IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2020y2020i1n9504835.html

Analytical and Numerical Solutions of Pollution Concentration with Uniformly and Exponentially Increasing Forms of Sources

Author

Listed:
  • N. Manitcharoen
  • B. Pimpunchat

Abstract

The study of pollution movement is an important basis for solving water quality problems, which is of vital importance in almost every country. This research proposes the motion of flowing pollution by using a mathematical model in one‐dimensional advection‐dispersion equation which includes terms of decay and enlargement process. We are assuming an added pollutant sources along the river in two cases: uniformly and exponentially increasing terms. The unsteady state analytical solutions are obtained by using the Laplace transformation, and the finite difference technique is utilized for numerical solutions. Solutions are compared by relative error values. The result appears acceptable between the analytical and numerical solutions. Varying the value of the rate of pollutant addition along the river (q) and the arbitrary constant of exponential pollution source term (λ) is displayed to explain the behavior of the incremental concentration. It is shown that the concentration increases as q and λ increase, and the exponentially increasing pollution source is a suitable model for the behavior of incremental pollution along the river. The results are presented and discussed graphically. This work can be applied to other physical situations described by advection‐dispersion phenomena which are affected by the increase of those source concentrations.

Suggested Citation

  • N. Manitcharoen & B. Pimpunchat, 2020. "Analytical and Numerical Solutions of Pollution Concentration with Uniformly and Exponentially Increasing Forms of Sources," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:9504835
    DOI: 10.1155/2020/9504835
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2020/9504835
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/9504835?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. van Genuchten, M. Th. & Alves, W. J., 1982. "Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation," Technical Bulletins 157268, United States Department of Agriculture, Economic Research Service.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. N. Manitcharoen & B. Pimpunchat & P. Sattayatham, 2020. "Water Quality Analysis for the Depletion of Dissolved Oxygen due to Exponentially Increasing Form of Pollution Sources," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Salah A. Faroughi & Ramin Soltanmohammadi & Pingki Datta & Seyed Kourosh Mahjour & Shirko Faroughi, 2023. "Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
    2. Abdon Atangana & S. C. Oukouomi Noutchie, 2013. "Two‐Dimension Hydrodynamic Dispersion Equation with Seepage Velocity and Dispersion Coefficient as Function of Space and Time," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Jui-Sheng Chen & Ching-Ping Liang & Cheng-Hung Chang & Ming-Hsien Wan, 2019. "Simulating Three-Dimensional Plume Migration of a Radionuclide Decay Chain through Groundwater," Energies, MDPI, vol. 12(19), pages 1-22, September.
    4. Mohammad Hossein Golestan & Carl Fredrik Berg, 2024. "Simulations of CO 2 Dissolution in Porous Media Using the Volume-of-Fluid Method," Energies, MDPI, vol. 17(3), pages 1-21, January.
    5. Palav, Mansi S. & Pradhan, Vikas H., 2025. "Redefined fourth order uniform hyperbolic polynomial B-splines based collocation method for solving advection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 484(C).
    6. Grifka, Jasmin & Nehler, Mathias & Licha, Tobias & Heinze, Thomas, 2023. "Fines migration poses challenge for reservoir-wide chemical stimulation of geothermal carbonate reservoirs," Renewable Energy, Elsevier, vol. 219(P1).
    7. Abhishek Sanskrityayn & Heejun Suk & Jui-Sheng Chen & Eungyu Park, 2021. "Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients," Sustainability, MDPI, vol. 13(14), pages 1-23, July.
    8. Moisés A. C. Lemos & Camilla T. Baran & André L. B. Cavalcante & Ennio M. Palmeira, 2023. "A Semi-Analytical Model of Contaminant Transport in Barrier Systems with Arbitrary Numbers of Layers," Sustainability, MDPI, vol. 15(23), pages 1-18, November.
    9. Ricardo Mendonça de Moraes & Luan Carlos de Sena Monteiro Ozelim & André Luís Brasil Cavalcante, 2022. "Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena," Sustainability, MDPI, vol. 14(7), pages 1-19, March.
    10. Tinesh Pathania & T. I. Eldho, 2020. "A Moving Least Squares Based Meshless Element-Free Galerkin Method for the Coupled Simulation of Groundwater Flow and Contaminant Transport in an Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(15), pages 4773-4794, December.
    11. Unknown, 1994. "Proceedings of an international workshop held in Kota Bharu, Kelantan, Malaysia, 24-27 October 1994: Agricultural Impacts on Groundwater Quality," ACIAR Proceedings Series 134721, Australian Centre for International Agricultural Research.
    12. Changbing Yang & Ramón H. Treviño & Susan D. Hovorka & Jesus Delgado‐Alonso, 2015. "Semi‐analytical approach to reactive transport of CO 2 leakage into aquifers at carbon sequestration sites," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 5(6), pages 786-801, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:9504835. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.