Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 281567, 23 pages
Research Article

Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle

1College of Information and Control Engineering, China University of Petroleum, East China, Qingdao 266580, China
2Research Institute of Geological Science, Sinopec Shengli Oilfield Company, Dongying 257015, China

Received 30 May 2012; Accepted 29 June 2012

Academic Editor: Piermarco Cannarsa

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 some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP), the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s discrete maximum principle. A modified gradient method with new adjoint construction is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.