
P. S. Voronkova, A. Yu. Flerova Modeling and investigation of the optimal control problem of selecting modes of the oil fields exploitation 

Abstract. In this paper, a mathematical model of the oil field development management based on modified Hubbert approach is constructed, which lets investigating the possibility of forecasting of the extracted oil amount, the time of field development and the profit of an oil producer. There were described 3 possible regimes of oil field exploitation: “standard” Hubbert regime, Shelf and Special regimes, and in which order these regimes can take place. It is shown that the optimal oil field management is comprised of a specific combination of basic regimes and only depends on the initial system parameters. Numerical experiment was conducted based on Permian basin structural parameters. The described experiment setup allows for numerical calculation of optimal recovery time and the corresponding amount of the recovered oil. Keywords: oil production; the problem of optimal control; the Pontryagin maximum principle PP. 47. References 1. Petrov V.V., Polyakov G.A., Polyakova T.V., Sergeev V.М. 2003. Dolgosrochnye perspectivy rossiyskoi nefti (analizy, trendy, scenarii) [Longterm prospects for Russian oil (analyzes, trends, scenarios)] Moscow: Phazis. 200p. 2. Vasil’ev F.P. 2002. Metody optimizacii [Optimization methods]. Moscow: Factorial Press. 824p.
