When is gray-box modeling advantageous for virtual flow metering?

TL;DR

This paper investigates when gray-box modeling, combining physics and machine learning, outperforms purely physics-based or data-driven models in virtual flow metering, especially under process mismatch, limited data, and nonstationary conditions.

Contribution

It provides a systematic analysis of scenarios where gray-box models are advantageous, demonstrating their benefits and limitations through synthetic data experiments.

Findings

Gray-box models outperform physics-based models with process-model mismatch.

Gray-box models improve accuracy over data-driven models with limited data.

Gray-box and data-driven models are similarly affected by noisy measurements.

Abstract

Integration of physics and machine learning in virtual flow metering applications is known as gray-box modeling. The combination is believed to enhance multiphase flow rate predictions. However, the superiority of gray-box models is yet to be demonstrated in the literature. This article examines scenarios where a gray-box model is expected to outperform physics-based and data-driven models. The experiments are conducted with synthetic data where properties of the underlying data generating process are known and controlled. The results show that a gray-box model yields increased prediction accuracy over a physics-based model in the presence of process-model mismatch. They also show improvements over a data-driven model when the amount of available data is small. On the other hand, gray-box and data-driven models are similarly influenced by noisy measurements. Lastly, the results indicate that a gray-box approach may be advantageous in nonstationary process conditions. Unfortunately, choosing the best model prior to training is challenging, and overhead on model development is unavoidable.