Abstract: Optimal control methods provide an effective way to determining the best polymer injection strategies to maximize the profits from oil recovery.The objected oriented design and implementation details are presented for the numerical solution of the optimal control problem，which involves the sub problems of reservoir simulation，adjoint equation and nonlinear programming.The polymer flooding model is discretized in a full implicit scheme and the derived nonlinear equations are handled by Newton-Raphson method，in order to construct the adjoint equations during the solution of forward model.An example of three-dimensional polymer injection problem is solved illustrating the practicality and efficiency of the realized algorithms.

Key words: optimal control, adjoint equation, polymer flooding, injection strategies

摘要： 为了获得聚合物驱油的最大利润，通过最优控制来确定聚合物的最佳注入策略是一种有效的方法。该最优控制问题的数值解涉及到油藏数值模拟、伴随方程和非线性规划问题。给出了基于面向对象的算法设计方案及其实现细节。利用全隐式差分格式离散化聚合物驱模型，并采用Newton-Raphson求解所得到非线性方程组，在求解前向模型的同时构造了伴随方程。对一个三维聚合物驱注入问题进行了实例求解，表明了所实现算法的实用性和有效性。

关键词: 最优控制, 伴随方程, 聚合物驱, 注入策略