Bayesian Neural Networks for Virtual Flow Metering: An Empirical Study

Abstract

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. The encouraging results combined with advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). We contribute to this development by presenting a probabilistic VFM based on a Bayesian neural network. We consider homoscedastic and heteroscedastic measurement noise, and show how to train the models using maximum a posteriori estimation and variational inference. We study the methods by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where we achieve an average error of 5-6% and 9-13% for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. The difference in prediction performance and uncertainty on historical and future data is explored in detail, and the findings motivate the development of alternative strategies for data-driven VFM.

On gray-box modeling for virtual flow metering

“…This may lead to a biased estimate of the model's predictive performance in future process conditions. In fact, in Grimstad et al (2021), data-driven virtual flow meters were developed for a diverse set of 60 wells from five petroleum assets and it was shown that data-driven VFMs may yield adequate predictions of historical flow rates but not necessarily for future flow rates. As a result, Grimstad et al (2021) motivates for use of other approaches, such as gray-box VFMs.…”