Uncertainty of Sand Particle Erosion Measurements in Two-Phase Fluid Flow Conditions: A Monte Carlo and Machine Learning Approach

Abstract Pipeline solid particle erosion depends on numerous independent variables and fluid flow parameters, making measurements or predictions inherently uncertain. Estimating these uncertainties is challenging due to a limited understanding of variable interactions. Because erosion is a major risk in many industries, accurately estimating uncertainties is vital for both safety and economic viability. This study examines uncertainties in previously gathered erosion measurements under two-phase flow conditions with sand in pipe elbows. The database includes ultrasonic measurements of gas–liquid–sand cases with vertical upward flows through standard elbows. Particle sizes range from 20 to 300 μm, and pipe diameters are 0.0762 and 0.1016 m. Measurements span multiple two-phase flow regimes, including annular, churn, and annular-mist flows. Initial uncertainty bounds were estimated using analytical correlations, yielding upper bounds of 1.45–2.78 times the measurements and lower bounds of 0.18–0.78 times the measurements. Subsequently, machine learning (ML) algorithms, including random forests, LightGBM, XGBoost, and Gaussian processes, were trained on the erosion database. These algorithms used gas and liquid velocities, pipe diameters, and particle sizes as independent variables, along with the initially estimated bounds. Finally, Monte Carlo (MC) simulations examined how uncertainties in these parameters affect the overall uncertainty. The MC-based bounds refined the original estimates, providing an updated range of 1.5–4.00 times the measurements for the upper bound and 0.04–0.78 times for the lower bound. This integrated approach provides a more accurate representation of pipeline erosion uncertainty, improving flow assurance across multiple industries.