Empirical model for predicting slug-pseudo slug and slug-churn transitions of upward air/water flow

A pseudo-slug flow is a type of intermittent flow characterized by short, frothy, chaotic slugs that have a structure velocity lower than the mixture velocity and are not fully formed. It is essential to accurately estimate the transition from conventional slug (SL) flow to pseudo-slug (PSL) flow, and from SL to churn (CH), by precisely predicting the pressure losses. Recent research has showed that PSL and CH flows comprise a significant portion of the conventional flow pattern maps. This is particularly true in wellbores and pipelines with highly deviated large-diameter gas-condensate wellbores and pipelines. Several theoretical and experimental works studied the behavior of PSL and CH flows; however, few models have been suggested to predict SL/CH and are very limited for SL/PSL transitions. Based on the experimental data, an empirical model was suggested to predict the SL/PSL/CH transition for air/water upward inclined flow. The proposed model correlates the modified gas Froude number with the inclination angle and modified liquid Froude number. The inclined flow dataset includes 125 data points of SL, PSL, and CH covering angle of inclination (θ) from 2^o to 89.4 ^°with a relatively large pipe diameter (D) of 0.1016 m. The developed model accurately predicted all data and captured the expected influence of inclination angle, pipe diameter, and gas density on the SL/PSL/CH transition. The developed model was tested favorably against three datasets (681 points) collected from twelve independent studies: 549 air/water two-phase points, 65 air/viscous liquid two-phase points, and 67 air/oil/water three-phase points.