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Combining Physics and Machine Learning to Understand Multiphase Transient Flow

Hybrid models combining physics and machine learning provide the most accurate Virtual Flow Metering (VFM). Equally significant, a hybrid approach is more robust and scalable than its constituent parts on their own.  

In recent years, artificial intelligence or machine learning has been the most popular technology to unlock the full potential of data across industries. Traditional physics-based modeling is less hyped in the era of digital transformation.  

To solve complex science and engineering problems such as multiphase transient flow however, we need novel methodologies that are able to integrate traditional physics-based modeling with state-of-the-art machine learning techniques. But why? 

Physics-based vs Machine Learning VFMs 

The physics-based approach to virtual flow metering relates to multiphase flow simulations. Physics-based modeling builds on well understood concepts in, e.g., thermodynamics, fluid dynamics, fluid modeling and optimization techniques. If the physics model is accurate, this approach is often a good solution. Yet, it requires deep domain knowledge as well as accurate PVT data and may incur significant computational cost. 

Machine Learning (ML) VFM systems are based on learning algorithms which find relationships between sensor data and output variables in a training dataset. The ML approach does not require deep knowledge about physics, but rather a good understanding of the learning algorithms and statistics. Yet, small datasets or changes in operational conditions limit the suitability of this approach.    

Comparison Physics-based vs Machine-learning models
Comparison of Physics-based and Machine-Learning VFMs [1]

Utilizing Machine Learning to improve physics-based modeling 

Machine learning methods are designed to exploit large datasets, reduce complexity and find new features in data. This is why there has been an explosive growth of machine learning applications in the high energy physics community over the last ten years [2]. 

By applying machine learning on real-life data and simulations from physics models, we can create ML models which mimic the physics and are faster and easier to deploy. Machine learning models can also be used to generate synthetic data, such as data tagging or missing sensors, to improve the robustness and accuracy of physics models. 

Incorporate Physics into Machine Learning 

The natural choice to incorporate physics into machine learning is referred to as Feature Engineering, that is to create physically meaningful features instead of using individual measurements directly. Needless to say, this approach requires both domain and machine learning knowledge. 

This is where Turbulent Flux comes in! We use physics models to create high level features by combining raw measurements with external static data, such as PVT and geometry data. These features will not only improve the accuracy of the machine learning model, but also make it more transparent and comprehensive. 

Diagram of Hybrid Physics-ML model

Hybrid Physics-ML models at Turbulent Flux 

There are multiple ways to construct a hybrid model. For example, we can combine the physics-based and ML models by weighting the predictions. The weights depend on the context and must be validated. 

We use ML models to replace or improve one or more components of a larger physics-based model. One example is where our FLUX VFM uses ML models to predict the water and oil ratio and the physics-based model to predict the gas and total liquid flow rates. Combining both ML and physics-based predictions, an average full-scale error of less than 4% was obtained for all phase flow rates. 

Merging the two principles of physics and machine learning combines the best of the two worlds, resulting in higher accuracy, better scalability and cost efficiency. In short, hybrid models will play an invaluable role in the future of modeling in the industry. 

[1] Timur Bikmukhametov, Johannes Jäschke. First Principles and Machine Learning Virtual Flow Metering: A Literature Review. Journal of Petroleum Science and Engineering, Volume 184, January 2020 

[2] Kim Albertsson et al. Machine Learning in High Energy Physics Community White Paper. Journal of Physics: Conference Series, Volume 1085, Issue 2 (

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