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

Raja Ram Yadav; Sujata Kushwaha; Joy Roy; Lav Kush Kumar

doi:doi:10.11648/j.wros.20231201.11

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

Raja Ram Yadav, Sujata Kushwaha, Joy Roy, Lav Kush Kumar

Published in Journal of Water Resources and Ocean Science (Volume 12, Issue 1)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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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TY  - JOUR
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
PY  - 2023
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
SP  - 1
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

Raja Ram Yadav

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India
Sujata Kushwaha

Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India
Joy Roy

Department of Mathematics, Aryavart Institute of Higher Education, Lucknow, India
Lav Kush Kumar

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2023
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
SP  - 1
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  -

Copy | Download