Modeling pseudo-slugs liquid holdup in slightly upward inclined pipes

Pseudo-slug flow is a sub-regime of intermittent flow that is characterized by short, undeveloped, frothy chaotic slugs, with a translational velocity less than the mixture velocity of the fluids. The liquid in the pseudo-slug body is insufficient to reach the upper pipe wall, resulting in large waves with entrained gas bubbles at the bottom part of the pseudo-slug body. This flow phenomenon in the pseudo-slug body is different from the well-known physical model of the conventional unit-cell slug flow. Although pseudo-slug flow occupies a significant area under the intermittent flow region of flow pattern map, theoretical modeling of its characteristics is still limited and scarce in the literature. The objective of this study is to develop a plausible physical model of liquid holdup in pseudo-slugs based on the observed physical and hydrodynamic behavior, based on which a dimensional predictive regression model is developed. This paper discusses liquid and gas entrainment mechanisms within the pseudo-slug body based on experimental observation. It shows that the pseudo-slug body can be divided into two regions, liquid film (wave) with entrained gas bubbles at the bottom, and gas core with entrained liquid droplets at the top. Experimental results show that the proposed dimensionless groups, namely, Stokes, Slippage, and Poiseuille numbers, are strongly correlated to pseudo-slug body liquid holdup experimental data and are capable of describing the experimentally observed physical behavior. A linearized regression model is developed to combine the liquid holdup proportionally in both regions of the pseudo-slug body and correlate them to the experimentally measured total pseudoslug liquid holdup using a wire-mesh sensor. A validation study of the proposed model with experimental data shows good agreement, outperforming all other existing slug liquid holdup correlations.