Flow assurance

Modeling Liquid Holdup in Pseudoslugs

The complete paper develops a plausible physical model of the experimentally observed pseudoslug liquid-holdup phenomenon and models physical and hydrodynamic behavior using a dimensional regression modeling approach.


Pseudoslug flow does not comply with the basic characteristics of conventional unit-cell slug flow. The liquid in the pseudoslug body is insufficient to reach the upper part of the pipe wall, resulting in only a large wave with entrained gas bubbles at the bottom part of the pseudoslug body. The pseudoslug body can be divided into two regions, liquid film (wave) with entrained gas bubbles at the bottom and gas core with entrained liquid droplets. The complete paper develops a plausible physical model of the experimentally observed pseudoslug liquid-holdup phenomenon and models physical and hydrodynamic behavior using a dimensional regression modeling approach.


Pseudoslug flow has been named differently in early studies because of its ambiguous flow behavior, while the term “pseudoslug” has been adopted widely in recent studies.

Pseudoslug flow is a subregime of intermittent flow that is characterized by short, undeveloped, frothy chaotic slugs, with translational velocity less than the mixture velocity of the fluids. It is a coherent flow pattern that occurs between conventional slug and segregated flow at certain flowing conditions. In pipelines where multiphase flow takes place, this flow pattern cannot be avoided. However, only limited studies exist on pseudoslug flow in general and on pseudoslug-characteristic parameters, specifically, such as pseudoslug-body liquid holdup. Most previous predictive methods overpredict pseudoslug-body liquid holdup, which is expected because the pseudoslug-body liquid holdup is smaller than slug-body liquid holdup because of the contiguous gas core.

This study fills a gap in the literature related to predicting pseudoslug liquid holdup using an experimental database of air/water in 0.076-m inner-diameter pipe with inclination angle ranging from 2° to 20° using a wire-mesh sensor as the main instrument to measure pseudoslug liquid holdup.

Entrainment Mechanism Within the Pseudoslug Body

Bubble generation and entrainment mechanisms in the pseudoslug body are different from those described in the unit-cell slug-flow model. The pseudoslug body consists of two main regions, a continuous gas core with entrained liquid droplets and a continuous liquid film with entrained gas bubbles, each governed by different entrainment mechanisms.

A significant difference in the slug-aeration mechanism is observed from that of conventional slug flow. Researchers have theorized that the slug-aeration process includes bubble generation at the slug front, bubble fragmentation in the mixing zone, bubble transportation to the developed slug body, and bubble shedding and carry-­under in the film region.

In this study, high-speed videos were analyzed to develop understanding of liquid and gas behavior and their entrainment mechanisms in the pseudoslug body. To facilitate physical modeling, the slug body is divided into two regions, the top gas core region and the bottom liquid-film region.

Liquid Entrainment in the Continuous Gas Core. Droplet atomization occurs at the crest of the liquid wave when it is sufficiently high to increase the local gas velocity above the wave, enabling breakage of the liquid wave crest. The atomized liquid phase is then entrained into the gas core.

Liquid droplets observed in front of the pseudoslug body demonstrate the continuous gas core within the pseudoslug body. Larger droplets travel a shorter distance in the axial direction before they redeposit into the continuous liquid-film region of the pseudoslug body. In addition, smaller droplets are deposited on the pipe wall.

Because pseudoslug velocity is less than the flow-mixture velocity, significant slippage takes place in the slug body. It is postulated that slippage is the predominant parameter that governs slug liquid holdup in the core region of the slug body. To provide experimental evidence of the existence of slippage, previous wire-mesh sensor measurements were further processed to obtain the gas and liquid velocities in the pseudoslug body. Using the mass-conservation equations of gas and liquid in the slug unit and the measured parameters, liquid and gas velocities in the pseudoslug body were determined. The liquid-film length and unit length can be determined from the measured pseudoslug frequency, and the superficial gas and liquid velocities within the pseudoslug body also can be calculated.

Sudden reduction in slippage indicates the occurrence of a conventional slug body in which no slippage exists. When structure velocity begins to deviate from slug translational-velocity correlation, the flow changes from conventional slug-flow-dominated to ­pseudoslug-flow-dominated. As the mixture velocity increases, slippage in the pseudoslug body decreases. At low mixture, velocity slippage increases with the decrease of inclination angle. This behavior is attributed to the continuous liquid-level increase in the slug body caused by gravity, reducing the gas flowing cross-sectional area and increasing gas velocity in the gas core. Consequently, flow is homogenized in the gas core.

Gas Entrainment and Shedding in the Continuous Liquid-Film Region. Experimental visualization of pseudoslug flow using a high-speed camera revealed three gas-entrainment mechanisms.

Gas Entrainment by Liquid Droplet Plunging Jet in the Film Region. The entrained liquid droplets in the gas core flow past the slug body, plunging into the preceding liquid film. This droplet behavior is attributed to the gas blowing through the slug body, resulting in high-velocity projectiles as liquid droplets. As these liquid droplets plunge into the liquid film preceding the pseudoslug body, they entrain gas bubbles into the film region. The gas bubbles are then picked up by the liquid-film zone in the pseudoslug body.

Gas Entrainment by Bubble Encapsulation and Droplet Plunging Jet in the Film Region of the Pseudoslug Body. Experimental observations show that pseudoslugs are undeveloped slugs, where the slug body is short with multiple vortices caused by the interfacial waves. Liquid vortices and gas circulation play a major role in entraining gas bubbles from the gas core into the continuous liquid-film zone in the pseudoslug body. As entrained liquid droplets in the gas core plunge into the liquid film, gas bubbles are entrained.

Gas Entrainment by Shear-Stress Mechanism. Gas bubbles are entrained under this mechanism because of the relative velocity between the continuous liquid zone in the pseudoslug body and the preceding liquid film in the leading Taylor bubble. However, experimental evidence reveals that this is a secondary gas entrainment mechanism in pseudoslug flow.

Model Development

The authors propose an empirical model for pseudoslug-body liquid holdup using a dimensional regression modeling approach. Although it is evident that the two regions of the pseudoslug body are coupled and interdependent through their interface, in this stage of this study, their flow behaviors were modeled independently. Then, a multiple linear regression model was developed to combine the liquid holdup in both parts of the pseudoslug body proportionally and correlate them to the total pseudoslug body. This section of the complete paper describes the modeling of each liquid holdup component, followed by the multiple linear regression model.

Model Evaluation

Fig. 1 illustrates the comparison between experimental measured pseudoslug body liquid holdup and the model prediction, showing good agreement. However, further improvements are required to account for the inclination-angle effects. When the experimental data are also compared with other available slug-body liquid-holdup models, the current model improves the prediction by reducing the average absolute error to 10.46%.

Fig. 1—Comparison of predicted liquid holdup in the pseudoslug body from a new correlation with measurements from the current study. HLPS=liquid holdup within pseudoslug body; HLPS=liquid volumetric fraction in the continuous liquid-film region.


A model is proposed for pseudoslug-body liquid holdup using a dimensional regression modeling approach. Previous experimental results show that the proposed dimensionless groups are strongly correlated to pseudoslug-body liquid-holdup experimental data. On the basis of physical and hydrodynamic behavior, the pseudoslug body is divided into two regions, liquid film (wave) with entrained gas bubbles at the bottom and gas core with entrained liquid droplets. The liquid holdups within these two regions were modeled using the dimensionless group first. A validation study of the proposed model using previous experimental data shows good agreement, outperforming all other existing slug liquid-holdup correlations.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19769, “Modeling Liquid Holdups in Pseudoslugs,” by Yilin Fan, SPE, Colorado School of Mines; Eissa Al-Safran, SPE, Kuwait University; and Eduardo Pereyra, SPE, The University of Tulsa, et al., prepared for the 2020 International Petroleum Technology Conference, Dhahran, Saudi Arabia, 13–15 January. The paper has not been peer reviewed. Copyright 2020 International Petroleum Technology Conference. Reproduced by permission.