# Mathematical modeling of oil spill migration on the surface of the Caspian Sea depending on weather conditions

## Authors

• A. Assylbekuly al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
• A. U. Abdibekova al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
• T. Т. Zhumagulov al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
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## Keywords:

oil spill, the Caspian Sea, oil slick, the environment, weather conditions, mathematical modeling

## Abstract

This paper considers the process of filling and migration of fossil fuels - oil - in the Caspian Sea,
depending on the weather conditions. As a rule, for environmentalists performing analysis of the
emergency, it is necessary to know in which direction will move the oil slick, formed because of
the spill, how to change the composition of the oil, how much oil will evaporate and a number
of other questions that can be answered using mathematical modeling. The theoretical basis of a
mathematical model for the process consists of the hydrodynamics equations of the sea, equations
of transfer and changes in the concentration of the oil component, as well as the continuity equation
is taken into account, expressing the an invariance of the total amount of mass of poured oil, which
have formed a film on the surface of the sea. As a result, the migration trajectory, the change in
concentration and temperature of the oil slick on the sea surface from a fixed source, depending
on weather conditions are defined. This model allows to calculate the area and determine the
migration trajectory of the oil slick on the Caspian sea depending on the weather conditions, and
carry out the numerical simulation of oil spills in the open sea at different initial masses of spilled
oil.

## References

[1] Mackay D., Lee S.Chi, Ma K., Shiu W.Y. Handbook of Physical-Chemical Properties and Environmental Fate for Organic
Chemicals. - Boca Raton: Taylor and Francis, 2006. - 4216 p.
[2] Boehm P.D., Fiest D.L., Mackay D., Paterson S. Physical-chemical weathering of petroleum hydrocarbons from the
IXTOC I blowout: chemical measurements and a weathering model // Environ. Sci. Technol. - 1982. -№16(8). -P. 498–505.
[3] Samoilov N.A., Conceicao A.A. Mathematical modeling of the evaporation of oil and petroleum products in the event
of spills // Proceedings of the Samara scientific center of RAS, Samara, -2010. –№1(9). –P. 2251–2254.
[4] Zhumagulov B.T., Monakhov V.N. The Fluid dynamics of oil production: Translated & ed. by AgipK CO. - Milan:
Interservice, 2003. - 307 p.
[5] Abdibekov U.S., Zhumagulov B.T., Zhakebaev D.B., Zhubat K.Z. Modelling of the decay of isotropic turbulence by the
LES // Mathematical Models and Computer Simulations. - 2013. -№4(5). -P 360–370.

2018-11-02

## How to Cite

Assylbekuly, A., Abdibekova, A. U., & Zhumagulov T. Т. (2018). Mathematical modeling of oil spill migration on the surface of the Caspian Sea depending on weather conditions. Journal of Mathematics, Mechanics and Computer Science, 92(4), 88–98. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/548

## Section

Applied Mathematics