Mathematical modeling of soil contamination as a result of technological processes

Authors

  • Андрій Петрович Олійник Ivano-Frankivsk National Tehnical University of Oil and Gas Karpatska, 15, Ivano-Frankivsk, 76019, Ukraine
  • Аліса Андріївна Мороз Ivano-Frankivsk National Technical University of Oil and Gas Karpatska 15, Ivano-Frankivsk, Ukraine, 76019, Ukraine https://orcid.org/0000-0003-3792-7865

DOI:

https://doi.org/10.15587/1729-4061.2015.35952

Keywords:

environmental state, anthropogenic factors of impact, mathematical model, diffusion equation

Abstract

We have analyzed contaminated areas of anthropogenic origin, particularly surface and underground water as well as soil. We have considered the state and nature of processes happening within the Dombrov mine (mining potash) and other industrial areas of Ukraine that are vulnerable to technogenic impact. The suggested mathematical models of diffusion processes are based on the use of two- and three-dimensional diffusion equations with a wide range of boundary and initial conditions. It is determined that exact solutions inhibit studying the peculiarities of their behavior depending on the type of boundary conditions, therefore we suggest using numerical solutions. The presented difference schemes of the method of variable directions for numerical realization of two-dimentional models in different frames account for environmental heterogeneity of matter distribution. The schemes allow to measure concentration of substances in real objects through building functions that model various boundary conditions. We have devised a program complex for their implementation and presented the test findings as well as their analysis. To model processes whose parameters depend on three spatial coordinates, we have suggested numerical schemes for implementing three-dimensional models that are absolutely stable and have the second order of accuracy at all spatial coordinates. The study is completed with specification of the directions for further research. 

Author Biographies

Андрій Петрович Олійник, Ivano-Frankivsk National Tehnical University of Oil and Gas Karpatska, 15, Ivano-Frankivsk, 76019

Doctor of technical scince, Professor

Department of Mathematical Methods in Engineering

Аліса Андріївна Мороз, Ivano-Frankivsk National Technical University of Oil and Gas Karpatska 15, Ivano-Frankivsk, Ukraine, 76019

PhD student

The department of mathematical models in engineering

References

  2. Kalininchenko, A. V., Kopishynska, A. P., Kopishynskyy, A. V. (2013). Environmental risks of shale gas bearing areas in Ukraine. Journal of Poltava State Agrarian Academy, 477 (2), 127–131.
  4. Semchuk, J. M., Paliychuk, L. V. (2007). Main tasks and research methods to study of groundwater in the area of mining potash. Scientific Bulletin IFNTUOG, 1 (15), 164–167.
  5. Guravel, M. Y., Klochko, T. A, Jaremenko, V. V. (2013). Evaluation of technological transformation in soils reclaimed areas. Scientists note Taurian National University Vernadsky Series Called "Geography", 26/65 (1), 55–61.
  6. Malyk, Y. A., Demkiv, A. (2013). Monitoring of Dombrowski career. National University "Lviv Polytechnic", Department of Applied Ecology and sustainable nature, 285–288.
  7. Kuderavets, R. S., Maksymchuk, V. Y., Horodyskyy, Y. (2009). Geomagnetic model hydrocarbon fields and prospective structures of the central part of the Dnieper-Donets depression. Scientific Bulletin IFNTUOG, 1 (19), 73–81.
  8. Protsko, J. I. (2010). The impact of oil and oil products in the soil. Journal of Poltava State Agrarian Academy, 2, 189–191.
  9. Saban, V. Z., Semchuk, J. M. (2009). Assessing the impact of secondary oil recovery methods intensifying environmental. Scientific Bulletin IFNTUOG, 4 (22), 142–147.
  10. Skyba, E. E., Semchuk, J. M. (2011). The influence of capillary raising groundwater on the distribution of oil pollution in soils. Scientific Bulletin IFNTUOG, 4 (30), 77–81.
  11. Ryzhakova, N. K. (2014). A new method for estimating the coefficient of diffusion and emanation of radon in the soil. Journal of Environmental Radioactivity, 135, 63–66. doi: 10.1016/j.jenvrad.2014.04.002
  12. Rampit, I. A. (2004). About measurements emanation of soil factor. ANRT, 3, 51–52.
  13. Migaszewski, Z. M. (2001). Element concentration in soils, and plant bioindicators in selected habitats of the Holly Cross Mts, Poland. Water, Air and Soil Pollut., 129, 369.
  14. Migaszewski, Z. M., Galuszka, A. (2008). Soil subhorizon – a potential geoindicator of environmental pollution. Polish J. of Evironmental Stud., 17 (3), 405–410.
  15. Silva, E. J. G., Tirabassi, T., Vilhena, M. T., Buske, D. (2003). A puff model using a three-dimensional analytical solution for the pollutant diffusion process. Atmospheric Research, 134, 131–136. doi: 10.1016/j.atmosres.2013.07.009
  16. Sahoo, B. K., Mayya, Y. S. (2010). Two-dimensional diffusion theory of trace gas emission into soil chamber for flux measurements. Agricultural and Forest Meteorology, 150 (9), 1211–1124. doi: 10.1016/j.agrformet.2010.05.009
  17. Arya, S. P. (1995). Modelling and parametrization of near source diffusion in weak winds. Journal of Applied Meteorology, 34 (5), 1112–1122. doi: 10.1175/1520-0450(1995)034<1112:mapons>2.0.co;2
  18. Anderson, D., Tannehyl, J., Pletcher, R. (1990). Vychyslytelnaya hydromehanyka and teploobmen. Peace, 384.
  19. Ermakov, S. M., Zhyhlevskyy, A. A. (1987). Matematycheskaya Theory of optimal experiment. Textbook Science, 320.

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Published

2015-02-27

How to Cite

Олійник, А. П., & Мороз, А. А. (2015). Mathematical modeling of soil contamination as a result of technological processes. Eastern-European Journal of Enterprise Technologies, 1(4(73), 4–9. https://doi.org/10.15587/1729-4061.2015.35952

Issue

Vol. 1 No. 4(73) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2015 Андрій Петрович Олійник, Аліса Андріївна Мороз

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