Empirical Correlations for Prediction Slug Liquid Holdup on Slug-Pseudo-Slug and Slug-Churn Transitions in Vertical and Inclined Two-Phase Flow

Most of the existing slug (SL) to churn (CH) or SL to pseudo-slug (PS) transition models (empirical and mechanistic) account for the effect of the SL liquid holdup (HLS). For simplicity, some of these models assume a constant value of HLS in SL/CH and SL/PS flow transitions, leading to a straightforward solution. Other models correlate HLS with different flow variables, resulting in an iterative solution for predicting these transitions. Using an experimental database collected from the open literature, two empirical correlations for prediction HLS at the SL/PS and SL/CH transitions (HLST) are proposed in this study. This database is composed of 1,029 data points collected in vertical, inclined, and horizontal configurations. The first correlation is developed for medium to high liquid viscosity two-phase flow (μL > 0.01 Pa·s), whereas the second one is developed for low liquid viscosity flow (μL ≤ 0.01 Pa·s). Both correlations are shown to be a function of superficial liquid velocity (VSL), liquid viscosity (μL), and pipe inclination angle (θ). The proposed correlations in a combination with the HLS model of Abdul-Majeed and Al-Mashat (2019) have been used to predict SL/PS and SL/CH transitions, and very satisfactory results were obtained. Furthermore, the SL/CH model of Brauner and Barnea (1986) is modified by using the proposed HLST correlations, instead of using a constant value. The modification results in a significant improvement in the prediction of SL/CH and SL/PS transitions and fixes the incorrect decrease of superficial gas velocity (VSG) with increasing VSL. The modified model follows the expected increase of VSG for high VSL, shown by the published observations. The proposed combinations are compared with the existing transition models and show superior performance among all models when tested against 357 measured data from independent studies.