Single-objective well control problems have been studied for many years as one of the most typical optimization problems by researchers worldwide. However, single-objective optimization often could not meet the needs in practical application processes leading to multi-objective optimization problems which have better adaptability in practical applications. In this study, a new method for multi-objective well controls optimization problem using support-vector regression (SVR) proxy model and non-dominated sorting genetic algorithm-II (NSGA-II) was developed. This method was named the multi-objective optimization with proxy model (MOO-PM). In the MOO-PM method, the net present value (NPV) and cumulative oil production (COP) were considered as the objective functions while the bottom hole pressure of production wells and water injection rate of injection wells were chosen as the optimization variables. To the best of our knowledge, this is the first time that SVR proxy model and NSGA-II are applied simultaneously to the optimization of well controls problems. Compared to reservoir simulation model, the SVR proxy model was computationally more efficient. This meant the large calculation time spent on reservoir simulation operation for multi-objective optimization was sharply reduced by using the SVR proxy model. Furthermore, the accuracy of the SVR proxy model was proved by comparing it to the results of simulation of optimized cases and non-optimized cases for a synthetic field as well as a real reservoir. It was concluded that MOO-PM method could obtain better results with higher efficiency.

多年来，单目标井控问题已被全球研究人员作为最典型的优化问题之一进行了研究。然而，单目标优化常常不能满足实际应用过程中的需求，从而导致多目标优化问题在实际应用中具有更好的适应性。在这项研究中，开发了一种使用支持​​向量回归（SVR）代理模型和非主导排序遗传算法-II（NSGA-II）的多目标井控优化问题的新方法。该方法被称为代理模型多目标优化（MOO-PM）。在MOO-PM方法中，以净现值（NPV）和累计产油量（COP）为目标函数，以生产井的井底压力和注入井的注水率为优化变量。据我们所知，这是第一次将SVR代理模型和NSGA-II同时用于优化井控问题。与油藏模拟模型相比，SVR代理模型的计算效率更高。这意味着通过使用SVR代理模型，可大大减少用于多目标优化的油藏模拟操作所花费的大量计算时间。此外，通过将SVR代理模型与合成场和实际油藏的优化案例和非优化案例的仿真结果进行比较，证明了SVR代理模型的准确性。得出的结论是，MOO-PM方法可获得更好的结果，效率更高。