Interpretable Scientific Machine Learning Approach for Correcting Phenomenological Models: Methodology Validation on an ESP Prototype

The electric submersible pump (ESP) is widely used in oil extraction processes and is recognized for its effectiveness as an artificial lift technique in the petroleum sector. Developing and improving predictive models for these systems can contribute to optimizing operational efficiency and maximizing oil production. These improvements facilitate ESP performance control and monitoring, potentially making the extraction process more economically and environmentally sustainable. This paper aims to develop a framework for creating an interpretable corrective model for the ESP phenomenological model using experimental data. Neural networks were employed to analyze the complexities and nonlinearities of the processes, followed by symbolic regression to generate a simplified and interpretable equation to improve the model’s predictive capacity. An uncertainty assessment of model parameters was performed using Markov chain Monte Carlo (MCMC) and propagated to the model prediction. Additionally, a regression model was created directly from the process data for comparison purposes. The comparative analysis indicated that the approach incorporating neural networks to generate synthetic data, followed by symbolic regression, improved the model’s ability to predict key variables such as intake pressure, choke pressure, and production flow.