Optimal Control for a Steady State Dead Oil Isotherm Problem

TL;DR

This paper investigates the optimal control of a steady-state dead oil isotherm modeled by nonlinear PDEs, establishing existence, regularity, and optimality conditions to improve oil recovery strategies.

Contribution

It provides the first rigorous proof of existence, regularity, and necessary optimality conditions for controlling a nonlinear PDE system in oil engineering.

Findings

Existence of optimal control established

Regularity results proved for the control problem

Necessary optimality conditions derived

Abstract

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions.