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.
Yang Lei. Shurong Li. Xiaodong Zhang. Qiang Zhang. Lanlei Guo. "Optimal Control of Polymer Flooding Based on Maximum Principle." J. Appl. Math. 2012 (SI08) 1 - 20, 2012. https://doi.org/10.1155/2012/987975