# Sub-regimes of horizontal gas-liquid intermittent flow: State-of-the-art and future challenges

Abderraouf Arabi, Youcef Zenati, Jack Legrand, El-Khider Si-Ahmed

► To cite this version:

Abderraouf Arabi, Youcef Zenati, Jack Legrand, El-Khider Si-Ahmed. Sub-regimes of horizontal gas-liquid intermittent flow: State-of-the-art and future challenges. Experimental Thermal and Fluid Science, 2024, 160, pp.111281. 10.1016/j.expthermflusci.2024.111281. hal-05168985

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# Sub-regimes of horizontal gas-liquid intermittent flow: State-of-the-art and future challenges

Abderraouf Arabi<sup>a,b,1,*</sup>, Youcef Zenati<sup>b</sup>, Jack Legrand<sup>c</sup>, El-Khider Si-Ahmed<sup>c</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

### Keywords:

Horizontal gas-liquid two-phase flow

Intermittent flow

Sub-regimes

Literature review

Flow maps

## ABSTRACT

Based on the shape of the interface elongated bubble/liquid slugs and the liquid slugs' aeration, the horizontal intermittent flow can be divided into three sub-regimes including plug (PG), Less Aerated Slug (LAS) and Highly Aerated Slug (HAS) flows. These flow sub-regimes were observed from experiments performed using air-water mixture and small pipe diameters. This paper presents an analysis of the results obtained with the aim of constituting the state-of-the-art of this sub-regimes classification.

The critical review, of the current state of knowledge, has led to the conclusion that the subdivision of intermittent flow into sub-regimes may provide a better means of apprehending, understanding and advancing in the modelling of slug parameters, Interfacial Area Concentration, Pipeline Integrity Management, intermittent flow behavior across singularities, as well as for the development of more realistic mechanistic models. The acquired knowledge can be beneficial for petroleum and gas, nuclear and chemical engineering industries among others.

Finally, based on the presented state-of-the-art, some recommendations are given for future works using this approach. These reflection paths will allow improving our comprehension on intermittent flow, promoting the development of more robust models.

## 1. Introduction

Gas-liquid two-phase flows are encountered traditionally in oil and gas production and transportation, nuclear engineering, heat exchangers and geothermal industries [23,31,40,42,52,73,83]. The development of various applications such as Organic Rankine Cycle (ORC) systems [171], membrane distillation (MD) [56], capture and storage of carbon dioxide (CO₂) (CCS) [79] and the utilization of the CO₂ in several cooling devices [28,147] have increased the number applications of gas-liquid two-phase flow. However, such flow, due the complex interaction between compressible and incompressible phases, remains challenging for both academic and industrial communities. The

difficulties associated with two-phase flow modeling are reflected in getting adequate estimation of various important parameters such as pressure drop, void fraction and heat and mass transfer coefficients. This information is important for design purposes as well as to optimize and secure the industrial facilities' operations.

From a historical point of view, the interest in the prediction of hydrodynamic parameters started in the '40-50 s in the context to better control costs and risks for industrial companies. The first models and flow pattern maps developed were based on a purely empirical approach using experimental data obtained at the laboratory scale. As Brill and Arirachakaran [29] and Shippen and Bailey [149] explain, the '70 s saw the research community question the reliability of empirical models and flow maps. This period was called "The Awakening Years". Indeed, the

**Abbreviations:** CCS, Carbon Capture and Storage; CUCS, Combined Ultrasonic-Conductance Sensor; CECM, Constant Electricity Current Method; CFD, Computational Fluid Dynamics; CMFD, Computational Multi-phase Fluid Dynamics; FPGA, Field-programmable Gate Array; HAS, Highly Aerated Slug; IAC, Interfacial Area Concentration; ID, Inner diameter; LAS, Less Aerated Slug; LDV, Laser Doppler Velocimetry; MCS, Multi-Electrode Conductance; MD, Membrane Distillation; ORC, Organic Rankine Cycle; PG, Plug; PIM, Pipeline Integrity Management; PWR, Pressurized Water Nuclear Reactor; TUFFP, Tulsa University Fluid Flow Project; TUS, Transmission Ultrasonic Sensor.

E-mail address: abderraouf.arabi@urv.cat (A. Arabi).

<footnote><sup>a</sup> SONATRACH, Direction Centrale Recherche et Développement, Avenue 1<sup>er</sup> Novembre, 35000, Boumerdes, Algeria</footnote>

<footnote><sup>b</sup> University of Sciences and Technology Houari Boumediene USTHB, Physics' Faculty Laboratory of Theoretical and Applied Fluid Mechanics, LMFTA, BP 32 El Alia 16111 Bab Ezzouar, Algiers, Algeria</footnote>

<footnote><sup>c</sup> Nantes Université, ONIRIS, CNRS, GEPEA, UMR-6144, 37 Bd de l'université, BP406, 44602 Saint-Nazaire, France</footnote>

<footnote>* Corresponding author at: SONATRACH, Direction Centrale Recherche et Développement, Avenue 1er Novembre, 35000, Boumerdes, Algeria.</footnote>

<footnote n="1">¹ Presently at Departament d'Enginyeria Mecànica, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Spain.</footnote>
Nomenclature

<table><tr><td>D</td><td>Pipe diameter [m]</td></tr><tr><td>DET</td><td>Determinism rate [-]</td></tr><tr><td>dP/dL</td><td>Pressure drop [Pa.m<sup>-1</sup>]</td></tr><tr><td>f</td><td>Friction factor [-]</td></tr><tr><td>f<sub>s</sub></td><td>Slug frequency [Hz]</td></tr><tr><td>Fr</td><td>Froude number [-]</td></tr><tr><td>I<sub>i</sub></td><td>Interfacial transfer term [-]</td></tr><tr><td>G</td><td>Mass flux [kg.m<sup>2</sup>s<sup>-1</sup>]</td></tr><tr><td>g</td><td>Gravitational acceleration [m.s<sup>-2</sup>]</td></tr><tr><td>J</td><td>Superficial velocity [m.s<sup>-1</sup>]</td></tr><tr><td>Kur</td><td>Kurtosis [-]</td></tr><tr><td>L<sub>s</sub></td><td>Slug length [m]</td></tr><tr><td>Ṁ</td><td>Mass flux [kg.m<sup>-3</sup>]</td></tr><tr><td>N<sub>f</sub></td><td>Inverse viscosity number [-]</td></tr><tr><td>q</td><td>Driving flux</td></tr><tr><td>R</td><td>Pipe radius [m]</td></tr><tr><td>r</td><td>Radial position [m]</td></tr><tr><td>Re</td><td>Reynolds number [-]</td></tr><tr><td>REC</td><td>Recurrence rate [-]</td></tr><tr><td>Std</td><td>Standard deviation [Pa]</td></tr><tr><td>T</td><td>Dimensionless number [-]</td></tr><tr><td>TT</td><td>Trapping time [-]</td></tr><tr><td>u'u'</td><td>Reynolds stress[m<sup>2</sup>.s<sup>-2</sup>]</td></tr></table>

<table><tr><td>V</td><td>Velocity [m.s<sup>-1</sup>]</td></tr><tr><td>V<sub>L, mean</sub></td><td>Mean liquid velocity [m.s<sup>-1</sup>]</td></tr><tr><td>V<sub>L, RMS</sub></td><td>Root mean square liquid velocity [m.s<sup>-1</sup>]</td></tr><tr><td>X</td><td>Lockhart-Martinelli parameter [-]</td></tr><tr><td>y<sub>b</sub></td><td>Radial position of elongated bubble head [m]</td></tr></table>

Greek letters

<table><tr><td>μ</td><td>Viscosity [Pa.s]</td></tr><tr><td>α<sub>i</sub></td><td>Interfacial area concentration [m<sup>-1</sup>]</td></tr><tr><td>α<sub>i1</sub></td><td>Group 1 bubbles interfacial area concentration [m<sup>-1</sup>]</td></tr><tr><td>α<sub>i2</sub></td><td>Group 2 bubbles interfacial area concentration [m<sup>-1</sup>]</td></tr><tr><td>η</td><td>Liquid holdup [-]</td></tr><tr><td>λ</td><td>Input phase fraction [-]</td></tr><tr><td>ρ</td><td>Density [kg.m<sup>-3</sup>]</td></tr><tr><td>σ</td><td>Aspect ratio [-]</td></tr></table>

Subscripts

<table><tr><td>1</td><td>Upstream</td></tr><tr><td>2</td><td>Downstream</td></tr><tr><td>G</td><td>Gas</td></tr><tr><td>L</td><td>Liquid</td></tr><tr><td>M</td><td>Mixture</td></tr><tr><td>mod</td><td>Modified</td></tr><tr><td>S</td><td>Superficial</td></tr></table>

appearance of the first predictive models that take into account both slip and the nature of the flow regime [25,129] prompted research to focus more on the fundamental aspect of flows. This decade saw the arrival of the first mechanistic or phenomenological models, based on the various physical phenomena occurring in each flow regime such as bubble coalescence, instabilities and phasic entrainment. Since the ‘80 s, the development of numerical solving methods and computing resources, notably with the revolutionary introduction of the PC, has provided more powerful tools for solving equations systems. These resources led to the emergence of the “Modeling Years” when complex models based on combined momentum equations and mechanistic models, incorporating fundamental physics were developed [149]. From this revolution, several commercial software packages have been developed for industry, we can cite OLGA, TACITE Ledaflo, Tulsa University Fluid Flow Project (TUFFP) Unified Model and PLAC used in the oil industry or TRACE, RELAP and APRIL employed in the field of nuclear thermal-hydraulics. In addition, the Computational Fluid Dynamics (CFD), or Computational Multi-Fluid Dynamics (CMFD) as recommended by Yadigaroglu [170], are increasingly used to simulate the hydrodynamics phenomena in 3D. This tool is still very useful to study complex multidimensional flows such as those found in production separators [24,91], slug catchers [133,136], manifolds [90] or gas-lift [105] in the oil and gas industry or in Pressurized Water Nuclear Reactor (PWR) [104].

The use of mechanistic models, since they take into account the physics of flows, and principally the flow regime [81], has increased the necessity to study gas-liquid flow experimentally on a laboratory-scale. By carrying out “controlled” experiments, we can visualize flows and make local measurements to understand the phenomena that occur in each regime, as well as the transitions between flow patterns, enabling us to build phenomenological models. The experimental data generated are also used to validate the models developed and the simulations obtained with CFD. The growing use of AI only reinforces the need for experimental data [179]. The models and flow maps developed for gas-liquid two-phase flow were also used as basis for other more complicate multiphase flow as gas-liquid-liquid flows [51,82,89,172], gas-liquid-solid flows [135,145,146] or gas-foam-liquid flows [11,36,46,66].

The intermittent flow is the most present regime in horizontal pipes, as shown by the majority of flow maps [70,95,98,103,111]. In this flow regime, elongated bubbles flow by intermittence over a liquid film and liquid slugs, which can be aerated [78]. This feature generates large fluctuations of flow parameters such as local pressure or void fraction generating vibrations in pipes, support of pipelines and phases separators [92], which can provoke resonance [87]. The high velocity of liquid slugs induces high wall shear stresses and high mass transfer [130]. These phenomena cause destruction of the protective inhibitor film, which doesn't work well for slug flow conditions [88]. This flow regime causes also time varying stresses in pipes inducing structural fatigue damage and failure [118]. The intermittent regime is considered as one of the major threats facing the pipeline industry [58]. For these reasons, care is taken to avoid the presence of this regime for some applications [4,14]. The intermittent nature of this regime makes it difficult to develop measuring instruments. For example, Zhai et al. [175] used only multi-electrode conductance (MCS) to measure the void fraction for stratified and wavy flows. While the authors coupled this instrument with transmission ultrasonic sensor (TUS), forming combined ultrasonic-conductance sensor (CUCS), to measure the same parameter for intermittent flow. The MCS and TUS were used for measuring the void fraction inside elongated bubble and liquid slugs, respectively. In addition, the multiphase flowmeters do not work well in the presence of intermittent flow [114,115].

The modelling of the intermittent flow remains also highly challenging, particularly because it is necessary to take into account some complicated phenomena such as the dynamic behavior of the interface, motion of a train of long bubbles, gas entrainment on the liquid slug, drift of small bubbles inside the liquid slugs and the statistical behavior of the slug length and frequency [59,117]. Added to these complex phenomena, the intermittent flow has a chaotic nature [60]. The literature is full of existing models for simulating intermittent flow behavior and estimating flow parameters [57,74,124,128,150,177]. These models are notably used in the petroleum industry to design pipeline transportation and slug catchers and for flow assurance issues. Therefore, efforts are continuing for advancing in the comprehension of this flow regime through experiments recourse [5,7,43,53,63,65,92,93,100-102,109,110,121,122,127,134,137,
<figure><img src="image_3.png" /><figcaption>Fig. 1. Flow regime map for the sub-regimes of the intermittent flow proposed by Thaker et Banerjee [155]. The schematic representation of each sub-regime is also depicted. Reprinted from Journal of Petroleum Science and Engineering, vol. 135, Jignesh Thaker, Jyotirmay Banerjee, Characterization of two-phase slug flow sub-regimes using flow visualization, page 566, Copyright © 2015, with permission from Elsevier.</figcaption></figure>

145,152,167,173,178].

As explained recently by Fan et al. [62] and Abdul-Majeed et al. [3], the pseudo slug was considered for a long time as a special case of the intermittent flow. The pseudo slugs are large waves, touching briefly the top of the pipe wall without blocking the entire pipe section area, according to Lin and Hanratty [107]. This behavior, in addition to the no applicability of mechanistic models, developed for the intermittent flow, for pseudo slug allowed considering it as a specific flow regime [62]. Consequently, the multiphase community has considered two types of intermittent flow, namely “conventional” intermittent flow and pseudo-slug flow [19]. On the other hand, the conventional intermittent has also subdivided into sub-regimes using different kind of classifications. For instance, Fan et al. [61] visually observed that at low gas superficial velocity, the liquid slugs are evolved from waves. The formation of liquid slugs is generated by more complex flow mechanisms for gas superficial velocity higher than 4 m/s. Woods and Hanratty [165] reported that the conventional intermittent flow can be divided into three sub-regimes according to the formation of liquid slugs. The authors used the distance from the inlet and the liquid height to identify the three sub-regimes. The observations were reported on a flow map using phasic superficial velocities as coordinates. Later, Dinaryanto et al. [54] reported by qualitative visualization of slug formation that there are three mechanisms behind the occurrence of the intermittent flow which are wave coalescences, wave growth and large disturbance waves mechanisms. The authors plotted the observed formation mechanisms in a flow map. The confrontation of the latter with the flow map proposed by Woods and Hanratty [165] showed the absence of any consensus between the two flow sub-regime classification.

Based on qualitative analysis of the elongated bubble/liquid slug interface shape and the aeration inside the liquid slugs for conventional intermittent flow, Thaker and Banerjee [155,156] proposed another approach to subdivide the intermittent flow into sub-regimes. Unlike the classification approaches of Fan et al. [61], Woods and Hanratty [165] and Dinaryanto et al. [54], the methodology of Thaker and Banerjee has been used by several research groups around the world. These experimental works are summarized in Appendix A. Noting that all these studies were done using pipe diameter less than 2' at atmospheric pressure with air-water mixture. In view of this background, some questions (possibly doubts) arise as to the usefulness of this classification: Have these works added values to our comprehension on the intermittent flow? If yes, what is the acquired knowledge? How can we evaluate this improvement? In other words: does the subdivision of the

intermittent flow into sub-regimes give an additional value on the current state-of-the-art about this flow regime?

The answer to these open questions is the motivation behind that drove us to carry out a review on the classification of this subdivision. In this paper, we present a detailed and critical review of the updating work carried out on intermittent flow sub-regimes aiming to capture the current “state-of-the-art” and to identify reflection paths. The presented state-of-the-art on acquired knowledge using this classification will be critically evaluated in order to measure its impact on the intermittent flow knowledge progress.

In order to be clear and easily understanding for the reader, the manuscript starts with a detailed description of the sub-regimes in Section 2. The physical mechanisms occurring in each flow sub-regime and the existing flow pattern maps will be discussed in Section 3 and 4, respectively. Section 5 is devoted to the different methods used to distinct and identify the sub-regimes. The constituted state-of-the-art is discussed separately for several areas in Sections 6 to 9. The main outcomes from this survey, in the form of recommendations for future works are presented in Section 10. The conclusions are summarized in Section 11.

## 2. Description of the sub-regimes

This section is devoted for the presentation and description of the different sub-regimes of the intermittent flow. We begin with a discussion of the various existing terminologies. Then, a detailed description of the three sub-regimes that are Plug, Less Aerated Slug and Highly Aerated Slug flows are given. Finally, we discuss “Slug and plug” flow.

### 2.1. Analogy between the different terminologies

Using an air-water mixture and a 25 mm ID pipe, Thaker and Banerjee [155] performed a series of visual observations covering a total of 406 experimental phasic flow conditions. Through the images obtained from a high-speed camera, the authors noted that the slug flow can be classified into five sub-regimes. The classification was made, as previously noted, by observing the elongated bubble/liquid slug interface and the gas bubbles inside the liquid slugs. These five sub-regimes are:

- onset of intermittent flow, where liquid slugs appeared episodically in a segregated flow,
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Examples of flow structures present in PG flow (a) liquid slug observed by Arabi et al. [15] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.424$ m/s and $V_{SG}=0.436$ m/s), Reprinted from Chemical Engineering Science, vol. 211, A. Arabi, Y. Salhi, Y. Zenati, E-K. Si-Ahmed, J. Legrand, On gas-liquid intermittent flow in a horizontal pipe: Influence of sub-regime on slug frequency, page 8, Copyright © 2019, with permission from Elsevier; (b) elongated bubble tail observed by Humami et al. [84] (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=0.31$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005-3, Copyright © 2018, with permission from AIP Publishing; (c) elongated bubble nose observed by Humami et al. [84] (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=0.31$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005-3, Copyright © 2018, with permission from AIP Publishing and (d) elongated bubble above liquid film observed by Arabi et al. [16] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.495$ m/s and $V_{SG}=0.436$ m/s). Reprinted from International Journal of Heat and Mass Transfer, vol. 181, Abderraouf Arabi, Yacine Salhi, Youcef Zenati, El-Khider Si Ahmed, Jack Legrand, A Discussion on the Relation Between the Intermittent Flow Sub-Regimes and the Frictional Pressure Drop, page 6, Copyright © 2021, with permission from Elsevier. Flow direction: from left to right.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Examples of flow structures present in LAS flow (a) liquid slug observed by Arabi et al. [15] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.424$ m/s and $V_{SG}=1.572$ m/s), Reprinted from Chemical Engineering Science, vol. 211, A. Arabi, Y. Salhi, Y. Zenati, E-K. Si-Ahmed, J. Legrand, On gas-liquid intermittent flow in a horizontal pipe: Influence of sub-regime on slug frequency, page 8, Copyright © 2019, with permission from Elsevier; (b) elongated bubble tail observed by Humami et al. (2018) (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=1.26$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005–4, Copyright © 2018, with permission from AIP Publishing; (c) elongated bubble nose observed by Humami et al. [84] (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=1.26$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005–4, Copyright © 2018, with permission from AIP Publishing; and (d) elongated bubble above liquid film observed by Arabi et al. [16] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.495$ m/s and $V_{SG}=1.572$ m/s), Reprinted from International Journal of Heat and Mass Transfer, vol. 181, Abderraouf Arabi, Yacine Salhi, Youcef Zenati, El-Khider Si Ahmed, Jack Legrand, A Discussion on the Relation Between the Intermittent Flow Sub-Regimes and the Frictional Pressure Drop, page 7, Copyright © 2021, with permission from Elsevier. Flow direction: from left to right.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Examples of flow structures present in HAS flow (a) liquid slug observed by Arabi et al. [15] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.424$ m/s and $V_{SG}=3.144$ m/s), Reprinted from Chemical Engineering Science, vol. 211, A. Arabi, Y. Salhi, Y. Zenati, E-K. Si-Ahmed, J. Legrand, On gas-liquid intermittent flow in a horizontal pipe: Influence of sub-regime on slug frequency, page 8, Copyright © 2019, with permission from Elsevier;; (b) elongated bubble tail observed by Humami et al. [84] (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=2.83$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005-4, Copyright © 2018, with permission from AIP Publishing; (c) elongated bubble nose observed by Humami et al. [84] (Air-water mixture, 26 mm ID pipe, $V_{SL}=0.44$ m/s and $V_{SG}=2.83$ m/s), Reprinted from AIP Conference Proceedings, vol. 2001, issue 1, Faris Humami, Okto Dinaryanto, Akhmad Zidni Hudaya, Arif Widyatama, Indarto, Deendarlianto, Experimental study on the characteristics of flow pattern transitions of air-water two-phase flow in a horizontal pipe, page 030005-4, Copyright © 2018, with permission from AIP Publishing; and (d) elongated bubble above liquid film observed by Arabi et al. [16] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.495$ m/s and $V_{SG}=3.144$ m/s). Reprinted from International Journal of Heat and Mass Transfer, vol. 181, Abderraouf Arabi, Yacine Salhi, Youcef Zenati, El-Khider Si Ahmed, Jack Legrand, A Discussion on the Relation Between the Intermittent Flow Sub-Regimes and the Frictional Pressure Drop, page 7, Copyright © 2021, with permission from Elsevier. Flow direction: from left to right.</figcaption></figure>
<table><caption>**Table 1**

Comparative analysis of interface characteristics of the three sub-regimes of the intermittent flow. Reproduced from Cao et al. [34].</caption><thead><tr><th>Flow characteristics</th><th>PG flow</th><th>LAS flow</th><th>HAS flow</th></tr></thead><tbody><tr><td>The gas holdup and bubble distribution range of liquid slug</td><td>Unaerated or little bubbles distributed at the top of the pipeline</td><td>Less aerated and many bubbles distributed at the top of the pipeline</td><td>High aerated and a large number of bubbles distributed throughout the pipeline section</td></tr><tr><td>The radial position of elongated bubble head</td><td>Approaching the top of the pipeline</td><td>Slightly below the top of the pipeline</td><td>Approaching the middle of the pipeline</td></tr><tr><td>The shape of elongated bubble tail</td><td>Steep hydraulic step, the top is not close to the top of the pipeline, longer tail region</td><td>Steep hydraulic step, the top is close to the top of the pipeline</td><td>Slow hydraulic step, the top is close to the top of the pipeline</td></tr><tr><td>The interface structure of the liquid film</td><td>Smooth interface and little bubbles in gas-liquid interface</td><td>Smooth interface and many bubbles continue to merge and breakup</td><td>Wavy interface and a lot of small bubbles in the liquid film</td></tr></tbody></table>

- slug and plug flow, characterized by the simultaneous presence of non-aerated and aerated liquid slugs, typical of those encountered in plug and slug flows, respectively,

- Less Aerated Slug flow (LAS flow), where the liquid slugs carry a small amount of gas bubbles,

- Highly Aerated Slug flow (HAS flow), composed of liquid slugs containing a large amount of small gas bubbles,

- slug and wavy flow, characterized by a wavy profile at the interface between the elongated bubble and the liquid film and slugs carrying a large amount of gas bubbles.

Note that these sub-regimes of the slug flow exist alongside with plug flow (PG flow), which is characterized by liquid slugs free of gas bubbles or specific shape of the elongated bubble. The observations of these five identified sub-regimes as well as those of the plug flow were represented by the authors in a map based on the Reynolds numbers of the gas ($Re_{SG}$) and liquid ($Re_{SL}$) given by:

$$Re_{SG} = \frac{\rho_{G} V_{SG} D}{\mu_{G}} \qquad (1)$$

$$Re_{SL} = \frac{\rho_{L} V_{SL} D}{\mu_{L}} \qquad (2)$$

where $D$, $V_S$, $\rho$, $\mu$ refer to pipe diameter, superficial velocity, density and viscosity, respectively. The indices $G$ and $L$ stand for gas and liquid, respectively.

It can be seen from the flow map of Thaker and Banerjee [155], depicted in Fig. 1, that the PG, LAS and HAS flows occupy the areas of low, intermediate and high gas Reynolds number. The slug and plug flow are located between the plug and LAS flow areas, and thus represents a transition between the two sub-regimes. The slug and wavy regimes take place in the range of high gas phase flow rates and low liquid phase flow rates. Note the same authors showed the role of bubbles, within liquid slugs, on various erosion-corrosion mechanisms [156]. Thus, this classification can help to better address the challenges of Pipeline Integrity Management (PIM). As pointed by Mohmmed et al. [117] in their review of the intermittent flow, there is a lack of knowledge in the field of slug flow-structure interaction.

In continuation of this work and using the same experimental setup, Thaker and Banerjee [155,156] divided the intermittent flow into three sub-regimes namely: PG, LAS and HAS flows. As noted by Arabi et al. [15], the “slug and plug” flow was grouped with the PG flow. The “slug

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) Plot of the measured radial position of elongated bubble head as function of mixture Froude number; (b) Measurements of elongated bubble head of 30 slug unit. Reproduced from Cao et al. [34].</figcaption></figure>

and wavy” flow are categorized as HAS flow. The latter classification has the advantage of being more practical and easier, creating less confusion. In addition, most of the work carried out using this approach has been based on this subdivision.

## 2.2. Description of PG, LAS and HAS flows

Based on the detailed description of the flow structure of each sub-regime given by Thaker and Banerjee [115,116] and by several articles published subsequently [15,17,19,33,34,55,84,139,142,159,176], the three sub-regimes can be described as follows.

**PG flow:** (Fig. 2): In this flow regime, the liquid slugs are free or transporting small quantities of gas bubbles. In addition, all these bubbles come from the detachment occurring at the upper portion of the liquid slug nose/elongated bubble tail. The nose of the elongated bubble has an asymmetric round nose. Generally, the tail of the elongated bubble has a hydraulic jump followed by a long tail which gives a staircase structure to the interface elongated bubble tail/liquid slug nose. The liquid film/elongated bubble interface is generally free of gas bubbles. Thus, the gas-liquid interface is clear.

**LAS flow:** (Fig. 3): The liquid slugs encountered in LAS flow contain small quantities of gas bubbles. Their low number (reflecting in the average distance between them) and relatively large size make them easy to distinguish. Meanwhile, an important concentration of gas bubbles forming a bubble cluster can be present in the front region of liquid slugs. The gas bubbles are generated along the entire length of the liquid slug nose/elongated bubble tail interface. This is materialized by the presence of gas bubbles through this interface as well as in the liquid
<figure><img src="image_9.png" /><figcaption>Fig. 6. Images of (a) Plug flow, (b) plug-to-slug transition and (c) slug flow taken by Sassi et al. [146] (Air-water mixture, 30 mm ID pipe). Flow direction: from right to left. The symbols $J_{fs}$ and $J_g$ refers to the liquid and gas superficial velocities, respectively. Copyright © 2020, Paulo Sassi et al.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Radial velocity profile of the intermittent flow sub-regimes obtained by Saini and Banerjee [142] (Air-water mixture, 25 mm ID). Reproduced from Saini and Banerjee [142].</figcaption></figure>

slug tail/elongated bubble nose. Compared to PG flow, the nose of the elongated bubble in LAS flow is situated closer to the center of the pipe. In addition, there are few quantities of dispersed bubbles in the film liquid below the elongated bubbles. These bubbles merge, grow and finally break.

HAS flow: (Fig. 4): In HAS flow, an important quantity of gas bubbles is present within the liquid slugs. Their small dimensions, higher concentration and the important length of the bubble clusters don't permit to discern between them. The important gas entrainment within liquid slugs is responsible of generating more turbulence, provoking the onset of secondary forces, leading to the apparition of eddies in the liquid slug front. The film liquid carries out a great quantity of gas bubbles. The

elongated bubble/liquid film interface is also similar to that of wavy flow.

The description of the exhibited interface for each sub-regime was summarized by Cao et al. [34] and provided in Table 1. Note that these descriptions remain only qualitative; and up-to-date, there are no clear and objective criteria for distinguishing the three sub-regimes. Cao et al. [34] also measured the radial position of elongated bubble nose. The results, depicted in Fig. 5.a for the three sub-regimes as function of the mixture Froude number ($Fr_M$), given by Eq. (3). Fig. 5.a, shows clearly that an increase of $Fr_M$ induces the bubble centering; meaning that the nose of bubbles becomes closer to the pipe center [132]. The authors reported that these two parameters are linearly dependent. According to Fig. 5.a, it also appears that the radial positions of 0.672 and 0.765 can be used as an objective criterion to discern between PG/LAS and LAS/ HAS flows. The fact that some of these points are not well predicted by these two transition lines can be explained by the relatively important fluctuation around the average of the measured radial position of elongated bubble nose. This is shown in Fig. 5.b when measurement of 30 elongated bubble noses observed under the same conditions of gas and liquid superficial velocities.

$$Fr_M = \frac{V_M}{\sqrt{gD}} \qquad (3)$$

with $V_M$ the mixture velocity given as:

$$V_M = V_{SL} + V_{SG} \qquad (4)$$

## 2.3. “Slug and plug” flow

On the other hand, if we focus on “slug and plug” flow, various terminologies have been used to designate it. We can cite “slug-plug” [84], “plug-slug” [166] or “plug-to-slug transition” [146]. This sub-regime is situated between plug flow and slug flow and has an intermediate characteristic between them as it appears in Fig. 6. Noting that
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Variation of (a) time averaged velocity ($V_L$, mean); (b) root mean square velocity ($V_L$, RMS) and (c) Reynolds stress ($u'u'$) of liquid film in function of $V_{SG}$ obtained by Saini and Banerjee [142] (air-water mixture, 25 mm ID). Reproduced from Saini and Banerjee [142].</figcaption></figure>

in the study of Abdulkadir et al. [2], where air-silicone oil mixture and a 67 mm ID pipe were used, the authors used the terminology “pseudo-slug” to describe the sub-regime between plug flow and slug flow. This observation is questionable knowing that the pseudo slug flow is present in the region of high and low gas and liquid superficial velocities, respectively [50,107] and noting that the authors did not provide any pictures or explain the criterion used to recognize this sub-regime. From

this analysis, we can easily guess that this observed flow is “slug and plug” flow.

### 3. Physical mechanisms involved in PG-to-LAS and LAS-to-HAS flow transitions

The pioneering works based on experimental visualization of the sub-regimes gave way, a few years later, to experimental studies using advanced local measurement instrumentsations. Using Laser Doppler Velocimetry (LDV) technique, Thaker and Banerjee [158] reported that an increase of gas superficial velocity induces an increase of the difference between velocities of the liquid film and the liquid slugs. Hence, this phenomenon induces the tearing of gas bubbles into liquid slugs from elongated bubbles. Noting that this study dealt only on the transition of PG-to-LAS flows. In the same period, Kong et al. [100] studied also this transition using 38.1 and 101.6 mm ID diameter pipes. By examining the void fraction profile and the size of small bubbles within liquid slugs, the authors found that the increase of gas or liquid superficial velocities results in a decrease of bubbles size inside liquid slugs. Indeed, an increase of gas and liquid superficial velocity induces the shearing-off and turbulent-impact due to the liquid turbulence, respectively. The pipe diameter has a strong effect on interfacial structure of intermittent flow. In fact, an increase of pipe diameter gives rise to larger elongated bubbles.

More recently, Zhai et al. [176] measured the liquid velocity profile and liquid film thickness through the developed field-programmable gate array (FPGA) based ultrasonic Doppler system for LAS and HAS flows. Knowing that the liquid velocity fluctuations depend on the quantities of gas bubbles, the obtained spatial-temporal velocity distribution allowed quantifying the dispersed gas bubbles present within liquid film and liquid slug. The results revealed that the bubbles present in liquid film and slugs gradually diffuse into the bottom of the pipe with the transition from LAS to HAS flows. In addition, it was reported that an increase of $V_{SG}$, and thus the transition to LAS from HAS flows, induces an increase of gas bubbles concentration present in liquid film. This transition provokes also an increase of the average radial liquid velocity profile of both flow structures. On the other hand, the velocity profile was found to be unstable, especially in the case of HAS flow, which demonstrates the complex dynamics of the gas bubble inside the liquid slugs.

Saini and Banerjee [142] carried out experiments to measure local liquid velocity signals in the liquid slug and in the liquid film for PG, LAS and HAS flows. The measurements were made using LDV mounted on an automated 3-D traverse, which allowed to move in steps of 1 mm radially. It was reported that there is a jump in the velocity magnitude when the probe moves from the liquid film to the liquid slug regions, as shown in Fig. 7. Thus, the liquid slug velocity is reduced by the liquid film. The increment of gas superficial velocity induces an increase of both liquid film and slug velocities. Meanwhile, this increase is more important in liquid slug. As a consequence, the rise of $V_{SG}$, and thus the transition to LAS flow and then to HAS flow, amplifies the phenomenon of liquid slugs' retardation by the liquid film.

Saini and Banerjee [142] also reported that an increase of gas superficial velocity, and thus the PG-to-LAS flows and LAS-to-HAS flows transitions, induces an increase of the time averaged velocity ($V_L$, mean), root mean square velocity ($V_L$, RMS) and Reynolds stress ($u'u'$) of liquid film, as depicted in Fig. 8.a, Fig. 8.b and Fig. 8.c, respectively. For $V_L$, mean, these authors explained that for fixed $V_{SL}$, an increment of $V_{SG}$ induces an increase of the gas momentum, provoking a drag on the liquid slug. The high velocity of the liquid slug induces an increase of the local velocity at the liquid film bulk. The fact that lowest values of $V_L$, RMS were obtained for PG flow, is due to, according to Saini and Banerjee [142], the low inertia of this sub-regime compared to viscous resistance which tends to retard the slug velocity. This phenomenon damps the velocity fluctuations. The increase of $V_{SG}$, and thus the transition to LAS and then to HAS flows induces the increase of inertia of the flow which
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Time series of bubble entrainment process by the interfacial shear induced waves mechanism observed by Talley et al. [154] (air-water mixture, 38.1 mm ID, $V_{SL}=1.00$ m/s and $V_{SG}=0.16$ m/s). Flow direction: from left to right. Reprinted from International Journal of Multiphase Flow, vol. 76, Justin D. Talley, Ted Worosz, Seungjin Kim, John R. Buchanan Jr., Characterization of horizontal air-water two-phase flow in a round pipe part I: Flow visualization, page 219, Copyright © 2015, with permission from Elsevier.</figcaption></figure>

generates more fluctuations of the liquid film velocity. For PG flow, the surface tension and viscous force are more important than the turbulence which results in low Reynolds stress. This equilibrium inverts with the increase of $V_{SG}$ which induces the presence of turbulent mixing (and secondary flow for the case of HAS flow) which impacts positively on the Reynolds stress.

Unlike the mentioned works, Arabi et al. [19] were interested by the identification of the physical mechanisms behind the PG-to-LAS and LAS-to-HAS flows transitions. The study was done by analyzing the acquired flow structures images. According to the authors, for low values of gas superficial velocities, the liquid slugs are free of transported gas bubbles. A slight increase of $V_{SG}$ induces the apparition of an instability at the end of the liquid slug nose/elongated bubble tail interface due to the slippage between the liquid film and the elongated bubble in this zone. This instability provokes a detachment of gas bubbles by the interfacial shear induced waves mechanism. Time series of this phenomenon captured by Talley et al. [154] are depicted in Fig. 9. Further details and explanation about this physical mechanism can be found in this reference. Note that the flow regime remains PG flow.

In addition to gas detachment by the interfacial shear induced waves mechanism, a further increment of gas flow rate induces an additional gas bubbles penetration coming from the entire liquid slug nose/elongated bubble tail interface. This liquid slug's aeration phenomenon is called the shearing-off mechanism and is responsible to the PG-to-LAS flows transition. An example of the process of bubble detachment by this mechanism is given in Fig. 10. This flow mechanism is explained in details in ref. [158]. The transition to HAS flow is due to the additional apparition of the mechanism of scooping of bubbles present in the liquid film into liquid slug. The interfacial shear induced waves and the shearing-off mechanisms are also present in HAS flow.

The three identified aeration mechanisms present within the PG, LAS and HAS flows are illustrated in Fig. 11. The black, red and blue arrows refer respectively to the mechanisms of interfacial shear induced waves, shearing-off and scooping of bubbles from the liquid film into liquid slug. As mentioned above, all the three mechanisms are present in HAS flows.

# 4. Flow pattern maps

## 4.1. Onset of the intermittent flow

Arabi et al. [14] performed a series of visual observations for an air-water mixture and differential pressure signal acquisition at the onset of intermittent flow. The main observation reported is the presence of flow structures typical of PG, LAS and HAS flows in the range of low, medium and high gas superficial velocities, respectively. This result showed that the three sub-regimes are present at the onset of intermittent flow. It also contradicts the flow map of Thaker and Banerjee [155] (Fig. 1), where the PG flow does not share a transition line with the segregated flow. The onset of the intermittent flow from stratified flow has been intensively studied in the literature [54,61,153,155,163]. Meanwhile, the process of the formation of liquid slugs remains not well understood. The results obtained by Arabi et al. [14], on the apparition of the different sub-regimes of the intermittent flow, when the intermittent flow transition occurs from the segregated flow can only reinforce the necessity to explore the relation between the nature of the flow sub-regime and the different slug formation mechanisms already reported in the literature. The knowledge acquired can be used to make progress in modeling this complex flow transition.

## 4.2. Existing flow maps

As the flow regimes, the sub-regimes of the intermittent were also analyzed to propose flow pattern map. A flow pattern map is a two-dimensional plot of the existence of flow regime including the transition boundaries separating the areas of each flow regime [41]. As it was mentioned in Section 2.1, Thaker and Banerjee [155] proposed a flow map using dimensionless numbers of both phases as coordinates. This flow map is based on observations carried out on 25 mm ID pipe. With the simplification of the classification of flow sub-regimes into PG, LAS and HAS flows, Thaker and Banerjee [156] simplified this flow map to leave only the three flow sub-regimes. After, Dinaryanto et al. [55], Zhai et al. [176], Humami et al. [84], Arabi et al. [19] and Cao et al. [34]
<figure><img src="image_13.png" /><figcaption>Fig. 10. Time series of bubble entrainment process by the shearing-off mechanism observed by Thaker and Banerjee [158] (Air-water mixture, 25 mm ID). Flow direction: from left to right. Reprinted from International Journal of Multiphase Flow, vol. 91, Jignesh Thaker, Jyotirmay Banerjee, Transition of plug to slug flow and associated fluid dynamics, page 69, Copyright © 2017, with permission from Elsevier.</figcaption></figure>

proposed also flow pattern maps based on their experimental observations carried out using 16, 20, 26, 30 and 46 mm ID pipes, respectively. The five flow maps, depicted in Fig. 12, use the classical gas and liquid superficial velocities as coordinates. The existence of certain discrepancies between the transition between the different sub-regimes obtained by various authors can be explained by the effect of the pipe diameter as well as by the difference in liquid superficial velocities range investigated in each study.

Observations of these flow maps show that the PG-to-LAS flows and LAS-to-HAS flows transitions are solely dependent on the gas superficial velocities. This remark doesn't hold for the map of Cao et al. [34]; when

the flow transition depends to the mixture velocity through the Froude number, $Fr_M$. This latter study is the only one to have expressed the transitions in equation form. Indeed, the PG-to-LAS and LAS-to-HAS flows transitions were observed for a critical mixture Froude number equal to 2.0 and 2.86, respectively.

Works carried out on the PG-to-slug flows transitions (and thus from PG-to-LAS flows), raise question about how phasic superficial velocities influence this transition. As synthesized by Arabi et al. [13], some authors reported that this transition depend on the gas superficial velocity when other ones found that it depends to the mixture velocity. In order to solve this issue, it is worth highlight the recent study carried out by Boutaghane et al. [27] about the utilization of the existing slug liquid holdup models in order to detect the plug-to-slug flows. The study was done by confronting different experimental observations collected from the literature with the flow transition given by each model. For each pipe diameter and liquid viscosity ranges, a specific slug liquid holdup model was found to be the most reliable. Given that the majority of models of liquid holdup in slug are based on the work of Gregory et al. [77], and thus, they use the mixture velocity as an input parameter, we can easily state that the PG-to-LAS flows depend on the latter, and not on the gas superficial velocity alone. Meanwhile, it is important to note that most of experimental observations have been done on limited range, as well as for low values, of liquid superficial velocities. In these conditions, the impact of the liquid superficial velocity cannot appear clearly. We believe that this small detail explains the debate as to which of the gas superficial or mixture velocities induces the transition from PG-to-LAS flows. Cao et al. [34], who carried out experiments for high values of $V_{SL}$, observed the influence of mixture velocity on both PG-to-LAS and LAS-to-HAS flows transitions. This finding confirms the explanation presented and allows extending it to the LAS-to-HAS flows transition.

The values of the critical mixture Froude number predicting the PG-to-LAS and LAS-to-HAS flows transitions, proposed by Cao et al. [34], are assessed with the flow maps of Thaker and Banerjee [155,156], Dinaryanto et al. [55], Humami et al. [84], Zhai et al. [176] and Arabi et al. [19]. For instance, the flow transitions given by these flow maps have been represented using $Fr_M$ vs $\lambda_L$ system in Fig. 13, where $\lambda_L$ refers to the inlet liquid fraction (Eq. (5)). The plot highlights that the critical values proposed by Cao et al. [34] are not valid for the experiment's conditions covered by the five previous studies. This finding can be explained by the fact that the experiments of Cao et al. [34] were carried out for a range of high liquid superficial velocities (between 0.7 and 2 m/s) compared to other studies.

$$ \lambda_L = \frac{V_{SL}}{V_M} \qquad (5) $$

It is well known that the pipe diameter plays a great role on the hydrodynamic behavior of gas-liquid two-phase flow and in the transition between the flow regimes [14,50,98,99]. Based on this statement and on the fact that all mentioned flow sub-regimes flow maps were developed using one pipe diameter, Arabi et al. [19] performed an original study about the best coordinate systems which can be used to predict the flow sub-regimes for great range of pipe diameter. The study was done by projecting the flow transitions of the existing flow pattern maps using

<figure><img src="image_14.png" /><figcaption>Fig. 11. Image of HAS flow collected by Arabi et al. [15] (Air-water mixture, 30 mm ID pipe, $V_{SL}=0.424$ m/s and $V_{SG}=3.144$ m/s). The white, red and blue arrows refer to the interfacial shear induced waves, shearing-off and scooping of bubbles mechanisms, respectively. Flow direction: from left to right. The contrast of the image was modified and the arrows were added using GIMP 2.10 Software, and were not part of the original source. Reprinted from Chemical Engineering Science, vol. 211, A. Arabi, Y. Salhi, Y. Zenati, E-K. Si-Ahmed, J. Legrand, On gas-liquid intermittent flow in a horizontal pipe: Influence of sub-regime on slug frequency, page 8, Copyright © 2019, with permission from Elsevier.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Existing flow sub-regime patterns maps. (a) Dinaryanto et al. [55] (16 mm ID); (b) Zhai et al. [176] (20 mm ID); (c) Humami et al. [84] (26 mm); (d) Arabi et al. [19] (30 mm ID); and (e) Cao et al. [34] (46 mm ID).</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 13. Assessment of PG-to-LAS and LAS-to-HAS flow transition criteria of Cao et al. [34] with the experimental flow transitions reported by Dinaryanto et al. [55], Zhai et al. [176], Thaker and Banerjee [155,156], Humami et al. [84], and Arabi et al. [19].</figcaption></figure>

different coordinates systems. The authors reported that the coordinate system T vs X, given by Eqs. (6) and (7), provide the best results. Indeed, exception for the flow map of Dinaryanto et al. [55], the PG-to-LAS and LAS-to-HAS flows transition lines are the closest in this representation as depicted in Fig. 14. The fact that T vs X plane was originally introduced by Taitel and Dukler [153] for modeling the intermittent-to-bubbly flows demonstrated, as noted by Arabi et al. [19], the existing analogy between this flow transition and the aeration mechanism of liquid slugs. The authors recalled that this analogy was postulated in 1985 by Barnea and Brauner [22] for building their slug liquid holdup mechanistic model. Thus, Arabi et al. [19] recommend to use these two dimensionless numbers for mapping the sub-regimes transitions.

$$T = \sqrt{\frac{(dP/dL)_L}{(\rho_L - \rho_G)g}} \qquad (6)$$

$$X = \sqrt{\frac{\left(\frac{dP}{dL}\right)_L}{\left(\frac{dP}{dL}\right)_G}} \qquad (7)$$

where $(\frac{dP}{dL})_L$ and $(\frac{dP}{dL})_G$ are the pressure gradient of liquid and gas phases. Both are calculated using the following equations:

$$(\frac{dP}{dL})_L = \frac{2f_L \rho_L V_{SL}^2}{D} \qquad (8)$$

$$(\frac{dP}{dL})_G = \frac{2f_G \rho_G V_{SG}^2}{D} \qquad (9)$$

f refers to Fanning friction factor. It is given by Eqs. (10) and (11) in the case of laminar and turbulent flows, respectively.

$$f_i = 16Re_{si}^{-1} \qquad (10)$$

$$f_i = 0.046Re_{si}^{0.2} \qquad (11)$$

where i stands for liquid (L) or gas (G).

Noting that in their study, Arabi et al. [19] didn't incorporate the flow transitions of Cao et al. [34]. Indeed, this later was published after Arabi et al. [19] submitted their paper. In Fig. 15, we plotted the transitions given by both flow maps using T vs X coordinates system. The

<figure><img src="image_17.png" /><figcaption>Fig. 14. Representation of transition lines of flow maps of Dinaryanto et al. [55] (16 mm ID), Zhai et al. [176] (20 mm ID), Thaker and Banerjee [155,156] (25 mm ID), Humami et al. [84] (26 mm ID) and Arabi et al. [19] (30 mm ID) using T vs X. Reproduced from Arabi et al. [19].</figcaption></figure>

large discrepancy can be explained by mainly the ranges of liquid superficial velocities investigated by the two studies, as it appears in the ranges of X.

## 5. Objective sub-regime identification tools

Traditionally, the identification and classification of sub-regimes (as well as flow regimes) is carried out from observation of flows through transparent pipes. Hence, this method can only be carried out at a laboratory scale. As a consequence, looking for objective methods is necessary. Knowing the unsteady nature of the gas-liquid flows, except of the stratified flow, the time series of flow parameters are characterized by the apparition of fluctuations. The latter have been used as a tool to recognize and distinct between the flow regimes [18,164]. Several mathematical methods been applied for this purpose.

Regarding the sub-regimes, Dinaryanto et al. [55] collected liquid holdup time-series signals using constant electricity current method (CECM) and static pressure signals for different sub-regimes of intermittent flow observed on a 16 mm pipe. The authors noted, as shown in Fig. 16, that in “slug and plug” flow (Fig. 16.a), the liquid holdup reaches a value of almost unity, which means that the liquid slugs are almost unaerated. In LAS flow (Fig. 16.b), the liquid holdup values in the liquid slugs have an approximate value of 0.9, which implies a higher aeration of the slugs compared to those of “slug and plug” flow. Due to their high aeration, the values recorded in the HAS flow (Fig. 16.d) do not exceed 0.8. In Fig. 16.c, the low values as well as the strong fluctuations observed in the “slug and wavy” flow are also due to the strong aeration of the liquid slugs. Concerning the static pressure signals, the authors have just noted qualitative differences in the signals shape for each sub-regime. Thaker et al. [159] noted that the passage of the liquid slug nose at the level of the measurement point is accompanied by a jump of the absolute recorded pressure. Smaller and larger peaks were recorded for PG and HAS flows, respectively. Arabi et al. [18] reported the same observations for pressure drop time series.

Saini and Banerjee [141] studied the static pressure time series obtained with PG, LAS and HAS flows by employing the recurrence analysis. By analyzing qualitatively the obtained recurrence plots, the authors concluded that PG flow is less chaotic. The increase of gas superficial velocity, and thus the aeration of liquid slugs induces an increase of chaos. Saini and Banerjee [141] further analyzed the recurrence plot through three qualitative parameters calculated from the recurrence analysis which are the recurrence rate (REC), determination rate (DET) and trapping time (TT). REC refers to the number of
<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Comparison between the flow transitions of Arabi et al. [19] and Cao et al. [34] using *T* vs *X*.</figcaption></figure>

data points which are recurrent within the threshold distance. DET is
defined as fraction of recurrence points that develops the diagonal lines,
while TT is the average time for which a specific state is trapped. The
representations of the three parameters as a function of gas superficial
velocity displayed in Fig. 17, show that transitions from PG-to-LAS flows
and LAS-to-HAS flow are accompanied by a change of the slope. Similar
method was used by the same authors to detect the onset of the inter-
mittent flow [140].

In contrasting with the studies of Saini and Banerjee [141], Arabi
et al. [18] analyzed the differential pressure signals using simple sta-
tistical techniques. The authors noted that unlike the PDFs obtained with
the void fraction or liquid holdup signals, those calculated with the

pressure drop signals do not allow discerning between PG and slug flows (including LAS and HAS flows). By plotting the standard deviation (Std) as function of the kurtosis (Kur) calculated from pressure drop time series, the authors found that the data for each sub-regime are clustered in the same zone forming a kind of flow map, as shown in Fig. 18. These authors proposed this feature space as an objective tool to distinguish between the three sub-regimes. Arabi et al. [18] also proposed two other feature spaces, based on parameters extracted from the PDF, as flow map to identify the sub-regimes.

6. Slug parameters modeling

The intermittent models, as all mechanistic models, deal with a high
number and complex equations, and thus, need closure relations [138].
The latter were most often obtained with empirical approaches [144].
This fact reinforces the need to perform experimental measurements. As
explained by Mohammadi et al. [116], closure relations have a dynamic
nature. In fact, generating additional data under new operating condi-
tions allow the development of new and more reliable correlations.
Assessment studies performed allow a better understanding of the level
of existing models’ predictions for different operating conditions
[37,44,45,47,48,123,131]. These studies are performed by confronting
the models’ predictions with an empirical database. As the precision of
the models depends on the accuracy of the closure models, these as-
sessments studies are very important. In general, the closure relations
used in the intermittent flow models are based on specific parameters for
these flow regimes such as slug frequency, elongated bubble trans-
lational velocity, slug length and slug liquid holdup. Noting that the slug
parameters are also used in mesh independence and for validation of
simulations obtained through CFMD simulations [49,94,119]. Akhlaghi
et al. [6] have used the slug parameters measured experimentally as
initial conditions for their numerical simulations. It was reported a

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Examples of liquid holdup signals collected using CECM for different sub-regimes by Dinaryanto et al. [55] (Air-water, 16 mm ID). The symbols J<sub>L</sub> and J<sub>G</sub> refers to the liquid and gas superficial velocities, respectively. Reprinted from AIP Conference Proceedings, vol. 135, Okto Dinaryanto, Arif Widyatama, Maya Prestinawati, Indarto, and Deendarlianto, Characterization of two-phase slug flow sub-regimes using flow visualization, 2001, page 030008–7, Copyright © 2018, with permission from AIP Publishing.</figcaption></figure>
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 17. Variation of recurrence quantification parameters (a) Recurrence rate (REC); (b) Deterministic rate (DET) and (c) Trapping time (TT) in function of VSG obtained by Saini and Banerjee [141]. Reproduced from Saini and Banerjee [141].</figcaption></figure>

reduction of 65 % in the computational domain. Thaker and Banerjee [156] explained that several erosion-corrosion phenomena are directly related to the slug parameters.

Among the slug parameters, the slug frequency ($f_s$), which designates the number of slugs passing through a pipe during a time period, is especially complex to predict. This prediction can be view from the

<figure><img src="image_23.png" /><figcaption>Fig. 18. Plot of the calculated standard deviation (Std) against kurtosis (Kur) of each sub-regime obtained by Arabi et al. [18]. Reproduced from Arabi et al. [18].</figcaption></figure>

numbers of existing correlations [15,35]. Summary of these models are presented in Appendix B. Arabi et al. [15] generated a slug frequency database for the three sub-regimes PG, LAS, and HAS flows using an air-water mixture and a 30 mm ID pipe. By comparing the predictions of several existing models with their data, the authors noticed that the level of prediction of each model depends on the nature of the sub-regime. Indeed, as shown in Fig. 19 where experimental slug frequency results obtained by Arabi et al. [15] and Thaker and Banerjee [156] are compared with the predictions given by different existing predictive models (summarized in Appendix B).

Based on this finding, the authors proposed the first predictive model that depends on the nature of the sub-regime. The proposed model is based on gas Strouhal number ($St_G$) and input liquid fraction. The gas based Strouhal number, given by Eq. (12), is often used to dimensionless the slug frequency [1,20,35,38,68,96,145]. In Fig. 20, the correlation for the three sub-regimes as well as the data obtained by Arabi et al. [15] used for the development of the correlation and the data of Thaker and Banerjee [156] which served for its validation, has been represented using the two dimensionless numbers. More recently, Cao et al. [33] also correlated the slug frequency by taking into account the nature of the sub-regimes.

$$St_G = \frac{f_s D}{V_{SG}} \qquad (12)$$

Arabi et al. [13] reported that an increase in the mixture velocity or mixture Froude number induces a decrease in the average slug length ($L_s$) in PG flow. The transition to slug flow is accompanied by an increase in the average slug length with increasing mixture velocity until an asymptotic value is reached. A plot of the results obtained by Thaker and Banerjee [156] suggests that the stabilization of the average length takes place with the transition to the HAS flow. It would be interesting to generate further results to confirm this finding.

As reported by Zitouni et al. [180], the empirical correlations predicting the slug length, summarized in Appendix C, can be classified into three broad categories: those dependent on the gas and liquid superficial velocities independently, those dependent only on the mixture velocity and those independent of both phasic superficial velocities. The trend observed in Fig. 21 may explain the reason for this disagreement between the different authors on the parameters influencing the slug length. This different behavior for the three sub-regimes can also be observed by comparing the results for the three sub-regimes with the predictions given by various existing models, especially with the correlations of Thaker and Banerjee [157] and Kim and Kim. [93], as can be
<figure><img src="image_24.png" /><figcaption>**Fig. 19.** Comparison of the predictions of various existing slug frequency predictive models with the experimental results obtained by Arabi et al. [15] and Thaker and Banerjee [156] for different sub-regimes.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>Fig. 20. Representation of the slug frequencies measured by Arabi et al. [15] and Thaker and Banerjee [156] using gas based Strouhal number ($St_G$) and input liquid fraction ($\lambda_L$) for different sub-regimes. The correlation of Arabi et al. [15] for each sub-regime is also depicted.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Fig. 21. Representation of the experimental results of dimensionless slug length ($L_s/D$) collected by Thaker and Banerjee [156] in function of mixture velocity ($V_M$). Reproduced from Thaker and Banerjee [156].</figcaption></figure>

seen in Fig. 22.

## 7. Frictional pressure drop modelling

The frictional pressure drop is the parameter which quantify the energy losses by the fluid when it crosses a pipe section. The direct relation of the frictional pressure drop with the pumping systems size and the energy consumption is indicative of the importance for the industrial to correctly predict it. In gas-liquid two-phase flow, the frictional pressure drop is considered generally equal to the addition to the terms generated by liquid, by gas and by the interaction between the two-phases. This latter is the most complicated for modeling [120].

Since the pioneering works of McAdams [113] and Lockhart and Martinelli [108], a great number of models have been proposed. These models were evaluated in several assessment studies [64,69,71,168]. The predictions given by the models can be high (up to 80 % as reminder recently by Cai et al. [32]).

For intermittent flow, an increase of slug frequency induces an increment of number of peaks in the frictional pressure drop time series

[106]. This behavior induces logically an increase of mean pressure drop collected. Arabi et al. [16] reported that the impact of the slug frequency on frictional pressure drop is directly related to the nature of the sub-regime, as shown in Fig. 23. From the figure, it appears that pressure drop is linearly correlated with the slug frequency, and the curve slope increases with the PG-to-LAS and LAS-to-HAS flows transitions. By comparing their results as well as those of Thaker et al. [159], Arabi et al. [16] found that the predictions of existing frictional pressure drop models depend on the nature of the sub-regime. Arabi et al. [16] proposed to consider the nature of the sub-regimes for pressure drop modeling.

## 8. Interfacial area concentration (IAC)

The two-fluid model, introduced by Ishii [85], considers the balance equations of mass, momentum and energy for each phase separately. The equations for each phase include terms due to the interfacial transfer between phases, notably for velocity, enthalpy, and heat flux [97]. Due to the fact that the two-fluid model treats each phase separately, it gives a better detailed description of the two-phase flow comparatively to homogeneous or drift-flux models [169]. Meanwhile, the difficulty to use this model lies with the necessity to accurately modeling the interfacial transfer terms ($I_i$), which significantly governs the interfacial exchanges between two phases. Generally, these terms are written as the product of the interfacial area concentration (IAC) ($\alpha_i$) and the driving flux ($q$) [97] (Eq. (13)). IAC is defined as the available interfacial area per unit mixture volume [99]. This parameter is estimated from flow regime based algebraic relations in TRACE and RELAP, two codes used in nuclear engineering [97]. This characteristic explains the necessity to well predict the flow regimes. The two mentioned codes use the same flow map for vertical and horizontal pipes. This anomaly pointed out by Kong [97] can be explained by the few numbers of studies carried out on horizontal flows comparatively to vertical upward flows. This statement highlights the necessity to advance in the IAC models development for horizontal pipes.

$$I_i = \alpha_i \times q \quad (13)$$

In the horizontal intermittent flow, considering the interfaces between both phases, especially inside the liquid slugs, we can easily guess that they are different for PG, LAS and HAS flows. Furthermore, In Kong et al. [100], it was reported that an increase of $V_{SG}$ induces an increase of the total interfacial area concentration in the below region of the pipe when the liquid film is present (Fig. 24.a). The comparison between the IAC values collected for Group (1) bubbles (representing the small spherical and distorted gas bubbles present within liquid slugs and liquid film) and Group (2) bubbles (representing the elongated bubbles) depicted respectively in Fig. 24.b and Fig. 24.c, respectively, shows that this increase of IAC is due to the Group (1) bubbles. One can see from this plot the important increase of IAC in the below part of the pipe section. This can be explained by that an increase of $V_{SG}$ (and thus the transition to LAS and then to HAS) induces an increase of the aeration in the liquid film as noted visually by Arabi et al. [16] (see for instance Fig. 3.d and Fig. 4.d). Through local measurements, Zhai et al. [176] confirmed that the liquid film in HAS flow exhibits more bubbles compared to LAS flow. These findings can be used for further investigations on the relation between IAC and the sub-regimes for development of most reliable models predicting this parameter. One should note that most of the existing studies about the sub-regimes are focused on the slug parameters (see for instance section 6). Therefore, they are more oriented for oil & gas than nuclear applications, when IAC is traditionally used [80].

## 9. Intermittent flow behavior through singularities

The presence of singularities in transport facilities causes variation of the static pressure as well as modification of the flow hydrodynamics
<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /><figcaption>**Fig. 22.** Comparison of the predictions of various existing models to predict the dimensionless slug length ($L_s/D$) with the experimental results for Thaker and Banerjee [156] for different sub-regimes.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Fig. 23. Representation of the experimental measured pressure drop ($\frac{dP}{dL}$) in function of slug frequency ($f_s$) obtained by Arabi et al. [16]. Reproduced from Arabi et al. [16]. The linear fits obtained for each sub-regime depicted here was not part of the original source.</figcaption></figure>

generating a redistribution of the void fraction and change in the flow regime [12,143]. It is important to note that the models and correlations developed for straight pipes are not necessarily valid in the case of pipes fitting with singularities [26,39,180]. To the best of our knowledge, Arabi et al. [17] performed the only study on the influence of sub-regimes on the behavior of intermittent flow through a singularity. The study concerned with a sudden expansion with aspect ratio ($\sigma$) of 0.562 placed between two horizontal pipes of 30 and 40 mm ID. It was found that the persistence or the dissipation (with or without reforma-tion) of the intermittent flow structures depends on the nature of the sub-regime. Indeed, it was observed a clear dissipation of liquid slugs in case of PG and LAS flows just after crossing the sudden expansion. The HAS flow displayed a persistence of the flow structures with a clear decrease of the liquid slugs' aeration.

However, the most interesting result was observed with the slug frequency. Thus, it was reported a persistence of the slug frequency for the PG and HAS flows. A clear decrease, up to 60%, was observed when the LAS flow is observed at the upstream pipe, as it appears when the relative error, $\epsilon$, (Eq. (14)) between upstream and downstream slug frequencies were represented as function of upstream mixture velocity Froude number ($Fr_{MI}$) in Fig. 25. Arabi et al. [17] suggested that more attention should be paid to the nature of the sub-regime to study the persistence or otherwise of the slug frequency when passing singularities. Indeed, the review of works focusing on the variation of the slug frequency at the passage of fittings, carried out by the researchers, highlighted the absence of any conclusion.

$$ \epsilon = \frac{f_{s,1} - f_{s,2}}{f_{s,1}} \qquad (14) $$

where the subscripts 1 and 2 refer to upstream and downstream the singularity, respectively.

It is interesting to note that de Oliveira et al. [48] reported a different behavior of slug frequency persistence between plug and slug flows upstream and downstream a 180° return bend. Almalki and Ahmed [10] presented results of slug frequency measured upstream and downstream three orifices with aspect ratio of 0.14, 0.25 and 0.56. The authors content themselves with representing them separately as a function of the gas superficial velocities. Meanwhile, if we examine the relative difference between upstream and downstream measured slug frequencies as function of mixture velocity (Fig. 26), we can see clearly that the relative difference depends strongly on the mixture Froude number. The observed trend is relatively similar to that observed in Fig. 25. Thus,

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /><figcaption>Fig. 24. Effect of $V_{SG}$ on the (a) total, (b) Group (1) bubbles and (c) Group (2) bubbles interfacial area concentration profile obtained by Kong et al. [100] (Air-water, 38.1 mm ID pipe). Reproduced from Kong et al. [100].</figcaption></figure>

and despite that Almalki and Ahmed [10] didn't consider the nature of sub-regime, we can conclude that the persistence of slug frequency across the orifices is also related to the nature of the sub-regimes. The analysis of these two studies, not done by Arabi et al. [17], confirm the statement made by the authors about the direct relation between the sub-regimes and the persistence of slug frequency across the singularities.
<figure><img src="image_37.png" /><figcaption>**Fig. 25.** Plot of relative difference between slug frequency values collected upstream and downstream ($\epsilon$) by Arabi et al. [17] in function of upstream mixture velocity Froude number. (Air-water mixture, 30 and 40 mm ID upstream and downstream pipes). Reproduced from Arabi et al. [17].</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>**Fig. 26.** Plot of relative difference between slug frequency values collected upstream and downstream by Almalki and Ahmed [10] in function of the mixture Froude number ($Fr_M$). (Air-water mixture, 26 mm ID pipe). Note that the results obtained with $\sigma = 0.56$ were not represented here. Indeed, these data are practically similar to those obtained with $\sigma = 0.25$.</figcaption></figure>

## 10. Recommendations for future works

A review about the subdivision of the horizontal intermittent gas-liquid two-phase into sub-regimes has been summarized in this paper. The obtained results were discussed in order to better assess the contribution of this classification to a number of intermittent flow challenges. The interesting results, as well as the low numbers of research's carried out with this approach, can only highlights the high potential of this approach. This statement reinforces the necessity to perform additional experiments. The following areas of investigations are highly recommended:

- It is important, as a first step, to measure slug liquid holdup for different sub-regimes in order to propose a quantitative criterion to discern between PG, LAS and HAS flow. Based on these future findings, predictive transitions, using for example the approach proposed recently by Boutaghane et al. [27], could be proposed.

- The efforts for searching of more generalized flow pattern map should be continued by the generation of database using different pipe diameters.

- As mentioned, these works dealt with only horizontal flow. It should be important to carry out experiments for inclined configurations.

- Study the sub-regimes using viscous and highly viscous liquid, large pipe diameter and at high pressure conditions to approach conditions close to that encountered in petroleum and gas industry.

- For nuclear applications, measurement of IAC for different sub-regimes should be considered.

- For chemical engineering applications, analyze the influence of the sub-regime nature on heat and mass transfer phenomena. Knowing that the heat and mass transfer behavior depends strongly to the interfacial area, interesting results can be expecting.

- Generate a database of slug parameters for the different kind of sub-regimes in order to propose more accurate correlations.

- Conducting local measurements of different parameters would provide better understanding on the behavior of each sub-regime.

- In addition, the works about the gas bubbles behavior inside the liquid slugs are still scarce. Perform experimental measurements on bubbles number, velocity and diameter will enable to propose more reliable and realistic mechanistic models.

- Study the behavior of the intermittent flow crossing different type of singularities by focusing on the different sub-regimes.

These experimental investigations will also be used notably to develop future mechanistic slug models which would take into account the elongated bubble/liquid slug interface and the physics of bubbles inside the liquid slugs, which still remains one of the weaknesses of the current models.

## 11. Conclusions

This paper presents the current state-of-the art about the subdivision of the horizontal gas-liquid intermittent flow into sub-regimes. These sub-regimes classification is based on the shape of the gas-liquid interface and the aeration with liquid slugs observed from experiments carried out at small pipe diameter, low pressure and low viscosity conditions. The reported experimental results in the open literature are presented and discussed. The summarized state of knowledge was critically evaluated confronted with the current gap and challenges of the intermittent flow.

The presented review showed that the flow structures as well as the existing physical mechanism of the three sub-regimes are totally different. Therefore, the slug flow parameters, pressure drop, interfacial area concentration are found different for each sub-regime. The nature of the flow has also an influence on pipeline integrity management (PIM) as well as the flow behavior crossing the sudden expansion. This review permits us to advance that this approach of subdivision of the intermittent flow can be a way to enhance the understanding of this kind of flow. The results obtained can be used to develop most reliable mechanistic models, by notably considering the different identified liquid slug's aeration mechanisms, and most accurate slug parameters correlations, which are used as closures.

Finally, some reflections paths that should be addressed for future works are given. These recommendations will allow advancing in the comprehension of these sub-regimes and to better apprehend this passionate and challenging flow regime.

### CRediT authorship contribution statement

**Abderraouf Arabi:** Writing – original draft, Visualization, Validation, Methodology, Formal analysis, Data curation, Conceptualization.

**Youcef Zenati:** Validation, Methodology. **Jack Legrand:** Writing – review & editing. **El-Khider Si-Ahmed:** Writing – review & editing.
Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgements

Authors would like to acknowledge the General Direction of Research and Development Technologies/Ministry of Higher Education and Research Sciences DGRSDT/MERS (ALGERIA) for their support.

Appendix A. Summary of previous experimental studies carried out on horizontal sub-regime of the intermittent flow

<table><thead><tr><th>Reference</th><th>Fluids used</th><th>Inner pipe diameter (ID) [mm]</th><th>Observed Sub-regimes</th><th>Flow map</th><th>Measured parameters</th><th>Instrumentations used</th></tr></thead><tbody><tr><td>Thaker and Banerjee [155]</td><td>Air-water</td><td>25</td><td>Onset of intermittent, slug and plug, LAS, HAS and slug and wavy</td><td>Yes</td><td>Slug frequency</td><td>High Speed Photography System</td></tr><tr><td>Thaker and Banerjee [156]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>Yes</td><td>Slug frequency, slug length and elongated bubble translational velocity</td><td>High Speed Photography System</td></tr><tr><td>Thaker and Banerjee [158]</td><td>Air-water</td><td>25</td><td>PG and LAS</td><td>—</td><td>Liquid velocity profile</td><td>High speed camera and Laser Doppler Velocimetry (LDV)</td></tr><tr><td>Kong et al. [100]</td><td>Air-water</td><td>38.1 and 101.6</td><td>PG, LAS and HAS*</td><td>—</td><td>Void fraction profile, interfacial area concentration, bubble velocity and Sauter-mean diameter</td><td>High speed camera and four-sensor conductivity probe</td></tr><tr><td>Dinaryanto et al. [55]</td><td>Air-water</td><td>16</td><td>PG, slug and plug, LAS, HAS and slug and wavy</td><td>Yes</td><td>Liquid holdup and pressure</td><td>High speed camera, Constant electricity current method (CECM) and absolute pressure transducers</td></tr><tr><td>Humami et al. [84]</td><td>Air-water</td><td>26</td><td>PG, slug and plug, LAS, HAS and slug wavy</td><td>Yes</td><td>—</td><td>High speed camera</td></tr><tr><td>Arabi et al. [15]</td><td>Air-water</td><td>30</td><td>PG, LAS and HAS</td><td>—</td><td>Slug frequency</td><td>Camera and differential pressure transducer</td></tr><tr><td>Saini and Banerjee [139]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure time series</td><td>High Speed Photography System and absolute pressure transducers</td></tr><tr><td>Saini and Banerjee [140]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure time series</td><td>High Speed Photography System and absolute pressure transducers</td></tr><tr><td>Saini and Banerjee [141]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure time series</td><td>High Speed Photography System and absolute pressure transducers</td></tr><tr><td>Arabi et al. [14]</td><td>Air-water</td><td>30</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure drop time series and slug frequency</td><td>Camera and differential pressure transducers</td></tr><tr><td>Arabi et al. [17]</td><td>Air-water</td><td>30 and 40 connected by a sudden expansion</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure drop time series and slug frequency</td><td>Camera and differential pressure transducer</td></tr><tr><td>Thaker et al. [159]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure drop</td><td>High Speed Photography System and absolute pressure transducers</td></tr><tr><td>Arabi et al. [16]</td><td>Air-water</td><td>30</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure drop and slug frequency</td><td>Camera and differential pressure transducer</td></tr><tr><td>Zhai et al. [176]</td><td>Air-water</td><td>20</td><td>LAS and HAS</td><td>Yes</td><td>Liquid velocity profile and liquid film thickness</td><td>High speed camera and field-programmable gate array based ultrasonic Doppler system</td></tr><tr><td>Saini and Banerjee [142]</td><td>Air-water</td><td>25</td><td>PG, LAS and HAS</td><td>—</td><td>Liquid velocity profile</td><td>High speed camera and Laser Doppler Velocimetry (LDV)</td></tr><tr><td>Cao et al. [34]</td><td>Air-water</td><td>46</td><td>PG, LAS and HAS</td><td>Yes</td><td>Radial position of elongated bubble head, elongated bubble velocity and liquid film thickness</td><td>High-speed camera</td></tr><tr><td>Cao et al. [33]</td><td>Air-water</td><td>46</td><td>PG, LAS and HAS</td><td>—</td><td>Slug length and slug frequency</td><td>High-speed camera</td></tr><tr><td>Arabi et al. [18]</td><td>Air-water</td><td>30</td><td>PG, LAS and HAS</td><td>—</td><td>Pressure drop time series fluctuations</td><td>Differential pressure transducer</td></tr><tr><td>Arabi et al. [19]</td><td>Air-water</td><td>30</td><td>PG, LAS and HAS</td><td>Yes</td><td>—</td><td>Camera</td></tr></tbody></table>

<footnote>*The nature of the sub-regime of the slug flow (LAS/HAS) was not considered by the authors. Meanwhile, the observation of the images of the flows taken by the authors (Figs 5 and 6 of Ref. [100]) allows to conclude that the study dealt with both LAS and HAS flows.</footnote>
## Appendix B. Summary of existing correlations to predict the slug frequency

<table><thead><tr><th>Reference</th><th>Developed Correlation for Slug Frequency</th></tr></thead><tbody><tr><td>Gregory and Scott [76]</td><td>f<sub>s</sub> = 0.0226 [V<sub>SL</sub>/gD (19.75/V<sub>M</sub> + V<sub>M</sub>)]<sup>1.2</sup></td></tr><tr><td>Fetter [67]</td><td>f<sub>s</sub> = 0.0175 [V<sub>SL</sub>/gD (21.3/V<sub>M</sub> + V<sub>M</sub>)]<sup>1.37</sup></td></tr><tr><td>Nydal et al. [126]</td><td>f<sub>s</sub> = 0.088 (V<sub>SL</sub> + 1.5)<sup>2</sup>/gD</td></tr><tr><td>Jepson and Taylor [86]</td><td>f<sub>s</sub> = V<sub>SL</sub>/D (0.00759V<sub>M</sub> + 0.01)</td></tr><tr><td>Manolis et al. [112]</td><td>f<sub>s</sub> = 0.0037Fr<sub>mod</sub><sup>1.8</sup><br>Fr<sub>mod</sub> = V<sub>SL</sub>/gD (V<sub>M,min</sub><sup>2</sup> + V<sub>M</sub><sup>2</sup>)<br>V<sub>M,min</sub> = 5m/s</td></tr><tr><td>Sanchez Silva et al. [151]</td><td>f<sub>s</sub> = 0.0148 V<sub>SL</sub>/gD [20.308/V<sub>M</sub> + 1.3436V<sub>M</sub>]<sup>1.2879</sup></td></tr><tr><td>Zabaras [174]</td><td>f<sub>s</sub> = 0.0226 [V<sub>SL</sub>/gD (19.75/V<sub>M</sub> + V<sub>M</sub>)]<sup>1.2</sup> *(0.836 + 2.75sinθ)</td></tr><tr><td>Fossa et al. [68]</td><td>St<sub>G</sub> = (0.044λ<sub>L</sub>)/(1 - 1.71λ<sub>L</sub> + 0.70λ<sub>L</sub><sup>2</sup>)<br>St<sub>G</sub> = f<sub>s</sub>D/V<sub>SG</sub>,<br>λ<sub>L</sub> = V<sub>SL</sub>/V<sub>SL</sub> + V<sub>SG</sub></td></tr><tr><td>Wang et al. [162]</td><td>St<sub>G</sub> = 0.05λ<sub>L</sub>/(1 - 1.675λ<sub>L</sub> + 0.768λ<sub>L</sub><sup>2</sup>)</td></tr><tr><td>Gokcal et al. [72]</td><td>f<sub>s</sub> = 2.623 V<sub>SL</sub>/N<sub>f</sub><sup>0.612D</sup><br>N<sub>f</sub> = D<sub>f</sub><sup>3</sup>√(ρ<sub>L</sub>(ρ<sub>L</sub> - ρ<sub>G</sub>)/g)</td></tr><tr><td>Vicencio et al. [160]</td><td>f<sub>s</sub> = 0.08 V<sub>SL</sub>/D (V<sub>SL</sub>/V<sub>SG</sub>)<sup>0.45</sup></td></tr><tr><td>Thaker and Banerjee [157]</td><td>St<sub>M</sub> = 0.036λ<sub>L</sub>/(1 - 1.432λ<sub>L</sub> + 0.739λ<sub>L</sub><sup>2</sup>)<br>St<sub>M</sub> = f<sub>s</sub>D/V<sub>M</sub></td></tr><tr><td>Al-Safran [8]</td><td>lnf<sub>s</sub> = [1.51 - 17.04D + 0.77ln(V<sub>SL</sub>) - 0.181ln(S)]<br>S = V<sub>G</sub>/V<sub>L</sub> = 1 + 1.95(μ<sub>L</sub>/μ<sub>0</sub>)<sup>0.01</sup> (V<sub>SG</sub>/V<sub>SL</sub>)<sup>1.5</sup><br>μ<sub>0</sub> = 1 Pa.s, reference viscosity</td></tr><tr><td>Abdulkadir et al. [1]</td><td>St<sub>G</sub> = 0.184λ<sub>L</sub><sup>274</sup></td></tr><tr><td>Baba and al. [21]</td><td>f<sub>s</sub> = 1.8102 V<sub>SL</sub>/N<sub>f</sub><sup>0.4687D</sup></td></tr><tr><td>Kong and Kim [96]</td><td>St<sub>G</sub> = 0.037λ<sub>L</sub>/(1 - 1.87λ<sub>L</sub> + 0.89λ<sub>L</sub><sup>2</sup>)</td></tr><tr><td>Cao et al. [35]</td><td>St<sub>G</sub> = 0.046λ<sub>L</sub>/(1 - 1.191λ<sub>L</sub> + 0.0212λ<sub>L</sub><sup>2</sup>)</td></tr></tbody></table>

## Appendix C. Summary of existings correlations to predict the slug length

<table><thead><tr><th>Reference</th><th>Correlation</th></tr></thead><tbody><tr><td>Brill et al. [30]</td><td>Ln(L<sub>s</sub>) = 0.059Ln(V<sub>M</sub>/0.3048) + 5.445√Ln(D/0.0254) - 3.851</td></tr><tr><td>Norris [125]</td><td>Ln(L<sub>s</sub>) = 4.859√Ln(D/0.0254) - 3.287</td></tr><tr><td>Gordon and Fairhurst [75]</td><td>Ln(L<sub>s</sub>) = 0.059Ln(V<sub>M</sub>) + 4.859√Ln(D) + 3.673 - 3.287</td></tr><tr><td>Scott et al. [148]</td><td>Ln(L<sub>s</sub>) = 28.495 [Ln(D/0.0254)]<sup>0.1</sup> - 26.6</td></tr><tr><td>Al-Safran et al. [9]</td><td>L<sub>s</sub> = 2.63DN<sub>f</sub><sup>0.321</sup><br>N<sub>f</sub> = D<sub>f</sub><sup>3/2</sup>√(ρ<sub>L</sub>(ρ<sub>L</sub> - ρ<sub>G</sub>)/g)</td></tr><tr><td>Wang [161]</td><td>L<sub>s</sub> = 10.1D + 16.8D/(1 + exp[-3.57ln(N<sub>f</sub>) - 5.4])</td></tr><tr><td>Thaker and Banerjee [157]</td><td>L<sub>s</sub> = 56.6DRe<sub>SL</sub><sup>-0.32</sup>Re<sub>SG</sub><sup>0.25</sup></td></tr></tbody></table>

(continued on next page)
(continued)

<table><thead><tr><th>Reference</th><th>Correlation</th></tr></thead><tbody><tr><td>Kim and Kim [93]</td><td>L<sub>s</sub> = <table><tr><td>10.71 Fr<sub>M</sub><sup>0.22</sup> Re<sub>M</sub><sup>0.07</sup> +</td><td>-0.09 Fr<sub>M</sub><sup>0.07</sup> Re<sub>M</sub><sup>0.21</sup></td><td>for &mu;<sub>L</sub>/&mu;<sub>G</sub> &lt; 4500</td></tr><tr><td>0.17 + 0.12</td><td>(V<sub>SG</sub>/V<sub>SL</sub>)<sup>-4.48</sup></td><td></td></tr><tr><td>264 Fr<sub>M</sub><sup>-0.13</sup> (&mu;<sub>L</sub>/&mu;<sub>G</sub>)</td><td>-0.33</td><td>for &mu;<sub>L</sub>/&mu;<sub>G</sub> &ge; 4500</td></tr></table></td></tr></tbody></table>

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