CO₂ water-alternating-gas (WAG) injection is an enhanced oil recovery method designed to improve sweep efficiency during CO₂ injection with the injected water to control the mobility of CO₂ and to stabilize the gas front. Optimization of CO₂ -WAG injection is widely regarded as a viable technique for controlling the CO₂ and oil miscible process. Poor recovery from CO₂ -WAG injection can be caused by inappropriately designed WAG parameters. In previous study (Chen and Reynolds, 2016), we proposed an algorithm to optimize the well controls which maximize the life-cycle net-present-value (NPV). However, the effect of injection half-cycle lengths for each injector on oil recovery or NPV has not been well investigated. In this paper, an optimization framework based on augmented Lagrangian method and the newly developed stochastic-simplex-approximate-gradient (StoSAG) algorithm is proposed to explore the possibility of simultaneous optimization of the WAG half-cycle lengths together with the well controls. The proposed framework is demonstrated with three reservoir examples.

CO ₂水交替气（WAG）注入是一种改进的采油方法，旨在通过注入水来提高CO ₂注入过程中的吹扫效率，以控制CO ₂的迁移率并稳定气体前沿。优化CO ₂ -WAG注入被认为是控制CO ₂和油混溶过程的可行技术。CO ₂回收率低-WAG注入可能由设计不当的WAG参数引起。在之前的研究中（Chen and Reynolds，2016），我们提出了一种优化井控的算法，该算法可以最大化生命周期的净现值（NPV）。但是，尚未很好地研究每个喷射器的喷射半周期长度对油采收率或NPV的影响。本文提出了一种基于增强拉格朗日方法和最新开发的随机-简单-近似-梯度（StoSAG）算法的优化框架，以探讨同时优化WAG半循环长度和井控的可能性。提出的框架通过三个储层实例进行了演示。