基于极大值原理的自由终端时间聚合物驱方案动态优化

Dynamic Optimization of Polymer Flooding with Free Terminal Time Based on Maximum Principle

针对自由终端时间的聚合物驱注入方案优化问题,建立聚合物驱最优控制模型。该模型以利润最大为性能指标,以聚合物驱的渗流力学方程为支配方程,以聚合物注入浓度及驱油结束时间为优化变量。对于该分布参数系统的自由终端时间最优控制问题,提出一种基于极大值原理的求解方法。首先引入标准化的时间变量,将原自由终端时间的聚合物驱最优控制问题转化为固定终端时间问题,然后利用极大值原理获得该问题的伴随方程及目标泛函的梯度,同时优化注入浓度和驱油结束时间,最后通过实例验证了所提出方法的有效性。

An optimal control model is established for making the dynamic injection strategies of polymer flooding with free terminal time, in which the maximum of profit is taken as the performance index, the fluid flow equations of polymer flooding as governing equations, the injection polymer concentration and the terminal time of polymer flooding as control variables. For this distributed parameter optimal control problem with free terminal time, a solution method based on maximum principle is proposed. Firstly, the free final time optimal control problem of polymer flooding was transformed into a fixed final time problem by introducing a normalized time variable. Then through the application of the maximum principle, adjoint equations of the problem and gradients of the objective functional are obtained to optimize the injection concentration and the terminal time simultaneously. Finally, the numerical results of an example illustrates the effectiveness of the proposed method.