Global sensitivity analysis for phosphate slurry flow in pipelines using generalized polynomial chaos

Slurry transportation via pipelines has garnered growing attention across various industries worldwide, thanks to its efficiency and environmental friendliness. It has emerged as a vital tool for conveying significant volumes of raw phosphate material from extraction points to industrial plants, where it is processed into fertilizers. Yet, optimal and secure pipeline operations necessitate the careful calibration of several physical parameters and their interplay to minimize energy losses. A thorough exploration of the flow pressure drop and the various factors that influence it constitutes a crucial step in attaining this goal. The computational fluid dynamics techniques required to simulate three-dimensional slurry pipe flows pose formidable challenges, primarily due to their high computational costs. Furthermore, numerical solutions for slurry flows are frequently subject to uncertainties arising from the initial and boundary conditions in the mathematical models employed. In this study, we propose the use of polynomial chaos expansions to estimate the uncertainty inherent in the desired slurry flow and perform a sensitivity analysis of flow energy efficiency. In this framework, five parameters are considered as random variables with a given probability distribution over a prescribed range of investigation. The uncertainty is then propagated through the two-phase flow model to statistically quantify their effect on the results. Our findings reveal that variations in slurry velocity and particle size play a pivotal role in determining energy efficiency. Therefore, controlling these factors represents a critical step in ensuring the efficient and safe transportation of slurry through pipelines.