Closed-loop reservoir management (CLRM) consists of continuous application of history matching and optimization of model-predictive control to maximize production or reservoir net present value (NPV) in any given period. Traditional field-scale implementation of CLRM by using a large number of reservoir models, in particular when uncertainty is accounted for, is computationally impractical. This presented machine-learning-assisted workflow uses the echo state network (ESN) coupled with an empirical water fractional flow relationship as a proxy to replace time-consuming simulations and improve the computational efficiency of the CLRM. The ESN, under the paradigm of reservoir computing, provides a specific architecture and supervised learning principle for recurrent neural networks (RNNs). ESNs, with randomly generated and invariant input weights and recurrent weights, greatly minimize the computational load and solve potential problems during typical backpropagation through time in traditional RNNs while it still obtains the benefits of RNNs to memorize temporal dependencies. Also, the linear readout layer makes the training much faster using analytical ridge regression. Field-level well control and production-response data are fed into the workflow to obtain a trained ESN and fitted fractional-flow relationship, which will represent/reproduce the dynamics of the reservoir under various well-control scenarios. Further production optimization is directly applied to the matched models to maximize reservoir NPV. The optimized well-control scenario is applied, and further observation is obtained to update the models. History matching and production optimization are performed again in a closed-loop fashion. The previously mentioned advantages make ESN a very powerful tool for CLRM, with both history matching and production optimization quickly accomplished, and make near-real-time CLRM possible. In this paper, two case studies will be presented to prove the effectiveness of the proposed workflow.

闭环油藏管理（CLRM）包括连续应用历史记录匹配和优化模型预测控制，以在任何给定时期内最大化产量或油藏净现值（NPV）。通过使用大量储层模型，特别是在考虑不确定性时，传统的现场规模实施CLRM在计算上是不切实际的。此提出的机器学习辅助工作流使用回声状态网络（ESN）和经验水分数流关系作为代理来代替耗时的模拟并提高CLRM的计算效率。在油藏计算范式下，ESN为递归神经网络（RNN）提供了特定的体系结构和监督学习原理。ESN，具有随机生成的且不变的输入权重和递归权重，极大地减少了计算负荷并解决了传统RNN在典型的反向传播过程中潜在的问题，同时仍获得了RNN的优点来记忆时间依赖性。而且，线性读出层使用解析岭回归来使训练更快。将现场水平的井控和生产响应数据输入到工作流程中，以获得训练有素的ESN和拟合的分流关系，这将代表/再现在各种井控方案下的储层动态。进一步的生产优化直接应用于匹配的模型，以最大化储层净现值。应用优化的井控方案，并获得进一步的观察以更新模型。历史记录匹配和生产优化以闭环方式再次执行。前面提到的优点使ESN成为CLRM的非常强大的工具，可以快速完成历史记录匹配和生产优化，并使近实时CLRM成为可能。在本文中，将通过两个案例研究来证明所提出的工作流程的有效性。