at non-source end boundary, is supposed to be zero. An analytical solution of the current boundary value problem is obtained using the Laplace Integral Transform Technique (LITT). The results obtained from the proposed problem are demonstrated graphically for a particular time functions in dispersion and groundwater velocity.
    VL  - 12
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India

  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India

  • Department of Mathematics, Aryavart Institute of Higher Education, Lucknow, India

  • Department of Applied Science, Babu Banarasi Das Institute of Technology and Management, Lucknow, India

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