The simultaneous flow of gas and liquid phases is encountered in several and varied applications as petroleum & gas, chemical, nuclear, cooling applications (Sassi et al., 2020a; Shen et al., 2021; Hosni et al., 2023; Arabi et al., 2024a). The complex interaction between the compressible and the incompressible phases, in gas-liquid two-phase flow, makes the modeling of the hydrodynamics as well as heat and mass transfer, more critical for this type of flow compared to single phase flow.
“Flow pattern” or “flow regime” refers to the spatial distribution of the phases in the pipe volume (Sassi et al., 2020b). These are the consequence of the existence of competing forces or mechanisms occurring within the multiphase flow at the same time. Each flow pattern has its intrinsic physical phenomena, and thus, several hydrodynamic, heat and mass transfer parameters are flow regime dependent (Carrarreto et al., 2020). This point explains the importance of studying, identifying and understanding the flow regimes (Boutaghane et al., 2023).
In the horizontal configuration, due to the perpendicularity of the gravitational acceleration to the flow direction, gravity forces play a large role in the flow regimes, mainly for the stratification of the two phases. This complexity is materialized in particular by the presence of the stratified regime where the lighter phase flows on top of the liquid phase. As a result, both phases flow separately. If we follow the classification used by Beggs and Brill (1973), the stratified flow is called a segregated regime. In addition to this regime, there are intermittent and dispersed flows. Taitel and Dukler (1976) divided the segregated flow into three flow regimes: smooth stratified flow, wavy stratified flow and annular flow. The presence of fluctuations at the liquid-gas interface distinguishes the stratified wavy regime from the smooth stratified regime. In annular flow, the liquid flows at the periphery of the pipe while the gas occupies the central part. Concerning the intermittent flow, it is composed generally of two hydrodynamic structures alternating with an apparent periodicity.
Traditionally, the domains of the existence of flow regimes are represented on two-dimensional plots called flow pattern maps. In general, the theoretical flow regime transition models are derived from the mechanistic model of Taitel and Dukler (1976), which is built from the stability of smooth stratified flow. Using the latter, the prediction of the flow regime will be done using the transition lines A, B, C and D summarized in the diagram of Fig. 1. According to Taitel and Dukler (1976), each flow regime transition can be detected using a specific coordinate system. The parameter X is called the Lockhart-Martinelli parameter and it is used as the abscissa for all transition lines. The detail of the parameters of Taitel and Dukler model in the case of horizontal pipe are given in Appendix A.
As Korelstein and Pereyra (2023) pointed out, the mechanistic flow pattern models such as that of Taitel and Dukler (1976), are seldom used. This is can be explained by the fact that these kinds of models are based on idealized assumptions that limit their quantitative agreement with the experiments. Thus, the empirical flow maps obtained from experimental observations are more popular. This common technique to build flow maps is always in use. Mandhane et al. (1974) collected a databank of 5,935 individual observations obtained on horizontal pipes to build a flow map. This map is considered as the reference one for horizontal adiabatic flows at atmospheric pressure or nearly so. A review of the literature on empirical flow maps shows the great diversity of existing maps. Indeed, each author, depending on the configuration of his test bench, used specific fluids and pipe diameters. The review carried out allowed us to identify the main existing parameters used as a coordinate system:
-
Liquid superficial velocity (VSL) vs gas superficial velocity (VSG) (Mandhane et al., 1974 ; Kong and Kim, 2017 ; Kong et al., 2018a);
-
Liquid mass flux (GL) vs gas mass flux (GG) (Govier and Omer, 1962);
-
Gas mass flux (GG) vs gas-to-liquid mass flux (GG/GL) (Baker, 1953);
-
Liquid mass flow rate (ML) vs gas mass flow rate (MG) (Ghajar, 2020);
-
Input gas fraction (λG) vs mixture velocity (VM) (Kostrein, 1949);
-
Liquid Reynolds number (ReSL) vs gas Reynolds number (ReSG) (Thaker and Banerjee, 2015);
-
Liquid Froude number (FrM) vs gas Froude number (FrSG) (Shell, 2007; Korelstein and Pereyra, 2023);
-
Mixture Froude number (FrM) or square mixture Froude number vs input liquid fraction (λL) (Beggs and Brill, 1973);
-
Mixture Froude number (FrM) vs gas-to-liquid superficial velocity (VSG/VSL) or liquid-to-gas superficial velocity (VSL/VSG) (Spedding and Nguyen, 1980);
-
F vs X (Breber et al., 1980 ; Lamari, 2001).
The formulas for the calculation of these parameters are summarized in Appendix B.
The superficial velocities, used among others by Mandhane et al. (1974), remain by far the most popular coordinate system. Some authors prefer to use dimensionless numbers in order to take into account the physical properties of both fluids. Recently, after a literature review, Kong et al. (2018a) pointed out the limited work that has been done on the effect of pipe diameter on horizontal two-phase flow phenomena. The authors made experimental observations of flow regimes using 38.1 and 101.6 mm ID pipes and water-air mixture. It was reported that the bubbly-to-intermittent flow occurs at a higher liquid superficial velocity in larger pipe diameter. Various studies (Kong et al., 2018a; Thaker and Banerjee, 2015; Dinaryanto et al., 2017; Deendralianto et al., 2019; Arabi et al., 2021b) showed that an increase in diameter leads to an increase in liquid superficial velocity for the stratified-to-intermittent transition.
Pereyra et al. (2012) proposed a methodology to quantify the confidence level in the prediction of gas-liquid two-phase flow regimes given by the flow maps or the transition models. This method consists in the projection of experimental regime observations into a flow map and calculating in percentage the experimental points of the flow regimes that were well successfully predicted by the examined map. As application, the authors evaluated the predictions of the unified model of Barnea (1987) with a database composed of 9,029 data points collected from 12 published studies. The authors first performed their study by projecting the data and the transition lines of the model using a VSL-VSG representation. They noted that the terminology used to classify the flow regimes influences the level of prediction of the model. The conditions, when the discrepancies occurred, were analyzed using dimensionless numbers. This methodology was used recently by Boutaghane et al. (2023).
Considering that there is no consensus on the best coordinate system, Korelstein and Pereyra (2023) proposed a new flow map that uses the gas and liquid Froude number as coordinates. These numbers were chosen after a simplification of the Taitel and Dukler (1976) model. This flow map was obtained from database collected from 18 references, covering a large range of pipe diameter (25.4 to 152.4 mm), pressure conditions (1 to 30 bars) and liquid viscosity (up to 10 mPa.s). According to the authors, this flow map has the advantage of being scalable to different pipe diameters and pressures, compared with that of Mandhane et al. (1974). Osundare et al. (2022) also reported the possibility of using the Froude number of the individual phases as coordinates.
The intermittent flow, which is often referred as slug flow (Mohmmed et al., 2021), is by far the most complex flow pattern. This flow is composed of a sequence of identical cells (Fig. 2), known as the unit cell, which consists of elongated bubble, or gas pocket, flowing over a liquid film and liquid slug. The liquid slug is also referred as liquid bridge or liquid piston in the literature. These two sequences can be seen as stratified and bubbly flows, as it appears clearly in Fig. 2. This flow regime induces large variation of mass flow rate, pressure, and velocity in both radial and axial directions being inherently unsteady (Ramos et al., 2020). This behavior induces severe consequences for industrial installations as the flow-accelerated corrosion, liquid impact-induced erosion, flow-induced vibration (Arabi et al., 2021a). In addition, the chaotic nature of the intermittent flow, makes the understanding of this flow pattern complicated, and thus its modeling as well.
To advance in the development of more reliable models, it is important to pursue the efforts made to study this flow regime experimentally at a laboratory scale. This kind of investigation allows a better understanding of this flow regime in order to propose more realistic mechanistic models. The generated experimental data allow also validating the developed models.
It is important to distinguish the pseudo-slug flow from the “classical” intermittent flow. The pseudo-slug flow is characterized by “short, undeveloped, frothy chaotic slugs, with a structure velocity less than the mixture velocity” as summarized recently by Fan et al. (2022). Figure 3 shows reconstructed pseudo slug and liquid slug structures. These 3D reconstructions were obtained using wire-mesh sensors by Soedarmo et al. (2030). The pseudo slug was considered for long years a special case of the intermittent flow. The studied performed these recent years on this kind of flow have demonstrate its difference from “classical” intermittent flow. The detailed review of these works is given in the review paper of Fan et al. (2022).
Less than 10 years ago, Thaker and Banerjee (2015, 2016a) reported, using high speed camera, that the flow structure of the “classical” intermittent flow can take several shapes. They proposed to classify these flow regimes into three dominant flow sub-regimes which are plug Flow, Less Aerated Slug (LAS) and Highly Aerated Slug (HAS) flows. Using this approach, some scholars reported that knowing the nature of the flow sub-regimes would help to better correlating the slug frequency (Arabi et al., 2020) and the frictional pressure drop (Arabi et al., 2021c). The interaction of the intermittent flow with the pipes (one of the major challenges of the intermittent flow as explained in the recent review paper about slug flow presented by Mohmmed et al. (2021) can be better understood by considering the sub-regimes (Arabi et al., 2021d)). These findings highlight the importance of using this sub-regime classification for a better knowledge of the intermittent flow (Arabi et al., 2024b).
Using this classification approach, several flow pattern maps were developed for 16 mm (Dinaryanto et al., 2018), 20 mm (Zhai et al., 2023), 25 mm (Thaker and Banerjee, 2016) and 26 mm (Humami et al., 2018) ID pipes. Meanwhile, an analysis of these works shows that each author restricted himself to represent the experimental observation obtained using one pipe diameter on a flow map. Thus, the effect of the pipe diameter on the plug-to-LAS flows and LAS-to-HAS flows transitions were not analyzed. Additionally, few of these studies (Thaker and Banerjee, 2015, 2016a; Saini and Banerjee, 2021, 2023; Zhai et al., 2023) were interested in the comprehension of the mechanism governing each sub-regime. A qualitative analysis, based on some captured images of the flows, was carried out. To the authors best knowledge, Saini and Banerjee (2023) and Zhai et al. (2023) are the only works where the sub-regimes were analyzed through quantitative measurements. Saini and Banerjee (2023) measured the liquid velocity using LDV in order to study the liquid turbulence. It was reported an increase of velocity, root mean square velocity and Reynolds stress of liquid film with the plug-to-LAS and LAS-to-HAS flows transitions. Zhai et al. (2023) developed field-programmable gate array (FPGA) based ultrasonic Doppler system to measure simultaneously the velocity profile and liquid film thickness. The velocity profiles were used to detect the presence of gas bubbles. This study, dealing with LAS, HAS and pseudo-slug flows, allowed observing that the increase of gas superficial velocity, and thus a LAS-to-HAS flows transition, is accompanied by an increase of the gas bubble concentration in the liquid film above the elongated bubble. It was also reported that this transition led to an increment of gas bubbles inside the liquid slugs. Their spatial distribution was found to be more complex for HAS flow. Meanwhile, these studies did not allow to identify the physical mechanisms behind the transitions between the sub-regimes.
In summary, the description of the intermittent flow in horizontal configuration remains complicate and incomplete. Indeed, despite the large number of theoretical, experimental and numerical investigations performed, there is still not a complete clear understanding about the phenomena governing this flow regime (Al-Kayiem et al., 2017). Subdividing intermittent flow into sub-regimes may be a way to better understand and address this highly complex and challenging flow. The purpose of this study is to get more knowledge on the sub-regimes of the intermittent flow by studying two aspects which have been not studied in the literature which are:
1/ Studying in detail the sub-regimes through a series of visual observations of the sub-regimes. The experiments were performed in a 30 mm ID pipe using air-water two-phase flow. The adopted methodology is detailed in section 2. Photos of flow structures obtained for different conditions of phase superficial velocities (Section 3.1) are discussed including the physical mechanisms governing each sub-regime.
2/ Proposing a more generalized flow map. To achieve this objective, the visual observations were first used for studying the predictions of the existing maps (section 3.2). In Section 3.3, an original study, using the transition lines obtained in the present study and those existing in the literature, is performed to discuss the best coordinate system to predict the flow transitions between the sub-regimes.