Geodesic
Numerical investigation of the oil extraction control problem by the economic criterion of solution quality
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 77-89

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We propose an economic and mathematical model of the optimal control problem for oil extraction according to the economic criterion of solution quality. The process of oil displacement in a layered reservoir is described by a 3D model of two-phase flow using the Buckley–Leverett scheme. The reservoir characteristics can change along $OX$, $OY$, $OZ$ axes. We formulate four hypotheses about water-oil displacement from the elementary volume of the layered reservoir, and describe a computational algorithm for defining “fictitious” (modified) relative permeabilities for a difference discrete analogue of random distribution. We also compare the basic engineering and economic performances of oil extraction both with and without regard to optimal control.
Keywords: economic and mathematical model, two-phase flow, probability law of distribution, random variable, layered reservoir, optimal control. 
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     author = {V. D. Slabnov},
     title = {Numerical investigation of the oil extraction control problem by the economic criterion of solution quality},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {77--89},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a7/}
}
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V. D. Slabnov. Numerical investigation of the oil extraction control problem by the economic criterion of solution quality. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 77-89. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a7/