Optimal Management of Oil Field Development in the Buckley–Leverett Model
We consider the problem of two-phase filtering (oil and water) in a horizontal layer of an oil deposit. We propose an asymptotic method for calculating both the filtering process and related optimal control problems, namely the problems of choosing optimal control actions to achieve maximum oil production at a given level of water resource consumption or a minimum water flow rate that provides the level of oil production required by the plan.
Keywordsfiltering asymptotics optimal control probabilistic methods
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- 1.Aziz, Kh. and Settari, A., Petroleum Reservoir Simulation, London: Applied Science Publishers, 1979. Translated under the title Matematicheskoe modelirovanie plastovykh sistem, Moscow: Inst. Komp’yut. Issled., 2004.Google Scholar
- 2.Samarskii, A.A., Koldoba, A.V., Poveshchenko, Yu.A., Tishkin, V.F., and Favorskii, A.P., Raznostnye skhemy na neregulyarnykh setkakh (Difference Schemes on Irregular Grids), Minsk: ZAO “Kriterii,” 1996.Google Scholar
- 3.Akhmetzianov, A.V., Kushner, A.G., and Lychagin, V.V., Nonlinear Models of Oil Frontal Displacement and Shock Waves, in 7th IFAC Conf. on Manufacturing Modelling, Management, and Control, 2013, pp. 1170–1175.Google Scholar
- 9.Akhmetzianov, A.V., Kushner, A.G., and Lychagin, V.V., Long-time Asymptotics for the Buckley–Leverett Models of Development of Oil and Gas Fields, in Proc. Conf. Application of Information and Communication Technologies, AICT 2017, Moscow, 20–22 September, 2017, pp. 505–507.Google Scholar
- 12.Riesz, F. and Szókefalvi-Nagy, B., Functional Analysis, New York: Dover, 1952. Translated under the title Lektsii po funktsional’nomu analizu, Moscow: Mir, 1979.Google Scholar