Modeling a unified slug liquid holdup correlation based on a comprehensive analysis of entering bubble sharpness

Liquid-gas two-phase slug flow is the most complex flow pattern encountered in pipelines, wellbores, and cooling systems in various energy systems. Accurately predicting the slug liquid holdup (H_LLS) is vital for the system design and operation because it is a crucial characteristic of slug flow that is closely related to the average liquid holdup and pressure drop. Most existing H_LLS models have limited applicability due to a lack of a physical basis for slug aeration mechanisms. This study proposes a new dimensionless number SP to estimate the sharpness of entering bubbles at the liquid slug front and semi-empirically correlates SP to H_LLS data, leading to the development of a unified H_LLS correlation. We formulate this dimensionless number and its relations using 880 experimental H_LLS data points, and the validity of the unified H_LLS correlation is tested using 1050 independent data points. The developed semi-empirical model closely agrees with experimental data obtained by varying the fluid properties (0.03 mPa·s ≤ µ_L ≤ 966 mPa·s, 0.027 N/m ≤ σ ≤ 0.07 N/m) and operating conditions, such as the pipe geometry (1 in. ≤ pipe internal diameter ≤ 3 in., –10° ≤ θ ≤ +90°).