Data-driven proxy model for waterflood performance prediction and optimization using Echo State Network with Teacher Forcing in mature fields

Abstract

Waterflood has been widely applied across the world as the most important secondary recovery process to improve reservoir performance. The schemes applied to waterflood projects involve key decision-making which aims to maximize the net present value (NPV) for a given period, improve recovery and sweep efficiency, maintain reservoir pressure, reduce water production, and avoid water recycling. Traditionally, the preferred approach to estimate the future performance of any given waterflood project is through the numerical reservoir simulation. However, despite the great power and intuition associated with the simulation models, sometimes this potential is unachievable due to massive computational requirements. Also, in some other cases, there may exist no simulation model to begin with. To tackle these problems, data-driven proxy models are proposed. In this research, we propose a novel machine-learning-based proxy model for waterflood performance prediction and further apply it for production optimization purpose to obtain the optimal future well control. The data-driven model is realized using the Echo State Network (ESN) under the paradigm of “Reservoir Computing” (RC). Compared with traditional ESNs, this specific methodology includes a feedback loop from the output into the high dimensional “reservoir” to achieve improved prediction results for separated phase production rates. Teacher Forcing (TF) technique is used for easier incorporation of the feedback information without introducing additional recurrent loops during the training process. Furthermore, training ESN proxy models utilizes Ridge Regression, thus all calculations within have analytical solutions that guarantee much improved speed when evaluating forward model-runs, which further lowers the computational demand during the optimization process. The proposed workflow is typically more suitable for mature fields since reliable production data after breakthrough from each producer could greatly improve the training process, and it can be used under the circumstance where no reservoir model has been established. In this research, we present two test examples where we apply ESN to learn the reservoir simulation results of waterflood and further perform open-loop optimization on each of them.