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

### 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

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[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. -No16(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. –No1(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. -No4(5). -P 360–370.

Published

2018-07-18

How to Cite

ASSYLBEKULY, A.; ABDIBEKOVA, A. U.; ZHUMAGULOV, B. T..
Mathematical modeling of oil spill migration on the surface of the Caspian Sea depending on weather conditions.

**KazNU Bulletin. Mathematics, Mechanics, Computer Science Series**, [S.l.], v. 92, n. 4, p. 88-98, july 2018. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/457>. Date accessed: 17 aug. 2018.
Section

Mathematics

**Keywords:**oil spill, Caspian Sea, oil slick, environment, weather conditions, mathematical modeling