# 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 theemergency, it is necessary to know in which direction will move the oil slick, formed because ofthe spill, how to change the composition of the oil, how much oil will evaporate and a numberof other questions that can be answered using mathematical modeling. The theoretical basis of amathematical model for the process consists of the hydrodynamics equations of the sea, equationsof transfer and changes in the concentration of the oil component, as well as the continuity equationis taken into account, expressing the an invariance of the total amount of mass of poured oil, whichhave formed a film on the surface of the sea. As a result, the migration trajectory, the change inconcentration and temperature of the oil slick on the sea surface from a fixed source, dependingon weather conditions are defined. This model allows to calculate the area and determine themigration trajectory of the oil slick on the Caspian sea depending on the weather conditions, andcarry out the numerical simulation of oil spills in the open sea at different initial masses of spilledoil.### References

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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.

Published

2018-11-02

How to Cite

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

**Journal of Mathematics, Mechanics and Computer Science**, [S.l.], v. 92, n. 4, p. 88-98, nov. 2018. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/548>. Date accessed: 18 nov. 2018.
Section

Applied Mathematics

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