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

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.