Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem

TL;DR

This paper derives necessary optimality conditions for a semi-discretized control problem involving a nonlinear PDE system modeling water-oil flow in an isothermal dead-oil scenario.

Contribution

It provides the first derivation of optimality conditions for a semi-discretized model of the classical water-oil PDE system.

Findings

Established necessary optimality conditions for the control problem.

Applied the conditions to a semi-discretized nonlinear PDE system.

Enhanced understanding of optimal control in oil reservoir models.

Abstract

We obtain necessary optimality conditions for a semi-discretized optimal control problem for the classical system of nonlinear partial differential equations modelling the water-oil (isothermal dead-oil model).