Journal of Applied Mathematics
Volume 2012 (2012), Article ID 987975, 20 pages
Research Article

Optimal Control of Polymer Flooding Based on Maximum Principle

1College of Information and Control Engineering, China University of Petroleum, Qingdao, 266580, China
2Research Institute of Geological Science, Sinopec Shengli Oilfield Company, Dongying 257000, China

Received 8 March 2012; Accepted 29 May 2012

Academic Editor: Xianxia Zhang

Copyright © 2012 Yang Lei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and the inequality constraint as the polymer concentration limitation. To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. A gradient method is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.