Optimal control for a class of distributed parameter system

Key words:  distributed parameter systems  optimal control  chemical flooding  control vector parameterization

Abstract:

An optimal control problem ( OCP) of the chemical flooding was investigated to maximize the cumulative net present value gained from oil-field development. The OCP is governed by a set of nonlinear partial differential equations and involves control constraints. The continuous adjoint equations and the gradients of the performance index were derived by using the necessary conditions of the OCP for distributed parameter systems. The nonlinear items of the state equations were fullly expanded in order to derive the adjoint equations. A numerical algorithm based on control vector parameterization was presented to solve the problem, which transformed the infinite dimensional OCP into nonlinear programming problem. An example of the injection concentration optimization in polymer flooding was solved and the optimal injection strategies were obtained， which illustrated the practicality and effectiveness of the proposed method.