Dynamic optimization of polymer flooding with free terminal time based on maximum principle

Polymer flooding is an important technology for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPS) for polymer flooding is established, which involves the performance index as maximum of the profit, the governing equations as the seepage equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The injection polymer concentration and the terminal time of polymer flooding are chosen as control variables. For this distributed parameter optimal control problem (OCP) with free terminal time, a solution method based on maximum principle is proposed. Firstly, the free terminal time OCP of polymer flooding is transformed into a fixed final time problem by introducing a normalized time variable. Then through application of the maximum principle, adjoint equations and gradients of the objective functional are obtained to optimize the injection polymer concentration and the terminal time simultaneously. Finally, the numerical results of an example illustrate the effectiveness of the proposed method.