Measurement of Groundwater Contaminant Concentration around a Landfill Flow through Heterogeneous Medium Using One-Dimensional Advection-Diffusion Equation

Main Article Content

Anantanit Chumsri, Areerat Vongkok, Suriyun Khatbanjong

Abstract

Leachate from poorly managed landfills poses a substantial threat to groundwater, which is a vital resource for irrigation and drinking. Uncontrolled waste disposal leads to seriously impaired water quality. Such landfills contribute leachate to contaminated groundwater, which negatively impacts the physical and qualitative characteristics of the increased groundwater pollutant concentration. Monitoring every facet of transport distribution is impractical. Therefore, a prediction of groundwater pollution concentration needs to be modeled to assist in following and examining the contaminated area. This study suggested groundwater pollutant concentrations are transported via the inhomogeneous medium and unsteady flow systems using the one-dimensional advection-diffusion equation. The numerical forward time-centered space finite difference method drives the transport of both solutes as they flow through the two systems. The resulting transport equations are produced and simulated, which have a close value with the analytical solution.

Article Details

References

  1. P. Alam, K. Ahmade, Impact of Solid Waste on Health and the Environment, Int. J. Sustain. Dev. Green Econ. 2 (2013), 165-168.
  2. T.A. Laniyan, O.O. Bayewu, G.O. Mosuro, Impact of Leachates on the Quality of Groundwater in Shagamu Southwestern, Nigeria in Groundwater – Some Urban Cities of Southwestern, Nigeria, Afr. J. Sci. Nat. 6 (2020), 46. https://doi.org/10.46881/ajsn.v6i0.141.
  3. O. Oyebode, F. Jimoh, S. Ajibade, S. Afolaluand, F. Oyebode, Strategic Monitoring of Groundwater Quality Around Olusosun Landfill in Lagos State for Pollution Reduction and Environmental Sustainability, Nat. Environ. Pollut. Technol. 22 (2023), 565-577. https://doi.org/10.46488/NEPT.2023.v22i02.003.
  4. W.N. Igboama, O.S. Hammed, J.O. Fatoba, M.T. Aroyehun, J.C. Ehiabhili, Review Article on Impact of Groundwater Contamination Due to Dumpsites Using Geophysical and Physiochemical Methods, Appl. Water Sci. 12 (2022), 130. https://doi.org/10.1007/s13201-022-01653-z.
  5. O. Omofunmi, A. Satimehin, A. Oloye, O. Umego, Effect of Landfill Leachates on Some Water Quality Indicators of Selected Surface Water and Groundwater at Ilokun, Ado-Ekiti, Nigeria, Makara J. Technol. 24 (2020), 72. https://doi.org/10.7454/mst.v24i2.3881.
  6. P. De Luca, L. Marcellino, Analytical and Numerical Properties of an Extended Angiogenesis PDEs Model, J. Math. Biol. 91 (2025), 62. https://doi.org/10.1007/s00285-025-02293-y.
  7. I.A. Mirza, M.S. Akram, N.A. Shah, W. Imtiaz, J.D. Chung, Analytical Solutions to the Advection-Diffusion Equation with Atangana-Baleanu Time-Fractional Derivative and a Concentrated Loading, Alex. Eng. J. 60 (2021), 1199-1208. https://doi.org/10.1016/j.aej.2020.10.043.
  8. K.N.I. Ara, M.M. Rahaman, M.S. Alam, Numerical Solution of Advection Diffusion Equation Using Semi-Discretization Scheme, Appl. Math. 12 (2021), 1236-1247. https://doi.org/10.4236/am.2021.1212079.
  9. M. Al-Lawatia, Solution of Advection-Diffusion Equations in Two Spatial Dimensions by a Rational Eulerian-Lagrangian Localized Adjoint Method over Hexagonal Grids, Int. J. Numer. Anal. Model. 9 (2012), 43-55.
  10. W. Klaychang, N. Pochai, Implicit Finite Difference Simulation of Water Pollution Control in a Connected Reservoir System, IAENG Int. J. Appl. Math. 46 (2016), 47-57.
  11. K. Suebyat and N. Pochai, A Numerical Simulation of a Three-Dimensional Air Quality Model in an Area Under a Bangkok Sky Train Platform Using an Explicit Finite Difference Scheme, IAENG Int. J. Appl. Math. 47 (2017), 1-6.
  12. P. Oyjinda, N. Pochai, Numerical Simulation to Air Pollution Emission Control Near an Industrial Zone, Adv. Math. Phys. 2017 (2017), 1-7. https://doi.org/10.1155/2017/5287132.
  13. P. Samalerk, N. Pochai, Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions, Abstr. Appl. Anal. 2018 (2018), 1-7. https://doi.org/10.1155/2018/1926519.
  14. A. Vongkok, N. Pochai, Numerical Models of Nitrogen Compound Measurements in a Stream with Removal Mechanism Using Saulyev Technique with Cubic Spline Interpolation, J. Interdiscip. Math. 22 (2019), 1235-1275. https://doi.org/10.1080/09720502.2019.1668153.
  15. A. Vongkok, N. Pochai, Numerical Simulations for Reactive Nitrogen Compounds Pollution Measurements in a Stream Using Saulyev Method, Ital. J. Pure Appl. Math. 43 (2020), 552-582.
  16. P. Maneechay, N. Pochai, S. Khatbanjong, A Vertically Averaged Groundwater Quality Measurement with Monitored Boundary Data, IAENG Int. J. Appl. Math. 54 (2024), 2669.
  17. R.K. Timothy, J.S. Maremwa, J.K. Kandie, Mathematical Modeling of the Flow of a Fertilizer-Water Mixture through Soil and Its Effects on Concentration and Plant Growth, Int. J. Stat. Appl. Math. 6 (2021), 37-43.
  18. S. Yena, N. Pochai, Numerical Simulation of a Two-Dimensional Vertically Averaged Groundwater Quality Assessment in Homogeneous Aquifer Using Explicit Finite Difference Techniques, Math. Stat. 8 (2020), 152-165. https://doi.org/10.13189/ms.2020.080211.
  19. M.M. Rahaman, H. Takia, M.K. Hasan, M.B. Hossain, S. Mia, K. Hossen, Application of Advection Diffusion Equation for Determination of Contaminants in Aqueous Solution: A Mathematical Analysis, Appl. Math. Phys. 10 (2022), 24–31.
  20. X. Chen, K. Zhang, Z. Ji, X. Shen, P. Liu, et al., Progress and Challenges of Integrated Machine Learning and Traditional Numerical Algorithms: Taking Reservoir Numerical Simulation as an Example, Mathematics 11 (2023), 4418. https://doi.org/10.3390/math11214418.
  21. T. R. Maitsa, Q. Hafiyyan, M. B. Adityawan, I. Magdalena, A. A. Kuntoro and H. Kardhana, Development of A 2D Numerical Model for Pollutant Transport Using FTCS Scheme and Numerical Filter, Makara J. Technol. 25 (2021), 3. https://doi.org/10.7454/mst.v25i3.3966.
  22. N. Pochai, Numerical Treatment of a Modified MacCormack Scheme in a Nondimensional Form of the Water Quality Models in a Nonuniform Flow Stream, J. Appl. Math. 2014 (2014), 274263. https://doi.org/10.1155/2014/274263.
  23. A. Kumar, D.K. Jaiswal, N. Kumar, Analytical Solutions to One-Dimensional Advection–Diffusion Equation with Variable Coefficients in Semi-Infinite Media, J. Hydrol. 380 (2010), 330-337. https://doi.org/10.1016/j.jhydrol.2009.11.008.
  24. A.E. Scheidegger, The Physics of Flow through Porous Media, University of Toronto Press, Toronto, 1957.
  25. J. D. Anderson, Computational Fluid Dynamics, McGraw-Hill, New York, 1995.
  26. G. Gurarslan, H. Karahan, D. Alkaya, M. Sari, M. Yasar, Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method, Math. Probl. Eng. 2013 (2013), 672936. https://doi.org/10.1155/2013/672936.