Multivariate Time-Series Methods with Uncertainty Estimation for Correcting Physics-Based Model: Comparisons and Generalization for Industrial Drilling Process

This study employs a hybrid methodology, integrating data-driven and physics-based models to refine the latter's predictions. Referred to as Hybrid Analysis and Modeling (HAM), this approach combines a physics-based model, solving multi-phase flow equations for cuttings transport, with advanced machine learning models to enhance predictive accuracy in hole cleaning operations. Previous research demonstrated two HAM methodologies (an intrusive and a non-intrusive approach) for uni-variate time-series data, improving predictions of the physics-based model. In this study, we develop multi-variate approaches with uncertainty estimation, comparing four machine learning models, ranging from simple linear methods to the advanced non-linear methods, i.e.: ARIMAX, XGBoost, Transformer, and Long-Short Term Memory (LSTM) models. Uncertainty estimates are also plotted to elucidate each model's capacity to refine the physics-based model, accounting for epistemic uncertainty arising from knowledge gaps in the machine learning model and/or aleatoric uncertainty inherent in the data. Applied to an industrial drilling process, the hybrid approach facilitates accurate prediction of a key variable, equivalent circulating density, essential for process monitoring. In the current study, the LSTM model outperforms others by avoiding overfitting on unseen test datasets. This work illustrates the potential of the presented hybrid methodology to generalize and enhance predictions across all depths and time-steps during drilling operations, contingent upon the availability of more measurement datasets for training/testing. Thus, HAM methodology holds promise for refining physics-based models in various process industry operations for correcting physics-based models in other process industry operations.