Numerical investigation of the oil extraction control problem by the economic criterion of solution quality

V. D. Slabnov

Institute of Economics, Management and Law, Kazan, Russia

Abstract: 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.

UDC: 05.13.18+01.02.05

Received: 25.08.2013