Development of a machine learning-based symbolic regression model for mixing time in large petroleum storage tanks

Abstract

This study investigates the use of Symbolic Regression, a machine learning technique, to develop a model for mixing time in large petroleum storage tanks stirred by side-entry impellers. Studies involving the mixing time for side-entry mixers are relatively scarce when compared to research on mixing time models for top-mounted impellers. This limited availability of predictive models for side-entry configurations highlights the relevance of this study and makes them an excellent case for applying Symbolic Regression in stirred tank modeling. Symbolic Regression was applied to mixing time data obtained for a large petroleum storage vessel. The study examines how key parameters, including oil viscosity, tank diameter, tank height, impeller inclination angle, and the number of impellers affect the mixing time in these large tanks. The data used for model development was generated via CFD simulations, with mixing time estimated through numerical analysis. To ensure reliable CFD results, a Grid Convergence Index (GCI) study was conducted, maintaining the GCI for the average fluid velocity within the tank below 5%. In addition, this work introduces advanced statistical tools for predictive modeling, which can be valuable not only for estimating mixing time but also for broader applications in fluid dynamics. The analysis includes Spearman rank correlation, analysis of variance (ANOVA), and Symbolic Regression. The proposed mixing time equation was developed using machine learning techniques trained on the CFD-generated data. The results indicate that the number of impellers, tank diameter, and tank height have the most significant impact. In contrast, within the investigated parameters range, oil viscosity and impeller inclination angle have a comparatively smaller statistical influence on the mixing time.