Dag Ljungquist

M. Hotvedt, B. Grimstad, D. Ljungquist et al.

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.

Mathilde Hotvedt, Bjarne Grimstad, Dag Ljungquist et al.

A virtual flow meter (VFM) enables continuous prediction of flow rates in petroleum production systems. The predicted flow rates may aid the daily control and optimization of a petroleum asset. Gray-box modeling is an approach that combines mechanistic and data-driven modeling. The objective is to create a computationally feasible VFM for use in real-time applications, with high prediction accuracy and scientifically consistent behavior. This article investigates five different gray-box model types in an industrial case study using real, historical production data from 10 petroleum wells, spanning at most four years of production. The results are diverse with an oil flow rate prediction error in the range of 1.8%-40.6%. Further, the study casts light upon the nontrivial task of balancing learning from both physics and data. Consequently, providing general recommendations towards the suitability of different hybrid models is challenging. Nevertheless, the results are promising and indicate that gray-box VFMs may reduce the prediction error of a mechanistic VFM while remaining scientifically consistent. The findings motivate further experimentation with gray-box VFM models and suggest several future research directions to improve upon the performance and scientific consistency.