Machine-Learning-Assisted Closed-Loop Reservoir Management Using Echo State Network for Mature Fields under Waterflood

Closed-loop reservoir management (CLRM) consists of continuous application of history matching and optimization of modelpredictive 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.