Smart well technologies, which allow remote control of well and production processes, make the problem of determining optimal control strategies a timely and valuable pursuit. The large number of well rates for each control step make the optimization problem difficult and present a high risk of achieving a suboptimal solution. Moreover, the optimal number of adjustments is not known a priori. Adjusting well controls too frequently will increase unnecessary well management and operation cost, and an excessively low number of control adjustments may not be enough to obtain a good yield. In this paper, we explore the capability of three derivative-free algorithms and a multiscale regularization framework for well control optimization over the life of an oil reservoir. The derivative-free algorithms chosen include generalized pattern search (GPS), particle swarm optimization (PSO) and covariance matrix adaptation evolution strategy (CMA-ES). These algorithms, which cover a variety of search strategies (global/local search, stochastic/deterministic search), are chosen due to their robustness and easy parallelization. Although these algorithms have been used extensively in the reservoir development optimization literature, for the first time we thoroughly explore how these algorithms perform when hybridized within a multiscale regularization framework. Starting with a reasonably small number of control steps, the control intervals are subsequently refined during the optimization. Results for the experiments studied indicate that CMA-ES performs best among the three algorithms in solving both small and large scale problems. When hybridized with a multiscale regularization approach, the ability to find the optimal solution is further enhanced, with the performance of GPS improving the most. Topics affecting the performance of the multiscale approach are discussed in this paper, including the effect of control frequency on the well control problem. The parameter settings for GPS, PSO, and CMA-ES, within the multiscale approach, are considered.

智能井技术允许对井和生产过程进行远程控制，这使得确定最佳控制策略的问题成为及时而有价值的追求。每个控制步骤的大量油井率使优化问题变得困难，并且存在实现次优解决方案的高风险。此外，最佳的调整次数不是先验的。过于频繁地调整油井控制将增加不必要的油井管理和运营成本，而控制调整的次数过少可能不足以获得良好的产量。在本文中，我们探索了三种无导数算法的能力和一个多尺度正则化框架的功能，以在油藏的整个生命周期内进行井控优化。选择的无导数算法包括广义模式搜索（GPS），粒子群优化（PSO）和协方差矩阵适应进化策略（CMA-ES）。选择这些算法涵盖各种搜索策略（全局/本地搜索，随机/确定性搜索），是因为它们具有鲁棒性和易于并行化的特性。尽管这些算法已在油藏开发优化文献中得到广泛使用，但我们还是第一次全面探讨了这些算法在多尺度正则化框架中进行混合时的性能。从合理数量的控制步骤开始，随后在优化过程中细化控制间隔。实验结果表明，CMA-ES在解决小规模和大规模问题中，在三种算法中表现最佳。当与多尺度正则化方法混合使用时，寻找最佳解决方案的能力得到了进一步增强，其中GPS的性能得到了最大的改善。本文讨论了影响多尺度方法性能的主题，包括控制频率对井控问题的影响。在多尺度方法中，考虑了GPS，PSO和CMA-ES的参数设置。